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It’s not Obama’s deficit … The New York Times analyzed Congressional Budget Office reports going back almost a decade, with the aim of understanding how the federal government came to be far deeper in debt than it has been since the years just after World War II. This debt will constrain the country’s choices for years and could end up doing serious economic damage if foreign lenders become unwilling to finance it… …You can think of that roughly $2 trillion swing as coming from four broad categories: the business cycle, President George W. Bush’s policies, policies from the Bush years that are scheduled to expire but that Mr. Obama has chosen to extend, and new policies proposed by Mr. Obama. The first category — the business cycle — accounts for 37 percent of the $2 trillion swing. It’s a reflection of the fact that both the 2001 recession and the current one reduced tax revenue, required more spending on safety-net programs and changed economists’ assumptions about how much in taxes the government would collect in future years. About 33 percent of the swing stems from new legislation signed by Mr. Bush. That legislation, like his tax cuts and the Medicare prescription drug benefit, not only continue to cost the government but have also increased interest payments on the national debt. Mr. Obama’s main contribution to the deficit is his extension of several Bush policies, like the Iraq war and tax cuts for households making less than $250,000. Such policies — together with the Wall Street bailout, which was signed by Mr. Bush and supported by Mr. Obama — account for 20 percent of the swing. About 7 percent comes from the stimulus bill that Mr. Obama signed in February. And only 3 percent comes from Mr. Obama’s agenda on health care, education, energy and other areas. | High | [
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Dawson Red High Gloss Stool with Storage More Views Dawson Red High Gloss Stool with Storage Free Delivery throughout the Republic of Ireland and Northern Ireland * subject to size and wight restrictions, see terms & conditions All prices shown here are Web Offers only. They are not available in store. Please ring to ensure items are on display in our store before visiting: 01 288 0218 or 074 936 2000 Price displayed are online prices only. Buy online or Call Us. Offers not available in store. | Mid | [
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63 Cal.App.3d 421 (1976) 133 Cal. Rptr. 809 JOY HEATON, Plaintiff and Respondent, v. MARIN COUNTY EMPLOYEES RETIREMENT BOARD, Defendant and Appellant. Docket No. 37617. Court of Appeals of California, First District, Division One. November 8, 1976. *423 COUNSEL Douglas J. Maloney, County Counsel, and Thomas G. Hendricks, Assistant County Counsel, for Defendant and Appellant. W.O. Weissich and Suzanne E. Graber for Plaintiff and Respondent. OPINION BRAY, J.[*] Defendant and appellant Marin County Employees Retirement Board appeals from a judgment of the Marin County Superior Court ordering the issuance of a peremptory writ of mandate. ISSUES PRESENTED 1. The Legislature has not evidenced an intent that disability claims arising under workers' compensation law and county employees' retirement law be treated differently. 2. The courts have not determined that decisions under workers' compensation law are not precedents with respect to the county employees' retirement law. *424 3. If a test requiring 100 percent (or thereabouts) causation is not adopted, the retirement board's right to hear disability claims will not be rendered meaningless. 4. This appeal is not frivolous. RECORD After more than nine years' employment in the Sheriff's Department of Marin County as a jail matron, respondent Mrs. Joy Heaton filed with appellant an application for service-connected disability retirement. Appellant granted her application reserving the issue of whether the disability was service-connected. Thereafter appellant appointed a hearing officer to determine that question. Hearings were held and the hearing officer filed his opinion finding "that Joy Heaton's disability is a result of injury or disease arising out of and in the course of her employment." Appellant then held a hearing at which no witnesses were heard nor testimony taken and denied respondent's application for service-connected retirement. Thereafter respondent filed in the Marin County Superior Court a petition for writ of mandate. The trial court found that appellant retirement board was required by the evidence and the law to uphold the opinion of the hearing officer that respondent was entitled to disability retirement benefits and that appellant's rejection of the hearing officer's opinion constituted a prejudicial abuse of discretion within the meaning of Code of Civil Procedure section 1094.5, subdivision (b). FACTS In 1964, respondent commenced employment in the Marin County Sheriff's Department as a matron in the county jail. Her duties were to take care of the needs of the female prisoners. In January 1970 the county jail facilities were moved and respondent was "locked in" at the new jail facilities which situation was stressful to her. In 1971 or 1972 she was third in seniority and had been promised a day shift. The new head matron, Evelyn Gosser, gave respondent a split shift which resulted in her working irregular hours. Respondent testified that she was told that if she "didn't like it, [she] knew what [she could] do about it." As a result, she became upset. She testified that she felt the principal cause of her nervousness was that Mrs. Gosser had become supervisor while she was *425 given the "dirty work" such as taking the female prisoners to court. She experienced problems of physical violence from female prisoners who resisted being placed in cells. Respondent testified that she became very nervous and that in the morning she would vomit and that sometimes there would be blood. She would have to take tranquilizers when she began to get ready for work and perspired heavily when she thought about going to work. She went to a doctor who prescribed various tranquilizers and advised her to quit her job. Respondent also testified that she had problems at home concerning her husband and children; however, she attributed her condition to her employment at the sheriff's department. She described herself as a "nervous wreck." She could not sleep, perspired profusely, vomited and suffered from diarrhea. Since July 1973 she has not worked. Arthur Kader, respondent's employer prior to her employment at the sheriff's department, testified that during her employment with him, she did not manifest the usual symptoms of nervousness such as shaking or vomiting. Alta Thiele, a friend of respondent, observed that respondent had become very nervous during the years she had worked at the sheriff's department. Mrs. Thiele assumed that respondent's job was the cause of her emotional problems. Dr. Tracy A. Newkirk examined respondent on February 5, 1974, at appellant's request. Dr. Newkirk's primary finding was that respondent was extremely anxious. From her history he could not find any anxiety reactions prior to her employment at the sheriff's department. He could not rule out the possibility that respondent suffered an acute anxiety reaction caused at least partially by her employment, which reaction continued despite her resignation. From this testimony the hearing officer found that respondent's disability was service-connected. 1. The Legislature has not evidenced an intent that disability claims arising under workers' compensation and county employees' retirement law be treated differently. It is appellant's basic contention that in situations involving retirement disability, there is a requirement that the employment be the sole or at *426 least the substantial contributing cause of the disability before retirement disability may be awarded. Appellant seeks to demonstrate this by contrasting county employees' retirement law and workers' compensation law to substantiate its claim that the Legislature and the courts intend that, despite the similarity in language, the two bodies of law are to be treated differently. The facts in this case are not in dispute. Appellant concedes that the trial court had the authority to exercise its independent judgment on the evidence in the case. (Strumsky v. San Diego County Employees Retirement Assn. (1974) 11 Cal.3d 28, 44-45 [112 Cal. Rptr. 805, 520 P.2d 29].) (1a) In so doing, the trial court found that appellant board abused its discretion in rejecting the hearing officer's finding that Mrs. Heaton was entitled to service-connected disability. Specifically, the trial court found: "... the effects of her job would be very substantially less than 50% of the causal situation for her disability, but we can't gainsay that it was one of the causative factors for disability, and I really think that is what is controlling." Appellant points out that the trial judge concluded that the disability arose out of a variety of causes, but that a part of the cause arose from employment. In the view of the judge it was this small part that entitled respondent to a full retirement for disability. Appellant challenges this interpretation. It appears that this question is one of first impression in this court. Section 31720 of the Government Code provides in pertinent part as follows: "Any member permanently incapacitated for the performance of duty shall be retired for disability regardless of age if, and only if: [¶] (a) His incapacity is a result of injury or disease arising out of and in the course of his employment, or [¶] (b) He has completed five years of service, and [¶] (c) He has not waived retirement in respect to the particular incapacity or aggravation thereof as provided by Section 31009." Appellant notes that a portion of the quoted language, to wit, "arising out of and in the course of his employment" is identical to that employed in section 3600 of the Labor Code (workers' compensation law). Appellant argues, nonetheless, that the Legislature intended that the two bodies of law be treated differently. Appellant suggests that the rationale for this distinction is the fact that workers' compensation awards are *427 subject to apportionment according to the degree of injury while retirement for disability is an all or nothing proposition. In support of its contention, appellant first maintains that Government Code section 31720 by its very language indicates that the circumstances of retirement disability should be limited to only the most extreme cases. Appellant cites to the language "if, and only if" to demonstrate legislative intent in this regard. A closer look at this provision merely evidences the legislative intent that retirement disability be awarded "if, and only if" the injury is service-connected. It does not in any way refer to some requisite seriousness of injury as a condition for disability retirement. The statute simply limits retirement disability to cases where the injury arose out of and in the course of employment. Appellant next directs the court's attention to several differences between workers' compensation law and county employees' retirement law which appellant argues indicate a clear legislative intent to differentiate the two systems. In this regard appellant points to the fact that the Legislature enacted Government Code section 31720.5 in 1951 to provide a presumption of service-connection for heart difficulties in the case of persons in active law enforcement and fire service. Appellant argues that the Legislature's failure to provide for such a presumption for "anxiety," as is the case here, must be presumed to be a deliberate exclusion and a legislative expression that in such a case, the employment must be the cause. Appellant further maintains that the legislative creation of a number of presumptions similar to Government Code section 31720.5 in Labor Code sections 3212 through 3212.7 (heart trouble, hernia, pneumonia, tuberculosis) indicates a clear legislative intent to differentiate between the two systems. Such logic is fallacious and the argument is without merit. The inferences are unsupported and the assumptions are questionable. Appellant cites Pathe v. City of Bakersfield (1967) 255 Cal. App.2d 409, 414 [63 Cal. Rptr. 220], as an articulation of its position that there is a distinction between the two systems: "It is indisputable that the Industrial Accident Commission and the pension board exist for entirely different reasons and were established to attain wholly independent objectives. The Industrial Accident Commission exists primarily to adjudicate workmen's compensation claims under the general laws adopted by the Legislature pursuant to the Constitution. Its main objective, therefore, is to carry out the legislative scheme which is to *428 provide adequate compensation for employees, public and private, who are injured in the course and scope of their employment while such employees are disabled and incapable of earning a living. On the other hand, the pension board is concerned only with the retirement of a limited class of public employees under a retirement system which was adopted primarily for the betterment of city government. Its objective is not only to recognize the public obligation to certain employees who after long and faithful service become incapacitated by age or physical disabilities, but it is also to make certain that these employees will be replaced by more capable employees for the betterment of the public service without undue hardship on the employees removed [citation]." Notwithstanding this basic distinction between the functions of the two independent tribunals, the court in Pathe concluded (at p. 416) that with regard to the case presented, the two laws are in harmony rather than in conflict. Moreover, the court in Minor v. Sonoma County Employees Retirement Bd. (1975) 53 Cal. App.3d 540, 544 [126 Cal. Rptr. 16], cited Pathe with approval for the proposition that it might be appropriate to analogize a workers' compensation rule to proceedings before a retirement board: "In view of the similarity of the service-connectedness language in the statutes governing retirement boards (Gov. Code, § 31720, subd. (a)) and workmen's compensation appeals boards (Lab. Code, § 3600), and the fact that, although the two schemes are independent and serve different functions, their purposes are `in harmony rather than in conflict' (Pathe v. City of Bakersfield, 255 Cal. App.2d 409, 416 [63 Cal. Rptr. 220]), application of such a nonstatutory rule by analogy might be appropriate." Thus it seems clear that the tendency is to view the two bodies of law as compatible rather than the opposite. An examination of the legislative record and history of Government Code section 31720 reveals no discussion of the precise issue appellant raises. A simple reading of subdivision (a) of section 31720 does not disclose the requirement which appellant would propose. Moreover there are two provisions in section 31720 which demonstrate that the disability does not have to be entirely service-connected. The section states that a member "permanently incapacitated ... shall be retired for disability ... if, and only if: [¶] (a) His incapacity is a result of injury or disease arising out of and in the course of his employment," not the result thereof. (Italics added.) Had the Legislature determined that the incapacity had to be completely service-connected the Legislature would have stated that his incapacity must be the result of his employment. *429 Also, under subdivision (b) a member who is permanently incapacitated for the performance of duty who has completed five years of service shall be retired regardless of whether the incapacity is a result of injury or disease arising out of and in the course of his employment. (2) It is a well established rule that courts are bound to give effect to statutes according to the usual, ordinary import of language employed in framing them. (People v. Jones (1964) 228 Cal. App.2d 74, 83 [39 Cal. Rptr. 302].) All that subdivision (a) requires is that the incapacity be a result of injury or disease arising out of and in the course of the claimant's employment. Appellant essentially urges this court to rewrite the statute to provide that disability retirement be awarded only when the incapacity is caused solely by an injury or disease arising out of employment. It is not the function of this court to legislate, and such a construction of the statute would severely limit its present applicability. (3) As is stated in Gorman v. Cranston (1966) 64 Cal.2d 441, 444 [50 Cal. Rptr. 533, 413 P.2d 133]: "It has long been settled in this state that pension legislation is to be liberally construed. In Jorgenson v. Cranston, 211 Cal. App.2d 292, 296 [27 Cal. Rptr. 297], the rule is stated thus: `"[P]ension legislation must be liberally construed and applied to the end that the beneficent results of such legislation may be achieved. Pension provisions in our law are founded upon sound public policy and with the objects of protecting, in a proper case, the pensioner and his dependents against economic insecurity. In order to confer the benefits intended, such legislation should be applied fairly and broadly."'" The question appellant presents should be left to the Legislature to determine whether revision is appropriate. The expressed purpose of the county employees' retirement law "is to recognize a public obligation to county and district employees who become incapacitated by age or long service in public employment ... by making provision for retirement compensation and death benefit ... and to provide a means by which public employees who become incapacitated may be replaced by more capable employees ... without inflicting a hardship upon the employees removed." (Gov. Code, § 31451.) The statutory scheme as a whole does not lend itself to the interpretation appellant would press upon this court. There is in the statute purposeful recognition of the public obligation to provide for the well-being of those public employees who become incapacitated and must be replaced by others. It is not for this court to arbitrarily limit the benefits presently extended by the Legislature. *430 2. The courts have not determined that decisions under the workers' compensation law are not precedents with respect to the county employees' retirement law. Appellant notes that under current law, it is entirely possible that an individual employee may have not only a claim for disability under the county employee's retirement law but also a claim for workers' compensation; thus it would appear that a hearing before either the retirement board or the Industrial Accident Commission would be binding on the other. Because there are cases which hold that determinations under the workers' compensation law are not res judicata as to retirement proceedings (Petry v. Board of Retirement (1969) 273 Cal. App.2d 124 [77 Cal. Rptr. 891]; Flaherty v. Board of Retirement (1961) 198 Cal. App.2d 397 [18 Cal. Rptr. 256]), appellant argues that this signifies that decisions made under the workers' compensation law are not precedents for county employees' retirement law. The cases cited by appellant regarding the interplay of workers' compensation decisions and retirement board decisions involve only principles of res judicata and do not concern the applicability to the latter system of rules developed under the former. In light of Pathe and Minor (see also Buckley v. Roche (1931) 214 Cal. 241, 245 [4 P.2d 929]), the great disparity in the two systems which appellant insists exists, does not appear to be profound. To the contrary, it appears that many of the similarities between the two have been recognized by the courts and acted upon accordingly. 3. If a test requiring 100 percent (or thereabouts) causation is not adopted, the retirement board's right to hear disability claims will not be rendered meaningless. (1b) Appellant's final argument is basically that this court should rewrite Government Code section 31720 to require that the employment must be the sole cause where the permanent incapacity is due to mental, rather than physical disability. This, appellant contends, is because it is completely beyond the art of the psychiatrist to delimit causation of psychiatric disorders. Thus, in every case (such as here) where the symptomatology is somewhat subjective, the expert would as a matter of course conclude that a contributing cause was a preexisting condition, family life, or employment conditions. Appellant argues this works an unfair result under retirement law, since even an infinitesimal contribution *431 to the disability might require full compensation, whereas under workers' compensation law, an employer bears only his share of what he has been found to have caused. It appears that appellant's remedy, here too, is with the Legislature. Appellant points to no authority which would compel this court to rule that an employee suffering a mental disability as a result of employment is required to bear a heavier and different burden than one who sustains a purely physical disability. Moreover, section 31722 of the Government Code which sets out the requirements for applying for service-connected disability explicitly recognizes that such a disability may be mental as well as physical in nature. That section states: "The application shall be made while the member is in service, within four months after his discontinuance of service, or while from the date of discontinuance of service to the time of the application he is continuously physically or mentally incapacitated to perform his duties." (Italics added.) This court has no authority to rewrite the law to conform to appellant's view of what it should be. Appellant's complaint is with the Legislature. 4. This appeal is not frivolous. (4) Respondent argues that this court should penalize appellant for taking a frivolous appeal. Respondent requests this court to take judicial notice pursuant to sections 451 and 452 of the Evidence Code of an unpublished opinion of this court wherein appellant raised the same issues on appeal that have been raised here. Respondent contends that appellant's purpose in pursuing this appeal is to make a "test" case out of respondent's disability claim and is patently unjust to her since it allows appellant to pursue a second opportunity to have the applicable law changed by this court. It appears that this is an attempt by respondent to circumvent the strictures of rule 977 of the California Rules of Court, which explicitly disallow citation to unpublished opinions, thereby establishing that they are not to be considered of precedential value. The power to penalize a party for filing a frivolous appeal is properly exercised when the appeal is entirely barren of merit and frivolous in the extreme. (Seidell v. Tuxedo Land Co. (1932) 216 Cal. 165, 171 [13 P.2d 686].) On its face, the instant appeal has raised substantial issues requiring more than a cursory inspection. It therefore seems improper to penalize appellant. *432 Contrary to appellant's assertion that careful review of workers' compensation law and county employees' retirement law will reveal different interpretation of language, the opposite appears to be the case. It cannot be denied that the two bodies of law, despite the fact that they are independent statutory schemes, overlap in some of their functions. Comparison of the two does not in any way support appellant's contention that under retirement law, employment must be the sole or substantial cause of disability before an award may be made. Neither does appellant direct this court's attention to any specific authority which might support such an interpretation. To construe the statute as appellant proposes would markedly alter the plain meaning of the language as it presently exists. Judgment affirmed. Molinari, P.J., and Sims, J., concurred. Appellant's petition for a hearing by the Supreme Court was denied January 27, 1976. NOTES [*] Retired Presiding Justice of the Court of Appeal sitting under assignment by the Chairman of the Judicial Council. | Mid | [
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cnxps.cmd.push(function () { cnxps({ playerId: '36af7c51-0caf-4741-9824-2c941fc6c17b' }).render('4c4d856e0e6f4e3d808bbc1715e132f6'); }); The Bulgarian state prosecution has decided not to charge Hezbollah with involvement in the 2012 bomb attack at the Burgas airport that killed five Israelis and their Bulgarian bus driver and wounded 32 other Israelis, The Jerusalem Post has learned.Instead, the prosecutor indicted the two men allegedly involved in the attack as if they were terrorists or even regular criminals who acted without connection to an organization. The word “Hezbollah” does not appear in the indictment.In addition, the indictment does not mention standard terrorism offenses such as “acting as part of a terrorist organization” or connecting the murder offense to terrorism. Instead, it makes a brief reference to Bulgarian Penal Code Section 108(a) regarding disturbing the public order.Under Section 108(a), anyone who by causing a “disturbance or fear among the population” or who threatens or forces “a competent authority... to perform or omit part of his/her duties, commits a crime,” in addition to other crimes they may have committed.Sources close to the case say that when the Bulgarian prosecutor on the case was confronted with these anomalies, he claimed that no one provided him with evidence demonstrating Hezbollah’s involvement.This, however, is in direct contradiction to evidence that came to light immediately after the attack. Bulgaria’s interior minister at the time, Tsvetan Tsvetanov, said in 2013, “We have established that the two [accused] were members of the militant wing of Hezbollah.” He also said, “There is data showing the financing and connection between Hezbollah and the two suspects.”In 2013, Tsvetanov’s successor, Tsvetlin Yovchev, told reporters before a commemoration ceremony, “There are clear signs that say Hezbollah is behind the Burgas bombing.”Also in 2013, responding to a discussion about Bulgarian-Israeli relations on Bulgarian National Television, then-foreign minister Nikolay Mladenov said that the government would not have issued a statement linking Hezbollah to the Burgas attack if it did not have solid evidence.Evidence produced by Bulgaria’s investigation into the Burgas bombing even led to the European Union placing Hezbollah’s armed wing on its blacklist, a move that was supported at the time by Mladenov, today the United Nation’s special coordinator for the Middle East peace process.The Post contacted Bulgaria’s Foreign Ministry, the State Agency for National Security, Interior Ministry, Justice Ministry and Prosecutor’s Office for a response to allegations that the prosecution was covering up Hezbollah’s involvement in the attack and ignoring evidence referred to by its ministers.In response, Milena Petrova from the Foreign Ministry said on behalf of the prosecution that “the content of the indictment is completely within the competences of the prosecutor who is in charge of the case.Neither Tsvetan Tsvetanov, in his capacity as then-interior minister, nor any other ministry or incumbent minister pay whatever regard to the decisions and legal acts of the judiciary.“The executive and the judiciary powers are separated and independent of each other. The prosecutor’s office is part of the judiciary of the Republic of Bulgaria,” the statement concluded.The statement does not deny the existence of evidence of Hezbollah’s involvement.Instead of denying the existence of such evidence, the statement contends that the prosecutor’s office is in a better position than former Bulgarian ministers to decide what issues should be included in an indictment and what issues should not be.Put differently, the Bulgarian prosecutor’s statement essentially acknowledges that there is a contradiction between the indictment it filed and the statements made by senior Bulgarian ministers in 2012 and 2013.SINCE 2013, the political parties running the Bulgarian government have changed three times, with swings ranging from a pro-Western direction to a more pro-Russian orientation.The Bulgarian Prime Minister Boyko Borisov, who reentered government in 2017, served as prime minister during the Burgas attack. Borisov’s pro-EU party Citizens for European Development of Bulgaria formed a coalition with the United Patriots, an amalgam of three far-right extremist parties.The new ruling parties are generally known to be less sympathetic to Israel and more concerned about a confrontation with Hezbollah. Ataka, one of the right-wing extremist parties in Borisov’s coalition, adopted its name from Joseph Goebbels’s Nazi newspaper Der Angriff (The Attack).The European Commission has frequently reprimanded Bulgaria for failing to root out corruption and failing to modernize its judiciary.Transparency International’s 2016 Corruption Perceptions Index named Bulgaria the most corrupt EU member state. The pro-Russia Socialist party said the government has failed to confront high-level misconduct and graft.Last week, the Bulgarian government survived a no-confidence vote in the parliament by 131-103. The parliamentary row was over the failure of the center-right government to tackle widespread graft.FORMER BULGARIAN officials and the EU are not the only officials who have confirmed Hezbollah’s involvement in the 2012 terrorist attack.Bulgarian officials and others leaked significant details relating to the investigation following the attack.Prime Minister Benjamin Netanyahu said in the past that the Bulgarian findings made it clear that Hezbollah was “directly responsible for the heinous act in Burgas.”A flood of media reports on multiple continents have discussed the roles of the defendants, Lebanese-Australian national Meliad Farah and Lebanese-Canadian national El Hajj Hassan, in the attack. There are also US court documents from other terrorism- and Hezbollah-related cases that have confirmed that the third attacker, who died in the attack, French-Lebanese national Jacques Felipe Martin (also known as Muhammad Hassan el-Husseini), was also connected to Hezbollah.The men are alleged to have entered Bulgaria using false drivers licenses printed in Lebanon.In 2013, the Bulgarian government presented evidence to the EU linking a Hezbollah operative’s ownership of a printer to doctored documents that enabled the 2012 terrorist attack.US analysts concluded that the bombers belonged to Hezbollah, and Farah and Hassan have both been named “Specially Designated Global Terrorists” by the Department of State under Executive Order 132246.Husseini was connected to the two living attackers by a SIM card and forged documents.Much of this information was disclosed at a meeting to the CP931, a special European working group related to confronting terrorism, according to an EU diplomat.In 2017, the FBI arrested Samer El-Debek for his participation in a Hezbollah cell in the United States.Debek was reportedly trained as a bomb-maker for Hezbollah.In his May 2017 statement under oath as part of the indictment against Debek, FBI Agent Daniel Ganci said Debek “received extensive training as a bomb-maker, has a high degree of technical sophistication in the area, and was trained in techniques and methods similar to those used to construct the improvised explosive device used in Hezbollah’s 2012 Burgas, Bulgaria, bus bombing.”According to the statement, Debek told FBI agents that he was familiar with the 2012 Hezbollah attack on the Israeli tour bus in Burgas and that the bomber Husseini was connected to his family (his aunt’s nephew). Debek identified a photograph of Husseini and said that he knew of Husseini’s membership in Hezbollah’s External Security unit, “the same unit in which Debek said he was a member.”Farah and Hassan have not been taken into custody despite Interpol search warrants being issued against them.THE TRIAL, which is being held in absentia of the defendants, was delayed for years, partially in order for the numerous Israeli families involved to gather evidence and coordinate their efforts, and partially because of changes in Bulgarian law.There was also a delay with the court hearing and a rejection of a request to hear Israeli witnesses in Israel without the need to travel to Bulgaria. The Israeli victims and their families are represented by lawyer Yaki Rand.The trial finally commenced on January 17 with a number of Bulgarian witnesses talking about the events surrounding the attack.Even as Hezbollah’s role and the more serious terrorism offenses were left out of the indictment, the Bulgarian prosecutor made statements to the press on January 17 emphasizing the terrorist side to the case.Sources have indicated that this continues the prosecutor’s fine line of vaguely acknowledging some terrorism in the case as a matter of maintaining minimal credibility, considering it was a major bombing event, but omitting Hezbollah’s involvement.Why has Bulgaria’s prosecution decided to keep Hezbollah out of the case in contradiction of its former ministers, the EU and the US? Why did the specific prosecutor on the case say he did not receive any evidence about Hezbollah? Could that mean that higher-ups did not pass on all of the evidence to him? Are the motivations part of a problematic cover-up, either ideological or based on fear of retaliation from Hezbollah, or might they be related to issues of maintaining the secrecy of intelligence sources or some more understandable reason? These questions remain unanswered, but the ongoing trial, with its next date set for February 6, may continue to shed light on the issue even as the prosecution seems intent on burying it. | Low | [
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1. Introduction {#sec1} =============== Placenta previa (placenta implanted over the internal cervical os) and placental abruption (premature separation of normally implanted placenta) are the major causes of antepartum haemorrhage in the third trimester of pregnancies and major contributors of obstetric haemorrhage in general \[[@B1]\]. Each of these conditions has a prevalence rate of 0.5% to 2% in most parts of the world \[[@B2]--[@B4]\]. Because of the changes in the lower uterine segment length and placental migration as the pregnancy advances, the prevalence of placenta previa has an inverse relation to the gestational age \[[@B5]\]. In other words, it is suggested that reporting of placenta previa in early gestation is likely to overestimate its actual prevalence at term. Placenta previa and placental abruption have long been recognized as major obstetric complications that result in maternal and fetal mortality as well as morbidity. The effect of these two bloody obstetric complications on perinatal health is multifactorial: blood loss, premature delivery, intrauterine growth restriction, the risk of perinatal asphyxia, the risk of sepsis, and hyperbilirubinemia \[[@B2], [@B6]--[@B8]\]. A Danish national cohort study was associated with an increased risk of neonatal mortality, prematurity, low Apgar scores, low birthweight, and transfer to a neonatal intensive care unit \[[@B9]\]. Several other studies from developing countries have also shown that pregnant women complicated by placenta previa are likely to have babies delivered preterm, low birth weight, asphyxiated, and requiring intensive neonatal care, while stillbirth or neonatal mortality may also occur \[[@B7], [@B10], [@B11]\]. To be specific, the risk of perinatal mortality in women with placental previa is estimated to be 4% to 8% but, when accompanied by prematurity, the death rate may increase to 50% \[[@B12]\]. On the other hand, the perinatal mortality in placental abruption cases may be as high as 20% to 47% \[[@B3], [@B13]\]. Specific to developed countries, a recent review has shown that 10--20% of all perinatal deaths are caused by placental abruption \[[@B14]\]. More than a decade back, studies in developed countries concluded that placental abruption had a profound impact on stillbirth \[[@B15], [@B16]\]. However, a large scale review in the United States in 2001 reported that the high perinatal mortality with abruption was mainly due to its strong association with preterm delivery \[[@B17]\]. But with the advancement of obstetric service, the perinatal mortality has been reported as decreasing \[[@B18], [@B19]\]. To the best of the author\'s knowledge, there is no published study that assessed placenta previa and placental abruption associated perinatal mortality and morbidity in Sub-Saharan Africa and in Ethiopia in particular. Thus, this study shades light on the most common complications of placenta previa and placental abruption with emphasis on the primary outcome predictors, the magnitude of perinatal mortality, and associated factors. Secondly, it gives a ground evidence on how soon or late women with placenta previa and placental abruption were coming to the hospital; what interventions were undertaken; and what was the condition of the neonates and mothers at discharge. In short, the findings of this study are instrumental to identify barriers and delays at the community and hospital level. The objective of this study was to determine the predictors of perinatal mortality associated with placenta previa and placental abruption. 2. Methods {#sec2} ========== This retrospective cohort study included all women with placenta previa and placental abruption who were admitted and managed in Hawassa University Hospital between January 2006 and December 2012. Hawassa University Hospital, located in the capital city of Southern Nation Nationalities and People Regional State of Ethiopia, has a catchment population of more than 16 million. During this study period, 9619 women gave birth in this hospital. Out of these, 511 women with singleton pregnancies were diagnosed to have antepartum haemorrhage (APH) at admission. Multiple births were excluded taking into account that they can have many other complications that might add to the complications attributed to the placenta previa or placental abruption independently. Further scrutiny of each of the 511 APH labelled patients\' charts revealed that there was change of the admission diagnoses through progressive evaluation of the pregnant women and examination of the placenta after delivery. As a result, 21 cases were later on identified as abortion (gestational age \< 28 weeks) \[[@B20]\]; 29 cases were due to heavy show; 6 cases were diagnosed to have local causes (cervical infection, polyps, leech infestation, and cervical carcinoma); and 23 cases were excluded because of incomplete documentation. A total of 432 cases were identified as eligible for analysis. The data sources for this study were individual patient\'s chart, admission, and discharge record books. Data related to the patients\' age, residence, distance travelled for hospital admission, duration of hospital stay, obstetric history, clinical condition, and laboratory results at admission and discharge were collected. When a pregnant woman presented with dark and nonclotting vaginal bleeding after 28 weeks of gestation, placental abruption was diagnosed. The finding of retroplacental clot/bloody jell or depression in the maternal placental surface after delivery was taken as confirmation for atypically presented placenta previa. Whereas ultrasound report of placenta praevia was taken as a final diagnosis. For the purpose of this study, the degree of maternal anaemia and the survival of babies in the perinatal period were taken as primary outcome indicators. In this study, APH was defined as any vaginal bleeding due to either placenta previa or placental abruption after 28 weeks of gestation before the delivery of the baby. The total time taken to reach the study hospital after the onset of APH symptoms (painless, bright red, and clotting vaginal bleeding in placenta previa; unexplained lower abdominal pain with or without dark nonclotting vaginal bleeding in placental abruption; and decreased or absent fetal kick in both) was taken as the duration before arrival. In this study, lengthy delay is to mean a period that lasted more than 12 hours since the onset of APH symptoms and long distance travelled implies 50 km or more to reach to the hospital. Gestational ages were categorized as very preterm (28--33 completed weeks), preterm (34--36 completed weeks), and term (37+ weeks). Perinatal status defined the fetal or early neonatal survival (from 28 weeks of pregnancy age up to the first 7 days of newborn age) \[[@B21]\] or otherwise after the onset of vaginal bleeding due to placenta previa or placental abruption. The mean minimum normal haemoglobin level during pregnancy at sea level is 11-12 gm/dL \[[@B22]\]. In this study, the degree of anaemia was categorized as severe, moderate, mild, and no anaemia when the haemoglobin level was \<7 gm/dL, 7--9.9 gm/dL, 10--11.9 gm/dL, and 12+ gm/dL, respectively. In this study, perinatal mortality and perinatal death are used interchangeably. Ethical approval of this study was obtained from Hawassa University College of Medicine and Health Sciences Institutional Review Board. Written informed consent from the women included in this study was not required as only already registered data were used. Moreover, confidentiality and anonymity are assured by analyzing and disseminating the data in aggregate. Data analysis was done using SPSS version 16.0 and Microsoft Office Excel 2010 computer software. Whisker and box plot was used to show the relation of perinatal mortality due to placenta previa and placental abruption with delay in arrival, gestational age, haemoglobin level, and fetal birth weight. The binary logistic regression model was applied to assess the association of perinatal mortality as a dependent variable with some selected variables as predictors. Kaplan-Meier survival curve with log rank test and receiver operating characteristic (ROC) curve (nonparametric method) were used to determine the strength of perinatal mortality predictors. *P* value \< 0.05 was taken as indicator of statistically significant association. 3. Results {#sec3} ========== 3.1. General Characteristics {#sec3.1} ---------------------------- Out of 432 antepartum haemorrhage cases included in this study, placenta previa and placental abruption constituted 253 (58.6%) and 179 (41.4%), respectively. The incidence of placenta previa and placental abruption in the study hospital during the study period was 2.6 and 1.9 per 1000 pregnant women. Placenta previa by type was totalis, partialis, and marginalis/low-lying which accounted for 151 (59.4%), 54 (21.5%), and 48 (19.1%), respectively. The degree of abruption (separation) for 107 (59.8%) was up to 50% or less and for the other 72 (40.2%) cases was over 50%. Twelve cases were diagnosed before the onset of vaginal bleeding. Otherwise, 420 (97.2%) women presented to the hospital after the onset of vaginal bleeding. Of which, 93 (21.5%) were admitted in a state of hemorrhagic shock (with unrecordable blood pressure and severe blood loss anaemia). Nearly three-fourths of the women were in the age range of 20--34 years and more than three-fifths came from rural areas ([Table 1](#tab1){ref-type="table"}). One hundred forty-five (33.6%) women traveled more than 100 km to reach the study hospital; the mean distance was 96 ± 93 km. When the proportions of mothers\' age, residence, and distance travelled were stratified by placenta previa and placental abruption, there was no much difference. Women with placental abruption came relatively earlier than women with placenta previa: \>12 hours delay before arrival in placenta previa and placental abruption group was 157 (62.1%) and 81 (45.%), respectively. Overall, 238 (55.1%) women accessed the study hospital more than 12 hours after onset of their bleeding. The median delay in accessing the study hospital was 16 (interquartile range: 7--48) hours. In more than half of the cases (51.2%), with almost equivalent proportion in both placenta previa and placental abruption, the gestational ages had reached term (37+ weeks). On arrival at the hospital, 142 (32.9%) were fetal demise, and 53 (12.3%) foetuses had abnormal fetal heart rate (persistent bradycardia, persistent tachycardia, or irregularly fluctuating from normal range to bradycardia or tachycardia). 3.2. Degree of Anaemia {#sec3.2} ---------------------- On admission, 334 (77.3%) of the women were found to have anaemia and the mean haemoglobin level was 9.0 ± 3.0 gm/dL ([Table 2](#tab2){ref-type="table"}). The distribution of severe, moderate, and mild anaemia was almost proportional. Severe and mild anaemia was detected in the majority of women with placenta previa and placental abruption, respectively. When these women were discharged from the hospital, the severity of anaemia was found even worsening. The proportion of overall severe anaemia increased from 27.8% on admission to 41.2% at discharge and moderate anaemia from 27.1% to 30.6%. In patients with placenta previa, severe anaemia increased from 33.2% on admission to 51.4% at discharge. In short, the proportion of anaemia increased from 201 (79.4%) to 234 (92.5%) in placenta previa cases and from 133 (74.3%) to 153 (85.5%) in placental abruption cases. [Figure 1](#fig1){ref-type="fig"} summarizes the change in haemoglobin level after delivery. In the majority of women, the haemoglobin levels at discharge were below the level on admission. Specifically, the drops in haemoglobin level were marked in those women who were better with the haemoglobin level \>7gm/dL on admission. 3.3. Interventions in the Hospital {#sec3.3} ---------------------------------- [Table 3](#tab3){ref-type="table"} shows the specific intervention carried out and fetal outcomes. It was possible to transfuse whole blood for 144 (33.3%) women. Of which, 106 (24.5%) were transfused with 1-2 units of blood (the transfusion criterion of the hospital is haemoglobin \<7 gm/dL for blood loss anaemia with or without hemodynamic instability; one unit blood is equivalent to 450 mL). As presented in [Figure 2](#fig2){ref-type="fig"}, all women with placenta previa and the majority of women with placental abruption whose haemoglobin level \<7 gm/dL at discharge were transfused 1-2 units of blood before having this amount of haemoglobin. Three women with placental abruption were not at all transfused despite having a haemoglobin level of \<7 gm/dL. Eighty-nine (20.6%) women were kept in the maternity ward before delivery for more than two days (median: 2.5 and IQR: 1--24 days). After delivery, 360 (83.3%) women were kept in the hospital for less than a week, with similar proportion in both placenta previa and placental abruption. Three-fourths of women gave birth by caesarean section. Active vaginal bleeding was the highest indication, 79.4% (258/325). One hundred forty-three (66.8%) of the perinatal deaths were delivered by caesarean section. Specifically, 92 (43%) caesarean sections were done for fetal demise and some other indications. 3.4. Perinatal Mortality {#sec3.4} ------------------------ As shown in [Table 3](#tab3){ref-type="table"}, there were 214 perinatal deaths, making the total perinatal mortality rate due to placenta previa and abruption about 495/1000 births or nearly 50%. The perinatal mortality rates associated with placenta previa and placental abruption were about 447/1000 births and 564/1000 births, respectively. Of the total perinatal deaths, 164 (38.0%) foetuses were found to be stillbirths (22 foetuses were admitted to the hospital with a positive fetal heart beat and died in utero) and 50 (11.6%) were early neonatal deaths. Out of the total perinatal deaths, placenta previa and placental abruption related deaths were 44.7% (113/253) and 56.4% (101/179), respectively. The proportion of stillbirths and early neonatal deaths in placenta previa and placental abruption were 34.4% versus 43.0% and 10.3% versus 13.4%, respectively. In [Table 4](#tab4){ref-type="table"}, the univariate analysis revealed that perinatal mortality due to placenta previa and placental abruption was strongly associated with long distance travel, lack of antenatal care, very low birth weight, and maternal severe anaemia. Other variables weakly associated with perinatal mortality due to placenta previa and placental abruption were maternal age above 20 years, rural residence, multiparity, and gestational age of 28--33 weeks during the time of delivery. For more than three-fifths of the total foetuses (62.5%), their birth weight was above 2500 gm and 259 (60.0%) of the foetuses were male, with comparable proportion in both placental abruption and placenta previa. The gestational age distribution of the perinatal deaths in weeks was 28--33 for 60 (28.0%), 34--36 for 52 (24.3%), and 37+ for 102 (47.7%). The Kaplan-Meier curve demonstrated that the perinatal mortality was the highest among placental abruption cases (log rank: *P* \< 0.0001), and in both placenta previa and placental abruption cases, the survival curve dropped sharply in the early period, which may indicate that the majority of the babies died in the first 24 hours of onset of the bleeding ([Figure 3](#fig3){ref-type="fig"}). [Figure 4](#fig4){ref-type="fig"} shows the relation of perinatal mortality with delay in arrival (a), gestational age (b), haemoglobin level (c), and fetal birth weight (d) as stratified by placenta previa and placental abruption. Both the median and IQR hours of delay among perinatal deaths were shorter than the survivors, which is another evidence to strengthen the findings in [Figure 3](#fig3){ref-type="fig"}. In women with placental abruption, the median gestational age and fetal birth weight were found to be lower in perinatal deaths than the survivors, whereas in women with placenta praevia, the median gestational ages of perinatal deaths and survivors were comparable. In both placental abruption and placenta previa, however, the median admission haemoglobin level of the cases resulting in perinatal deaths group was much lower than the survivors. In [Table 5](#tab5){ref-type="table"}, the crude odds ratios in the binary logistic regression have shown that long distance travel, lengthy delay in accessing the hospital, preterm gestational age, low blood pressure, anaemia on admission, and others were strongly associated with perinatal mortality. In the adjusted odds ratios, however, lengthy delay, preterm gestational age, anaemia level, being male, and delivered vaginally were independent predictors of perinatal mortality. Since the adjusted binary logistic regression model showed highly statistically significant association of perinatal mortality with low gestational age and haemoglobin level (OR 1.4 and 1.9, resp.), receiver operating characteristic curve (ROC) was depicted to test the two variables predictive validity in perinatal mortality ([Figure 5](#fig5){ref-type="fig"}). As the area under the curve shows, haemoglobin level on admission was more sensitive and more specific to determine perinatal mortality than the gestational age. In this series of cases, there was no maternal death reported; couvelaire uterus was detected in 18 women with placental abruption who gave birth by caesarean section; and caesarean hysterectomy was done in 13 cases of placenta previa (12 for placental adherence and one for intractable postpartum haemorrhage). 4. Discussion {#sec4} ============= This study has shown that the perinatal mortality in women with placenta previa and placental abruption was about 50%, which is probably one of the highest in the world \[[@B3], [@B7], [@B10]--[@B13], [@B23]\]. Placenta previa associated perinatal mortality (about 45%) in particular was more than two- to threefold of some less developed countries \[[@B6], [@B23]\] and more than fifteenfold of a report from developed countries \[[@B9], [@B15], [@B24]\]. The perinatal deaths associated with placental abruption alone were also too high but were not as high as those in the recent report from Pakistan \[[@B25]\]. Similarly, the proportion of severely anaemic women both on admission and at discharge was surprisingly high, probably because of the big delay in reporting to the hospital, further blood loss after admission, and inadequate blood transfusion. Unlike placental abruption, in which bleeding can be concealed and may be complicated with coagulopathy and further blood loss \[[@B26]\], bleeding due to placenta previa is immediately revealed and likely to make many of the pregnant women and their family seek prompt medical care. Relative ease of diagnosis in placenta previa is also an advantage for health professionals to undertake timely appropriate interventions and prevent further blood loss and associated maternal and perinatal complications. In this study, however, among women with placenta previa, more than one-third on admission and more than half at discharge were severely anaemic, which is probably the major reason why perinatal deaths were nearly proportional or higher than previously reported \[[@B3], [@B12], [@B13], [@B17]--[@B19], [@B23]\]. In general, the number of women with severe anaemia was quite large in both placenta previa and placental abruption group, which both contributed to about 50% of perinatal mortality. Among others, the adjusted binary logistic regression model also demonstrated that severe anaemia and delay in arrival were strong predictors for high perinatal mortality. Due to the excessive blood loss characteristic of these two obstetric problems, some degree of anaemia is inevitable regardless of the quality of care available in the country where the pregnant women reside. Maternal anaemia resulting from bleeding was not reported to be contributors to perinatal mortality in some of the previous studies of placental previa and placental abruption \[[@B3], [@B12], [@B13], [@B23], [@B25]\]. This is probably because of the settings of advanced obstetric care and easy access of health facilities for the majority of pregnant women reported \[[@B9]\]; it might have resulted in a reduction of placenta previa and placental abruption related complications. In the author\'s opinion, delay in arrival was probably at the epicenter of the whole problem of the patients included in this study. This is because, the longer pregnant women stay bleeding at home, the more they are likely to be severely anaemic. As a result, there is a high chance the foetuses will get asphyxiated or dead. Furthermore, since the hospital has been functioning as a referral with blood transfusion and operation facility, it is likely that it has more complicated placenta previa and placental abruption cases that had travelled long distance. Lengthier delay in arriving to the hospital was also observed among women with placenta previa than women with placental abruption, which was probably why many women with placenta previa were found in a severely anaemic state that has contributed to their significant overall perinatal deaths. One may pose a question, why was there such significant delay in arrival and long distance travel? Since this study was based on registered data, it was not possible to get an exact answer for this question. However, from day to day observation in the hospital, it is possible to speculate that lack of health care seeking behavior (probably because of unawareness of available health services for this kind of problem), lack of local midwives for early referral, inability to get access to health facilities (usually due to financial problem and lack of ambulance service in the rural area), and delay in getting proper and satisfying treatment in health facilities including the hospital where these cases were managed might have contributed to high perinatal mortality and high blood loss anaemia. Whatever the barrier for early arrival was, the lengthy delay was the most likely factor for severe blood loss and high perinatal death. Regardless of the delay in time, however, several studies have shown that placenta previa and placental abruption are known to triple the rate of perinatal mortality primarily due to prematurity \[[@B7], [@B8], [@B10], [@B12], [@B13], [@B17], [@B25]\]. In this study, however, as ROC curve showed, prematurity was not as sensitive and specific as haemoglobin level was in predicting perinatal mortality. The gestational age for more than two-thirds of the perinatal deaths was 34 weeks and above. But this finding has to be interpreted very cautiously. The relatively low perinatal deaths among very premature foetuses (28--33 weeks) may not be a true reflection as there were only a very small number of babies delivered prematurely. Taking into consideration the available intensive neonatal care and the reported neonatal survival rate, by definition, the viable gestational age for foetuses delivered in developed and developing countries including this study starts from 20--24 weeks \[[@B9], [@B15], [@B24]\] and 28 weeks \[[@B21]\], respectively. This could mean that if this study had included babies born before 28-week gestation with similar problems, prematurity might have been as well the leading associated problem for high perinatal mortality. Otherwise, since the area under the curve is said to be an effective and combined measure of sensitivity and specificity for assessing the inherent validity of a predictor \[[@B28]\], above all, haemoglobin level on admission was the strongest predictor of perinatal mortality. The finding of about one-third of the women with severe anaemia and more than one-fifth presenting in shock on admission may also explain how critically ill the women themselves were. Probably it was because of such life threatening anaemia due to blood loss why nearly 80% of the women were subjected to give birth within 24 hours of their arrival to the hospital. Additionally, the finding of the majority of the women with further worsening anaemia indicate the continuous blood loss even after arrival to the hospital (probably due to the high caesarean delivery rate) and lack of adequate blood transfusion. The explanation for the worsening haemoglobin level at discharge probably goes beyond the continuous blood loss even after arrival. The finding of more than half of women with placenta previa and more than one-fourth of women with placental abruption having severe anaemia at the time of discharge is an objective evidence to show the inadequate blood transfusion in the study hospital. Had it been possible, all women with severe anaemia should have been transfused with blood or had iron infusion and been discharged with haemoglobin level of 7 gm/dL and above. In a clinical setting such as the one in this hospital, like many others in low income countries, getting blood donor is a daily challenge and iron infusion is not yet in routine practice. As a result, many of severely anaemic patients are discharged after assessing only the overall clinical condition. Limitations of this study are as follows: firstly the findings of this study could not be taken as incidence representing the general population in the hospital\'s catchment area. This is because the included mothers came mainly from a rural population where about 94% of pregnant women give birth at home \[[@B16]\]. Therefore, the reported cases in this study, if not representative, may reflect the magnitude of similar problems probably with worse outcomes back in the villages. Secondly, some asymptomatic or mild form of abruption may be under reported. Thirdly, some of the women might have variable degrees of anaemia in their pregnancy even before the onset of bleeding due to either placenta previa or placental abruption, which this study was not able to address. In Africa, severely anaemic pregnant women were reported to be between 1% and 5% \[[@B29]\] and 3% in Ethiopia \[[@B20]\]. Fourthly, some of the women discharged with severe anaemia might have had further complications which this study was not able to determine. Fifthly, although perinatal mortality is extended up to 28 weeks of postnatal period; this study was limited to the time the neonates were discharged from the hospital. 5. Conclusions {#sec5} ============== Low maternal haemoglobin level and delay in arrival were strong predictors of perinatal mortality due to placenta previa and placental abruption. The perinatal mortality was nearly 50% and 76.6% of these were stillbirths. The proportion of severe anaemia and perinatal mortality was probably one of the highest in the world. To reduce the burden of placenta previa and placental abruption related perinatal mortality, (1) comprehensive obstetric care including blood transfusion and iron infusion set up should be availed as close as possible to the villages where the study participants came from, and (2) there should be a strategy to let the community know the importance of antenatal care, maternal, and fetal risks of vaginal bleeding during pregnancy. Future studies should give emphasis on assessing the reasons for the delay in accessing and availing comprehensive obstetric care. Conflict of Interests ===================== The author would like to declare that there are no competing interests. {#fig1} {#fig2} {#fig3} {#fig4} {#fig5} ###### General characteristics of cases stratified by placenta previa and placental abruption, 2006--2011, Hawassa University Hospital, Ethiopia. Variable Placenta previa (*N* = 253) Abruptio placenta (*N* = 179) Total (*N* = 432) ---------------------------------- ----------------------------- ------------------------------- ------------------- Mothers\' age in years \<20 12 (4.7) 12 (6.7) 24 (5.6) 20--34 181 (71.6) 140 (78.2) 321 (74.3) 35+ 60 (23.7) 27 (15.1) 87 (20.1) Mothers\' residence Urban 86 (34.0) 77 (43.0) 163 (37.7) Rural 167 (66.0) 102 (57.0) 269 (62.3) Distance traveled in km \<50 98 (38.7) 80 (44.7) 178 (41.2) 50--100 70 (27.7) 39 (21.8) 109 (25.2) 101--200 37 (14.6) 42 (23.5) 79 (18.3) \>200 48 (19.0) 18 (10.0) 66 (15.3) Duration before arrival in hours ≤12 96 (37.9) 98 (54.7) 194 (44.9) \>12 157 (62.1) 81 (45.3) 238 (55.1) Parity 0 39 (15.4) 48 (26.8) 87 (20.1) I--IV 111 (43.9) 93 (52.0) 204 (47.2) V+ 103 (40.7) 38 (21.2 141 (32.6) Gestational age in weeks 28--33 54 (21.3) 30 (16.8) 84 (19.4) 34--36 74 (29.3) 53 (29.6) 127 (29.4) 37+ 125 (49.4) 96 (53.6) 221 (51.2) Antenatal care Yes 153 (60.5) 128 (71.5) 281 (65.0) No 100 (39.5) 51 (28.5) 151 (35.0) Diastolic BP in mmHg Unrecordable 13 (5.1) 3 (1.7) 16 (3.7) \<60 65 (25.7) 12 (6.7) 77 (17.8) 60+ 175 (69.2) 164 (91.6) 339 (78.5) Fetal heart beat Negative 71 (28.1) 71 (39.7) 142 (32.9) Abnormal 32 (12.6) 21 (11.7) 53 (12.3) Normal 150 (59.3) 87 (48.6) 237 (54.8) BP: blood pressure. ###### The proportion and degree of anaemia at the time of admission and discharge as stratified by placenta previa and placental abruption, 2006--2011, Hawassa University Hospital, Ethiopia. Haemoglobin in gm/dL Mean Severe anaemia (\<7) Moderate anaemia (7--9.9) Mild anaemia (10--11.9) No anaemia (12+) ---------------------- --------------- ---------------------- --------------------------- ------------------------- ------------------ At admission Total **9.0 ± 3.0** **120 (27.8)** **117 (27.1)** **97 (22.4)** **98 (22.7)** PP 8.7 ± 3.0 84 (33.2) 75 (29.6) 42 (16.6) 52 (20.6) PA 9.5 ± 3.0 36 (20.1) 42 (23.5) 55 (30.7) 46 (25.7) At discharge Total **7.9 ± 2.6** **178 (41.2)** **132 (30.6)** **77 (17.8)** **44 (10.2)** PP 7.6 ± 2.6 130 (51.4) 62 (24.5) 42 (16.6) 19 (7.5) PA 8.4 ± 2.5 48 (26.8) 70 (39.1) 35 (19.6) 26 (14.5) PP: placenta previa (*N* = 253). PA: placental abruption (*N* = 179). ###### Specific interventions and fetal outcome stratified by placenta previa and placental abruption, 2006--2011, Hawassa University Hospital, Ethiopia. Variable Placenta previa (*N* = 253) Abruptio placenta (*N* = 179) Total (*N* = 432) ------------------------------------------ ----------------------------- ------------------------------- ------------------- Whole blood transfused 1-2 units 67 (26.5) 39 (21.8) 106 (24.5) 3+ units 32 (12.6) 6 (3.4) 38 (8.8) Hospital arrival to delivery time (days) ≤1 188 (74.3) 155 (86.6) 343 (79.4) 2--7 34 (13.4) 15 (8.4) 49 (11.3) ≥8 31 (13.3) 9 (5.0) 40 (9.3) Hospital stay after delivery (days) ≤6 211 (83.4) 149 (83.2) 360 (83.3) ≥7 42 (16.6) 30 (16.8) 72 (16.7) Mode of delivery Vaginal\*\* 18 (7.1) 89 (49.7) 107 (24.8) Caesarean section 235 (92.9) 90 (50.3) 325 (75.2) Fetal outcome Alive 140 (55.3) 78 (43.6) 218 (50.4) Still birth 87 (34.4) 77 (43.0) 164 (38.0) Early neonatal death\* 26 (10.3) 24 (13.4) 50 (11.6) Fetal sex Male 145 (57.3) 114 (63.7) 259 (60.0) Female 108 (42.7) 65 (36.3) 173 (40.0) Fetal weight (gm) 1000--1499 21 (8.3) 24 (13.4) 45 (10.4) 1500--2499 72 (28.4) 45 (25.1) 117 (27.1) 2500--3999 154 (60.9) 104 (58.1) 258 (59.7) 4000+ 6 (2.4) 6 (3.4) 12 (2.8) \*Within seven days of birth. \*\*Including two vacuum and one forceps assisted delivery. ###### Univariate analysis on perinatal mortality in relation to selected demographic and obstetric factors among women with antepartum haemorrhage (APH), 2006--2011, Hawassa University Hospital, Ethiopia. Variable Total APH\* (*N* = 432) Perinatal deaths (*N* = 214) *P* value ------------------------------- ------------------------- ------------------------------ ----------- Mothers\' age in years \<20 24 6 (25.0) 20--34 321 166 (51.7) 0.04 35+ 87 42 (48.3) Mothers\' residence Urban 163 69 (42.3) Rural 269 145 (53.9) 0.02 Distance traveled in km \<50 178 66 (37.1) ≥50 254 148 (58.3) \<0.0001 Antenatal care Yes 283 124 (43.8) No 149 90 (60.4) 0.001 Parity 0 87 31 (35.6) I--IV 204 104 (51.0) 0.04 V+ 141 79 (56.0) Gestational age in weeks 28--33 84 60 (71.4) 34--36 127 52 (40.9) \<0.0001 37+ 221 102 (46.2) Maternal anaemia on admission Severe 113 104 (92.0) Moderate 121 52 (43.0) \<0.0001 Mild 91 27 (30.0) No anaemia 107 31 (29.0) Fetal weight (gm) 1000--1499 45 36 (80.0) 1500--2499 117 66 (56.4) \<0.0001 2500--3999 258 112 (43.4) 4000+ 12 0 \*Placenta previa + placental abruption; APH: antepartum haemorrhage. ###### Binary logistic regression on predictors of perinatal mortality in women with placenta previa and placental abruption, 2006--2011, Hawassa University Hospital, Ethiopia. ------------------------------------------------------------------------------------------------ Variable Crude Adjusted\*\* -------------------------------- ---------- ------------------- ---------- --------------------- Long distance traveled\* 0.002 0.8 (0.63, 0.90) 0.31 1.0 (0.99, 1.01)\ Lengthy delay before arrival\* 0.005 1.01 (1.00, 1.02) 0.003 1.01 (1.005, 1.02)\ Low gestational age\* \<0.0001 1.1 (1.08, 1.22) \<0.0001 1.4 (1.16, 1.65)\ No antenatal care 0.008 0.6 (0.39, 0.87) 0.07 0.34 (0.11, 1.09)\ Low blood pressure\* \<0.0001 1.02 (1.01, 1.03) 0.94 1.0 (0.98, 1.02)\ Anaemia\* \<0.0001 1.5 (1.41, 1.68) \<0.0001 1.9 (1.42, 2.59)\ Male fetal sex 0.009 1.7 (1.14, 2.51) \<0.0001 11.8 (3.13, 44.25)\ Vaginal delivery \<0.0001 1.4 (1.16, 1.58) \<0.0001 2.5 (1.55, 3.97) ------------------------------------------------------------------------------------------------ \*Continuous; all others are dichotomous. \*\*Adjusted for all variables in this table; other variables like maternal age, parity, and residence did not show significant association in the crude odds ratio. [^1]: Academic Editor: Lee P. Shulman | Mid | [
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Just bought this binding and used it today... Just bought this binding and used it today for the first time at the resort. I wanted to do some easy tele-turns on a gentle slope so I was in 'walk/hike' mode on the binding. 2nd or 3rd turn the ski popped off and went down the hill. luckily someone saw it and I retrieved it. Question- i stepped in, it clicked, and i pulled the lever up on the toe piece, heard it click. Is there something else I should be doing or ??? didn't think the ski should come off so easy. Retention on a tech-system binding is a function of the heel in combination with the toe. It's not really designed to be able to tele-turn. 2 other thoughts. It's good practice whenever you step in to rotate the boot 3-4 times. This will make sure the toe pins cut out any snow/ice in the metal boot inserts. Also, there are a couple of "clicks" when you pull the toe lever up in walk mode. More clicks = more retention, though still not truly enough for tele. | Low | [
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Q: how to verify that google analytics is working correctly on a subdomain (no access to root domain) I am trying to add google analytics to a project that is located under a subdomain. The subdomain has been was pointed to my my project by the domain owner, so I do not have access to the domain itself. When I add the tracking code the status (shown under Property > Tracking Info) Status: Tracking Not Installed Last checked: 04-Jan-2014 00:00:05 PST The Google Analytics tracking code has not been detected on your website's home page. For Analytics to function, you or your web administrator must add the code to each page of your website. Is there any way to verify the tracking code is installed on the subdomain without having to access the domain root? Although the tracking status is uninstalled, I am getting activity in Standard Reports > Realtime. Does this mean that it is working despite the status report? Am I likely to get correct tracking information with this setup? A: You do not need access to the root domain and if the realtime statistics track traffic then most likely your GA setup works correctly. Most likey you did not implement the code at the place in the source code where Google expects it (which usually works but is still flagged as an error in verification). If you use Google Chrome as browser you can additionally use two nice extensions to verify that your setup is correct: Google Tag Assistant - verifys various Google Tags without mch detail Google Analytics Debugger - provides some detail which data is sent to google, which plugins (e.g. ecommerce) are loaded by the analytics code etc. | High | [
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The New Hampshire 2020 primary is still almost a year away, but state legislators are already working to disenfranchise voters. HB 1264, a law set to go into effect in July 2019, will change the definition of what it means to be a “resident” of New Hampshire, forcing people with out-of-state driver’s licenses or car registrations to switch to the state versions if they register to vote. While it may sound like an archaic DMV issue, it’s actually a burden on the right to vote. In New Hampshire, students are lawfully permitted to vote in the town where they live while attending school. By requiring people to pay up to hundreds of dollars in vehicle registration fees if they register to vote, the law unconstitutionally restricts voting rights and, in particular, targets New Hampshire’s students and young people to dissuade them for voting. That’s why we just filed a lawsuit on behalf of two Dartmouth College students, both of whom were eligible to vote in the 2018 elections but now would be forced to update their driver’s licenses if they participate in 2020. For our plaintiffs, this fight is about having a voice in the issues that matter most to them. Caroline, a sophomore, is heavily involved in get-out-the-vote efforts on her campus. She’ll be living in New Hampshire until at least 2021 and wants to make sure her voice will be heard by legislators in New Hampshire on the issues she cares about. Maggie, another student in our case, wants to vote for candidates who will act on climate change. As she puts it, “I spend more of my time [in New Hampshire] than anywhere else, and these state and local politicians can affect anything from my access to health care to the quality of air I breathe.” Stretching back to the passage of the 26th Amendment — which lowered the voting age to 18 in 1971 — New Hampshire has repeatedly tried to exclude students from its elections. In the early 1970s, New Hampshire disqualified citizens from voting in a municipality if they had a “firm intention” of leaving that town at a fixed time in the future. In 1972, a federal court struck the law down because it explicitly targeted college students. Learn more about the case That didn’t stop state legislators from trying other tricks to stop students from voting. In 2012, the New Hampshire Legislature enacted a law that amended the voter registration form to suggest, inaccurately, that voters would be obligated to apply for New Hampshire driver’s licenses if they register to vote. The law was clearly passed with partisan intent. In fact, in September of 2012, the New Hampshire Speaker of the House Bill O’Brien described the language as necessary because college students were “[v]oting as a liberal. That’s what kids do.” The ACLU of New Hampshire challenged the 2012 law, and a court struck it down as unconstitutional. New Hampshire should have learned its lesson. Instead, following the 2016 election, legislators went back to the drawing board to target young voters. The process by which HB 1264 was passed alone reveals it to be a partisan attempt to restrict students’ right to vote. Despite the fact that the law changes the definition of a New Hampshire resident for motor vehicle purposes, the bill was considered by the Election Law Committees of both houses of the state legislature. One of the chief advocates for the law was the New Hampshire Secretary of State’s Office — the agency in charge of administrating elections. The Division of Motor Vehicles did not even take a position on this legislation, nor did it offer a cost estimate. And legislators supporting the law made known their intention to dissuade students from voting. Young people can and should play a leadership role in our country’s democracy. States that put unnecessary and unjustified barriers in the way of young people voting are violating the Constitution and doing a disservice to the democratic process. New Hampshire is a repeat offender when it comes to suppressing voting rights. We will see them in court to protect students’ right to vote. | High | [
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Statement by the Spokesperson on the agreement to form a new Council of Ministers in Bosnia and Herzegovina Bruxelles, 05/08/2019 - 19:40, UNIQUE ID: 190805_12 Statements by the Spokesperson Statement by the Spokesperson on the agreement to form a new Council of Ministers in Bosnia and Herzegovina Today’s agreement of political party leaders in Bosnia and Herzegovina to form a new Council of Ministers - facilitated by EU Special Representative Ambassador Lars-Gunnar Wigemark - is an important step forward, first and foremost for the country and its citizens. The formation of a government is also crucial for the country’s advancement in the European Union integration process. The political parties have firmly committed to establish functioning authorities and to continue with the implementation of necessary legislative and socio-economic reforms as well as with concrete steps in the key area of fighting corruption and organised crime. To keep the necessary momentum, we expect the political leadership in Bosnia and Herzegovina to proceed with the formation of authorities and to enable the regular functioning of all institutions without further delay to ensure reform implementation in line with European standards and values. | High | [
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Shenoy v Kaleida Health (2018 NY Slip Op 01008)
Shenoy v Kaleida Health 2018 NY Slip Op 01008 Decided on February 9, 2018 Appellate Division, Fourth Department Published by New York State Law Reporting Bureau pursuant to Judiciary Law § 431. This opinion is uncorrected and subject to revision before publication in the Official Reports.
Decided on February 9, 2018
SUPREME COURT OF THE STATE OF NEW YORK
Appellate Division, Fourth Judicial Department
PRESENT: WHALEN, P.J., SMITH, LINDLEY, NEMOYER, AND CURRAN, JJ.
1288 CA 17-00721
[*1]SADASHIV S. SHENOY, M.D., PLAINTIFF-RESPONDENT,
vKALEIDA HEALTH, ET AL., DEFENDANTS, AND RALPH BENEDICT, M.D., DEFENDANT-APPELLANT.
GIBSON, MCASKILL & CROSBY, LLP, BUFFALO (JOSEPH W. DUNBAR OF COUNSEL), FOR DEFENDANT-APPELLANT. GARVEY & GARVEY, BUFFALO (MATTHEW J. GARVEY OF COUNSEL), FOR PLAINTIFF-RESPONDENT. Appeal from an order of the Supreme Court, Erie County (Joseph R. Glownia, J.), entered November 2, 2016. The order denied the motion of defendant Ralph Benedict, M.D. for summary judgment dismissing the complaint against him. It is hereby ORDERED that the order so appealed from is unanimously reversed on the law without costs, the motion is granted, and the complaint against defendant Ralph Benedict, M.D. is dismissed. Memorandum: Plaintiff, a doctor employed by defendant Kaleida Health (Kaleida), performed a surgery in which the patient died. As a result of this incident, and pursuant to Kaleida policy, plaintiff underwent a neuropsychological competence assessment by Ralph Benedict, M.D. (defendant). Defendant thereafter submitted a written report detailing his findings and opinions to both Kaleida's internal review body and plaintiff's personal physician. Plaintiff then commenced the instant action and asserted, inter alia, causes of action for defamation and, in effect, tortious interference with economic relations against defendant based on allegations that defendant's written report and associated oral comments damaged plaintiff's reputation and professional and business relationship with Kaleida. Supreme Court denied defendant's motion for summary judgment dismissing the complaint against him. Defendant appeals, and we now reverse. We agree with defendant that the court erred in denying that part of his motion with respect to the causes of action for defamation against him. "It is well settled that summary judgment is properly granted [dismissing a defamation cause of action] where a qualified privilege obtains and the plaintiff[] offer[s] an insufficient showing of actual malice" (Trails W. v Wolff, 32 NY2d 207, 221 [1973]). Here, defendant established as a matter of law that his written report and associated oral commentary were protected both by the " common interest' " qualified privilege (Liberman v Gelstein, 80 NY2d 429, 437 [1992]; see Shapiro v Health Ins. Plan of Greater N.Y., 7 NY2d 56, 60-61 [1959]), and by the statutory qualified privilege of Education Law § 6527 (5) (see Colantonio v Mercy Med. Ctr., 135 AD3d 686, 691 [2d Dept 2016], lv denied 28 NY3d 903 [2016]; Cooper v Hodge, 28 AD3d 1149, 1150 [4th Dept 2006]). In opposition, plaintiff failed to raise a triable issue of fact on the issue of actual malice (see Farooq v Coffey, 206 AD2d 879, 880 [4th Dept 1994]). We further agree with defendant that the court erred in denying that part of his motion with respect to the defamation causes of action on the alternative ground that the allegedly defamatory statements are expressions of pure opinion (see Balderman v American Broadcasting Cos., 292 AD2d 67, 72-73 [4th Dept 2002], lv denied 98 NY2d 613 [2002]; Roth v Tuckman, 162 AD2d 941, 942 [3rd Dept 1990], lv denied 76 NY2d 712 [1990]). "Expressions of opinion . . . are deemed privileged and, no matter how offensive, cannot be the subject of an action for [*2]defamation" (Mann v Abel, 10 NY3d 271, 276 [2008], cert denied 555 US 1170 [2009]). Contrary to plaintiff's contention, that part of the motion seeking summary judgment dismissing the defamation causes of action is not premature merely because defendant has not been deposed (see Colantonio, 135 AD3d at 693). " A mere chance that somehow, somewhere, on cross examination or otherwise plaintiff[] will uncover something which might add to [his] case but obviously of which now [he has] no knowledge, is mere speculation and conjecture and is not sufficient' " to establish that a summary judgment motion is premature (Trails W., 32 NY2d at 221). Finally, we agree with defendant that his motion also should have been granted with respect to the causes of action for, in effect, tortious interference with economic relations because defendant established as a matter of law that his conduct was "insufficiently culpable' to create liability for [tortious] interference with . . . economic relations" (Carvel Corp. v Noonan, 3 NY3d 182, 190 [2004]). Entered: February 9, 2018 Mark W. Bennett Clerk of the Court | Low | [
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The development of electronic devices with printed circuit boards typically involves many steps known as a design flow. This design flow typically starts with a specification for a new electronic device to be implemented with a printed circuit board. The specification of the electronic device can be transformed into an electronic device design, such as a netlist, for example, by a schematic capture tool or by synthesizing a logical design, sometimes referred to as a register transfer level (RTL) description of the electronic device. The netlist may be specified in an Electronic Design Interchange Format (EDIF) or the like, which can describe nets or connectivity between various components or parts in the electronic device design. The design flow may continue by verifying functionality of the electronic device design, for example, by simulating, emulating, or prototyping the electronic device design and verifying that the results of the simulation or emulation correspond with an expected output from the electronic device design. The functionality also can be verified by formally verifying with one or more solvers or statically checking the electronic device design for various attributes that may be problematic during operation of the electronic device built utilizing the electronic device design. Once the electronic device design has been functionally verified, the design flow may utilize the logical design to generate a layout design for the electronic device. This procedure can be implemented in different ways, but typically, through the use of a layout tool, which can place and interconnect various components or parts into a representation of a printed circuit board. For example, the layout tool implemented in a computing system can present a graphical view of the printed circuit board and allow a designer to utilize the layout tool to place parts from a library onto the printed circuit board in the graphical view. The design flow may perform one or more design for manufacturability (DFM) procedures on the layout design, which can determine whether the electronic device described in the layout design can be manufactured. The design for manufacturability procedures can include a design for fabrication (DFF) processes, a design for assembly (DFA) processes, a design for test (DFT) processes, or the like. The design for fabrication processes can determine whether a bare printed circuit board can be fabricated based on the layout design. The design for assembly processes can determine whether components can be disposed or coupled to the printed circuit board during assembly of the electronic device. The design for test processes can identify whether testing procedures can be utilized on manufactured electronic devices, for example, to detect process defects during assembly, perform electrical verification of a manufactured electronic device, or the like. The design for test processes may be able to identify whether the electronic device, when built, can be tested by a particular fabricator to identify process defects, such as whether a component has been placed and soldered to the printed circuit board correctly. The design for test processes also may determine whether the electronic device can be electrically verified during testing procedures, for example, by performing at speed testing of the electronic device and sampling signaling at various test points in the electronic device under test. Often, however, practical constraints, such as fabricator test capabilities, space on the layout design available for test points, or the like, may result in the testing procedures to not being able to verify a portion of the electronic device. This inability to test the portion of the electronic device can reduce test coverage and leave the electronic devices built based on the layout design susceptible to undetected manufacturing-related faults. In other instances, the design for test processes may determine that a fabricator has the capability of testing manufactured electronic devices for the layout design, but the testing procedures may be time-consuming, expensive, or both than other available options. In these instances, the developer of the electronic system can decide whether to re-design the electronic device or to accept the reduced test coverage and/or more time-consuming, expensive, or both testing procedures and move forward with production of the electronic design. | Mid | [
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Pappmine The Pappmine or Cardboard Mine in English was an anti-tank mine that was developed by Germany and used by the Wehrmacht during World War II. Design The Pappmine was designed to be a low cost, and easy to produce cardboard anti-tank mine which could relieve pressure on the overstretched metalworking industry. The Pappmine was made entirely of non-metallic materials to prevent detection by electric mine detectors. The Pappmine was a close copy of the Soviet TMB series of cardboard mines except the Pappmine was better waterproofed to resist moisture and rotting. The Pappmine was black in color and consisted of a container with a lid. The lid covered the full diameter of the container and both the top and bottom edges of the container were rounded and held together by a band of cardboard. In the center of the lid, there was a pressure plate of thick green glass which resembled a glass stopper. In the center of the mine, the pressure plate sat on top of a glass igniter that was embedded in of TNT. Only pressure on the plate caused an explosion and pressure on the cardboard side of the mine would not set it off. of pressure on the plate crushed the igniter creating a flash which then passed to the priming charge which exploded the TNT filling. A 3-second delay could also be incorporated in the igniter. The Pappmine relied on blast effect to destroy enemy tanks and it did not have a shaped charge warhead. References Category:Anti-personnel mines Category:World War II weapons of Germany Category:Land mines of Germany | High | [
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Q: SceneKit - Movement + Gravity = Strange Movement My Scene: One ball (Dynamic Physics Body) One cube as platform (Static Physics Body) Default Scene-Gravity Default masses When I run the scene the ball falls correctly on the platform. But when I add movement (delta-time movement on the x-axis in the render method), the ball falls strange/slowly down. Did I do something wrong? A: Dynamic physics bodies should only be moved using physics, e.g.applyForce(_:at:asImpulse:) You may be able to get it to work by calling resetTransform() after updating the position, but at a cost to performance. https://developer.apple.com/documentation/scenekit/scnphysicsbody/1514782-resettransform | Mid | [
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Email to a Friend HH: Joined by Washington Post columnist Charles Krauthammer. You also see him, of course, on the Fox News all stars. Charles, at this hour, the prime minister of Great Britain, David Cameron, has announced that Tornadoes and Typhoon aircraft will be over the skies of Libya, probably later tonight. What do you think of what’s unfolding in Libya? CK: Well, the President’s statement was very difficult to understand, very confusing. I love when he says let me be perfectly clear, let me be unambiguous, and then he gets ambiguous. On the one hand, he talks about population protection. That’s a minimalist policy. His administration has been talking from the beginning of Gaddafi has to go, which is regime change. That’s maximalist. And then Obama did something sort of in between, where he said one of the non-negotiable conditions is that Gaddafi withdraw from Ajdabiyah, Misurata and Az Zawiyah. Now if you look at the map, that means you’re telling Gaddafi he’s got to pull back, basically give up all the territorial gains of the last couple of weeks, and pull back essentially to Tripoli, which he’s not going to do. And is Obama saying, therefore, that this thing is going to continue unless he pulls back? That’s much more than population protection. So it isn’t clear what the objective is, and it’s also not clear what the U.S. is going to do. Obama made it sound as if no Americans on the ground. That’s fine. We understand that. But his people are telling Fox News that there are not going to be any aircraft over Libya. It’s all going to be logistic support. Is that really what we’re going to do? HH: Well, that is what is so confusing about this. Let me play for the audience a little bit of President Obama’s statement earlier today. BHO: I also want to be clear about what we will not be doing. The United States is not going to deploy ground troops into Libya, and we are not going to use force to go beyond a well-defined goal. HH: And let’s contrast that with David Cameron in the Parliament earlier today. DC: The attorney general has been consulted, and the government is satisfied, that there is a clear and unequivocal legal basis for the deployment of U.K. forces and military assets. He advised the cabinet this morning, and his advice was read and discussed. The Security Council has adopted Resolution 1973 as a measure to maintain or restore international peace and security under Chapter 7 of the United Nations charter. The resolution specifically authorizes notifying member states to use all necessary measures to enforce a no-fly zone, and to protect civilians and civilian populated areas, including Benghazi. At cabinet this morning, we agreed the U.K. will play its part. Our forces will join an international operation to enforce the resolution if Gaddafi fails to comply with its demand that he ends attacks on civilians. The defense secretary and I have now instructed the chief of the defense staff to work urgently with our allies to put in place the appropriate military measures to enforce the resolution, including a no-fly zone. And I can tell the house that Britain will deploy Tornadoes and Typhoons, as well as air-to-air refueling and surveillance aircraft. HH: So that’s a little bit different tone than President Obama adopted, Charles Krauthammer. What do you think of the clarity gap between Great Britain and the United States? CK: It doesn’t surprise me at all. When Obama announced a tripling of our forces in Afghanistan, what did he say? We’re going to do the surge, and then the very next sentence, this was at West Point, December 1, 2009, the very next sentence, he says we’re going to begin our withdrawal in 18 months. I mean, what kind of commander-in-chief is this? We’re going to surge, but we’re going to leave? And now even Libya, let me be unambiguous, we’re going to participate, we’re going to protect, but you know what? Nothing on the ground. And then, this is not what he said officially, but what his people are telling the press, no Americans over Libya. Maybe a Cruise missile, maybe Naval gunfire. You know, what I think Obama wants is an immaculate campaign with no American ever in danger, which is nice. I mean, I’m an American. I don’t want to see an American in danger. But to me, if you do that, what you’re going to end up with is a stalemate. If you’re going for population protection, you’re going to get a withdrawal of some of the forces of Gaddafi. And since there is nothing in here about changing the regime, you’re going to end up with a West Libya and an East Libya, with a Gaddafi Libya and a rebel Libya. And what are we going to do? Protect it until the end of time, which would be a prolongation of this? What we should have done is right very early on, immediately early on, and before all this international nonsense and cover, attack, attack hard, and this man was on the ropes. He was in an enclave in Tripoli with no support, having lost the entire country, and we let him off that hook. And now he’s all the way to Benghazi, and I think what this policy is going to give us is a country split in two, and an ongoing commitment. HH: Is it Somalia 2.0 in terms of an ungovernable western Libya? CK: Well, Somalia, there was no objective at all. It was to feed the population in a crazy, chaotic civil war. I was always uneasy about it. It didn’t have any strategic objective at all, and that’s why I think it sort of collapsed. HH: No, I meant sort of a failed state run by Islamist extremists. CK: Right. Yeah, well, that’s the other problem, is we do not know who the rebels are, who’s going to emerge, what the tribal situation is. It’s very complicated, and we know less about the opposition in Libya than we certainly knew in Iraq, and we certainly knew in Afghanistan and other places. So that is, I mean, that’s a problem above everything else. But remember, this administration had said early on, the President himself said Gaddafi has to go. If you say that, and you’re president of the one superpower on the planet, you have to be thinking ahead about the successor regime. You have to know something about them. And Obama appears to me to be acting nothing but reactively to placate public opinion, and that’s where we are now. HH: Let me ask you what your advice would be about Yemen, at least to Jay Carney, because he ought to get this question, which is today in Yemen, Saleh’s people mowed down at least 45 demonstrators, killed 45, may have wounded more than 200. So you’ve got population predation going on in both Yemen and Libya. How would you explain, Charles, the different attitude of the United States towards the Arabs in Yemen, and the Arabs in Libya who are being murdered by their government? CK: I would simply say the United States is not omnipotent. If we were, we would be everywhere, and we would be consistent, and we would stop every slaughter on the planet, and we would be in the Congo right now. And why aren’t we in the Ivory Coast? Ivory Coast had an election, the dictator lost the election, he refused to accept the other side, he’s been shooting people in the streets. I mean, where are we going to go with this? I think you have to have two things in order to act. You have to have a moral justification, you’re protecting slaughter, maybe preventing a genocide. But you also have to have a strategic rationale. Otherwise, we will spend ourselves into penury, into destitution, and into very great sorrow by deploying all over the world. So I mean, it seems to me we have to be extremely hard-headed as well as idealistic about this. You have to have a moral rationale and a strategic one. If you only have one and not the other, you don’t act. HH: Now I want to switch domestically, Charles, because yesterday on this program, Mark Steyn was on, got picked up by the Daily Caller today. And Mark said, “I think John Boehner has basically climbed into the Bob Dole suit,” and that’s the headline, and that they picked up the tape, and that will ricochet around. Fair, unfair, and do you expect the Speaker to do anything over the next two weeks to get out of that Bob Dole suit that many people think he’s put on? CK: Well, I don’t think he’s been actively putting on anything. I think he’s getting maneuvered by a pretty, let me say activist, freshmen class, that I think is misreading the terrain here. They’re the ones who are giving Boehner a hard time. They are impatient about cutting $2 billion dollars a week. I’m happy to cut $2 billion a week. That’s $100 billion a year. That’s not chump change. It puts the Democrats on the defensive week after week. And in a situation where the Democrats, the President and Harry Reid are not going to give you anything on a deal that goes until October 1, and therefore, you therefore have no leverage, why not go week by week? It’s not efficient, it’s nuts, it’s no way to run a railroad, but that’s because the Democrats, who had control of the House and the Senate and the presidency last year, never passed a budget. And this is a $1.7 trillion dollar deficit. So I don’t understand why, you know, the zeal of the conservatives, the freshmen in the House of ending this process in the short term won, we win. And the one that you go until October 1, we’re going to lose. HH: I’m with Steyn on this, and my friend, Powerline’s John Hinderaker, said $6 billion dollars is the equivalent in caloric content of one-third of one French fry in a Big Mac supersized meal. And he did all the stats, Charles. It’s not real money. But you get the last minute. But I wanted to make sure people knew there was… CK: If you’re talking about discretionary spending, which is only a 12…an eighth of the budget anyway, and you’re cutting $2 billion a year, and you end up with $100 billion in cuts? That’s a serious cut. The real money, everyone knows, is in entitlements, and that’s to come elsewhere. And that’s why I wouldn’t shut down the government over these discretionary cuts. It makes no sense, it’s nuts, and it would, we’re down to the presence of…and to no one else’s. | Low | [
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package ram //Licensed under the Apache License, Version 2.0 (the "License"); //you may not use this file except in compliance with the License. //You may obtain a copy of the License at // //http://www.apache.org/licenses/LICENSE-2.0 // //Unless required by applicable law or agreed to in writing, software //distributed under the License is distributed on an "AS IS" BASIS, //WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. //See the License for the specific language governing permissions and //limitations under the License. // // Code generated by Alibaba Cloud SDK Code Generator. // Changes may cause incorrect behavior and will be lost if the code is regenerated. import ( "github.com/aliyun/alibaba-cloud-sdk-go/sdk/requests" "github.com/aliyun/alibaba-cloud-sdk-go/sdk/responses" ) // ListVirtualMFADevices invokes the ram.ListVirtualMFADevices API synchronously // api document: https://help.aliyun.com/api/ram/listvirtualmfadevices.html func (client *Client) ListVirtualMFADevices(request *ListVirtualMFADevicesRequest) (response *ListVirtualMFADevicesResponse, err error) { response = CreateListVirtualMFADevicesResponse() err = client.DoAction(request, response) return } // ListVirtualMFADevicesWithChan invokes the ram.ListVirtualMFADevices API asynchronously // api document: https://help.aliyun.com/api/ram/listvirtualmfadevices.html // asynchronous document: https://help.aliyun.com/document_detail/66220.html func (client *Client) ListVirtualMFADevicesWithChan(request *ListVirtualMFADevicesRequest) (<-chan *ListVirtualMFADevicesResponse, <-chan error) { responseChan := make(chan *ListVirtualMFADevicesResponse, 1) errChan := make(chan error, 1) err := client.AddAsyncTask(func() { defer close(responseChan) defer close(errChan) response, err := client.ListVirtualMFADevices(request) if err != nil { errChan <- err } else { responseChan <- response } }) if err != nil { errChan <- err close(responseChan) close(errChan) } return responseChan, errChan } // ListVirtualMFADevicesWithCallback invokes the ram.ListVirtualMFADevices API asynchronously // api document: https://help.aliyun.com/api/ram/listvirtualmfadevices.html // asynchronous document: https://help.aliyun.com/document_detail/66220.html func (client *Client) ListVirtualMFADevicesWithCallback(request *ListVirtualMFADevicesRequest, callback func(response *ListVirtualMFADevicesResponse, err error)) <-chan int { result := make(chan int, 1) err := client.AddAsyncTask(func() { var response *ListVirtualMFADevicesResponse var err error defer close(result) response, err = client.ListVirtualMFADevices(request) callback(response, err) result <- 1 }) if err != nil { defer close(result) callback(nil, err) result <- 0 } return result } // ListVirtualMFADevicesRequest is the request struct for api ListVirtualMFADevices type ListVirtualMFADevicesRequest struct { *requests.RpcRequest } // ListVirtualMFADevicesResponse is the response struct for api ListVirtualMFADevices type ListVirtualMFADevicesResponse struct { *responses.BaseResponse RequestId string `json:"RequestId" xml:"RequestId"` VirtualMFADevices VirtualMFADevices `json:"VirtualMFADevices" xml:"VirtualMFADevices"` } // CreateListVirtualMFADevicesRequest creates a request to invoke ListVirtualMFADevices API func CreateListVirtualMFADevicesRequest() (request *ListVirtualMFADevicesRequest) { request = &ListVirtualMFADevicesRequest{ RpcRequest: &requests.RpcRequest{}, } request.InitWithApiInfo("Ram", "2015-05-01", "ListVirtualMFADevices", "", "") return } // CreateListVirtualMFADevicesResponse creates a response to parse from ListVirtualMFADevices response func CreateListVirtualMFADevicesResponse() (response *ListVirtualMFADevicesResponse) { response = &ListVirtualMFADevicesResponse{ BaseResponse: &responses.BaseResponse{}, } return } | Mid | [
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Up To 50% Off On PS Game Deals, The Sale Goes Until June 16 PlayStation Days of Play was announced earlier this week, where PS presented a beautiful new limited-edition gold PS4 for $249.99 USD, together with discounts on DualShock 4, PlayStation Gold Wireless Headset, and major PS4-exclusive games at retailers across the country. Today, with the start of Days of Play, the players can enjoy some pretty awesome games on discounts. The PlayStation Store is in on with the deals on big games, Playstation Plus memberships, and a much more. For the first time, Nioh, MLB The Show 17 and Horizon Zero Dawn are on sale for $39,59 each. And also, you can save up to 50% on games like Uncharted 4: A Thief’s End, Watch Dogs 2 and Call of Duty: Infinite Warfare. PS4 Games on Sale – Days of Play: BATTLEFIELD 1 CALL OF DUTY: INFINITE WARFARE COD: INFINITE WARFARE – DIGITAL DELUXE CALL OF DUTY: INFINITE WARFARE – LEGACY EDITION COD: INFINITE WARFARE – SEASON PASS FINAL FANTASY XV FINAL FANTASY XV DIGITAL PREMIUM EDITION HORIZON HORIZON ZERO DAWN DIGITAL DELUXE EDITION MASS EFFECT: ANDROMEDA – DELUXE EDITION MASS EFFECT: ANDROMEDA MLB THE SHOW 17 NIOH – DIGITAL DELUXE NIOH LIVE PREY THE LAST GUARDIAN UNCHARTED 4: A THIEF’S END WATCH DOGS WD 2 – DELUXE EDITION WD 2 – GOLD EDITION YAKUZA YOOKA-LAYLEE You can access the online multiplayer modes in any PS4 game you own without the PS Plus subscription, until June 16. The Days of Play’s Free Multiplayer Week starts now! Through the Days of Play campaign, you can save a full year of Plus membership, with the free monthly games, exclusive discounts, online game saves and more. It does not matter if you are signing up or joining for another year, you will get $10 off a 12-month subscription at PS Store now. But if you are already a PS Plus member and you need to renew your subscription during the promotion window, turn off “auto-renew” to receive the discounted pricing. Starting now until June 20, you can get a $15 credit when you spend $100 or more at the PS Store using your PSN Wallet. | Mid | [
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155 Conn. 413 (1967) HOWARD A. WILLARD, JR., ET AL. v. THOMAS C. McKONE, GUARDIAN AD LITEM, ET AL. Supreme Court of Connecticut. Argued June 9, 1967. Decided July 20, 1967. KING, C. J., ALCORN, HOUSE, THIM and RYAN, JS. *414 Bruce W. Manternach, with whom, on the brief, were Colin C. Tait and James A. Wade, for the appellants (plaintiffs). Joseph G. Lynch, with whom, on the brief, was George D. Royster, Jr., for the appellees (defendants). HOUSE, J. On November 22, 1963, the Probate Court for the district of Hartford removed John B. Willard as trustee of a testamentary trust created by the will of Howard A. Willard. John B. Willard, hereinafter referred to as the trustee, and other adult beneficiaries of the trust appealed the removal order to the Superior Court and have appealed to this court from the judgment of the Superior Court dismissing their appeal. The only issue on this appeal, therefore, is whether the Superior Court erred in concluding that the Probate Court did not abuse its discretion in ordering the removal of the trustee. Whether there was adequate ground for the removal of the trustee was a question addressed to the sound discretion of the *415 Probate Court, and its conclusion could not be disturbed on appeal unless that discretion was abused. General Statutes § 45-263; Phillips v. Moeller, 148 Conn. 361, 368, 170 A.2d 897; Peck v. Searle, 117 Conn. 573, 584, 169 A. 602; Carroll v. Arnold, 107 Conn. 535, 542, 141 A. 657; Murdoch v. Elliot, 77 Conn. 247, 256, 58 A. 718. Primary jurisdiction to remove a fiduciary who becomes incapable of executing his trust, or who neglects to perform the duties thereof, or who wastes the estate in his charge is vested in the Probate Court. General Statutes § 45-263. "The Superior Court, on appeal, could go no further than to determine whether that discretion had been legally and reasonably exercised." Gwynn v. Tierney, 138 Conn. 425, 428, 85 A.2d 250; Crane v. Manchester, 143 Conn. 716, 719, 126 A.2d 567; Baldwin v. Tradesmens National Bank, 147 Conn. 656, 659, 165 A.2d 331. This is necessarily so since "to say that the Superior Court on appeal from probate may exercise the discretion committed to Courts of Probate is inconsistent with the principle implicit in the well-established rule that an appeal lies from the exercise of discretion by the Probate Court only in case of abuse of discretion." 1 Locke & Kohn, Conn. Probate Practice § 218, p. 446. In view of the limited jurisdiction of the Superior Court on such an appeal as this, we are confronted at the start with the problem of what evidence the Superior Court may properly receive. Its function is to determine whether the Probate Court reasonably exercised its discretion under the circumstances. The proceedings in Probate Court hearings are, however, not recorded, and that court makes no finding which the Superior Court may review on appeal. The Superior Court cannot know *416 what was in the mind of the probate judge or all the facts which were known and considered by him. It is for this reason that on such an appeal as this the trial is de novo, and the Superior Court "may receive any evidence on matters covered by the reasons of appeal which would be relevant and competent at the probate hearing." 1 Locke & Kohn, op. cit. § 213, p. 437; see id. § 186, p. 381. The plaintiffs have made an extensive attack on the finding of the court. We particularly note the confusion concerning the existence of a mortgage as security for a loan of trust funds which the trustee made to his wife. In an accounting for the year ending December 31, 1961, the trustee represented that the loan was secured by a first mortgage on her property in West Hartford, and the Probate Court expressed disapproval of the loan because the mortgaged property was owned by the trustee and his wife as joint tenants with the right of survivorship. The record discloses that there was no security for the loan despite the contrary representation in the account. The trial court found that the trustee represented to the Probate Court that the loan was secured by a mortgage when in fact it was not. Under these circumstances, although the trustee's representation was untrue in fact, there is nevertheless support for the court's conclusion that the Probate Court, relying upon the misrepresentation, reasonably could have found that the trustee's acceptance of a mortgage on real property in which he had an interest conflicted with his duties as a trustee. The finding is not subject to any material correction. See Practice Book § 628; see also such cases as Solari v. Seperak, 154 Conn. 179, 182, 224 A.2d 529; National Broadcasting Co. v. Rose, 153 Conn. 219, 222, 215 A.2d 123. *417 It is unnecessary to review in detail the court's finding of facts which amply supports its conclusions that the Probate Court could reasonably have found that the trustee failed to obey a decree of the court and that his handling of the estate was lax, unbusinesslike, unwise and not in keeping with normal and acceptable probate practices. Courts of Probate have primary jurisdiction over the accounts of testamentary trustees. General Statutes §§ 45-4, 45-267; see Phillips v. Moeller, 147 Conn. 482, 487, 163 A.2d 95. All testamentary trustees, unless excused by the will creating the trust, are required to render an annual account to the Probate Court having jurisdiction. General Statutes § 45-268. The trustee rendered accounts for the years ending December 31, 1959, December 31, 1960, and December 31, 1961. A hearing on the three accounts was held on July 12, 1962, at which time the court raised a number of questions concerning the accounts, and the hearing was adjourned with the understanding that the court would send the trustee a memorandum indicating its wishes with respect to the accounts. This the court did by letter dated August 2, 1962. In the letter the court indicated its approval of the 1959 and 1960 accounts but required, within thirty days, the filing of a substitute account for the year ending December 31, 1961, reflecting the effect of the sale of a house and lot to Albro Case and indicating the repayment of a loan of § 10,000 from the trust fund to the trustee's wife. Six months later, on February 5, 1963, the trustee filed a substitute account for the year 1961 which, as we have already noted, misrepresented that the loan to the trustee's wife was secured by a first mortgage on real property located in West Hartford. The court issued a notice of a hearing *418 on the accounts to be held March 14, 1963. At the hearing, the trustee represented to the court that the loan to his wife was secured by a mortgage when, in fact, this was not so. The court expressed disapproval of the loan from the trust to the trustee's wife, represented as being secured by property in which, it appeared, the trustee had an interest. It also raised a further question about the property sold to Case and the security of a chattel mortgage from Case, that transaction not being covered in the account. The court then adjourned the hearing, stating that a final hearing would be held, probably within two months. On June 18, 1963, the court entered a decree accepting and approving the accounts for 1959 and 1960, but disapproving and disallowing the substitute account for 1961, and ordering the trustee to file a second substitute annual account for 1961 indicating restoration to the trust estate of $9000 in connection with the sale of real estate to Case and restoration of § 10,000 to the trust estate resulting from the liquidation of the note from the trustee's wife. No appeal was taken from this decree, and the trustee has not complied with this order of the court. During the following months there was correspondence between the trustee and the Probate Court in which the court reiterated its requirement that the trustee comply with its decree of June 18. In October, the trustee telephoned to the court and stated that he had liquidated the note of his wife and that he could not file under oath the substitute account ordered on June 18 because the sale of the property to Case had not occurred the way the court assumed it had. On October 25, 1963, the guardians ad litem for certain minors and undetermined and unborn heirs *419 conferred with the probate judge and requested that a hearing be set on the removal of the trustee. On November 1, 1963, the court ordered the trustee to appear on November 22 to show cause why he should not be removed as trustee for neglecting to perform the duties of his trust and for failing to file a second substitute annual account for 1961, as ordered in the June 18, 1963, decree. At the hearing the court stated the history of the prior hearings, that its decree of June 18 had not been appealed from and that the trustee had not obeyed the court. It thereupon entered an order finding that the trustee was neglecting to perform the duties of his trust, removing him as trustee and appointing a successor trustee. In addition to finding that the trustee had failed to obey the order of the Probate Court, the trial court also found that the trustee swore to an accounting which was incorrect and testified under oath to having done so, that he made mortgage loans of trust funds without causing the title of the property securing the loans to be examined, that he made mortgage loans of trust funds without requiring evidence of insurance protecting the trust interest as mortgagee, that he had unduly delayed recording security instruments protecting the trust assets, and that he gave a mortgage loan on property which was subject to mechanics' liens without requiring lien waivers and without making any investigation of the credit standing of the borrower. We cannot agree with the trustee's assertion that these latter findings are irrelevant to the issues on this appeal. The evidence printed in the appendix to the brief of the defendants supports the findings, and we note, inter alia, that the § 12,500 mortgage deed from Case dated December 21, 1960, which deed the trustee *420 left with the mortgagor to have recorded, was not recorded until March 23, 1962. From these facts, the trial court concluded that the Probate Court could reasonably have found that not only had the trustee failed to obey a decree of the court from which no appeal had been taken but the trustee's handling of the trust fund was lax, unbusinesslike, unwise and not in keeping with normal and acceptable probate practices and, accordingly, that there was no abuse of the discretion of the Probate Court in removing him. These were conclusions which the trial court could reasonably draw from the facts which it found. It is unquestioned that the trustee neither appealed from nor complied with the June 18, 1963, decree of the Probate Court ordering him to file a second substitute account. The order of the Probate Court, that the trustee file a substitute account, was made within the court's jurisdiction and in the performance of its statutory duty. The trustee refused to comply with the order. He is not relieved from the burden of his default by the fact that he did not agree with the reasons for the court's order. "Obedience to the order of the court was the trustee's first duty. An appeal would have protected his every right." Morse v. Ward, 92 Conn. 286, 293, 102 A. 586. The circumstance that the will gave to the trustee powers to invest trust funds "in his absolute discretion, unrestricted by any legislation limiting the authority of a trustee in investing the properties and funds of his trust" does not excuse him from a full and accurate accounting of his administration nor remove his administration of the trust from judicial supervision. Phillips v. Moeller, 148 Conn. 361, 371, 170 A.2d 897; Conway v. Emeny, 139 Conn. 612, 619, 96 A.2d 221. *421 The remaining contentions of the plaintiffs require little comment. The June 18, 1963, decree was a proper order issued following due notice and a full hearing on March 14, which the trustee attended. As that decree recites, the March 14 hearing "came by adjournment to the present time and place." There is no requirement that parties be present when the court makes its decision and renders its order. The decree was rendered on June 18, following proper notice and the formal hearing held on March 14; accordingly, the thirty-day time limitation for taking any appeal commenced to run on the date the decree was entered. General Statutes § 45-289. The plaintiffs' assertion that the Probate Court did not afford the trustee a full hearing pursuant to the provisions of General Statutes § 45-263 is not supported by the record. There was conflicting testimony as to what happened at the removal hearing, and the trial court refused to find the facts upon which the plaintiffs' claim is predicated. The question of credibility is for the trier. Solari v. Seperak, 154 Conn. 179, 183, 224 A.2d 529; Morrone v. Jose, 153 Conn. 275, 277, 216 A.2d 196. The trial court could reasonably and logically conclude that the plaintiffs failed to prove that the Probate Court had abused its discretion in removing Willard as trustee. There is no error. In this opinion the other judges concurred. | Mid | [
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President Obama may have mitigated the IRS fallout, but Republicans will have more opportunities to hash out the scandal. AP Photo/Pablo Martinez Monsivais May 16, 2013 ADVERTISEMENT President Obama on Wednesday night ousted the acting commissioner of the Internal Revenue Service, Steven Miller, over the agency's improper targeting of conservative groups, which Obama called "inexcusable." Miller's firing marked the first major, concrete move by the president to dampen a flurry of scandals threatening to disrupt his second-term agenda. The administration even released a letter in which Treasury Secretary Jack Lew told Miller to resign to "restore public trust" in the IRS. But will the termination make a difference? Among commentators, the consensus is that the move, though decisive, won't be enough to nip the crisis in the bud — at least not entirely. "That's not how Republicans work," says Joan McCarter at Daily Kos. "But this swift reaction of the White House could make a prolonged hissy fit by Republicans politically damaging to them." Obama's harshest critics, however, aren't impressed. "Nice try, Mr. President," says Joe Battenfield at the Boston Herald. "Feigning anger, firing an unknown bureaucrat and fleeing the podium won't cut it with voters, or stop the hemorrhaging of the scandals that have spawned a Watergate-like feel around the Obama administration." Obama took no questions and, more importantly, no responsibility for the ugly episode of the federal government abusing its power for political reasons. This was just political theater designed to distance Obama from something that happened on his watch... The problem for Obama is that what happened in the IRS was all about partisan politics. The IRS was harassing conservative groups opposed to Obama's re-election, and the big question is why any low-level bureaucrat would be engaged in a concerted effort to hurt Obama's opponents. [Boston Herald] Conservatives say one reason the backlash will continue is that Republican politicians aren't the only ones unlikely to be satisfied by the administration's damage-control efforts, which also included Attorney General Eric Holder's announcement that the Justice Department had launched an investigation into the IRS' actions. While the agency focused extra scrutiny on applications for tax-exempt status coming from Tea Party groups and other conservative organizations, Aaron Goldstein at The American Spectator questions whether the Obama administration's moves will "be sufficient to mollify the public." The IRS scandal resonates with Americans in a way that Benghazi hasn't and the AP scandal probably won't. Most Americans don't like the IRS to begin with so any impropriety they commit is going to hit a raw nerve. [American Spectator] Even if the administration faces continued attacks, however, Obama's forceful response is bound to help, the president's supporters say. Obama needed to make clear that the White House had no role in the IRS' ham-fisted blunder. "Clearly the president of the United States didn't know about what was happening in low level bureaucracies, but he's still the boss of government," Jonathan Prince, who worked in the Obama State Department, tells Politico. "He had to say 'I care, I'm angry.'" So it seems Obama has managed to mitigate the fallout, at least for the time being. If nothing else, notes Jennifer Epstein at Politico, Team Obama can enjoy the spoils of winning one news cycle. "After days of anxiety, Democratic operatives said the White House has found its footing," Epstein says. That stability may not last long, though: On Friday, congressional Republicans will have the opportunity in a hearing to hash out the IRS debacle, putting the Obama administration back on the defensive. | Mid | [
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Revolutionary Vice-Presidential Candidate On Importance of Alternatives To Two Major Parties Eugene Puryear is a captivating orator, able to disentangle complex political ideologies and do so with a fiery ease. At 30 years-old, he is the vice presidential candidate for the Party for Socialism and Liberation (PSL), running alongside another powerful activist, Gloria La Riva. Both candidates have a lengthy record in social mobilization—in anti-war campaigns, union struggles, and the movements for immigrant rights and Black Lives. La Riva has been a union president and an activist for immigrant rights and in solidarity with Latin America since the 1970s. Puryear has been active in resistance against police terror in communities and mass incarceration for over 15 years. He is the author of the book, “Shackled & Chained: Mass Incarceration in Capitalist America.” Puryear tells Shadowproof that their campaign is a way to bring both the experiences and the demands of these movements into the electoral arena, while constructing principled alliances around “a real people’s platform.” If you’re looking for the answer to the dystopian hellscape that is American politics, they are it. “I don’t believe any space should be sanitized from the truth,” Puryear recently stated in a speech on the socialist alternative to corporate politics for the Nyumburu Black Male Initiative program at the University of Maryland. The socialist alternative being offered by the PSL campaign aims to underline what socialism is, and why it is the solution to issues of food insecurity, lack of healthcare, racist policing, housing, climate change, unaffordable education, and other points of concern. Puryear explains that they’re seeking “to build a more organized and stronger movement, which means making contact with and bringing together the millions of people who are interested in these ideas. It’s not enough to want a different sort of society, or have great ideas—we need a well-organized movement to fight for change.” Third party candidates have always faced the ire of voters, forced to take on blame for running “spoiler campaigns,” but Puryear argued that spoiler mythology is wrong even on technical terms, stating “numerous academic studies have revealed ‘third parties’ typically draw more from people who would not have voted rather than people planning to vote for mainstream candidates.” Their campaign also rejects what he calls “spoiler scaremongering,” as it is “based on the highly anti-democratic assumption that the only important social forces and voices are the (s)elected politicians of the major parties.” “If the major parties are so corrupt and tied to the top .01% that they lose voters, they are the only ones to blame,” Puryear declares. Despite the tremendous hurdles facing third party candidate, Puryear tells Shadowproof that there are benefits to running. “For us, the biggest benefit of running is the campaigning itself. Imagine a general election in which the choice were just between Hillary Clinton, who actually has quite a right-wing record, and Donald Trump, a racist ultra-right candidate. That is a sham choice—and completely out of tune with the spirit of the people,” according to Puryear. “Our campaign is an opportunity to tell people that they don’t have to accept that, that we can continue to promote socialist politics and strengthen the movements against what King described as ‘three evils’: poverty, war and militarism. “Even though we’re running in the election, a big part of our message is actually that elections are not an instrument for the type of change needed to really meet the scale of our problems. The mass social movements which have brought progressive changes to this country were never birthed from, or beholden to a single electoral cycle, important as they may have been at times. Progressive change, is, as a rule, the result of broad social movements powered by an uncompromising core,” Puryear states. When it comes to Bernie Sanders, Puryear is not under any impression that a Sanders presidency would genuinely mean a Socialist presidency. While many of the policies he advocates are admirable, “they would not by themselves transform who holds power in society.” Puryear contends that under Sanders, “we would still have capitalism—dominated by financial and corporate elites—while life would be more tolerable and livable for the vast majority.” Tolerability should not be the goal. “We do not want to make life simply tolerable for the working class, but truly worth living,” Puryear contends. “Socialism’s central principle is to use the resources of society, human and material, to meet the needs of the broad population, and the democratically established goals.” Sanders’ mantra of “breaking up the banks” is also not enough, and to this, the PSL campaign says that these banks should be seized and put under the people’s control “given that they have accrued centuries of wealth that was commonly produced, and they are central to all economic decision-making.” From his defense of the occupation of Afghanistan, military escalation in Syria, the drone wars and “kill-list,” and the backing of the state of Israel, Sanders’ foreign policy is also an issue of contention as it exists, as Puryear says, “in the orbit of imperialism.” “Genuine socialism has to be internationalist—and we call for closing the Pentagon’s far-flung military bases, bringing the troops home, and respecting self-determination of all historically oppressed nations throughout the world,” Puryear said. “None of this would really be possible just by electing a socialist president under the given system. So the question isn’t so much if a socialist can get elected, but whether we can have a revolutionary transformation of society—and we think, especially given the general trends towards vast inequality and climate disaster—that this is both possible and urgent.” Puryear does, however, recognize that the energy surrounding Bernie Sanders’ campaign is different than the one around Obama’s 2008 run, and he argues that the reason for this has more to do with Sanders’ policies than his persona. “It is more substantive than symbolic; a reflection especially of young people’s increasing rejection of capitalism and gravitation towards radical and socialistic ideas,” Puryear says. “For years, we’ve seen these polls that show young people [are] trending left. A recent GOP pollster called young people ‘horrifyingly’ left. But with Occupy Wall Street and now the Sanders campaign, we’re seeing that mood politically manifested in a mass way.” “While excitement about an individual candidate is not negative in and of itself, if it defines one’s political commitment, it could lead to demoralization and passivity if he loses. It could also lead to real political confusion among his supporters if Sanders were to win and then move to the right in the general election campaign, or be elected and then continue many of the same policies of his predecessors. That’s the danger of fixing a movement around a politician.” Puryear adds that most Sanders supporters their campaign has interacted with seem hopeful about and interested in a genuine “political revolution” that would exist beyond Sanders, as opposed to being entirely attached to him. When asked if Hillary Clinton, who is likely to seize the Democratic nomination and presidency, is a threat to working class peoples, communities of color, and those abroad, all of which often intersect, Puryear responded she is a “very serious threat.” “The ultimate proof of this is the fact she has gotten support from a huge range of very prominent neoconservatives, whose whole philosophy is based on the aggressive projection of U.S. military power, even if it risks a third world war.” “She has been a central supporter of the wars in Iraq, Libya and Syria—in fact a manager of the last two. She is deeply ingratiated with the Pentagon high command,” Puryear adds. “The arrogant U.S. attempt to assert complete geopolitical control of the broader ‘Middle East’ is a bedrock of her worldview. That this resulted in literally millions of deaths, the destruction of whole nations, a massive flow of refugees, as well as a worldwide hate movement against Muslims, is of no concern to her.” “In addition, Hillary is more hawkish and interventionist, as you say, with respect to Latin America—where she has supported coups—and also the very provocative moves against both Russia and China and various regime change efforts… These conflicts could easily flare up into wider conflagrations. We can’t forget that she’s a proud follower of Henry Kissinger.” The best response to (another) Clinton presidency is to “turn the multiplicity of surging movements and broadly left-leaning views of many younger people into a durable independent movement.” Puryear says that such a movement would be able to participate in elections and hold elected officials accountable for their crimes, but “ultimately the movement has to be aimed at taking power away from those who allow exploitation and oppression to exist.” Puryear acknowledges, “The energy of the Sanders campaign, in part, has to do with the fact that it’s not just fighting back. It’s fighting for something, and we have to continue that aspect by building into our movements the positive vision and program of what we want the world to look like.” This brings us to what Puryear and the PSL campaign want for the left in the United States, and what this left—some of which has been recharged by Bernie Sanders—can do to build socialism: “Build stronger socialist organizations. That’s the fundamental thing. The Capitalist-Imperialist system we live under, as these elections have illustrated, is transparently controlled by a very small percentage of the population. They exist in a social world that is a revolving door between government, the military, corporate America, and elite educational institutions and think tanks. They are tightly and centrally organized and they have used all sorts of sabotage and repression to obstruct movements from below.” Puryear asserts, “The reality is that they control the political system and mass communications. They create the ‘policy consensus’ on all the main issues that govern the vast majority’s lives. They determine which countries will be targeted next, how many people will be sent to kill and die. They decide which neighborhoods are developed, and for whom, and which ones will be allowed to deteriorate. They decide what factories stay open, which ones move, and which infrastructure projects receive financing. They shape the curriculum in the schools, the food we eat, the consumer goods we buy and what fills the airwaves.” “This is really a form of class dictatorship, but with the appearance of choice in the electoral system. So we can’t expect to fundamentally resolve any of these issues and change that power through a corrupt, anti-democratic election system,” Puryear further argues. “We need to be as well organized as they are—with our own movement infrastructure, our own policies and strategic planning, our own media, our own united fronts, our own education, our own division of labor and healthy internal processes. “The fact that the vast majority of people are exploited and oppressed shows there is the need for systemic change, but that will be a protracted and complex process, fueled by the sacrifice and dedication of people who want to change the world. That’s the perspective of our organization, the Party for Socialism and Liberation.” | High | [
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Online Interior Designers At Your Service Monthly Archives: July 2015 A living room basically tells all about a home with a simple glance. The manner in which you arrange your living room will either portray a welcoming message or vice versa. Unlike the other rooms in any given home, the living room is commonly used as a social space where one can receive his or her visitors at any time. For this reason and many others, the living room is the one place that neatness should be observed at all times. A neat living room entails organization and proper spacing of furniture. Apart from routine cleaning, every living room should have proper spacing to ensure that guests and the host have enough space while entering a home. Experts are of the opinion that living room sofas should be placed up close in a manner that facilitates easy conversation when seated in the room. Every room has a focal point or rather a strategic place that determines the positioning of furniture. A window set and a fire place are some of the examples that are used to determine the location of furniture. In most living rooms, sofas are placed in a uniform position and in the same direction. The television set in this case is mostly used as the focal point of the room and is used to determine the manner in which the sofas are arranged. Useful Tips; A properly arranged living room should have a flexibility trait in the sense that the pieces of furniture are spaced in a manner that can easily be moved or redesigned if need be. All the pieces of furniture in a living room must face the same direction and placed across the focal point. Spacing makes the living room look more beautiful and should be considered whenever furniture arrangement takes place. A neat living room allows one to pass through it without necessarily stumbling on other objects. Experts still find the traditional symmetry arrangement of furniture as the most convenient and neat. In this type of arrangement, two sofas sit across each other with a third one directly opposite the focal point of the room (television set). A common mistake that one ought to avoid at all cost is pushing the pieces of furniture close to the wall or a certain corner of the living room. Most people do this unknowingly, with good a intention of creating more space at the central place and then end up making the living room to look empty. Before redesigning your home, its important to first start with high quality furniture. It’s like making a 5 star dish – you need to first start with the best available ingredients. Many a times, shoppers tend to concentrate on the price of a commodity and forget all about the quality. Although it’s wise to shop on a budget, poor quality goods may end up costing the buyer more than he or she could have spent in the first place. Furniture shopping also operates under the same theory that cheap is actually expensive. In order to get a long lasting piece of furniture, one has to go for quality and not fix his or her mind on getting something cheap or easily affordable. Most shoppers forget the fact that piece of furniture is actually meant to serve you for a long time, unlike most equipment that can easily be replaced when they get damaged. On the other hand, buying an expensive piece of furniture does not necessarily guarantee that you will the best furniture out there. Other factors such as style and certain qualities in a given piece of furniture also have to be considered. Getting a piece of furniture that will light up your home needs commitment and time to shop for the right one. It’s also difficult to predict whether a piece of furniture is long-lasting by looking at it. Composition of Wooden Furniture Wooden surfaces are either made of hardwood or softwood. Having the relevant knowledge on the composition of the furniture actually prevents you from making a mistake when buying one. Contrary to the common misinterpretation that hardwood furniture has a hard surface, most of them are actually soft can easily be dented. When buying a piece of furniture, you can be able to tell the quality of the wood by simply drawing a line using your fingernail without necessarily causing damage. Materials that will display a visible line are not of good quality, therefore will serve you for a long time as intended. Structurally, you check out if plywood used in making the furniture has unexposed knots. The more knots you find on a piece of furniture, the less durable that material is. Quality wooden furniture that is found at a relatively lower price is mostly covered with veneers. This is used to cover pieces of furniture made of low-quality wood. This actually improves the general strength and durability of the furniture but only limits its refinishing. Construction of Wooden Furniture According to experts, joint construction best determines the quality of a given piece of furniture. Any piece of furniture that has been held together by the use of nails or staples is of a very poor quality and cannot stand the test of time when it comes to serving you. You are advised to look out for furniture pieces that either have mortise and tenon or dovetail joints. Proportionality of the piece of furniture should be a priority right from the start. Inspect the piece of furniture to ensure to ensure all its legs are able to touch the ground. This is normally an indication that the furniture you are about to purchase is of high quality. | Mid | [
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Q: Hide navgrid in jqgrid How can hide navgrid in jgqrid? I want show jqgrid without navgrid. A: If you need create navigator bar to be able to use navButtonAdd or inlineNav you can use navGrid with corresponding parameters $("#grid").jqGrid("navGrid", "#pager", {add: false, edit: false, del: false, search: false, refresh: false}); As the result the table with navigator bar will be created, but it will be empty: Another way is opposite: you can create navigator grid with all buttons, but hide it immediately. Such behavior could be helpful if you need to show/hide navigator button based on context (depend on selected row for example) or based on the permission of the user on the backend. See the answer for details. If you need to hide the whole navigator bar you can use code like $("#pager").find("table.navtable").hide(); | Mid | [
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Induction of specific tolerance to class I-disparate renal allografts in miniature swine with cyclosporine. Previous studies in miniature swine have suggested that the mechanism underlying the spontaneous development of tolerance in one third of one-haplotype class I disparate renal allografts (i.e., ag----ad) involves a relative T cell help deficit at the time of first exposure to antigen. If this hypothesis were correct, then one might expect the administration of an immunosuppressive agent capable of inhibiting lymphokine production during this period to lead to the induction of tolerance to class I MHC antigens in two-haplotype class I mismatched renal allografts (i.e., gg----dd), which are otherwise uniformly and acutely rejected. This hypothesis was tested in eight two-haplotype class I disparate, class II matched donor-recipient pairs, in which recipients were treated with cyclosporine 10 mg/kg, i.v. q.d. for 12 days. This protocol led to the induction of long-term (greater than 100 days) specific tolerance in 100% of recipients, as compared with control animals that rejected grafts in 13.7 +/- 0.9 days (P less than 0.0001). The specificity of tolerance was assessed both in vivo with subsequent skin grafts and in vitro by mixed lymphocyte response (MLR) and cell-mediated lymphocytotoxicity (CML). Survival of donor-specific skin grafts was prolonged compared with skin grafts bearing third-party class I antigens (19.5 +/- 2.0 versus 11.5 +/- 2.0 days, n = 4, P less than 0.05). Tolerant recipients had markedly diminished or absent anti-donor MLR and CML responses, but maintained normal reactivity to third party. Four of eight CsA-treated recipients showed detectable levels of anti-donor IgM, while none demonstrated the presence of anti-donor IgG, which was found in all rejecting controls. | High | [
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Two additional endorsements from Navajo Agencies announced FLAGSTAFF - The candidates for Congressional District 1 are vying for support from the Navajo Nation and other tribes in the District currently represented by Republican Rick Renzi. Following a presentation to the Chinle Agency of the Navajo Nation, a resolution of support for Democratic Candidate Howard Shanker was passed. At the end of December 2007, Shanker received a similar endorsement from the Western Navajo Agency. Last summer, during President Shirley's State of the Nation address to the Navajo Nation Council, Shanker was honored with a ceremonial blanket and plaque for his outstanding service to the Navajo Nation. Arizona Congressional District 1 is heavily populated with Native Americans, a constituency that accounts for almost a quarter of the District's voters. Of the many tribes represented in this district, the Navajo Nation is by far the largest. The Shanker campaign, which emphasizes "accountability, sustainability and responsibility," resonates with a wide swath of Native American and non-Native American voters throughout the District. It is still early in the process, but within the Native American community, Shanker has already been endorsed as a candidate by the Dine Hataalii Association, a prestigious association of more than 300 Navajo medicine men and women. Shanker also has strong ties with and support from 'Azee'Bee Nahagha' (Native American Church) of the Dine' Nation. Shanker has received endorsements from various Navajo Chapters including the Tuba City Chapter, Bird Springs Chapter, Coal Mine Chapter and Cameron Chapter. Last fall, Shanker was named as the Grand Marshal in the recent Western Navajo Fair and Parade. In November, Shanker helped represent the Navajo Nation at Congressional Committee hearings in Washington D.C. to pressure the federal government to clean up uranium contamination on the reservation. As an attorney, Shanker also represents the Navajo Nation, the White Mountain Apache Tribe, the Yavapai-Apache Tribe, the Havasupai Tribe and others in the case that, to date, has succeeded in halting the federal government from allowing the use of reclaimed sewer water to make snow on the sacred San Francisco Peaks-a site that has religious significance to 13 of the tribes in the southwestern United States. Among Shanker's individual Native American supporters: the Chairman of the Hopi Tribe, Navajo Code Talkers, Apache Medicine Men, Rodney Grant (actor from "Dances with Wolves"), and Russell Means (political activist and actor from Last of the Mohicans), as well as the Colorado River Indian Tribes. To learn more about Howard Shanker and his campaign, go to www.Shanker2008.com. Campaign news is also available at www.myspace.com/HowardShanker. Comments Comments are not posted immediately. Submissions must adhere to our Use of Service Terms of Use agreement. Rambling or nonsensical comments may not be posted. Comment submissions may not exceed a 200 word limit, and in order for us to reasonably manage this feature we may limit excessive comment entries. | High | [
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To prevent young children from entering an area such as a swimming pool without supervision, safety enclosures are provided. In some cases, such as for pool fences, they may be required by law. These safety enclosures generally include a self-latching device which is arranged to operate automatically on closing of the gate of the fence and prevents the gate from being reopened without manual release of the mechanism. One form of such a self-latching device is a magnetic latching device, an example of which is described in WO92/03631. Moreover, there is a need to provide a self-latching device that is able to remove any false sense of security for the user, i.e. able to warn a user that when the gate visually appears to be closed, but the self-latching device is in its unlatched condition. In addition, the applicant understands that improvements can still be made in the industry to drive a much safer environment for young children. | Mid | [
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Q: Unix How to check if a specific word is entered in as an argument I'm writing a script in Unix but I need a way to check an argument that is entered in the command line is a specific word. So if when using the script the user types: $ ./script hello my script can tell that "hello" was entered as an argument and can display a message appropriately. And if the user types something other than "hello" as an argument then my script can display another message. Thanks. A: This should work: #!/bin/bash if [[ $1 == hello ]];then echo "hello was entered" else echo "hello wasn't entered" fi | Mid | [
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Mol Syst Biol. (2020) 16: e8955 Introduction {#msb198955-sec-0001} ============ Cells rely on the transient activation of signal transduction pathways to rapidly adapt to changes in the environment. Molecular mechanisms that enable strong, but transient activation of signal transduction include the induction of positive regulators, such as the activation or induction of transcriptional co‐regulators, and of negative feedback mechanisms, such as transcriptional induction of genes encoding negative feedback proteins or the post‐translational activation of negative feedback regulators. The innate immune response is the first line of defense against pathogens. Upon infection, pathogens are rapidly detected, followed by the activation of signal transduction pathways that stimulate the production of interferons. Interferons are cytokines with antiviral and immunomodulatory effects (Tang *et al*, [2018](#msb198955-bib-0074){ref-type="ref"}). Due to these immunomodulatory functions, interferon pathway activation has recently been discussed to enhance the impact of checkpoint inhibitors in immunotherapies (Wang *et al*, [2019](#msb198955-bib-0075){ref-type="ref"}). Type I interferons are secreted and act via autocrine and paracrine induction of signal transduction. Thereby, an antiviral state is established both in infected and uninfected cells. In addition to antiviral genes acting directly on viruses, many of the induced genes are involved in pathogen recognition and the production of interferons as well as having immunomodulatory functions, giving rise to a highly dynamical system that consists of multiple waves of interferon production and release (Marie *et al*, [1998](#msb198955-bib-0045){ref-type="ref"}; Sato *et al*, [1998](#msb198955-bib-0063){ref-type="ref"}). IFNα belongs to the type I interferons and signals via the interferon alpha receptors 1 and 2 (IFNAR1 and IFNAR2) (Novick *et al*, [1994](#msb198955-bib-0050){ref-type="ref"}; Domanski *et al*, [1995](#msb198955-bib-0014){ref-type="ref"}). Upon binding of IFNα, IFNAR1 and IFNAR2 dimerize, leading to the activation of the associated Janus kinases JAK1 and TYK2 and tyrosine phosphorylation of the receptors. Subsequently, the latent transcription factors signal transducer and activator of transcription 1 (STAT1) and STAT2 (Platanias *et al*, [1994](#msb198955-bib-0054){ref-type="ref"}) are recruited to the phosphorylated receptors and are activated by tyrosine phosphorylation. Phosphorylated STAT1 can form homodimers (Decker *et al*, [1991](#msb198955-bib-0012){ref-type="ref"}), STAT1:STAT2 heterodimers by binding to phosphorylated STAT2 (Li *et al*, [1996](#msb198955-bib-0036){ref-type="ref"}) or, by binding to interferon response factor 9 (IRF9) and phosphorylated STAT2, can form the interferon‐stimulated gene factor 3 (ISGF3), which translocate to the nucleus and induce expression of antiviral, immunomodulatory, and feedback genes (Schindler *et al*, [1992](#msb198955-bib-0065){ref-type="ref"}). Positive feedback proteins include IRF9, STAT1, and STAT2 (Lehtonen *et al*, [1997](#msb198955-bib-0035){ref-type="ref"}), and negative feedback proteins include SOCS1, SOCS3, USP18, and IRF2 (Harada *et al*, [1989](#msb198955-bib-0021){ref-type="ref"}; Song & Shuai, [1998](#msb198955-bib-0070){ref-type="ref"}; Malakhova *et al*, [2006](#msb198955-bib-0044){ref-type="ref"}). The extent of the overall response depends on the balance of the induced feedback mechanisms. Pre‐exposure to a ligand can result in three scenarios: (i) desensitization of the pathway defined as lower activation upon stimulation, (ii) the same activation upon stimulation as without prestimulation, or (iii) hypersensitization of the pathway defined as higher activation of the pathway upon stimulation. Recombinant IFNα has been used as treatment against chronic viral infections such as infection with the hepatitis B virus (HBV) and as an anti‐tumor drug (Friedman, [2008](#msb198955-bib-0018){ref-type="ref"}). However, it was observed that many patients do not respond to the therapy (Suk‐Fong Lok, [2019](#msb198955-bib-0071){ref-type="ref"}). Non‐responsiveness was correlated with pre‐activation of the endogenous IFNα signal transduction pathway (Chen *et al*, [2005](#msb198955-bib-0009){ref-type="ref"}) showing elevated levels of ISGs in liver biopsies of patients with chronic HCV infection (Sarasin‐Filipowicz *et al*, [2008](#msb198955-bib-0061){ref-type="ref"}) or in hepatocytes isolated from patients with chronic HBV infection (Zhu *et al*, [2012](#msb198955-bib-0078){ref-type="ref"}). This desensitization of the pathway by pre‐activation of the IFNα signal transduction pathway, also called refractoriness, was confirmed both in cell culture and *in vivo* experiments in mice (Larner *et al*, [1986](#msb198955-bib-0033){ref-type="ref"}; Makowska *et al*, [2011](#msb198955-bib-0043){ref-type="ref"}). USP18 was proposed as a factor contributing to pathway desensitization (Sarasin‐Filipowicz *et al*, [2009](#msb198955-bib-0062){ref-type="ref"}). Despite the reported evidence for an impact of pre‐activation of IFNα signal transduction on the responsiveness of the IFNα signal transduction pathway, the specific conditions that result in pathway desensitization remained unclear. Further, it has not yet been explored whether also hypersensitization of the pathway might be possible. To unravel the molecular mechanisms that determine how pre‐activation of the IFNα signal transduction pathway impacts the response to further ligand exposure, a mathematical model of the IFNα signal transduction pathway was established that comprises multiple feedback loops. The model was calibrated with quantitative time‐resolved measurements of pathway components and target genes for different IFNα dose combinations using Huh7.5 and HepG2‐hNTCP cell lines and primary human hepatocytes as cellular model systems. With this approach, we showed that while prestimulation with a high dose of IFNα results in desensitization of the signal transduction pathway, prestimulation with a low dose of IFNα can hypersensitize the pathway. Model simulations and experimental evidence revealed that not only USP18 but also SOCS1 are required for pathway desensitization, while induction of IRF9 and STAT2 contributes to pathway hypersensitization and the basal amount of IRF9 controls the dynamics of the ISGF3 transcription factor complex formation. Analysis of primary human hepatocytes from different donors identified patient‐to‐patient variability of basal USP18 levels as the key determinant controlling the patient‐specific pathway desensitization threshold. Mathematical model simulations exploring a virtual patient cohort demonstrated that the abundance of STAT2 determines the patient‐specific extent of the antiviral response. Results {#msb198955-sec-0002} ======= Prestimulation with a low IFNα dose hypersensitizes the pathway and prestimulation with a high IFNα dose desensitizes the pathway {#msb198955-sec-0003} --------------------------------------------------------------------------------------------------------------------------------- To examine the impact of prestimulation with IFNα on the dynamics of IFNα signal transduction, we first established IFNα concentrations that resulted in low, intermediate, and high pathway activation. We exposed growth factor‐depleted Huh7.5 cells for 1 h to different concentrations of IFNα and monitored by quantitative immunoblotting the amount of tyrosine‐phosphorylated STAT1 and STAT2 (pSTAT1~Cyt~, pSTAT2~Cyt~) in cytoplasmic lysates (Fig [1](#msb198955-fig-0001){ref-type="fig"}A). At a dose of 2.8 pM IFNα (equal to 10 international units (IU)), 50% of maximal STAT1 phosphorylation and 10% of maximal STAT2 phosphorylation were reached, at 28 pM IFNα (equal to 100 IU) 90% of maximal STAT1 phosphorylation and 80% of maximal STAT2 phosphorylation were achieved, and at 1,400 pM IFNα (equal to 5000 IU) 100% of maximal STAT1 phosphorylation and 100% of maximal STAT2 phosphorylation were observed. For subsequent experiments, we selected 2.8 pM IFNα (low), 28 pM IFNα (intermediate), and 1,400 pM IFNα (high) as prestimulation doses. Since STAT proteins translocate to the nucleus upon activation, we additionally measured pSTAT1 in nuclear lysates ([Appendix Fig S1A](#msb198955-sup-0001){ref-type="supplementary-material"}) as well as in total cell lysates ([Appendix Fig S1B](#msb198955-sup-0001){ref-type="supplementary-material"}), showing a comparable dose--response behavior. To ensure the linearity of detection in the enzymatic assays (chemiluminescence) employed for quantitative immunoblotting, we not only measured the abundance of pSTAT1 in total cellular lysates by chemiluminescence employing a CCD camera‐based device ([Appendix Fig S1B](#msb198955-sup-0001){ref-type="supplementary-material"}), but also by fluorescence using a near‐infrared fluorescence scanner ([Appendix Fig S1C](#msb198955-sup-0001){ref-type="supplementary-material"}). The comparison of the chemiluminescence‐based quantifications with the fluorescence‐based quantifications revealed a Pearson correlation coefficient of 0.99, showing a comparable detection range for both methods ([Appendix Fig S1D](#msb198955-sup-0001){ref-type="supplementary-material"}). To assess the impact of IFNα prestimulation on the dynamics of STAT1 and STAT2 phosphorylation, growth factor‐depleted Huh7.5 cells were either left untreated or were prestimulated with 2.8 pM or 1,400 pM IFNα. After 24 h of prestimulation, the cells were stimulated with 1,400 pM IFNα and were lysed every 10 min for up to 1 h (Fig [1](#msb198955-fig-0001){ref-type="fig"}B). The dynamics of STAT1 and STAT2 tyrosine phosphorylation (pSTAT1, pSTAT2) in cytoplasmic (exemplified in Fig [1](#msb198955-fig-0001){ref-type="fig"}C) and nuclear extracts were examined by quantitative immunoblotting and subsequently quantified (Fig [1](#msb198955-fig-0001){ref-type="fig"}D). The quantitative analysis revealed that in cells without IFNα‐prestimulation, addition of IFNα resulted in a sharp increase of both pSTAT1 and pSTAT2 reaching maximal levels 30 min after stimulation, but a higher fold change of pSTAT1 compared with pSTAT2 was observed, both in cytoplasm and nucleus. The levels of pSTAT1 and pSTAT2 remained elevated for the entire observation time. Surprisingly, we observed in cells prestimulated with the low IFNα dose that stimulation with 1,400 pM IFNα resulted at 30 min in elevated phosphorylation of primarily STAT2 in the nucleus compared to the phosphorylation levels observed in the nucleus of untreated cells. The observed increased phosphorylation levels were sustained for the entire observation period suggesting hypersensitization of the IFNα signal transduction pathway. On the contrary, in cells prestimulated with the high dose of IFNα, the stimulation with 1,400 pM IFNα did not elicit phosphorylation of STAT1 and STAT2 neither in the cytoplasm nor the nucleus, suggesting pathway desensitization (Fig [1](#msb198955-fig-0001){ref-type="fig"}D). To determine the impact of residual IFNα from the prestimulation, we removed the ligand after 20.5 h prestimulation by washing, reapplied the ligand after 3 h growth factor‐depletion and monitored the dynamics of IFNα induced STAT1 and STAT2 phosphorylation by quantitative immunoblotting ([Appendix Fig S2A](#msb198955-sup-0001){ref-type="supplementary-material"}). These experiments demonstrated that ligand removal after 20.5 h of prestimulation resulted in the same level of hyper‐ or desensitization of the IFNα pathway as achieved by 24 h of prestimulation without ligand removal. However, ligand removal after only 1 h of prestimulation prevented the establishment of altered sensitivity toward IFNα stimulation, which correlated with incapacity to induce expression of positive and negative feedback proteins during 1‐h IFNα stimulation ([Appendix Fig S2B](#msb198955-sup-0001){ref-type="supplementary-material"}). {#msb198955-fig-0001} To closer investigate the impact of prestimulation with a low or high IFNα dose on IFNα‐induced gene expression, we selected twenty interferon‐stimulated genes (ISGs) with different dynamics in gene expression based on a previously published microarray analysis performed with IFNα‐stimulated Huh7.5 cells (Maiwald *et al*, [2010](#msb198955-bib-0041){ref-type="ref"}). We focused our in depth analysis shown in Fig [1](#msb198955-fig-0001){ref-type="fig"}E on three ISGs representing an early, an intermediate, and a late dynamics. As an ISG with early transient dynamics, we selected the C‐X‐C motif chemokine 10 (*CXCL10*). The interferon‐induced GTP‐binding protein MX1 (*MX1*) was selected for its intermediate transient dynamics and interferon alpha‐inducible protein 6 (*IFI6*) as a gene with a late response. The mRNA expression of these three ISG in Huh7.5 was investigated by qRT‐PCR analysis for a total observation time of 48 h comprising 24 h of prestimulation with the low or high dose of IFNα or no prestimulation and 24 h of stimulation with 1,400 pM IFNα. Prestimulation with 1,400 pM IFNα induced a strong activation of *CXCL10*,*MX1,* and *IFI6* during the first 24 h (Fig [1](#msb198955-fig-0001){ref-type="fig"}E). During the prestimulation phase, both *CXCL10* and *MX1* showed a peak of maximal mRNA expression at 8 h and a subsequent decline of mRNA expression either to basal levels for *CXCL10,* or to 60% of maximal expression for *MX1**,*** whereas the mRNA expression of *IFI6* increased during the entire observation period. Stimulation with 1,400 pM IFNα after 24 h of prestimulation with the high dose of IFNα did not result in a further increase of *IFI6* mRNA expression, *MX1* mRNA expression levels were marginally elevated and the mRNA expression of *CXCL10* remained at basal levels. These results showed that the pathway desensitization observed at the signal transduction level established by prestimulation with the high IFNα dose propagates to the expression of target genes. These findings also held true for the early transcripts *SOCS3*,*IRF1*,*IFIT2*,*IRF2*,*SOCS1,* and *CXCL11* ([Appendix Figs S3A and S4A](#msb198955-sup-0001){ref-type="supplementary-material"}), for the intermediate transcripts *ZNFX1*,*NMI*,*STAT2*,*TRIM21*,*STAT1*,*IFIT1*,*USP18,* and *EIF2AK2* ([Appendix Figs S3B and S4B](#msb198955-sup-0001){ref-type="supplementary-material"}) as well as for the late transcripts *ISG15*,*IRF9,* and *IFITM3* ([Appendix Figs S3C and S4C](#msb198955-sup-0001){ref-type="supplementary-material"}). Prestimulation with 2.8 pM IFNα induced lower gene expression compared to prestimulation with the high dose of IFNα (Fig [1](#msb198955-fig-0001){ref-type="fig"}E versus F). However, cells prestimulated for 24 h with the low dose of IFNα responded to stimulation with 1,400 pM IFNα and responded faster compared to cells that had not been prestimulated with IFNα albeit with lower maximal mRNA levels. For example for CXCL10 and MX1 maximal peaks of gene expression were already observed at 4 h after stimulation of cells prestimulated with 2.8 pM IFNα (Fig [1](#msb198955-fig-0001){ref-type="fig"}F), compared to maximal gene expression observed at 8 h after stimulation of cells without prestimulation (Fig [1](#msb198955-fig-0001){ref-type="fig"}E). In summary, prestimulation with a low dose of IFNα resulted in hypersensitization of signal transduction and accelerated target gene expression, while prestimulation with a high dose of IFNα caused pathway desensitization and prevented the induction of target gene expression. Establishment of a mathematical model of IFNα‐induced signal transduction and gene expression to unravel the mechanisms of IFNα dose‐dependent pathway sensitization {#msb198955-sec-0004} -------------------------------------------------------------------------------------------------------------------------------------------------------------------- To elucidate how prestimulation with a low dose of IFNα generates hypersensitization of signal transduction, while prestimulation with a high dose of IFNα results in pathway desensitization, we established an ordinary differential equation (ODE) model (Fig [2](#msb198955-fig-0002){ref-type="fig"}). Rate equations were derived from the law of mass‐action according to chemical reaction network theory, including Michaelis--Menten kinetics. The ODE model incorporates IFNα‐induced signal transduction starting with activation of the receptors IFNAR1 and IFNAR2, followed by the phosphorylation of STAT1 and STAT2, complex formation of the phosphorylated STAT proteins as well as their translocation to the nucleus and induction of feedback proteins. It integrates the prestimulation as well as the stimulation with different IFNα doses over time. {ref-type="ref"}). Negative regulators are depicted in red. c: cytoplasm, n: nucleus, dim: dimer, rec: receptor, a: active, OccGASbs: occupied binding sites containing gamma‐activated sequence, OccGASbs + OccISREbs: occupied binding sites containing gamma‐activated sequence and interferon‐stimulated response element.](MSB-16-e8955-g004){#msb198955-fig-0002} In brief, IFNAR1 and IFNAR2 in complex with JAK1 and TYK2 are summarized as one species termed Receptor (Rec). Upon binding of IFNα, the receptor becomes phosphorylated and therefore activated (aRecIFN). The activated receptor phosphorylates cytoplasmic STAT1 (STAT1c) or STAT2 (STAT2c). Upon phosphorylation, STAT1 homodimers (pSTAT1dimc) can be formed. Similarly, pSTAT1pSTAT2 heterodimers (pSTAT1pSTAT2c) can be formed upon phosphorylation of STAT1 and of STAT2. In the mathematical model, phosphorylation and dimerization of STAT1 and STAT2 were approximated by single reactions in which the active receptor complex forms and induces dimer formation directly. Binding of IRF9c to pSTAT1pSTAT2c heterodimers results in the formation of ISGF3c. The three complexes pSTAT1dimc, pSTAT1pSTAT2c, and ISGF3c translocate to the nucleus and induce expression of target genes. In the nucleus, pSTAT1 homodimers (pSTAT1dimn) induce the expression of *SOCS3* mRNA by binding to STAT1 transcription factor binding sites called occupied gamma‐activated sequence‐binding sites (OccGASbs). The promoters of the genes encoding the positive feedback proteins IRF9, STAT1, and STAT2 as well as the negative feedback proteins USP18, SOCS1, and IRF2 harbor gamma interferon‐activated sites (GAS) in combination with interferon‐stimulated response elements (ISRE). Since pSTAT1:pSTAT2 heterodimers and ISGF3 bind to these combined GAS and ISRE sites, both, nuclear pSTAT1pSTAT2n and ISGF3n, contribute to the formation of occupied GAS‐ and ISRE‐binding sites (OccGASbs + OccISREbs) in the promoters of these genes. By means of the model, the gene induction by ISGF3n was estimated to be stronger than by pSTAT1pSTAT2n, which is in agreement with literature showing that IRF9, STAT1, and STAT2 all contribute to binding to the ISRE (Qureshi *et al*, [1995](#msb198955-bib-0055){ref-type="ref"}). Inside the nucleus, all transcription factor complexes can dissociate into their individual components that can translocate back to the cytoplasm. The individual components STAT1, STAT2, and IRF9 have the freedom to shuttle between cytoplasm and nucleus (Meyer *et al*, [2002](#msb198955-bib-0048){ref-type="ref"}; Banninger & Reich, [2004](#msb198955-bib-0004){ref-type="ref"}). The induced feedback mRNAs are translated into proteins, taking gene‐specific time delays for translation into account, which were incorporated via linear chains between mRNA and protein targets (MacDonald, [1976](#msb198955-bib-0040){ref-type="ref"}). For both the transcriptional and translational processes, gene‐specific saturation levels were taken into account. Signal termination involves SOCS3, USP18, and SOCS1. USP18 binds to IFNAR2 and thereby inhibits downstream substrate phosphorylation (Malakhova *et al*, [2006](#msb198955-bib-0044){ref-type="ref"}), while SOCS proteins act at the receptor level directly inhibiting formation of the active receptor‐IFN complex (aRecIFN) by inhibiting JAK family members (Chen *et al*, [2000](#msb198955-bib-0008){ref-type="ref"}). SOCS1 additionally mediates degradation of the activated receptor complexes (Piganis *et al*, [2011](#msb198955-bib-0053){ref-type="ref"}). Additionally, the transcriptional modulator IRF2 was incorporated to capture transient dynamics of SOCS1mRNA (Harada *et al*, [1989](#msb198955-bib-0021){ref-type="ref"}). Turnovers of all species include basal production and degradation. To capture dynamic properties of the system, the IFNα‐signal transduction model was calibrated with 1,918 data points generated under 25 experimental conditions, comprising quantitative time‐resolved data obtained at the protein and the RNA level. Identifiability of model parameters was addressed by computing the profile likelihood (Raue *et al*, [2009](#msb198955-bib-0058){ref-type="ref"}) for each parameter ([Appendix Fig S10](#msb198955-sup-0001){ref-type="supplementary-material"}). Out of 85 model parameters, 74 parameters were identifiable, i.e., finite confidence intervals were obtained ([Appendix Table S3](#msb198955-sup-0001){ref-type="supplementary-material"}). From the remaining eleven parameters, three showed confidence intervals open to minus infinity and eight open to plus infinity. However, no further model reduction was applied due to the biological relevance of these parameters (see [Materials and Methods](#msb198955-sec-0010){ref-type="sec"}). We tested three additional mechanisms, (i) a cytoplasmic phosphatase dissociating pSTAT1dimc, pSTAT1pSTAT2c, and ISGF3c, (ii) STAT2 functioning as an adapter for USP18 (Arimoto *et al*, [2017](#msb198955-bib-0002){ref-type="ref"}), and (iii) pSTAT1dimn inducing OccGASbs+OccISREbs by formulating alternative mathematical models ([Appendix Fig S5A](#msb198955-sup-0001){ref-type="supplementary-material"}). We re‐estimated the model parameters for each of these three hypotheses and calculated the Bayesian information criterion (BIC). In all three cases, the goodness‐of‐fit was nearly the same, however, due to the additional parameters, the BIC was significantly worse and these additional mechanisms were rejected ([Appendix Fig S5B](#msb198955-sup-0001){ref-type="supplementary-material"}). In summary, we established an ODE model of IFNα signal transduction consisting of seven feedback proteins that could contribute to pathway sensitization to different extents. IFNα dose‐dependent induction of feedback proteins and pathway sensitization {#msb198955-sec-0005} ---------------------------------------------------------------------------- We hypothesized that sensitization of the IFNα signal transduction pathway is determined by the IFNα‐induced feedbacks differing in their dose--response behavior as well as in their dynamics. To address this assumption, we performed time‐resolved analysis of the protein levels of the known negative feedback regulator USP18, the positive feedback regulator IRF9 and additionally accounted for the total protein amount of STAT1 and STAT2 (tSTAT1 and tSTAT2) that we assumed to act as additional positive regulators of the system in response to IFNα. To obtain a quantitative understanding of the influence of these signal transduction components on pathway activation, we in parallel performed time‐resolved analysis of pSTAT1 and pSTAT2. Growth factor‐depleted Huh7.5 cells were left untreated or were stimulated with different IFNα doses ranging from 2.8 to 2,800 pM (for untreated, 2.8, 28, and 1,400 pM IFNα see Figs [3](#msb198955-fig-0003){ref-type="fig"}A and [EV1](#msb198955-fig-0001ev){ref-type="fig"}A; for 8.4, 280, and 2,800 pM IFNα see Fig [EV1](#msb198955-fig-0001ev){ref-type="fig"}A). The changes of concentrations of signal transduction components were monitored by quantitative immunoblotting at different time points up to 32 h and were used to calibrate the mathematical model. For all investigated doses, both, data points and model trajectories, revealed transient phosphorylation of cytoplasmic and nuclear STAT1 (pSTAT1) and STAT2 (pSTAT2) that returned close to basal levels 8 h after stimulation. In addition, stimulation with 1,400 pM IFNα resulted in a dampened second peak of pSTAT1 and pSTAT2 around 12 h as visible in the data and captured by the model (Fig [3](#msb198955-fig-0003){ref-type="fig"}A). The model suggested that the second peak of pSTAT1 and pSTAT2 is already triggered by stimulation with IFNα doses above 2.8 pM (Fig [EV1](#msb198955-fig-0001ev){ref-type="fig"}A). Interestingly, we observed in both model and data a different time‐dependent and dose‐dependent induction of the feedback proteins IRF9, USP18 as well as of the total STAT1 and STAT2 proteins. While saturation levels of IRF9 protein were already detected after 6 h of stimulation with 2.8 pM IFNα (Figs [3](#msb198955-fig-0003){ref-type="fig"}A and [EV1](#msb198955-fig-0001ev){ref-type="fig"}A), the other feedback proteins showed a more graded IFNα dose‐dependent increase in the maximal responses. USP18 protein reached maximal induction only upon stimulation with 140 pM IFNα for 24 h (Fig [EV1](#msb198955-fig-0001ev){ref-type="fig"}B, USP18~Cyt~) and reached a plateau at 8 h of stimulation (Figs [3](#msb198955-fig-0003){ref-type="fig"}A and [EV1](#msb198955-fig-0001ev){ref-type="fig"}A), while total STAT1 and STAT2 protein levels reached a plateau only at 14--16 h after stimulation with IFNα doses of 140 pM or more (Figs [3](#msb198955-fig-0003){ref-type="fig"}A, and [EV1](#msb198955-fig-0001ev){ref-type="fig"}A and B, tSTAT1~Cyt~, tSTAT2~Cyt~, tSTAT1~Nuc~, tSTAT2~Nuc~). Subsequently, the expression of feedback proteins remained sustained. Thus, we detected an IFNα dose‐dependent increase of USP18, tSTAT1, and tSTAT2 at 24 h of stimulation. Maximal levels of IRF9 protein were reached at 8 h upon stimulation with as little as 2.8 pM IFNα and were maintained at 24 h. Further, after 4 h of IFNα stimulation, we detected an induction of IRF9 already in response to stimulation with 2.8 pM IFNα, whereas for STAT1, STAT2, and USP18 only minor increases were observed even for the highest IFNα doses tested (Fig [EV1](#msb198955-fig-0001ev){ref-type="fig"}B). One hour of stimulation sufficed to induce pSTAT1 and pSTAT2 as well as tSTAT1~Nuc~ and tSTAT2~Nuc~, but not the other components. {#msb198955-fig-0003} {#msb198955-fig-0001ev} To examine the impact of different IFNα doses on mRNA expression profiles, mRNA expression was monitored by qRT‐PCR at different time points after stimulation with 2.8, 28, and 1,400 pM IFNα (Fig [3](#msb198955-fig-0003){ref-type="fig"}B) and the impact of prestimulation with IFNα was examined (Fig [EV2](#msb198955-fig-0002ev){ref-type="fig"}A). Similar to the findings at the protein level, sustained expression profiles for *STAT1*,*STAT2*,*IRF9,* and *USP18* mRNAs were observed for 24 h of stimulation with IFNα. For *STAT1*,*STAT2,* and *USP18* mRNA, a gradual increase in mRNA expression in response to rising IFNα dose was detected, whereas for *IRF9* again mRNA expression levels close to saturation were already detected with as little as 2.8 pM IFNα (Fig [3](#msb198955-fig-0003){ref-type="fig"}B). On the other hand, a more transient expression dynamics was observed for *IRF2*,*SOCS1,* and *SOCS3* mRNA, with *SOCS1* and *IRF2* showing mRNA levels still above basal expression after 24 h of IFNα stimulation (Fig [3](#msb198955-fig-0003){ref-type="fig"}B). Interestingly, transient high levels of *SOCS3* mRNA that returned within 8 h to basal mRNA levels were only observed in cells stimulated with 1,400 pM IFNα, whereas in cells stimulated with 2.8 or 28 pM IFNα only a minor induction of *SOCS3* mRNA was detectable. Further, IFNα stimulation of prestimulated cells only showed an induction of *STAT1, STAT2, USP18, SOCS1,* and *SOCS3* mRNA upon prestimulation with 2.8 pM IFNα, but not upon prestimulation with 1,400 pM IFNα (Fig [EV2](#msb198955-fig-0002ev){ref-type="fig"}A). *IRF9* mRNA expression remained at maximal levels that was already induced by prestimulation with 2.8 pM IFNα. Likewise, at the protein level, prestimulation with as little as 2.8 pM resulted in maximal IRF9 levels that did not further increase upon stimulation with high IFNα concentrations in the observed time period of 8 h (Fig [EV2](#msb198955-fig-0002ev){ref-type="fig"}B). For USP18, STAT1, and STAT2, prestimulation with IFNα doses higher than 28 pM for 24 h resulted in saturated levels that could not be further increased by stimulation with high IFNα doses. Altogether, the differences in timing and IFNα dose‐dependent induction of the feedbacks on protein and mRNA level were accurately captured by our ODE model of IFNα signal transduction. {#msb198955-fig-0002ev} The results shown in Figs [3](#msb198955-fig-0003){ref-type="fig"}A and B, and [EV1](#msb198955-fig-0001ev){ref-type="fig"}A, and B only display IFNα dose‐dependent relative changes in the expression of feedback proteins. However, to dissect the specific contribution of each component, absolute values are essential. Therefore, the amount of STAT1, STAT2, IRF9, and USP18 molecules per cell was determined experimentally in growth factor‐depleted Huh7.5 cells that were either left untreated or were stimulated with 2.8, 28, or 1,400 pM of IFNα for 24 h (Fig [3](#msb198955-fig-0003){ref-type="fig"}C). This quantitative analysis revealed that the feedback proteins had a different abundance and again showed a different dose dependency among each other. The amount of STAT1 protein molecules per cell ranged from 500,000 to 1,000,000 molecules under basal conditions and gradually increased in an IFNα dose‐dependent manner. In contrast, the amount of STAT2 protein was only 50,000 molecules at basal level and thus one order of magnitude lower compared to STAT1. However, STAT2 protein levels showed a much higher fold change upon treatment with 1,400 pM IFNα. The feedback proteins IRF9 and USP18 were present at very low levels under basal conditions. Upon treatment with IFNα, IRF9 protein levels increased starting from treatment with 2.8 pM IFNα, while USP18 protein levels only showed a minor increase after stimulation with 2.8 and 28 pM IFNα. The protein abundances determined by the calibrated model were very well in line with the experimental data. To evaluate whether our mathematical model is capable to capture hypersensitization and desensitization of the pathway, growth factor‐depleted Huh7.5 cells were prestimulated with 2.8, 28, and 1,400 pM IFNα or left untreated and were subsequently stimulated with 1,400 pM IFNα at 24 h. As shown in Fig [3](#msb198955-fig-0003){ref-type="fig"}D, and for additional IFNα doses in Fig [EV2](#msb198955-fig-0002ev){ref-type="fig"}B, the calibrated mathematical model was able to describe the experimental data. In summary, experimental data and model trajectories revealed that at IFNα concentrations of 28 pM and below, hypersensitization of STAT2 phosphorylation in the nucleus was observed in the first 2 h of the observation period. Only a very small hypersensitization effect was detected on nuclear STAT1 phosphorylation with 2.8 pM IFNα prestimulation after 1 h (Figs [3](#msb198955-fig-0003){ref-type="fig"}D and [EV2](#msb198955-fig-0002ev){ref-type="fig"}B). A gradual increase in desensitization of STAT1 and STAT2 phosphorylation in the cytoplasm and nucleus was observed for prestimulation with IFNα concentrations higher than 28 pM (Fig [EV2](#msb198955-fig-0002ev){ref-type="fig"}B). Taken together, the mathematical model that was calibrated based on the experimental data revealed that the feedback components of IFNα signal transduction differ with respect to their IFNα dose dependencies and their induction dynamics. Prestimulation with doses below 28 pM IFNα resulted in hypersensitization of the pathway as indicated by elevated phosphorylation of STAT1 and STAT2, while IFNα doses higher than 28 pM established a gradual IFNα dose‐dependent desensitization of the pathway. Our calibrated mathematical model was able (i) to simultaneously describe dose‐dependent activation of the pathway, (ii) to characterize time‐dependent induction of feedback components over a measurement period of 24 h, and (iii) to capture both dose‐dependent hypersensitization and desensitization of the pathway. Model‐based analysis of the dynamics of pSTAT1 complex formation and model validation {#msb198955-sec-0006} ------------------------------------------------------------------------------------- We employed the mathematical model of IFNα‐signal transduction to examine the impact of the IFNα prestimulation dose on the dynamics of the formation of the transcriptionally active pSTAT1‐ and pSTAT2‐containing complexes in the nucleus upon stimulation with a high dose of IFNα. In principle pSTAT1 homodimers, pSTAT1:pSTAT2 heterodimers and pSTAT1:pSTAT2:IRF9 (ISGF3) trimers can form. The model‐based analysis revealed that in cells without prior exposure to IFNα, total STAT1 levels are in excess compared to STAT2 and IRF9 and therefore initially primarily pSTAT1 homodimers are formed in the nucleus that bind to gamma interferon‐activated site (GAS) elements in promoter regions (Fig [4](#msb198955-fig-0004){ref-type="fig"}A). The mathematical model indicated that simultaneously pSTAT1:pSTAT2 heterodimers are formed, albeit with slower dynamics. Finally, after 4 h, ISGF3 complexes are formed that bind to interferon‐stimulated response element (ISRE) and become the dominant transcription factor complexes. This delay in formation of ISGF3 is caused by IFNα‐induced IRF9 upregulation and coincides with the dynamics of the induction of IRF9 (Fig [3](#msb198955-fig-0003){ref-type="fig"}A). Interestingly, the model indicated that upon prestimulation with 28 pM IFNα, which increases the abundance of IRF9 (Fig [3](#msb198955-fig-0003){ref-type="fig"}C), stimulation with 1,400 pM IFNα resulted in an immediate rise in ISGF3 complexes as well as a much reduced formation of pSTAT1 homodimers. This effect is even more pronounced upon prestimulation with 280 pM followed by stimulation with 1,400 pM IFNα, triggering primarily an immediate increase in ISGF3 complexes. Therefore, we hypothesized that the formation of pSTAT1 homodimers is reduced as a function of an increasing prestimulation dose. Consequently, the expression of GAS‐controlled genes should be reduced upon stimulation with 1,400 pM IFNα in cells prestimulated with low to intermediate IFNα doses, because under these conditions primarily ISGF3 complexes are formed that bind to ISRE sequences. {#msb198955-fig-0004} To experimentally verify the model‐predicted consecutive occurrence of the different transcription factor complexes, we performed electrophoretic mobility shift assays (EMSA) as previously reported (Forero *et al*, [2019](#msb198955-bib-0015){ref-type="ref"}). Experiments using a probe comprising the GAS‐binding region of the *IRF1* promoter (Fig [EV3](#msb198955-fig-0003ev){ref-type="fig"}A, left panel) showed that in mock prestimulated Huh7.5 cells an early DNA:protein complex is induced after 1 h (corresponding to 25 h after mock prestimulation) of stimulation with 1,400 pM IFNα. This DNA:protein complex is absent at 4 and 6 h post‐IFNα stimulation of Huh7.5 cells (corresponding to 28 and 30 h after mock prestimulation, respectively). As shown in Fig [EV3](#msb198955-fig-0003ev){ref-type="fig"}A, right panel, incubation of the lysate‐DNA mixture with an antibody recognizing STAT1 led to a supershift, which was absent upon addition of antibodies detecting STAT2 or IRF9, confirming the specificity of the detected complex as pSTAT1 homodimer. In accordance with our assumption in the mathematical model, no major binding of the pSTAT1:pSTAT2 heterodimer to the GAS region was observed. On the contrary to non‐prestimulated Huh7.5 cells, formation of pSTAT1 homodimeric complexes induced by stimulation with 1,400 pM IFNα is much reduced in cells prestimulated with 280 pM IFNα for 24 h. To quantitatively compare the obtained results with our model predictions, we predicted the dynamics of occupied GAS‐binding sites induced by 1,400 pM IFNα in untreated Huh7.5 cells and in Huh7.5 cells prestimulated with 280 pM IFNα for 24 h (Fig [4](#msb198955-fig-0004){ref-type="fig"}B, left panel). The corresponding 68%‐confidence intervals were computed as proposed in Kreutz *et al* ([2012](#msb198955-bib-0032){ref-type="ref"}). The simulation showed a steep increase of occupied GAS‐binding sites within the first hour after stimulation, which was suppressed upon prestimulation of cells with IFNα. As shown in Fig [4](#msb198955-fig-0004){ref-type="fig"}B, left panel, the mean values of pSTAT1 homodimeric complexes detected by EMSA (*N* = 3) were in agreement with the model prediction and experimentally confirmed a rapid but transient formation of pSTAT1 homodimers in response to stimulation with IFNα, which was much reduced upon IFNα prestimulation, validating the model‐predicted early occurrence of pSTAT1 homodimers in response to IFNα stimulation. {#msb198955-fig-0003ev} To investigate the IFNα‐induced dynamics of the formation of the other STAT1‐containing transcription factor complexes, we performed co‐immunoprecipitation (co‐IP) experiments. We stimulated non‐prestimulated Huh7.5 cells or Huh7.5 cells prestimulated with 280 pM IFNα for 24 h for 1--6 h (corresponding to 25--30 h after prestimulation) with 1,400 pM IFNα. The cellular lysates were used for immunoprecipitation experiments using antibodies recognizing STAT2 and co‐immunoprecipitated pSTAT1 was detected by quantitative immunoblotting (Fig [EV3](#msb198955-fig-0003ev){ref-type="fig"}B). With these co‐IP experiments the dynamics of the sum of IFNα‐induced formation of pSTAT1:pSTAT2 heterodimers and pSTAT1:pSTAT2:IRF9 trimers (ISGF3) was detected. In non‐prestimulated Huh7.5 cells the signal for co‐immunoprecipitating pSTAT1 was maximal after 1 h of stimulation with 1,400 pM IFNα and slowly decreased thereafter but not reaching baseline after 6 h of stimulation (25--28 h after mock prestimulation). Upon prestimulation of Huh7.5 cells with 280 pM IFNα for 24 h, higher levels of total STAT2 were observed, while the overall signal of co‐immunoprecipitated pSTAT1 was lower. Distinctively, it was already detectable after 24 h of prestimulation and increased to a much lower extent by stimulation with 1,400 pM IFNα compared to the amount detected in untreated cells. To compare the experimental results obtained by the quantification of co‐immunoprecipitated pSTAT1 (*N* = 3) to the predictions by our mathematical model, we calculated the dynamics of the sum of pSTAT1:pSTAT2 heterodimers and the pSTAT1:pSTAT2:IRF9 trimers (ISGF3) induced by 1,400 pM IFNα in non‐prestimulated Huh7.5 cells and Huh7.5 cells prestimulated with 280 pM IFNα for 24 h and computed 68%‐confidence intervals. As shown in Fig [4](#msb198955-fig-0004){ref-type="fig"}B, middle panel, the model‐predicted broad peak of the sum of pSTAT1:pSTAT2 heterodimers and ISGF3 was in line with the experimental data and was reduced to around one‐third upon prestimulation of the cells. Additionally, to quantify in non‐prestimulated and prestimulated Huh7.5 cells the dynamics of IFNα‐induced ISGF3 complex formation, co‐IP experiments were performed using antibodies recognizing IRF9 and co‐immunoprecipitated pSTAT1 was detected by quantitative immunoblotting (Fig [EV3](#msb198955-fig-0003ev){ref-type="fig"}C). The signal for IRF9‐precipitated pSTAT1 increased upon stimulation of non‐prestimulated Huh7.5 cells with 1,400 pM IFNα with a peak at 4 h post‐IFNα treatment (28 h after mock prestimulation). Upon prestimulation of Huh7.5 cells with 280 pM IFNα for 24 h, IRF9 levels were strongly increased and co‐immunoprecipitated pSTAT1 was now already peaking at around 1 h after IFNα stimulation (25 h after prestimulation). The mean values for pSTAT1 (*N* = 3) at the different time points of IFNα stimulation of untreated and prestimulated Huh7.5 cells were in line with the model‐predicted dynamics of ISGF3 complex formation in response to IFNα stimulation confirming the late increase of ISGF3 transcription factor complexes in untreated cells and acceleration of the formation to 1 h after IFNα stimulation in cells prestimulated with 280 pM IFNα. Overall, these results confirmed our model predictions that whereas pSTAT1 homodimers are rapidly and transiently formed in response to IFNα stimulation, it takes several hours until enough IRF9 protein has been produced to assemble significant amounts of the ISGF3 complex before it becomes the dominant transcription factor complex. To experimentally demonstrate the impact of these transcription factor complexes on the expression dynamics of target genes, we had to first identify interferon target genes whose expression is primarily regulated by the presence of GAS‐ or ISRE‐binding sites. As shown in [Appendix Fig S6A](#msb198955-sup-0001){ref-type="supplementary-material"}, bioinformatics analyses revealed that promoter regions of the *IRF1* and *SOCS3* genes harbor primarily putative GAS sequences, while the *DDX58*,*HERC5,* and *IFI44L* genes contain primarily putative ISRE sites in proximity to the transcription start site. To experimentally verify that these genes are primarily driven by either GAS or ISRE sites, we stimulated Huh7.5 cells with 5,000 IU/ml of either IFNγ or IFNα (corresponding to 1,400 pM IFNα) ([Appendix Fig S6B](#msb198955-sup-0001){ref-type="supplementary-material"}). In line with the promoter analysis, stimulation with IFNγ, which only induces phosphorylation of STAT1 and therefore the formation of pSTAT1 homodimers, resulted in a sustained expression of *IRF1* and *SOCS3*, but not of the other genes. In agreement with our model‐based prediction that IFNα triggers the transient formation of pSTAT1 homodimers and the sustained formation of ISGF3 complexes, IFNα induced a transient expression of *IRF1* and *SOCS3* with a peak around 1 h after IFNα stimulation, while it induced a sustained expression for *DDX58*,*HERC5,* and *IFI44L* in the timeframe of 4 h. In sum, these experiments established that the expression of *IRF1* and *SOCS3* is controlled by the presence of GAS sequences, whereas the expression of *DDX58*,*HERC5,* and *IFI44L* is primarily dependent on the presence of ISRE sites in Huh7.5 cells. To further evaluate the distinct IFNα dose‐dependent formation of IFNα‐induced transcription factor complexes as predicted by the mathematical model (Fig [4](#msb198955-fig-0004){ref-type="fig"}A), we simulated the dynamics of the occupancy of GAS‐binding sites upon stimulation with 1,400 pM IFNα after prestimulation with 28 and 280 pM IFNα. Prestimulation with these IFNα doses was predicted by the mathematical model to reduce pSTAT1 homodimer formation and consequently the occupancy of GAS‐binding sites in a dose‐dependent manner upon stimulation with 1,400 pM IFNα (Fig [4](#msb198955-fig-0004){ref-type="fig"}C, upper left panel). The corresponding 68%‐confidence intervals (shaded areas in Fig [4](#msb198955-fig-0004){ref-type="fig"}C) were computed as proposed in Kreutz *et al* ([2012](#msb198955-bib-0032){ref-type="ref"}). To verify this model prediction, we examined the dynamics of the production of the GAS‐dependent transcripts *IRF1* and *SOCS3* upon stimulation with 1,400 pM IFNα in untreated cells and after prestimulation with 28 and 280 pM IFNα (Fig [4](#msb198955-fig-0004){ref-type="fig"}C, symbols in upper right panels). In accordance with the mathematical model, the dynamics of the expression of these genes was reduced by the prestimulation with 28 and 280 pM IFNα and reflected the predicted reduced formation of the pSTAT1 homodimers. Conversely, the dynamics of the formation of ISGF3 complexes and consequently the occupancy of ISRE‐binding sites upon stimulation with 1,400 pM IFNα after prestimulation with 28 and 280 pM IFNα was predicted. In contrast to the GAS‐ and ISRE‐binding sites controlling the expression of *STAT1*,*STAT2*,*IRF9*,*IRF2*,*USP18,* and *SOCS1* that are occupied by ISGF3 and pSTAT1:pSTAT2 heterodimers, the ISRE‐binding sites are only occupied by ISGF3. The model predicted that the prestimulation with 28 pM IFNα resulted in a higher initial level of occupied ISRE‐binding sites at 24 h and an accelerated increase of occupied ISRE‐binding sites upon stimulation with 1,400 pM IFNα. Prestimulation with 280 pM IFNα was predicted to further increase the initial occupancy of ISRE‐binding sites after 24 h and the maximum occupancy of ISRE‐binding sites upon stimulation with 1,400 pM IFNα was predicted to be similar as in cells that were not prestimulated (Fig [4](#msb198955-fig-0004){ref-type="fig"}C, lower left panel). The experimental analysis of the dynamics of the ISRE‐dependent transcripts *DDX58*,*HERC5,* and *IFI44L* confirmed upon prestimulation with 28 pM IFNα a higher basal expression at 24 h and an accelerated gene induction compared to cells that were not prestimulated. Upon prestimulation with 280 pM IFNα, the basal expression of *DDX58*,*HERC5,* and *IFI44L* was even higher at 24 h and the maximum expression upon stimulation with 1,400 pM IFNα was similar to cells that were not prestimulated, reflecting the predicted dynamics of the occupied ISRE‐binding sites (Fig [4](#msb198955-fig-0004){ref-type="fig"}C, symbols in lower right panels). These measured transcripts were linked to the amount of occupied binding sites predicted by the mathematical model by estimating gene‐specific parameters, i.e., mRNA synthesis and degradation rate, time delay of mRNA production, and the Hill coefficient, while all remaining model parameters were fixed. This allowed to overlay the measured dynamics of this gene set with the simulated model trajectories (Fig [4](#msb198955-fig-0004){ref-type="fig"}C, lines in upper and lower right panels). We further validated our model prediction using SOCS3 protein dynamics. We first predicted the IFNα‐induced dynamics of occupied GAS‐bindings sites (OccGASbs) in Huh7.5 cells without prestimulation and in cells prestimulated for 24 h with 2.8 and 28 pM IFNα that were subsequently stimulated with 1,400 pM IFNα (Fig [EV3](#msb198955-fig-0003ev){ref-type="fig"}C). Also with these lower prestimulation doses, we observed that the amount of the OccGASbs was reduced in a dose‐dependent manner. In Fig [EV3](#msb198955-fig-0003ev){ref-type="fig"}D, the experimental data points of quantified SOCS3 protein expression were overlaid with simulated model trajectories. The corresponding 68%‐confidence intervals (shaded areas in Fig [EV3](#msb198955-fig-0003ev){ref-type="fig"}D) were computed as proposed in Kreutz *et al* ([2012](#msb198955-bib-0032){ref-type="ref"}). The results showed that in untreated cells and cells prestimulated with 2.8 pM IFNα, SOCS3 expression was rapidly induced upon stimulation with 1,400 pM IFNα, while only a minor induction of the SOCS3 protein was observed in cells prestimulated with 28 pM IFNα, thereby confirming our model‐based hypothesis and thus validating the capacity of the model to predict the dynamics of IFNα‐induced formation of the different STAT1 transcription factor complexes in Huh7.5 cells. Next, we investigated whether the model could be applied to analyze the dynamic behavior of signal transduction induced by a therapeutic agent such as Roferon (interferon α‐2a, Roche). First, equipotent doses of Roferon and the research grade IFNα, which we utilized in this study, were determined by a subgenomic HCV replicon assay (Fig [EV4](#msb198955-fig-0004ev){ref-type="fig"}A). According to the obtained IC~50~ values (Fig [EV4](#msb198955-fig-0004ev){ref-type="fig"}B) that were verified in a dose--response experiment measuring pSTAT1 and pSTAT2 by quantitative immunoblotting (Fig [EV4](#msb198955-fig-0004ev){ref-type="fig"}C), Huh7.5 cells were prestimulated with a low dose of 1.2 pM Roferon (corresponding to 2.8 pM IFNα), a high dose of 608 pM Roferon (corresponding to 1,400 pM IFNα), or were left untreated. After 24 h, the cells were stimulated by adding a high dose of 608 pM Roferon and phosphorylation of cytoplasmic (Fig [EV4](#msb198955-fig-0004ev){ref-type="fig"}D) and nuclear (Fig [4](#msb198955-fig-0004){ref-type="fig"}D) STAT1 and STAT2 was investigated for up to 4 h by quantitative immunoblotting. The experimental data and the model trajectories were highly similar to those obtained in the experiments performed with the research grade IFNα (Fig [1](#msb198955-fig-0001){ref-type="fig"}D). Again, prestimulation with a high dose of Roferon resulted in pathway desensitization as indicated by lower levels of both nuclear and cytoplasmic pSTAT1 and pSTAT2, while prestimulation with a low dose of Roferon generated pathway hypersensitization, most evident for nuclear pSTAT2, confirming that dose‐dependent sensitization of IFNα signal transduction in Huh7.5 cells is also established by Roferon. {#msb198955-fig-0004ev} To address whether the extent of pathway sensitization is cell type‐specific, we examined Roferon‐induced phosphorylation of STAT1 and STAT2 in the nucleus of HepG2‐hNTCP cells, which are commonly used to study infection of hepatitis B virus (Hoh *et al*, [2015](#msb198955-bib-0023){ref-type="ref"}). We measured the abundance of STAT1, STAT2, IRF9, and USP18 in HepG2‐hNTCP cells (Fig [EV5](#msb198955-fig-0005ev){ref-type="fig"}A), which were significantly different from the corresponding abundances detected in Huh7.5 cells (Fig [3](#msb198955-fig-0003){ref-type="fig"}C). While STAT1 and STAT2 were of lower abundance in HepG2‐hNTCP cells than in Huh7.5 cells, the number of molecules per cell of IRF9 and USP18 were higher in untreated HepG2‐hNTCP cells. To determine differences in parameters of the IFNα signal transduction model between HepG2‐hNTCP and Huh7.5 cells, we employed our previously established method to identify cell type‐specific parameters based on L~1~ regularization (Merkle *et al*, [2016](#msb198955-bib-0047){ref-type="ref"}). This analysis revealed that the basal synthesis rate of *STAT1* mRNA and the parameter comprising phosphorylation and association of STAT1 and STAT2 were different in HepG2‐hNTCP cells compared to Huh7.5 cells. 301 data points generated for three experimental conditions were used for calibration of these additional model parameters, and the protein abundance of STAT1, STAT2, IRF9, and USP18 determined for HepG2‐hNTCP cells were incorporated (Figs [4](#msb198955-fig-0004){ref-type="fig"}E and [EV5](#msb198955-fig-0005ev){ref-type="fig"}B). The other dynamic parameters were fixed to parameter values estimated from the Huh7.5 IFNα dataset. Distinct from Huh7.5 cells that were kept in 1.5 ml medium, HepG2‐hNTCP cells were cultivated in 1 ml and therefore the applied Roferon doses were adjusted accordingly (see [Materials and Methods](#msb198955-sec-0010){ref-type="sec"}). HepG2‐hNTCP cells were prestimulated for 24 h with a low dose of 1.8 pM Roferon, a high dose of 887 pM Roferon or were left untreated and were subsequently stimulated with a high dose of 887 pM Roferon. The experimental results (Fig [4](#msb198955-fig-0004){ref-type="fig"}E) revealed that prestimulation with a high Roferon dose very much decreased the Roferon‐induced presence of pSTAT1 and pSTAT2 in the nucleus of HepG2‐hNTCP cells confirming desensitization of the pathway. However, hypersensitization of pSTAT2 phosphorylation upon prestimulation with a low Roferon dose was less pronounced compared to Huh7.5 cells (Fig [4](#msb198955-fig-0004){ref-type="fig"}D). As shown in Fig [4](#msb198955-fig-0004){ref-type="fig"}E, the obtained model trajectories were in line with the experimental data confirming that the mathematical model is capable to represent the IFNα dose‐dependent sensitization of the IFNα signal transduction pathway independent of the cell type. {#msb198955-fig-0005ev} To investigate the impact of the different ratio between the STAT proteins and IRF9 in HepG2‐hNTCP cells on formation of pSTAT1‐containing transcription factor complexes, we simulated with our mathematical model the dynamics of pSTAT1:pSTAT1 homodimers, pSTAT1:pSTAT2 heterodimers, and ISGF3 complexes in the nucleus of HepG2‐hNTCP cells ([Appendix Fig S7A](#msb198955-sup-0001){ref-type="supplementary-material"}). Unlike Huh7.5 cells, the mathematical model predicted a rapid formation of ISGF3 complexes within 30 min due to the higher amounts of IRF9 compared to STAT1 being present in untreated HepG2‐hNTCP cells. Stimulation with IFNα results in a gradual increase in IRF9 production and therefore in a further increase in the formation of ISGF3 complexes 2 h later. Further, the mathematical model suggested that in HepG2‐hNTCP cells pSTAT1:pSTAT1 homodimers and pSTAT1:pSTAT2 heterodimers are formed with a similar dynamics as in Huh7.5 cells in response to IFNα stimulation, but the amounts of these complexes are lower. Additionally, our mathematical model simulations indicated that prestimulation of HepG2‐hNTCP cells with 28 or 280 pM IFNα for 24 h reduces the formation of these complexes in a dose‐dependent manner, while the formation of the ISGF3 complex is, similar to Huh7.5 cells, much accelerated. To experimentally validate in HepG2‐hNTCP cells the impact of the formation of these transcription factor complexes on the expression dynamics of the target genes selected for Huh7.5 cells, we first stimulated HepG2‐hNTCP cells with 5,000 IU/ml of either IFNγ or IFNα (corresponding to 1,400 pM IFNα) ([Appendix Fig S7B](#msb198955-sup-0001){ref-type="supplementary-material"}). Similar to Huh7.5 cells, stimulation with IFNγ induced in HepG2‐hNTCP cells the expression of *IRF1* and *SOCS3*, but not of *DDX58*,*HERC5,* and *IFI44L*. In line with the mRNA expression dynamics observed in Huh7.5 cells, IFNα stimulation of HepG2‐hNTCP cells resulted after 4 h in the induction of the expression of *DDX58*,*HERC5,* and *IFI44L* and in an immediate increase in the expression of *SOCS3* with a peak at around 1 h after IFNα stimulation. For *IRF1* an approximately 50‐fold increase of mRNA expression was observed within 1 h after IFNα stimulation, which was in line with the mRNA expression dynamics in Huh7.5 cells and confirmed *IRF1* as an immediate early gene of IFNα‐induced responses. However, in HepG2‐hNTCP cells the IFNα‐induced expression of *IRF1* was more sustained suggesting that the down regulation of the *IRF1* expression in HepG2‐hNTCP is potentially modulated by the cell context‐specific activation of other transcription factors. This is in line with previous reports that the expression of *IRF1* can also be regulated by the NFκB and MAP‐kinase pathways (Yarilina *et al*, [2008](#msb198955-bib-0077){ref-type="ref"}), and therefore, we did not include *IRF1* in our further analyses. We simulated with our mathematical model the dynamics of the occupancy of GAS‐binding sites induced in HepG2‐hNTCP cells either untreated or prestimulated with 28 or 280 pM IFNα by stimulation with 1,400 pM IFNα. Prestimulation with 28 pM IFNα was predicted to have little impact on the peak amplitude of the occupancy of GAS‐binding sites, while prestimulation with 280 pM IFNα reduced the peak amplitude of occupied GAS‐binding sites by an order of magnitude ([Appendix Fig S7C](#msb198955-sup-0001){ref-type="supplementary-material"}, upper left panel). In accordance with the model prediction, the dynamics of the expression of experimentally measured expression of *SOCS3* was only slightly reduced by the prestimulation with 28 pM IFNα, but almost completely abolished by prestimulation with 280 pM IFNα ([Appendix Fig S7C](#msb198955-sup-0001){ref-type="supplementary-material"}, upper right panel). Moreover, similar to Huh7.5 cells, the mathematical model predicted for HepG2‐hNTCP cells a higher initial level of occupied ISRE‐binding sites at 24 h of prestimulation and an accelerated increase of occupied ISRE‐binding sites upon stimulation with 1,400 pM IFNα ([Appendix Fig S7C](#msb198955-sup-0001){ref-type="supplementary-material"}, lower left panel), which was in agreement with the experimentally observed expression of the ISRE‐dependent transcripts *DDX58*,*HERC5,* and *IFI44L* ([Appendix Fig S7C](#msb198955-sup-0001){ref-type="supplementary-material"}, lower right panel). These experiments demonstrate that the mathematical model can also predict the dynamics of IFNα‐induced transcription factor complex formation in another liver cell line and thus confirm the broader applicability of the mathematical model. To conclude, upon stimulation of untreated cells pSTAT1 primarily contributes to the presence of pSTAT1 homodimers and subsequently pSTAT1:pSTAT2 heterodimers. In cells prestimulated with a low IFNα dose, IRF9 levels are increased and therefore ISGF3 complexes prevail. Furthermore, an IFNα dose‐dependent pathway sensitization was also confirmed for the therapeutic agent Roferon and the sequential formation of STAT1‐containing transcription factor complexes is not specific for a certain cell type, but rather observed for both Huh7.5 and HepG2‐hNTCP cells. USP18 is not sufficient to desensitize IFNα‐induced signal transduction {#msb198955-sec-0007} ----------------------------------------------------------------------- Since it was previously reported that USP18 acts as key negative regulator of IFNα signal transduction and we observed that an increase of USP18 correlated with an increase of pathway desensitization (Figs [3](#msb198955-fig-0003){ref-type="fig"}C compared to D, and [EV1](#msb198955-fig-0001ev){ref-type="fig"}), we investigated whether USP18 alone is sufficient to establish pathway desensitization. First, we studied the impact of knockdown of USP18 on the effect of prestimulation with IFNα and on the establishment of pathway desensitization. One day prior to the start of the experiment, Huh7.5 cells were transfected with siRNAs targeting USP18. Subsequently, the cells were prestimulated with 1,400 pM IFNα for 24 h and were stimulated with 1,400 pM IFNα or were left untreated. IFNα‐induced phosphorylation and feedback induction was investigated by quantitative immunoblotting (Fig [5](#msb198955-fig-0005){ref-type="fig"}A, [Appendix Fig S8B](#msb198955-sup-0001){ref-type="supplementary-material"}) and qRT‐PCR ([Appendix Fig S8C](#msb198955-sup-0001){ref-type="supplementary-material"}). As shown in [Appendix Fig S8A](#msb198955-sup-0001){ref-type="supplementary-material"}, upon stimulation with IFNα, cells transfected with the non‐targeting control siRNA showed a comparable dynamics of activation of the IFNα signal transduction pathway relative to the dynamics observed in untransfected Huh7.5 cells, indicating that the method did not interfere with the dynamics of the IFNα signal transduction pathway. Therefore, the data obtained in cells transfected with control siRNA were scaled together with data obtained in untransfected Huh7.5 cells. The quantitative analysis shown in the first panel of Fig [5](#msb198955-fig-0005){ref-type="fig"}A identified an average knockdown efficiency of 94.5 ± 2% at the USP18 protein level after 24 h of stimulation with 1,400 pM IFNα. In control cells incubated with 1,400 pM IFNα, a transient increase of pSTAT1 and pSTAT2 in the cytoplasm was observed at 3 h that returned close to basal levels after 8 h and showed a dampened second peak beyond 12 h (Fig [5](#msb198955-fig-0005){ref-type="fig"}A, right panel). On the contrary, in cells transfected with USP18 siRNA, pSTAT1, and pSTAT2 levels in the cytoplasm remained sustained beyond 24 h. Nuclear pSTAT1 and pSTAT2 levels showed a comparable sustained dynamic behavior upon USP18 knockdown ([Appendix Fig S8B](#msb198955-sup-0001){ref-type="supplementary-material"}). The experimentally observed levels of pSTAT1 and pSTAT2 in cytoplasm and nucleus in USP18 knockdown cells were captured by the calibrated mathematical model and confirmed the role of USP18 as a negative regulator of IFNα signal transduction (Fig [5](#msb198955-fig-0005){ref-type="fig"}A and [Appendix Fig S8B](#msb198955-sup-0001){ref-type="supplementary-material"}). In addition, USP18 knockdown resulted in an increased induction of the mRNAs of feedback genes ([Appendix Fig S8C](#msb198955-sup-0001){ref-type="supplementary-material"}) and of the feedback proteins STAT1 (Fig [5](#msb198955-fig-0005){ref-type="fig"}A, tSTAT1~Cyt~), STAT2, IRF9, and USP18 ([Appendix Fig S8B](#msb198955-sup-0001){ref-type="supplementary-material"}). As described by the data and the model trajectories, stimulation of control and USP18 knockdown cells 24 h after prestimulation with a high IFNα dose triggered only a weak increase in pSTAT1 and pSTAT2. The knockdown experiments confirmed USP18 as a major negative feedback, which is also captured by the calibrated mathematical model. {#msb198955-fig-0005} To investigate whether an increase in the abundance of USP18 alone is sufficient to cause desensitization of the IFNα signal transduction pathway, we established a stable Huh7.5 cell line with inducible USP18 expression. Instead of prestimulation with IFNα, cells were pretreated with doxycycline for 24 h to induce the expression of USP18 protein. Figure [5](#msb198955-fig-0005){ref-type="fig"}B (first panel) shows that USP18 protein expression was induced to a similar extent as in parental Huh7.5 cells stimulated for 24 h with 1,400 pM IFNα. In control cells, Huh7.5 cells transduced with the empty TetON vector, doxycycline treatment did not induce the expression of USP18 protein. In these control cells, a similar dynamics of IFNα‐induced signal transduction was observed as in untreated parental Huh7.5 cells and therefore data of both conditions were scaled together ([Appendix Fig S9A](#msb198955-sup-0001){ref-type="supplementary-material"}). Stimulation of the inducible USP18 overexpressing cell line (Huh7.5‐TetON‐USP18) with 1,400 pM IFNα for up to 6 h resulted in a slightly lower activation of pSTAT1 and pSTAT2 relative to cells that had not been prestimulated with IFNα, which is in agreement with USP18 acting as a negative regulator of the pathway (Fig [5](#msb198955-fig-0005){ref-type="fig"}B). Unexpectedly, distinct from cells prestimulated for 24 h with 1,400 pM IFNα that showed desensitization of pSTAT1 and pSTAT2 activation in the cytoplasm, the USP18 overexpressing cell line that contained comparable amounts of USP18 did not show this strong desensitization but rather displayed a significantly higher extent of pathway activation than the prestimulated cells (Fig [5](#msb198955-fig-0005){ref-type="fig"}B and [Appendix Fig S9B](#msb198955-sup-0001){ref-type="supplementary-material"}). The experimental data and the mathematical model together indicated that USP18 alone is not sufficient to cause pathway desensitization. Therefore, we tested whether in addition SOCS1 is required. To identify possible mechanisms that could explain pathway desensitization and the USP18 overexpression data, different model structures were tested. While USP18 and SOCS1 both inhibit activation of the receptor, the impact of these molecules on internalization of the active receptor was unclear. Internalization of the active receptor could be enhanced by SOCS1, by USP18 or only if both molecules were binding. We tested different model structures and evaluated the resulting goodness‐of‐fit by means of the Bayesian information criterion (BIC) (Fig [5](#msb198955-fig-0005){ref-type="fig"}C). As exemplified by the fit of nuclear pSTAT1 (Fig [5](#msb198955-fig-0005){ref-type="fig"}C) and the lowest BIC value (Fig [5](#msb198955-fig-0005){ref-type="fig"}D), the model captured the experimental data best when taking both SOCS1‐mediated and SOCS1:USP18‐mediated degradation of the activated receptor into account. We concluded that, USP18 indeed acts as a negative regulator and impacts signal attenuation, but since USP18 overexpression alone was not sufficient to induce pathway desensitization, we propose that USP18 acts as a cofactor for SOCS1‐mediated degradation of active IFNα receptor complexes. Identification of components predictive for sensitization of the IFNα signal transduction pathway in cell lines and primary human hepatocytes {#msb198955-sec-0008} --------------------------------------------------------------------------------------------------------------------------------------------- To dissect mechanisms that regulate dose‐dependent sensitization of IFNα signal transduction in hepatoma cell lines, we employed the mathematical model to simulate in Huh7.5 and HepG2‐hNTCP cell lines the amounts of STAT1, STAT2, IRF9, and USP18 protein for untreated cells and for cells prestimulated with 1.2 pM or 608 pM Roferon for 24 h (Fig [6](#msb198955-fig-0006){ref-type="fig"}A). The model simulations were in line with the corresponding experimental data (Figs [3](#msb198955-fig-0003){ref-type="fig"}C and [EV5](#msb198955-fig-0005ev){ref-type="fig"}A) and revealed the presence of slightly lower amounts of IRF9 and USP18 in untreated Huh7.5 cells compared to untreated HepG2‐hNTCP cells and an IFNα dose‐dependent increase in the amounts of STAT1, STAT2, IRF9, and USP18 in both cell systems. We hypothesized that the amount of one or several of these proteins may be predictive for the sensitization of the IFNα signal transduction pathway. To test this model‐derived hypothesis in primary human hepatocytes, we first investigated the patient‐to‐patient variability in the abundance of the feedback proteins STAT1, STAT2, IRF9, and USP18 by quantitative immunoblotting in patient‐derived primary human hepatocytes that were isolated from tumor‐free tissue of six patients (black bars in Fig [6](#msb198955-fig-0006){ref-type="fig"}B). The basal levels of STAT1 ranged from 10^5^ to 10^6^ molecules per cell, whereas for STAT2 10^4^ to 10^5^ molecules per cell were present, similar to untreated Huh7.5 and HepG2‐hNTCP cells (Figs [3](#msb198955-fig-0003){ref-type="fig"}C and [EV5](#msb198955-fig-0005ev){ref-type="fig"}A). IRF9 amounts were similar to STAT2 amounts, and being more than one order of magnitude higher expressed in primary human hepatocytes than in the untreated cell lines. In addition, USP18 amounts highly varied between the patients, the abundance being slightly lower than the abundance of IRF9. {#msb198955-fig-0006} To test whether these patient‐specific amounts lead to differences in pathway sensitization, we prestimulated primary human hepatocytes with 2.8 and 1,400 pM IFNα (Patients 1--3) or with 1.2 and 608 pM Roferon (Patients 4--6) or left cells untreated. After 24 h, primary human hepatocytes were stimulated with 1,400 pM IFNα (Patients 1--3) or 608 pM Roferon (Patients 4--6), respectively, and phosphorylation of cytoplasmic (Patients 1--3) or total (Patients 4--6) STAT1 and STAT2 was investigated for up to 4 h by quantitative immunoblotting (Fig [6](#msb198955-fig-0006){ref-type="fig"}C). Additionally, the cytoplasmic (Patients 1--3) or total (Patients 4--6) amounts of STAT1, STAT2, IRF9, and USP18 were measured ([Appendix Fig S10](#msb198955-sup-0001){ref-type="supplementary-material"}). We utilized our calibrated mathematical model of the IFNα signal transduction pathway to analyze the experimental data (Fig [6](#msb198955-fig-0006){ref-type="fig"}B and C, and [Appendix Fig S10](#msb198955-sup-0001){ref-type="supplementary-material"}) and defined additional primary human hepatocyte‐specific model parameters based on L~1~ regularization. Altogether 816 data points belonging to three experimental conditions were used for the calibration of these parameters. The following parameters were different in primary human hepatocytes compared to Huh7.5 cells: the amount of the receptor complex (Rec), the basal and induced synthesis rate of *STAT2* mRNA, the degradation rate of *SOCS1* mRNA, and the dissociation rate of nuclear ISGF3. The calibrated mathematical model was able to simultaneously represent the patient‐specific abundance of STAT1, STAT2, IRF9, and USP18 (green rectangles in Fig [6](#msb198955-fig-0006){ref-type="fig"}B), which was in good agreement with the experimental determinations, and captured the patient‐specific dynamics observed in the time‐resolved measurements (lines in Fig [6](#msb198955-fig-0006){ref-type="fig"}C, [Appendix Fig S10](#msb198955-sup-0001){ref-type="supplementary-material"}). Both experimental data and mathematical model showed that for all patients untreated primary human hepatocytes rapidly respond to IFNα/Roferon stimulation, while primary human hepatocytes that were prestimulated with a high dose of IFNα/Roferon showed qualitatively little response. Interestingly, prestimulation with a low dose of IFNα/Roferon seemed to result in hypersensitization in primary human hepatocytes from patient 1, 3, 4, and 6, but not in the primary human hepatocytes from the other two patients. To better quantify sensitization of the pathway, we first simulated with the calibrated mathematical model---as a proxy for the activation of an antiviral response---time courses for the amount of occupied GAS and ISRE promoter‐bindings sites (active promoters of the antiviral genes) for different Roferon prestimulation doses followed by stimulation with 608 pM or no further stimulation. Second, we defined the absolute antiviral response as the area under the curve from 24 to 28 h after stimulation with 608 pM Roferon and subtracted by the area under the curve from 24 to 28 h with no stimulation (ΔAUC). To obtain the relative antiviral response, we divided the value of the absolute antiviral response obtained with prestimulated cells by the value of the response in untreated cells. A relative antiviral response of more than one corresponds to pathway hypersensitization, a value lower than one to pathway desensitization. We displayed the resulting values for the Huh7.5 and the HepG2‐hNTCP cell lines as well as for the six patient‐derived primary human hepatocytes (Fig [6](#msb198955-fig-0006){ref-type="fig"}D, left panel). These calculations showed that the extent of pathway hypersensitization upon prestimulation with 1.2 pM Roferon was rather small and variable. HepG2‐hNTCP as well as primary human hepatocytes from patients 2 and 5 showed almost no pathway hypersensitization, while primary human hepatocytes from patients 1, 3, and 4 showed intermediate pathway hypersensitization. Interestingly, pathway hypersensitization was prominent in Huh7.5 cells and in primary human hepatocytes from patient 6. Further, the model simulations confirmed that pathway desensitization was rather pronounced in all cellular model systems and not only detected in Huh7.5 and HepG2‐hNTCP cells, but also in primary human hepatocytes from all patients. However, the extent of pathway desensitization induced by 608 pM Roferon varied between primary human hepatocytes from different patients and was strongest in primary human hepatocytes from patients 1, 2, and 5 (Fig [6](#msb198955-fig-0006){ref-type="fig"}D, right panel). These results indicated the existence of a cell context‐ and patient‐specific desensitization threshold that might be predictable by the amounts of pathway components. To calculate the Roferon dose dependency of this cell context‐ and patient‐specific pathway desensitization threshold, we plotted the relative antiviral response as a function of the prestimulation amount of Roferon (Fig [7](#msb198955-fig-0007){ref-type="fig"}A, left panel). Additionally, we calculated for the hepatoma cell lines and the primary human hepatocytes the Roferon prestimulation dose beyond which the pathway is desensitized, which we term desensitization threshold (Fig [7](#msb198955-fig-0007){ref-type="fig"}A, symbols). We again observed very different responses for the distinct cellular systems. While primary human hepatocytes from patients 2, 4, and 5 as well as HepG2‐hNTCP showed pathway desensitization between 1--10 pM of Roferon and thus a low desensitization threshold, primary human hepatocytes from patient 3 and Huh7.5 cells showed a desensitization threshold that corresponds to two orders of magnitude higher Roferon doses. To determine which cellular factor is primarily responsible for this behavior, we plotted for each cellular system the desensitization threshold versus the basal amounts of STAT1, STAT2, IRF9 ([Appendix Fig S11A](#msb198955-sup-0001){ref-type="supplementary-material"}), and USP18 (Fig [7](#msb198955-fig-0007){ref-type="fig"}A, right panel). For STAT2, only a weak anti‐correlation was observed, while for STAT1 and IRF9 almost no correlation was observed ([Appendix Fig S11A](#msb198955-sup-0001){ref-type="supplementary-material"}). However, we observed a linear anti‐correlation between the amount of USP18 in untreated cells and the desensitization threshold, revealing that cells with low amounts of USP18 can tolerate a higher Roferon dose before showing desensitization of IFNα signal transduction. {ref-type="fig"}B and [7](#msb198955-fig-0007){ref-type="fig"}B are shown.For each patient in the virtual patient cohort, a stimulation with 608 pM Roferon was simulated and the relative antiviral response (ΔAUC(24--28 h) of OccGASbs+OccISREbs compared to untreated) was calculated. The relative antiviral response was plotted against the cellular abundance of STAT2. Spearman\'s rank order correlation coefficient (*r*) and *P*‐value (*p*) are indicated.For each patient in the virtual patient cohort, a stimulation with 608 pM Roferon was simulated and the absolute antiviral response (ΔAUC(24--28 h) of OccGASbs + OccISREbs) was calculated. The absolute antiviral response was plotted against the cellular abundance of STAT2. Spearman\'s rank order correlation coefficient (*r*) and *P*‐value (*p*) are indicated.](MSB-16-e8955-g013){#msb198955-fig-0007} To deduce which factors are predictive *in vivo* for the antiviral response to Roferon, we employed our mathematical model calibrated to primary human hepatocytes to establish a virtual patient cohort. The majority of model parameters was taken from the calibrated model, and these parameters were assumed to be fixed. Five model parameters were assumed to be patient‐specific: the abundance of STAT1, STAT2, IRF9, and USP18 as well as the residual amounts of endogenous IFNα in the supernatant (i.e., blood plasma). To determine the patient‐relevant IFNα levels and the patient‐to‐patient variability of IFNα, we analyzed plasma levels of IFNα in a cohort of 36 patients that were chronically infected with HBV (Fig [7](#msb198955-fig-0007){ref-type="fig"}B). IFNα levels ranged from 0.00186 to 0.152 pM, with a mean of 0.0440 ± 0.0362 pM (concentrations equal to 0.019 ± 0.016 pM Roferon). Means and variances of the abundance of STAT1, STAT2, IRF9, and USP18 were determined based on the measured amounts of molecules per cell in patient‐derived primary human hepatocytes (Fig [6](#msb198955-fig-0006){ref-type="fig"}B) assuming a log‐normal distribution. By combining these abundances with the residual IFNα concentration (corresponding to a prestimulation dose) measured in the blood plasma, we generated our virtual patient cohort consisting of 114 patients (Fig [7](#msb198955-fig-0007){ref-type="fig"}C). Model simulations were performed by randomly choosing patient‐specific parameters assuming log‐normal distributions for each of the five parameters. The patient‐specific characteristics shown in Fig [7](#msb198955-fig-0007){ref-type="fig"}C were monitored after a simulation time of 24 h. For each virtual patient, we evaluated a stimulation with 608 pM Roferon and calculated the relative and absolute antiviral response. To determine which patient‐specific factor is predictive for the extent of the antiviral response, we calculated correlations between the relative antiviral response and the cellular abundance of STAT1, STAT2, IRF9, and USP18 as well as the residual amount of Roferon (as a proxy for the prestimulation dose) (Fig [7](#msb198955-fig-0007){ref-type="fig"}D and [Appendix Fig S11B](#msb198955-sup-0001){ref-type="supplementary-material"}). For STAT1 and STAT2, we observed a weak positive correlation between the cellular abundance of the respective protein and the relative antiviral response, while no correlation was observed for the abundance of IRF9 and USP18 as well as for the residual amount of Roferon. Next, we calculated correlations between the absolute antiviral response and cellular components. Only a rather weak correlation of the abundance of STAT1, IRF9, and USP18 and no correlation of residual Roferon with the absolute antiviral response was visible ([Appendix Fig S11C](#msb198955-sup-0001){ref-type="supplementary-material"}). However, interestingly, a very strong correlation of the absolute antiviral response with the abundance of STAT2 was observed (Fig [7](#msb198955-fig-0007){ref-type="fig"}E). Together, these results indicated that for the *in vivo* situation which was simulated by the patient cohort, the amount of STAT2 is predictive for the antiviral response stimulated by Roferon. In conclusion, primary human hepatocytes isolated from six different patients showed striking heterogeneity in the abundance of STAT1, STAT2, IRF9, and USP18. The plasma samples from patients chronically infected with HBV revealed a high patient‐to‐patient variability of IFNα plasma levels. Model simulations revealed that the basal abundance of USP18 controls the threshold between hyper‐ and desensitization of IFNα signal transduction. By taking into account the measured heterogeneity in protein abundance of pathway components and IFNα, we identified STAT2 as a key predictor for the patient‐specific Roferon‐induced antiviral response. Discussion {#msb198955-sec-0009} ========== Based on quantitative, time‐resolved data, we showed that dependent on the IFNα dose prestimulation of hepatoma cell lines and primary human hepatocytes with IFNα leads to desensitization or hypersensitization of pathway activation and thereby the antiviral response. Based on these measurements, we established a mathematical model of IFNα signal transduction and unraveled that USP18 alone is not sufficient to establish pathway desensitization, but also requires the involvement of SOCS1. Our model‐based analysis of patient‐derived primary cells revealed that the patient‐specific abundance of the feedback protein USP18 sets the threshold for pathway desensitization. By simulating the antiviral response upon treatment with different doses of IFNα in a virtual patient cohort, we identified the patient‐specific STAT2 level as key predictor for the individual extent of the therapeutically inducible antiviral response. The phenomenon of pathway sensitization was previously reported for interferon‐induced signal transduction, but the underlying mechanisms were only partially understood. Hypersensitization of IFNγ‐induced signal transduction as indicated by enhanced pSTAT1 levels upon stimulation with interferon was observed in monocytes that were primed with IFNγ produced by PBMCs during macrophage development and stimulated with IFNα (Hu *et al*, [2002](#msb198955-bib-0024){ref-type="ref"}). Additionally, enhanced levels of transcription factor complexes (ISGF3 and GAF) were shown in IFNγ‐prestimulated macrophages upon restimulation with IFNα (Lehtonen *et al*, [1997](#msb198955-bib-0035){ref-type="ref"}). So far, the majority of previously published studies focused on IFNα‐induced pathway desensitization that is also referred to as ligand refractoriness. By treating fibroblasts with multiple rounds of IFNα, long‐term ligand desensitization was observed for up to 3 days as assessed by the analysis of target gene expression. This pathway desensitization was dependent on protein synthesis since treatment with cycloheximide prevented long‐term pathway desensitization (Larner *et al*, [1986](#msb198955-bib-0033){ref-type="ref"}). Hepatocytes isolated from mice receiving multiple injections of IFNα over time showed only a weak induction of pSTAT1 and reduced amounts of ISGF3 upon the second stimulation (Sarasin‐Filipowicz *et al*, [2009](#msb198955-bib-0062){ref-type="ref"}). Furthermore, desensitization of IFNα‐induced signal transduction can also be established in cells prestimulated with IFNβ, IFNλ1, or IFNλ4. For example, HLLR1‐1.4 cells that were prestimulated with IFNβ‐ or IFNλ1 showed upon IFNα stimulation a reduced induction of pSTAT1, pSTAT2, pTYK2, and pJAK1 and of their target genes (Francois‐Newton *et al*, [2011](#msb198955-bib-0016){ref-type="ref"}). Likewise, a reduced induction of pSTAT1 and reduced target gene expression upon IFNα stimulation was observed in Huh7 overexpressing IFNλ4, as well as in primary human hepatocytes with elevated IFNλ4 levels due to HCV infection (Sung *et al*, [2017](#msb198955-bib-0072){ref-type="ref"}). In U5A cells primed with IFNβ, a reduced induction of pSTAT1 upon stimulation with IFNα2 was detected (Wilmes *et al*, [2015](#msb198955-bib-0076){ref-type="ref"}). Interestingly, hepatocytes isolated from mice injected first with IFNβ and subsequently with IFNα showed reduced pSTAT1 levels and ISGF3 DNA binding, but mice injected first with IFNλ2, and later with IFNα only showed a very minor effect on pSTAT1 induction and ISGF3 DNA binding upon exposure to IFNα (Makowska *et al*, [2011](#msb198955-bib-0043){ref-type="ref"}). We showed in the presented work that prestimulation of Huh7.5 cells, HepG2‐hNTCP cells, and primary human hepatocytes with both the research grade IFNα and the therapeutic agent Roferon results in IFNα signal transduction pathway sensitization. Distinct from previous reports, we provide evidence that prestimulation with IFNα is also able to establish hypersensitization of IFNα‐induced signal transduction. To unravel the mechanism which determines that prestimulation with a low dose of IFNα leads to pathway hypersensitization while prestimulation with a high dose of IFNα leads to pathway desensitization, we established a model based on coupled ordinary differential equations, which comprises four positive and three negative feedbacks. Previously, Maiwald *et al* ([2010](#msb198955-bib-0041){ref-type="ref"}) reported an IFNα signal transduction model that focused on the early antiviral response (up to 4 h) and identified IRF9 as a crucial positive feedback. In our model, we additionally incorporated two positive (STAT1 and STAT2) and three negative (SOCS1, SOCS3, and USP18) transcriptional feedbacks, as well as an IRF2‐mediated feedback enhancing degradation of the *SOCS1* mRNA. While the positive feedbacks STAT1, STAT2, and IRF9 act at the cytoplasmic level by providing more proteins for formation of heterodimers and ISGF3 complexes, the negative feedbacks SOCS1, SOCS3, and USP18 operate at the receptor level via downregulation of the receptor. In contrast to other signal transduction models of the JAK/STAT pathway (Swameye *et al*, [2003](#msb198955-bib-0073){ref-type="ref"}; Bachmann *et al*, [2011](#msb198955-bib-0003){ref-type="ref"}), our model covers a comparatively wide time range (up to 32 h) in which two stimulations with a delay of 24 h are performed. Our analysis showed that the transcriptional feedbacks mediated by STAT1 and STAT2 only become relevant after approximately 10 h of ligand addition, while the other transcriptional regulators are already induced within the first 4 h. Our model allowed us to predict the dynamics of the different IFNα‐induced transcription factor complexes and to quantitatively link these to gene expression. IFNα‐target genes in Huh7.5 cells can be classified into three groups: Genes that are primarily regulated by GAS sites (*IRF1* and *SOCS3*), genes that are primarily regulated by ISRE sites (*DDX58*,*HERC5,* and *IFI44L*) and genes that are regulated by both GAS and ISRE sites (*STAT1*,*STAT2*,*IRF9*,*IRF2*,*USP18,* and *SOCS1*). The connections between transcription factor complexes and mRNA expression of genes can be influenced by cell context‐specific alterations in methylation patterns and differences in the activation of signal transduction pathways leading to an impact of additional transcription factors. In our study, we observed for most of the analyzed genes in Huh7.5 and HepG2‐hNTCP cells a highly comparable expression dynamics upon stimulation with IFNα. *IRF1* was induced in both cell types as an immediate early gene within 1 h with an approximately 50‐fold increase, but showed in HepG2‐hNTCP cells a more sustained behavior. This prolonged expression indicates cell type‐specific modulation of the *IRF1* mRNA expression, which is potentially due to an impact of the NFκB and MAP‐kinase pathways as previously reported (Yarilina *et al*, [2008](#msb198955-bib-0077){ref-type="ref"}) or differences in epigenetic modifications present in HepG2‐hNTCP cells versus Huh7.5 cells. In line with this hypothesis, we previously reported that cell type‐specific differences in the expression dynamics of *SOCS3* can be explained by differences in promoter‐binding elements and epigenetic modifications (Merkle *et al*, [2016](#msb198955-bib-0047){ref-type="ref"}). Utilizing model reduction techniques (Maiwald *et al*, [2016](#msb198955-bib-0042){ref-type="ref"}), we showed that the data can be described sufficiently if we assume that the first gene group is induced by nuclear pSTAT1 homodimers, the second gene group is regulated by nuclear ISGF3 and the third gene group is also induced by nuclear ISGF3 and, to a lesser extent, by nuclear pSTAT1:pSTAT2 heterodimers. Interestingly, the mathematical model predicted that pSTAT1 homodimers form early after IFNα stimulation, whereas ISGF3 complexes form later, which is corroborated by the experimental evidence obtained by EMSA and co‐immunoprecipitation experiments and explains the temporal order of target gene expression. For mathematical modeling approaches, it is of particular importance to combine model‐guided experimental design (Kreutz & Timmer, [2009](#msb198955-bib-0031){ref-type="ref"}) with careful selection of experimental methods yielding informative data with favorable signal‐to‐noise ratio to accurately define dynamic behavior. For the detection of the dynamics of the formation of pSTAT1 homodimers in complex with GAS‐binding regions, EMSA was most reliable as demonstrated by the small confidence intervals. Several independent EMSA experiments revealed that maximal binding activity is observed within 1 h of IFNα stimulation. However, to examine the dynamics of the formation of the large trimeric ISGF3 complex and the heterodimeric complexes, co‐immunoprecipitation experiments were most robust yielding reproducible quantifications in independent experiments. Specifically, we employed co‐immunoprecipitation experiments by performing STAT2 immunoprecipitations and quantifying co‐immunoprecipitating pSTAT1 to verify the model‐predicted dynamics of the sum of IFNα‐induced formation of pSTAT1:pSTAT2 heterodimers and pSTAT1:pSTAT2:IRF9 trimers. We cannot exclude that non‐canonical complexes such as pSTAT1:STAT2 (Ho *et al*, [2016](#msb198955-bib-0022){ref-type="ref"}) are also detected in these experiments. However, Ho *et al* showed that these complexes remain in the cytoplasm and are not relevant for type 1 interferon signaling. Further, since our experiments show that the IFNα‐induced dynamics of STAT1 and STAT2 phosphorylation is very similar and this is also reflected by the trajectories of the mathematical model (Fig [3](#msb198955-fig-0003){ref-type="fig"}A), we assume that even if a hypothetical pSTAT1:STAT2 complex would form, it would have the same dynamics as the model‐simulated pSTAT1:pSTAT2 complex. The temporal order of INFα‐induced formation of pSTAT1‐containing transcription factor complexes is highly dependent on the ratio between the components STAT1, STAT2, and IRF9. For example, Huh7.5 cells that are not prestimulated with IFNα harbor per cell approximately 10^6^ molecules STAT1, while the abundance of IRF9 is 100‐fold lower. Therefore, the initial amount of ISGF3 that forms early upon INFα stimulation is very limited and only after IRF9 is *de novo* transcribed and translated, ISGF3 can become the dominant transcription factor complex. In HepG2‐hNTCP cells, which in comparison with Huh7.5 cells contain lower concentrations of STAT1 and STAT2 but higher amounts of IRF9, ISGF3 complexes can form earlier. Our analysis of primary human hepatocytes demonstrates that the ratio between STAT1, STAT2, and IRF9 varies substantially between different patient‐derived samples, suggesting patient‐specific dynamics in both ISGF3 formation and antiviral gene response. Of note, we are not excluding other connections between transcription factors and gene expression, but they are apparently not necessary to describe our experimental data. It has previously been reported that the IFNα‐inducible pSTAT1:pSTAT2 heterodimer preferentially binds to sequences that closely resemble GAS elements (Ghislain *et al*, [2001](#msb198955-bib-0020){ref-type="ref"}). Our experimental data are not contradicting this notion, as in our model, the pSTAT1:pSTAT2 heterodimer activates genes that are controlled by both GAS and ISRE sites. In our EMSA, we induced a supershift of GAS‐binding complexes with antibodies against STAT1, but not against STAT2, thus excluding major contributions of the pSTAT1:pSTAT2 heterodimer to the dynamics of GAS‐only regulated genes such as *IRF1* and *SOCS3*. To the best of our knowledge, our mathematical model for the first time describes sensitization of the IFNα‐induced signal transduction pathway quantitatively and provides a mechanistic understanding of dose‐dependent desensitization and hypersensitization of the IFNα pathway. This enabled us to show that the prestimulation dose determines whether the system is in a hypersensitized or a desensitized state and confirmed these findings by applying the model to measurements performed with a second ligand Roferon and another cell line HepG2‐hNTCP. The SOCS proteins play an important role in the negative regulation of signal transduction through cytokine receptors. The transcription of various SOCS proteins is upregulated upon cytokine stimulation, whereof specifically SOCS1 and SOCS3 are known to inhibit IFNα signal transduction (Krebs & Hilton, [2001](#msb198955-bib-0030){ref-type="ref"}). As revealed by crystal structure analysis, SOCS1 binds to the JAK1 kinase domain and the Elongin B/C adaptor complex and thereby acts as a direct inhibitor of the catalytic activity of JAK1, JAK2, and TYK2. It was also proposed that besides inhibiting downstream pathway activation, SOCS1 prevents JAK autophosphorylation and it was hypothesized that SOCS1 distinct from SOCS3 might not require receptor binding (Liau *et al*, [2018](#msb198955-bib-0037){ref-type="ref"}). In addition to their different mode of action, SOCS proteins also differ in their binding affinities for target proteins, rendering SOCS3 much less potent than SOCS1. We here showed that while *SOCS1* is expressed upon IFNα stimulation for more than 24 h and thereby contributes to long‐term pathway desensitization, *SOCS3* expression is transient and returns to basal levels 8 h after IFNα stimulation. This rapid but transient GAS‐dependent induction of SOCS3 mRNA is meditated by the early formation of pSTAT1 homodimers, while the GAS‐ and ISRE‐dependent SOCS1 expression is controlled by late formation of pSTAT1:pSTA2 heterodimers and ISGF3 complex. Thus, we observed a temporal division of labor by the feedback proteins SOCS1 and SOCS3 in regulating IFNα signal transduction, reminiscent of the ligand dose‐dependent division of labor observed for CIS and SOCS3 in Epo‐induced JAK2/STAT5 signal transduction (Bachmann *et al*, [2011](#msb198955-bib-0003){ref-type="ref"}). Besides these negative regulatory effects of the SOCS proteins, it was shown that USP18 inhibits IFNα signal transduction by binding to IFNAR2 and thereby inhibiting downstream substrate phosphorylation (Malakhova *et al*, [2006](#msb198955-bib-0044){ref-type="ref"}). A pivotal role of USP18 in desensitization of IFNα signal transduction was established based on knockdown, knockout, and overexpression experiments. It was observed that knockout of the USP18 gene in mouse embryonic fibroblasts and knockdown of USP18 expression in the human hepatoma cell line Huh7.5 lead to prolonged responsiveness to IFNα and enhanced antiviral efficacy against HCV (Randall *et al*, [2006](#msb198955-bib-0057){ref-type="ref"}). In complementary experiments, overexpression of the USP18 protein in HLLR1‐1.4 cells led to a strong reduction in the levels of pSTAT1 and pSTAT2 upon stimulation with IFNα. Similarly, prestimulation with IFNβ resulted in the induction of USP18 protein and concomitantly prevented the induction of pSTAT1 as wells as pSTAT2 upon stimulation with IFNα (Francois‐Newton *et al*, [2011](#msb198955-bib-0016){ref-type="ref"}). Further, overexpression of EGFP‐USP18 under the control of the CMV promoter resulted in a reduction of the co‐localization of HaloTag‐IFNAR1 and SNAPf‐IFNAR2c in U5A cells treated with IFNα (Wilmes *et al*, [2015](#msb198955-bib-0076){ref-type="ref"}). USP18^−/−^ mice injected with IFNα displayed a higher amplitude of STAT1 phosphorylation in the liver compared to control mice, retained responsiveness to a second IFNα injection, and displayed elevated pSTAT1 levels at all examined time points (Sarasin‐Filipowicz *et al*, [2009](#msb198955-bib-0062){ref-type="ref"}). Taken together, it was proposed that USP18 causes desensitization of IFNα signal transduction by impairing the formation of functional IFNα‐binding sites (Francois‐Newton *et al*, [2011](#msb198955-bib-0016){ref-type="ref"}). In line with these findings, we observed in Huh7.5 cells that knockdown of USP18 by siRNA transfection in combination with IFNα prestimulation resulted in sustained phosphorylation levels of STAT1 and STAT2 as well as sustained expression of target genes over 24 h, thus supporting the role of USP18 as a negative regulator contributing to long‐term desensitization of the IFNα signal transduction pathway. However, our experiments showed that cells that harbor elevated levels of USP18 due to overexpression do not present the same extent of pathway desensitization as parental cells prestimulated with IFNα. These results suggested that USP18 is necessary but not sufficient for desensitization of IFNα signal transduction. Based on our calibrated mathematical model, we proposed a mechanism whereby USP18 and SOCS1 act together on reducing the available receptor copy numbers on the cell surface, suggesting USP18 as a cofactor for SOCS1‐mediated receptor degradation. We have previously shown using Epo‐induced AKT and ERK signal transduction as an example that the abundance of pathway components plays a crucial role in cell context‐specific pathway regulation (Adlung *et al*, [2017](#msb198955-bib-0001){ref-type="ref"}). In the presented study, we observed major differences in the response to repeated IFNα stimulation between primary human hepatocytes isolated from individual patients and detected a high patient‐to‐patient variability in basal protein levels of the IFNα signal transduction pathway. The mathematical model predicted that the prevailing level of USP18 defines at which interferon dose the turning point between hyper‐ and desensitization of the pathway is located. It was previously proposed that the initial expression of USP18 serves as a predictor for sustained viral release in chronic HCV patients prior to receiving an interferon‐based triple therapy. However, the predictive value of USP18 has been controversially discussed. It was suggested that high initial expression levels of USP18 in peripheral blood mononuclear cells correlate with a better response to the treatment (Frankova *et al*, [2015](#msb198955-bib-0017){ref-type="ref"}). On the other hand, the results of another study on chronically HCV‐infected patients showed that the response to IFNα‐based treatment was linked to cell‐specific ISG activation patterns. The ISG baseline in the group of non‐responders was lower in macrophages, but higher in hepatocytes, which might explain these discrepancies (Chen *et al*, [2010](#msb198955-bib-0010){ref-type="ref"}). We identified by simulating a virtual patient cohort based on measured patient‐specific differences the protein abundance of STAT2 as the best predictor for the patient‐specific antiviral response. The protein abundance of STAT1, correlated less with the patient‐specific hypersensitization of the antiviral response. These results differ from pathway hypersensitization observed by Hu *et al* ([2002](#msb198955-bib-0024){ref-type="ref"}) upon IFNγ prestimulation, showing that STAT1 is in their context the main transcription factor and accordingly the key component for pathway hypersensitization. In Huh7.5, HepG2‐hNTCP and the six patient‐derived primary human hepatocytes, the abundance of STAT1 is one order of magnitude higher than the abundance of STAT2, while in the monocytes used to investigate IFNγ‐induced pathway hypersensitization STAT1 protein levels were close to the detection limit, revealing cell type‐specific differences in the protein abundance of STAT1. In addition, IFNγ signal transduction relies on the pSTAT1 homodimer as the key transcription factor complex, while the amounts of STAT2 are crucial for the formation of the ISGF3 complex. By means of our mathematical model, uncertainties of predictions can be computed based on the input data of the model (Kreutz *et al*, [2012](#msb198955-bib-0032){ref-type="ref"}; Kaschek *et al*, [2019](#msb198955-bib-0027){ref-type="ref"}). Of note, the findings derived from the simulation of the virtual patient cohort do not account for uncertainties of clinical measurements. The experimental data and analyses by the mathematical model demonstrated that control of the IFNα‐induced signal transduction is multifactorial and that the different components determine distinct aspects of the dynamics of pathway activation. The amount of IRF9 controls how fast ISGF3 complexes are formed and thereby the speed of the response, whereas the abundance of STAT2 determines how many ISGF3 complexes can be formed and herewith the extent of an antiviral response. As a consequence, USP18 determines pathway sensitization and STAT2 is a predictor of the patient‐specific antiviral response. The activation of the interferon pathway is an important response of the innate immune system to protect from viruses and tumors. In chronic hepatitis C virus (HCV) infection, it has previously been shown that patients with strong ISG‐signatures have a lower chance of responding to treatment with IFNα, clearly demonstrating the *in vivo* relevance of interferon pathway desensitization (Chen *et al*, [2005](#msb198955-bib-0009){ref-type="ref"}). While interferon therapy is no longer relevant for chronic HCV infection due to the approval of highly effective direct‐acting antivirals (Pawlotsky *et al*, [2015](#msb198955-bib-0051){ref-type="ref"}), it is an effective therapy for chronic HBV infection with regard to a functional cure, i.e., HBsAg loss (Lok *et al*, [2017](#msb198955-bib-0039){ref-type="ref"}). However, only a subset of patients achieves a sustained virological response after interferon therapy. In addition, interferon therapy is associated with considerable side effects. Thus, approaches and biomarkers that are helpful to identify patients that would benefit from interferon therapy are of great importance. Importantly, our findings might also be of relevance for other diseases. Indeed, it was recently shown that the interferon response activated by the PARP inhibitor Niraparib was able to potentiate the efficacy of checkpoint inhibitors used in cancer immunotherapy (Wang *et al*, [2019](#msb198955-bib-0075){ref-type="ref"}). Checkpoint inhibitors act by blocking inhibitory immune pathways and are used to treat various types of cancers (Le *et al*, [2015](#msb198955-bib-0034){ref-type="ref"}). However, response rates greatly differ between cancer etiologies and in patients with immune‐inactive tumors with low heterogeneity of intratumor neo‐antigens, responses are mostly poor (McGranahan *et al*, [2016](#msb198955-bib-0046){ref-type="ref"}). Thus, mathematical model‐based interferon pathway modulation could help to sensitize such tumors to checkpoint blockade. Collectively, we show that the abundance of STAT2 and of USP18, in combination with information on patient‐specific IFNα levels allow us to propose with our calibrated mathematical model an IFNα treatment regime to prevent pathway desensitization and to optimize an antiviral or anti‐tumor response. Materials and Methods {#msb198955-sec-0010} ===================== Reagents and Tools table {#msb198955-sec-0011} ------------------------ Reagent/ResourceReference or SourceIdentifier or Catalog Number**Experimental models**Huh7.5Blight *et al* ([2002](#msb198955-bib-0005){ref-type="ref"})HepG2‐hNTCPNi *et al* ([2014](#msb198955-bib-0049){ref-type="ref"})Primary human hepatocytesUniversity of Leipzig/University Hospital HeidelbergPlasma samplesUniversity Hospital FreiburgHuh7/LucUbiNeoLohmann and Bartenschlager ([2014](#msb198955-bib-0038){ref-type="ref"})**Recombinant DNA**Human USP18 cDNAGenomics and Proteomics Core Facility of the DKFZ<https://www.ncbi.nlm.nih.gov/nuccore/AL136690>pMOWS‐TreT‐puroPfeifer *et al* ([2010](#msb198955-bib-0052){ref-type="ref"})**Antibodies**Phospho‐Stat1 (Tyr701)Cell Signaling9167Phospho‐Stat2 (Tyr690)Cell Signaling4441USP18Cell Signaling4813STAT1Merck06‐501STAT2Merck06‐502IRF9/ISGF3cBecton Dickinson610285IRF9Abcamab126940IRF9 for IPCell Signaling76684CalnexinEnzo Life SciencesAdi‐SPA‐860HDAC1Santa Cruzsc81598β‐ActinSigma‐AldrichA5441SOCS3Abcamab16030SOCS3 for IPMerck04‐004Goat anti‐rabbit HRPDianova111‐035‐045Goat anti‐mouse HRPDianova115‐035‐146Goat anti‐Rabbit IRDye 800CWLI‐COR Biosciences926‐32211**Oligonucleotides and other sequence‐based reagents**Primers for quantitative RT‐PCR of human genesThis studysee Table [1](#msb198955-tbl-0001){ref-type="table"}ON‐TARGETplus Human USP18 siRNADharmacon (GE healthcare)11274ON‐TARGETplus Non‐targeting pool siRNADharmacon (GE healthcare)D‐001810‐10‐20GAS‐binding region of the IRF1 promoter for EMSAThis study5′‐CATTTCGGGGAAATCAGGC‐3′**Chemicals, Enzymes, and other reagents**Human IFN Alpha A (Alpha 2a)PBL Assay Science11000‐1Roferon‐ARochePZN 08543409Human IFN GammaR&D Systems285‐IF‐100DoxycyclineClontech (Fisher Scientific)NC0424034Protein G sepharose beadsGE Healthcare17‐0618‐01Protein A sepharose beadsGE Healthcare17‐0780‐01ECL Western Blotting ReagentsGE HealthcareRPN2235/RPN2236Pierce BCA Protein Assay KitThermo‐Fisher23225RNeasy kitQiagen74136QIAshredder spin columnQiagen79656High Capacity cDNA Reverse Transcription KitApplied Biosystems4368814Lipofectamine RNAiMaxInvitrogen13778100\[γ‐^32^P\]‐adenosine triphosphate (3000 Ci/mmol)PerkinElmerBLU002H250UCT4 polynucleotide kinaseNew England BiolabsM0201SIllustra ProbeQuant G‐50 Micro ColumnsGE Healthcare28903408poly\[dI‐dC\]Sigma10108812001**Software**GelInspectorSchilling *et al* ([2005](#msb198955-bib-0064){ref-type="ref"})R package dMod version 04Kaschek ([2017](#msb198955-bib-0026){ref-type="ref"}); Kaschek *et al* ([2019](#msb198955-bib-0027){ref-type="ref"})R package blotit version 01Kaschek ([2011](#msb198955-bib-0025){ref-type="ref"})Promotor analysis Findpatterns of the GCG sequence analysis package using W2HSenger *et al* ([1998](#msb198955-bib-0068){ref-type="ref"})Geneious v11.1https://www.geneious.comLightCycler480SW1.5.1Rochetrust R package Version 0.1‐7Geyer ([2004](#msb198955-bib-0019){ref-type="ref"})Image Quant TLGE Healthcare**Other**InfiniteF200Pro plate readerTecanSonopulsBandelinImageQuant LAS4000GE HealthcareOdyssey near‐infrared fluorescence scannerLI‐COR BiosciencesNanodrop2000Thermo ScientificLigthCycler480Roche Methods and Protocols {#msb198955-sec-0012} --------------------- ### Cell culture, primary cells, and plasma samples {#msb198955-sec-0013} The human hepatocellular carcinoma cell lines Huh7.5 and HepG2‐hNTCP were kindly provided by Ralf Bartenschlager, University of Heidelberg, Heidelberg, Germany and Stephan Urban, University Hospital Heidelberg, Heidelberg, Germany, respectively (Blight *et al*, [2002](#msb198955-bib-0005){ref-type="ref"}; Ni *et al*, [2014](#msb198955-bib-0049){ref-type="ref"}). Huh7.5 cells were cultivated in growth medium containing sodium pyruvate (Dulbecco\'s Modified Eagle Medium \#31053 (Gibco), 10% FCS (Gibco), 1% GlutaMAX (Gibco), 1 mM Sodium pyruvate (Gibco), 100 U/ml penicillin⁄streptomycin (Gibco)), while HepG2‐hNTCP cells were cultivated in the absence of sodium pyruvate and using 1% Glutamin (Gibco) instead of GlutaMAX. Cell line authentication was performed using Multiplex Cell Authentication by Multiplexion (Heidelberg, Germany) as described (Castro *et al*, [2013](#msb198955-bib-0006){ref-type="ref"}). The SNP profiles matched known profiles or were unique. Purity of cell lines was validated using the Multiplex cell Contamination Test by Multiplexion (Heidelberg, Germany) as described (Schmitt & Pawlita, [2009](#msb198955-bib-0066){ref-type="ref"}). No Mycoplasma, SMRV, or interspecies contamination was detected. Primary human hepatocytes were prepared at the University of Leipzig and at the University Hospital Heidelberg. Informed consent of the patients for the use of tissue for research purposes was obtained corresponding to the ethical guidelines of University of Leipzig and University Hospital Heidelberg, respectively. Tissue samples were acquired by partial hepatectomy and originate from healthy sections of resected liver tissue. Hepatocytes were isolated as described recently (Kegel *et al*, [2016](#msb198955-bib-0029){ref-type="ref"}), and hepatocytes were cultivated in adhesion medium (Williams' Medium E (Biochrom F1115), 10% FCS (Gibco), 0.1 μM dexamethasone, 0.1% insulin, 2 mM [l]{.smallcaps}‐glutamine (Gibco), 100 U/ml penicillin⁄streptomycin (Gibco)). Plasma samples from patients with chronic HBV infection were obtained after informed consent at the University Hospital Freiburg (ethics committee approval number: 227/15). Plasma levels of IFNα were assessed by a custom multiplex assay (Eve Technologies Corp, Canada). ### siRNAs transfection, plasmids, and retroviral transduction {#msb198955-sec-0014} For knockdown studies, cells were transfected with 50 nM siRNA using Lipofectamine RNAiMax (Invitrogen) according to manufacturer\'s protocol. Cells were incubated with the siRNA complexes for 20 h. The following siRNAs of Dharmacon (GE healthcare) were used ON‐TARGETplus Human USP18 (11274) siRNA---SMARTpool, and ON‐TARGETplus Non‐targeting pool. *USP18* cDNA (<https://www.ncbi.nlm.nih.gov/nuccore/AL136690>) was provided by the Vector and Clone Repository of the Genomics and Proteomics Core Facility of the DKFZ and subsequently cloned in pMOWS‐TreT‐puro (Pfeifer *et al*, [2010](#msb198955-bib-0052){ref-type="ref"}) using MefI/EcoRI and BamHI restriction enzymes (NEB). For stable transduction, 800,000 phoenix ampho cells were seeded in 6‐well plates (TPP) and the next day co‐transfected with 8 μg pMOWS‐TreT‐USP18‐puro or pMOWS‐TreT and 2 μg pMOWS‐TAM2 using calcium phosphate precipitation in growth medium supplemented with 25 μM chloroquine. After 8‐h incubation, medium was replaced by growth medium and incubated overnight. The next day supernatant was harvested, filtered, and supplemented with 8 μg/ml polybrene. 1 ml of supernatant was added to 200,000 Huh7.5 cells seeded in 6‐well plates (TPP), which were transduced by centrifugation for 3 h at 340 *× g* at 37°C. Selection was performed using 0.75 μg/ml puromycin (Sigma), starting 48 h after transduction. ### Time course and sensitization experiments {#msb198955-sec-0015} 600,000 Huh7.5 cells or 1,000,000 HepG2‐hNTCP were seeded in 6‐well plate format (TPP) 1 day in advance. Prior to stimulation, cells were washed three times with DPBS (Pan Biotech) and growth factor‐depleted in starvation medium (Dulbecco\'s Modified Eagle Medium \#31053 (Gibco), 1% (*v*/*v*) GlutaMAX (Gibco), 1 mM Sodium pyruvate (Gibco)) supplemented with 1 mg/ml BSA and 25 mM HEPES (Gibco) for 3 h (Huh7.5 cells). HepG2‐hNTCP cells were growth factor‐depleted overnight (15 h) in starvation medium without sodium puryvate and HEPES. The Huh7.5 cells were kept in 1.5 ml of the indicated medium, and the HepG2‐hNTCP were cultivated in 1 ml of the medium described above. Due to these differences in media volume, the amount of Roferon added per ml was adjusted to ensure that the same total amount of Roferon was added per well. For co‐immunoprecipitation experiments, 1.5 million Huh7.5 cells or 2.5 million HepG2‐hNTCP were seeded on 60 mm tissue culture dishes (TPP) and kept in 3.7 ml of the respective medium. After growth factor depletion, cells were stimulated on a 37°C heating block by addition of interferon alpha 2a (PBL 11000‐1), Roferon (Roche, PZN 08543409), or with recombinant human interferon gamma (R&D, 285‐IF‐100) and harvested at different time points. For sensitization experiments, cells were prestimulated with IFNα and stimulated 24 h later by addition of IFNα. For primary human hepatocytes, 1 or 1.5 million viable cells were seeded in 6‐well collagen‐coated plates (Bio Coat, Corning) 1 day prior to the experiment. The next day, cells were gently washed twice with DPBS (PAN Biotech) before cells were growth factor‐depleted for 3 h in starvation medium (Williams' Medium E (Biochrom F1115), 2 mM [l]{.smallcaps}‐glutamine (Gibco), 100 U/ml penicillin⁄streptomycin (Gibco)) prior to the experiment. ### Equipotent concentration of IFNα and Roferon {#msb198955-sec-0016} For model purposes, interferon concentrations given in units/ml and μg/ml were converted to nM based on information supplied by the datasheet (IFNα‐2a) or product information (Roferon). In addition, the activity of Roferon (Roche) and IFNα‐2a (PBL) were compared using the Huh7/LucUbiNeo cell line (Lohmann & Bartenschlager, [2014](#msb198955-bib-0038){ref-type="ref"}), a Huh7‐Lunet cell line with a stably replicating HCV genotype 1b (Con1) subgenomic replicon under the selective pressure of G418 (0.5 mg/ml). The replicon contains a neomycin phosphatase as well as a firefly luciferase reporter gene instead of the viral structural genes and harbors replication‐enhancing mutations in the nonstructural genes (Con1‐ET). To perform the titration, 75,000 cells were seeded in 96 well plate format in the absence of G418 and the next day IFNα and Roferon was added in two‐step serial dilutions. After 48 h, cells were lysed in luciferase lysis buffer (1% Triton‐x 100, 25 mM glycyl‐glycine pH 7.8, 15 mM MgSO~4~, 4 mM EGTA pH 7.8, 10% glycerol, 1 mM DTT) and stored at −80°C. Luciferase activity was measured on a Mithras2 LB 943 (Berthold Technologies). Signal intensities were normalized to untreated cells and were fitted by four‐parameter Hill kinetics to determine the IC~50~ concentrations (Fig [EV4](#msb198955-fig-0004ev){ref-type="fig"}A). Based on these data, equipotent concentrations for IFNα and Roferon were calculated (Fig [EV4](#msb198955-fig-0004ev){ref-type="fig"}B). ### Cell lysis, immunoprecipitation and quantitative immunoblotting {#msb198955-sec-0017} Cellular fractionation was performed to obtain cytoplasmic and nuclear protein lysates. Lysis buffers were freshly supplemented with the protease inhibitors Aprotinin and AEBSF (Sigma). Cells were lysed in 250 μl cytoplasmic buffer (10 mM Hepes, 10 mM KCl, 0.1 mM EDTA, 0.1 mM EGTA, 1 mM NaF, 1 mM Na~3~VO~4~, 0.4% NP40) and gently scraped and transferred to Eppendorf tubes. Lysates were vortexed for 10 s and centrifuged at 1,000 *× g*, at 4°C for 5 min. Supernatants were transferred (cytoplasmic fraction) and pellets were washed with 250 μl washing buffer (10 mM Hepes, 10 mM KCl, 0.1 mM EDTA, 0.1 mM EGTA, 1 mM NaF, 1 mM Na~3~VO~4~,) and centrifuged at 1,000 *× g*, at 4°C for 5 min. Supernatants were discarded and 45 μl nuclear lysis buffer was added (20 mM Hepes, 25% Glycerin, 400 mM NaCl, 1 mM EDTA, 1 mM EGTA, 1 mM NaF, 1 mM Na~3~VO~4~, 0.4% NP40). Lysates were vortexed 10 s every 2 min for 15 min in total. Nuclear fraction was collected by taking the supernatant after 5 min centrifugation at 20 817 *× g* at 4°C. Total cell lysates were prepared by lysing cells in 1 × RIPA lysis buffer (1% NP40, 0.5% DOC, 0.1% SDS, 250 mM NaCl, 2.5 mM EDTA, 50 mM Tris pH 7.2). Cells were lysed in 250 μl lysis buffer, scraped, transferred to Eppendorf tubes, tumbled for 20 min at 4°C, and subjected to sonication (Sonopuls, Bandelin, for 30 s, with 75% amplitude, 0.1 s on 0.5 s off). Whole cell lysates were collected after 10 min centrifugation at 4°C at 20,817 *× g*. The concentration of protein lysates was determined by Pierce™ BCA Protein Assay Kit (Thermo‐Fisher) and measured on the InfiniteF200Pro plate reader (Tecan). 10 or 20 μg samples were prepared for quantitative immunoblotting. SOCS3 was immunoprecipitated overnight with SOCS3 antibody (Merck) and protein G sepharose beads (GE Healthcare) supplemented with 0.1 ng SBP‐SOCS3. For co‐immunoprecipitation experiments, 650 μg or 1,200 μg of total cell lysates were incubated overnight with STAT2 antibody (Merck) or IRF9 antibody (Cell Signaling) and protein A sepharose beads (GE Healthcare). Samples were loaded in randomized order to avoid correlated blotting errors (Schilling *et al*, [2005](#msb198955-bib-0064){ref-type="ref"}). Blots were developed using self‐produced ECL solutions (Solution 1: 0.1 M Tris pH 8.5, 2.5 mM Luminol, 0.4 mM p‐coumaric acid; Solution 2: 0.1 M Tris pH 8.5, 0.018% H~2~O~2~) or using ECL Western Blotting Reagents (GE healthcare) on the CCD camera‐based ImageQuant LAS4000 (GE Healthcare). To remove previous antibody signals, HRP groups were quenched with H~2~O~2~ as described previously (Sennepin *et al*, [2009](#msb198955-bib-0069){ref-type="ref"}) or antibodies were removed by incubation with stripping buffer (0.063 M Tris pH6.8, 2% SDS, 0.7% β‐mercaptoethanol) at 65°C. Bands were quantified using ImageQuant software (GE healthcare). For fluorescence‐based detection ([Appendix Fig S1](#msb198955-sup-0001){ref-type="supplementary-material"}), blots were developed using the Odyssey near‐infrared fluorescence scanner (LI‐COR Biosciences) using a secondary antibody coupled to IRDye 800CW near‐infrared dye. The following antibodies were used Phospho‐Stat1 (Tyr701) (58D6) \#9167; Phospho‐Stat2 (Tyr690) \#4441; USP18 (D4E7) \#4813, all from Cell Signaling. STAT1, CT \#06‐501; STAT2, CT \#06‐502 both from Merck. IRF9/ISGF3c \#610285 (Bectin Dickenson), Calnexin \#Adi‐SPA‐860 (Enzo Life Sciences), HDAC1 (10E2) \#sc81598 (Santa Cruz), β‐Actin \#A5441 (Sigma‐Aldrich), and SOCS3 \#ab16030 (Abcam). IP was performed using the following antibodies SOCS3 \#04‐004 (1B2), STAT2 CT \#06‐502, both from Merck, and IRF9 \#76684 (D2T8M) from Cell Signaling. Secondary antibodies include rabbit and mouse specific antibodies raised in goat, coupled to HRP (Dianova) and Goat anti‐Rabbit IRDye 800CW \#926‐32211 (LI‐COR Biosciences). ### Number of molecules per cell using recombinant proteins {#msb198955-sec-0018} cDNA of human USP18 (https://www.ncbi.nlm.nih.gov/nuccore/AL136690) was provided by Genomics and Proteomics Core Facility of the DKFZ and subsequently cloned in pGEX2T vector (GE Healthcare) using BamHI and EcoRI/MfeI (NEB) restriction sites. Recombinant proteins were produced upon IPTG addition in transformed BL21‐CodonPlus(DE3)‐RIL competent bacteria (Agilent) and were purified using GST or SBP isolation as described previously (Raia *et al*, [2011](#msb198955-bib-0056){ref-type="ref"}). SBP‐SOCS3 calibrator was kindly provided by Anja Zeilfelder (Klingmüller lab, DKFZ, Heidelberg). SBP‐STAT1ΔN, SBP‐STAT2ΔN, and GST‐IRF9 were established previously in our laboratory (Maiwald *et al*, [2010](#msb198955-bib-0041){ref-type="ref"}). Concentration of calibrators was determined using BSA protein standard (Pierce) on SDS‐PAGE gel stained with SimplyBlue Safe stain (Invitrogen) according to manufacturer\'s protocol. To determine molecules per cell, the cell number of Huh7.5 or HepG2‐hNTCP was counted with the Neubauer improved counting chamber for each treated condition. For primary human hepatocytes from Patients 1--3, a dilution curve was established, which was based on protein concentrations derived from different amounts of cells lysed in 250 μl 1 × RIPA lysis buffer. For primary human hepatocytes from Patient 4--6, cells were fixed with paraformaldehyde and nuclei were stained with DAPI. 16 images per condition were taken using a Motorized Widefield Microscope (Zeiss Cell Observer). Using Fiji software, the respective number of cells per dish was quantified. Different amounts of calibrators were spiked in 10 μg whole‐cell lysates and quantitative immunoblotting was performed with the indicated antibodies. The linear regions of the calibration curves were fitted with a linear regression model in R, and the amount of endogenous signal was interpolated. Uncertainties were computed as standard error of the mean of the different samples assuming log‐normally distributed signals. ### Quantitative RT‐PCR {#msb198955-sec-0019} Total RNA was extracted using RNeasy kit (Qiagen) according to manufacturer\'s instruction. Clearing of the lysates was achieved using QIAshredder spin column (Qiagen). RNA concentrations were determined by absorbance (Nanodrop2000, Thermo Scientific), and reverse transcription was performed with 1 μg of RNA in 20 μl according to manufacturer\'s instruction (High Capacity cDNA Reverse Transcription Kit from Applied Biosystems). Quantitative PCR was performed on the LigthCycler480 (Roche) using primers and dual hybridization probes in 2× Probes Master (Roche). Cycling protocol consisted of 5 min pre‐incubation at 95°C, 50 amplification cycles (95°C for 10 s, 60°C for 30 sec and acquisition at 72°C for 1 s), and 2 min cooling. Quantification cycles (Cq) were determined by absolute quantification with second derivative maximum method using the software LightCycler480SW1.5.1. Samples for calibration curve were included in each measurement to assess efficiency of primer hybridization. Data were normalized with the geometric mean of the reference genes hypoxanthine‐guanine phosphoribosyltransferase (*HPRT*), TATA box‐binding protein (*TBP*), and glyceraldehyde‐3‐phosphate dehydrogenase (*GAPDH*). Primers were designed using the Universal Probe Library Assay Design Center (Roche Applied Biosciences) and manufactured by Eurofins. The utilized UPL probes and primers sequences for human genes are listed in Table [1](#msb198955-tbl-0001){ref-type="table"}. ###### Primers for quantitative RT‐PCR of human genes Genes Accession \# Primer fwd Primer rev UPL Probe \# ----------- -------------- --------------------------- ---------------------------- -------------- *CXCL10* NM_001565.3 gaaagcagttagcaaggaaaggt gacatatactccatgtagggaagtga 34 *CXCL11* NM_005409.3 agtgtgaagggcatggcta tcttttgaacatggggaagc 76 *DDX58* NM_014314.3 tgtgggcaatgtcatcaaaa gaagcacttgctacctcttgc 06 *GAPDH* NM_002046 agccacatcgctcagacac gcccaatacgaccaaatcc 60 *HPRT* NM_000194.2 cgagcaagacgttcagtcct tgaccttgatttattttgcatacc 73 *HERC5* NM_016323.3 cttccagtgaaagtatcatcaagtg ccagagcaaaatgctttgatt 67 *IFI44L* NM_006820.3 tgacactatggggctagatgg ttggtttacgggaattaaactgat 15 *IFI6* NM_002038.3 gggctccgtcactagacctt aaccgtttactcgctgctgt 40 *IFIT2* NM_001547.4 tggtggcagaagaggaagat gtaggctgctctccaaggaa 27 *IFITM3* NM_021034.2 gatgtggatcacggtggac agatgctcaaggaggagcac 76 *IRF1* NM_002198.1 ttggccttccacgtcttg gagctgggccattcacac 36 *IRF2* NM_002199.3 tgaagtggatagtacggtgaaca cggattggtgacaatctcttg 56 *IRF9* NM_006084.4 aactgcccactctccacttg agcctggacagcaactcag 77 *ISG15* NM_005101.3 ggcttgaggccgtactcc ctgttctggctgaccttcg 24 *ISG56* NM_001548.3 gctccagactatccttgacctg agaacggctgcctaatttacag 9 *MX1* NM_30817.1 gagctgttctcctgcacctc ctcccactccctgaaatctg 42 *NMI* NM_004688.2 ttcaggcgctgctgtttt tgtgtcatctttatcagcttcca 24 *EIF2AK2* NM_002759.1 cggtatgtattaagttcctccatga gacaaagcttccaaccagga 62 *SOCS1* NM_003745.1 gccccttctgtaggatggta ctgctgtggagactgcattg 87 *SOCS3* NM_003955.3 tctccttcaattcctcagcttc gttcagcattcccgaagtgt 13 *STAT1* NM_007315.3 tgagttgatttctgtgtctgaagtt acacctcgtcaaactcctcag 32 *STAT2* NM_005419.2 ggaacagctggagacatggt tcctgatagctaaccaggcaac 17 *TBP* NM_003194.3 cggctgtttaacttcgcttc cacacgccaagaaacagtga 3 *TRIM21* NM_003141.3 tgagcggaaactgaaagtga tggagacctttagggggttt 24 *USP18* NM_017414.3 tatgtgagccaggcacgat tcccgacgtggaactcag 75 *ZNFX1* NM_021035.2 tcgctggcagctttatagg tggcgttcatagctgaggat 64 Primers are listed in 5′‐ to 3′‐end orientation. John Wiley & Sons, Ltd ### Transcription factor binding site identification {#msb198955-sec-0020} Promoter analysis of the following human genes was performed of a 3,000 bp region consisting of 1,250 bp in front and 1,750 bp inside the corresponding gene: *IRF1* (\>NC_000005.10:c132492039‐132489039 *Homo sapiens* chromosome 5, GRCh38.p13 Primary Assembly); *SOCS3* (NC_000017.11:78358329‐78361329 *Homo sapiens* chromosome 17, GRCh38.p13 Primary Assembly); *DDX58* (\>NC_000009.12:c32527446‐32524446 *Homo sapiens* chromosome 9, GRCh38.p13 Primary Assembly); *HERC5* (\>NC_000004.12:88455354‐88458354 *Homo sapiens* chromosome 4, GRCh38.p13 Primary Assembly); and *IFI44L* (\>NC_000001.11:78619137‐78622137 *Homo sapiens* chromosome 1, GRCh38.p13 Primary Assembly). The promoter analysis was performed using Findpatterns of the GCG sequence analysis package using W2H (Senger *et al*, [1998](#msb198955-bib-0068){ref-type="ref"}). The following consensus sequences were tested: GAS (gamma‐activated sequence) TTNCNNNAA (Darnell *et al*, [1994](#msb198955-bib-0011){ref-type="ref"}); and ISRE (interferon‐stimulated response element) TTTCNNTTYY (Dill *et al*, [2014](#msb198955-bib-0013){ref-type="ref"}). Gene annotation is displayed using Geneious v11.1 (Kearse *et al*, [2012](#msb198955-bib-0028){ref-type="ref"}). ### Electrophoretic mobility shift assay (EMSA) {#msb198955-sec-0021} Electrophoretic mobility shift assays were performed with nuclear protein lysates obtained from cellular fractionation. Oligonucleotides probes used in the assay were synthesized (Sigma) harboring the GAS‐binding region of the human IRF1 promoter (5′‐CATTTCGGGGAAATCAGGC‐3′). After annealing, oligonucleotides were end‐labeled with \[γ‐^32^P\]‐adenosine triphosphate (3,000 Ci/mmol; PerkinElmer) using the T4 polynucleotide kinase (New England Biolabs) and further purified by gel filtration on Illustra ProbeQuant G‐50 Micro Columns (GE Healthcare). Nuclear lysates (5 μg) were normalized in 19‐μl reaction mixtures containing 20 mM HEPES, pH 7.9; 1 mM DTT; 0.1 mM EDTA; 50 mM KCl; 1 mM MgCl~2~; 5% glycerol; 200 μg/ml BSA; and 1 μg poly\[dI‐dC\] (Sigma). The reaction was placed on ice for 20 min before incubating with ^32^P‐labeled oligonucleotide probes (10,000 cpm) for 20 min at room temperature. For the supershift samples, the lysate‐DNA mixture was incubated with 2 μg of antibodies recognizing either STAT1 (Merck, CT \#06‐501), STAT2 (Merck, CT \#06‐502), or IRF9 (Abcam, ab126940) for 10 min at room temperature. Samples were resolved on a 4.5% native polyacrylamide gel (37.5:1) in a 0.5 × Tris‐borate‐EDTA (TBE) buffer for 6 h at 130 V at 4°C. Gels were dried for 60 min at 80°C and visualized by PhosphorImager. ### Data processing and estimation of uncertainties {#msb198955-sec-0022} Immunoblot data were normalized to housekeepers Calnexin, Actin, HDAC1, or recombinant SBP‐SOCS3 using GelInspector (Schilling *et al*, [2005](#msb198955-bib-0064){ref-type="ref"}). For each target, data points were scaled together by means of the *R* package *blotIt* (Kaschek, [2011](#msb198955-bib-0025){ref-type="ref"}) assuming log‐normally distributed signals. Independent experiments that contained more than three overlapping data points with 1,400 pM IFNα treatment were used as a reference for scaling. Different scaling factors for each gel as well as time course values used for parameter estimation were simultaneously determined by generalized least squares estimation, with data points assumed to be log‐normally distributed. Uncertainties correspond to 68%‐confidence intervals of the estimated data points. For the control model (Huh7.5), 10,945 single data points ([Dataset EV1](#msb198955-sup-0003){ref-type="supplementary-material"}) were scaled by *blotIt* to obtain 1,902 data points with confidence intervals that served for calibration of the model ([Dataset EV2](#msb198955-sup-0004){ref-type="supplementary-material"}). In addition, the 16 determined amounts of molecules per cell of the feedback proteins were utilized for model calibration. For the validation of the control model with EMSA and protein data (Figs [4](#msb198955-fig-0004){ref-type="fig"}B and [EV3](#msb198955-fig-0003ev){ref-type="fig"}D), 134 single data points ([Dataset EV3](#msb198955-sup-0004){ref-type="supplementary-material"}) were scaled to obtain 45 data points with confidence intervals (Dataset EV4). For the validation of the control model with qRT‐PCR data (Fig [4](#msb198955-fig-0004){ref-type="fig"}C), 315 single data points ([Dataset EV3](#msb198955-sup-0005){ref-type="supplementary-material"}) were averaged to obtain 105 data points with standard error of the mean ([Dataset EV4](#msb198955-sup-0006){ref-type="supplementary-material"}). For the Roferon model (Fig [4](#msb198955-fig-0004){ref-type="fig"}D), 891 single data points ([Dataset EV7](#msb198955-sup-0009){ref-type="supplementary-material"}) were scaled to obtain 221 data points with confidence intervals ([Dataset EV8](#msb198955-sup-0010){ref-type="supplementary-material"}) and for the HepG2‐hNTCP model, 1,274 single data points ([Dataset EV9](#msb198955-sup-0011){ref-type="supplementary-material"}) were scaled to 305 data points with confidence intervals ([Dataset EV10](#msb198955-sup-0012){ref-type="supplementary-material"}). For the validation of the HepG2‐hNTCP model with qRT‐PCR data ([Appendix Fig S7C](#msb198955-sup-0001){ref-type="supplementary-material"}), 252 single data points ([Dataset EV11](#msb198955-sup-0013){ref-type="supplementary-material"}) were averaged to obtain 84 data points with standard error of the mean ([Dataset EV12](#msb198955-sup-0014){ref-type="supplementary-material"}). For patient‐derived primary human hepatocytes, no biological replicates were available. Here, experimental errors were estimated from the signal variance of the hepatocytes prestimulated with 1,400 pM IFNα, assuming that the corresponding underlying time course stays constant after stimulation ([Dataset EV13](#msb198955-sup-0015){ref-type="supplementary-material"}). ### Parameter estimation and model development for the Huh7.5 cell line {#msb198955-sec-0023} The modeling process was performed by means of the *R* package *dMod* (Kaschek, [2017](#msb198955-bib-0026){ref-type="ref"}; Kaschek *et al*, [2019](#msb198955-bib-0027){ref-type="ref"}). In total, the mathematical model consists of 41 species and 75 reactions that were derived by the law of mass‐action and Michaelis--Menten kinetics. The reactions are justified based on published literature ([Appendix Table S1](#msb198955-sup-0001){ref-type="supplementary-material"}). Observables were computed with respect to model states as indicated in [Appendix Table S2](#msb198955-sup-0001){ref-type="supplementary-material"}. Parameter values of the global optimum for the Huh7.5 core model and profile likelihood‐based confidence intervals are shown in [Appendix Table S3](#msb198955-sup-0001){ref-type="supplementary-material"}. Parameters were log‐transformed to ensure positivity and enable optimization over a broad range of magnitudes (Raue *et al*, [2013](#msb198955-bib-0059){ref-type="ref"}). Calculation of analytical steady‐state expressions (Rosenblatt *et al*, [2016](#msb198955-bib-0060){ref-type="ref"}) and application of model reduction for ODE models (Maiwald *et al*, [2010](#msb198955-bib-0041){ref-type="ref"}) was incorporated by a set of parameter transformations ([Appendix Table S4](#msb198955-sup-0001){ref-type="supplementary-material"}). In some cases during the model simplification procedure, parameter values were fixed instead of changing the model structure to keep a biological meaningful model structure. Parameters were estimated by the method of maximum likelihood performing a deterministic multi‐start optimization of 1,000 randomly chosen parameter sets by means of the trust region optimizer *trust* (Geyer, [2004](#msb198955-bib-0019){ref-type="ref"}). Parameter values were not restricted by fixed borders. Instead, in order to prevent the optimizer from finding solutions with very low or high parameter values, we constrained the model parameters with a weak L~2~ prior that contributed with one to the likelihood, if the parameter differed by five orders of magnitude from 1. When computing the profile likelihood ([Appendix Fig S12](#msb198955-sup-0001){ref-type="supplementary-material"}), these L~2~ priors were substracted in order to ensure an exclusively data‐based identifiability analysis. To show reliability of the optimization, the 200 best optimization runs were displayed as a waterfall plot sorted by their objective values ([Appendix Fig S13](#msb198955-sup-0001){ref-type="supplementary-material"}; Raue *et al*, [2013](#msb198955-bib-0059){ref-type="ref"}). Different local optima were found multiple times, and the global optimum was found in 18 of the 200 cases. To test identifiability of the parameters and to calculate confidence levels for the estimated values, the profile likelihood (Raue *et al*, [2009](#msb198955-bib-0058){ref-type="ref"}) was computed for each parameter. In total, 12 initial values, 17 scaling and offset parameters and 56 dynamical parameters were estimated for the Huh7.5 model. Profile likelihoods ([Appendix Fig S12](#msb198955-sup-0001){ref-type="supplementary-material"}) showed finite confidence intervals for 74 out of 85 parameters. From the remaining parameters, three showed confidence intervals open to minus infinity and eight were open to plus infinity. However, due to the biological significance of the parameters and to ensure that the model selection analysis and the application of the model to different cell systems by L~1~ regularization was performed without additional constraints, no further model reduction was applied. Estimated parameter values with corresponding confidence intervals and the resulting model parameters obtained after transformation are summarized in [Appendix Table S4](#msb198955-sup-0001){ref-type="supplementary-material"}. For the receptor model, different structures were evaluated by means of the Bayesian information criterion (Schwarz, [1978](#msb198955-bib-0067){ref-type="ref"}). ### Application of the Huh7.5 model to HepG2‐hNTCP and primary human hepatocytes {#msb198955-sec-0024} To analyze experimental measurements performed with the Roferon, the calibrated Huh7.5 model (control model) was utilized with all parameters being fixed except for scaling and offset parameters as well as the binding affinity of the ligand (parameter BindIFN) that were re‐estimated by the method of maximum likelihood. For analysis of the HepG2‐hNTCP data, the previously estimated binding affinity for Roferon was fixed. Scaling and offset parameters as well as parameters corresponding to the molecules per cell in the system, i.e., totSTAT1, totSTAT2, totIRF9, and synthUSP18, were re‐estimated. The four parameters, synthUSP18mRNAbasal_OE, synthUSP18_inh, synthUSP18mRNAbasal_inh, and synthUSP18mRNA_inh, that were used for incorporation of inhibitor and overexpression conditions were not considered. The remaining 60 parameters of the model were estimated with an additional L~1~ constraint as previously described (Merkle *et al*, [2016](#msb198955-bib-0047){ref-type="ref"}). In our case, a combination of L~1~ and L~2~ prior, i.e., an elastic net (Zou & Hastie, [2005](#msb198955-bib-0079){ref-type="ref"}), was applied that penalizes least when parameters take the exact value as in the control model. Penalization strength was chosen such that L~1~ and L~2~ prior contribute to the same extent if the parameter value differed by one order of magnitude to the control model. Optimization was performed by means of a trust region optimizer which was adapted to L~1~ regularization as part of the dynamic modeling framework *dMod*. For each of 25 different regularization strengths, we performed 200 optimization runs starting from randomly chosen parameter sets. The 5,000 resulting fits were evaluated by means of a combination of goodness‐of‐fit and number of parameters being different from the control model. Based on Bayesian information criterion, we defined the objective value 4 × ln(*n*) × *k* − 2 × ln(*L*), where *n* is the number of data points, *k* the number of parameters different from the control model and *L* the value of the likelihood function. Compared to classical BIC, our definition favors models with low amounts of necessary L~1~ parameters. The resulting parameter estimates are summarized in [Appendix Tables S5 and S6](#msb198955-sup-0001){ref-type="supplementary-material"}. For the HepG2‐hNTCP model, we obtained two out of the 60 L~1~ parameters (indicated by ratio_parameter) to be different from Huh7.5. For the analysis of primary human hepatocyte data, we performed L~1~ regularization similar to the case of HepG2‐hNTCP. For each of six patients, parameters defining the number of molecules per cell of the proteins as well as scaling and offset parameters were re‐estimated. The remaining primary human hepatocyte‐specific parameters were assumed to be the same for all patients and were estimated by means of L~1~ regularization (see [Appendix Table S7](#msb198955-sup-0001){ref-type="supplementary-material"} for parameter estimates). For the primary human hepatocyte model, we obtained five out of 60 L~1~ parameters to be different from Huh7.5 cells. The gene‐specific parameters that were estimated to link the occupied binding sites predicted by the mathematical model to the respective target genes (Fig [4](#msb198955-fig-0004){ref-type="fig"}C) are listed in Table S8. Author contributions {#msb198955-sec-0027} ==================== Experimental methods: FK; MT. Main experiments: FK; MT. Mathematical model: MR; TM. Model calibration and analysis: MR. Experiments with Roferon in Huh7.5 and determination of number of molecules per cell of primary human hepatocytes: TN. Electrophoretic mobility shift assays: VGM. Determination of equipotent doses of IFNα and Roferon: CD. Preparation of primary human hepatocytes from patients: AV; MW; ST; KH; GD; DS. Measuring IFNα levels in cHBV patients: TB. Project design: MB; JT; MS; UK. Manuscript writing: FK; MR; MT; MS; UK. Preparation of figures: FK; MR; MT; MS; UK. Manuscript revision and editing: TB; MB; JT; MS; UK. Project funding: MB; JT; UK. Approval of manuscript: all authors. Conflict of interest {#msb198955-sec-0028} ==================== The authors declare that they have no conflict of interest. Supporting information ====================== ###### Appendix ###### Click here for additional data file. ###### Expanded View Figures PDF ###### Click here for additional data file. ###### Dataset EV1 ###### Click here for additional data file. ###### Dataset EV2 ###### Click here for additional data file. ###### Dataset EV3 ###### Click here for additional data file. ###### Dataset EV4 ###### Click here for additional data file. ###### Dataset EV5 ###### Click here for additional data file. ###### Dataset EV6 ###### Click here for additional data file. ###### Dataset EV7 ###### Click here for additional data file. ###### Dataset EV8 ###### Click here for additional data file. ###### Dataset EV9 ###### Click here for additional data file. ###### Dataset EV10 ###### Click here for additional data file. ###### Dataset EV11 ###### Click here for additional data file. ###### Dataset EV12 ###### Click here for additional data file. ###### Dataset EV13 ###### Click here for additional data file. ###### Model EV1 ###### Click here for additional data file. ###### Review Process File ###### Click here for additional data file. The authors thank the Genomics and Proteomics Core Facility of the German Cancer Research Center (DKFZ), for providing cDNA of USP18. Furthermore, we would like to thank Agnes Hotz‐Wagenblatt for excellent assistance with the GCG sequence analysis package using W2H for SOCS3 promoter analysis. Furthermore, we would like to thank Anja Zeilfelder for providing the SBP‐SOCS3 calibrator and Luisa Schwarzmüller for generation of the SBML model file. The human hepatocellular carcinoma cell lines, Huh7.5 and HepG2‐hNTCP, were kindly provided by Ralf Bartenschlager and Stephan Urban, respectively. The authors thank Raphael Engesser, Helge Hass, Daniel Kaschek, Christian Tönsing, Clemens Kreutz, and Joep Vanlier for fruitful discussions during the development of the mathematical model. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)---Project number 272983813---TRR 179. This work was also supported by the DFG within FOR1202 and within the Germany\'s Excellence Strategy (CIBSS---EXC‐2189---Project ID 390939984) and by the German Ministry of Education and Research (BMBF) within "Multi‐Scale Modeling of Drug Induced Liver Injury" (MS_DILI, 031L0074A, 031L0074B), within the Liver Systems Medicine network (LiSyM, 031L0042, 031L0048) and within the EraSysAPP consortium IMOMESIC (031A604A, 031A604B, 031A604C). We further acknowledge support by the Ministerium für Wissenschaft, Forschung und Kunst Baden‐Württemberg (MWK) through bwHPC. Data availability {#msb198955-sec-0025} ================= The model structure and equations can be found in [Model EV1](#msb198955-sup-0016){ref-type="supplementary-material"} (Model_EV1.xml, exemplified for Huh7.5 cells stimulated with 1,400 pM IFNα. This model was deposited in BioModels (Chelliah *et al*, [2015](#msb198955-bib-0007){ref-type="ref"}) and assigned the identifier MODEL2005110001 (<https://www.ebi.ac.uk/biomodels/MODEL2005110001>). The raw data files from quantitative immunoblots and quantitative RT‐PCR data before and after processing with blotIt have been provided as Datasets [EV1](#msb198955-sup-0015){ref-type="supplementary-material"}--[EV13](#msb198955-sup-0015){ref-type="supplementary-material"}. [^1]: These authors contributed equally to this work [^2]: These authors contributed equally to this work as last authors | Mid | [
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######################################################################## ## ## Copyright (C) 1995-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {} center (@var{x}) ## @deftypefnx {} {} center (@var{x}, @var{dim}) ## Center data by subtracting its mean. ## ## If @var{x} is a vector, subtract its mean. ## ## If @var{x} is a matrix, do the above for each column. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## ## Programming Note: @code{center} has obvious application for normalizing ## statistical data. It is also useful for improving the precision of general ## numerical calculations. Whenever there is a large value that is common ## to a batch of data, the mean can be subtracted off, the calculation ## performed, and then the mean added back to obtain the final answer. ## @seealso{zscore} ## @end deftypefn function retval = center (x, dim) if (nargin != 1 && nargin != 2) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("center: X must be a numeric vector or matrix"); endif if (isinteger (x)) x = double (x); endif nd = ndims (x); sz = size (x); if (nargin != 2) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("center: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); if (n == 0) retval = x; else ## FIXME: Use bsxfun, rather than broadcasting, until broadcasting ## supports diagonal and sparse matrices (Bugs #41441, #35787). retval = bsxfun (@minus, x, mean (x, dim)); ## retval = x - mean (x, dim); # automatic broadcasting endif endfunction %!assert (center ([1,2,3]), [-1,0,1]) %!assert (center (single ([1,2,3])), single ([-1,0,1])) %!assert (center (int8 ([1,2,3])), [-1,0,1]) %!assert (center (logical ([1, 0, 0, 1])), [0.5, -0.5, -0.5, 0.5]) %!assert (center (ones (3,2,0,2)), zeros (3,2,0,2)) %!assert (center (ones (3,2,0,2, "single")), zeros (3,2,0,2, "single")) %!assert (center (magic (3)), [3,-4,1;-2,0,2;-1,4,-3]) %!assert (center ([1 2 3; 6 5 4], 2), [-1 0 1; 1 0 -1]) %!assert (center (1, 3), 0) ## Test input validation %!error center () %!error center (1, 2, 3) %!error <DIM must be an integer> center (1, ones (2,2)) %!error <DIM must be an integer> center (1, 1.5) %!error <DIM must be .* a valid dimension> center (1, 0) | Mid | [
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Suffolk broadband uptake triggers council windfall More than 20 per cent of local residents are now signed up to superfast broadband connections in Suffolk. Suffolk County Council has received a boost to funding following the successful uptake of superfast broadband by residents in its area. The number of properties able to connect to superfast broadband in the county has now exceeded 75,000, the East Anglian Daily Times reports. Achieving this key milestone means the Better Broadband for Suffolk Programme has now reached 20 per cent of potential users in the area and the council is set to receive additional funding to redouble its efforts to reach the remaining 80 per cent as a result. Council Leader Mark Bee told the news provider: "We are ... hitting significant milestones in the programme and it is vitally important that people who now have access to increased speeds and superfast fibre, take the opportunity to upgrade to these new services." A key target for the project will now be achieving innovative solutions to help drive increased access to superfast connections in those areas that have been deemed hard to reach to date. | Mid | [
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Primary Candida meningitis and chronic granulomatous disease. The occurrence of two rare entities in a single patient can be fortuitous or may signify some deeper relationship. A young boy was recently treated for primary Candida meningitis. Autopsy findings suggested to an experienced pathologist the presence of chronic granulomatous disease (CGD), unrecognized during his life. The patient's identical twin brother was tested and found to have the typical laboratory features of CGD. The literature on Candida meningitis was reviewed and 15 cases were discovered that apparently arose in the absence of recognized predisposing causes. All but one of these cases occurred in males, and most occurred during the first three decades of life. The case reports and literature review presented herein suggest that CGD should be suspected when a case of "primary" Candida meningitis is encountered. | High | [
0.6744186046511621,
29,
14
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[Epiphyseal chondroblastoma. Clinical and anatomo-radiographic aspects]. The clinical radiological and anatomohistological features of fourteen cases of epiphyseal chondroblastoma are described. The seat, origin, and evolution of the tumor are discussed. The diagnosis of the epiphyseal localization is easy, but there are same problems in the differential diagnosis of the epiphyseal-metaphyseal of metaphyseal forms. | High | [
0.6876640419947501,
32.75,
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The recent skydiving death of Sean Carey may have some interesting parallels for spaceflight and space exploration. As Abby Sewell said in the Los Angeles Times: The deaths reflect a divergent nationwide trend: equipment upgrades and safety rules have reduced overall skydiving fatalities among novices — but the smaller, more aerodynamically designed parachutes have allowed more experienced divers to take more risks. Increasingly, industry veterans said, fatal accidents involve experts attempting advanced maneuvers with high-performance equipment. We are likely to see a similar trend in human spaceflight over the next few decades. As suborbital and orbital spaceflight become more routine, safety will improve as operators benefit from experience (the learning-curve effect). At the same time, however, low-cost access to space and in-space infrastructure such as propellant depots will enable explorers to undertake riskier missions into deep space with increasing frequency. The result will be an increasing number of fatalities among NASA and commercial explorers on advanced missions to the Moon, the asteroids, Mars, and beyond, while near-space missions become safer and more routine. That should not be a cause for alarm, however. It is part of the normal process of opening a new frontier. | Mid | [
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--- abstract: | In this paper, a new class of positive semi-definite tensors, the MO tensor, is introduced. It is inspired by the structure of Moler matrix, a class of test matrices. Then we focus on two special cases in the MO-tensors: Sup-MO tensor and essential MO tensor. They are proved to be positive definite tensors. Especially, the smallest H-eigenvalue of a Sup-MO tensor is positive and tends to zero as the dimension tends to infinity, and an essential MO tensor is also a completely positive tensor. [**Key words.** ]{} [Positive (semi-)definite tensor, completely positive tensor, H-eigenvalue, MO-tensor, MO-like tensor, Sup-MO value.]{} [**AMS subject classifications.** ]{}[15A18, 15A69, 15B99.]{} author: - 'Yi Xu[^1]' - 'Jinjie Liu[^2]' - 'Liqun Qi[^3]' title: 'A NEW CLASS OF POSITIVE SEMI-DEFINITE TENSORS [^4]' --- Introduction ============ In recent decades, tensors, as the natural extension of matrices, have been more and more ubiquitous in a wide variety of applications, such as data analysis and mining, signal processing, computational biology and so on [@CZPA; @KB]. The positive (semi-)definiteness of tensors is an intrinsic property for tensors, which is closely related with the nonnegative polynomials. In 2005, the concepts of positive (semi-)definiteness and eigenvalues of matrices were extended to tensors [@Q]. Positive (semi-)definite tensors have widely applications in polynomial optimization, spectral hypergraph theory, magnetic resonance imaging and so on [@Q; @Q14; @QYW]. Though the verification of positive (semi-)definite tensors has been shown to be NP-hard by Hillar and Lim [@HL], the positive (semi-)definiteness of some tensors with special structures have been verified, such as even order symmetric diagonally dominated tensors, even order symmetric B tensor, even order symmetric $M$-tensors and so on, see [@LQ16; @Q; @QL17; @QS; @ZQZ]. Furthermore, completely positive tensors, which is connected with nonnegative tensor factorization, also have significant applications in polynomial optimization problems, statistics, data analysis and so on. They were first introduced in [@QXX14]. An even order completely positive tensor is a positive semi-definite tensor. In [@QL], two well-known classes of test matrices, Pascal matrices and Lehmer matrices were extended to Pascal tensors and Lehmer tensors. They are easily checkable and were proved to be completely positive tensors [@QL]. There is another class of test matrices, the Moler matrices. A Moler matrix is a positive definite symmetric matrix. One of its eigenvalues is quite small, and it is usually used for testing eigenvalue computations. In the following section, we prove that the smallest eigenvalue of a Moler matrix approaches 0, when the dimension of the Moler matrix, $n\rightarrow+\infty$. Inspired by the good properties of Moler matrix, we construct a new class of positive semi-definite tensors. Since there have been $M$-tensors already, we name this new class of tensor as MO tensor, which come from first two letters of Moler. The remaining part of this paper is organized as follows. In Section 2, we review some basic concepts and preliminary results to help our work. The main results are given in Section 3. In that section, we construct MO tensors, which include Sup-MO tensors and essential MO tensors with the concept of MO value. Meanwhile, some related properties are proved. Some final remarks are made in Section 4. Preliminaries ============= In this part, we will review some basic definitions and lemmas which are useful in our following research. We call $\mathcal{A}(n,m)$ a real $m$th order $n$-dimensional tensor if $$\mathcal{A}(n,m)=(a_{i_1 \cdots i_m}), i_j\in[n], j\in[m],$$ where $[n] := \{1, \cdots, n\}$. All the real $m$th order $n$-dimensional tensors form a $n^{m}$-dimensional linear space denoted by $T_{n, m}.$ Furthermore, if all the entries $a_{i_1 \cdots i_m}$ of $\mathcal{A}(n,m)$ are invariant under any index permutation, $\mathcal{A}(n,m)$ is a symmetric tensor. Denote the set of all the real symmetric tensors of order $m$ and dimension $n$ by $S_{n, m}$. Obviously, $S_{n, m}$ is a linear subspace of $T_{n, m}.$ Let $\mathcal{A}(n,m)=(a_{i_1\cdots i_m})\in T_{n, m}$ and ${\bf x}\in\mathbb{R}^n.$ Then $\mathcal{A}(n,m){\bf x}^m$ is an $m$th degree homogeneous polynomial defined by $$\mathcal{A}(n,m) {\bf x}^m=\sum_{i_1, i_2, \cdots, i_m=1}^{n} a_{i_1 \cdots i_m}x_{i_1}x_{i_2} \cdots x_{i_m}.$$ We call tensor $\mathcal{A}(n,m)$ as a positive definite ([**PD**]{}) tensor if $\mathcal{A}(n,m){\bf x}^m > 0,$ for any non-zero vector ${\bf x}\in\mathbb{R}^n,$ and as positive semi-definite ([**PSD**]{}) tensor if $\mathcal{A}(n,m){\bf x}^m\geq 0,$ for any vector ${\bf x}\in\mathbb{R}^n.$ Let ${\bf x} =(x_1, x_2, \cdots, x_n)^{\top}\in\mathbb{R}^n,$ then ${\bf x}^{[m]}$ is a vector in $\mathbb{R}^n$ denoted as $${\bf x}^{[m]}=(x_1^m, x_2^m, \cdots, x_n^m)^\top .$$ To identify the positive (semi-)definiteness of tensors, the spectral theory of tensors plays an important role for the desired identification. In [@Q], H-eigenvalues and Z-eigenvalues of tensors were introduced. It was shown there that an even order symmetric tensor is positive (semi-)definite if and only if all of its H-eigenvalues or Z-eigenvalues are positive (nonnegative). Various easily checkable positive (semi-)definite tensors have been discovered consequently [@CLQ; @LWZZL; @QS; @ZQZ]. [@Q] Let $\mathcal{A}(n,m)\in T_{n, m}, \lambda\in\mathbb{R}.$ If $\lambda$ and a nonzero vector ${\bf x}\in\mathbb{R}^n$ are the solutions of the following polynomial equation: $$\mathcal{A}(n,m) {\bf x}^{m-1}=\lambda {\bf x}^{[m-1]},$$ then we call $\lambda$ an [**H-eigenvalue**]{} of $\mathcal{A}(n,m),$ and ${\bf x}$ an [**H-eigenvector**]{} of $\mathcal{A}(n,m)$ associated with the H-eigenvalue $\lambda.$ \[theo-1\] [@Q] Let $\mathcal{A}(n,m)\in S_{n, m},$ and $m$ be even. Then $\mathcal{A}(n,m)$ is positive definite (positive semi-definite) if and only if all of the H-eigenvalues of $\mathcal{A}(n,m)$ are positive (non-negative). Furthermore, we have \(1) $$\lambda_{min}(\mathcal{A}(n,m))=\min\frac{\mathcal{A}(n,m){\bf x}^m}{\|{\bf x}\|_m^m},$$ \(2) $$\lambda_{min}(\mathcal{A}(n,m))=\min \{\mathcal{A}(n,m){\bf x}^m:\|{\bf x}\|_m =1\},$$ where ${\bf x}\in\mathbb{R}^n,$ and $\|{\bf x}\|_m =(\sum_{i=1}^{n}|x_i|^m)^{\frac{1}{m}}.$ [@QL] Let $\mathcal{A}(n,m)\in S_{n, m}.$ We call $\mathcal{A}(n,m)$ a [**completely positive tensor**]{} if there exist an integer $r$ and some ${\bf u}^{(k)}\in\mathbb{R}_{+}^n, k\in [r]$ such that $$\mathcal{A}(n,m)=\sum_{k=1}^{r}({\bf u}^{(k)})^m.$$ [@QL] Let $\mathcal{A}(n,m)\in S_{n, m}.$ If $\mathcal{A}(n,m)$ is a completely positive tensor, then all the H-eigenvalues of $\mathcal{A}$ are nonnegative. [@JN] Let $\mathcal{A}(n,2)\in \mathbb{R}^{n\times n}$. We call $\mathcal{A}(n,2)$ the $n$-dimensional [**Moler matrix**]{} if $$\mathcal{A}(n,2)_{i,j}=\left\{ \begin{array}{cc} i, & i=j \\ \min\{i,j\}-2, & i\neq j \\ \end{array} \right..$$ In the following proposition, we give a proof to show that the Moler matrix is a positive definite matrix, and its smallest eigenvalue tends to zero in decreasing as its dimension tends to infinity. Let $\mathcal{A}(n,2)\in \mathbb{R}^{n\times n}$ be an $n$-dimensional Moler matrix. (1) $\mathcal{A}(n,2)$ is positive definite; (2) Let $\lambda_{min}(\mathcal{A}(n,2))$ be the smallest eigenvalue of $\mathcal{A}(n,2).$ Then $\lambda_{min}(\mathcal{A}(n,2))\searrow 0.$ \(1) We note that $\mathcal{A} (n,2)=LL^\top$, where $$L_{i,j}=\left\{ \begin{array}{cc} 1, & i=j \\ -1, & i>j \\ 0, & i<j \\ \end{array} \right..$$ Therefore, $\mathcal{A}(n,2)$ is positive definite. \(2) $0 < \lambda_{min}(\mathcal{A}(n+1,2))\leq\lambda_{min}(\mathcal{A}(n,2))$ are easily obtained. Assume that $ {\bf x}=\left(1,\frac{1}{2},\frac{1}{2^2},\cdots,\frac{1}{2^{n-1}}\right)^\top.$ We have $\displaystyle L^\top {\bf x} =\left( \begin{array}{c} \displaystyle\frac{1}{2^{n-1}} \\ \vdots\\ \displaystyle\frac{1}{2^{n-1}} \\ \end{array} \right),$ $$\frac{{\bf x}^\top \mathcal{A}(n,2){\bf x}}{{\bf x}^\top {\bf x}}=\frac{3n}{4^n-1}\geq \lambda_{min}(\mathcal{A}(n,2)),$$ which means $\lambda_{min}(\mathcal{A}(n,2))\searrow 0,$ when $n\rightarrow +\infty.$ Main Results ============ In order to introduce a new class of tensors with positive semi-definiteness, we first introduce concepts called the [**MO value**]{}, the [**MO set**]{} and the [**Sup-MO value**]{}. \(1) Let $m$ be an even number. We call $\alpha(m)$ as the [**MO value**]{}, if $\mathcal{A}(n,m) := \mathcal{M}(n,m)-\alpha(m)\mathcal{N}(n,m)$ is positive semi-definite for any $n$, where $$\label{1} \mathcal{M}(n,m)_{i_1,i_2,\cdots,i_m}=\left\{ \begin{array}{cc} i_1,&i_1=i_2=\cdots=i_m\\ \min\{i_1,i_2,\cdots,i_m\}, & else \\ \end{array} \right.,$$ $$\label{2} \mathcal{N}(n,m)_{i_1,i_2,\cdots,i_m}=\left\{ \begin{array}{cc} 0, & i_1=i_2=\cdots=i_m \\ 1, & else \\ \end{array} \right..$$ We call the set of all MO values as the [**MO set**]{} $\Omega(m);$ (2) We call $\alpha^*(m)=\sup\{\Omega(m)\}$ as the [**Sup-MO value**]{}. We also define [**Sub-MO value**]{} $\alpha_*(m)$ of $\Omega(m)$ as $\alpha_*(m)=\inf\{\Omega(m)\}$. It is worth noting that $\alpha(m)$ is a parameter only related to $m$. Hence, when we consider to explore its properties, it is necessary to show these properties still hold when $n\rightarrow\infty$. In this paper, we mainly focus on the properties of $\alpha^*(m)$. Based on the aforementioned concepts, MO tensors and Sup-MO tensors are given as following. Let $m$ be an even number. We call $\mathcal{A}(n,m)\in S_{n,m}$ a [**MO tensor**]{}, if $$\mathcal{A}(n,m)=\mathcal{M}(n,m)-\alpha(m)\mathcal{N}(n,m),$$ where $\mathcal{M}(n,m)$ and $\mathcal{N}(n,m)$ are defined in $(1)$ and $(2)$, respectively, and $\alpha(m)\in\Omega(m).$ \(2) We call $\mathcal{A}(n,m)\in S_{n,m}$ a [**Sup-MO tensor**]{}, if $$\mathcal{A}(n,m)=\mathcal{M}(n,m)-\alpha^*(m)\mathcal{N}(n,m).$$ The theorem in the following shows that the Sup-MO tensor $\mathcal{A}(n, m)$ can be reduced to the Moler matrix when $m = 2$. \[p-1\] Let $\Omega(m)$ be the MO set, $\mathcal{A}(n,m)\in S_{n,m}$ be a Sup-MO tensor. When $m=2$, we have $\alpha^*(2)=2=\max\{\Omega(2)\}.$ From the property of the Moler matrix, we get $2 \in \Omega(2)$. Then we need to prove that 2 is the Sup-MO value in this case. If $\alpha^*(2)>2,$ then there exists an $\alpha\in (2,\alpha^*(2))\cap\Omega(2)$ such that $$\mathcal{M}(n,2)-\alpha\mathcal{N}(n,2)=\mathcal{M}(n,2)-2\mathcal{N}(n,2)-(\alpha-2)\mathcal{N}(n,2),$$ where $\mathcal{M}(n,m)$ and $\mathcal{N}(n,m)$ are defined in $(1)$ and $(2)$, respectively. Let ${\bf x}=\left(1,\displaystyle\frac{1}{2},\cdots,\displaystyle\frac{1}{2^{n-1}}\right)^\top \in\mathbb{R}^n$, $${\bf x}^\top (\mathcal{M}(n,2)-\alpha\mathcal{N}(n,2)){\bf x}={\bf x}^\top (\mathcal{M}(n,2)-2\mathcal{N}(n,2)){\bf x}-(\alpha-2){\bf x}^\top \mathcal{N}(n,2){\bf x}.$$ Since $${\bf x}^\top (\mathcal{M}(n,2)-2\mathcal{N}(n,2)){\bf x}=\displaystyle\frac{3n}{4^n-1}, \ {\rm and}\ {\bf x}^\top \mathcal{N}(n,2){\bf x}= \displaystyle\frac{8}{3}-\frac{4}{2^{n-1}}+\frac{4}{3(4^{n-1})},$$ when $n\rightarrow +\infty$, we have $${\bf x}^\top (\mathcal{M}(n,2)-\alpha\mathcal{N}(n,2)){\bf x}<0,$$ which is against to $\alpha\in \Omega(2).$ Hence $\alpha^*(2)=2.$ In the following work, a special class of MO tensors, the essential MO tensors are discussed. The following theorem shows the relationship between the essential MO tensors and the completely positive tensors. Then some properties of Sup-MO values in MO tensors are given. Let $\mathcal{A}(n,m)\in S_{n,m}$. We call $\mathcal{A}(n,m)$ the $m$th order $n$-dimensional [**essential MO tensor**]{} if $$\mathcal{A}(n,m)_{i_1,\cdots,i_m}=\left\{ \begin{array}{cc} i_1, & i_1=i_2=\cdots=i_m \\ \min\{i_1,i_2,\cdots,i_m\}-1, & otherwise \\ \end{array} \right..$$ \[thm3.5\] Let $\mathcal{A}(n,m)$ be an $m$th order $n$-dimensional essential MO tensor. It is positive definite for all $n$, even $m.$ Furthermore, it is a completely positive tensor for all $n$ and $m$, such as $\mathcal{A}(n,m)=\sum\limits_{i=1}^n {\bf e}^m_i+\sum\limits_{i=2}^n {\bf r}^m_i$, where $({\bf e}_i)_j=\left\{ \begin{array}{cc} 1, & j=i \\ 0, & otherwise \\ \end{array} \right., $ $({\bf r}_i)_j=\left\{ \begin{array}{cc} 1, & j\geq i \\ 0, & otherwise \\ \end{array} \right.$. Let $\mathcal{B}(n,m)_{i_1,\cdots,i_m}=\left\{ \begin{array}{cc} 1, & i_1=i_2=\cdots=i_m=1 \\ 1, & i_1,i_2,\cdots,i_m\geq 2\\ 0, & otherwise \\ \end{array} \right. $. Since $\mathcal{B}(n,m)=(1,0,\cdots,0)^m+(0,1,\cdots,1)^m,$ $\mathcal{B}(n,m)$ is a complete positive tensor. Let $\mathcal{C}(n,m)=\mathcal{A}(n,m)-\mathcal{B}(n,m).$ Then $$\mathcal{C}(n,m)=\left\{ \begin{array}{cc} i_1-1, & i_1=i_2=\cdots=i_m\geq 2 \\ 0, & \min\{i_1,i_2,\cdots,i_m\}=1 \\ \min\{i_1,i_2,\cdots,i_m\}-2, & otherwise \\ \end{array} \right..$$ Let $\mathcal{A}(n-1,m)_{i_1,i_2,\cdots,i_m}=\mathcal{C}(n,m)_{i_1+1,i_2+1,\cdots,i_m+1}, i_j\in [n-1],j\in[m].$ Then $\mathcal{A}(n-1,m)$ is an $m$th order $n-1$ dimensional essential MO tensor. Furthermore, if $\mathcal{A}(n-1,m)$ is the completely positive tensor, $\mathcal{A}(n,m)$ is the completely positive tensor. By the same way, we could get $\mathcal{A}(i,m), i\in [n],$ are all essential MO tensors. When $n=1$, $\mathcal{A}(1,m)$ is equal to the positive number 1. By induction, we get that $\mathcal{A}(n,m)$ is a completely positive tensor and also a positive definite tensor. \[thm3.6\] \(1) Let $\Omega(m)$ be the MO set, and $\mathcal{M}(n,m), \mathcal{N}(n,m)$ be defined in $(1)$ and $(2)$, respectively. For all $n$ and even $m$, $1$ is always a MO value, i.e., $1\in\Omega(m)$. \(2) $\mathcal{M}(n,m)-\alpha\mathcal{N}(n,m)$ is completely positive for all $n$ and $m$, while $\alpha\in [0, 1].$ \(1) Since $\mathcal{M}(n,m)-\mathcal{N}(n,m)$ is an essential MO tensor for all $n$ and even $m$, we get that $1$ is a MO value. \(2) Since $\mathcal{N}(n,m)={\bf e}^m-\sum\limits_{i=1}^n {\bf e}^m_i$, $$\mathcal{M}(n,m)=\sum\limits_{i=1}^n {\bf e}^m_i+\sum\limits_{i=2}^n {\bf r}^m_i+{\bf e}^m-\sum\limits_{i=1}^n {\bf e}^m_i=\sum\limits_{i=2}^n {\bf r}^m_i+{\bf e}^m,$$ where ${\bf e}=(1,1,\cdots,1)^{\top}.$ So if $\alpha \in [0, 1]$, $$\mathcal{M}(n,m)-\alpha\mathcal{N}(n,m)=\sum\limits_{i=2}^n {\bf r}^m_i+(1-\alpha){\bf e}^m+\alpha\sum\limits_{i=1}^n {\bf e}^m_i$$ is completely positive. \[thm3.65\] $\alpha_*(m)$ exists, and $-\frac{1}{2}\leq\alpha_*(m)\leq0.$ From Corollary \[thm3.6\](2), $\alpha_*(m)\leq 0$. Let ${\bf x}=(1,-1,0,\cdots,0)^{\top},$ when $\alpha<-\frac{1}{2}$, $$(\mathcal{M}(n,m)-\alpha\mathcal{N}(n,m)){\bf x}^m=1+2\alpha<0,$$ so $\alpha_*(m)=\inf\{\Omega(m)\}$ exists, and $\alpha_*(m) \geq -\frac{1}{2}.$ Based on Theorem \[thm3.5\] and Corollary \[thm3.6\], the MO set $\Omega(m)$ is nonempty. \[pro-alp\] Let $\Omega(m)$ be the MO set, and $\mathcal{M}(n,m), \mathcal{N}(n,m)$ be defined in (\[1\]) and (\[2\]), respectively. Then, \(1) for any $\alpha_1(m), \alpha_2(m)\in \Omega(m),$ $[\alpha_1(m),\alpha_2(m)]\subseteq \Omega(m);$\ (2) for all even $m\geq 4,$ $1<\alpha^*(m)<2;$\ (3) $\alpha^*(m)=\max\{\Omega(m)\};$\ (4) $\alpha^*(m)\searrow 1,$ when $m\rightarrow+\infty.$ \(1) It is obvious. \(2) Since $1\in \Omega(m)$ for all even $m$, $\Omega(m)\neq \emptyset.$ Let us consider the tensor $\mathcal{M}(n,m)-2\mathcal{N}(n,m)$ and $\displaystyle {\bf x}=\left(1,\displaystyle\frac{1}{2},\cdots,\displaystyle\frac{1}{2^{n-1}}\right)^\top \in\mathbb{R}^n.$ Then $$(\mathcal{M}(n,m)-2\mathcal{N}(n,m)){\bf x}^m=2\displaystyle\sum_{i=1}^n ({\bf e}_i^\top {\bf x})^m+\sum_{i=2}^n({\bf r}_i^\top {\bf x})^m-({\bf e}^\top {\bf x})^m,$$ where ${\bf e}=(1,\cdots,1)^\top $. When $m\geq 4$ and $n\geq 2,$ we have $$\displaystyle\sum_{i=1}^n({\bf e}_i^\top {\bf x})^m=\sum_{i=1}^n\frac{1}{(2^m)^{i-1}}\leq\displaystyle \frac{2^m}{2^m-1}\leq\frac{16}{15},$$ $$\displaystyle\sum_{i=2}^n({\bf r}_i^\top {\bf x})^m\leq\sum_{i=1}^{n-1}\frac{1}{(2^m)^{i}}\leq\displaystyle \frac{2^m}{2^m-1}\leq \frac{16}{15},$$ and $$({\bf e}^\top {\bf x})^m=(\sum_{i=1}^n\displaystyle\frac{1}{2^{i-1}})^m=\displaystyle\left(\frac{1-\displaystyle\frac{1}{2^{n}}}{1-\displaystyle\frac{1}{2}}\right)^m\geq\left(\frac{3}{2}\right)^m.$$ Then $$(\mathcal{M}(n,m)-2\mathcal{N}(n,m)){\bf x}^m\leq \frac{48}{15}-\left(\frac{3}{2}\right)^m<0.$$ Therefore, for all even $m$, $2$ is an upper bound of $\Omega(m)$. Then $\alpha^{*}(m)$ exists and $\alpha^*(m)<2$. Now we prove $\alpha^*(m)>1$. Let $$\mathcal{U}(n,m)=\mathcal{M}(n,m)-\mathcal{N}(n,m), \mathcal{V}(n,m;\beta)=\mathcal{U}(n,m)-\beta\mathcal{N}(n,m), \beta=\alpha-1.$$ First, we need to prove that there exists $\beta\in(0,1)$ such that $$\mathcal{V}(n,m; \beta){\bf x}^m=(1+\beta)\sum_{i=1}^n({\bf e}_i^\top {\bf x})^m+\sum_{i=2}^n({\bf r}_i^\top {\bf x})^m-\beta({\bf e}^\top {\bf x})^m\geq 0,$$ for all $n\in\mathbb{R}$ and ${\bf x}\in\mathbb{R}^n$ satisfying $||{\bf x}||_m=1.$ If ${\bf e}^\top {\bf x}=0$, then $\mathcal{V}(n,m; \beta){\bf x}^m\geq 0$ for all $\beta \in [0,1]$. If ${\bf e}^\top {\bf x}\neq 0$, then there exists ${\bf y}=(y_1, y_2, \cdots, y_n)\in\mathbb{R}^n$ and ${\bf z}=(z_1, z_2, \cdots, z_n)\in\mathbb{R}^n$ such that $$y_1={\bf e}^\top {\bf x}, y_i={\bf r}_i^\top {\bf x}, i=2,\cdots,n,$$ and $$z_i=\displaystyle\frac{y_i}{y_1}, i=1,\cdots,n.$$ Then $z_1=1$ and $$\mathcal{V}(n,m; \beta){\bf x}^m=y_1^m\left[(1+\beta)\left(\sum_{i=1}^{n-1}(z_i-z_{i+1})^m+z_n^m\right)+\sum_{i=2}^n z_i^m-\beta\right].$$ Let $$g_{n,m}({\bf z},\beta)=(1+\beta)\left(\sum_{i=1}^{n-1}(z_i-z_{i+1})^m+z_n^m\right)+\sum_{i=2}^n z_i^m,$$ and $$\label{eq-g} f_{n,m}(\beta)~=\displaystyle\min_{{\bf z}\in\mathbb{R}^n, z_1=1} ~g_{n,m}({\bf z},\beta).$$ It is easy to get $$0\leq f_{n+1,m}(\beta)\leq f_{n,m}(\beta), \mbox{for all}~ \beta \in [0,1].$$ Hence, $$f_{m}(\beta)=\displaystyle\lim_{n\rightarrow+\infty}f_{n,m}(\beta)$$ exists for all $\beta\in[0,1]$. In fact, if there exists $ \beta \in [0,1]$ such that $f_m(\beta)=0,$ then by the definition of $f_{n,m}(\beta),$ there exists ${\bf z}^*\in\mathbb{R}^n$ with $z_1^*=1$ such that $(1- z_2^*)^m<\varepsilon$ and $z_2^*<\varepsilon,$ for any $\varepsilon>0,$ which is impossible. Then $f_m(\beta)>0$. Furthermore, $f_m(0)>0.$ Additionally, when $m\geq 4,$ assuming that ${\bf z}^*=\left(1, \displaystyle\frac{1}{2},0,\cdots,0\right)^\top,$ we get $g_{n,m}({\bf z}^*,1)=\displaystyle\frac{5}{2^m}.$ Thus $f_m(1)\leq f_{n,m}(1)\leq \displaystyle\frac{5}{2^m}<1.$ Moreover, since $m$ is even, $$g_{n,m}({\bf z},\beta_1)\leq g_{n,m}({\bf z},\beta_2), \mbox{for all}~ {\bf z}\in\mathbb{R}^n, \beta_1, \beta_2 ~\mbox{with}~ 0\leq \beta_1\leq\beta_2.$$ Then $f_{n,m}(\beta_1)\leq f_{n,m}(\beta_2)$ and $f_m(\beta_1)\leq f_m(\beta_2),$ which means that $f_m(\beta)$ is a nondecreasing function in $\beta$ on $[0,1].$ Then we prove that $f_m(\beta)$ is a continuous function in $\beta$ on $(0,1)$. Denote $f_m(\beta^+)$, $f_m(\beta^-)$, as the right-hand and left-hand limit on $\beta \in (0,1)$, $f_m(0^+),$ $f_m(1^-)$ as the right-hand limit on $0$, and left-hand limit on $1$ of the function $f_m(\beta)$, respectively. Since $f_m(\beta)$ is a nondecreasing function, for any $\beta\in(0,1),$ $f_m(\beta^+)$, $f_m(\beta^-)$, $f_m(0^+),$ $f_m(1^-)$ exist and $f_m(\beta^+)\geq f_m(\beta^-)$. Assuming that $f_m(\beta^+)>f_m(\beta^-)$, and $\delta=\frac{f_m(\beta^+)-f_m(\beta^-)}{2}>0,$ for $0<\beta_1<\beta<\beta_2$, there exists $N^*$, when $n>N^*$, we have $$\begin{aligned} f_{n,m}(\beta_1)&\leq f_{m}(\beta_1)+\displaystyle\frac{f_m(\beta^+)-f_m(\beta^-)}{2}\\ &\leq f_{m}(\beta^-)+\displaystyle\frac{f_m(\beta^+)-f_m(\beta^-)}{2}\\ &=\displaystyle\frac{f_m(\beta^+)+f_m(\beta^-)}{2},\\ \end{aligned}$$ and $$f_{n,m}(\beta_2)\geq f_m(\beta_2)\geq f_m(\beta^+).$$ Thus, when $n>N^*$, $$f_{n,m}(\beta_2)-f_{n,m}(\beta_1)\geq \displaystyle\frac{f_m(\beta^+)-f_m(\beta^-)}{2}=\delta>0.$$ Since $g_{n,m}({\bf z},\beta)$ is continuous in $\beta$, and the level set of $g_{n,m}({\bf z},\beta)$ is bounded, according to Proposition 4.4 in [@BS], $f_{n,m}(\beta)$ is continuous in $\beta$. When $\beta_1\rightarrow\beta, \beta_2\rightarrow\beta$, we obtain that $f_{n,m}(\beta^+)-f_{n,m}(\beta^-)\geq \displaystyle\frac{f_m(\beta^+)-f_m(\beta^-)}{2}=\delta>0$, which is a contradiction. Hence, $f_m(\beta)$ is continuous in $\beta$ on $(0,1)$. Finally, $$\partial(f_{n,m}(\beta))_{\beta}=\left\{\sum_{i=1}^{n-1}(z_i^*-z_{i+1}^*)^m+({z_n^*})^m\right\},$$ where ${\bf z}^*\in\displaystyle\arg\min_{{\bf z}\in\mathbb{R}^n,z_1=1}g_{n,m}({\bf z},\beta)$. Noting that $f_{n,m}(\beta)< 1,~ \mbox{for any}~ \beta\in [0,1]$, there exists $N>0$ such that, when $n>N$, $||\eta_{n,m}||< 1, \forall \eta_{n,m} \in \partial(f_{n,m}(\beta))_{\beta}$ and $||\eta_m||< 1, \forall \eta_m\in \partial(f_{m}(\beta))_{\beta}$. Hence, for all ${\bf z}\in\mathbb{R}^n$ with $z_1=1$, there exists only one $\beta^*(m)\in(0,1)$ satisfying $f_m(\beta^*(m))=\beta^*(m).$ Besides that, when $0<\beta\leq{\beta}^*(m),$ $g_{n,m}({\bf z},\beta)\geq f_{n,m}(\beta)\geq f_m(\beta)\geq\beta;$ When ${\beta}^*(m)\leq\beta<1, f_m(\beta)\leq\beta.$ This means that there exists $1>\beta>0$ satisfying $$\mathcal{V}(n,m; \beta){\bf x}^m\geq 0,$$ and there exists $\alpha=1+\beta>1$, satisfying $$\mathcal{M}(n,m)-\alpha\mathcal{N}(n,m)\succeq 0.$$ Thus $\alpha^*(m)>1.$ In addition, ${\beta}^*(m)=\alpha^*(m)-1$ is proved. Apparently, $\alpha^*(m)-1\geq \beta^*(m).$ If $\alpha^*(m)-1> \beta^*(m)$, there exists $\beta_1$ such that $\beta^*(m)<\beta_1<\alpha^*(m)-1.$ Since $f_m(\beta_1)<\beta_1$, by the definition of $f_m(\beta),$ there exists $N>0$ such that, when $n>N,$ $f_{n,m}(\beta_1)-\beta_1<0.$ Therefore, $\mathcal{U}(n,m)-\beta_1\mathcal{N}(n,m)\not\succeq 0,$ which is a contradiction. Thus $\beta^*(m)=\alpha^*(m)-1.$ \(3) From Theorem \[p-1\], when $m=2,$ $\alpha^*(2)=\max\{\Omega(2)\}.$ According to (2), when $m\geq 4,$ $\mathcal{M}(n,m)-\alpha^*(m)\mathcal{N}(n,m)\succeq 0,$ which means that $\alpha^*(m)\in \Omega(m).$ Therefore, $\alpha^*(m)=\max\{\Omega(m)\},$ for all even $m$. \(4) Since $0<f_{n,m}(\beta)<1, \beta\in [0,1],$ when $m$ is even and $m\geq4,$ there exists a ${\bf z}^*\in\arg\displaystyle\min_{{\bf z }\in \mathbb{R}^n,z_1=1} g_{n,m}({\bf z},\beta)$ satisfying $$(z_i^*-z_{i+1}^*)^m\leq 1, i=1,\cdots,n-1, (z_i^*)^m\leq 1, i=2,\cdots,n.$$ Then $$\begin{aligned} &(z_i^*-z_{i+1}^*)^{m+2}\leq (z_i^*-z_{i+1}^*)^m, i=1,\cdots,n-1;\\ &(z_i^*)^{m+2}\leq (z_i^*)^m, i=2,\cdots,n. \end{aligned}$$ Hence, $f_{n,m+2}(\beta)\leq f_{n,m}(\beta),$ and there exists $N>0$, when $n>N,$ $f_{m+2}(\beta)\leq f_{m}(\beta).$ By the definition of ${\beta}^*(m)$ above, without losing generality, assuming that $0\leq\beta\leq{\beta}^*(m),$ we obtain that $f_{m-2}(\beta)\geq f_m(\beta)\geq \beta.$ Therefore, ${\beta}^*(m-2) \geq {\beta}^*(m)$, which means $\alpha^*(m-2)\geq \alpha^*(m).$ Since $\beta^*(m)\geq 0$ and $\beta^*(m)$ is nonincreasing, $\beta^*=\displaystyle\lim_{m\rightarrow+\infty}\beta^*(m)$ exists. If $\beta^*\neq 0,$ then there exists a $N>0,$ when $n>N$ and $m>N,$ we have $f_{n,m}(\beta^*(m))\geq f_m(\beta^*(m))=\beta^*(m)\geq \beta^*>0.$ However, in the other side, when $n>N$ and $m>N,$ $f_{n,m}(\beta^*(m))\rightarrow 0$, which is a contradiction. Hence, $\beta^*=0$ and $\displaystyle\lim_{m\rightarrow+\infty}\alpha^*(m)=1.$ We could use the following algorithm to compute $\alpha^*(m)$. \[alg-1\] - - Let $\beta^0=1, \beta^1=\beta_0^1=1, n=1, k=0, \varepsilon>0,$ $m$ be a even number ; - Solve the problem (\[eq-g\]) to get $f_{n,m}(\beta_k^n);$ - If $f_{n,m}(\beta_k^n)-\beta_k^n<-\varepsilon$, then $\beta_{k+1}^n=\frac{\beta_k^n}{2}$, if $f_{n,m}(\beta_k^n)-\beta_k^n>\varepsilon$, $\beta_{k+1}=\frac{\beta_k^n+1}{2}$, $k=k+1$, goto S2; else denote $\beta^n=\beta^n_k$ - If $|\beta^n-\beta^{n-1}|<\varepsilon$, stop and output $\beta^{n}+1$; else $n=n+1$, $k=0$, goto S2. It is not hard to compute $f_{n,m}(\beta)$ since (\[eq-g\]) is a convex problem. By computing, we get that $\alpha^*(4)=1.1429$, $\alpha^*(6)=1.0323$, $\alpha^*(8)=1.0079$. In the final work, a property of the minimal eigenvalue of the Sup-MO tensor is obtained. Then, the positive definiteness of Sup-MO tensors is proved. \[p-3\] Let $\Omega(m)$ be an MO set. For all even $m\geq 4$ and $\alpha^*(m)=\max\{\Omega(m)\},$ $\mathcal{A}(n,m; \alpha^*(m))$ is a Sup-MO tensor, i.e., $$\begin{aligned} &\mathcal{A}_{i_1,\cdots,i_m}(n,m; \alpha^*(m))=\mathcal{M}(n,m)-\alpha^*(m)\mathcal{N}(n,m)\\ &=\left\{ \begin{array}{cc} i_1, & i_1=i_2=\cdots=i_m, \\ \min\{i_1,i_2,\cdots,i_m\}-\alpha^*(m), & otherwise. \\ \end{array} \right. \end{aligned}$$ Assume that $\lambda_{min}(\mathcal{A}(n,m; \alpha^*(m)))$ is the smallest eigenvalue of $\mathcal{A}(n,m; \alpha^*(m)).$ Then,\ $\lambda_{min}(\mathcal{A}(n,m; \alpha^*(m)))$ strictly decreases to $0$, when $n\rightarrow\infty$. Furthermore, $\mathcal{A}(n,m; \alpha^*(m))$ is positive definite. By Theorem \[theo-1\], it is easy to see that $\lambda_{min}(\mathcal{A}(n,m; \alpha^*(m)))$ decreases in $n$, for all even $m$. In the following, we prove that it is strictly decreasing to $0$. $g_{n,m}({\bf z},\beta), f_{n,m}(\beta)$ and $f_{m}(\beta)$ are defined as (3-5). Since $1>f_m(\beta^*(m))=\beta^*(m)>0$, $f_{n,m}(\beta^*(m))\rightarrow\beta^*(m)$. Suppose that ${\bf z}^*\in\displaystyle\arg\min_{{\bf z}\in\mathbb{R}^n, z_1=1} g_{n,m}({\bf z},\beta^*(m))$. Because $z_1^*=1$, $||{\bf z}^*||_m\geq 1$. Let $w_i^*=z_i^*-z_{i+1}^*,i=1,\cdots,n-1$, $w_n^*=z_n^*.$ Then, when $m\geq 4,$ $$\beta^*(m)\leq g_{n,m}({\bf z}^*,\beta^*(m))=f_{n,m}(\beta^*)\leq f_{n,m}(1)<\frac{5}{2^m}<1.$$ By the definition of $g_{n,m}({\bf z}^*,\beta^*(m)),$ $\displaystyle\sum_{i=2}^n (z_i^*)^m\leq \frac{5}{2^m}<1$, which means that $|z_2^*|\leq {\displaystyle\frac{5^\frac{1}{m}}{2}}<1.$ Thus $w_1^*=1-z_2^*\geq 1-\displaystyle\frac{5^\frac{1}{m}}{2}$. Hence, when $m\geq 4,$ $||{\bf w}^*||_m\geq 1-\displaystyle\frac{5^\frac{1}{m}}{2}.$ According to Theorem \[theo-1\] $$0\leq\lambda_{min}(\mathcal{A}(n,m; \alpha^*(m)))\leq \displaystyle\frac{\mathcal{A}(n,m; \alpha^*(m))({\bf w}^*)^m}{||{\bf w}^*||_m^m}.$$ By the definition of ${\bf w}^*$, $\mathcal{A}(n,m; \alpha^*(m))({\bf w}^*)^m\rightarrow 0,$ when $n\rightarrow+\infty$. Since $||{\bf w}^*||_m\geq 1-\displaystyle\frac{5^\frac{1}{m}}{2},$ we get that $\lambda_{min}(\mathcal{A}(n,m; \alpha^*(m)))\rightarrow 0$, when $n\rightarrow\infty$. Then we prove that the decreasing of $\lambda_{min}(\mathcal{A}(n,m; \alpha^*(m)))$ is strict. Consider the following program: $$\begin{aligned} \min & \mathcal{A}(n,m; \alpha^*(m)){\bf x}^m \nonumber\\ s.t.& ||{\bf x}||_m=1 .\nonumber \end{aligned}$$ Then its KKT conditions are $$\begin{cases} & \mathcal{A}(n,m; \alpha^*(m)){\bf x}^{m-1}=\lambda{\bf x}^{[m-1]} \\ & ||{\bf x}||_m=1. \end{cases}$$ The smallest solution $\lambda_{n,m}$ and the corresponding vector ${\bf x}\in\mathbb{R}^n$ of above program are the smallest H-eigenvalue and H-eigenvector of $\mathcal{A}(n,m; \alpha^*(m))$. If $\lambda_{n,m}= \lambda_{n+1,m}$ for some $n$, then there exist ${\bf x}\in\mathbb{R}^n$ and $\bar{{\bf x}}\in\mathbb{R}^{n+1}$ with $\bar{{\bf x}}=({\bf x}^\top,0)^\top$ satisfying $$\mathcal{A}(n,m; \alpha^*(m)){\bf x}^{m-1}=\lambda_{n,m}{\bf x}^{[m-1]},$$ $$\mathcal{A}(n+1,m; \alpha^*(m))\bar{{\bf x}}^{m-1}=\lambda_{n+1,m}\bar{{\bf x}}^{[m-1]}.$$ Hence, $$\sum_{i_2,\cdots,i_m=1}^{n+1}\mathcal{A}(n+1,m; \alpha^*(m))_{n+1,i_2,\cdots,i_m} \bar{x}_{i_2} \cdots \bar{x}_{i_m}=\lambda_{n+1,m}\bar{x}_{n+1}^{m-1}.$$ Since $\bar{{\bf x}}=({\bf x}^\top,0)^\top,$ the above equation is $$\sum_{i_2,\cdots,i_m=1}^{n}\mathcal{A}(n+1,m; \alpha^*(m))_{n+1,i_2,\cdots,i_m} x_{i_2} \cdots x_{i_m}=0.$$ Because $$\sum_{i_2,\cdots,i_m=1}^{n}\mathcal{A}(n,m; \alpha^*(m))_{n,i_2,\cdots,i_m} x_{i_2} \cdots x_{i_m}=\lambda_{n,m}x_{n}^{m-1},$$ we have $$\begin{aligned} &\sum_{i_2,\cdots,i_m=1}^{n}\mathcal{A}(n,m; \alpha^*(m))_{n,i_2,\cdots,i_m} x_{i_2} \cdots x_{i_m}\\ -&\sum_{i_2,\cdots,i_m=1}^{n}\mathcal{A}(n+1,m; \alpha^*(m))_{n+1,i_2,\cdots,i_m} x_{i_2} \cdots x_{i_m} \\ =&\alpha^*(m)x_{n}^{m-1}=\lambda_{n,m}x_{n}^{m-1}. \end{aligned}$$ According to the above proof, $\alpha^*(m)>1>\lambda_{n,m}$. Therefore, $x_n=0$. By the same discussion, we get ${\bf x}=0$, which is against $||{\bf x}||_m=1.$ Thus, $\lambda_{min}(\mathcal{A}(n,m; \alpha^*(m)))$ strictly decreases. Finally, together with Corollary \[thm3.6\], we have $\mathcal{A}(n,m; \alpha^*(m))$ is positive definite. Final Remarks ============= In this paper, we construct the MO tensor with introducing the concepts of the MO value and the MO set. Then we mainly discuss two special cases of the MO tensor: the Sup-MO tensor and the essential MO tensor. We prove that an even order essential MO tensor is a completely positive tensor and positive definite. Then, some related properties of the Sup-MO value of an even order Sup-MO tensor are given. Furthermore, the positive definiteness of an even order Sup-MO tensor is proved, since the minimal H-eigenvalue of the Sup-MO tensor strictly decreases to 0, when $n\rightarrow\infty$. In the future work, some of the applications of the Sup-MO tensor and the properties of Sub-MO value and Sub-MO tensor will be discussed. There are three further research questions for the MO tensor, the Sup-MO tensor and the Sub-MO tensor. 1\. Are the Sup-MO tensors SOS (sum-of-squares) tensors? For the definition of SOS tensors, see [@CLQ]. An SOS tensor is a PSD tensor, but not vice versa. This theory can be traced back to David Hilbert [@Hi]. We randomly tested some Sup-MO tensors, and found that they were SOS tensors. We will study this in the future study. 2\. We cannot verify whether $\alpha_*(m)$ can be reached or not. Hence, we do not know whether $\Omega(m)$ is compact or not. If the $\Omega(m)$ is compact, how to get the length of the MO set $\Omega(m)$ is also an interesting work. We will continue to explore the properties of $\alpha_*(m)$ and $\Omega(m)$. 3\. Since the properties of the Moler matrices make them to be good test matrices for the linear equations and eigensystems, we will try to find that if the Sup-MO tensor can also be a good candidate for testing in some tensor computation software packages or not. [99]{} J.F. Bonnans and A. Shapiro, *Perturbation Analysis of Optimization Problems*, Springer, New York, 2013. H. Chen, G. Li and L. Qi, SOS tensor decomposition: theory and applications, *Commun. Math. Sci.*, **14** (2016) 2073-2100. A. Cichocki, R. Zdunek, A.H. Phan and S. Amari, *Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multiway Data Analysis and Blind Source Separation*, Wiley, New York, 2009. D. Hilbert, Über die Darstellung definiter Formen als Summe von Formenquadraten, *Math. Ann.*, **32** (1888), 342-350. C.J. Hillar and L.H. Lim, Most tensor problems are NP-hard, *J. ACM*, **60** (2013), 45. T.G. Kolda and B.W. Bader, Tensor decompositions and applications, *SIAM Rev.*, **51** (2009), 455-500. C. Li, F. Wang, J. Zhao, Y. Zhu and Y. Li, Criterions for the positive definiteness of real supersymmetric tensors, *J. Comput. Applied. Math.*, **255** (2014), 1-14. Z. Luo and L. Qi, Positive semidefinite tensors (in Chinese), *Sci. Sin. Math.*, **46** (2016), 639-654. Z. Luo and L. Qi, Completely positive tensors: Properties, easily checkable subclasses and tractable relaxations, *SIAM J. Matrix Anal. Appl.*, **37** (2016), 1675-1698. J.C. Nash, *Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation*, CRC Press, 1990. L. Qi, Eigenvalues of a real supersymmetric tensor, *J. Symbolic Comput.*, **40** (2005), 1302-1324. L. Qi, H$^+$-eigenvalues of Laplacian and signless Laplacian tensors, *Commun. Math. Sci.*, **12** (2014), 1045-1064. L. Qi and Z. Luo, *Tensor Analysis: Spectral Theory and Special Tensors*, SIAM, Philadelphia, 2017. L. Qi and Y. Song, An even order symmetric B tensor is positive definite, *Linear Algebra Appl.*, **457** (2014), 303-312. L. Qi, C. Xu and Y. Xu, Nonnegative tensor factorization, completely positive tensors, and a hierarchical elimination algorithm, *SIAM J Marix Anal. Appl.*, **35** (2014), 1227-1241. L. Qi, G. Yu and E.X. Wu, Higher order positive semidefinite diffusion tensor imaging, *SIAM J Imaging Sci.*, **3** (2010), 416-433. L. Zhang, L. Qi and G. Zhou, $M$-tensors and some applications, *SIAM J. Matrix Anal. Appl.*, **35** (2014), 437-452. [^1]: Mathematics Department, Southeast University, 2 Sipailou, Nanjing, Jiangsu Province 210096, China. Email: [[email protected]]{}. This author’s work is supported by National Natural Science Foundation of China Nos. 11501100, 11571178 and 11671082. [^2]: Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong. Email: [[email protected]]{}. [^3]: Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong. Email: [[email protected]]{}. This author’s work is supported in part by the Hong Kong Research Grant Council Nos. PolyU 15302114, 15300715, 15301716 and 15300717. [^4]: To appear in: Journal of Industrial and Management Optimization | Mid | [
0.6311111111111111,
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13701229 What is the next term in 106, -191, -734, -1565, -2726? -4259 What is the next term in 3597, 5341, 7061, 8751, 10405, 12017, 13581? 15091 What comes next: -606, -1231, -1630, -1803? -1750 What is next in 9601, 18974, 28335, 37684, 47021, 56346, 65659? 74960 What comes next: -2337949, -2337960, -2337971? -2337982 What is the next term in 366, 2106, 6280, 13932, 26106, 43846, 68196, 100200? 140902 What comes next: -720698, -720722, -720776, -720872, -721022, -721238, -721532, -721916? -722402 What comes next: 490964, 490939, 490914? 490889 What is the next term in -1607, -3447, -5515, -7799, -10287? -12967 What is next in -184188, -184186, -184184, -184182, -184180? -184178 What is the next term in -1075, -2118, -3181, -4264? -5367 What is the next term in 2464318, 4928553, 7392800, 9857065, 12321354, 14785673? 17250028 What comes next: 1501, 3086, 5723, 9412, 14153? 19946 What comes next: -313781, -313761, -313707, -313601, -313425? -313161 What comes next: 1010, 2128, 3544, 5234, 7174, 9340? 11708 What is next in 3214, 4309, 5466, 6685? 7966 What comes next: -259564, -259571, -259578, -259585? -259592 What comes next: -10278, -10635, -11010, -11409, -11838, -12303, -12810, -13365? -13974 What is next in 9464, 6916, 2, -13462, -35660, -68776? -114994 What is the next term in -1919096, -1919448, -1919800, -1920152, -1920504? -1920856 What is the next term in -212, -485, -734, -959, -1160? -1337 What comes next: 10079, 10141, 10241, 10379, 10555, 10769? 11021 What is next in -401285, -401269, -401245, -401213, -401173, -401125? -401069 What is the next term in 118878, 114717, 110556, 106395? 102234 What is the next term in -2010, -7862, -17544, -31044, -48350, -69450, -94332, -122984? -155394 What comes next: -3233524, -3233543, -3233576, -3233623? -3233684 What is next in -13648253, -27296536, -40944819, -54593102? -68241385 What is the next term in 15233, 61047, 137423, 244373, 381909, 550043, 748787? 978153 What comes next: -572, -278, 36, 370, 724? 1098 What is the next term in -255806, -511621, -767432, -1023239, -1279042, -1534841? -1790636 What comes next: 442074, 442089, 442104? 442119 What is next in 205548226, 205548222, 205548216, 205548208, 205548198? 205548186 What comes next: 13649, 13631, 13607, 13565, 13493, 13379, 13211? 12977 What comes next: -347258, -347256, -347242, -347210, -347154, -347068, -346946, -346782? -346570 What is the next term in -30, -109, -308, -687, -1306, -2225, -3504? -5203 What is next in -24108, -47824, -71540, -95256, -118972? -142688 What is next in -8702, -17979, -27830, -38261, -49278, -60887? -73094 What is next in -1601271, -3202482, -4803635, -6404730, -8005767? -9606746 What comes next: -130200, -130250, -130300, -130350? -130400 What is the next term in -408, -481, -606, -789, -1036? -1353 What is next in -751262, -751352, -751442, -751532, -751622? -751712 What comes next: -3360, -3493, -3700, -3987, -4360, -4825? -5388 What is next in 526, 1055, -162, -4841, -14698, - | Low | [
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So there's a new Eric Martsolf interview in this week's SOD. He talks about his new children's gym, Brady being a dumbass, blahblahblah. The usual stuff, however, there's an interesting little excerpt about Brady & Eric after the big sex tape reveal in the coming months. Spoiler: click to toggle "The excuse that Eric gives [for sleeping with Kristen] is so far-fetched. Brady's going to have a hard time accepting it." | Low | [
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Few life stories are as densely packed with intrigue as Christopher Marlowe's, the subject of Peter Whelan's 1992 drama, "The School of Night," which had its belated American premiere Sunday at the Mark Taper Forum. In addition to being the second-greatest Elizabethan playwright after Shakespeare, Marlowe was a rowdy Cambridge-educated poet-rebel, a profane apostate given to sententious drollery, probably a homosexual (as suggested by his infamous tag line, "Them that love not tobacco and boys are fools") and very likely a spy. If that doesn't whet the gossipy appetite, his death at 29 -- the result of a vicious indoor brawl -- has excited enough conspiracy theories for an Oliver Stone biopic. Just imagine the film in which all motives lead to a fatal dagger plunged above the eye of London's most audacious bad-boy. But during the tedious, information-larded first act, I couldn't help wishing for a new production of one of Marlowe's own luridly comic tragedies, whose overreaching protagonists charge the stage with a plundering Renaissance determination to crack through known limits. The heavy blank-verse artillery of "Tamburlaine the Great" or "Doctor Faustus" isn't likely to be reverberating in the Taper any time soon. Yet Marlowe's unbridled theatrical gusto, outlandish as it might seem to a culture weaned on Shakespeare's exquisitely inward art, would make a better introduction to this canonical trailblazer than Whelan's more pedestrian theater-history whodunit. The production, directed by Bill Alexander (who staged the play for the Royal Shakespeare Company), is attractively arrayed on Simon Higlett's spare wood-paneled set. Design-wise, the invitation to travel back in time is enticingly rendered. Russell H. Champa's dim lighting heightens the sense of uncertain menace, and Robert Perdziola's costumes manage to flaunt both bodies and frippery. But the drama takes too long to find its stride. The sluggish setup situates us in Marlowe's last months, when the fruits of fame proved to be no guarantee of safety in a society drowned in discord. Paranoia was rampant in this treasonous urban caldron, and anyone rumored to have been members of "the School of Night," the secret salon in which men such as Marlowe (Gregory Wooddell) and Sir Walter Ralegh (Henri Lubatti) once traded freethinking blasphemies, understood their days of London liberty were numbered. The cat's-cradle plot, informed by documentary sources and fleshed out by speculative fantasy, makes much ado about Marlowe's irreverent wit in the face of brewing danger. But Wooddell's "Kit," as Marlowe was called, is like a blustering, unsinister Rupert Everett, who offered a fleeting but dashing Marlowe cameo in the 1998 blockbuster "Shakespeare in Love." Speaking of William Shakespeare, Whelan gives him a prime role in his tale, although there's no evidence that Marlowe and he were buddies. (The most Stephen Greenblatt is willing to concede in "Will in the World," his acclaimed 2004 study, is that "[t]hey must have known each other personally; the world they inhabited was far too small for anonymity.") Here, Shakespeare (John Sloan), operating under the stage alias of Tom Stone, is portrayed as a sponge soaking up the planet's lyrical wisdom. His professional livelihood depends on him being at once politically inconspicuous and opportunistic. A scene in which Marlowe lectures Shakespeare, his junior by a couple of months but much further behind him in artistic stature (Bardolatry wasn't an overnight phenomenon), signals the problem Whelan has in figuring out whether he is writing a murder mystery or a master's thesis. The topic under discussion is the purpose of comedy, and Marlowe comes out with such prissy remarks ("I know that we are never more vulnerable than when we laugh") that he seems more like a doomed don than an enfant terrible constitutionally incapable of suppressing unauthorized truths. Popular historical characters are hard to fictionalize. Indeed, it's easier to go along with the portrait of a lesser-known light such as Marlowe's ex-roommate Thomas Kyd (Michael Bakkensen), famous only for having written "The Spanish Tragedy," than it is to accept a depiction of a quietly cocky young Shakespeare, who by 1592 would have had more reason to be jealous of Marlowe than the other way around. The second act, launched by a delightful commedia dell'arte routine, deepens in thematic interest as Marlowe's destiny darkly comes to fruition. This turbulent theatrical golden age in which public and private selves literally bleed into each other is niftily re-created. But Marlowe's "Edward the Second" or "The Jew of Malta" could better reveal why it's worth remembering. | Low | [
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Q: Conversion methods for QJsonValue always return their default value I am trying to convert QJsonValues into their correct data types, but the conversion always ends up returning their default value. For example, I have the following JSON object: { "val1": 99, "val2": true, "val3": "test" } I'm getting these values with: QJsonValue val1 = jsonObj.value("val1"); QJsonValue val2 = jsonObj.value("val2"); QJsonValue val3 = jsonObj.value("val3"); Now, if I check these QJsonValues in the Debug view, they all have their correct value and data types. I'm seeing... val1 as 99 - QJsonValue(Number) val2 as true - QJsonValue(Bool) val3 as "test" - QJsonValue(String) I now do the following: int valInt1 = val1.toInt(); bool valBool2 = val2.toBool(); QString valString3 = val3.toString(); This will give me 0 for valInt1, false for valBool2 and "test" for valString3. For some reason, toString() seems to be working correctly, but the other conversion methods all result in their default value. With val1 I can do the following to make it work: int valInt1 = val1.toString().toInt(); But that is not an option for bool values. Does anyone know how I could solve this problem? I believe I'm doing everything right here. Not sure what the issue might be and the documentation does things exactly how I would do them, but the conversions always return default values. A: I have solved this problem for now by converting the JsonObject to a QVariantMap and ignoring the QJsonValues. They are either bugged or I do not understand how they work. QVariantMap map = jsonObj.toVariantMap(); int valInt1 = map.value("val1").toInt(); bool valBool2 = map.value("val2").toBool(); QString valString3 = map.value("val3").toString(); | Mid | [
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A bit of sad news for the maker community today: TechShop is shutting down nationwide. Founded in 2006, TechShop is (or, I guess, was) pretty much heaven for the adventurous do-it-yourself’er. Imagine a big building filled with everything from sewing machines to laser cutters to woodworking equipment to welding rigs. Pay a membership fee, take a few classes to make sure you didn’t cut your fingers off or burn the building down, and bam: you had access to it all. Like the shirt above, the general philosophy was “Don’t try it at home — try it here!” Membership was usually around $1,000 a year depending on when you bought in — it certainly wasn’t cheap, but it was cheaper than buying any one piece of the bigger equipment yourself. They also handled the maintenance, which, when it comes to many of these massive machines with their piles of proprietary parts, is a money pit in its own right. TechShop CEO Dan Woods sent out a notice to members, which Makezine has in full. The short version: the business model wasn’t working, and they’ve been broke for a while. The TechShop homepage (heads up: the page is now one big PDF), meanwhile, confirms the news. All locations are closed as of this morning, November 15th. Those looking for membership refunds are instructed to email the trustee handling the bankruptcy process, which seems… not fun. It’s a bummer for all involved, and likely a rather massive shock for the artists, designers and entrepreneurs who considered it home base. In my many visits to TechShop (I’ve been a member for a few years now) I’ve met countless people who used the shop’s gear for everything from cranking out items for their online storefronts, to making shirts for their bands, to creating stencils for murals that stretch entire blocks in San Francisco. TechShop’s sudden shutdown will definitely leave a big hole to fill. | Mid | [
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Q: Filtering http/https traffic destined for a juniper router I need to find a way to harden my network so that all juniper routers reject web management and any http / https traffic that is destined for them specifically. This is what I came up with so far: edit delete system services web-management edit firewall family inet filter local_web_filter set term block_web from destination-address 127.0.0.1/32 set term block_web from port http set term block_web from port https set term block_web then log set term block_web then reject tcp-reset set term default-term then accept set interfaces lo0 unit 0 family inet filter input local_web_filter set interfaces lo0 unit 0 family inet address 127.0.0.1/32 commit write memory I have little experience configuring juniper routers, so any help would be much appreciated. A: A few remarks: if you disable the web management service, you wouldn't have to block HTTP(S) traffic anymore, since there's no service listening on that port. should you be wanting to filter traffic to the router's web management interface, then your firewall filter is not very useful for a few reasons: you're only blocking traffic towards localhost. So only traffic from your router to your router's web interface could match that. If you want to make sure nothing reaches the web management interface, you should match on any IP address used by the router. Since you're applying the filter on the loopback interface, I'd just remove the match on the destination address. you're matching on port 80 and port 443, which implies both source and destination ports. You should explicitly match on destination-port 80 and destination-port 443. write memory is not a valid JunOS command | Mid | [
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Mega-resort projects planned for St. Maarten, St. Kitts Panoramic view of the southeastern peninsula of St. Kitts, site of the future 2,500-acre Christophe Harbour residential, retail and marina complex. (Credit: Larry Luxner) St. Maarten and St. Kitts will soon be home to two unrelated mega-resorts that aim to dramatically boost tourism to both Eastern Caribbean islands. The first project, Maarten Quarter, is a $110 million joint venture between Royal Caribbean Cruises Ltd. and Trident Development, a subsidiary of Hill International. The second is Christophe Harbour, a $170 million hotel, retail and marina venture led by South Carolina-based Kiawah Partners that encompasses 2,500 acres on the southeastern peninsula of St. Kitts. Both projects were profiled as case studies during last week’s 16th annual Caribbean Hotel and Tourism Investment Conference, held at the Sheraton Puerto Rico Hotel & Casino in San Juan. Adam C. Petrillo, executive vice-president of Trident, spoke to NIMB following a presentation on Maarten Quarter — a “mixed-use hospitality project with retail” on a 9.5-acre parcel located within the existing port of Philipsburg, on the Dutch side of the 34-square-mile island 190 miles east of Puerto Rico. “We’re answering the call of both the cruise industry and St. Maarten as well,” said Petrillo. “Our challenge today is accommodating these massive vessels. Royal Caribbean’s Allure of the Seas and Oasis of the Seas are each a billion-dollar investment, carrying 8,000 passengers and crew each.” Petrillo noted that in 2011, St. Maarten received 1,656,159 cruise ship arrivals in 596 ship calls, surpassing the 2010 figure by 344,200. Officials attribute that impressive growth to the direct marketing to cruise-line executives and itinerary planners by Theo Hayliger, deputy prime minister and harbor affairs minister, and by Mark Mingo, CEO of Harbour Group. “They did a magnificent job reinvigorating Front Street and redeveloping Philipsburg. The island is now unrivaled in the Caribbean, and we view Maarten Quarter as an absolute necessity,” said the Miami-based executive. “The longer you can keep passengers on your shore spending money, the better off you are. But if there’s too much congestion, people get frustrated and move on,” he said. “By creating unique offerings and attractions, they tend to want to stay longer — and being close by, they’re less concerned about missing their boat.” Even so, he told NIMB, “St. Maarten is in a very strong position, particularly from the cruise industry standpoint. It’s the farthest east and south as you can go on a seven-day cruise from Fort Lauderdale or Miami. It has the facilities to accommodate large ships, as well as an incomparable mix of entertainment, retail shopping and hotels. And the dual French and Dutch culture on one island is very unique.” Maarten Quarter is to employ 250 workers in the construction phase and 400 full-time workers upon its completion in 2014. The project is expected to break ground by September or October of this year; Petrillo said he’s been in negotiations with Hilton, Marriott and Inter-Continental about managing the 125-room hotel its planners envision. “We’ve also had contact with some international restaurant and entertainment brands, and major rum manufacturers,” he said without elaborating. Familiar with the Caribbean Hill International isn’t exactly a newcomer to the Caribbean. Its most recent project there was its venture with RCCL in building the cruise-ship port of Falmouth, Jamaica — a $200 million endeavor. “In Falmouth, we did an extensive sea-bottom reclamation and created real estate from dredging and filling. This project is not as large because there are no marine works. Rather, this is an existing property within the port. St. Maarten can already accommodate 7-8 cruise ships. We’re not building any additional pier space,” Petrillo explained. “What we’re really aiming to do is create new offerings in entertainment, food and beverages so we have a sustainable business after the cruise ships leave. How many retail shops will depend on the number of lead tenants we bring in, though it probably won’t exceed 20 in total.” Hill, founded in 1976, has 3,200 employees worldwide and has worked on dozens of impressive projects ranging from the $4 billion expansion of Dubai International Airport to the partial rebuilding of the Pentagon following 9/11. Yet securing money for Maarten Quarter has been a major headache, said Petrillo. “There’s probably never been a more challenging time to find money for mixed-use projects in the Caribbean. It’s very hard to find equity sources for projects of this scope and complexity,” he said. “Banks are generally averse to hotel construction risks, and are either unable or unwilling to lend.” In the end, he said, “we were able to work through the Dutch Ministry of Finance and an insurance company. We have two firms listed on the New York Stock Exchange sponsoring this, but to fill in the additional capital pockets, we really had to be creative and look to both the hotel and gaming industry to be able to pull this together.” As soon as financing arrangements are completed this summer, a formal joint venture will be signed between Trident and RCCL. Global downturn stalls St. Kitts resort project A much larger project is planned for the twin-island nation of St. Kitts & Nevis. Christophe Harbour Beach House Christophe Harbour is the brainchild of Kiawah Partners, which in the mid-1970s developed 10,000-acre Kiawah Island into an exclusive resort community with more than 4,000 residential units. In 1999, Kiawah acquired the 390-acre Doonbeg golf community in Ireland, and now sees St. Kitts as its next great investment opportunity. Phil Keb, executive vice-president of Cristophe Harbour Development Corp., said his company has spent $170 million since 2006 on land acquisition, bungalows and a beach-house restaurant as well as golf and marina development. The 2,500-acre property encompasses six beaches and 13 miles of shoreline on the southeastern peninsula of St. Kitts. “Our master plan has been approved for 2,000 units, a marina, multiple hotels and a golf course,” said Keb, adding that in the past three years, he’s racked up more than $55 million in lot sales. St. Kitts already boasts Port Zante, which is located in the capital, Basseterre, and which can already receive the world’s largest cruise ships. Cristophe Harbour aims rather to lure wealthy yacht owners, which is why its developers are dredging the harbor to accommodate 18- to 20-foot yachts. That and the planned marina will cost around $25 million to $30 million. There’s also a residential and retail complex valued at $10 million. But the global economic downturn has forced Kiawah Partners to lower its expectations for the time being. “When the project first got started, capital was available so we started our marina and golf project,” said Keb. “We spent about $10 million doing bulk earthmoving work. When we realized that capital markets were not cooperating like we though they would, we stopped construction on the golf course, and will restart once we have demand.” So far, Christophe Harbour has sold 47 lots. About 80 percent of those buyers are from the United States, 10 percent from Europe and the remaining 10 percent from the Asia-Pacific region and the Middle East. “Given the state of the market, we’ve done fairly well. It’s all about selling a lifestyle,” said Keb. “We have 25 founding members who bought real-estate. We made a commitment to them that we’d provide amenities.” All told, said the executive, “we’re looking at new investments of $50 million for primary capital projects focused on allowing us to continue to sell real-estate. That’s the name of the game for us. We will soon announce a 125-room luxury hotel and a $5 million to $10 million co-investment along with a developer from Dubai.” Keb said Christophe Harbour is benefitting from a unique program approved by the twin-island nation in 1984 that grants St. Kitts citizenship to anyone investing at least $400,000 in an approved local property. That’s a strong attraction for foreigners — particularly wealthy Arabs — who have difficulty entering the United States with their current passports. “If you have a St. Kitts passport, it allows you to travel to 132 countries visa-free, so there’s strong interest in that,” said Keb. “If we’re lucky, we’ll get enough traction on this program to break ground and announce the first hotel soon.” | Mid | [
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Q: Java; Runtime Interpretation; Strategies To Add Plugins I'm beginning to start on my first large project. It will be a program very similar to Rosetta Stone. It will be a program, used for learning a foreign language, written in Java using Swing. In my program I plan on the user being able to select downloaded courses to learn from. I will be able to create an English course since I am a native English speaker. However, I want people who speak other languages to be able to write courses for users to use as well (this is an essential part for my program to work). Since I want the users to be able to download courses of languages they want, having it hard-coded into the program is out of the question. The courses needed to be interpreted during the runtime. Also since I want others to collaborate with my work (ie make courses), I need to make it easy for them to do so. What would be the best way to go about doing this? The idea I have come up with is having a strict empty course outline (hard-coded) with a simple xml file which details the text and sounds to be used. The drawback to this is that it extremely limits the author. Different languages may need to start out with learning different parts. Any advice on the problem at hand as well as the project as a whole will be greatly appreciated. Any links to any relevant resources or information would also be greatly appreciated. Think you for your time and effort, Joseph Pond A: Simply, you should base your program on a system such as Eclipse RCP, or the Netbeans Platform. Both of these systems already deal with exactly this problem, and both are perfectly adequate for this task. They're not just for IDEs. It's a larger first step as you will need to learn one of these platforms beyond simply just Swing. But, they solve the problem, and their overall organization and technique will serve your program well anyway. Don't reinvent this wheel, just learn one of these instead. A: If you are set on doing this from scratch (Will's idea isn't bad), What I would do is first lay down the file format that would be easiest to create your language course in. It could be XML, plaintext or some other format you come up with yourself. You will probably need some flexibility in the language format because you will want to actually be able to specify things like questions and answers. XML is a pain because of all the extra terminators, but it gives a good amount of meta-data. If you like XML for that, you may consider defining your language file in YML, it gives you the data of XML but uses whitespace delineators instead of angle brackets. You probably also want to define your file in the language it's created for, so you might or might not want to require english words as keys. If you don't want any english, you may have to skip both XML and YML and come up with your own file format--possibly where the layout and/or special symbols define the flow and "functionality". Once you have defined the file format, you won't have to worry about hard-coding anything... you won't be able to because it will already be in the file. Plug-in functionality would be nice as well... This is where your definition file also contains information that tells you what class to instantiate (reflectively) and use to parse/display the data. In that way you could add new types of questions just by delivering a new jar file. If this is confusing, sorry, this is difficult in a one-way forum because I can't look at your face and see if you're following me or if I'm even going in the right direction. If you think I'm on the right track and want more details (I've done a bit of this stuff before) feel free to leave a follow-up question (or an email address) in a comment and I'd be glad to discuss it with you further. | Mid | [
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After the terror attack that killed 84 people in Nice, RT heard both sides of the issue of hatred and intolerance in France in a debate with political commentator Mo Ansar and French writer and commentator Alexandre Mendel. On July 14, 84 people were killed and over three hundred injured in the French city of Nice when a truck was deliberately driven into crowds during Bastille Day celebrations. The Nice attack, which has been linked to ISIS, is the second in a week within the EU. Tensions flared during a minute silence for the victims of the attack. An angry exchange was caught on video between a man and a woman after he'd told her to go back to her own country. #Nice, une population sous tension après l'attentat du 14 juillet. pic.twitter.com/1eN2OakDgy — Remy Buisine (@RemyBuisine) July 18, 2016 RT: We're seeing yet more examples of the fear and sometimes hatred of Muslims. Isn't the real issue here that non-Muslims don't understand Islam and they can't tell the difference between a Muslim and a Muslim extremist? Mo Ansar: I think that is part of the issue. I think ignorance is festering on both sides of the debate. I think there are non-Muslims who have a very poor understanding what Islam and Muslims are. As we’ve seen from the Nice attacker, his lifestyle was about as far removed from an Islamic and Muslim life as it is possible to be. We’ve also seen something similar with the Brussels attacks. But at the same time, very important civilizational questions are being asked of new migrants who have settled in communities here about what is their understanding of European liberalism, democracy, the ideas of tolerance and enlightenment. But the difficulty we have is immigrants, even people at home, are looking around at their governments, they’re looking at the politics and policies of fear and prejudice at home and abroad and we are seeing very little tolerance here. And behavior and ignorance is breeding behavior and even more ignorance. RT: What is your opinion about the examples of tensions and violence on the streets, hatred towards Muslims? Where is all this is coming from? Alexandre Mendel: I don’t think there is hatred towards the Muslims. I think France has reached its level of tolerance against radical Islamism. People are literally fed up by Islamic hate towards us. We welcomed them 30 years ago and the third generation hates us, commits attacks against us. In just one year, France lost 230 citizens during the attacks. I guess there are some reasons why the French are fed up. Don’t forget that next year the presidential election will be held. I am sure the French will get their revenge by voting. I’ve never seen any big Muslim demonstrations against the Islamic terrorism. So, I don’t think there is a problem with Islamophobia. Islamophobia is a sickness. There is a legitimate fear about Islam. Because every attack we’ve been through someone said: “Allah Akbar”… | Mid | [
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Following confirmation that the International Criminal Court indictee Bosco Ntaganda has now left the US Embassy in Kigali and is being escorted to The Hague by ICC officials, the Foreign Secretary, William Hague, said: “I am pleased to hear today that Bosco Ntaganda is on his way to The Hague. This is a hugely significant day for victims of conflict in the region. I hope it will contribute to a resolution of the problems in the eastern DRC along with determined efforts to implement wider peace agreements. I welcome the cooperation of the Rwandan government and all those who have enabled this transfer to take place. Britain is fully committed to supporting and cooperating with the International Criminal Court.” | Mid | [
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Q: How do I print off a calendar currently in HTML table format? I have a calendar I want to print off, see the following image; I am using a HTML table and the colours are set by background-color. In order to print off background colours in IE you have to make a setting in the Advanced Settings to do this. My manager does not like this solution, it means having to configure all PCs that use it. So the question then is how else can I do this? I have access to SSRS but I do not know how I would do this using that. Maybe another alternative is to download a colour image to populate the cell? A: The only solution I can find is to insert an image of the colour instead. That is what I am doing now for want of a better alternative. | Low | [
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Q: Find all finite fields k whose subfields form a chain: if $k'$ and $k''$ are subfields of $k$, then either $k' \subseteq k''$ or $k'' \subseteq k'$. Find all finite fields $k$ whose subfields form a chain: that is, if $k'$ and $k''$ are subfields of $k$, then either $k' \subseteq k''$ or $k'' \subseteq k'$. So, I understand that I'm trying to find the values of $n$ such that the subfields of $\mathbb{F}_{p^n}$ (where $\mathbb{F_{p^n}}$ is the Galois field of order $p^n$) form a chain. However, I'm unsure of where to begin. If anyone could point me in the right direction that would really help. This problem is found in Rotman's Advanced Modern Algebra. A: Recall that finite fields must have order a power of a prime. Moreover, if $k\subseteq k'$, then $k'$ is a vector space over $k$. Hence, if $|k|=p^n$, with $p$ prime, and $|k'|=p^m$, then if the dimension of $k'$ over $k$ is $d$ it follows that $p^m=(p^n)^d = p^{nd}$; that is, we must have that $n|m$. In fact, Theorem. Let $k$ and $k'$ be finite fields, with $|k|=p^n$ and $|k'|=q^m$, where $p$ and $q$ are primes and $n$ and $m$ are positive integers. Then $k\subseteq k'$ if and only if $p=q$ and $n|m$. With this theorem, your problem turns into a problem about divisibility: for which integers $m$ is it the case that if $d_1$ and $d_2$ are divisors of $m$, then either $d_1|d_2$ or $d_2|d_1$? (Or, if you go via the Galois correspondence, as suggested by Mariano, you are asking: which finite cyclic groups have the property that their subgroups form a chain under inclusion?) A: First read Mariano's comment and Arturo's answer. If that is not enough, then... Take a look at the diagram in this question. Ignore that extraneous long vertical line connecting the field at the bottom with the one at the top. You notice that the subfields of $\mathbb{F}_{2^{12}}$ don't form a chain, as required in your exercise. For example, neither of the intermediate fields $\mathbb{F}_4$ and $\mathbb{F}_8$ is a subfield of the other. But there is clue in that diagram that allows us to diagnose, why that happened! 1. In that diagram two subfields are connected with a line, iff one is an extension of the other, but there are no intermediate fields between them. Why don't you begin by writing the degree of the extension (of the two fields involved) adjacent to each line? Notice something about those numbers? The numbers are prime factors of 12. In general you will need to use $[k:\mathbb{F}_p]$ in place of 12. 2. Look at those fields in the diagram, where "branching" occurs, i.e. those fields that are at the bottom of two (or in a more general case two or more) lines. Notice something about the numbers attached to those lines? The prime numbers on those lines are distinct. 3. How could we prevent that from ever happening? If $p$ and $q$ are two different prime factors of $n$, and $G$ is a cyclic group of order $n$ generated by $g$, then $g^p$ and $g^q$ generate subgroups of orders $n/p$ and $n/q$ respectively. What does Galois theory tell you about the fixed fields of those two subgroups? | Mid | [
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Sen. Orrin Hatch has requested that the FBI make it known immediately if any witness in its one-week investigation into sexual misconduct allegations leveled against Supreme Court nominee Brett Kavanaugh is uncooperative. His fear is that these witnesses or people advising them will delay, stretching out when the Senate may get to a final vote in this highly charged confirmation process. Hatch, a senior member of the Senate Judiciary Committee, made his request in a letter sent Saturday to FBI Director Christopher Wray. The Republican senator from Utah wrote that Christine Blasey Ford — the woman who says Kavanaugh sexually assaulted her during a party they attended in high school — as well as others who attended the gathering have agreed to cooperate with the investigation. But if anyone tries to delay the process, Hatch asked that White House lawyers be notified. The Utah senator said one “key reason” that has caused him concern over potential delays was learning during last Thursday’s committee hearing that Ford would have preferred to have been interviewed privately in California, rather than at a televised committee hearing. He wrote that Ford’s attorneys did not inform her of numerous offers by the Senate Judiciary Committee chairman to conduct a public or private interview wherever she preferred. “The lawyers’ refusal led directly to a public hearing, against Dr. Ford’s express wishes,” Hatch wrote. “This is deeply troubling.” Hatch last week initially was opposed to any further delay of a final vote on Kavanaugh’s nomination. He later said he backed the short delay, even though he’d like to vote sooner. Hatch and Sen. Mike Lee both voted to advance the nomination to the full Senate last Friday as another GOP colleague, Jeff Flake of Arizona, successfully pushed for a one-week delay before a final vote while the FBI investigates the allegations. While Hatch’s letter focuses only on those allegations involving Ford, the FBI has been in contact with at least one other woman — Deborah Ramirez — who also alleges the Supreme Court nominee sexually assaulted her. Hatch has said that he believes Kavanaugh over the accusers, saying initially Ford must be “mistaken” about her memory of Kavanaugh pinning her down and assaulting her nearly four decades ago. After hearing Ford’s testimony, Hatch said the women did not have evidence to corroborate her claim, and said he believed the Senate should confirm the nomination. | Mid | [
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Q: PartialView or Model Inheritance Supposing I need to print the logged user on every page of my app. Currently, I'm going with Model inheritance, using an ActionFilter that fills the user in my base Model, and displaying it : ( using a DisplayTemplate ) <% = Html.DisplayFor( x => x.CurrentUser ) %> What about using a PartialView, called in the MasterPage using <% = Html.Action("UserName", "BaseController") %> Could this simplify things a bit in small to medium (20 models) applications ? A: I think BaseViewModels are monsters that shouldn't be allowed to exist. I can't think of a scenario where they don't become bloated with all sorts of superfluous logic that not all pages need. RenderAction() has come a long way since MVC 1 and its finally getting full output caching support in MVC 3. Because you gain a whole bunch of composibility with RenderAction that you don't get with a ViewModelBase I prefer it. Consider also that ViewModelBases also need ViewMasterModelBases to function resulting in even more tightly coupled logic that isn't easily swapped out. | Low | [
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Pyridyl derivatives of benzaldehyde as potential antisickling agents. Compounds that bind to sickle hemoglobin (Hb S) producing an allosteric shift to the high-affinity Hb S that does not polymerize are being developed to treat sickle cell anemia (SCA). In this study, three series of pyridyl derivatives of substituted benzaldehydes (Classes I-III) that combine structural features of two previously determined potent antisickling agents, vanillin and pyridoxal, were synthesized. When analyzed with normal human whole blood, the compounds form Schiff-base adducts with Hb and left shift the oxygen equilibrium curve (OEC) to the more soluble high-affinity Hb, more than vanillin or pyridoxal. Generally, Class-I compounds with an aromatic aldehyde located ortho to the pyridyl substituent are the most potent, followed by the Class-II compounds with the aldehyde at the meta-position. Class-III compounds with the aldehyde at the para position show the weakest activity. The structure-activity studies of these pyridyl derivatives of substituted benzaldehydes demonstrate significant allosteric potency that may be useful for treating SCA. | High | [
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Mara: Got your voice mail and wanted to let you know that Cheryl Nelson will be handling this file. Cheryl will give you a call. Sara ps Her phone number is 713-345-4693 Sara Shackleton Enron North America Corp. 1400 Smith Street, EB 3801a Houston, Texas 77002 713-853-5620 (phone) 713-646-3490 (fax) [email protected] [email protected] 12/12/2000 09:35 AM To: [email protected] cc: Subject: ISDA Master Agreement between Enron North America Corp. and Cargill, Incorporated Dear Sara, Attached please find our response to the draft Amendment to the CSA for the above-referenced Agreement. You will note that I have added some additional language which our Legal Dept. prefers to include in Amendments, which I trust will be acceptable to you as well. As mentioned briefly over the telephone the other day, I have also incorporated some changes with respect to Letter of Credit provisions. The changes to the LC terms are those which our Credit Department is requiring as a result of a review of Cargill's LC language. The main issue is that an LC issued as collateral can no longer be transferable. I note from the file on our ISDA negotiations that Enron may have preferred transferability in order to be able to transfer an LC to its Affiliates. If this is still the case, we can certainly discuss options which may specify and limit transferability accordingly. I look forward to your response at your earliest opportunity. Regards, Mara Alexander Sr. Documentation Analyst Cargill, Incorporated Tel: 952.984.3417 Fax: 952.984.3872 e-mail: [email protected] - 31409_Amnd_CSA.doc | Mid | [
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All those who have spent the past few years complaining about Judd Apatow movies — about the length or the plotlines or that they’re all about shlubby guys getting attractive girls or that they’re nothing but pot jokes — all those people can take it up with the circa 2000 NBC executives who pulled the plug on “Freaks and Geeks,” the beloved, yet low-rated, teen angst dramedy he executive produced with creator Paul Feig that helped launch the careers of Seth Rogen, Jason Segel and many others. “Even to this day, I think I didn’t want to admit that ‘Freaks and Geeks’ was cancelled,” Apatow said March 10 at the Paley Center for Media in Beverly Hills. “Everything I’ve done, in a way, is revenge for the people who cancelled ‘Freaks and Geeks.’ It’s really demented, but it’s just like ‘you were wrong about that person, and that person and that person. And that writer and that director.’ And I really should get over that.” Apatow, who still frequently works with that same core people from that show, was speaking in a Q&A with Entertainment Weekly’s Dan Snierson in front of an intimate crowd of friends and colleagues like Garry Shandling (who hired him as a writer on “The Larry Sanders Show”), Jenni Konner (who works with him on “Girls” and whom Apatow hired for another short-lived cult show, “Undeclared”) and Apatow’s wife, Leslie Mann, and daughter Iris. Before the show, he could be seen taking selfies with Ed Begley Jr., who appeared on “Larry Sanders” and also in the film “Pineapple Express,” which Apatow helped pen. Apatow received the 2014 PaleyFest Icon Award, which recognizes individual creative achievements in television. The event also kicked off PaleyFest, the Center’s annual tribute to the medium with weeks of panels focused on past and current programs. “I am, like, so proud that I’m the person who’s getting the credit for discovering Judd,” said Roseanne Barr, one of Apatow’s former bosses. “I like what you do because you can weave a story so well and with such sensitivity, it’s so touching,” Barr said before the Q&A. “It’s just very humanistic and plus, pee-your-pants funny.” Although Apatow is an executive producer on “Girls,” most of his writing and directing time is now spent in film. Will he ever return to TV? “TV is so much work, it’s crazy,” Apatow said. “It’s so much harder than movies — a thousand times harder than movies. We’re about to do our fourth season [of “Girls”] and I’ve never been a part of something that’s gone that far. And it’s wonderful to imagine how they grow up.” Apatow did say that he loves “The Americans” and (perhaps?) joked about remaking Joss Whedon’s “Buffy the Vampire Slayer.” Until then, he’ll just have to settle for “The Simpsons,” which is producing a version of a spec script he wrote of the Fox sitcom when he was still a struggling writer. He said they rewrote most of it. | Mid | [
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12/09/2008 @ 12:01AM In Depth: Twenty Most Affluent U.S. Neighborhoods The data come from the U.S. Census Bureau’s three-year American Community Survey, which gathered findings between 2005 and 2007 and ranks cities, towns and Census-designated places (CDPs) with populations between 20,000 and 65,000. To determine the most affluent neighborhoods, we looked at the median income in each of these places. 4. McLean, Va. Median Household Income: $156,292 This Washington, D.C., suburb is favored by government insiders because of its upscale homes and easy access to the Dulles Technology Corridor, the Blue Ridge Mountains and upscale shopping mecca Tysons Corner Center. | Mid | [
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Pages Thursday, March 21, 2013 Japan Home Loven Make Cleansing Pad: Overview Lately, a lot of cleansing aids have been released in the market. Gadgets like Clairsonic and the likes are here and there. They promote cleansing aids that feature specialized facial brushes that will help you deep clean your pores. As we all know, clean pores means better skin. I don't have perfect skin. In fact, I have to visit my dermatologist twice a month just to get my facial done to ensure that my face is clean (and yet I still break out often). This makes me want to try out products like Clairsonic. Sadly, however, I don't have the money to buy my own so I just have to deal with that and work with what I have. For people like me, here's a product feature that you may be interested in. I bought this thing at Japan Home for roughly PHP69. Pretty cheap, huh? It's a facial cleansing pad that helps remove deep seated dirt in your pores. It has small, soft bristles to help with removing dirt and dead skin cells. I started using this last November and I have been loving this ever since. Whenever I use this, I feel like my skin is thoroughly cleansed. Also, I feel that my skin has gotten a lot better (not perfect) since then. The small bristles really does help in cleaning my pores and what's great is that it doesn't irritate the skin. It's not abrasive as one would probably assume. It feels kinda nice (like a massage) and your skin feels really clean afterwards. I am happy to share and recommend this product to you, my dear readers. About Anna LuisaAugust 7Filipina girl in her mid-20s with a passion for all things K-Pop related and beauty. If you are a company and you would like to sponsor and/or advertise on my blog, feel free to e-mail me at [email protected] Social Media Followers Follow Lots of Girl Stuff by Email Giveaways Ends once I reach 1000 Subscribers on Youtube. Read video description to see the mechanics. Message me to sponsor, if interested, at [email protected]. I'm open for giveaway collabs and product reviews. Thanks! | Mid | [
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Physiologically based pharmacokinetic models of small molecules and therapeutic antibodies: a mini-review on fundamental concepts and applications. The mechanisms of absorption, distribution, metabolism and elimination of small and large molecule therapeutics differ significantly from one another and can be explored within the framework of a physiologically based pharmacokinetic (PBPK) model. This paper briefly reviews fundamental approaches to PBPK modeling, in which drug kinetics within tissues and organs are explicitly represented using physiologically meaningful parameters. The differences in PBPK models applied to small/large molecule drugs are highlighted, thus elucidating differences in absorption, distribution and elimination properties between these two classes of drugs in a systematic manner. The absorption of small and large molecules differs with respect to their common extravascular routes of delivery (oral versus subcutaneous). The role of the lymphatic system in drug distribution, and the involvement of tissues as sites of elimination (through catabolism and target mediated drug disposition) are unique features of antibody distribution and elimination that differ from small molecules, which are commonly distributed into the tissues but are eliminated primarily by liver metabolism. Fundamental differences exist in the ability to predict human pharmacokinetics based upon preclinical data due to differing mechanisms governing small and large molecule disposition. These differences have influence on the evolving utilization of PBPK modeling in the discovery and development of small and large molecule therapeutics. | High | [
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Dissipation and residue of MCPA (4-chloro-2-ethylphenoxyacetate) in wheat and soil. A rapid and simple HPLC method has been developed for the quantitation of 4-chloro-2-methylphenoxyacetic acid (MCPA) in both wheat and soil samples. Samples were extracted in acidic media and cleaned up by solid-phase extraction with C(18) cartridges before HPLC-DAD detection. The limits of detection and quantification of MCPA were 0.02 ng and 0.01 mg/kg for both wheat and soil. The mean recoveries ranged from 87.1% to 98.2%, and the RSDs ranged from 0.604% to 3.44% for the three spiked levels (0.01, 0.1, 0.5 mg/kg). The proposed method was successfully applied to the analysis of MCPA residues in wheat and soil samples from an experimental field. The dissipation half-lives in soil were calculated to be 3.22 days (Beijing) and 3.10 days (Tianjin), respectively. Direct confirmation of the analytes in real samples was achieved by gas chromatography-mass spectrometry. The results indicated that at harvest time, the residues of MCPA in wheat were well below the maximum residue levels and were safe to apply in wheat. | Mid | [
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This invention relates to accessories for the prevention of loss or misplacement of cigarette lighters. More particularly, the invention relates to an accessory for securing a lighter to the person or to a fixed support. Cigarette lighters carried on the person frequently are lost or misplaced, as by falling from a pocket, being left behind after use, or being taken by another after use. Also, the lighters may be carried in one of various pockets, or in a purse, where they may be mixed with other articles, and they may not be as accessible as desired, or they may bulge the pocket at times. | Low | [
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Q: Ruby on Rails - Rakefile validates_uniqueness_of I am using a rakefile to fetch information from one website and saving it to my database. Using the TMDB-Gem, this code @movie = TmdbMovie.browse(:order_by => "release", :order => "asc", :page => 1, :per_page => 2, :language => "en", :expand_results => true) browses the oldest movies (:order_by => "release") and saves them to my database, but as i'll be running this rake quite frequently, the returned and saved movies will be the same. Every movie has a tmdb_id and every id is unique How can i make the rakefile check that the returned movie's tmdb_id is unique, and if there is already a movie with that id, skip and save the next movie. I tried it in my Movies model validates_uniqueness_of :tmdb_id but it gives an error when running the rake command and it doesn't save movies. Basically, how can I, through the rakefile, validate the uniqueness of the tmdb_id This is my rake file namespace :db do task :pull_tmdb_data => :environment do Tmdb.api_key = "API KEY" Tmdb.default_language = "en" @movie = TmdbMovie.browse(:order_by => "release", :order => "asc", :page => 1, :per_page => 2, :language => "en", :expand_results => true) @movie.each do |movie| Movie.create(title: movie.name, description: movie.overview, release_date: movie.released, tmdb_id: movie.id) end end end A: You're right to use validates_uniqueness_of :tmdb_id in your Movie model. You didn't show how you were saving the movies to your database, but .save doesn't cause an exception when validations fail, whereas .save! does. The key would be to use a save method that doesn't raise an error when validations fail. Edit - Now that I understand what you're actually trying to do, you should be able to do something like: per_page = 100 number_of_movies = Movie.count page = number_of_movies/per_page+1 @movies = TmdbMovie.browse(:order_by => "release", :order => "asc", :page => page, :per_page => per_page, :language => "en", :expand_results => true) browses the oldest movies (:order_by => "release") So if you've already pulled 435 movies, it'll only return movies 400-500 in the next call .. I did it this way because I wasn't sure if there was an offset option, but if there is you could just offset the query by Movie.count, which would be better. | Low | [
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Pella curse tablet The Pella curse tablet is a text written in a distinct Doric Greek idiom, found in Pella, the ancient capital of Macedon, in 1986. Ιt contains a curse or magic spell (, katadesmos) inscribed on a lead scroll, dated to the first half of the 4th century BC (circa 375–350 BC). It was published in the Hellenic Dialectology Journal in 1993. It is one of four known texts that may represent a local dialectal form of ancient Greek in Macedonia, all of them identifiable as Doric. These suggest that a Doric Greek dialect was spoken in Macedonia, as was previously proposed based on the West Greek forms of names found in Macedonia. As a result, the Pella curse tablet has been forwarded as an argument that the Ancient Macedonian language was a dialect of North-Western Greek, and one of the Doric dialects. The spell was written by a woman, possibly named Dagina, and was intended to cause her former lover to marry her. Interpretation The tablet is also described as a "mixed curse" due to the supplicative nature of the appeal. For example, the word ΕΡΗΜΑ or "abandoned" is quite common in appeals to divine powers. It is a magic spell or love charm written by a woman, possibly named Dagina (Ancient Greek: Δαγίνα), whose lover Dionysophōn (Διονυσοφῶν, gen.: Διονυσοφῶντος) is apparently about to marry Thetima (Θετίμα, "she who honors the gods"; the Attic Greek form is Theotimē - Θεοτίμη). She invokes "Makron and the demons" (parkattithemai makrōni kai [tois] daimosi - παρκαττίθεμαι μάκρωνι καὶ [τοῖς] δαίμοσι; in Attic, παρκαττίθεμαι is parakatatithemai - παρακατατίθεμαι) to cause Dionysophon to marry her instead of Thetima. Dagina also wants him never to marry another woman, unless she herself recovers and unrolls the scroll. She wishes for herself to grow old by the side of Dionysophon. Katadesmoi or defixiones were spells written on non-perishable material, such as lead, stone or baked clay, and were secretly buried to ensure their physical integrity, which would then guarantee the permanence of their intended effects. The language is a distinct form of North-West Greek, and the low social status of its writer, as (arguably) evidenced by her vocabulary and belief in magic, strongly suggests that a unique form of West Greek was spoken by lower-class people in Pella at the time the tablet was written. This should not, however, be taken to indicate that only those of middling or low social status practiced magic in the Ancient Greek world; quite wealthy individuals might also use lead katadesmoi (curse tablets) for love, revenge, and to bind their opponents in athletic contests. Text and translation Greek 1. [ΘΕΤΙ]ΜΑΣ ΚΑΙ ΔΙΟΝΥΣΟΦΩΝΤΟΣ ΤΟ ΤΕΛΟΣ ΚΑΙ ΤΟΝ ΓΑΜΟΝ ΚΑΤΑΓΡΑΦΩ ΚΑΙ ΤΑΝ ΑΛΛΑΝ ΠΑΣΑΝ ΓΥ- 2. [ΝΑΙΚ]ΩΝ ΚΑΙ ΧΗΡΑΝ ΚΑΙ ΠΑΡΘΕΝΩΝ ΜΑΛΙΣΤΑ ΔΕ ΘΕΤΙΜΑΣ ΚΑΙ ΠΑΡΚΑΤΤΙΘΕΜΑΙ ΜΑΚΡΩΝΙ ΚΑΙ 3. [ΤΟΙΣ] ΔΑΙΜΟΣΙ ΚΑΙ ΟΠΟΚΑ ΕΓΩ ΤΑΥΤΑ ΔΙΕΛΕΞΑΙΜΙ ΚΑΙ ΑΝΑΓΝΟΙΗΝ ΠΑΛΕΙΝ ΑΝΟΡΟΞΑΣΑ 4. [ΤΟΚΑ] ΓΑΜΑΙ ΔΙΟΝΥΣΟΦΩΝΤΑ ΠΡΟΤΕΡΟΝ ΔΕ ΜΗ ΜΗ ΓΑΡ ΛΑΒΟΙ ΑΛΛΑΝ ΓΥΝΑΙΚΑ ΑΛΛ᾽ Η ΕΜΕ 5. [ΕΜΕ Δ]Ε ΣΥΝΚΑΤΑΓΗΡΑΣΑΙ ΔΙΟΝΥΣΟΦΩΝΤΙ ΚΑΙ ΜΗΔΕΜΙΑΝ ΑΛΛΑΝ ΙΚΕΤΙΣ ΥΜΩΝ ΓΙΝΟ- 6. [ΜΑΙ ΦΙΛ]ΑΝ ΟΙΚΤΙΡΕΤΕ ΔΑΙΜΟΝΕΣ ΦΙΛ[ΟΙ] ΔΑΓΙΝΑΓΑΡΙΜΕ ΦΙΛΩΝ ΠΑΝΤΩΝ ΚΑΙ ΕΡΗΜΑ ΑΛΛΑ 7. [ΤΑΥΤ]Α ΦΥΛΑΣΣΕΤΕ ΕΜΙΝ ΟΠΩΣ ΜΗ ΓΙΝΗΤΑΙ ΤΑ[Υ]ΤΑ ΚΑΙ ΚΑΚΑ ΚΑΚΩΣ ΘΕΤΙΜΑ ΑΠΟΛΗΤΑΙ 8. [....]ΑΛ[-].ΥΝΜ .. ΕΣΠΛΗΝ ΕΜΟΣ ΕΜΕ Δ᾽ ΕΥ[Δ]ΑΙΜΟΝΑ ΚΑΙ ΜΑΚΑΡΙΑΝ ΓΕΝΕΣΤΑΙ 9. [-]ΤΟ[.].[-].[..]..Ε.Ε.Ω[?]Α.[.]Ε..ΜΕΓΕ [-] English 1. Of [Theti]ma and Dionysophon the ritual wedding and the marriage I bind by a written spell, and of all other 2. wo[men], both widows and maidens, but of Thetima in particular, and I entrust to Makron* and 3. [the] daimones, and (only) when I should dig up again and unroll and read this, 4. [?] that she might wed Dionysophon, but not before, for I wish him to take no other woman than me, 5. and that [I] grow old with Dionysophon, and no one else. I [am] your supplicant: 6. Have pity on [Phil?]a*, dear daimones, for I am (a) dagina? of all my dear ones and I am abandoned. 7. But guard [this] for my sake so that these things do not happen, and wretched Thetima perishes miserably. 8. ... but that I become happy and blessed. Points of interpretation "Makron" (line 2) is most probably the name of the dead man in whose grave the tablet was deposited. This was commonly done in the belief that the deceased would "convey" the message to the Chthonic spirits of the Greek underworld (the "daimones" in lines 3 and 6). The missing word in line 6 between "I am your supplicant" and "have pity" (here reconstructed as [Phil?]a) is carved at the edge of the tablet and the only things we can read of it are that it is a short word that ends in-AN. "PHILAN" is a likely reconstruction, but by no means the only one possible. If true, the word "PHILAN" could equally well be either the personal name "Phila" or the feminine adjective "phila", "friend" or "dear one". In the latter case, an alternative reading of line 6 would be: "Have pity on your dear one, dear demons". In the former case, a personal name would be perfectly placed but, as the name of the person who wrote the curse is not mentioned elsewhere, it is impossible to know with certainty what the missing word is. The word "DAGINA" (line 6) is inexplicable and previously unattested, even as a personal name. The alternative has been suggested by Dubois, that it is a misspelling, and that the writer intended to write "dapina" (the difference between Γ and Π being a single stroke). If true, this may mean that dapina is an (also unattested) Macedonian rendering of what would be written "ταπεινή", tapeinē (humble, lowly, brought low), in standard Attic. In this case the inscription reads: "for I am lowly from all my dear ones and abandoned" etc. Another possibility is that Dagina is perhaps related to δαγύς, a doll or puppet, especially as used in magic (cf. LSJ p. 364). Similarly, ΙΜΕ is also unexplained, but seems to be taken as a misspelling of ΕΜΙ (εμι) (i.e., Attic εἰμι), "I am." Dating According to D. R. Jordan (Duke University), the tablet has been dated to the "Mid-IV [century] or slightly earlier". Significance The discovery of the Pella curse tablet, according to Olivier Masson, substantiates the view that the ancient Macedonian language was a form of North-West Greek: "Yet in contrast with earlier views which made of it {i.e. Macedonian} an Aeolic dialect (O. Hoffmann compared Thessalian) we must by now think of a link with North-West Greek (Locrian, Aetolian, Phocidian, Epirote). This view is supported by the recent discovery at Pella of a curse tablet (4th cent. BC), which may well be the first 'Macedonian' text attested (provisional publication by E. Voutyras; cf. the Bulletin Epigraphique in Rev. Et. Grec. 1994, no. 413); the text includes an adverb "opoka" which is not Thessalian." Of the same opinion is James L. O'Neil's (University of Sydney) presentation at the 2005 Conference of the Australasian Society for Classical Studies, entitled "Doric Forms in Macedonian Inscriptions" (abstract): "A fourth‐century BC curse tablet from Pella shows word forms which are clearly Doric, but a different form of Doric from any of the west Greek dialects of areas adjoining Macedon. Three other, very brief, fourth century inscriptions are also indubitably Doric. These show that a Doric dialect was spoken in Macedon, as we would expect from the West Greek forms of Greek names found in Macedon. And yet later Macedonian inscriptions are in Koine avoiding both Doric forms and the Macedonian voicing of consonants. The native Macedonian dialect had become unsuitable for written documents." Professor Johannes Engels of the University of Cologne argues that the Pella curse tablet provides evidence to support that Macedonian was a North-West Greek dialect: "Another very important testimony comes from the so-called Pella curse tablet. This is a text written in Doric Greek and found in 1986 [...] This has been judged to be the most important ancient testimony to substantiate that Macedonian was a north-western Greek and mainly a Doric dialect." See also Ancient Macedonian language Doric Greek Phiale of Megara References Citations Sources Further reading External links PHI Greek Inscriptions (Epigraphical Database): Makedonia (Bottiaia) — Pella — ca. 380-350 BC, SEG 43:434 "Love Charms In Their Social Context" – Prof. Radcliffe G. Edmonds III, Bryn Mawr College Category:4th-century BC manuscripts Category:1986 archaeological discoveries Category:Ancient Pella Category:Archaeological artifacts Category:Archaeological discoveries in Greece Category:Curse tablets Category:Doric Greek inscriptions Category:Greek religion inscriptions Category:Occult texts Category:Religion in ancient Macedonia Category:Votive offering Category:Witchcraft | Mid | [
0.607427055702917,
14.3125,
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <title>Flot Examples: Symbols</title> <link href="../examples.css" rel="stylesheet" type="text/css"> <!--[if lte IE 8]><script language="javascript" type="text/javascript" src="../../excanvas.min.js"></script><![endif]--> <script language="javascript" type="text/javascript" src="../../jquery.js"></script> <script language="javascript" type="text/javascript" src="../../jquery.flot.js"></script> <script language="javascript" type="text/javascript" src="../../jquery.flot.symbol.js"></script> <script type="text/javascript"> $(function() { function generate(offset, amplitude) { var res = []; var start = 0, end = 10; for (var i = 0; i <= 50; ++i) { var x = start + i / 50 * (end - start); res.push([x, amplitude * Math.sin(x + offset)]); } return res; } var data = [ { data: generate(2, 1.8), points: { symbol: "circle" } }, { data: generate(3, 1.5), points: { symbol: "square" } }, { data: generate(4, 0.9), points: { symbol: "diamond" } }, { data: generate(6, 1.4), points: { symbol: "triangle" } }, { data: generate(7, 1.1), points: { symbol: "cross" } } ]; $.plot("#placeholder", data, { series: { points: { show: true, radius: 3 } }, grid: { hoverable: true } }); // Add the Flot version string to the footer $("#footer").prepend("Flot " + $.plot.version + " – "); }); </script> </head> <body> <div id="header"> <h2>Symbols</h2> </div> <div id="content"> <div class="demo-container"> <div id="placeholder" class="demo-placeholder"></div> </div> <p>Points can be marked in several ways, with circles being the built-in default. For other point types, you can define a callback function to draw the symbol. Some common symbols are available in the symbol plugin.</p> </div> <div id="footer"> Copyright © 2007 - 2013 IOLA and Ole Laursen </div> </body> </html> | Low | [
0.50943396226415,
33.75,
32.5
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<FE> <HEADER competition="U18 Men friendlies 2015" quarter="4" time="ENDE" logo="http://live.fibaeurope.com/www/gallery/16B89DBC-0E4B-471D-8CCC-C61D57D28BA2.jpg" duration="31.1988"> <TEAM name="Germany U18 Men 2015" logo="http://live.fibaeurope.com/www/gallery/FC5371F0-3201-4830-9143-A681A8929BAB.jpg" pts="67" fouls="3" /> <TEAM name="Turkey U18 Men 2015" logo="http://live.fibaeurope.com/www/gallery/6E1AF23C-5015-47B4-AF67-51D97FB879D2.jpg" pts="70" fouls="4" /> <QUARTERS> <QUARTER n="1" scoreA="13" scoreB="17" /> <QUARTER n="2" scoreA="25" scoreB="25" /> <QUARTER n="3" scoreA="17" scoreB="16" /> <QUARTER n="4" scoreA="12" scoreB="12" /> </QUARTERS> </HEADER> <SHOTCHART Quarters="4" duration="31.1914"> <TEAM Name="Germany U18 Men 2015"> <P N="T. Taras" Nr="5" FGP="33.3" FTP="50.0" P2P="25.0" P3P="50.0" PTS="6" /> <P N="L. Figge" Nr="6" FGP="40.0" FTP="100.0" P2P="50.0" P3P="0.0" PTS="6" /> <P N="D. Krämer" Nr="7" FGP="50.0" FTP="100.0" P2P="100.0" P3P="0.0" PTS="4" /> <P N="L. 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Özel" Nr="5" FGP="50.0" FTP="0.0" P2P="25.0" P3P="100.0" PTS="8" /> <P N="E. Yilmaz" Nr="6" FGP="50.0" FTP="0.0" P2P="50.0" P3P="50.0" PTS="5" /> <P N="E. Taskiran" Nr="7" FGP="46.2" FTP="100.0" P2P="55.6" P3P="25.0" PTS="15" /> <P N="A. Berisha" Nr="8" FGP="33.3" FTP="50.0" P2P="33.3" P3P="0.0" PTS="4" /> <P N="B. Ülker" Nr="9" FGP="20.0" FTP="60.0" P2P="50.0" P3P="0.0" PTS="7" /> <P N="R. Öncel" Nr="10" FGP="25.0" FTP="50.0" P2P="33.3" P3P="0.0" PTS="4" /> <P N="M. Tunc" Nr="11" FGP="0.0" FTP="0.0" P2P="0.0" P3P="0.0" PTS="0" /> <P N="E. Gazi" Nr="12" FGP="66.7" FTP="0.0" P2P="100.0" P3P="50.0" PTS="5" /> <P N="E. Bayrak" Nr="13" FGP="40.0" FTP="0.0" P2P="66.7" P3P="0.0" PTS="4" /> <P N="Ö. Yurtseven" Nr="14" FGP="45.5" FTP="50.0" P2P="50.0" P3P="0.0" PTS="11" /> <P N="Y. 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player="10" quarter="4" /> <S m="1" t="02:19" x="895" y="224" team="1" player="14" quarter="4" /> <S m="0" t="01:37" x="1450" y="160" team="1" player="4" quarter="4" /> <S m="2" t="01:24" x="997" y="500" team="0" player="6" quarter="4" /> <S m="1" t="01:00" x="199" y="652" team="1" player="10" quarter="4" /> <S m="0" t="00:56" x="785" y="213" team="0" player="13" quarter="4" /> <S m="1" t="00:21" x="94" y="533" team="1" player="9" quarter="4" /> <S m="1" t="00:13" x="666" y="218" team="1" player="6" quarter="4" /> <S m="1" t="00:12" x="260" y="699" team="0" player="10" quarter="4" /> <S m="0" t="00:12" x="677" y="251" team="0" player="21" quarter="4" /> </SHOTS> </SHOTCHART> <OVERVIEW duration="31.2142"> <GAME CompID="1713" CompCode="" Competition="Men´s A2 friendly games 2013" Round="" ID="34886" GameCode="" TeamA="U20 Try out Team1" ScoreA="0" TeamB="U20 Try out Team2" ScoreB="2" StartTime="10:30:00" Quarter="1" Time="10:00" Status="1" /> <GAME CompID="1713" CompCode="" Competition="Men´s A2 friendly games 2013" Round="" ID="34887" GameCode="" TeamA="U20 Try out Team1" ScoreA="3" TeamB="U20 Try out Team2" ScoreB="0" StartTime="10:00:00" Quarter="2" Time="10:00" Status="1" /> <GAME CompID="9279" CompCode="" Competition="U18 Men friendlies 2015" Round="" ID="68392" GameCode="" TeamA="Germany U18 Men 2015" ScoreA="67" TeamB="Turkey U18 Men 2015" ScoreB="70" StartTime="18:00:00" LogoA="http://live.fibaeurope.com/www/gallery/68F1BB20-99AD-49E7-B99A-466C09179CE4.gif" LogoB="http://live.fibaeurope.com/www/gallery/2DF961C7-0CC9-457B-AA5A-17D59515B1DB.jpg" Quarter="4" Time="00:00" Status="1" /> </OVERVIEW> <BANNER file="http://live.fibaeurope.com/www/gallery/54B86B48-2B01-49F6-B59F-C8F1C23F9848.jpg" duration="15.5996" /> </FE> | Mid | [
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require('./check-versions')() process.env.NODE_ENV = 'production' const ora = require('ora') const rm = require('rimraf') const path = require('path') const chalk = require('chalk') const webpack = require('webpack') const config = require('../config') const webpackConfig = require('./webpack.prod.conf') const spinner = ora('building for production...') spinner.start() rm(path.join(config.build.assetsRoot, '*'), err => { if (err) throw err webpack(webpackConfig, function (err, stats) { spinner.stop() if (err) throw err process.stdout.write(stats.toString({ colors: true, modules: false, children: false, chunks: false, chunkModules: false }) + '\n\n') if (stats.hasErrors()) { console.log(chalk.red(' Build failed with errors.\n')) process.exit(1) } console.log(chalk.cyan(' Build complete.\n')) console.log(chalk.yellow( ' Tip: built files are meant to be served over an HTTP server.\n' + ' Opening index.html over file:// won\'t work.\n' )) }) }) | Low | [
0.468041237113402,
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Tuesday, August 30, 2011 I’m so excited that I can hardly breathe. Tomorrow we set off in The Silver-Winged Unicorn to the vast expanse of The Karoo, one of my favourite places in the world. Two of my favourite people in the world, and I. We will stay in Nieu Bethesda where the air is clear, my heart squeezes in pleasure and the stars are sprinkled liberally in the night skies. A place where donkeys amble about on the dusty streets and there is no petrol station, no grocery store, no ATM. Bliss. Thursday, August 25, 2011 I’ve decided to do a thing, due to my blocked writing channels. A couple of years ago I wrote a month of 100 words – basically 100 words exactly, every day, for a month, it’s a fabulous website and documented a very beautiful time in my life and I really enjoyed it so I've decided it's time for something like that again. A while ago I downloaded a list of thirteen writing prompts from a website somewhere and I’m now going to do them. Some of my blogs will be stories I’ve made up, using the prompts. They’re quite cool, and a bit difficult, but I need a challenge. I’ll tell you the prompt after each story. Here’s the first: The walls of the flat are thin, and it’s a hot evening so the balcony doors are open to let in what I hoped would be some cool air. In fact it is only letting in more of the hot, still breaths of the sweating city and the noise from the next door flat. The air fills with the shrieking that one expects to hear when something really bad happens. It’s followed by some ineffectual interjections from a lower voice, one of those overly calm kinds that would certainly make me shriek louder. I step onto the balcony in search of the non-existent breeze and because I’m a voyeur and can’t hear properly, the thin walls muffling the noise. As I settle into the canvas chair on my balcony and put my glass of wine filled with ice-fighting-for-its-life-in-the-heat, I see a flurry of letters being thrust from the next door balcony and I smell a tiny whiff of cheap perfume from the papers that flutter lazily downwards. Someone’s history, left to fend for itself on the hot city pavement below. Contemplating running down the stairs to gather them up and read them but too hot to move, I sip on my wine. The ghosts of the melted ice form condensation on the side of the glass and cool my lips momentarily. The shrieking continues but moves further away, finally punctuated with the slam of a door. I take another sip and watch a black cat hunting a chip packet on the other side of the street. Prompt 1: Write a scene showing a man and a woman arguing over the man’s friendship with a former girlfriend. Do not mention the girlfriend, the man, the woman, or the argument. I’m not sure that I got it quite right but I had fun doing it so that’s okay, right? Wednesday, August 24, 2011 My one CD-drive on my computer at Real Work suddenly decided not to work yesterday afternoon. It was a wet and grey day here. You may think I’m losing the plot and flitting from computers to weather illogically. There is method to my madness. The link will soon be made clear (well, sort-of.) I work at one of the largest tertiary educational institutions down at the foot of Africa so one expects the pimply youths running our IT department to be of an extremely high grade. This was the conversation I had. I’ll let you decide: Shiny: Hello? Pimply Youth? IT Geek: Ah, yes, hmmm, um. The network is a bit slow. I’m just waiting for remote access. Shiny: Ah, okay. Slow? Yes. I’ve noticed. IT Geek: It’s cloudy you see. Shiny: Yes, I’ve noticed that too. What does that have to do with remote access? IT Geek: Well, you know when a woman has a caesarean section? Shiny: Urm, yes? IT Geek: Well, when they’ve had one, and it’s cloudy and grey, they get moody and slow. Shiny: (completely stumped silence) IT Geek: Network access and, therefore, remote access are the same. I couldn’t make this shit up. He did, however, after this gem of wisdom, fix the problem so I guess I should just be grateful. Tuesday, August 23, 2011 Remember last year’s Women’s Day treat that was organised by Real Work? The talk on post-partum depression? Well, this year, they outdid themselves, inspiring (yet another) Letter I should Send. In order to celebrate women, which is the point of Women’s Day. We were invited to a talk and ‘light refreshments’. The topic this year: “Alcohol Abuse: Do we care?” Seriously. Dear Real Work Party Planning Committee, Thank you, again, for thinking of us and rewarding us with a little treat to celebrate Women’s Day. Unfortunately, “Alcohol Abuse – Do we care?” is honestly the most awful topic I’ve ever heard of. I didn’t think you could beat last year’s awful topic, but you seem to have managed. I’m amazed, but in horrified way. Why on god’s green earth would you think that we’d like to celebrate our womanliness discussing such a depressing topic, with the added assumption in the title of the talk that we don’t care about it? Next year you could go for something more upbeat, perhaps “Toenail infections – when to seek medical help” or something like that? I do want to say, though, thanks again for organising lunch snacks. You sure know how to make a lady feel good on Women’s Day. Thank you, too, for putting in the effort to plan the celebration. How does one get onto the committee? Just a question… I’m not planning on ousting you all or anything, really. Monday, August 22, 2011 I want to write, and I've started about four gazillion (give or take) blogs and lost momentum. They're piling up over there, on the other side of my desk, past the Ferrero Rocher wrapper (empty, unfortunately). I have so much to say, my mind is bouncing between the darkest depths and knowing stuff needs to be outed and complete inertia. See? Completely turmoiled, my head is.I really do have lots to say. Hell, I haven't even begun with all the Spain stories and we've been back for, what, three months? Ai. How does time fly so? The Spain stories are going dull at the edges, losing their distinct lines, they must be written quick, before they curl up like Autumn leaves and fall off the tree into nooks and crannies that I can't reach. So here I am, waffling, in an attempt to get the momentum going. Enough already. Hopefully you'll see me again tomorrow. I can't promise intelligable writing - is that even a word? - but I will, at least, try to write. Before the thoughts in my head devour me alive. Thursday, August 11, 2011 There’s something about mist that is lovely. Perhaps only for those of us who don’t have to experience it too often, though, I’d think. It just feels to me like a hug from The Weatherman, albeit a slightly damp hug. It seems to me that in thick mist, like that that fell over The City Beneath the Mountain this morning, the trees and plants get away with doing things they can’t (or won’t?) normally do. Like jumping up and down, or wiggling their trunks, or dancing a little. They know, that, if we humans notice, we’ll shake our little heads and blame it on a trick of the mist on our eyes. There is the most beautiful huge old Wild Fig tree down there, on the other side of the river. It’s so big that it’d take about six tree-hugging hippies, depending on how long their arms are, to hug it. It stretches into the sky with its branches waving very much toward the direction in which the wind blows, like a wild hairstyle. Today, as I looked across when we drove past on the way to The Ivory Tower, I swear I saw it, through the mist, wave one of its ancient tree hands at me. I waved back, in the hope that a human response might encourage it to wave again, even when its not misty. Monday, August 1, 2011 She thought that if she carefully opened up her chest and took her heart out it might help. She did it gently, knowing the fragility of it all and wrapped it in layer upon layer of the softest, reddest satin and put it in a beautiful engraved wooden box that her grandmother had given her as a child. She’d said it was a magic box and could be used quite safely to hold secrets and valuable things. Carefully she placed the box in her bedside cupboard and whispered some unintelligible words as she closed it and lay down on her bed. It didn’t help, though, the box couldn’t protect her heart. Her despair leaked out of her, a gush of red, a waterfall of disillusionment, into a puddle of hopelessness. And her heart gently stopped beating in its beautiful red satin outfit. She sighed and was peaceful at last. | Low | [
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Image projectors may be used to project images onto a projection surface, such as a screen or other surface. In some applications, video projectors may be used to enhance, compliment, or otherwise augment objects on the surface to create a dynamic and enjoyable user experience, such as, for example, an amusement park attraction. For example, characters or objects may be projected on a surface that virtually “interact” with real objects on the surface. Conventional video projectors have a number of limitations. In particular, conventional video projectors have limited color gamut and brightness. Due to these limitations, presentations using only conventional video projectors can appear dull and flat. Further, in situations where ambient lighting is present, the resulting image can appear washed out and unrealistic. On the contrary, laser projectors, such as laser scanning projectors, have increased brightness and color gamut as compared to conventional video projectors. In particular, laser projectors can project pure saturated, i.e. monochromatic red, green, and blue color tones, allowing a significantly wider color gamut than conventional video projectors. However, known calibration techniques for laser projectors require significant user interaction, are time-intensive, and are often not very accurate. As such, there is a need for a technique that can be used to more accurately and automatically calibrate laser projectors. The information included in this Background section of the specification, including any references cited herein and any description or discussion thereof, is included for technical reference purposes only and is not to be regarded subject matter by which the scope of the invention as defined in the claims is to be bound. | Mid | [
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Nikolai Myaskovsky Nikolai Yakovlevich Myaskovsky or Miaskovsky or Miaskowsky (; ; 20 April 18818 August 1950), was a Russian and Soviet composer. He is sometimes referred to as the "Father of the Soviet Symphony". Myaskovsky was awarded the Stalin Prize five times, more than any other composer. Early years Myaskovsky was born in Modlin Fortress, near Warsaw, Congress Poland, Russian Empire, the son of an engineer officer in the Russian army. After the death of his mother the family was brought up by his father's sister, Yelikonida Konstantinovna Myaskovskaya, who had been a singer at the Saint Petersburg Opera. The family moved to Saint Petersburg in his teens. Though he learned piano and violin, he was discouraged from pursuing a musical career, and entered the military. However, a performance of Tchaikovsky's Pathétique Symphony conducted by Arthur Nikisch in 1896 inspired him to become a composer. In 1902 he completed his training as an engineer, like his father. As a young subaltern with a Sappers Battalion in Moscow, he took some private lessons with Reinhold Glière and when he was posted to St Petersburg he studied with Ivan Krizhanovsky as preparation for entry into the Saint Petersburg Conservatory, where he enrolled in 1906 and became a student of Anatoly Lyadov and Nikolai Rimsky-Korsakov. A late starter, Myaskovsky was the oldest student in his class but soon became firm friends with the youngest, Sergei Prokofiev, and they remained friends throughout the older man's life. At the Conservatory, they shared a dislike of their professor Anatoly Lyadov, which, since Lyadov disliked the music of Edvard Grieg, led to Myaskovsky's choice of a theme by Grieg for the variations with which he closed his String Quartet No. 3. Early works Prokofiev and Myaskovsky worked together at the conservatory on at least one work, a lost symphony, parts of which were later scavenged to provide material for the slow movement of Prokofiev's Piano Sonata No. 4. They both later produced works using materials from this period—in Prokofiev's case the Third and Fourth piano sonatas; in Myaskovsky's other works, such as his Tenth String Quartet and what are now the Fifth and Sixth Piano Sonatas, all revisions of works he wrote at this time. Early influences on Myaskovsky's emerging personal style were Tchaikovsky, strongly echoed in the first of his surviving symphonies (in C minor, Op. 3, 1908/1921), which was his Conservatory graduation piece, and Alexander Scriabin, whose influence comes more to the fore in Myaskovsky's First Piano Sonata in D minor, Op. 6 (1907–10), described by Glenn Gould as "perhaps one of the most remarkable pieces of its time", and his Symphony No. 3 in A minor, Op. 15 of 1914, a turbulent and lugubrious work in two large movements. Myaskovsky graduated in 1911 and afterwards taught in Saint Petersburg, where he also developed a supplementary career as a penetrating musical critic. (He was one of the most intelligent and supportive advocates in Russia for the music of Igor Stravinsky, though the story that Stravinsky dedicated The Rite of Spring to Myaskovsky is untrue.) Called up during World War I, he was wounded and suffered shell-shock on the Austrian front, then worked on the naval fortifications at Tallinn. During this period he produced two diametrically opposed works, his Symphony No. 4 (Op. 17, in E minor) and his Symphony No. 5 (Op. 18, in D major). The next few years saw the violent death of his father, an ex-Tsarist general who was murdered by Red Army soldiers while waiting for a train in the winter of 1918–19, and the death of his aunt, to whom he was closely attached, in the winter of 1919–20. His brother-in-law, the husband of his sister Valentina Yakovlevna, had committed suicide before the War because of financial troubles. Myaskovsky himself served in the Red Army from 1917 to 1921; in the latter year he was appointed to the teaching staff of the Moscow Conservatory and membership of the Composers' Union. Thereafter he lived in Moscow, sharing an apartment with his widowed sister Valentina and her daughter. (He also had a married sister, Vera.) Middle years In the 1920s and 1930s Myaskovsky was the leading composer in the USSR dedicated to developing basically traditional, sonata-based forms. He wrote no operas—though in 1918 he planned one based on Dostoyevsky's novel The Idiot, with a libretto by Pierre Souvtchinsky; but he would eventually write a total of 27 symphonies (plus three sinfoniettas, two concertos, and works in other orchestral genres), 13 string quartets, 9 piano sonatas as well as many miniatures and vocal works. Through his devotion to these forms, and the fact that he always maintained a high standard of craftsmanship, he was sometimes referred to as 'the musical conscience of Moscow'. His continuing commitment to musical modernism was shown by the fact that along with Alexander Mosolov, Gavriil Popov and Nikolai Roslavets, Myaskovsky was one of the leaders of the Association for Contemporary Music. While he remained in close contact with Prokofiev during the latter's years of exile from the USSR, he never followed him there. Myaskovsky's reaction to the events of 1917–21 inspired his Symphony No. 6 (1921–1923, rev. 1947—this is the version that is almost always played or recorded) his only choral symphony and the longest of his 27 symphonies, sets a brief poem (in Russian though the score allows Latin alternatively—see the American Symphony Orchestra page below on the origins of the poem—the soul looking at the body it has abandoned.) The finale contains quite a few quotes—the Dies Irae theme, as well as French revolutionary tunes. The years 1921–1933, the first years of his teaching at the Moscow Conservatory, were the years in which he experimented most, producing works such as the Tenth and Thirteenth symphonies, the fourth piano sonata and his first string quartet. Perhaps the best example of this experimentative phase is the Thirteenth symphony, which was the only one of his works to be premiered in the United States. In the 1920s and 1930s Myaskovsky's symphonies were quite frequently played in Western Europe and the USA. His works were issued by Universal Edition, one of Europe's most prestigious publishers. In 1935, a survey made by CBS of its radio audience asking the question "Who, in your opinion, of contemporary composers will remain among the world's great in 100 years?" placed Myaskovsky in the top ten along with Prokofiev, Rachmaninoff, Shostakovich, Richard Strauss, Stravinsky, Sibelius, Ravel, de Falla and Fritz Kreisler. The next few years after 1933 are characterized mostly by his apparent discontinuation of his experimental trend, though with no general decrease in craftsmanship. The Violin Concerto dates from these years, the first of two or three concerti, depending on what one counts, the second being for cello, and a third if one counts the Lyric Concertino, Op. 32 as a concerto work. Another work from the period up to 1940 is the one-movement Symphony No. 21 in F-sharp minor, Op. 51, a compact and mostly lyrical work, very different in harmonic language from the Thirteenth. Despite his personal feelings about the Stalinist regime, Myaskovsky did his best not to engage in overt confrontation with the Soviet state. While some of his works refer to contemporary themes, they do not do so in a programmatic or propagandistic way. The Symphony No. 12 was inspired by a poem about the collectivization of farming, while No. 16 was prompted by the crash of the huge airliner Maxim Gorky and was known under the Soviets as the Aviation Symphony. This symphony, sketched immediately after the disaster and premiered in Moscow on 24 October 1936, includes a big funeral march as its slow movement, and the finale is built on Myaskovsky's own song for the Red Air Force, 'The Aeroplanes are Flying'. The Salutation Overture was dedicated to Stalin on his sixtieth birthday. Final decade The year 1941 saw Myaskovsky evacuated, along with Prokofiev and Aram Khachaturian among others, to what were then the Kabardino-Balkar regions. There he completed the Symphony-Ballade (Symphony No. 22) in B minor, inspired in part by the first few months of the war. Prokofiev's Second String Quartet and Myaskovsky's Symphony No. 23 and Seventh String Quartet contain themes in common—they are Kabardinian folk-tunes the composers took down during their sojourn in the region. The sonata-works (symphonies, quartets, etc.) written after this period and into the post-war years (especially starting with the Symphony No. 24, the piano sonatina, the Ninth Quartet) while Romantic in tone and style, are direct in harmony and development. He does not deny himself a teasingly neurotic scherzo, as in his last two string quartets (that in the Thirteenth Quartet, his last published work, is frantic, and almost chiaroscuro but certainly contrasted) and the general paring down of means usually allows for direct and reasonably intense expression, as with the Cello Concerto (dedicated to and premiered by Sviatoslav Knushevitsky) and Cello Sonata No. 2 (dedicated to Mstislav Rostropovich). While not particularly experimental, there is no suggestion—as with some earlier works—that Scriabin or Arnold Schoenberg might still have been an influence. In 1947 Myaskovsky was singled out, with Shostakovich, Khachaturian and Prokofiev, as one of the principal offenders in writing music of anti-Soviet, 'anti-proletarian' and formalist tendencies. Myaskovsky refused to take part in the proceedings, despite a visit from Tikhon Khrennikov pointedly inviting him to deliver a speech of repentance at the next meeting of the Composers' Union. He was only rehabilitated after his death from cancer in 1950, leaving an output of eighty-seven published opus numbers spanning some forty years and students with recollections. (There is also a recollection in the Volkov book Testimony.) Legacy Character and influence Myaskovsky was long recognized as an individualist, even by the Soviet establishment. In the 1920s the critic Boris Asafyev commented that he was "not the kind of composer the Revolution would like; he reflects life not through the feelings and spirit of the masses, but through the prism of his personal feelings. He is a sincere and sensible artist, far from 'life's enemy', as he has been portrayed occasionally. He speaks not only for himself, but for many others". Myaskovsky never married and was shy, sensitive and retiring; Pierre Souvtchinsky believed that a "brutal youth (in military school and service in the war)" left him "a fragile, secretive, introverted man, hiding some mystery within. It was as if his numerous symphonies provide a convenient if not necessary refuge in which he could hide and transpose his soul into sonorities". Stung by the many accusations in the Soviet press of "individualism, decadence, pessimism, formalism and complexity", Myaskovsky wrote to Asafiev in 1940, "Can it be that the psychological world is so foreign to these people?" When somebody described Zhdanov's decree against "formalism" to him as "historic", he is reported to have retorted "Not historic – hysterical". Shostakovich, who visited Myaskovsky on his deathbed, described him afterwards to the musicologist Marina Sabinina as "the most noble, the most modest of men". Mstislav Rostropovich, for whom Myaskovsky wrote his Second Cello Sonata late in life, described him as "a humorous man, a sort of real Russian intellectual, who in some ways resembled Turgenev". As professor of composition at Moscow Conservatory from 1921 until his death, Myaskovsky exercised an important influence on his many pupils. The young Shostakovich considered leaving Leningrad to study with him, and those who did become his students included Aram Khachaturian, Dmitri Kabalevsky, Vissarion Shebalin, Rodion Shchedrin, German Galynin, Andrei Eshpai, Alexei Fedorovich Kozlovsky, Alexander Lokshin, Boris Tchaikovsky, and Evgeny Golubev. The degree and nature of his influence on his students is difficult to measure. What is lacking is an account of his teaching methods, what and how he taught, or more than brief accounts of his teaching; Shchedrin makes a mention in an interview he did for the American music magazine Fanfare, and a section in Testimony, if authentic, is another. It has been said that the earlier music of Khachaturian, Kabalevsky and other of his students has a Myaskovsky flavor, with this quality decreasing as the composer's own voice emerges (since Myaskovsky's own output is internally diverse such a statement needs further clarification)—while some composers, for instance the little-heard Evgeny Golubev, kept something of his teacher's characteristics well into their later music. The latter's sixth piano sonata is dedicated to Myaskovsky's memory and the early "Symphony No. 0" of Golubev's pupil Alfred Schnittke, released on CD in 2007, has striking reminiscences of Myaskovsky's symphonic style and procedures. Recordings Myaskovsky has not been as popular on recordings as have Shostakovich and Prokofiev. Nonetheless, most of his works have been recorded, many of them more than once, including the Cello Concerto, the Violin Concerto, many of the Symphonies, and much of his chamber and solo music. Between 1991 and 1993 the conductor Yevgeny Svetlanov realized a massive project to record Myaskovsky's entire symphonic output and most of his other orchestral works on 16 CDs, with the Symphony Orchestra of the USSR and the State Symphony Orchestra of the Russian Federation. In the chaotic conditions prevailing at the breakup of the USSR, Svetlanov is rumoured to have had to pay the orchestral musicians himself in order to undertake the sessions. The recordings began to be issued in the West by Olympia Records in 2001, but ceased after volume 10; the remaining volumes were issued by Alto Records starting in the first half of 2008. To complicate matters, in July 2008, Warner Music France issued the entire 16-CD set, boxed, as volume 35 of their 'Édition officielle Evgeny Svetlanov'. In a testimony printed in French and English in the accompanying booklet, Svetlanov describes Myaskovsky as "the founder of Soviet symphonism, the creator of the Soviet school of composition, the composer whose work has become the bridge between Russian classics and Soviet music ... Myaskovsky entered the history of music as a great toiler like Haydn, Mozart and Schubert. ... He invented his own style, his own intonations and manner while enriching and developing the glorious tradition of Russian music". Svetlanov also likens the current neglect of Myaskovsky's symphonies to the neglect formerly suffered by the symphonies of Gustav Mahler and Anton Bruckner. Advocates One of Myaskovsky's strongest early advocates was the conductor Konstantin Saradzhev. He conducted the premieres of Myaskovsky's 8th, 9th and 11th symphonies and the symphonic poem Silence, Op. 9 (which was dedicated to Saradzhev). The 10th Symphony was also dedicated to Saradzhev. In 1934 Myaskovsky wrote a Preludium and Fughetta on the name Saradzhev (for orchestra, Op. 31H; he also arranged it for piano 4-hands, Op. 31J). In the 1930s, Myaskovsky was also one of two Russian composers championed by Frederick Stock, the conductor of the Chicago Symphony Orchestra. The other was Reinhold Glière, whom he met in 1940 and commissioned to write his "Feast in Fergana", Op. 75, a large-scale orchestral fantasia. Stock met Myaskovsky in March 1938 at the invitation of the Composers Union. He commissioned Myaskovsky's 21st Symphony (Symphony-Fantasy in F-sharp minor) for the Chicago Symphony's Fiftieth Anniversary. The first performance was in Moscow on November 6, 1940 (conducted by Aleksandr Gauk); Stock conducted the Chicago premiere on December 26, 1940. Honours and awards 1916 – Glinka prize (shared, 350 rubles) for Piano Sonata No. 2 Stalin Prizes: 1941 – first class for Symphony No. 21 1946 – first class for String Quartet No. 9 1946 – first class for Concerto for Cello and Orchestra 1950 – second class for Sonata No. 2 for cello and piano 1951 (posthumous) – first class for Symphony No. 27 and String Quartet No. 13. People's Artist of the USSR (1946) Order of Lenin List of works List of compositions by Nikolai Myaskovsky References Notes Further reading Alexei Ikonnikov, Myaskovsky: his life and work. Translated from the Russian. New York: Philosophical Library, 1946. Reprinted by Greenwood Press, 1969, . Harlow Robinson, Sergei Prokofiev: A Biography, (new paperback edition)—referred to in main text. David Fanning, liner notes to Myaskovsky: Symphony No.6, Deutsche Grammophon 289 471 655–2. Malcolm MacDonald, liner notes to Myaskovsky: Symphony No.6, Warner 2564 63431-2. Philip Taylor, liner notes to Myaskovsky: Symphony No.27, Cello Concerto, Chandos 10025. Andrew Huth, liner notes to Tchaikovsky & Myaskovsky: Violin Concertos, Philips 289 473 343–2. Gregor Tassie, Myaskovsky and his recordings, Classical Record Quarterly, summer, 2012. Gregor Tassie, Myaskovsky, Musical Opinion, October 2012. Gregor Tassie, Nikolay Myaskovsky: the conscience of Russian music, Scarecrow Press/Rowman & Littlefield, summer 2014. . Gulinskaya, Zoya K. (1981, 1985). Nikolai Jakowlewitsch Mjaskowski (Russian, translated (by Dieter Lehmann; Ernst Kuhn) into German). Moskva: Izd-vo Muzyka / Berlin: Verlag Neue Musik. ; . External links Myaskovsky. Piano Sonata No.3 in C Minor, Op.19 on Instant Encore A Myaskovsky website List of students from the above website Myaskovsky opus list Myaskovsky String Quartet No. 8 Soundbites and Discussion Detailed article about Myaskovsky and his works Nikolai Myaskovsky took lessons in harmony from Reinhold Glière Cello Concerto review About Piano Sonatas Nos. 2, 3 and 4 Category:1881 births Category:1950 deaths Category:20th-century classical composers Category:People's Artists of the USSR Category:Recipients of the Order of Lenin Category:Russian classical composers Category:Russian male classical composers Category:Russian Romantic composers Category:Russian military personnel of World War I Category:Soviet composers Category:Soviet male composers Category:Stalin Prize winners Category:People from Masovian Voivodeship Category:Pupils of Anatoly Lyadov Category:Pupils of Nikolai Rimsky-Korsakov Category:19th-century male musicians | Mid | [
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Q: Why is the image not showing in IE7? I have an image on this page in the blue bar area. It shows up fine in FF, Safari, IE8 & Chrome, but it does not show up in IE7. Here is the HTML: <div id="featuredImage"> <img src="images/website_design_charlotte.jpg" width="960" height="159" alt="" /> </div> Here is the CSS: #featuredImage { position: absolute; z-index: 9; top: 129px; left: 0; } #featuredImage img { width: 986px; height: 159px; position: relative; z-index: 10; } Would appreciate some help getting this to show up properly in IE7. Thanks! A: A few lines down in your HTML you have this: <!--[if IE]> <link rel="stylesheet" type="text/css" href="styles/style-ie.css" /> <![endif]--> ... which means all the other browsers are using Water.css for the stylesheet, but IE is using style-ie.css. Since you say it is working for IE8, the problem may be in your code that determines the browser version. | Mid | [
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Selective impairment in GLUT4 translocation to transverse tubules in skeletal muscle of streptozotocin-induced diabetic rats. We previously reported that insulin induces the translocation of GLUT4 to both the plasma membrane and the transverse tubules (T-tubules) in rat skeletal muscle (Am J Physiol 270:E667-E676, 1996). The aim of the present study was to investigate whether the insulin-resistant glucose utilization of skeletal muscle from streptozotocin (STZ)-induced diabetic rats is linked to an impaired translocation of GLUT4 to the plasma membrane, the T-tubules, or both surface compartments. Whole-body insulin-mediated glucose disposal, assessed during a hyperinsulinemic-euglycemic clamp, was reduced by 48% (P < 0.01) in diabetic rats as compared with controls. Subcellular membrane fractions enriched with plasma membranes, T-tubules, or GLUT4-enriched intracellular membranes were isolated from hindlimb muscles of control and insulin-stimulated rats, and GLUT4 content was measured by Western blot analysis. In the absence of insulin (unstimulated), GLUT4 content in muscle of diabetic rats was markedly lower (by approximately 40%) in both the T-tubules and the intracellular membrane fraction as compared with controls. In contrast, the transporter protein levels were similar in the plasma membrane fraction. In skeletal muscle of control animals, the hyperinsulinemic clamp induced GLUT4 translocation from the intracellular membrane pool to both the plasma membrane and the T-tubule-enriched fractions (approximately 2.2-fold to approximately 2.5-fold). Surprisingly, insulin increased plasma membrane GLUT4 content to comparable levels in control and diabetic rat skeletal muscle. However, insulin-mediated GLUT4 translocation to the T-tubules was significantly reduced in the same muscle. Whole-body insulin action was significantly correlated with GLUT4 protein levels in the T-tubules, but not with the transporter content in either plasma membranes or intracellular membranes. These results strongly suggest that peripheral resistance to insulin action on glucose disposal in STZ-induced diabetic rats is caused by a selective impairment of GLUT4 translocation to skeletal muscle T-tubules. | Mid | [
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melissa-mccarthy-weight-loss-journey-photos melissa-mccarthy-weight-loss-journey-photos-01 Melissa McCarthy is known for her physical comedy and for advocating that women love themselves at any size. 3 of 8 melissa-mccarthy-weight-loss-journey-photos-02 However, as body-positive as she is, she has recently dropped some serious weight — 75 pounds to be exact! 4 of 8 melissa-mccarthy-weight-loss-journey-photos-03 "She's in the best shape of her life," an insider told OK! Magazine, "and it's not from any crazy crash diets or obsessive workouts." 5 of 8 melissa-mccarthy-weight-loss-journey-photos-04 Instead, she tried a more relaxed approach, saying in a recent interview, "I truly stopped worry about [my weight]." 6 of 8 melissa-mccarthy-weight-loss-journey-photos-05 "I think there's something to kinda loosening up and not being so nervous and rigid about it that, bizarrely, has worked." 7 of 8 melissa-mccarthy-weight-loss-journey-photos-06 It wasn't just simple vanity that made Melissa want to drop weight, according to the insider. She also had her kids in mind. "She knew eating right would give her more energy to be the best mom and wife possible." 8 of 8 melissa-mccarthy-weight-loss-journey-photos-07 Lucky for her, she has the complete support of her husband. "[He] loves her no matter her body type, and she knows that!" melissa-mccarthy-weight-loss-journey-photos melissa-mccarthy-weight-loss-journey-photos-01 Melissa McCarthy is known for her physical comedy and for advocating that women love themselves at any size. melissa-mccarthy-weight-loss-journey-photos-02 However, as body-positive as she is, she has recently dropped some serious weight — 75 pounds to be exact! melissa-mccarthy-weight-loss-journey-photos-03 "She's in the best shape of her life," an insider told OK! Magazine, "and it's not from any crazy crash diets or obsessive workouts." melissa-mccarthy-weight-loss-journey-photos-04 Instead, she tried a more relaxed approach, saying in a recent interview, "I truly stopped worry about [my weight]." melissa-mccarthy-weight-loss-journey-photos-05 "I think there's something to kinda loosening up and not being so nervous and rigid about it that, bizarrely, has worked." melissa-mccarthy-weight-loss-journey-photos-06 It wasn't just simple vanity that made Melissa want to drop weight, according to the insider. She also had her kids in mind. "She knew eating right would give her more energy to be the best mom and wife possible." melissa-mccarthy-weight-loss-journey-photos-07 Lucky for her, she has the complete support of her husband. "[He] loves her no matter her body type, and she knows that!" | Mid | [
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Several European countries have erected fences to keep migrants out, and, according to the numbers, every case appears to have a large impact. Hungary was a popular pathway for refugees on their way to Germany during the fall. When the daily illegal border crossings were at 7,000 per day, Prime Minister Viktor Orban decided to erect a fence along the border to Serbia and Croatia. The result speaks for itself: When the fence went up Oct. 17, the influx went down to 870 from 6,353 only a day earlier. Illegal border crossing were steadily below 40 per day throughout the rest of the month. The number picked up slightly in February, after migrants destroyed part of the fence, but it remains in the low hundreds. (RELATED: Hungary’s Trump-Style Fence Keeps Refugees Out) Another successful example is Macedonia — the first step on the Balkan route, which separates Greece from the rest of the EU. Macedonia had more than 60,000 migrants enter the country in January. The migrant influx was cut significantly, leaving tens of thousands stranded in Greece. The desperation among refugees led to clashes with Macedonian military in late February. WATCH: [dcquiz] Germany’s rising anti-immigration party, Alternative fur Deutschland (AfD), proposed a fence along its border in March. AfD leader Joerg Meuthen mentioned several examples where fences work, particularly in Spain, where it forces North African migrants to take a long detour to get to Europe. (RELATED: Germany’s Nationalist Party Proposes Fence To Stop Immigration) “They have to go around the Mediterranean” to find a way in, Meuthen said at a rally, according to news agency AFP. “Yes, fences have an impact.” Follow Jacob on Twitter Content created by The Daily Caller News Foundation is available without charge to any eligible news publisher that can provide a large audience. For licensing opportunities of our original content, please contact [email protected]. | Mid | [
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#' @templateVar class map #' @template title_desc_tidy #' #' @param x A `map` object returned from [maps::map()]. #' @template param_unused_dots #' #' @evalRd return_tidy( #' "term", #' long = "Longitude.", #' lat = "Latitude.", #' .post = "Remaining columns give information on geographic attributes #' and depend on the inputted map object. See ?maps::map for more information." #' ) #' #' @examples #' #' library(maps) #' library(ggplot2) #' #' #' ca <- map("county", "ca", plot = FALSE, fill = TRUE) #' tidy(ca) #' qplot(long, lat, data = ca, geom = "polygon", group = group) #' #' tx <- map("county", "texas", plot = FALSE, fill = TRUE) #' tidy(tx) #' qplot(long, lat, #' data = tx, geom = "polygon", group = group, #' colour = I("white") #' ) #' @export #' @seealso [tidy()], [maps::map()] #' @aliases maps_tidiers tidy.map <- function(x, ...) { df <- as.data.frame(x[c("x", "y")]) names(df) <- c("long", "lat") df$group <- cumsum(is.na(df$long) & is.na(df$lat)) + 1 df$order <- 1:nrow(df) names <- do.call("rbind", lapply(strsplit(x$names, "[:,]"), "[", 1:2)) df$region <- names[df$group, 1] df$subregion <- names[df$group, 2] as_tidy_tibble(df[stats::complete.cases(df$lat, df$long), ]) } | Mid | [
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It’s Beckham Vs Barton This Weekend And The French Media Uses A Cheeky Cover Photo To Gain Attention Ligue 1 has certainly gained more audience across Europe over the past two years mainly because of the emergence of PSG under Qatari businessman Nasser Al-Khelaifi and the likes of Joe Cole, lavezzi, Javier Pastore, Joey Barton entering the Fashion capital. This year a whole new brand of super stars were drafted to the French League and the latest superstar to enter Ligue 1 is David Beckham, who completed the switch from LA Galazy during the January window. Beckham will play alongside Zlatan Ibrahimovic and Thiago Silva who were brought in at the start of the season. The Former England captain is all set to make his debut for PSG this Sunday when they host Joey Barton’s Marseille and the French media has already started hyping it with a sensational cover photo where Barton is portrayed as a devil and Beckham as an angel. A well planned strategy to use the stars as a bait to gain attention. Joey Barton for his part stirred up things as he claimed the former England International will not pose much threat when Marseille travel to Parc de Princes this Sunday. However, Joey also makes some interesting observations on the differences between playing in England and France. He does not say, as others have suggested anything disrespectful about Becks. “I think David would accept that it’s okay to say that he is past his prime.” However, we should also accept that David probably still has the quality to hit a dead ball and crosses as good as almost anyone in the game. His stats on assists throughout his career must be incredible. His long shots are also decent and he will need to be watched. [youtube width=”500″ height=”300″]9yMfR3tGeZ0[/youtube] For once the man has talked sensibly, but knowing Barton – expect some studs up challenges on the pitch! | Mid | [
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The Winnipeg Jets forward is having a hard time coping after several close friends -- including former Jet Igor Korolev -- passed away after the horrific plane crash that claimed the lives of 43 people, many of whom were members of Lokomotiv Yaroslavl in the Kontinental Hockey League. "He was my good friend, so it's really sad," said Antropov. "Anytime one of your close buddies or family passes away, it's a tough situation. I'm always going to remember him." Antropov first got to know Korolev when both were members of the Toronto Maple Leafs, as a 19-year-old looking to find his way in a new country. "He did a lot of good things for me," said Antropov, who was born in Kazakhstan and joined the Maple Leafs in 1999-2000. "He was a big brother for me. He took me under his wing. I didn't speak any English. Our houses in Toronto were five minutes apart and he took care of me for the first couple of years. He did everything for me and guided me through my first couple of years in North America." "Actually, he's the Godfather of my son, so it's a tough loss for us." When news of the crash began to spread on Monday morning, Antropov was in disbelief. "I phoned his wife and I had a really tough time talking to her," said Antropov. "I didn't know what to say. It's really tough." Antropov actually spent part of the NHL lockout playing for Lokomotiv, so the news was devastating. "I knew eight or nine guys there, I took it really hard and I still can't believe it happened," said Antropov. "It's a big loss, not just for myself and my family but the whole hockey world. I'm thinking about it pretty much every day. It's always in my head, unless I'm playing with my kids. Then you sit down and relax and boom, it pops out again." NO NEWS: Jets general manager Kevin Cheveldayoff said there was nothing new to report regarding the contract negotiations with restricted free agent Zach Bogosian. "Things are pretty much status quo," said Cheveldayoff. "Just conversations as they go. It's something that will play itself out over time." Bogosian's agent Bob Murray seemed to echo those comments. "We will continue to talk in hopes of getting something resolved, but timing is impossible to predict," Murray wrote in an email. | Mid | [
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Green Flash Brewing Co. Co-founders Mike and Lisa Hinkley announced that Virginia Beach-based developers, The Miller Group, will lead both development and construction of the Green Flash East Coast brewery in Virginia Beach, located at Corporate Landing and General Booth Blvd. Green Flash execs selected The Miller Group because of the company’s solid history as a Virginia Beach-based developer with fully integrated capabilities and extensive experience in building industrial and manufacturing facilities. The Miller Group’s community connections will ensure that subcontracting and other project needs will be primarily outsourced to Virginia Beach locals, another determining factor that was of importance to the Green Flash team. Green Flash announced the Virginia Beach brewery location in March 2013, and The Miller Group has noticed an uptick in interest from out-of-town businesses looking closely at Virginia Beach as a location for development, specifically in the area immediately surrounding the future brewery site. The Miller Group estimates that more than 250 Virginia Beach area residents will have a hand in building the 58,000-square-foot brewing facility from groundbreaking to finish. After the construction is complete, Green Flash will create permanent jobs for more than 40 people in the region. Surrounding the project is positive speculation on the long-term economic benefits that the city and residents of Virginia Beach will reap from the Green Flash brewery’s presence. Mike Hinkley, co-founder and chief executive officer of Green Flash, and Tim Harkins, president of The Miller Group, met while Hinkley was in the early stages of seeking a location for their 2nd brewery. While Green Flash was investigating Virginia Beach as a possibility, The Miller Group was extremely helpful, and the leaders developed a comfortable working relationship. “The Miller Group championed Virginia Beach and the community,” states Hinkley with regards to the decision. “They are genuinely interested in fostering both economic and cultural growth to directly benefit residents.” Because of their solid experience and locally focused intentions, I completely trust The Miller Group as our on-site Virginia Beach liaison, confident that their team will work well with our existing engineering advisors as well as choose Virginia-based contractors to see the project to fruition.” While there will be immediate job opportunities for local contractors when they break ground, and permanent brewery jobs upon opening, The Miller Group is most excited about the long- term impact Green Flash may have on the city in other areas. “Green Flash will have a tremendous impact on Virginia Beach and the entire Hampton Roads area,” says Whit Hill, vice president of The Miller Group. “It is a slam dunk from a real estate, economic and cultural perspective. Green Flash’s presence in Virginia Beach is certain to revitalize the immediate area and beyond, and we are excited to be a part of this new chapter for Virginia Beach.” “This announcement is a major step in the development of this project, and brings Green Flash one step closer to expanding their East Coast customer base,” said Warren D. Harris, director of Virginia Beach Economic Development. “This addition to Corporate Landing will not only bring new jobs and visitors to Virginia Beach, but will propel this area of the city into even more growth. Green Flash’s presence in Virginia Beach speaks volumes about the vibrant economic climate here.” Green Flash announced the Virginia Beach brewery location in March 2013, and The Miller Group has noticed an uptick in interest from out-of-town businesses looking closely at Virginia Beach as a location for development, specifically in the area immediately surrounding the future brewery site. The developers are also seeing a surge in craft beer interest among locals, with crowds flocking to establishments that feature Green Flash and other craft brews. This emerging interest among residents is expected to increase exponentially when the brewery opens. As the end of the high season in Virginia Beach draws near, Green Flash will create a valuable new draw for both visitors and locals alike. The Miller Group predicts that Green Flash will become a destination for a whole new generation of tourists who are interested in craft beer. While it is impossible to predict what will happen after the brewery opens, Green Flash and The Miller Group are enthusiastic about the potential impact the new destination may have on Virginia Beach in the long and short term. The craft beer tourist demographic will demand a range of other supporting businesses and this domino effect could be tremendous for economic growth in Virginia Beach. | Mid | [
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Activities In srinagar Book hotels in Srinagar with Room service facility through Yatra.com and get amazing deals. Know about the best Srinagar hotels with Room service facility with their services, amenities, and read reviews from people before you make the final booking. Use promo code HOTEL18 and get up to 70% OFF on Srinagar hotels booking. Srinagar Hotels Are you looking for hotels in Srinagar with Room service? If you are planning to travel or looking for hotel in Srinagar with Room service, for your comfortable stay in the city, you would need to find the best hotel rooms that suit your requirements. You can find the best & cheap deals on Srinagar hotels with Room service and book the same online in an easy and convenient manner. The website features the pictures of the hotel rooms for your viewing and lists the prices for each types of accommodation in Srinagar. Check out best hotel offers on more than 672 Srinagar hotels with Room service on Yatra.com. You can easily find and book your hotels in Srinagar with given below steps:- FAQs Could not find what you are looking for? Q. Which is a good place or market to shop for authentic Kashmiri artifacts?By Mahagauri on Jan 21,2018 A. Checkout the Kashmir Government Arts Emporium located inside the Bahu Plaza Shopping Complex in Panama Chowk of Srinagar. From apparels to home décor items and artifacts, this government emporium offers authentic Kashmir crafts and art work. The place usually shuts down by 6:30 in the evening, so plan a visit accordingly. For more information, see: https://www.yatra.com/india-tourism/shopping-in-srinagar/kashmir-government-arts-emporiumBy Unmesh on Jan 21,2018 Q. Is there an entry fee to visit the Hari Parbat Fort?By Kiran on Jan 20,2018 What are the popular places to visit in Srinagar, apart from the Dal Lake?By Fravash on Jan 19,2018 A. Plan a trip to the famous Shankaracharya Temple, check out the lovely tulips at the Indira Gandhi Tulip Garden, while experiencing the natural beauty of the valley in Nishat and Shalimar Bagh. The Jamia Mosque and Kheer Bhawani Temple are also worth a visit for religious travelers. For more options, see: https://www.yatra.com/india-tourism/attractions-in-srinagarBy Indrani on Jan 19,2018 Q. I have heard a lot about food in Srinagar Which are some of the not-to-be-missed traditional cuisines in Srinagar?By Sanket on Jan 18,2018 A. Rice is the staple food of Srinagar and you can get both vegetarian and non vegetarian cuisines as per your preference. Try out the lotus root, fish, and spinach and chicken dishes along with Dum Aloo and Rogan Josh as trademark staple foods of the region. By Yashas on Jan 18,2018 Q. What is the condition of the highways to Srinagar both from Jammu side and Leh side if planning a road trip?By Dayaram on Jan 17,2018 A. Both the highways including the National Highway 1A, connecting the valley to the rest of India, and National Highway 1D, connecting it to Leh, are in very good condition and ideal for road travel. Be mindful of the possibility of snow blockage in winters. By Uppas on Jan 17,2018 Q. Is travelling to Srinagar by air a good option?By Idhant on Jan 16,2018 A. Yes, travelling to Srinagar by air is indeed a very good option. The city has an international airport which is well connected by regular flights with metropolitan cities and other areas. The Srinagar international airport is around 11 km from the main city center. By Ishan on Jan 16,2018 Q. Which is a good season or time to visit Srinagar?By Sumedh on Jan 15,2018 A. One of the best times to visit Srinagar is from April to October. The average temperature ranges from 14 °C to 30 °C making it neither too cold nor too hot and an ideal time for travelers. Winters should usually be avoided as it can get too cold. By Anugya on Jan 15,2018 Q. Is it safe to plan a trip to Srinagar?By Dhigana on Jan 14,2018 A. Srinagar as the capital of Jammu and Kashmir is by and large safe although the state does have certain high risk zones. Srinagar is safe for tourists and attracts a large number of travelers and tourists from across the globe each year, especially in the summers. By Naviya on Jan 14,2018 Q. What are the timings to visit the Dachigam Wildlife Sanctuary?By Vidyut on Jan 13,2018 Suggest a good Indian restaurant in Srinagar near Dal Lake that serves authentic Kashmiri food?By Chumban on Jan 12,2018 A. Drop in at Char Chinar near Dal Lake, which offers an exotic outdoor setting and equally exotic Indian and Kashmir flavors for you to choose from. Chicken Malai Tikka and Grilled Chicken are the two most popular dishes served on the menu of Char Chinar. For more options, see: https://www.yatra.com/india-tourism/places-to-eat-in-srinagar/By Chitrita on Jan 12,2018 Q. Can I get private cabs or taxis in Srinagar?By Chakrika on Jan 11,2018 A. Yes, you can easily hire cabs and taxis in Srinagar for local travel. The fares are not regulated and you may be better off bargaining on the same to ensure a value-for-money travel deal. By Elavarasi on Jan 11,2018 Q. How I can book Srinagar hotels in 5 star category?By Bhupendra on Jan 10,2018 A. To get the 5 star Srinagar hotels you just need to choose the options "star rating" in your left and click on the given filter options according to your needs. By Paramartha on Jan 10,2018 Q. Can I book luxury hotels in Srinagar with yatra?By Shameena on Jan 09,2018 A. In Srinagar luxury hotel booking with Yatra is very easy, you can choose the "luxury hotels" filter under the "hotels by themes" category. By Vithala on Jan 09,2018 Q. Which is a good area to shop for dry fruits in Srinagar?By Nandish on Dec 29,2017 How far is Gulmarg from Srinagar Can we return the same day?By Sushma on Dec 28,2017 A. Gulmarg is located at a distance of 60 km from Srinagar and is popular for its adventure sports, especially skiing in the winter months. A same-day return is possible provided you leave Srinagar early and plan your trip well. For more options, see: https://www.yatra.com/activities/details/product/TOR_49282P4By Angad on Dec 28,2017 Q. Which are some good 3 star house boats in Srinagar?By Sarakshi on Dec 27,2017 A. Houseboat Omars Ruby Yacht, Peer Palace Houseboat, Ashoka Group Of House Boats, Savoy Group of Houseboat, and Valley House Boats are some of the well known 3 star house boat options available in Srinagar. Book in advance, especially in summer, to avoid disappointment. For more options, see: https://www.yatra.com/hotels/house-boats-in-srinagarBy Anram on Dec 27,2017 Which are some of the good luxury hotels in Srinagar?By Manana on Dec 21,2017 A. Some of the well known luxury hotels in Srinagar include Comrade Inn, Akbar Group of Heritage Houseboat, Impex Hill Resorts, Golden Flower Heritage Houseboat, and New Jacquline Heritage Houseboats. For more options, see: https://www.yatra.com/hotels/luxury-hotels-in-srinagarBy Nandini on Dec 21,2017 | Low | [
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Simulation-based mastery learning in medical students: Skill retention at 1-year follow up. Context: Deficits in basic skill performance and long-term skill retention among medical students and novice doctors are a persistent problem. This controlled study tested whether the addition of a mastery learning component to simulation-based teaching is associated with long-term retention and performance of peripheral venous catheter insertion. Methods: Fourth-year medical students were assigned to receive either the control (simulation without mastery learning, n = 131) or the intervention (simulation + mastery learning, n = 133) instruction in peripheral venous catheter insertion. Performance was assessed at one year post-instruction. Eighty-four students from the control group and 71 from the intervention group participated in the assessment. Results: Students who received the mastery learning instruction achieved higher overall test scores than did controls (median mastery learning score: 20.0, IQR 2.0; median control score 19.0, IQR 3.0; Mann-Whitney U test, p < 0.001, effect size d = 0.82). Pass rates also differed significantly between the groups, with 74.5% (n = 53) of the intervention group passing compared with 33% (n = 28) of the control group (p < 0.001). Conclusions: Mastery learning is an effective means of teaching practical skills to medical students, and is associated with higher scores at a 1-year follow up. | High | [
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Explanations of vote President The next item is the explanations of vote. Bogusław Liberadzki in writing. - (PL) Mr Leinen's report specifically states that the most significant innovation in the Commission proposal is to make it possible to fund not only European political parties, but also affiliated political foundations at European level from the Union budget. I agree that the proposed regulation will improve the financial stability of European political parties and the funding of their election campaigns in the European Parliament elections in 2009. Zita Pleštinská (SK) A year ago it still looked like the date for the enlargement of the Schengen area would be postponed until 2009. I am glad that we have all stepped up our efforts and found a constructive solution to make the free movement of people without passport controls a reality. I thus welcome the report by Mr Carlos Coelho confirming the accession of nine new Member States to the Schengen area. I believe that the free movement of people without passport controls is a real success story of European integration, which is why I was happy to vote for this report. The accession of the new Member States, including Slovakia, to the Schengen area, says clearly to the people of Europe that the Iron Curtain, built by the totalitarian Communist regimes between Western and Eastern Europe, will be consigned to the history books after 21 December 2007. For me, the vote on this report is a historic event since it is taking place in the same week as the Slovak and Czech Republics will commemorate - on 17 November - the 18th anniversary of the fall of the totalitarian regime that used to prevent citizens from travelling around Europe. I believe that all European citizens will welcome this Christmas present. Frank Vanhecke (NL) Mr President, I voted against the Coelho report primarily to draw attention to the numerous problems with the open-border policy of the Schengen Agreement. After all, the Schengen system stands or falls by a strict, watertight control of its external borders on the one hand - which, to be perfectly clear, is not taking place - and by a rigorous approach to crime in all Member States, coordinated in all Member States, on the other - which is found far too rarely. Finally, all Schengen countries must also conduct a strict immigration policy, something that is completely at variance with, for example, the waves of mass legalisation seen in quite a few Member States in recent years. In these circumstances, as an individual and as a politician, I cannot rejoice at no longer having to pass through border controls at internal borders, since criminals and illegal immigrants do not have to do so either, and that is pernicious to our society. Oldřich Vlasák (CS) Mr President, allow me to speak about the report by my colleague Mr Carlos Coelho on the draft Council decision on the full application of the provisions of the Schengen acquis in the nine Member States that joined the EU in 2004. I personally believe that this decision is absolutely vital. The accession of our countries, including my home country, the Czech Republic, should not be postponed under any circumstances. All the analyses to date objectively state that all these countries are adequately prepared for the enlargement of the Schengen area. Thanks to an incredible effort by the relevant Members States, the many experts involved in the inspections, the police, judicial authorities, officials and others, today these Member States are sufficiently prepared to apply all the provisions of the Schengen acquis in a satisfactory manner. I therefore assume that the Justice and Home Affairs Council will also express its support for this decision on 6-7 December this year. The symbolic importance of the elimination of the internal borders that our citizens associate with joining the Schengen area will go down in history and can only be compared with the fall of the Iron Curtain almost 20 years ago. Zuzana Roithová (CS) Ladies and gentlemen, I am delighted that - in spite of the technical problem - we all joined together to vote on the report confirming that the new Member States, including the Czech Republic, will be ready to join the Schengen area as early as 2008. I appreciate the effort and openness of the Member States and the Commission during the intense technical consultations required prior to the enlargement. The enlarged Schengen area will no doubt present greater challenges for Europe's internal security, but on the other hand, and I would like to emphasise this, it is the culmination of the efforts to achieve free movement in a truly integrated area. Next year Europe will be united as it has never been before. The Iron Curtain is definitely gone and I thank you for that. Sylwester Chruszcz - (PL) Mr President, Poland's accession to the Schengen area brings with it not only potential benefits linked to convenience in crossing borders, but also threats. One negative phenomenon that Poland has already been experiencing for a number of years is the difficulties encountered by citizens of our eastern neighbours in entering our country, including Poles living in Belarus and Ukraine. A lack of border controls may lead to many negative phenomena associated with criminality and illegal immigration. We are also concerned about action taken to remove national border controls in Member States in favour of pan-European EU border services. That is why I abstained from voting on this matter. Pedro Guerreiro in writing. - (PT) As we have long argued, we consider that the areas of Justice and Home Affairs are central competences of States, particularly of the Portuguese State. We therefore oppose their progressive transfer to the supranational institutions of the EU in a process that justifies every new 'advance' on the basis of the previous 'advance'. Such is the case with the creation of the 'Schengen area' with its Schengen acquis, which serves as a catalyst for the communitarisation of policies or measures linked to border control - visas, asylum or immigration - or police and judicial mechanisms. All the more so when such 'communitarisation' happens in a framework in which the major EU powers, in concert, make sure that the decision-making process gives them the possibility of defending and safeguarding their interests, which is not the case for Portugal. As we have stated, essential international and European cooperation between sovereign States with equal rights concerning these matters is one thing, but the unacceptable handing over of fundamental elements for the safeguarding of national sovereignty and democracy to supranational institutions dominated by the major EU powers to create 'Fortress Europe' is quite another. Hence our vote. Luca Romagnoli in writing. - (IT) Mr President, ladies and gentlemen, I am voting against this report since, as I have already explained at length on several occasions, including recently, during my speeches in Parliament, I am firmly opposed to the Schengen Agreement. I am particularly opposed to it when this Agreement becomes the vehicle for illegal immigrants and dangerous movements within the EU. The borders of these countries that want to become part of the Schengen acquis are an easy target for criminals. They would provide another means of entry for uncontrolled immigration from former Soviet bloc countries and from the Middle East,. not to mention the social disorder that the free movement of citizens within the EU undeniably causes Italy and other countries. Lars Wohlin The Schengen cooperation must remain open to all Member States who wish to join and participate in the cooperation. On the other hand, it is extremely important that all the countries participating in the cooperation already satisfy the requirements at the time of joining, because the cooperation entails a common external border. If there are deficiencies in one country, Sweden has no way of checking the border protection. The investigations made show that there are problems which need to be tackled, and the reasonable thing would be to delay joining until all the requirements have been satisfied. Jan Andersson, Göran Färm and Inger Segelström With this explanation of vote, we the undersigned Swedish Social Democrat Members of the European Parliament would like to clarify how we voted on the Braghetto report. We think it is very important to set up a recovery plan for bluefin tuna. Bluefin tuna has been an endangered species for a long time following massive overfishing. In time this risks damaging the whole ecosystem in the fishing waters concerned. However, we think that the Commission's resolution is not entirely adequate and therefore voted against it. We voted for the Committee's Amendments 4 and 6 - two amendments which entail the removal of two, in our opinion questionable, exemptions for bluefin tuna fishing. We also supported Amendment 13 which would have meant that we should adopt a recovery plan worthy of the name. The proposal went considerably further than the original proposal, which is something we fully support. The level of bluefin tuna stocks is still dangerously low and the European Union must take greater responsibility for the recovery of bluefin tuna stocks. Gérard Deprez in writing. - (FR) I would like to explain my vote on the report on the recovery plan for bluefin tuna in the Eastern Atlantic and the Mediterranean. In view of the truly critical state of bluefin tuna stocks, the European Union is reacting as follows through this regulation: a steady reduction of catch quotas, a restriction on fishing periods, and a stepping up of control measures to combat illegal fishing. I support these proposals. I am, however plagued by a certain pessimism. Firstly this is because scientists are already saying that the provisions in this regulation are not enough to guarantee the recovery of stocks. They believe there would be good reason to set quotas going well beyond the annual catch rates set by ICCAT (the International Commission for the Conservation of Atlantic Tunas). I am inclined to believe them, so I have lent my support to Amendment 13 tabled by the Group of the Greens/European Free Alliance. In view of the presence in the Mediterranean of fleets from non-EU countries such as Libya, Turkey, Tunisia, Japan and China, which are not members of ICCAT, it is clear that the regulation we are looking at will only have an effect if these countries sign up to the provisions it lays down, and there is no certainty they will. Pedro Guerreiro in writing. - (PT) The establishing of an EU multi-annual recovery plan for bluefin tuna is the practical implementation of one of the measures adopted by the International Commission for the Conservation of Atlantic Tunas. The plan provides, amongst other things, for a steady reduction in the catch quota, closed seasons, an increase in minimum size and an observer scheme on board fishing vessels and on fish farms. The recommendation adopted also provides for financial compensation to be paid to fishermen during the closed season with a view to safeguarding the fleet and employment in the sector. We also think it is important to improve control, periodically updating the volume of catches by the various vessels to prevent some countries from exceeding allocated quotas to the detriment of others, as happens at present. You will recall that the bluefin tuna fishing season was closed from September to December because it was suspected that some countries had already exceeded the quotas, as turned out to be the case. Finally, we regret the rejection of our proposal underlining the fact that small-scale coastal and traditional fisheries, in addition to providing thousands of jobs, enable the sustainable exploitation of fisheries resources. David Martin in writing. - I voted in favour of this proposal for a Council regulation, which sets out a plan for the recovery of bluefin tuna stocks in the Eastern Atlantic and the Mediterranean. Under the proposal, fishers will be compensated for losses caused by closed seasons and quota reductions designed to allow the stock to recover. It recommends no derogations on seasons or minimum sizes. Firm action is needed to make sure this fish stock is not depleted beyond repair. Ilda Figueiredo in writing. - (PT) We voted against this resolution that picks up the main aspects of neoliberal policies at Community level and tries to encourage their implementation at world level. It is a resolution that accepts flexicurity as a concept to be developed and integrated into the National Reform Programmes of each Member State, that attempts to hide the real implications and objectives inherent in the Lisbon Strategy and in its guidelines for economic and employment policies, in particular the associated liberalisations and privatisations. We cannot accept a resolution that welcomes the intention to develop an external dimension to the Lisbon Strategy, specifically the promotion of market liberalisation on a worldwide scale, accentuating its neoliberal nature and interference in the economic guidelines of third countries. The Commission communication on its contribution to the October meeting of Heads of State or Government states that the re-launch of the Lisbon Strategy for growth and jobs has been a success, but it should have added the words 'for the large national and international economic and financial groups' who have seen their profits grow exponentially, whereas workers have had to face an erosion of their rights. Timothy Kirkhope in writing. - I and my British Conservative colleagues believe firmly in the Member States of the European Union pursuing policies that will enhance Europe's competitive position in the globalised economy. We believe that Europe should pursue the Lisbon Agenda vigorously by securing a deal in the world trade talks, pushing for further deregulation to free industry and business to compete in world markets, driving forward liberalisation in the internal market, implementing effectively the Services Directive and adhering to a sound competition policy. All of this must be underpinned by an unshakeable commitment to free trade and open markets. Some of these elements are present in this motion and we welcome that. Sadly, however, we believe that overall this joint motion is a huge missed opportunity. It should have set down the basic principles of an EU approach to globalisation as outlined above, but does not do so. There are elements in this motion which would take Europe in a direction which would undermine the ability of the EU to compete successfully in the globalised economy. Marie-Noëlle Lienemann in writing. - (FR) This resolution should have provided a chance to affirm a few urgent matters and to state what the European Parliament is actually expecting of the European Union institutions to ensure a revival of growth, shared social progress in our 27 Member States and development for the developing countries. There is none of this, but just the same old story of what a good thing globalisation is. There is nothing about a democratic counterweight to the ECB imposing a monetary policy that favours industry and jobs. There is nothing about a strategy to counteract the EU's permeability to hedge funds and sovereign wealth funds. There is nothing about Community preference and the strict imposition of social (ILO) or environmental standards. There is nothing about development aid, which is essential for co-development. Why are we surprised about the low growth in Europe, social problems and the people's mistrust? David Martin in writing. - I voted for this composite resolution which responded to the Commission paper 'The European interest: succeeding in the age of globalisation'. The resolution highlights a number of ways the Union can take advantage of the opportunities globalisation allows: promoting a level playing field in competition and trade issues; improving EU policymaking so it is more joined up; and emphasising the need for the social dimension of the EU to be reinforced. Peter Skinner in writing. - I welcome this resolution which draws attention to a series of interrelated issues - social rights through to financial regulations and the impact of how, as a result of expanding markets, the citizen can make sense of them. There is a balance to be had between liberal market conditions and issues of the needs of developing countries and it is absolutely necessary that we continue to debate this issue time and time again. Bart Staes Europe will not succeed in combating the increasing poverty and global warming - the major challenges of globalisation - if it constantly puts the emphasis on liberalisation. Indeed, it is free trade that causes these problems. Globalisation creates the illusion that the general level of prosperity in the world is gradually increasing, but at the same time I note a steady increase in the gap between rich and poor in the Member States. Liberalisation is also the cause of the great environmental disaster that lies ahead unless we hasten to take decisive, enforceable measures to combat global warming. Lacking a vigorous policy in this field is criminally irresponsible. Investing in an energy-efficient economy and creating jobs in that area is nevertheless a promising course of action. The 'polluter pays' principle is disregarded all too frequently. As a Member of the Group of the Greens/ European Free Alliance I regret the absence of this input. If Europe wants a single market with free movement of people, goods, services and capital, it should also lay down high social and environmental standards that offer protection and set an example to the rest of the world. The proposed text remains vague and superficial and once again typifies the Commission's policy. Mario Borghezio (IT) Mr President, ladies and gentlemen, it would be truly hypocritical if Parliament, after voting by a very large majority for Mrs Angelilli's oral amendment, which sends the condolences and support of the European Parliament to the family of a victim of such an unmotivated and serious crime in our country, then fails to adopt a clear position to prevent these acts, this massacre of honest citizens, which is happening due to the lack of controls. No one wants there to be xenophobia in Italy, especially towards members of a people such as the Romanians, who, as an editorial in the newspaper L'Avvenire reminded us, have given us such artists as Mircea Eliade, Ionesco and Cioran. This is a great civilisation and one that is closely related to our own. The influx of criminals, and specifically the emergence of Roma groups, is another matter entirely. For these, border controls and deterrents are needed, with the introduction of a fingerprint recognition system so that we know who is coming into our country and what their intentions are, if possible, and more importantly so that we can pinpoint the exact date of entry. Although we do not want to introduce draconian measures in Europe, if we are saying that checks must be carried out after three months, then we need to know the exact date of entry and this, as Mr Amato admitted in the Italian Chamber of Deputies, is not the case at present. Robert Evans Mr President, I voted in favour of this resolution because I recognise that the free movement of persons is a fundamental principle of the European Union and one which must be respected and defended by all Member States. Furthermore, I think we are right to emphasise yet again that the EU was actually founded on measures to combat all forms of racism and xenophobia and indeed all forms of discrimination. Equally, we should all in this House recognise that the Roma people of Europe are perhaps the most discriminated against, in some countries to totally unacceptable levels. We should understand that the assimilation, social integration and protection of the Roma minority are objectives that this European Union has yet to achieve. I think that this is an aim that we should all work for, along with the spirit of free movement. Carlo Fatuzzo (IT) Mr President, ladies and gentlemen, I voted against the resolution on freedom of movement in the European Union tabled by centre-left groups - I will explain why in a minute - after declaring that I am absolutely and totally in favour of Mario Mantovani's proposal to block entry into the EU and therefore Italy for non-EU nationals for three years. For EU nationals, I am very much in favour of the right to freedom of movement of workers, citizens and tourists, provided that this is not a licence to kill. It is inconceivable that a 45-year-old woman should die on her way home from work and a doctor a few days away from retirement should be killed during an attempted burglary at his home in Milan. Both of these events have occurred in the past few days in Italy. This is not freedom of movement! Marian-Jean Marinescu (RO) I voted in favour of the resolution regarding freedom of movement submitted by the PSE, ALDE, Verts and GUE/NGL Groups, although it only partially fulfils the purpose for which I believe this resolution should be drafted. I believe the text of the resolution should have constituted an even clearer support for the European citizens residing in countries other than their country of origin, implicitly for the Romanian citizens residing in Italy who obey the Italian laws. The voted text does not condemn the xenophobic attitudes toward Romanian citizens and does not refer to the amplification of the tension between the Romanian community in Italy and the Italian people, which is also generated by the inadequate enforcement of the decree issued by the Italian Committee of Ministries and statements of certain Italian politicians. I also believe that, as mentioned in the common PPE-DE and UEN resolution, the efficient enforcement of the legal provisions by the Italian authorities would have prevented this situation. I ask both the European Commission and the Italian authorities to take into consideration the provisions of the common resolution of the PPE-DE and UEN Groups as well, which are not included in the text adopted today. Frank Vanhecke (NL) Mr President, things are actually becoming more and more ridiculous. Now a majority in this House even deems it necessary to level an accusation of xenophobia at the people and government of Italy. In addition, the motion for a resolution states that the Italian Government's approach to the problem of crime among the Romanian Roma present there in massive numbers has contributed to rising tensions. Italy therefore has only itself to blame for all this and should have participated in the European Social Fund programmes for the integration of the Roma. I should like to make it clear at this juncture that the people and government of Italy have a right to defend themselves, and that what has happened mainly goes to show that the Directive is unsuitable and that it must be made easier, not more difficult, to deport criminals - criminals, mark you, not decent people working to make ends meet. David Martin in writing. - I voted in favour of this joint resolution, which notes that the right of free movement is a fundamental one accorded to all EU citizens. Member States have an obligation to look after the citizens of other Member States living in their territories, and to ensure dignity and respect for the rights of all citizens of the Union, no matter where they are living. Luca Romagnoli in writing. - (IT) Mr President, ladies and gentlemen, I am strongly opposed to these motions for resolutions and want to express my firm opposition. This has all stemmed from belated and inconclusive action taken by the Italian government, which has realised that Italy is facing a crisis, unfortunately only following terrible incidents perpetrated by EU nationals. Directive 2004/38/EC is clear when it says that 'All Union citizens shall have the right of residence on the territory of another Member State [...] if they [...] have sufficient resources for themselves and their family members not to become a burden on the social assistance system of the host Member State'. Therefore, these motions for resolution seem pointless and pretextual. The treaties impose freedom of movement of citizens within the EU and no one wants to engage in discrimination based on the country of origin. However, once EU citizens commit serious and execrable violent crimes in another Member State or if they are unable to give a reason for their visit, as the Directive requires, it is in the interests of the entire Union that they should be sent back to their own country. Silvia-Adriana Ţicău in writing. - (RO) I voted in favour of the resolution regarding free movement, initiated by PSE together with other political groups, because I consider it to be extremely important for the situation created in Italy not to create a dangerous precedent questioning the very respect of European Union fundamental principles. I believe this situation should be solved immediately in order not to allow the European Union citizens to be discriminated against, irrespective of their nationality. The measures proposed by the resolution will protect all European citizens from abuse. The EU needs all its citizens and Romanians should feel the solidarity of European people because there are thousands of Romanians working abroad who are appreciated for their hard work, honesty and correctness. The Union's Charter to be annexed to the Reform Treaty lists the fundamental rights of European citizens: dignity, freedom, equality, solidarity, citizenship, justice. The EU guarantees democracy, rule of law, human rights, as well as the protection of minorities. In this context, the measures proposed by the resolution will contribute to the better integration of the Roma community. Zita Pleštinská (SK) To reiterate what is said in the motion for a resolution, I, too, would like to congratulate the Portuguese Government for putting forward a proposal providing a technical transitional solution - SISone4all - which will allow the new Member States to be connected to the Schengen Information System in 2007, before the Commission introduces the new Schengen Information System II. Congratulations are also due to the new Member States entering the Schengen area on the tremendous efforts they made to meet all the Schengen requirements in such a short period of time. Enlargement of the Schengen area to include nine new states from 21 December 2007 is also the richly deserved outcome of the European Parliament's actions to stick to the original date. This is why I voted for this motion for a resolution. Pedro Guerreiro in writing. - (PT) We voted against this resolution because we are opposed in principle to the communitarisation of Justice and Home Affairs, an area at the heart of state sovereignty. The 'Reform' Treaty is an attempt to turn the communitarisation of Justice and Home Affairs into a common policy. Communitarisation - that is, the loss of national sovereignty - is all the more serious when it is promoted in a context characterised by Community policies and measures which dangerously compromise citizens' rights, freedoms and guarantees that represent the progress of civilisation and fundamental democratic achievements. Consider the restrictive asylum policy and the increasing difficulties faced by asylum seekers in securing their rights and guarantees. Look at immigration policy with its security-orientated approach, its criminalisation of irregular immigrants, its inhuman 'detention centres' and repatriation measures, its discriminatory, exploitative and predatory treatment of human resources from third countries. Note the growing use of information and the ever-increasing storage of data - including biometric data - available to a wider set of bodies, including third countries, for example the access of US bodies to air passenger data. Hélène Goudin and Nils Lundgren The current political climate in Pakistan is certainly critical, since the President has declared a state of emergency and clear violations of human rights have been committed through deprivation of liberty, violence against peaceful demonstrators, and silenced media. We are firmly opposed to this but we are also opposed to the European Parliament, through this resolution, making yet another attempt to have the EU take over the independent foreign policies of the Member States. The UN is the only body which, on behalf of its members, has the competence and authority to apply pressure in the global community. It is very important to restore stability and peace and to restore respect for human rights in Pakistan, but that is not a task which the EU should take away from the Member States. Peter Skinner in writing. - I agree the state of emergency declared (de facto martial law) should be ended and the state of civil law reimplemented with immediate effect and voted for this. For many of us who are observers of Pakistani politics, it is depressing to see how badly affected the Pakistani communities without our constituencies feel. A return to a democratic procedure is essential for credibility and the due process of Pakistani politics. Eija-Riitta Korhola (FI) Mr President, our Group considered the amendment regarding the recognition of the role of nuclear power in our declaration on the climate conference to be an essential part of this resolution. That is why we want to express our satisfaction that Parliament confirmed this by adopting Amendment 7. We are not alone in our view. The UN's climate panel, the IPCC, also confirmed the role of nuclear power as a low-emission form of energy. Perhaps, too, we should remind ourselves that this House took an historic decision in connection with Mr Reul's report, with 509 votes in favour. The European Parliament recognised that nuclear power was, at the present, the EU's most important energy source with low carbon dioxide emissions, and at the same time highlighted its role in the fight against climate change. On the other hand, our Group did not support section 25 in the resolution because in our opinion it needlessly linked or compared the peaceful use of nuclear power with the spread of nuclear weapons and the threat of terrorism. We should remember that there are no moral censors in the atmosphere. It does not shun one form of energy or sympathise with another for ideological reasons. Only freedom from emissions has any importance, and now the emissions are not welcome. In any case, I wish to say we are pleased that this House sent out a clear message for the Climate Conference and recognised the seriousness of the threat of climate change. Karin Scheele (DE) Mr President, my delegation, the Austrian Social Democrats, abstained from voting on the report on the Bali conference for precisely the reasons that Mrs Korhola has also raised. We support the other political messages of this report. The report is very good. My delegation cannot support the sending of a signal that nuclear power is an essential element in combating climate change. I also think that it should be up to the countries and continents themselves which strategy they follow. I should like to reemphasise my delegation's support for all elements of this report, including the exclusion of nuclear power projects from the Clean Development Mechanism. However, we did not want to back this political signal in favour of nuclear power, so we abstained. In order to show our agreement with the rest of the report, which is good overall, we did not vote against it. Bairbre de Brún, Jens Holm and Eva-Britt Svensson in writing. - We support the resolution dealing with the upcoming Bali conference. The resolution expresses several important points. Among other things it clarifies the significant amount of emissions which are emitted from the livestock sector. It also emphasises the importance of relevant support to developing countries in their prevention and mitigation work to limit the negative effects of climate change. However, we do not support the proposal that nuclear energy should be seen as a tool which is necessary to prevent climate change. Edite Estrela I voted in favour of the motion for a European Parliament resolution on limiting global climate change to 2 degrees Celsius - the way ahead for the Bali Conference on Climate Change and beyond (COP 13 and COP/MOP 3). Having regard to the fact that climate change is a major challenge facing societies today, I think it is fundamental for the European Union to renew its leading role in the Bali Conference and for a global post-2012 climate agreement to be reached. Elisa Ferreira in writing. - (PT) Amendment 7 destroys all the spirit of compromise which prevailed during the negotiations over the final text. The fact that it was adopted introduces a fundamental change in a text that should have retained a broad parliamentary consensus on the Bali challenges. Thus, in the spirit of that overall objective and, although as shadow rapporteur I indicated to the Socialist Party that I would be voting in favour, I personally found myself forced to abstain in the final vote in protest against two aspects: the introduction into the text of the abovementioned Amendment 7 which supports nuclear energy, and the method employed by the Group of the European People's Party (Christian Democrats) and European Democrats in the light of the spirit of compromise which prevailed during the negotiations over the text. Ilda Figueiredo in writing. - (PT) It is true that we are noticing very marked, rapid, and unnatural climate changes that result from many factors, but particularly from the predatory nature of neoliberal policies. We need effective measures to adapt human society to new living conditions. The climate changes anticipated in various scientifically credible and reasoned scenarios might not be slow and gradual, depending on the measures taken in the meantime. There is an urgent need to take deeper, cross-cutting measures to avoid more serious problems in the future, even the proliferation of human and environmental tragedies. However, we also stress the need to break with neoliberal policies at European and global level, otherwise the major powers and the multinationals will continue to impose their own interests in terms of profits, both the exploitation of natural resources and in international trade, including trading in greenhouse gas emissions, which will have an extremely adverse impact on balanced human development. Hélène Goudin and Nils Lundgren Environmental problems are transboundary and therefore the UN Climate Conference is an important diplomatic arena for change at the global level. In the resolution in question, the EU aims to gather the Member States under a common flag in order to steer the conference negotiations in what the EU considers to be the right direction. Limiting climate change is a good objective, but it is regrettable that in the EU's hands global environmental policy is overstepping the boundary into foreign policy at the same time as we dictate to third countries and Member States how their national climate policies should look. The June List considers that every country should have its own vote at the Climate Conference and we have therefore chosen to vote against this resolution. David Martin in writing. - I voted for this resolution from the Climate Change Committee setting out the EU's proposed negotiating position for the start of talks on the future of global climate change cooperation post-2012. It sets out a sound and progressive EU position to drive reductions in global greenhouse gas emissions, taking note of the social impact of climate change, the EU's desired intention to restrict global warming to 2°C or less, and the vital need for global buy-in to the system. Mairead McGuinness in writing. - On behalf of the Fine Gael Delegation (EPP-ED): Fine Gael Members voted in favour of this motion for a resolution, as we believe it is important to have the European Parliament's view on climate change stated in advance of the Bali Conference. However, we voted against Amendment 7, as we are traditionally opposed to nuclear power. Peter Skinner in writing. - I would like to thank the rapporteurs on this issue which brings into focus the issues surrounding one of the most important problems of our time. Caps on emissions with targets to reductions alongside alternative non-carbon based energy production are not accepted by some jurisdictions in the way the EU has agreed. But this Conference can go a long way to unite and coordinate international action. Silvia-Adriana Ţicău in writing. - (RO) The resolution on limiting climate changes to 2 degrees Celsius is an extremely important document for our future and, for this reason, I voted in favour of its adoption. Climate changes represent a major challenge with catastrophic consequences on the environment and human communities. We are dealing with a problem we should address with short, medium and long-term measures. Climate changes already have disastrous effects on agriculture, hydrologic systems, forests, fauna and flora. Countries such as Greece, Romania, Bulgaria, Spain and Portugal have dealt with periods of drought, as well as with floods. The EU should reaffirm its role as the leader in reducing climate changes. The financial mechanisms available for protecting water resources, avoiding deforestation and promoting non-polluting technologies should be increased and accessed by the Member States. We have to allow each Member State to define its own energy mix in order to provide its energy resources. At the same time, Member States that generate nuclear energy should ensure the security of such installations and, especially, adequate waste management. Research funds for decreasing the quantity of waste and increasing the security of installations are required. Frank Vanhecke (NL) Mr President, by no means do I want to detract from the sterling work done by the two rapporteurs on this report on the European Neighbourhood Policy, but I wish to point out that the report contains a gap. It fails to draw attention to the immense challenge presented by immigration from the south, in which regard I take the view that the North African countries themselves also bear tremendous responsibility. I should have liked this report to include a plea for a joint policy between EU Member States and North African countries to combat illegal immigration, one that called the North African countries themselves to task and made good neighbourly relations and financial and material support from Member States dependent on goodwill, on a joint approach to this enormous challenge. This - as I see it - fundamental aspect is lacking in the report, and I have therefore abstained from voting. Pedro Guerreiro in writing. - (PT) Following the decision to take new and significant steps in European capitalist integration, specifically at the level of what is known as 'role of the EU in the world' that is reflected in the ongoing 'constitutional' project - now revived in the 'Reform' Treaty - and in the current EU policies, the majority of the EP is approving a report, which is compulsory reading..., on strengthening the European Neighbourhood Policy (ENP). Any doubts concerning the EU's real purposes and ambitions in relation to the ENP would soon be cleared up on reading this report. It amounts to a programme for actually interfering in and controlling the whole area of the Mediterranean, the Middle East, Central Asia and Eastern Europe. It is a programme which aims to achieve such objectives as: 'triggering and strengthening the commitment of the governments of the ENP countries to political and economic reforms'; their assimilation of EU 'common policies'; their 'alignment with EU foreign policy'; and the creation of a free trade area'. The report also advocates 'more joint actions between the EU and the USA' for 'the promotion of democracy, the enhancement of energy security and the strengthening of regional security in the EU's neighbourhood', a point so transparent that it was toned down in the vote in plenary. It would be best to read the report... Janusz Lewandowski in writing. - (PL) The Neighbourhood Policy is taking on new significance at a time when further expansion of the European Union is going out of fashion. It is different in nature in the Mediterranean Neighbourhood compared with the Eastern European Neighbourhood, where many countries released from the Soviet area of influence are openly declaring a desire to accede to the European Community. In this event, as Poles, Hungarians and Lithuanians well understand, any substitute forms of involvement will not satisfy national ambitions. They have less influence on the required direction in political and economic evolution in these countries. They provide less of an incentive to reinforce the procedures of a state based on democracy and the rule of law and economic market principles and a genuine respect for citizens' rights. Looking at this from the perspective of a European Union border country like Poland, it would appear that the best policy is maximum openness to the aspirations of countries located beyond our eastern border. This is clearly linked to creating an area of stability around the European Union and limiting the field of action of demagogy, of which there is plenty in young democracies. There is also justification for a budgetary effort based on ENPI, the new instrument to replace the TACIS and MEDA programmes, which supports the desired processes in our part of the world. So far, the Eastern European Neighbourhood has been less well funded than the Mediterranean Neighbourhood. The larger the European Union becomes, the greater our responsibility for the Old Continent will be. Athanasios Pafilis The report on the European Neighbourhood Policy summarises the ways and means of imperialistic intervention in neighbouring countries. It falls within the EU's overall imperialist strategy worldwide. As usual, the report uses 'democratic reforms' and 'democratisation' in the neighbouring countries as the most suitable pretext for exerting coercion and pressure on governments that do not align themselves with its policies. This is to support and fund the action of the numerous civil society organisations, so that they can further their undermining role within these countries and promote the interventionist plans of the EU. The European Parliament calls upon the neighbouring countries to participate in the EU's anti-migration policy by intensifying repressive measures against migrants. It calls upon them to cooperate closely with all its repressive mechanisms, such as Europol and the border protection agency Frontex; it incorporates them into the EU's plans to restrict democratic freedom and strike at popular movements, on the pretext of combating terrorism. It openly calls for 'joint actions between the EU and the USA in advancing goals', such as joint imperialist interventions and the sharing of the spoils. It is in the interests of the people to resist and overturn the imperialist plans of the EU and USA in this area and to intensify their struggle for national independence and popular sovereignty. Pierre Schapira in writing. - (FR) Strengthening the European Neighbourhood Policy (ENP), as detailed in this report, requires a deepening of cooperation between the two shores of the Mediterranean via a heightened dialogue between governments, local authorities and representatives of civil society. It is also essential to remember that the ENP must follow the line set by the European Union's development policy. Almost all the countries to the south and east of the Mediterranean are developing countries, according to the official list drawn up by the OECD's Development Assistance Committee. Achieving the millennium development goals should therefore be a priority of EU action in the region. Miroslav Mikolášik (SK) I am in favour of strengthening the relationship with Ukraine and I support further structured dialogue with this country, which is our neighbour directly to the east. During the last elections Ukraine showed great determination to make democratic changes. It decided to continue with a coalition that is clearly pro-European, modern and progressive. We must also remember that Ukraine is a vast country with attractive economic potential and a serious partner in economic relations. It is high time we signed an agreement with Ukraine on economic cooperation, on a free trade area. We must respond to the fact that Ukraine is going to join the World Trade Organisation. I fully support the creation of a reliable energy transit system between Ukraine and the EU. I am very much in favour of cooperation in agriculture and environmental matters, but I would put most emphasis on scientific and educational cooperation, and on strengthening the dimension of the knowledge-based economy. Zita Pleštinská (SK) Ukraine is a neighbour of strategic importance to the EU and a natural 'bridge' connecting the EU with Russia and Central Asia. It is a large country whose Orange Revolution has put it on the road to democracy. Ukraine has become a key partner of the European Union's neighbourhood policy. Our cooperation with Ukraine must improve and we must give all possible diplomatic and political support to Ukraine's accession to the WTO. Negotiations on the free trade area should start as soon as possible so that an ambitious agreement can be signed as soon as possible. We all understand how complicated the situation is in Ukraine: it is a very young and fragile democracy. Today this country finds itself facing a strategic decision: to move towards Russia or to move towards the European Union? That is why the excellent balanced report by the rapporteur, Mr Zbigniew Zaleski, comes at the time when Ukraine needs a clear European perspective. I welcome this report and I gave it my unequivocal support during the vote. I believe that following the early parliamentary elections the country will be able to form a government that will bring Ukraine even closer to our common European house. Czesław Adam Siekierski - (PL) Mr President, the European Union's intention should be to build stronger and increasingly close relations with Ukraine. Mr Zaleski's report, which we have accepted, contains many suggestions on how this might be done. Ukraine should be our strategic partner, not just because of its specific geographical situation and size, but particularly because of the role it plays in the region in relations with Russia and the Central Asian states. It is therefore in the EU's interests to strengthen and develop economic and political ties with this country. We are all aware of how much more work lies ahead for the Ukrainian people on the road to achieving Western standards in their economy, in their standard of living and social matters and in strengthening the democratic system in the state. The EU should provide aid for achieving these goals, and one way of doing this would be to conclude a free-trade agreement with Ukraine, as well as to support its accession to the WTO. This would help to reinforce the market economy, democracy and the civil state, which will bring Ukraine closer to EU membership. Bringing the EU and Ukraine together is a long and difficult process. It is one that is proceeding on a number of levels, but it is necessary nonetheless. For the two sides to come together, Ukraine must continue with the economic and social reforms it has begun, maintain its pro-European policy slant and strengthen its democracy. For its part, the EU must send out a clear signal to show that there are prospects for Ukrainian membership of the EU. Hélène Goudin and Nils Lundgren The June List welcomes increased trade and deeper economic relations with Ukraine. Such a development would benefit both parties in the short and long term alike. However, it can be seen that the underlying purpose of this report is not only to develop economic relations but to conduct foreign policy on the part of the EU. The tone of the report is manifestly dictatorial and the proposals for cooperation given are presented almost exclusively on the EU's terms and with the EU's own interests in the foreground. Therefore the June List has chosen to vote against this report. David Martin in writing. - I voted in favour of this report, for which I was the Socialist Group shadow. It notes the areas where the EU and Ukraine should strengthen their relationship, discusses a free trade area with the Ukraine, energy supplies, and relations with Russia. I would like to see a stronger and deeper relationship between the EU and the Ukraine, and trade and economic relations are a vital part of that. Pedro Guerreiro in writing. - (PT) EU relations with the Ukraine fall under European Neighbourhood Policy which, as the report stresses, aims at supporting the development of the market economy in the EU's neighbouring countries, in other words, capitalism. The report aims at the signature of a free trade agreement (FTA), i.e. Ukraine's integration 'into the EU single market' by the 'gradual adoption by Ukraine of the Community's acquis'. Thus the report: 'Calls on Ukraine... to pay more attention to market liberalisation by guaranteeing the successful achievement of the privatisation process, the dismantling of monopolies' (read: public undertakings) 'and the independence of Ukraine's national bank'; encourages 'the approximation and convergence of standards in the agricultural, industry and services sector' through 'conformity to Community standards', and, in the light of Ukraine's conditional adhesion to the Single Economic Space (SES) with Russia and other former Soviet Union Republics, 'recalls that certain provisions included in the SES agreement, if fully implemented, might be in conflict with the establishment of a functioning FTA with the EU'. Believe it or not, as the rapporteur states, 'the agreement with Russia would in fact prevent Ukraine from any real form of economic sovereignty and stake a heavy claim on the country's independence'. Enough said... Pedro Guerreiro We find some of the trends that 'will to some extent form the EU's humanitarian approach in the future' very worrying and extremely negative, taking the form of initiatives such as the 'EU response to situations of fragility in developing countries' or the 'European Consensus on Development', aimed basically at African countries but also at Caribbean and Pacific countries. An analysis of those initiatives reveals that the central issue of including 'development' as one of the external dimensions for achieving the strategic objectives of the EU's major powers (CFSP/ESDP), which is tantamount to saying the promotion of 'development' as an instrument for interference and control in a strategy which, significantly, does not rule out 'coercive military intervention'. Hence a whole programme and panoply of instruments which, in our opinion, amalgamate and confuse the 'borders' between 'aid' and interference, for example in such fundamental issues as 'state-building'. There is certainly an urgent need to show solidarity with many countries that have inherited disastrous situations from colonialism and that are the victims of decades of interference, but such solidarity, in order to be effective, must be based on respect for the principles of national sovereignty and independence and on an effective and genuine development aid and cooperation policy. Carlo Fatuzzo (IT) Mr President, ladies and gentlemen, it is with great pleasure that I say I voted in favour of Elizabeth Lynne's proposal to tackle the poverty that exists in Europe. However, before this packed Parliament here in Strasbourg, I must criticise the fact that in Italy there is discrimination against elderly pensioners, who are made to live in poverty if they become incapacitated after the age of 65, but are given a significant allowance if they become incapacitated before the age of 65. Mr President, since on 12 December 2007 the new Treaty will be signed in Brussels, giving binding legal force to the Charter of Fundamental Rights, I ask that infringement proceedings be brought against Italy on 12 December because it is violating the right of the elderly to receive the same treatment as all other citizens. Jan Andersson, Göran Färm and Inger Segelström We Swedish Social Democrats voted in favour of the report. It is important that the fight against poverty and social exclusion is intensified in Europe. However, we would like to clarify our position. Paragraph 32 speaks of the setting up of a decent minimum wage at Member State level. The report states clearly that this should be done together with the social partners where applicable. We therefore consider that the collective agreement model we have in the Nordic countries is covered by the formulation. Charlotte Cederschiöld, Christofer Fjellner and Anna Ibrisagic The Swedish Conservatives are positively inclined towards large parts of the report on social reality stocktaking. In the case of many of the proposals, such as those concerning economic migration and increased opportunities to combine gainful employment and family, we have been a driving force in national policy. However, the Swedish Conservatives have chosen to vote against the report because several of the proposals cross the boundaries of the principle of subsidiarity. We do not, for example, consider that the European Parliament should concern itself with treatment programmes at correctional institutions or the treatment of gambling addiction. Nor should the European Parliament have opinions on the regime under which Member States choose to operate their health care, and we do not accept the assertion that deregulation would damage the quality of care. Labour market policy measures, such as the introduction of minimum wages, should also be left to be decided at the national level. Ilda Figueiredo in writing. - (PT) We voted in favour of the report because it records important data on the social situation: 78 million European citizens continue to live in poverty, 8% of the European Union suffers from in-work poverty and the gap between rich and poor in many Member States is increasing. It also includes some positive recommendations, such as the need to fix a decent minimum wage, protect unemployment benefit and support people with disabilities, although it does not tackle the root causes of the social situation and does not call for an end to neoliberal policies, which we are proposing. Consequently, few demands are made as regards the policy changes required. Unfortunately, it only partly includes the proposals in my opinion adopted in the Committee on Women's Rights and Gender Equality, among which I would highlight the appeal to the Community institutions and the Member States to give maximum priority to women's social integration and women's rights, by altering their respective policies accordingly, including that on income distribution policy. Timothy Kirkhope in writing. - I and my British Conservative colleagues believe that social policy should be for Member States to decide. We are anxious that European competences should not be extended in this sphere and that countries should not be pressured to adopt policies that could be unhelpful to their well-being in economic and social terms. We also believe that the 'European social model' is a barrier to economic and social development. There are issues in this report which we support, such as helping people out of poverty, assisting people back into work, support for disabled people and care for the elderly. Policies in these and other social matters are best delivered by Member States, taking account of national circumstances. We believe fundamentally that strong economies are the best route to obtaining social progress in societies. Carl Lang in writing. - (FR) This report on social reality stocktaking in Europe sets out its true economic and social condition from the start. It is an admission of powerlessness within an ocean of Europeanist absurdities churned out by the ultraliberal, globalist thought police. Since 2000, none of the measures to combat unemployment, poverty and exclusion have achieved anything. Worse still, while the European Union calls for greater economic immigration and the protection of its so-called social model, the report reminds us that 78 million Europeans are living in poverty. It forgets to mention what accompanies the hell of poverty, which is not just economic. It is psychological for millions of Europeans who feel culturally and socially adrift on their own soil as they watch their work disappearing abroad in relocations. It is also physical, when violence and insecurity largely generated by immigrant populations frustrated by the difficulties they have in integrating aggravate the whole situation. The solution is therefore not to recognise the hybrid ultraliberal schizophrenic European system, but to challenge it in order to put forward a Europe of recovered identities, which applies protection and Community preference to Europeans first of all! Bogusław Liberadzki I agree that social integration and social security are among the European Union's fundamental values and are a fundamental right of all citizens. The report correctly stresses the need to take ethnic and faith-based heterogeneity into account in EU legislation in order to protect all people from violence and discrimination. I also agree with the formula that access to goods and services should be the right of every EU citizen. José Albino Silva Peneda Social policy falls to a large extent under the competence of the Member States which is why I am in favour of promoting the open method of coordination as well as the exchange of best practices aimed at combating social exclusion. Social security systems must be based on principles which motivate the recipients to seek employment opportunities and not act as a perverse incentive for inactivity. The low level of education of the population and the high school dropout rate should make us stop and think, since it is the least qualified individuals who are the most vulnerable to social exclusion. This situation is particularly worrying in my country, Portugal, where in 2005 more than 39% of young people (aged between 18 and 24) had completed only lower secondary school education. That trend must be reversed and citizens must be given the necessary skills for a successful entry into the labour market. Since this proposal goes along those lines, I voted in favour of it. Andrzej Jan Szejna in writing. - (PL) I am voting in favour of Mrs Lynne's report on social reality stocktaking. She has quite rightly commented that the revived Lisbon Strategy focuses not only on economic results and competitiveness, but also on a drive for greater social cohesion and the social dimension of sustainable growth. Social integration and social security are fundamental EU values. They are the fundamental right of everyone, regardless of their ethnic origin, age, gender, level of disability, sexual orientation or faith. Unfortunately, part of EU society continues to live in poverty. Member States are proposing various forms of protection from poverty and social exclusion. I therefore believe that there should be a deepening of cooperation and an exchange of best practice models between Member States in this area. Attention should also be given to the problem of youth unemployment and to the fight against child poverty, as children from poor families have less opportunity to access future employment. Lars Wohlin There are many praiseworthy statements about anti-discrimination and the importance of equal treatment in this report which deserve attention. Unfortunately, it also contains extremely far-reaching statements concerning, among other things, the introduction of minimum wages. Sweden is opposed to politically determined minimum wages. Quite regardless of what people think is reasonable social policy, the EU must accept that Member States choose different solutions. This must not become yet another example of where the EU goes in and regulates in detail in an area which must lie entirely and completely at the Member State level. The EU countries are also at very different levels of development. Introducing minimum wages will prevent the poorest countries from competing. | Mid | [
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Quotations for bosom Love is a secret no man knows Till it within his bosom glows. [ Proverb ] To nourish a viper in one's bosom. [ Proverb ] See how the orient dewShed from the bosom of the mornInto the blowing roses(Yet careless of its mansion newFor the clear region where it was born)Round in itself incloses,And in its little globe's extentFrames, as it can, its native element. [ Andrew Marvell ] A sea beforeThe Throne is spread; - its pure still glassPictures all earth-scenes as they pass.We, on its shore,Share, in the bosom of our rest,God's knowledge, and are blest. [ Cardinal Newman ] Flatterers are the bosom enemies of princes. [ South ] Lord of the lion heart and eagle eye, Thy steps I follow with my bosom bare, Nor heed the storm that howls along the sky. [ Smollett ] Canst thou not minster to a mind diseased;Pluck from the memory a rooted sorrow;Raze out the written troubles of the brain;And, with some sweet oblivious antidote,Cleanse the foul bosom of that perilous stuff,Which weighs upon the heart? [ William Shakespeare ] Remorse, the fatal egg by pleasure laid,In every bosom where her nest is made.Hatched by the beams of truth, denies him rest,And proves a raging scorpion in his breast. [ Cowper ] The charm of eloquence - the skillTo wake each secret string,And from the bosom's chords at willLife's mournful music bring;The overmastering strength of mind, which swaysThe haughty and the free,Whose might earth's mightiest ones obeyThis charm was given to thee. [ Mrs. Embury ] Excitement is the drunkenness of the spirits.Only calm waters reflect heaven in their bosom. [ Marguerite de Valois ] Canst thou not minister to a mind diseas'd, Pluck from the memory a rooted sorrow, Raze out the written troubles of the brain? And with some sweet oblivious antidote, Cleanse the stuff'd bosom of that perilous stuff Which weighs upon the heart? [ William Shakespeare, Macbeth ] What man would be wise, let him drink of the riverThat bears on his bosom the record of time;A message to him every wave can deliverTo teach him to creep till he knows how to climb. [ John Boyle O'Reilly ] I have play'd the fool, the gross fool, to believeThe bosom of a friend will hold a secretMine own could not retain. [ Massinger ] Confidence is a plant of slow growth in an aged bosom. [ William Pitt ] There is a witness of the evil deed in one's own bosom. [ Danish Proverb ] No friend to a bosom friend; no enemy to a bosom enemy. [ Proverb ] The ill that comes out of our mouth falls into our bosom. [ English Proverb, collected by George Herbert ] Commend a fool for his wit or a knave for his honesty, and he will receive you into his bosom. [ Fielding ] Commend a fool for his wit, or a knave for his honesty, and they will receive you into their bosom. [ Fielding ] Unkind language is sure to produce the fruits of unkindness - that is, suffering in the bosom of others. [ Benthem ] Make not a bosom friend of a melancholy sad soul.... He goes always heavy-loaded, and thou must bear half. [ Fenélon ] Remember that every drop of rain that falls bears into the bosom of the earth a quality of beautiful fertility. [ G. H. Lewes ] Friends are the leaders of the bosom, being more ourselves than we are, and we complement our affections in theirs. [ A. Bronson Alcott ] Yes, I live in God, and shall eternally. It is His hand upholds me now; and death will be but an uplifting of me into His bosom. [ Wm. Mountford ] The mother forms the first rudiments of the infant mind, and instills into the infant bosom the first principles of virtuous action. [ J. Iredell ] Every desire is a viper in the bosom, who, when he was chill, was harmless, but when warmth gave him strength, exerted it in poison. [ Johnson ] It is the very nature of grace to make a man strive to be most eminent in that particular grace which is most opposed to his bosom sin. [ Thomas Brooks ] Let the day have a blessed baptism by giving your first waking thoughts into the bosom of God. The first hour of the morning is the rudder of the day. [ Beecher ] There is many a rich stone laid up in the bowels of the earth, many a fair pearl laid up in the bosom of the sea, that never was seen nor never shall be. [ Bishop Hall ] Earth has one angel less, and heaven one more since yesterday. Already, kneeling at the throne, she has received her welcome, and is resting on the bosom of her Saviour. [ Hawthorne ] As the films of clay are removed from our eyes, Death loses the false aspect of the spectre, and we fall at last into its arms as a wearied child upon the bosom of its mother. [ Bulwer ] I met a brother who, describing a friend of his, said he was like a man who had dropped a bottle and broken it and put all the pieces in his bosom where they were cutting him perpetually. [ H. W. Beecher ] Was genius ever ungrateful? Mere talents are dry leaves, tossed up and down by gusts of passion, and scattered and swept away; but Genius lies on the bosom of Memory, and Gratitude at her feet. [ Landor ] Heaven is attracting to itself whatever is congenial to its nature, is enriching itself by the spoils of earth, and collecting within its capacious bosom whatever is pure, permanent and divine. [ Robert Hall ] So we fall asleep in Jesus. We have played long enough at the games of life, and at last we feel the approach of death. We are tired out and we lay our heads back on the bosom of Christ, and quietly fall asleep. [ H. W. Beecher ] The deep mellow voice of the waves of the mighty deep is full of mystery and awe; and the ocean moaning over the dead it holds in its bosom, lulls them to unbroken slumbers in the chambers of its unfathomable depths. [ Haliburton ] There are evil spirits who suddenly fix their abode in man's unguarded breast, causing us to commit devilish deeds, and then, hurrying back to their native hell, leave behind the stings of remorse in the poisoned bosom. [ Schiller ] When at last the angels come to convey your departing spirit to Abraham's bosom, depend upon it, however dazzling in their newness they may be to you. you will find that your history is no novelty, and you yourself no stranger to them. [ James Hamilton ] When a child can be brought to tears, not from fear of punishment, but from repentance for his offence, he needs no chastisement. When the tears begin to flow from grief at one's own conduct, be sure there is an angel nestling in the bosom. [ Horace Mann ] He who boasts of being perfect is perfect in folly. I never saw a perfect man. Every rose has its thorns, and every day its night. Even the sun shows spots, and the skies are darkened with clouds; and faults of some kind nestle in every bosom. [ Spurgeon ] Are we capable of so intimate and cordial a coalition of friendship as, that one man may pour out his bosom - his very inmost soul, with unreserved confidence to another, without hazard of losing part of that respect which man deserves from man. [ A. Burn ] There must be something beyond man in this world. Even on attaining to his highest possibilities, he is like a bird beating against his cage. There is something beyond, O deathless soul, like a sea-shell, moaning for the bosom of the ocean to which you belong! [ Chapin ] We may scatter the seeds of courtesy and kindness around us at so little expense. Some of them will inevitably fall on good ground, and grow up into benevolence in the minds of others; and all of them will bear fruit of happiness in the bosom whence they spring. [ Bentham ] Liberty is one of the choicest gifts that heaven hath bestowed upon man, and exceeds in value all the treasures which the earth contains within its bosom, or the sea covers. Liberty, as well as honor, man ought to preserve at the hazard of his life, for without it life is insupportable. [ Cervantes ] Liberty is the richest inheritance which man has received from the skies! When shall its sacred fire burn in every bosom, and kindling with the thrilling force of inspiration, spread from heart to heart and from mind to mind, and be the common privilege and birthright of every human being? [ Acton ] Deliberate long before thou consecrate a friend; and when thy impartial judgment concludes him worthy of thy bosom, receive him joyfully, and entertain him wisely; impart thy secrets boldly, and mingle thy thoughts with his; he is thy very self; and use him so; if thou firmly think him faithful, thou makest him so. [ F. Quarles ] There is a voice from the tomb sweeter than song. There is a remembrance of the dead to which we turn even from the charms of the living. Oh, the grave! the grave! It buries every error, covers every defect, extinguishes every resentment. From its peaceful bosom spring none but fond regrets and tender recollections. [ Washington Irving ] Surely you will not calculate any essential difference from mere appearances; for the light laughter that bubbles on the lip often mantles over brackish depths of sadness, and the serious look may be the sober veil that covers a divine peace. You know that the bosom can ache beneath diamond brooches; and how many blithe hearts dance under coarse wool! [ Chapin ] The man whose bosom neither riches nor luxury nor grandeur can render happy may, with a book in his hand, forget all his torments under the friendly shade of every tree; and experience pleasures as infinite as they are varied, as pure as they are lasting, as lively as they are unfading, and as compatible with every public duty as they are contributory to private happiness. [ Zimmermann ] Association is the delight of the heart not less than of poetry. Alison observes that an autumn sunset, with its crimson clouds, glimmering trunks of trees, and wavering tints upon the grass, seems scarcely capable of embellishment. But if in this calm and beautiful glow the chime of a distant bell steal over the fields, the bosom heaves with the sensation that Dante so tenderly describes. [ Willmott ] Consider what you have in the smallest chosen library. A company of the wisest and wittiest men that could be picked out of all civil countries, in a thousand years, have set in best order the results of their learning and wisdom. The men themselves were hid and inaccessible, solitary, impatient of interruption, fenced by etiquette; but the thought which they did not uncover to their bosom friend is here written out in transparent words to us, the strangers of another age. [ Emerson ] What profusion is there in His work! When trees blossom there is not a single breastpin, but a whole bosom full of gems; and of leaves they have so many suits that they can throw them away to the winds all summer long. What unnumbered cathedrals has He reared in the forest shades, vast and grand, full of curious carvings, and haunted evermore by tremulous music; and in the heavens above, how do stars seem to have flown out of His hand faster than sparks out of a mighty forge! [ Beecher ] Love is the river of life in this world. Think not that ye know it who stand at the little tinkling rill, the first small fountain. Not until you have gone through the rocky gorges, and not lost the stream; not until you have gone through the meadow, and the stream has widened and deepened until fleets could ride on its bosom; not until beyond the meadow you have come to the unfathomable ocean, and poured your treasures into its depths - not until then can you know what love is. [ Henry Ward Beecher ] See a fond mother encircled by her children; with pious tenderness she looks around, and her soul even melts with maternal love. One she kisses on its cheeks, and clasps another to her bosom; one she sets upon her knee, and finds a seat upon her foot for another. And while, by their actions, by their lisping words, and asking eyes, she understands their numberless little wishes, to these she dispenses a look, and a word to those; and whether she grants or refuses, whether she smiles or frowns, it is all in tender love. [ Krummacher ] The love of a mother is never exhausted; it never changes, it never tires. A father may turn his back on his child, brothers and sisters may become inveterate enemies, husbands may desert their wives, wives their husbands; but a mother's love endures through all; in good repute, in bad repute, in the face of the world's condemnation, a mother still loves on, and still hopes that her child may turn from his evil ways, and repent; she still remembers the infant smiles that once filled her bosom with rapture, the merry laugh, the joyful shout of Iris childhood, the opening promise of his youth; and she can never be brought to think him all unworthy. [ W. Irving ] With whatever respect and admiration a child may regard a father, whose example has called forth his energies, and animated him in his various pursuits, he turns with greater affection and intenser love to a kind-hearted mother; the same emotion follows him through life; and when the changing vicissitudes of after years have removed his parents from him, seldom does the remembrance of his mother occur to his mind, unaccompanied by the most affectionate recollections. Show me a man, though his brow be furrowed, and his hair grey, who has forgotten his mother, and I shall suspect that something is going on wrong within him; either his memory is impaired, or a hard heart is beating in his bosom. [ Mogridge ] Link To This Page If you have a website and feel that a link to this page would fit in nicely with the content of your pages, please feel free to link to this page. Copy and paste the following html into your webpage. (You may modify the link text to suit your needs). This site uses cookies to deliver our services and to show you relevant ads. By using our site, you acknowledge that you have read and understand our Privacy Policy and Cookie Policy. You can manage your privacy settings on the policy pages. Your use of services at Litscape.com is subject to these policies and terms of service. | Mid | [
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4 min read 'Mom' Cat Found Taking Care Of Abandoned Kittens Isn't Actually A Mom Rescuers named him Mrs. Doubtfire. When staffers at New Jersey's Homeless Animal Adoption League (HAAL) heard about a mom and her kittens abandoned on the side of the road, they thought they knew exactly what to expect - and ended up with quite the surprise. "We received a call about abandoned kittens in a laundry basket left on the curb on a street in East Orange," Joann LoGreco of HAAL told The Dodo. "We don't usually do street rescues but the area was close to our shelter and it was starting to rain so we decided to go take a look." Homeless Animal Adoption League Wanting to help, volunteers from the shelter ventured out into the cold in search of the abandoned family. Finally, they came across the abandoned bin sitting on a curb, with a mother cat and her six babies inside. Homeless Animal Adoption League "Mom was quiet and looked up as if to say thank God you found us," the shelter wrote on its Facebook page. Homeless Animal Adoption League The rescuers quickly scooped up the little family and took them back to their shelter. They fed them and made sure all of the kittens were OK, and were delighted that everyone was in good health. The next day, they went to examine the mom cat, and got the shock of their lives. Homeless Animal Adoption League "Mom was not a mom at all," the shelter wrote. "She was a he. That sweet cat taking care of those little babies was a male. He could have been the dad or a big brother from another litter, but to those little kittens he was their protector and surrogate mom." Homeless Animal Adoption League | Mid | [
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Tag: fashion consultant Fashion is an ever-changing part of life. You can create a style of your very own. Get as much information as possible and follow the tips you think suit you. Start out by checking the tips from the article below. Pull the hair up from your shoulders for a casual, but nice, look. Having long hair can be a pain, especially if you are trying to work or study. To avoid hassles with your longer hair, pull it up into a messy bun that will add some flair to your look. A fabulous handbag can spruce up any outfit, but match it up with other bags you may also need to carry. For example, if you carry a briefcase, coordinate your handbag with your briefcase. Avoid carrying more than one bag at a time. Watch for new fashion trends. Magazines can help you see what is on the runway right now. These are the best places to look for up and coming styles and the latest fashion trends. Casual up-dos are a good way to pick up the hair from your shoulders. Having your hair in your face can be a faux pas at work or even during class. When you’re out of time, put your hair up in a bun! You should never carry around tons of makeup. Instead, pick your desired products in colors that are appropriate for the season. Think about what you will need from the time you get up until you go to bed. Like other items, makeup will go bad when it has been opened for too long. Makeup products can harbor bacteria, which can be transfered to your eyes and skin when applied. A great fashion tip is to always be on the lookout for new changes in style. Understanding these styles can help you to remain in the fashion loop. Magazines are great information sources for new styles from season to season. If you are a full figured individual, purchase clothing in dark colors, such as black and navy; they help slim the figure. These colors will camouflage your shape and reduce the appearance of any bulges you may have. Skirts with elastic waistbands will feel better on. Hair Accessories Make sure you use all of your beauty products before you discard them. You might want to purchase a squeezer that can be used for getting every last drop out of products that come in tubes. You can turn a bottle on the side or upside down to help you get all the product out. Consider removing squeeze tops altogether as you reach the bottom so you can draw out the remaining supply. These are cost savings methods that can keep money in your pocket. There are so many options available in terms of hair accessories. Headbands, bows, and extensions are part of the hair accessories you have to be conscious of. You ought to have many hair accessories as part of your look. To get an athletic look, incorporate a ponytail into your style. When going for an evening out, select a fashionable barrette that complements what you are wearing. Make sure you clean your closet on a regular basis. You might think that having more clothes means you have more choices, but this is not always the case. That over-stuffed and cluttered-up closet will really cramp your fashion style. Clear out your wardrobe and donate everything that no longer fits and you haven’t worn within the past few months. Keep items that can coordinate with a variety of other pieces or ones that can work for various venues. If your locks tend to frizz, seek out a moisturizing conditioner and shampoo set. It will protect your hair and help prevent the follicles from absorbing additional moisture. Avoid products which create volume; this includes products containing wheat or rice. Some people think that fashion is all about the clothing. What some don’t realize is that lackluster hair can detract from the most beautiful outfit. You need to take the time to style your hair with fashion sense too, and take care of it with the best products for your particular type. If you want to have a slimmer appearance, select dark colored clothing. These items help to downplay your body size (particularly if you are a little heavier) and will hide problem areas. Make sure your skirt has elastic in the waistband for added comfort. If you have a few extra pounds on your frame, avoid horizontal stripes. These stripes put greater emphasis on your width, which will cause you to appear even wider than you really are. The best stripe pattern for everyone other than extremely thin woman is vertical stripes, as they make you look taller and leaner. Never make the vital mistake of believing clothes are what makes you fashionable. Your hair can easily ruin an outfit if it’s not looking its best. Set aside some money for effective hair products and devote some time to getting your hair to complement the overall look you want to achieve. Are new jeans something you need? There are numerous styles and sizes to choose from upon entering a store. Sometimes it may seem like it is too much and overwhelms you. Choose classic styles such as a boot cut or straight leg jean. These styles look great on nearly anyone and are well worth the money. Common wisdom is to avoid horizontal stripes if you happen to be on the heavy side. This pattern makes you look wider and is completely unflattering. If you love stripes, try a vertical pattern instead. This elongates your frame, drawing the eye up and down. If you don’t have much money for clothes, let friends know. For example, if one of your friends has an accessory or article of clothing you love, she may be willing to turn it over to you when it no longer suits her. That way, you get some great stuff for free. Do not automatically trust a size label. Always try on clothes before buying them. Today’s sizes aren’t based on any standard measurements. Sizes vary among brands. When purchasing online, make sure to check out the sizing chart. Also, make sure they have a satisfactory return policy if anything you buy doesn’t fit. Every great outfit starts with a solid foundation. A properly fitted bra can define your figure and create an attractive silhouette. Your look will be smoother and tighter with underwear that provide the proper support. There is a lot of slimming undergarment options in the market that can slim a few inches off your waist or behind. Wedged Heels Drink more water so that you do not get cracking nails or dry cuticles. Dry hands are typically caused by dehydration. This is very important when it is cold and dry outside. Give your nails a treat by massaging them twice a day with moisture rich shea butter. You can also apply it to your hands, and wear gloves over them while you sleep. Seek out footwear with wedged heels. They are a top choice for many women for the height boost and slimming effects. If your wedged heels are very thick, it’s possible you can’t walk in them. Try not to be disheartened if someone makes a remark about your appearance. Dressing like a hollywood star is just not necessary to fashion style. The one and only thing you have to focus on is the way you feel about yourself. Sure, it’s easier said than done, but you can’t waste your time dressing to please other people. It’s a thankless task. If you are self-conscious about your weight and want to look as slim as possible, avoid wearing any type of floral patterns with large shapes. These shapes emphasize your large figure, which you will want to steer clear of. Find a dress with smaller patterns to reduce the emphasis on your body size and more on the detail. If you want to wear some shorts to an afternoon event with your colleagues and friends, you need to make sure that you do not wear socks that are visible. Kindergarten kids do this – not adults. To keep your look sophisticated and grown-up, wear sandals with your shorts or pair shoes with low-cut socks that hit below the ankle. When you drink enough water, your nails and skin will look better. If you’re not drinking enough water, your fingernails will be dry. Since the air in winter time is normally dry and cold, it is important you keep yourself hydrated. Use shea butter once or twice daily to moisturize your nails. Additionally, you can apply a thick hand cream or shea butter to your hands and wear cotton gloves over them while you sleep. How your hair looks really tells a story. It is important that your hairstyle reflects your true self. If you happen to be a career-oriented woman, then a classic and professional style will serve you best. For moms that are constantly busy, an easily washable look is optimal. Add your own unique touch to your style. Ruffle your hair, wear an open shirt or wear mismatched shoes. Looking perfect is nearly impossible, but pulling off a slightly chaotic and completely unique look is easy, and fun too! Keep a sewing kit around for minor repairs. If you bust a zipper, lose a button, or rip a seam, you can easily fix the problem. Bring the essentials in your kit to be prepared for the worst at all times. Fashion Consultant Since fashion is not stagnant, you need to keep informed about the current trends. Quick looks at online resources and fashion magazines can give you an idea for what’s trending for the current season. You can select what you prefer and what you think fits your style. To help you get a better idea of fashion, you may want to consider getting a fashion consultant. People are so busy today, how can they have time to browse in stores, too? A fashion consultant can help a busy person like you make great fashion choices without having to invest to much time in it. Part of fashion is choosing the right kind of accessories to wear as well. Great accessories include earrings, necklaces and watches. The right hairstyle and shoes can boost your look. Take a look at fashion magazines to get truly inspired. This winter, the fashion trend to watch for is quilted fabric. There are many types of clothing with this type of fabric. Although clothing made of quilt is made to be a little loose, don’t overdo it; when it is too loose, you will look larger. Choose a wardrobe that is 80% traditional and 20% trendy and updated. Those classic pieces are your real fashion foundation; they’ll support your look no matter the season. Find out what the hot color is right now, and add a belt of that shade to your black pants. You can make your classic shirt a little snazzy by accenting it with a scarf that has a lot of color in it. How your hair looks really tells a story. Therefore, make sure how you wear your hair is a good representation of you. For example, women who are participating in corporate affairs should opt for classic styles such as the shoulder-length bob. A busy mom, however, wants a more simple cut. Don’t forget the importance of accessories. A good outfit can look great if paired with proper accessories. A belt, scarf, piece of jewelery, handbag and of course, the right shoes can go a long way toward making an outfit truly fashionable. Consider the complete ensemble when dressing to pick the right items to accessorize. Find out what palette of colors bring out your true beauty by consulting with a color fashion expert. It all depends on what kind of skin tone you have as well as eyes and hair which determine how the colors appear to people. Determining the colors that flatter you will give you an edge when you are out shopping for clothes. Buy some new clothes on credit. When you pay it off at the end of the month, you’ll be able to look good without going into debt. Bring anti-wrinkle clothing with you on the road if you travel for work. Many hotel rooms offer ironing boards and irons, but you shouldn’t take time doing that if you don’t have to. Usually, it is best to hang up your clothes immediately when you get to the hotel. Keep up with fashion news online. You can find a lot of information by doing a little research online. If this seems difficult, just give it a shot. Give yourself a monthly clothes budget. Limit your spending to a particular amount per month, so that you do not go overboard with this expense. You simply have to use your head; you can still look great on a budget. With jewelry, remember that sometimes less is more. You might love your entire jewelry collection, but you should not wear it all. You can create the wrong impression when you wear too many jewelry pieces at a time. Showcase individual jewelry items by wearing them by themselves. You should now have some tips you can use. Do what works for you, and forget about the rest. You don’t need to use every tip or jump on every fashion bandwagon. Actually, if you would like to be unique, then don’t follow everyone else. When you get your hands on new clothes, do what you can to keep them clean and cared for. Pricey clothes should get dry cleaned or washed by hand, so that your laundry machines do not tear them up and age them. Is fashion a mystery to you? Do you want to become more fashionable? If you have been thinking about this subject then you will want to gather new ideas and the following article will show you how. If you want to remain in style this season, try pairing black and white together. These simple colors are back with a vengeance. Models are sporting colorless looks at every fashion show. You can easily incorporate the colors into your outfits, such as pairing a white shirt with black pants or wearing a black and white dress. The possibilities are nearly endless with white and black pieces. Don’t buy clothes just because they’re on sale. If it does not flatter you, it is actually a bad deal. It will simply be a loss of space and money. Be the creator of your own fashion styles. Many people are fashion followers, but what stands out is a fashion leader. You have to be comfortable with yourself in order to do this. Although once you decide to follow this path, you will notice the increase in compliments you receive. Get your hair up and off your shoulders with a casual up-do. Use this style when long hair feels like a hassle due to the discomfort of a hot and busy day. When you’re short on time, a simple hair elastic and a couple of pins can help you to look your best with a quick and fashionable hair style. If you own a beauty kit, do not store a ton of makeup in it. It is best to change the colors seasonally, rather than keep everything in it at all times. Make certain to have colors for night and day wear. Makeup does actually go bad over time. Bacteria can also form over time. Combining white with black is a perfect combination that is fashionable this season. There are a variety of options that you give yourself when you wear white and black. You can easily incorporate the colors into your outfits, such as pairing a white shirt with black pants or wearing a black and white dress. There literally is no end to the possibilities when combining black and white items together. If your hair tends to frizz out of control, avoid rubbing it dry with a towel after you wash it. This can also damage the quality of your hair due to the roughness. You are just going to want to cover it with a towel and push down to get moisture off. After it reaches the dryness of your desire, remove the towel and comb the hair. Watch for new fashion trends. Understanding these styles can help you to remain in the fashion loop. Magazines get looks directly from the runway, so they are often the first to publish new trends. A dark shirt paired with a dark skirt can help to slim you. Colors that are dark camouflage your body size and de-emphasize unsightly bulges. Make sure your skirt has elastic in the waistband for added comfort. Get the most out of your beauty products to save the most money possible. If the product is in a tube, you can use the squeezers that were made to use up toothpaste. To get the last drops of bottled products, store them at an angle, or even upside-down. Slicing the packaging open will let you scoop out the last bit of product. You can save some money by doing this. Use every bit of your favorite beauty products before discarding them. If the product is in a tube, use a toothpaste squeezer to completely empty it. Try to get the last of the product by turning them upside down and squeezing the last bit out. Don’t forget to take off the top as well. This can save you money. It’s time to clean the closet out! While you might think that having a lot of clothes gives you a ton of options, this really is not the case. Your fashion choices can go awry if your closet is too cramped or cluttered. Sift through everything and toss things you don’t wear regularly, find flattering or that don’t fit you well. A select few choices that are stylish and versatile will prove more useful than clothes that were trendy twenty years ago. Clean out your closet. When you stick to looks you know work, you’ll have a better wardrobe. A closet with minimal clothing will be hard to find a good outfit in. Sift through your wardrobe, tossing any items that don’t fit well or that you haven’t worn in a year or more. A wardrobe comprised of a few classic, versatile pieces will be more wearable than a closet full of outdated styles. If you are on the heavy side, avoid wearing clothes with horizontal stripes. These will make you appear wider than you are. Look for more linear styles, with vertical patterns that draw attention to height rather than width. Be careful with sizes. Don’t purchase any clothes until you’ve tried them on. Dimensions aren’t always the same. Sizes vary among brands. If you buy clothes online, use their size chart. Also, check return policies for clothes that don’t fit. Keep an eye out for the sizes of clothes. This means that, no matter what it is, you need to try it on before buying it. Sizes have no bearing on measurements any more. In fact, different brands have different sizing. If you must buy clothing online, you should at least be sure to check the sizing chart. Also, check return policies for clothes that don’t fit. Do not simply go with the general consensus when it comes to fashion. You are different than other people; therefore, what looks good on you may not look good on someone else. Follow what you like, not what others like. Go with your gut feelings. They won’t steer you wrong. Never follow a fashion trend simply because it is “in” at the moment. Just because something looks fantastic on the super slim runway model, it does not mean it will look good on your body shape and size. Use your own taste as a guideline instead of blindly following fashion magazines. You are going to want to go with your gut on this. They are your best judgement tool. Subscribe to fashion magazines and newsletter to stay current with the newest fashion trends. This will help you stay on top of the constantly changing world of fashion. If you want a (semi) permanent accessory for the warm summer months, try highlights. Just make sure your hair remains healthy so you it does not fade. Conditioning is an essential part of hair treatment or it will end up damaged. Plus-sized women can give the illusion of being smaller by avoiding large floral patterns. The large shapes accentuate you being rather large, and this is very unflattering. An alternative would be to pick small florals, which will give the perception of you being smaller in size as well. To have great fashion, you need to start with the basics. You want a bra that correctly fits you to make your body look very appealing. Underwear should always give support and make you look tighter and smoother. Just look online or through those mail catalogs if you want to find something that’s right for you. There are certainly many options to choose from. One way to keep your nails moisturized is to keep the rest of your body moisturized by drinking the recommended eight glasses of filtered water a day. Being dehydrated can cause them to stay dry. That is particularly the case when winter air is dry and cold. Use shea butter to moisturize cuticles and nails every day. For really deep moisturizing, apply the shea butter before bed and then slip on some cotton gloves for a night long treatment. Check new clothing for loose stitching. These threads will only hurt your appearance, so you should get rid of them immediately. A sharp pair of scissors will do the best job. This easy step will help you make sure your style is right. Don’t tease your hair, or it will become damaged over time. Try and style your hair around one textured look. This will make you appear like you don’t have a particular style, instead of bringing out your individuality. Teasing your hair actually results in damaged or brittle hair instead of giving it volume. Don’t style your hair in a way that creates two different textures. Rather than looking funky and edgy, you will probably look indecisive. Sometimes fashion is addition by subtraction so donate the clothing you no longer wear. This advice serves two purposes, it helps out individuals who are less fortunate than you and it cuts down on the clutter in your closet, giving you easier access to the outfits you love. Dress for your body type. If you have great legs, show them off with an appropriate dress. Highlight them with a short-yet-reasonable skirt and a great pair of heels, and you are sure to look spectacular. By using your best features to your advantage, you will look great! For the fall and winter, quilted fabrics are going to be in. It’s a great look for coats and even skirts. You want this fabric to be loose, but not too loose. If it’s too loose you will look bigger. Fashion Consultant Pay attention to the fabrics your outfits are made of. It is vital that you read the label to see what materials went into making the garment. You might find clothes that shrink after a couple of washes. Don’t waste your money purchasing inferior goods that won’t look great for long. A fashion consultant is a great investment if you want help improving your style. This will help you to stay fashionable with all of the seasonal trends. A fashion consultant can help a busy person like you make great fashion choices without having to invest to much time in it. Talk to a color consultant to see what color they see you wearing well. Certain colors may suit you better, and this valuable advice can improve how you look. Choose colors that look good on you to create a unique look that corresponds to your personality. To get ready for the next fashion season, try picking up some items with floral patterns. Now, they’re not back in a big way, but the floral pattern is reemerging as a top fashion design. Don’t be intimidated to wear a shirt, pants or even a floral patterned dress. Just be aware that patterns in clothing can be paired with similar patterns or they can really pop when paired with a basic piece of clothing. Wear clothes that fit your personality. It is very common for people to try to wear trendy fashions even when they don’t compliment the individual. Follow fashion trends, but only incorporate the trends that feel most natural into your wardrobe. Own your own style, whatever it is. If you are carrying some extra weight in the middle, don’t wear fitted clothes. This clothing shows every ripple, fold and roll. Use clothing that fits loose, and you will show a better body. Always have enough closet space for your clothes. You do not want too many clothes because this could stretch and damage any new clothes that you get. There should always be one or two inches of space between clothing items in the closet. Lips Appear Tall women need to not wear tight clothing. The reason for this is that your body can look a little disproportionate with the fabric clinging tightly to a lengthy body. Keep your looks simple and elegant with clean lines. Many stores offer tall sizes, so invest in some quality pieces that fit your longer frame. Cosmetic surgery isn’t the only option for fuller lips. A shiny gloss over light colored lipstick can be the perfect answer. Lips appear fuller when light reflects off of a shiny finish. Dark lipstick makes lips appear thinner so stay away from it. If you have a friend or work colleague who knows a lot about fashion, you should make sure that you make time to check in with them regularly. They can help you by providing fashion advice you can use to always look good. You can stay prepared this way. Everyone should find a style that makes them look fabulous. What that means is that you should feel confident when you put together a new wardrobe to show to people. Use the advice you just learned. Look at all the white clothes that you purchase to make sure that they aren’t too see through. White clothing can be see through if it is not made well. When wearing a light colored shirt, be sure your bra is the same color as your skin. Focus on the following article. It’s a lot to learn, but it’s so worth it! Learning all that you can about fashion is going to help you look better and feel better. When wearing sheer clothes, make sure the sheer parts are in the right areas. If you select an item that shows a bit too much skin, you will just look like you are trying too hard. Never purchase any additions to your wardrobe simply because they happen to be on sale. If the outfit is not flattering for your figure, then you should never purchase it, regardless of how great the price is. It might end up wasting space in your closet. If you tend to have frizzy hair, avoid rubbing or tugging your hair with the towel as you dry it. This causes damage to your hair, making it more likely to frizz. Use the towel to wrap up the hair and push it slightly to absorb any moisture. After you are done brush it with a comb quickly. Packing for travel means choosing various neutral shades than can make matching combinations. When the colors all go together, you can use them daily without any worries. Accessories can easily provide the finishing touches you need. If you are carry to much weight and desire a more leaner look, choose a dark colored blouse over a skirt that is equally as dark. The slimming effects of the dark colors will avoid accenting any major body problems. Your skirt should have an elastic waistband for more comfort. Stay away from horizontal stripes if you’re overweight. Wearing stripes can create the illusion that you are even wider than you actually are. Look for patterns with vertical lines so your height is emphasized instead of your width. Many are under the impression that fashion only pertains to clothes. These people fail to understand that bad hair can very easily ruin a great outfit. Purchase products that suit the type of hair that you have, and invest a few extra minutes in the morning to make sure your hair looks great. Keep an eye out for the sizes of clothes. Don’t purchase any clothes until you’ve tried them on. Most sizes are not based on actual measurements. They vary between brands. When purchasing clothing online, look at any provided charts for sizing. Check and see if you will be able to return the clothes if they do not fit. Wedgies are back! They help shorter women add some height to their frame and they also elongate the body, making you look like you weight less. They look especially good when created from natural fibers such as wood, cork or wicker. Wedgies are back! Due to the shape and style of the shoe if they are worn with the right clothes they can have a slimming affect and of course they will increase your height as well. When you’re getting a pair of heels that are wedged, you have to remember that if they’re too think, they could be impossible to walk in. Is it time to invest in a new pair of jeans? There are dozens of cuts, sizes, and fits of jeans to choose from in each store you go to. This can be quite overwhelming. Select classic clothing like straight or boot cut jeans. These are the most useful styles, and almost anyone can wear them. Do not simply go with the general consensus when it comes to fashion. What looks hot on a model may not look as good on you. Develop your own sense of style, something that really works for you, and you’re sure to always feel your best. Listen to your own instincts. They won’t steer you wrong. Never follow a fashion trend simply because it is “in” at the moment. The runway model may look great, but it may cause you to look more like a sideshow at the carnival. Follow your own tastes, not the flavor of the month being touted by the fashion rags. Listen to your own instincts in this matter. They will not mislead you. Lip Gloss Give thin hair more volume by applying a small amount of mousse. Some people are trying to bring back the big hair of the 80’s, but this is a mistake. It wasn’t flattering then, and it’s not flattering now. Fuller, more defined lips can be achieved with the use of a lip pencil that has been blended with a sponge applicator to avoid hard lines. Apply lip gloss or a little petroleum jelly as the next step. Give your lips a fuller look by applying a little more lip gloss in the very center of your lips. Eye shadow can help your lips become highlighted because they accentuate the shade of your lips. In the middle of your lips, just add a little smudge. Don’t let others get you down about your wardrobe. You do not need to have a Hollywood perfect look. What’s most important is being comfortable and confident in your appearance and how you present yourself to other people. Know what looks good on your body. If you’re small, soft, delicate fabrics are best. If you have a large bust, buy eye-catching clothing that will draw attention away from it. Those who are pear-shaped want light colors on top and darks on the bottom. A lot of new jackets have some loose stitches that are around the shoulders or vents. You can ruin your fashion look by forgetting to remove them before wearing your outfit. Just get some scissors and cut them to remove them. That’s a simple style tip for you. Adding more natural, filtered water in your daily routine will help with preventing cracking nails and dry cuticles. The drying and cracking of cuticles and nails could be a result of dehydration in the body. This works especially well during the wintertime while the air is both dry and cold. Shea butter can be used on your cuticles and nails to moisturize them at least once or twice a day. Cotton gloves over your moisturized hands while you sleep is another good option. Don’t worry about fashion rules; play with your own style. It’s impossible to know if something looks great until you give it a shot. Give different colors, fabrics and styles a try by mixing and matching for a whole new look. You might be surprised to find you have created a new and fashionable look for yourself. Consider hiring a fashion consultant to shop with you from time to time. People are so busy today, how can they have time to browse in stores, too? Picking up a fashion consultant wouldn’t be the worst thing you could do. For example, while you’re shopping, having someone there to assist you in choosing the right attire could be a great idea. Patterns are making a big comeback in the fashion world. This is especially true with floral patterns. Wearing a floral dress, pants, or shirt is a good idea. Just make sure to complement the outfit smoothly in your choice of shoes, accessories and additional clothing. The upcoming trend is for quilted fabrics. Many article of clothing use this fabric, such as jackets and skirts. It is important to keep the quilted fabric to a minimum, because it is bulky and can make you look heavier than you really are. Try to wear things that seem different to you. You might be surprised at how good some new trend looks with your figure, and you won’t really know about it unless you give it a try. It is a great way for adding variety into your fashion wardrobe. Step out of your fashion box by trying on things you wouldn’t ordinarily be drawn to in the store. This practice makes you more open to options, and you will know if something different looks good on you. It is a fantastic way to add variety to your wardrobe. Never wear visible socks with shorts. This is a look that is appropriate for kindergarten children. Keep your socks cut to the ankle and your embarrassment under wraps. Talk to a professional about the best colors for you. Colors look different based on skin tone, eye color and even hair. Knowing which colors are truly “yours” will help you select the most dazzling fashions. Sell or trade old clothes to save money on fashions. Either donate your old clothes or sell them. Some will buy your clothing outright or even let you trade for items they have on hand. Use solid blocks of color to manage what people see when they look at you. For example, a solid black pant paired with a bold paisley shirt will keep eyes up top. Dark pants work with any top and helps people meet your eyes so that you can directly communicate with them. A color consultant can help you figure out what looks good on you. Colors look different based on skin tone, eye color and even hair. Finding a color that looks great on you can help you find pieces that make you look your best. Crew necks or boat necks are typically the wrong choice for large-breasted women. A v-neck is a much better style to enhance the bosom and keep you looking your best. You might look boxy or plump if you don’t wear a shirt with a v-neck, so you want to make sure that you keep up with your appearance to look good. Try it out for yourself and you will see the difference. One accessory many people do not think about is their eyeglasses. Many people overlook their glasses when trying to look chic. If you wear glasses, that’s another opportunity for you to express yourself in a fashion forward way. Try on different styles to find one that makes you look great. If you wish your lips were fuller, you don’t need collagen injections. Stick with a lip gloss or light colored lipstick. Your lips will have the appearance of fullness as the light bounces of the shine. Dark lipstick only makes lips seem smaller. All it takes is a little time to research online to figure out what you need to do for each season. Spending time investigating your options each season will ensure you are always well-presented. Spend some time online and you can learn about the new trends of each season. A little bit of research goes a long way in dressing your best for each season and occasion. Keep a sewing kit around for minor repairs. There are all kinds of dreadful things that can happen to your garments! You could blow out a zipper, rip an inseam, split your skirt up the side, or any one of a number of different embarrassing things. A good place to keep these items is in a bag. That way, they’ll be handy when you need them. Shop local thrift stores. This will help you if you seek bargains and/or you want to try a vintage look. There is buried treasure to be had at these stores. Check your local shops regularly for fabulous finds and deals. Make the most of your good features. If you have long legs or sexy shoulders, highlighting the body parts you most love will help you feel confident. Also, it will detract unwanted attention from other areas of your body. You can find a lot of good ideas at the mall when looking at mannequins. Aren’t you feeling a lot more comfortable about your fashion, now? No matter your budget, you can start to look great. Just create a good image so you feel good about yourself now and in the future. Make sure that your style is your own and geared to your liking. Right and wrong styles don’t exist. Everyone needs to find what fashions they wish to follow. If someone tells you that what you’re wearing is not fashionable, then kindly tell them that their opinion is not going to influence your choices. Fashion is constantly changing nowadays. You decide what fashion is to you, and you have the power to utilize the most recent fashion trends. Keep on reading for some great tips on staying fashionable. Keep your eye on fashion articles as the season changes. Styles are always changing and a good way to stay in the loop is to check out the different fashion magazines from time to time. They usually share the new trends before anyone else. For a simple, quick way to boost your look, choose a great belt. Available in a wide array of fabrics and styles, belts offer endless opportunities to express your fashion style. When you’re wearing a monochrome look, a pop of color around your midsection can add interest to your outfit. Pare down the number of items you have in your makeup case. Use a few products you like that are in colors appropriate for the season. Think about both night and day uses. Makeup, like many other products, can go bad once open. Also, there are many germs in the environment that you will not want to expose your makeup to. Never purchase any additions to your wardrobe simply because they happen to be on sale. Regardless of the discount, it is not a good deal if you do not look good in it and it does not fit your style. It will simply gather dust on a hanger and end up wasting your money. Some people make the mistake of thinking that clothing is the only concern in fashion. Hair is just as important as anything that is being worn and can make the difference between a great look and a bad one. Get a cut that is flattering and manageable, and invest in hair products and accessories that help you achieve a look that meshes well with your personal style. You can wear jeans with a shirt and high-heel shoes in more formal occasions, but this will work best with black jeans. Blue jeans usually look more casual, but they will work sometimes as well. If you carry a few extra pounds, then avoid wearing clothes with horizontal stripes. Certain patterns will draw attention to how wide your body is. Therefore, you should select a vertical pattern that puts emphasis on your height rather than your width. Keep your eyes open for trends as the seasons change. Styles change all the time and reading magazines can keep you up to date. They will find the new trends the most quickly. Never follow a fashion trend simply because it is “in” at the moment. Someone might look great with certain clothes on, but other people may not. Use your own taste as a guideline instead of blindly following fashion magazines. Listen to your own instincts in this matter. They are your best judgement tool. Create a style that is unique. Too many people are like mice to the pied piper when it comes to following fashion. Of course, you will need the confidence to pull it off, but taking the leap and marching to the beat of your own drummer will probably score you more compliments than you think. If plus sized clothing is what you typically wear, but you want to look smaller than that, do not wear floral patterns with large imagery. The large imagery puts attention on your size, which does not flatter you. An alternative would be to pick small florals, which will give the perception of you being smaller in size as well. Use up your makeup before throwing out the container. For tubed products, use a toothpaste tube squeezer to get every last drop. You can turn a bottle on the side or upside down to help you get all the product out. You can also take the the tops off when it reaches the end. This can save you money. Makeup is a big part of fashion, so make sure your lips are looking great with any outfit. Before you apply lipstick, first outline your lips with a pencil and blend the edges. Slick on a layer of lip gloss or Vaseline over the liner. Accentuate your upper lip with a little more gloss at the center to create a pouty look. Just try and make your lips stand out as much as possible. Put just a dab on the center of each lip. Stay away from horizontal stripes if you’re overweight. These stripes put greater emphasis on your width, which will cause you to appear even wider than you really are. Look for patterns with vertical lines so your height is emphasized instead of your width. Wearing the right fashions isn’t all about finding the right clothing. You should also know some tips for matching your accessories to your clothes. A lot of people just need to make sure that their belt matches their shoes. This gives you a great fashionable look. Get the basics if you want to be fashionable. Your figure will be more defined and your silhouette more attractive with a bra that is properly fitted to your figure. Your look will be smoother and tighter with underwear that provide the proper support. Hide figure flaws with one of the many effective slimming undergarments on the market today. Drinking filtered, pure water will help you avoid cracked nails and dry cuticles. Hydration pays a very important role in preventing dry cuticles and cracked nails. This will help your nails when the weather is cold and dry. Use shea butter once or twice daily to moisturize your nails. You are going to want to think about using shea butter on your hands before sleep as well to keep them maintained healthy. Drink more water in order to stop nails from cracking and cuticles from being dry. If you are not properly hydrated, your nails will probably reflect it, appearing dry and brittle. If you live in a cold climate, this becomes especially important. Shea butter can be used on your cuticles and nails to moisturize them at least once or twice a day. You might want to use gloves after you apply the butter to ensure that it does not rub off. If someone critiques how you dress, do not let it get you down. Not everyone is going to have the same fashion sense. Just wear a style that will make you comfortable and you will soon meet others you enjoy your style. Sometimes new jackets have loose stitching in the shoulder area. You can ruin your fashion look by forgetting to remove them before wearing your outfit. Just get some scissors and cut them to remove them. This is simple and effective. Add a little spark of individual panache to keep your fashion look in style. Ruffle up your hair or wear socks that do not match. Perfection cannot be achieved, but controlled chaos is the next best thing. You don’t have to adhere to the status quo when it comes to how you dress. You won’t know how it looks until you try. Mix it up with different materials, styles and colors. The look you create will certainly be a unique one. Sell or trade clothes that you don’t wear anymore. This can be online or even at a consignment shop. Some shops will let you trade clothing, while some will give you cash. Find clothes that suit you. If you have great legs, show them off with an appropriate dress. Figure out how to highlight them. The point is, focus on your best attributes. The way you style your hair speaks wonders about you and your personality. Therefore, it is imperative that your hairstyle represents who you are. For instance, a shoulder-length bob might look good on you if you are a career woman. On the other hand, that same hairstyle on a busy mom would be too high-maintenance. Fashion Consultant You could go to a color consultant if you are not sure which colors look good on you. Colors look different based on skin tone, eye color and even hair. Pick colors that make you stand out and look your best when deciding on which clothes to get. Bring a fashion consultant along to your shopping trips every now and then. If you are a busy person then it may be necessary to help keep you updated with all the latest fashion trends. A fashion consultant can help a busy person like you make great fashion choices without having to invest to much time in it. Everyone likes to turn things up a notch with great accessories, but there’s such a thing as wearing too many accessories. The best way of looking stunning is simply showcasing a single accessory, such as a necklace or bracelet. This leads people to focus their attention on that one item and gives you the appearance of being well-organized. When buying clothes, be mindful of the fabric from which the clothes are made. All materials will be listed on the garment tag. Just because a piece fits off the rack doesn’t mean that it will still fit after being washed a few times. Don’t bother throwing away money on pieces that are likely to fray, shrink or lose their shapes. Regulate how much money you spend on clothes each month by establishing a budget. You are taking steps to improving your overall wardrobe, but it is important you set some limits in order not to spend more than your bank account allows. Even when you limit yourself, you should still be able to afford the pieces you need, particularly if you frequent sales. Problems with oil in both hair or skin is caused by hormonal issues. These imbalances can be caused by high levels of stress. Relaxation therapy can go a long way in improving the quality of your hair and skin. Share your fashion sense with friends by going shopping with them and making suggestions about pieces that might look great on them. Occasionally, people just need a little help choosing outfits from someone who understands fashion and style. Solid colors are good for your weight. If you are a heavy person, dark colors work best since they draw light to the clothes which makes you appear smaller. Yet, smaller people should wear lighter and brighter colors to appear larger to people that view them. To look stunning, play up your best features. No matter what type of body you have, you want to make the best parts stand out, which gives you the most amount of confidence in your appearance. By accentuating your best features, you will draw people’s eyes to these and not your worst. Sport a scoop- or boat-neck shirt to highlight your collarbone, for instance, or slip into a skinny pencil skirt to draw attention to your well-toned calves. Be careful with quantity when it comes to accessories. The best way of looking stunning is simply showcasing a single accessory, such as a necklace or bracelet. This is the perfect way to draw attention to the special piece. Right now, skinny jeans are really in. That said, even a curvy girl can look great in these pants. These jeans will look great regardless of your figure since they flatten the body. They go with lots of shoes, jackets, and shirts, as well. Carry along a small sewing kit in your purse so you are always prepared for an emergency. This allows you to fix any problem, be it a rip in the seam of your pants when you bend over, or a zipper which breaks. But as long as you have your little emergency survival kit with you, a quick trip to the bathroom can allow you to fix just about anything. If you want to find the inside track on all the latest fashion trends, try researching online. Online research provides an almost overwhelming abundance of information about fashion and trends. You may be pleasantly surprised by the tips and advice you find, giving you plenty of inspiration for new ways to wear your wardrobe. Don’t underestimate the power of accessories. No matter what type of outfit you’re wearing, the right accessories can definitely add to it. Accessories include jewelry, shoes, belts, scarves and handbags. Consider the complete ensemble when dressing to pick the right items to accessorize. Sometimes less can be more with jewelry. As much as you love the pieces of jewelry you own, it’s not necessary to wear everything at the same time. Too many accessories is not a good look. Wear a little bit of jewelry to get an elegant and classy look. You no longer have to be clueless about fashion. Incorporating fashion in your daily life can be done easily in numerous ways. Apply the tips you’ve read today the next time you go clothes shopping. When you want your cheekbones to appear higher, you can use a simple bronzer on the lower parts of your cheekbone. This will make your cheek bones look much higher. This is a great way to look fashionable. This is just one simple tip for success. Looking good translates to feeling good. You are going to smile when you gaze at your well-groomed self in the mirror. Your visual appeal and confidence will rub off on other people, so your day should be a better one. Keep reading for helpful ideas on how you can accomplish this. A classic color combination is black and white. Once again, this combination is popular. You are likely to see many folks wearing this combination. It’s so simple to create black and white combinations using just a shirt and pants or a dress. The versatility of these two colors makes the possibilities endless. Try to spend your fashion money on basic pieces. Invest in pieces that work well together and will never go out of style. You can easily update a simple black pencil skirt with tops and jackets yearly. Wear black jeans with a dressy top and high heels for a classy look. You want to avoid colored jeans if you are trying to dress up. Sheer outfits are super sexy, but always make sure you’re aware of how sheer your clothes really are. If your pants, skirt or shirt are too sheer in private areas, the result can be a cheap or trashy look that will not make you feel classy. Develop a style that is all your own. You can create your own trends. Make sure that you are comfortable in doing this, as it will help to individualize your look. Find your own style and flaunt it. Too many individuals try to copy others; looking great often involves putting your own spin on things. You have to have a certain kind of personality to do this, however, once you do it, you can receive compliments on your unique style. There are endless accessories made just for hair. The sky is really the limit here, and you can choose from different braids and headbands, bows and ribbons, clips and curlers, and much, much more. Your wardrobe should have several of these. You can match your scrunchy to the color you’re wearing, for instance. A night out calls for the perfect matching headband. Fashion isn’t about perfection. There isn’t anyone who has perfect fashion. Second, any attempt for perfection sends the signal that you are trying way too hard. Many of the greatest looks of all time come from people who are not afraid to emphasize their flaws. Avoid rubbing your hair if it frizzes easily. This will only make your hair much worse and lead to a “frizzier” appearance. Rather, just wrap your hair and squeeze to take the water out. Once dry, remove the towel and style as usual. Watch out for sizing. The best idea is to always see how something looks on first. Sizes are not about one’s measurements anymore. They are different depending on the brand. If you buy clothes online, use their size chart. Also look for if you can return clothes if they don’t fit. Wear dark colored blouses and skirts to make yourself look skinnier if you’re overweight. Dark colors help emphasize your good parts and tone down the overweight extras you don’t want people to notice. An elastic waistband in your skirt provides more comfort. Avoid fashion trends solely based on popularity. What works for fashion models won’t necessarily work for you. Do not follow the crowd. Instead, choose your outfits yourself. Trust your instincts when it comes to this. Following your inner voice will help you develop a personal style. Do not automatically trust a size label. Don’t buy clothing that you haven’t tried on. Sizes aren’t just based on set measurements anymore. They are different depending on the brand. If you have to buy online, look at their sizing chart. Check and see if you will be able to return the clothes if they do not fit. Be mindful and aware of your physique’s good traits and not so desirable attributes. Find fabric that is padded to help you look like you have curves if you don’t possess them. Choose some brightly-colors pants or skirts if you want to draw attention away from your chest. Pear-shaped women can offset the imbalance by wearing dark colors from the waist down, complemented with light colored blouses. Are you in the market for a new pair of jeans? There are numerous styles and sizes to choose from upon entering a store. It can be pretty intimidating. Pick styles that are more classic such as straight leg jeans or a boot cut. These styles look great on most people and they will help you get the most out of your money. Apply a bit of mousse to add volume to thin hair, but use a light hand so you don’t overdo. Although big hair is gaining popularity again, it is not flattering on most people. Become aware of your body’s weaknesses and strengths. Petite? Look for fitted styles and soft fabrics that enlongate your body and give you some bulk. Busty women want clothing that brings the attention to a different part of the body. You can use lighter colors for shirts or blouses and darker colors for pants or skirts to balance out a pear-shaped body. Good fashion is not all about finding a great outfit, it is necessary for you to find matching shoes. Usually, you just need to match your belt color to your shoe color. This will give you a timeless look that is always fashionable. Don’t feel down if someone comments on the way you are dressing. Everyone need not look like a celebrity on the red carpet when they dress. Fashion is about looking good and confident in whatever you wear and making your own style choices. Shea Butter Pay attention to the fabrics your outfits are made of. Check the tag to find the specific material of an item. If the clothes fits now, it may not fit after you wash it several times. Be careful not to waste your cash on clothes that most likely will break down or shrink after a limited amount of daily wear and care. One way to keep your nails moisturized is to keep the rest of your body moisturized by drinking the recommended eight glasses of filtered water a day. Cuticles and nails are usually dry from a lack of hydration. This is very important when it is cold and dry outside. Shea butter can be used on your cuticles and nails to moisturize them at least once or twice a day. You can also put on shea butter or some other type of hand cream on your hands and place a cotton glove on top while you go to sleep. Try to match the hairstyle that you choose to your personality. Thus, gear the hairstyle you choose to the season and your personality. If you are in business, try a professional style. If you are a mom leading a hectic life, you can choose a style that is wash and go. A fashion consultant may be a very helpful investment on an occasional shopping trip. This will help you to stay fashionable with all of the seasonal trends. A fashion consultant can help a busy person like you make great fashion choices without having to invest to much time in it. Spend some time with a professional color consultant to find out which colors flatter you. It all depends on what kind of skin tone you have as well as eyes and hair which determine how the colors appear to people. When you find the colors that most flatter you, you can then buy clothing that makes you look your very best. The next time you’re out shopping, try on a piece that you wouldn’t typically wear. Not only will this open your mind, but you may end up looking great, too! It is a great way to put some variety into your wardrobe. Large bosoms do not work well with crew neck tops and boat necks. You should wear v-necks instead. A v-neck will draw the eye where you want it to go. Experiment with different shirts and you will see how much better you look with a V-neck shirt. Solid Colors When you find you’re very greasy, it’s likely a hormone imbalance is causing the problem. Your body’s hormones can get out of balance when you are suffering stress. If this is you, then attempt relaxation therapy. This can help control your hormone levels and decrease your skin and hair’s oil production. Control any attention on your body using solid colors. You can get a lot of attention by wearing patterned items with solid colors of skirts or pants. Match your dark pants with a bright top to draw attention to the upper half of your body. One accessory many people do not think about is their eyeglasses. Many people skimp when it comes to their eyewear. You can show your style off by choosing certain prescription eyeglass frames. Try on several frame styles to find a pair you’ll love to wear that accentuate your facial features and add to your personal style. Compensate your weight using solid colors. If you’ve overweight, then dark colors should be worn in order to draw light to your clothes and make you appear smaller than you really are. Light or bright colors can help you visually gain weight. It’s a great idea to keep a needle and thread in your purse. If the unthinkable happens while you are out, you can use it to make a quick mend. Always keep essentials in your bag. Some online research can help you see what is “in” each season. Enough research should help you figure out what to do as each season approaches. You need to make your best features stand out. If you have great legs or arms, make sure to accentuate that part of your body. By accentuating your best features, you will draw people’s eyes to these and not your worst. A pencil skirt can show off your waist region in the best way. Do not over do your accessorizing. Showcase one key accessory such as a necklace or bracelet. This leads people to focus their attention on that one item and gives you the appearance of being well-organized. Check out the latest trends in fashion online. Spending some of your time online doing research is an easy way to discover a lot of knowledge. Just do a little research to see what fashion advice you can learn about in a short amount of time. Keep a small sewing kit in your bag for on-the-go repairs. If your zipper bursts or a seam rips, you want to be able to fix it right there instead of having an embarrassing moment. Keep your kit in your bag at all times to ensure that you are prepared for fashion emergencies that can and do arise. Always have enough closet space for your clothes. Too many clothes within a small space can cause clothes to become stretched or damaged, affecting their fit and appeal. There should always be one or two inches of space between clothing items in the closet. Head out shopping with your friends and get them to let you choose a few outfits for them. Sometimes, you can take friends shopping and pick out some outfits that look great on them. Although it is a challenge to find just the right swimsuit, it is still important. Your suit needs to fit perfectly. If you are smaller in the bust, it is essential that you find a well-fitting top that will stay in place. If your bust is small, choose a suit with some padding. You should go to a few thrift stores. This will help you if you seek bargains and/or you want to try a vintage look. While these stores are well-known for things that don’t look right, there can be some hidden gems amongst the rest of it. You just never know until you look, the store down the street could be holding several pairs of your favorite jeans at a fabulous price! Begin making subtle changes to your wardrobe. You do not want to drastically change because it could result in a bad transformation. Just try adding little changes to smaller things like your hair or your jewelry. Wear your regular clothes in original ways, or combined with unexpected accessories. Also, turn your scarf into a bracelet. Everyone tends to pay more attention to you when you are looking your best. It starts with you in the mirror and follows into the looks of pedestrians on the street. To light up people’s faces, it is essential to look good. Follow these simple tips to accomplish this easily. When trying to look your best always pay attention to the littlest details. Lots of people will dress in very extravagant outfits but forget to add one small detail, such as a beautiful necklace, that could bring it all together beautifully. Travel with nice luggage, and have more than one umbrella to choose from. It can be difficult to stay fashionable if you are not used to it. The hardest part here is actually figuring out where to start from to look your best. There are so many different factors that go into finding the perfect look. The following article contains fashion tips to help you gain more knowledge on being fashionable. Handbags compliment outfits; however, if you carry any other bags, ensure that your purse complements them as well. If you are also carrying a briefcase or a laptop bag, make certain that it looks good with your purse. Avoid carrying more than two bags at any time. Don’t buy clothes just because they’re on sale. If it’s not really your style or going to look good on you anyway, it’s just not worth the savings you see in the price. It will sit in your closet and be a waste of money. Wearing white and black is classic and that is popular this season. This year many black and white outfits are on the runway. These colors are simple to mix; try wearing a crisp, white top with black trousers, or pick up a a funky dress in black and white. There literally is no end to the possibilities when combining black and white items together. Sheer clothing is often thought of as sexy, but it is important that you consider just how sheer it is and where. You want to ensure that you are fitting an image that is proper for the environment that you are in, so be conscious of what you wear. You can dress up jeans by pairing them with a shirt that is more dressy and a pair of heels, but this is only acceptable if you plan on wearing black jeans. Blue and other colored jeans only work with a blouse and heels as a dress-casual look. This season, the classic pairing of black and white has once again become popular. A number of outfits showcasing this combination have appeared on the runways. There are many ways to pair these colors. When it comes to this combination, there are unlimited possibilities. Some people make the mistake of thinking that clothing is the only concern in fashion. However, hair is important too; it can set the tone for your entire look. Make sure you keep your hair looking at its best and use the best products that you can afford to do this. Whenever you travel, carry along easy to coordinate, neutral colored items you can quickly mix and match. Using only a few garments, you can create outfits that will never look tacky. You can pull your whole look together with a belt, scarf or some other colorful accessory. Look at clothing sizes carefully before you buy. Don’t purchase something that you haven’t tried on. Today’s sizes aren’t based on any standard measurements. They are different depending on the brand. When you shop on the Internet, you should always look for a size reference chart. Find out their return policy as well. There are people who believe that fashion just means clothing. Your hair also plays a huge role in the way you look. You need to take the time to style your hair with fashion sense too, and take care of it with the best products for your particular type. Are new jeans something you need? There are dozens of cuts, sizes, and fits of jeans to choose from in each store you go to. It may be a lot to handle. Stay simple and pick straight leg, boot cut or another traditional cut. These choices go well with most tops and flatter most people. Avoid any horizontal stripes if your weight is higher. Certain patterns will draw attention to how wide your body is. Instead, go for vertical stripes, which appear to elongate your body and make you seem thinnger. Do not follow trends just because they are popular. What may look great on that runway model may make you look like a carnival side show. Do not follow the crowd. Instead, choose your outfits yourself. You must trust your instincts regarding fashion. They aren’t going to let you down. Is it time to update you jeans? If you have been in a clothing store lately, you know that the number of different sizes and fits available have mushroomed. It can be too much to handle at times. Stay simple and pick straight leg, boot cut or another traditional cut. These are the most useful styles, and almost anyone can wear them. If plus sized clothing is what you typically wear, but you want to look smaller than that, do not wear floral patterns with large imagery. Depending on the fabric, these shapes can actually emphasize your largest attributes, creating an unflattering look. Pick patterns that have small flowers as opposed to big ones. Don’t follow all popular fashion trends. What fits the model on the runway might look silly on you on the street. Wear things that are your taste and not everything you read in magazines. Rely on your instinct and individual taste when making fashion choices. You won’t be led down the wrong path. Do you know how to choose the shoes that go with your outfit? Most of the time, you can’t go wrong by matching your shoes to your belt or handbag. When you care about the details, you’ll always stand out as being fashionable. Latest Trends Keep your nails and cuticles healthy enough to maintain your manicure by drinking plenty of water. If you are not properly hydrated, your nails will probably reflect it, appearing dry and brittle. This is more prevalent during winter. Shea butter creams are best to use on your hands at least once daily. Putting shea butter on your hands and encasing them in cotton gloves as you sleep is also a good idea. Fashion newsletters can be subscribed to for help keeping up with the latest trends. This is a good way to stay up to date with the latest trends and get the fashionable items you need for your wardrobe before any of your friends start following the trend. Don’t pay attention to the negative things that other people say. The thing about opinions is that they’re utterly meaningless unless they’re your opinions! All you need to do is carve out a style that feels natural to you. There are bound to be others out there who will appreciate your unique look. Mousse can be used to add volume to thin hair, but do not use too much. The more you use, the more likely you are to create a retro look from the 1980’s. Adjust the amount of mousse to obtain the look you desire. There are personal shoppers that will help you choose fashionable clothing. Consider hiring one if you need some extra assistance. You probably don’t have enough time to keep up with the latest fashions if you have other priorities. You can consider hiring a professional to help you with clothes shopping. Show your personality through your fashion quirks. Leave your hear messed up or a shirt unbuttoned. You can’t be perfect, so you should aim for controlled chaos. For fun and function, ask a professional colorist which colors will look best on you. Your skin, hair and eye color can all dramatically impact how your clothing looks on you. Finding a color that looks great on you can help you find pieces that make you look your best. Jackets often have some stitches that are looser than others. These threads do not look good and should be removed. You should get rid of them by using scissors. Increase your style with this simple strategy. Clothing in solid colors helps you direct attention where you want it. Prints and patterns on tops can be showcased by wearing solid colors on the bottom. Dark bottoms with a lighter top will bring a persons eyes to yours. Dress to suit your figure. Low-cut blouses may not work for you, but you may have great legs. Try wearing some great heels and a skirt that allows those legs to shine! Play up your assets. Not going overboard with accessories is critical to fashion success. The best way of looking stunning is simply showcasing a single accessory, such as a necklace or bracelet. A single piece garners more attention and tells the world you are organized. Fashion Consultant Choose a wardrobe that is 80% traditional and 20% trendy and updated. Classic pieces that last from year to year will form the foundation of your wardrobe and will support fun seasonal changes. When you’re wearing all black, consider a pop of color in a trendy hue, such as on a belt. Wearing a colorful scarf can dress up a nice shirt. You may want to hire a fashion consultant when shopping occasionally. If you are a busy person then it may be necessary to help keep you updated with all the latest fashion trends. Picking up a fashion consultant wouldn’t be the worst thing you could do. For example, while you’re shopping, having someone there to assist you in choosing the right attire could be a great idea. Go a little bolder with the coloring in your wardrobe. You’ve probably looked twice at a man wearing a pink top. Use purples, yellows, deep blues, oranges, pinks, or reds to add flair to black dress pants or jeans. Try to avoid muted tones as these are dull and uninspiring. Surprisingly, patters are beginning to be seen more and more in the fashion world of late, especially floral. Floral can be a lot of fun. Just make sure to complement the outfit smoothly in your choice of shoes, accessories and additional clothing. Take friends shopping with you and have them pick clothing that you think works with their styles. It can be difficult for someone to step outside of their comfort zone without a little bit of help. Pay attention to and understand the clothing that you purchase. In particular, examine what materials it is constructed from. It may fit in the dressing room, but can quickly lose shape once you have washed it. Make sure you do not waste your money on any clothing you think will fray, shrink or lost shape. Don’t forget the importance of accessories. Dated outfits can be updated by using accessories. A carefully chosen bag, belt or scarf can make all the difference between a fashion success or disaster. The right accent pieces should play an important part in your daily dressing routine. Your hair makes a statement about you. It is important that your hairstyle reflects your true self. If, for example, you are a serious business woman, try a classic such as the bob that is both professional and easy to care for. However, if you are mom who is constantly running around, picking a style that is simpler and easier to manage will work best. Jeans are popular all the time, but currently, skinny jeans seem most popular. You need not be thin to wear skinny jeans. They can work with almost every figure since they smooth and flatten the bottom half of the body. Also, they can match a variety of different styles as well. Keep a small sewing kit in your bag for on-the-go repairs. You may be away from home when a seam tears or a zipper bursts, and you will want to take care of this problem immediately to avoid any embarrassment. A good place to keep these items is in a bag. That way, they’ll be handy when you need them. When it comes to jewelry, you can wear too much of a good thing. Even though you love all your jewelery, you don’t have to wear all of it at the same time. Too much of anything can cancel out the good. Try to match your jewelry with your outfit and the season that you are in. An outfit is never complete without accessories. Such complementary accessories include belts, bracelets, jewelery, hats and more. Shoes and hairstyles are another way to add something extra to your look. For matching outfits, read fashion magazines. If you have friends that always come across as particularly fashionable, get some hints from them regularly. You will always have a heads up on what is current in fashion by doing this. You will feel better prepared as a result. Don’t shy away from adding color to your look. Everyone notices people with bright or unusual colors. Use purples, yellows, deep blues, oranges, pinks, or reds to add flair to black dress pants or jeans. Keep the neutrals and muted colors in the office. To keep your clothes looking their best, take proper care of them. If you hang your clothes after wearing them, you can wash them less. If you want your clothes to last longer, bypass machine drying them in favor of air drying on hangers. It can be a challenge if you don’t always know what to wear. Thankfully, this article has prepared you for that. Use them tips to find see the improvements to can make to yourself. When your fashion goal is to look and feel marvelous, pay attention to detail. Lots of people will dress in very extravagant outfits but forget to add one small detail, such as a beautiful necklace, that could bring it all together beautifully. When traveling, use luggage that matches your outfit. Dressing nicely doesn’t have to be hard. If you have the latest knowledge about fashion, being fashionable is second nature. This article has tips for you to go right to the head of any fashion line! Read on to obtain more fashion advice. A classic color combination is black and white. Once again, this combination is popular. Many runway outfits are using this combination. This look can be easily incorporated into your look. For example, you could wear black pants with a white shirt or you could wear a dress that’s black and white. When it comes to this combination, there are unlimited possibilities. Spend the majority of your fashion budget on the basics. Invest your money on classy pieces that are timeless. Buy quality pants, skirts, blouses and jackets in solid colors like black, creme and beige that can be mixed and matched with more trendy things easily. Develop a style that is all your own. You can create your own trends. You have to be comfortable with yourself in order to do this. Although once you decide to follow this path, you will notice the increase in compliments you receive. You should not purchase an item of closing just because it is on sale at a great price. If it does not flatter you, it is actually a bad deal. It will just remain in your wardrobe as a reminder that you wasted money. If you struggle with frizz, don’t vigorously dry your hair with your towel after washing it. This causes damage to your hair, making it more likely to frizz. Instead, wrap it up and push on the towel to get most of the moisture off. After it reaches the dryness of your desire, remove the towel and comb the hair. Pull the hair up from your shoulders for a casual, but nice, look. Long hair is a real pain during busy times. It’s so simple to just throw your hair up into a bun, because today’s looks are all messy anyway. Don’t listen to the people saying that wearing white once Labor Day has passed is wrong. They’re actually the ones who are wrong. You can, and should, wear any color that you find appealing and flattering, no matter the season. If you look best in white, by all means, wear it all year ’round. People should not view you negatively as a result. Simple Colors If you’re overweight, don’t wear horizontal stripes. Because the eye only follows the direction of the stripes, even skinnier people are going to look a lot wider with this pattern. So, just imagine how large you’ll look wearing it. Instead, go for vertical stripes, which appear to elongate your body and make you seem thinnger. If you want to remain in style this season, try pairing black and white together. These simple colors are back with a vengeance. The best part about these simple colors is that you can throw together an endless array of outfits. These colors are easily incorporated into a wardrobe and used in a variety of ways. There are many different style combinations that you can come up with in these colors. Be careful with sizing. The best idea is to always see how something looks on first. Sizes these days tend to be less consistent, being based on things other than just measurements. They are different depending on the brand. When purchasing clothing online, look at any provided charts for sizing. Check and see if you will be able to return the clothes if they do not fit. If you have problem with frizzy hair, do not use a towel to rub your hair after shampooing. The rubbing motion will damage the hair and create frizz. Try patting your follicles instead. After you have done that, unwrap your hair and comb it. Be fashionable by getting a little funky. Have some messy hair, don’t button your shirt all the way, or pick out shoes that don’t really match. Perfection is impossible, but controlled chaos helps you stand out in a crowd with distinct fashion taste. Clean your closet out. Sometimes you may think that you will have more outfits to choose from if you have more clothes. If you closet is cramped or cluttered, your fashion choices will be hindered. It is time to toss or give away anything that you have not worn in the last year, as well as items that no longer fit well. Classic clothing that can be mixed and matched will be of more use to you that stuff from past decades that you’ve been holding on to. You don’t have to adhere to the status quo when it comes to how you dress. You will never know if something is good if you do not try it. Mix and match colors and styles to find the ones you like. You might be surprised to find you have created a new and fashionable look for yourself. Makeup is a big part of fashion, so make sure your lips are looking great with any outfit. Before you apply lipstick, first outline your lips with a pencil and blend the edges. Apply lip gloss or a little petroleum jelly as the next step. Use an extra dab of gloss in the middle of your top lip. You can also use an eyeshadow on your lips. Put just a dab of eye shadow in the middle of both your upper and lower lips. Shorts are a great way to keep cool and look good, but don’t commit a fashion faux pas by wearing shorts with visible socks. Kindergarten kids may get away with this, but adults shouldn’t. Try to look adult-like; avoid socks with shorts. Determine what is good and bad for your body shape. If you are small, you need to find softer fabrics with fitted looks that help to give your body some length. Yet if you are fully figured then you are going to want to cover up to keep your image intact. Finding the appropriate style for your shape is one of the best things that you can do to improve your fashion sense. You can spend less money on new clothes if you sell or swap the ones you no longer want. Certain Internet sites allow you to do this, or you could seek out a consignment shop in your area. You can get some money from thrift stores for your old clothing items. If you don’t have much money for clothes, let friends know. They may be willing to part with fashionable items they have tired of. This is a wonderful way to get fashionable pieces without spending any money. Always take a look and see what your clothes are made out of. Look at the tag to see what each item is made out of. Just because the item fits you well in the dressing room, doesn’t necessarily indicate that it will still fit once its washed. Don’t waste your money purchasing inferior goods that won’t look great for long. Big hair is out, so don’t tease it. Additionally, do not use different textures in one hairstyle. You may give the appearance of being indecisive about your style instead of the singular look you were aiming for. Where do you want eyes to fall? Your use of solid colors will dictate where people look first. Solid bottoms will open the gate to more elaborate tops that can get you attention. Dark bottoms with a lighter top will bring a persons eyes to yours. You don’t have to adhere to the status quo when it comes to how you dress. You aren’t sure if something is going to look great until it is on you! One fun way to try things on is the mix and match method. You will look marvelous and create a look you love by giving yourself more options. Try to construct your style around your body shape and size. Do you maintain a long, round or rectangular shape to your body? Your shape will determine which styles and clothing cuts will be flattering on you. A fashion consultant may be a very helpful investment on an occasional shopping trip. People with stressful jobs or busy family lives often feel they do not have time to be fashionable. You can consider hiring a professional to help you with clothes shopping. If you want to know what’s in season, you should research different fashion sites and even different geographical areas regularly. Enough research should help you figure out what to do as each season approaches. There are many ways in which you can update your wardrobe cheaply, such as selling old items or even trading them with friends. You can put these up for an auction or sell them to a local shop for profit. Many shops will pay you for your clothes or give you the option to trade for items that are in stock at their store. Fashion is always changing, but reading about the latest fads can help you. Browsing online and reading fashion magazines will let you know what the current trends are. Pick and choose within reason and follow advice that suits your personal fashion sense. Flattering Colors Give yourself a monthly clothes budget. By limiting your spending, you will have a great wardrobe without debt. You can still shop for the clothes you likes, but make good decisions about what you choose to buy. Consult a professional fashion consultant or personal shopper to determine your most flattering colors. The same color of clothing can look dramatically different on two different people due to variations in skin tone, eye color, and hair colors. For you best look ever, use these flattering colors to build your fashion wardrobe. Use the 80/20 rule for your wardrobe–80% classic and 20% trendy. Having classic items provide a solid foundation from which to choose from no matter what season it is. If you’re wearing something basic like black pants, choose a bright colored belt that makes your outfit “pop.” Likewise, a trendy colored scarf can add modern style to a classic shirt or blouse. Avoid fitted clothes if you put on a little more weight this season. They will only bring out the bulges and bumps. Find tops that are fitted up top, but have a looser or flared fit around your waist. This will highlight the assets of your shape while hiding any unsightly bums. Pay a visit to the thrift store in your town to find deals on clothing. Your local thrift store is often a goldmine when it comes to vintage and high-end clothing at a bargain price. Although there are some bad clothing items there, there are also a few clothing diamonds hidden in the rough. The price is right, so it’s worth the time you spend perusing the racks. Wear a belt if you’re going to tuck your shirt into your pants. You may not like belts, so suspenders are an option for this look as well. Make sure your shoes match your suspenders or belt. Your clothes will last longer and look better if you care for them properly. You won’t need to wash clothes as often if you hang them up after you wear them. Rather than using the dryer, you can keep your clothes looking good by hanging them on hangers. You do not have to have cosmetic surgery for your lips to appear fuller. A light colored pink gloss or shiny finished lipstick can do the trick. These colors attract light and make your lips look larger. Dark lipstick makes lips appear thinner so stay away from it. When you buy clothes that are white, always try it on in someplace that has bright light. A lot of people don’t do that and are shocked to discover their white clothing is see-through. If you have a white shirt on, always choose a bra that is as similar to your skin tone as possible. It is possible for you to be fashionable. It can even be a lot of fun. Put a few of the tips into practice and before you know it your friends will be coming to you for fashion advice and envying your sense of style. You have to keep a dress that works in daytime and nighttime situations in your wardrobe. If you’re constantly busy all day long, then this dress is going to be vital for you. In daytime hours, it can be dressed down with pumps and a bright accessory, then dressed up in the evening with heels and jewels. Maybe you felt like you’d never get into fashion. Good fashion sense shows people that how you look is important to you. Use this article to educate yourself about fashion. Add a belt for a fashion upgrade. There are so many different styles of belts to choose from, offering endless color and design combinations to choose from. Pair a brightly colored belt with your skinny jeans, or create a fashionable look by adding a bold patent leather belt to your outfit for a night out on the town. Sheer apparel can look good if done correctly. For example, if you find a blouse with sheer sleeves, that would probably look very nice. You want to ensure that you are fitting an image that is proper for the environment that you are in, so be conscious of what you wear. Spend your fashion money on basics. Buy clothes that are timeless and coordinate well. A basic black pencil skirt can be worn for many years and be updated each year with a top or jacket that goes along with the fashion of the day. Always watch the trends and changes in the fashion world. Style is constantly changing, so keep up with fashion magazines to learn about the latest trends. They are most often the source for new trends. Don’t buy something simply because of a great price. If it’s not really your style or going to look good on you anyway, it’s just not worth the savings you see in the price. Instead, it will languish in your closet, reminding you of money you shouldn’t have spent. Develop a style that is all your own. Too many individuals try to copy others; looking great often involves putting your own spin on things. You have to have a certain kind of personality to pull off fashion forward unique style, but if you try it, you can bask in multiple compliments for being different. Wearing sheer clothes can make you look sexy, but you have to make sure that you are very careful about how sheer the clothing is and in what area. Wearing see-through items will make you appear to be more trashy than classy. Being fashionable does not mean that everything must be perfect! First, there are no perfect people, and it is an unattainable goal. If you are trying to achieve perfections, you look may appear to be trying too hard. You can make a look uniquely yours by incorporating a single unexpected flaw, like messy hair or an untucked shirt. A dark shirt paired with a dark skirt can help to slim you. Shadows don’t show when you wear black, masking rolls and other unsightly bumps. An elastic waistband in your skirt provides more comfort. Horizontal Stripes Do not strive for perfection in fashion. Try not to aim for perfection, as this is not achievable. Also, if you attempt perfection, you may look like you are investing too much time and effort into the process. Disheveled looks with messy hair, non-matching shoes, or not completely buttoned pieces like those of Kate Moss can look great. If you have some weight to lose, avoid wearing clothes with horizontal stripes or similar patterns. This will make your body look much wider than it is. What you want are vertical stripes instead of horizontal stripes. Vertical patterns make you look taller instead of wider. Make sure that you use all of your beauty products. You can get the most out of tube containers by using squeezers typically sold for toothpaste. Turn the bottle upside down or on its side to get the most out that you can. Removing the caps from product containers is also a good idea once there is almost nothing left in the bottle. Utilize all these cost saving tips to get the most out of your beauty products. Mousse is a great way to volumize your hair, but be careful not to go overboard. Many people are going with the big hair that was made famous in the 80s, but the truth is the hairstyles back then were not very flattering or fashionable when worn on most people. If you are overweight, never wear clothes that have a horizontal stripe pattern. Because the eye only follows the direction of the stripes, even skinnier people are going to look a lot wider with this pattern. So, just imagine how large you’ll look wearing it. Wearing clothing with vertical patterns will make you appear slimmer. Teasing your hair to add volume should be avoided as it can cause damage and brittleness to your hair. Also, never style your hair so that it is two different textures. You may want to look different and like you are on the cusp of fashion, but you will probably just end up appearing confused. Watch out for sizing. Never purchase an item of clothing without seeing how you look in it. Sizing is not based on any standard methodology. Different brands have different measurements and sizes. If you have to buy online, look at their sizing chart. Make sure they have a return policy that allows your to obtain a refund if necessary. Sometimes fashion is addition by subtraction so donate the clothing you no longer wear. You’ll save time in choosing outfits, as well as help out the less fortunate who can’t afford new clothes. Are you in need of a new pair of pants or jeans? You will probably find that there are a wide range of styles, fits and colors. You may feel overwhelmed. Simple styles, including straight-leg and boot-cut, are never bad choices. You will get a lot of wear out of them, and it should flatter your body type. Fashion Consultant If you don’t have much money for clothes, let friends know. Let your friends know you would enjoy owning some of their items when they are ready to part with them. You can benefit from these free clothes, and keep yourself stylish. Bring a fashion consultant along to your shopping trips every now and then. If you are a busy person then it may be necessary to help keep you updated with all the latest fashion trends. Picking up a fashion consultant wouldn’t be the worst thing you could do. For example, while you’re shopping, having someone there to assist you in choosing the right attire could be a great idea. One way to keep your nails moisturized is to keep the rest of your body moisturized by drinking the recommended eight glasses of filtered water a day. These can often dry out when hydration is lacking. When the weather outside is cold and heaters suck the moisture from inside air, this can be critical. Also, make sure that you moisturize your nails daily to maintain health. Cotton gloves over your moisturized hands while you sleep is another good option. While wearing shorts isn’t a fashion sin, wearing them with visible socks is something to avoid. Kindergarten kids do this – not adults. Make sure to avoid wearing long sock with your shorts if you want to look sophisticated. To help you get a better idea of fashion, you may want to consider getting a fashion consultant. People with stressful jobs or busy family lives often feel they do not have time to be fashionable. To make sure you look great in spite of your schedule, get someone to assist you in your fashion choices. To maximize your clothing, sell the items that you are not using. Many Internet classified ad sites or even auctions let you sell your clothing easily, but there are also second-hand stores which you can sell items through as well. Some shops deal only in trade and some will pay you cash for your old fashions. Quilted fabrics are a pretty and practical trend coming for fall and winter wear. It’s a great look for coats and even skirts. This fabric is intended to be loose fitting, but wear it too loose and you’ll look fat. Use bleach to keep white clothing looking new. Just use it cautiously or you could risk yellowing your favorite clothes. Take a fashion chance and try a style that is different from your tried and true. Not only will this open your mind, but you may end up looking great, too! This is a great way to rejuvenate your wardrobe. Go out and buy some new eyeglasses! Don’t neglect your glasses here. With a minimal investment, you can have a stylish pair of glasses that go with any outfit. You can show your style off by choosing certain prescription eyeglass frames. Try on several frame styles to find a pair you’ll love to wear that accentuate your facial features and add to your personal style. Visible socks shouldn’t be worn with shorts. Doing this is a total faux-pas. You’re an adult now, so you can do better than wearing knee-high socks and shorts together. Everyone likes to turn things up a notch with great accessories, but there’s such a thing as wearing too many accessories. Showcase one key accessory such as a necklace or bracelet. This will keep your outfit looking organized and help you capture a person’s attention in the right way. There are ways you can make your lips appear fuller short of going under the knife. Try using lipstick that is lighter in color or some lip gloss that is shiny. Your lips will appear bigger as the light bounces off of them. Stay away from darker colors because they cause your lips to appear smaller than they are. Create a monthly clothing budget. With a budget, you can focus on making the best choices for your wardrobe, without going broke! You may focus on particular items each month, or see what you find that works with your current wardrobe and budget. Keep the look of your eyeglasses up to date. Many people overlook their glasses when trying to look chic. Your glasses are the first thing people see, so have fun with them! Try on a few different styles and find the one that works with your facial features. Don’t shy away from adding color to your look. You know you’ve noticed someone in a pair of tight red jeans before. Bright colors can add needed flair to your wardrobe. Try to avoid muted tones as these are dull and uninspiring. Since fashion is always changing, you will benefit by reading about new trends. Fashion magazines and the Internet are great tools for finding out what is in style for a specific season. You should, of course, select the things that you prefer. If you have a friend who is a hopeless case, you may need to take her shopping and suggest clothing that flatters her. Occasionally, people just need a little help choosing outfits from someone who understands fashion and style. Establish a monthly budget just for clothing and fashion accessories. Since you are trying to improve your wardrobe you are going to want to limit yourself on how much you spend. This way you know that you aren’t overspending on improving your wardrobe. You can still get a lot of clothes on a budget, you just have to be smart about it. Don’t let other people control the things you wear. Style is not limited to being either right or wrong. Each person must decide for themselves what fashions they would like to follow. If anyone tries to tell you what to wear or not wear, politely let them know that you do not care what they think. Adding some bright colors to the clothes you’re wearing is a great fashion tip you should always use. Have you ever noticed the color of a man wearing a pink shirt? Add different vibrant colors to your arsenal such as purple, blue and yellow for a creative look. Save muted colors for work. Check out the latest trends in fashion online. There is a lot of helpful information online. There is always someone posting about the greatest fashion trends. Always remember that accessories are important. A good outfit can look great if paired with proper accessories. Belts, shoes and bags can transform an outfit. Consider every piece of your outfit to ensure you look amazing. Dress yourself to fit the style of personality you have. In many sad cases, individuals try wearing styles that might be trendy, but do not fit their personality. People will notice if you are trying to be someone you aren’t. No matter why type of personal style sense you project, make sure its worn with confidence. Go out and put some extra clothes on that credit card of yours. If you have every intention of paying back your credit card then there is nothing wrong with buying a little time to get some clothes now. If you have felt that fashion is something intimidating, know that it doesn’t have to be that way. If you have the desire to learn the field, you can master it in no time. Practice good habits now and things will work out for you in the grand scheme of things. Restraint when choosing jewelry is essential. A lot of people think that wearing their tennis bracelet with their necklace, rings and earrings creates a great look. Well, the truth is that it’s just too much! You can ruin the look and effect you want by wearing too much. Wear a little bit of jewelry to get an elegant and classy look. Anyone who is not fashionable and up on the latest trends can be overwhelmed when going on a shopping trip. If you are going shopping and not having fun then you should seek some fashion help. Fortunately, the following article has fashion advice that can help. Don’t buy a blouse, shoes, shirt, or dress just because it’s on sale for a good price. Remember, no dress or other clothing item out there is ever worth purchasing unless it fits your fashion sense perfectly and accentuates your body. Instead, it will languish in your closet, reminding you of money you shouldn’t have spent. You should not purchase an item of closing just because it is on sale at a great price. If it does not flatter your figure or fit your style, it’s not worth it no matter how great a deal it is. You’ll just hang it in the closet and never get any use out of it. The classic pairing of white and black will make a comeback this season. You’ve probably seen lots of models wear this combination. You don’t have to make black and white the primary colors either. You can accessorize using black and white accents. These colors will go with anything that you’re wearing, no matter how plain or how ornate. When it comes to this combination, there are unlimited possibilities. Sheer outfits are super sexy, but always make sure you’re aware of how sheer your clothes really are. Sheer clothing in the wrong areas can turn your sexy look into a brassy one. Create a style that is all your own. Many people are fashion followers, but what stands out is a fashion leader. Once you begin developing your own unique style, you will receive many compliments. You can easily dress up your jeans with a fancy top and a nice pair of heels. You can use colored jeans, but only if you’re trying to achieve a casual look. Do not keep an abundance of makeup in your beauty kit. Use a few products you like that are in colors appropriate for the season. You may also want to have separate day and evening makeup kits. Makeup, like many other products, can go bad once open. Makeup products can harbor bacteria, which can be transfered to your eyes and skin when applied. You do not need to have too much makeup in your kit. Only choose the products that are in the colors that go well with your skin. Consider what you will need for both evening and day time. Makeup does not last forever once you begin using it. It can also grow germs if it sits for a long time. If you have frizzy hair, avoid rubbing it to dry with a towel. This can damage your hair and cause more frizziness. Instead, wrap your hair in a towel and apply gentle pressure, patting or squeezing the moisture from your hair. After it reaches the dryness of your desire, remove the towel and comb the hair. Moisturizers in your shampoo and conditioner are essential if you hair has a tendency to frizz in damp weather. This will add a protective layer along your hair’s cuticle, allowing it to remain soft and luxurious. Avoid anything that volumizes; that includes wheat and rice. Make sure you try bringing neutral colors on your next trip so you can mix up your outfits on the daily. You will not have to think about wearing clashing colors, which means you can create a lot of outfits using only a few items. Accessories will take the look from day to night, if necessary. For those with frizz problems, when drying hair, don’t rub it with a towel. It will damage and frizz out your hair. Use the towel to wrap up the hair and push it slightly to absorb any moisture. When you are happy, brush and comb your hair. Wearing white clothes after Labor Day is actually okay. Thankfully, those days are over and you should feel free to wear the colors you like best that flatter you most, no matter what time of the year or season it is. So, if it’s white you want to wear, wear it proudly and ignore people who say you shouldn’t. There’s no such thing as the fashion police out there. They’re not running around locking people up for wearing white after Labor Day! Stay away from horizontal stripes if you don’t want your body appearing wider. Because the eye only follows the direction of the stripes, even skinnier people are going to look a lot wider with this pattern. So, just imagine how large you’ll look wearing it. Instead, wear clothing with vertical patterns, which will draw attention to height rather than girth. An online fashion newsletter is a great source for information about trends and classic looks. This helps keep you up to date on the last fashion trends. Wedge heels are popular for boots and sandals. These are great for women who wish to not only look slimmer, but also want to seem taller as well. When you’re getting a pair of heels that are wedged, you have to remember that if they’re too think, they could be impossible to walk in. If you wear plus sizes and want to give an impression of a smaller size, avoid floral patterns that have large flowers and shapes. The larger patterns will highlight the fact that you are large as well, and will not be an attractive choice for you. Focus instead on small patterns and prints to take the attention away from your overall size. Every woman should have a few essentials to build on in her wardrobe. Black tailored pants, one pair of designer jeans and a pair of black heels are some items which one must include. A little, classic black dress is also essential. There are a certain few pieces that should be in every woman’s wardrobe. You should own two pair of dress trousers, jeans hemmed for high heels and jeans that are a casual length to be worn with sneakers. For a wide variety of special events, the perfect little black dress is a must. You can stay on top of fashion by being unique. Leave your hear messed up or a shirt unbuttoned. Nobody looks perfect, so if your style includes a little chaos, your unique fashion sense can make you stand out. Did you know that drinking more filtered water can actually help you to prevent dry, cracked nails and cuticles? Cuticles and nails are usually dry from a lack of hydration. This is very important when it is cold and dry outside. Use shea butter to moisturize your cuticles a couple times daily. Shea butter can also be applied to hands before you retire for the night. Wear gloves over them while sleeping. If you want to provide your hair with volume, do not tease it; this will just damage your hair and make it brittle. Also make sure to maintain a style that only requires one texture. This look will make you look indecisive and silly. You may have heard many different fashion do’s and don’ts. However, it is important to try out new things and to do what makes you happy. Things might not look good until you actually test them out. Mix and match a variety of colors, fabrics and styles, even when the “rules” suggest not to. You can ultimately create a look that is really special and makes you look like a million bucks. You may have heard many different fashion do’s and don’ts. However, it is important to try out new things and to do what makes you happy. You will never know if something is good if you do not try it. Mix and match colors and styles to find the ones you like. The only way to figure out your style is to play around with it. Use your style of dress to accentuate your assets and hide your flaws. Low-cut blouses may not work for you, but you may have great legs. You can also wear a short skirt, but make sure that it looks professional. Show off your best assets. Bring a fashion consultant along to your shopping trips every now and then. This is especially true if you are busy with work and family. This is a great way to assure you always buy clothes that make you look your best. An early fashion tip for you: quilted fabrics are making a comeback and will be in style this fall. There are many types of clothing with this type of fabric. The best way to adorn yourself in this fabric is by wearing it slightly loose, without going overboard. One of the trends in recent years has been the return of patterns in women’s clothing. Floral patterns are especially popular. You can relax now and think about wearing that floral blouse, dress and pants. Just be aware that patterns in clothing can be paired with similar patterns or they can really pop when paired with a basic piece of clothing. Patters, especially floral, are making a comeback. Do not be shy to wear a floral dress, shirt and even pants. Just be careful about accessorizing floral prints with other patterns; if you wear an especially bold or large floral print, choose shoes or other accessories with tiny patterns or go with solid colors. Don’t wear long socks with shorts. This look is common on the kindergarten playground, and it works for that age group. Try to remain as elegant and mature as possible with your look. An important part of fashion is being daring enough to wear something you might not normally wear. That is great, as it keeps your mind open to new things, and you don’t know if something unknown may look great on you! It is a great way for adding variety into your fashion wardrobe. Keep your style updated without spending a lot by using a resale store to sell or trade the clothes you no longer wear. There are many places to go when selling your clothing items such as an online auction or perhaps something local likes a consignment shop. There are quite a few stores that will let you trade in old clothes for money or other clothes in stock. Sell or trade old clothes to save money on fashions. Use one of the many online auction websites to add to your clothing budget or trade for some new styles at the nearby consignment shop. You may either receive money back from your items or get store credit. The quality of the material that your clothing is made of matters a great deal. Take a look at the tag on the interior of the clothing. It may fit in the dressing room, but can quickly lose shape once you have washed it. Avoid spending your money on clothes that could fray, shrink or become misshaped. Remember that clothes aren’t all you have to worry about when trying to look fashionable. Your hair also matters a lot. Your hair should be an extension of you and your personality. For example, women who are participating in corporate affairs should opt for classic styles such as the shoulder-length bob. If you’re a busy mom, a style that looks great with minimal effort will be your best bet. Spend time with a fashion consultant and find out the colors that flatter you. Skin, eye and hair color cause certain colors to look great or not so great on anyone. Pick colors that make you stand out and look your best when deciding on which clothes to get. If your chest is large, do not wear clothes with a boatneck or crew neck neckline. You should wear v-necks instead. A shirt without a v-neck may make you look plump and boxy. A v-neck can accent your frame and mimic your shape, giving you a more fashionable look. Try different styles out, and you might notice that v-neck shirts look better for you. Pack your outfits with care when traveling so they don’t wrinkle too much. Although most hotels include irons, you can save more time by skipping the iron if you don’t need it. When you get to your hotel, it is good thinking to hang up your clothes. If you are a business traveler, it is a good idea to have many articles of clothing that are easy to care for and don’t wrinkle easily. This way, you won’t have to spend a lot of time ironing or searching for an ironing board and iron in your hotel room. Usually, it is best to hang up your clothes immediately when you get to the hotel. You’ve learned all you can, now put it to use! From here on out you should be able to create looks that look you feel good in, and you should wear clothes with pride. You will look good and feel good about yourself all the time! Because fashion evolves constantly, staying up-to-date on trends can be beneficial to your personal style. The Internet is filled with online versions of fashion magazines showing the latest trends. Don’t be afraid to mix and match your clothing. When you look good with what you are wearing, everyone will notice you. This can help your social life and your self-esteem. Becoming fashionable is a way to improve your life. The following article contains a set of fashion tips that will steer you in the right direction. Try to spend your fashion money on basic pieces. Target items that are always in fashion, yet work with other styles as well. Everything goes with a good pair of blue jeans, and that black top will definitely match any skirt or pants you have in the closet. If you keep it basic, you can always throw an outfit together. Sheer outfits are super sexy, but always make sure you’re aware of how sheer your clothes really are. Wearing clothing items that are sheer in private areas can make you appear trashy rather than classy. Keep your eye on fashion articles as the season changes. Style is constantly changing, so keep up with fashion magazines to learn about the latest trends. They are most often the source for new trends. If you want to remain in style this season, try pairing black and white together. These simple colors are back with a vengeance. This year many black and white outfits are on the runway. You don’t have to make black and white the primary colors either. You can accessorize using black and white accents. These colors will go with anything that you’re wearing, no matter how plain or how ornate. When it comes to the types of fashion choices you can make here, the sky is really the limit. There are so many options available in terms of hair accessories. Accessories for your hair include scrunchies in a myriad of colors and fabrics, headbands, elegant barrettes, and even clip-on hair extensions. Your wardrobe should include several hair accessories. For instance, to appear athletic, try wearing an athletic suit with a ponytail holder that matches. When you are going out on the town, choose a headband that compliments your outfit. Create a style that is all your own. There are so many people out there that follow what they see, but the truly original people create their own personal style. This isn’t right for everyone, but it is a great way to get compliments on originality. If you’re heavy and wish to look slimmer, try wearing a dark or black colored blouse over a dark skirt. Dark colors help hide the excess weight you are carrying and help you look thinner. Elastic waistbands can help make skirts more comfortable. Have a set amount of makeup with your beauty kit. Use a few products you like that are in colors appropriate for the season. Make certain to have colors for night and day wear. Makeup does not last forever once you begin using it. Additionally, if germs have gotten into the product, they can increase during prolonged periods of not being used. The old adage about avoiding white once Labor Day has passed no longer applies. It doesn’t matter what you want to wear; choose colors that you feel comfortable with. If white is your color, don’t be afraid to wear it when you wish. There is no one with a real sense of style that will make a comment. Hair Accessories If you have some weight to lose, avoid wearing clothes with horizontal stripes or similar patterns. This pattern makes you look wider and is completely unflattering. Instead, go for vertical stripes, which appear to elongate your body and make you seem thinnger. Always remember that there are tons of different options available to you when looking for hair accessories. Hair accessories include ponytail holders, headbands, hair bows as well as hair extensions. Having some different types of accessories around is a smart move for the fashion-conscious person. The right hair accessory can set off an entire outfit. If it’s a fancy night on the town instead, pick a classy hairband to match your outfit. Stay away from patterned clothing with large shapes if you are overweight. This will make you look larger and that is very unflattering. Instead, choose smaller shapes and you will look much better. If you have frizzy hair, look for a shampoo and conditioner that has moisturizing properties. You will be able to cure your frizz and make your hair stay down when you apply enough conditioner as you shower. Avoid the ingredients wheat or rice that are found in many volumizing products. Some basic items belong in every woman’s closet. You should have two pairs of dark dress pants, jeans hemmed for use with sneakers and jeans hemmed for use with heels. Let’s not forget the mainstay for every woman, the little black dress. Wearing white clothes after Labor Day is actually okay. Any color is fine, as long as it fits you. If your best color is white, you should certainly wear white all year. Few can find fault with a fabulously dressed, confident woman, no matter what color she’s wearing. A little bit of mousse can make your hair appear fuller. Overusing mousse to create hairstyles reminiscent of the 80s is tempting for some people. However, these overdone styles tend not to be flattering for the majority of people. Be cautious when it comes to sizing. Always try on clothes before buying them. Sizes have no bearing on measurements any more. They vary significantly amongst the various designers and store brands. If you are brave enough to buy clothes off an online site, carefully examine their sizing chart first. How liberal is their return policy? Your shoes are a major part of your look. Usually, you just need to match your belt color to your shoe color. This can create a classical look, which can go a long way in establishing professionalism. Plus-sized women can give the illusion of being smaller by avoiding large floral patterns. Large shapes can make you look even larger. Instead, choose a floral pattern with smaller flowers to take the emphasis away from the large parts of your body. Consider your figure type when you dress. You might not want to wear something like a blouse that’s low-cut, but you may be more confident with your legs. In this case, you can slip on some elegant heels and keep you skirt length short to show off your great legs. Work with your strengths. Don’t forget about matching shoes with the rest of your outfit. Generally, just make sure that your belt matches your shoes in color tone. This makes you look more classic and fashionable. One great way to help your fashion wardrobe is to donate anything from your closet that you no longer wear. This kills two birds with one stone. First, you are getting clothes to those who need them, and second, the time required to put together your outfit for the day is decreased. Shea Butter An early fashion tip for you: quilted fabrics are making a comeback and will be in style this fall. Anything can have this fabric in it, from skirts to blouses to jackets. Although it’s a loose fitting fabric, don’t get it too loose or you’ll look bigger than you want to look. You can prevent dry cuticles and cracking nails by drinking more pure filtered water. Your nails and cuticles may be dry due to lack of hydration. This will help your nails when the weather is cold and dry. Moisturize your hands on a daily basis with a little olive oil, shea butter or conditioning cream. If you use shea butter or a heavy cream for your hands inside a pair of gloves, you can moisturize while you sleep. To get ready for the next fashion season, try picking up some items with floral patterns. Now, they’re not back in a big way, but the floral pattern is reemerging as a top fashion design. Don’t be afraid to wear floral patterned dresses, blouses or even shorts or pants. If you are shy about the bold patterns, consider a splash of them, such as a scarf or handbag with the rest of your outfit remaining more neutral. Try to eliminate loose stitches from the new clothing that you purchase. These threads do not look good and should be removed. Carefully remove them, being careful not to damage the clothes. This is an easy step you can take to bring your style up. Step out of your fashion box by trying on things you wouldn’t ordinarily be drawn to in the store. Doing this helps to broaden your fashion thinking, and helps you find some great new looks you may have never noticed. At the very least, it will help you add some diversity to your closet. Teasing hair to create volume only causes the hair to become damaged and possibly break. You should not style your hair with different textures. You may want to look different and like you are on the cusp of fashion, but you will probably just end up appearing confused. Your hair makes a statement about you. It’s important that your hair reflects your personality. For example, a shoulder-length bob is a good classic style for a woman who plans on going corporate. If you are a mom leading a hectic life, you can choose a style that is wash and go. There are fashion rules, but definitely don’t be afraid to try some experiments. It’s impossible to know if something looks great until you give it a shot. You can try out new combinations by mixing colors and materials. You may unintentionally nail the perfect look, and playing around is the best way to develop your own personal style. When washing whites, use bleach to extend the longevity of your clothing. Don’t use too much, though, it can cause your items to start to yellow. Why not hire a fashion consultant? People are so busy today, how can they have time to browse in stores, too? Their expertise will get you fashionable once again. Avoid fitted clothes if you put on a little more weight this season. This will emphasize any lumps or bulges that you probably want to hide. Loose-fitting items give you the exact opposite effect. And if you’re choosing a darker color, you’ll even experience a slimming effect. Don’t wear long socks with shorts. That is how kindergarteners dress, not grownups. Be certain you have an air of sophistication and avoid wearing socks with short pants. No fashionable outfit is complete without great accessories. Your earrings, bracelets and watches should match the style of your outfit. The proper hairstyle and shoes are also a must. When it comes to matching outfits with your accessories, you can find numerous amounts of information in magazines. If your wardrobe is full of white clothes, bleach them when washing to keep things fresh and new. However, you want to avoid using a lot of bleach here. Too much bleach will cause the items to develop a yellowish hue. Once this happens, you can’t fix it! Come up with a budget for the amount you spend on clothes every month. Utilize your money strategically so you can buy several pieces which really maximize your entire wardrobe. With some smart solutions, you can still invest in some great clothing pieces on a budget. Spend time with a fashion consultant and find out the colors that flatter you. The color of your skin, eyes and hair can all affect which colors best suit you and create the effects you desire, such as looking slimmer. Discovering the color palette that suits you best will give you confidence when choosing clothing. If you pay your bills in full each month, use credit to purchase that new wardrobe. As long as it’s possible for you to pay back the money you used on your credit cards, use it to buy some clothes to create a new wardrobe. Your confidence increases when you look great and see your new look reflected in the mirror, and the reactions of other people. To always look fashionable, use the tips shared here. Don’t let others determine what you should wear. There really is no such animal is the right style. Everyone needs to come to their own fashion decisions. If someone tries to control what you wear, just politely tell them to back off. | Mid | [
0.5489361702127661,
32.25,
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When I ran update I got this "Failed to fetch http://mozilla.debian.net/dists/squeeze ... ts/Release Unable to find expected entry iceweasel-4.0/binary-i386/Packages in Meta-index file (malformed Release file?) Some index files failed to download, they have been ignored, or old ones used instead." Do I have a problem and can it be cured? what besenmuckel showed you is the a factoid key. Just type this as message in IRC and our bot will answer with some instructions. Kano cares about the most important keys, e.g. !iceweasel - so they are up-to-date. The wiki article about IRC usage, I showed you some time before too, if you are not familiar with IRC, it should be a good lecture how to use it Cheers TheOne PS: btw the reason for this message is that the iceweasel 4.0 repository is not reachable anymore - maybe you noticed the iceweasel/firefox versioning story, I hope that ends soon | Mid | [
0.586466165413533,
39,
27.5
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--- author: - 'Pekka Koskela, Nageswari Shanmugalingam and Yuan Zhou' date: title: '**Intrinsic Geometry and Analysis of Diffusion Processes and $L^\fz$-Variational Problems** ' --- Introduction\[s1\] ================== Let $\boz\subset\rr^n$ be a domain (connected open subset). Denote by $\mathscr A(\boz)$ the collection of all matrix-valued measurable maps $A=(a_{ij})_{1\le i,\,j\le n}:\boz\to\rr^{n\times n}$, which are [*elliptic*]{}, that is, for each $A\in\mathscr A(\boz)$, there exists a continuous function $\lz:\boz\to[1,\,\fz)$ such that $$\label{e1.1} \frac1{\lz(x)}|\xi|^2\le \langle A(x)\xi,\,\xi\rangle\le \lz(x)|\xi|^2$$ for almost all $x\in\boz$ and all $\xi\in\rr^n$, where $$\langle A(x)\xi,\,\xi\rangle=\sum_{i,\,j=1}^n\xi_ia_{ij}\xi_j.$$ An [*Hamiltonian*]{} associated to $A$ is given by $H(x,\,\xi)=\langle A(x)\xi,\,\xi\rangle$. Associated to each diffusion matrix $A\in\mathscr A(\boz)$, there is a “Riemannian metric" (differential structure) on $\boz$: for all $ x\in\boz$ and for each vector $\xi\in T_x\boz$, the length of $\xi$ is given by $\sqrt{H(x,\,\xi)}$. The corresponding differential operator $L_Au={\rm div}(A\nabla u)$ generates a regular, strongly local bilinear Dirichlet energy form $\mathscr E_A $ with domain $\mathscr D(\mathscr E_A)$ in $L^2(\boz)$. Notice that $C^\fz_c(\boz)$ is a core of $\mathscr E_A $, $\mathscr D_\loc(\mathscr E_A)=W^{1,\,2}_\loc(\boz)$, and for all $f,h\in \mathscr D(\mathscr E_A)$, $$\mathscr E_A(f,h)=\int_\boz\langle A(x)\nabla f(x),\nabla h(x)\rangle\, dx.$$ For the details see for example [@fot]. Moreover, the [*intrinsic distance $d_A$*]{} associated to $A$ is defined by $$d_A(x,\,y)=\sup\{u(x)-u(y)\}$$ for all $x,\,y\in \boz$, where the supremum is taken over all $u\in C(\boz)\cap W_\loc^{1,\,2}(\boz)$ such that $H(x,\,\nabla u(x))\le 1$ almost everywhere. The ellipticity implies that $d_A$ is locally comparable to the Euclidean distance. We define the [*pointwise Lipschitz constant*]{} by setting $$\lip_{d_A} u(x)=\limsup_{y\to x}\frac{|u(y)-u(x)|}{d_A(x,\,y)},$$ and its [*local variant*]{} $$|Du|_{d_A}(x)= \lim_{r\to0} \lip_{d_A}(u,\,B(x,\,r)),$$ where and in what follows $$\lip_{d_A}(u,\,K)=\sup_{x,\,y\in K, y\ne x}\frac{|u(y)-u(x)|}{d_A(x,\,y)}.$$ Then $\lip_{d_A}(K)$ denotes the collection of all $u$ with $\lip_{d_A}(u,\,K)<\fz$. When $A=I_n$, $d_A$ is the Euclidean distance, and it is always omitted in the above notation. Motivated by the work of Norris [@n97], who showed that the intrinsic distance determines the small time asymptotics of heat kernel, Sturm [@s97] asked the following question: Is a diffusion process determined by the intrinsic distance? In other words, do the intrinsic differential and distance structures coincide in the sense that for $u\in \lip_{d_A}(\boz)$, $H(x,\,\nabla u(x))=(\lip_{d_A}u(x))^2$ almost everywhere? The answer to this question is not always in the positive as shown by Sturm’s construction [@s97 Theorem 2]: for each $A\in\mathscr A(\boz)$, there exists a $\wz A\in \mathscr A(\boz)$ with $d_{\wz A}=d_A$ but $$\langle \wz A(x)\xi,\,\xi\rangle<\langle A(x)\xi,\,\xi\rangle$$ for all $\xi\in\rn\setminus\{0\}$; see also [@kz] for a different example. On the other hand, with the additional assumption that $A$ is continuous, Sturm [@s97 Proposition 4] proved that the intrinsic differential and distance structures coincide. The first aim of this paper is to obtain a better understanding on the properties of $A$ that determine the (non-)coincidence of intrinsic differential and distance structures. It turns out that weak upper semicontinuity plays a critical role. A function $u$ is said to be [*weak upper semicontinuous*]{} at $x\in\boz$ if there exists a set $E$ with $|E|=0$ such that $$u(x)\ge\limsup_{(\boz\setminus E)\ni y\to x}u(y),$$ and is said to be weak upper semicontinuous on $\boz$ if it is weak upper semicontinuous at almost all $x\in\boz$. A diffusion matrix $A$ is said to be *weak upper semicontinuous* at $x\in\boz$ (resp. on $\boz$) if for every $\xi\in S^{n-1}$, $\langle A(\cdot)\xi,\xi\rangle$ is weak upper semicontinuous at $x$ (resp. at almost all $x\in\boz$). Denote by ${\mathscr A}_{\rm wusc}(\boz)$ the collection of all $A\in\mathscr A(\boz)$ that are weak upper semicontinuous on $\boz$. We prove the following results. 1. For all $n\ge1$, the diffusion matrix $A$ belongs to $\mathscr A_{\rm wusc}(\boz)$ if and only if the intrinsic differential and the local intrinsic distance structures coincide in the sense that for all $u\in C^1_\loc(\boz)$, $|Du|^2_{d_A}(x)= H(x,\,\nabla u(x)) $ almost everywhere; see Theorem \[t2.3\]. 2. If $n=1$, or if $n\ge2$ and $A\in\mathscr A_{\rm wusc}(\boz)$, then the intrinsic distance and differential structures always coincide, that is, for all $u\in\lip(\boz)$, $(\lip_{d_A}u(x))^2= H(x,\,\nabla u(x)) $ almost everywhere; see Theorems \[t2.1\] and \[t2.2\]. 3. If $n\ge2$ and $A\notin\mathscr A_{\rm wusc}(\boz)$, the (non-) coincidence of the intrinsic distance and differential structures depend on the geometry of the non-weak-upper-semicontinuity set of $A$. Indeed, we construct two examples via a large Cantor set and a large Sierpinski carpet to show that both coincidence and noncoincidence may happen; see, respectively, Theorem \[t3.1\] and Proposition \[p3.1\]. The proofs of Theorems \[t2.2\] and \[t2.3\] rely on the (key) Lemmas \[l2.1\] and \[l2.2\]. The proof of Theorem \[t3.1\] is more intricate; we use an approximation of the distance by Norris [@n97] to derive some careful estimates on a good set of the distance function based on geometric properties of our Sierpinski carpet. Proposition \[p3.1\] uses the geometry of the complement of our large Cantor set. We also consider the $L^\fz$-variational problem associated with an arbitrary matrix-valued map $A\in\mathscr A(\boz)$: the goal is to study the local minimizers of the functional $$F(u;U)=\esssup_{x\in U} H(x,\,\nabla u(x))$$ over the class of Lipschitz functions on $U\Subset\boz$ with a given boundary data. This study was initiated by Aronsson [@a1; @a2; @a3; @a4] in the case $H(x,\,\xi)=|\xi|^2$, that is, $A=I_n$. He introduced the idea of absolute minimizer, that is, minimize $F$ on all open subset of $U$. To be precise, let $U$ be an open subset such that $\overline U\subset \boz$. A function $u\in \lip(U)$ is said to be an [*absolute minimizer for $H$*]{} on $U$ if for every open subset $V\Subset U$ and $v\in \lip(V)\cap C(\overline V)$ with $u|_{\partial V}= v|_{\partial V}$, we have $$\esssup_{x\in V} H(x, \nabla u(x)) \le {\esssup}_{x\in V} H(x, \nabla v(x)).$$ Moreover, given a function $f\in \lip (\partial U)$, $u\in \lip(U)$ is said to be an [*absolutely minimizing Lipschitz extension* ]{} of $f$ if $u$ is an absolute minimizer for $H$ and $u|_{\partial U}=f$. In recent years, the study of the $L^\fz$-variational problem, even for more general Hamiltonians but with some smoothness, has advanced significantly; see [@acj] for a survey and [@ceg; @j93] for some seminal works. The $L^\fz$-variational problem is still interesting even if the Hamiltonian is not smooth or even continuous. See for example [@acj; @gpp; @cp; @cpp] and the reference therein. In this case, one cannot always derive an Aronsson equation from the $L^\fz$-variational problem. Our results concerning absolute minimizer are as follows: 1. For arbitrary $A\in\mathscr A(\boz)$ and the Hamiltonian $H(x,\,\xi)=\langle A(x)\xi,\,\xi\rangle$, we show that the absolute minimizer is completely determined by the intrinsic distance, and then obtain the existence and uniqueness of the absolute minimizer given a boundary data; see Theorem \[t4.1\]. Consequently, if $A,\,\wz A\in\mathscr A(\boz)$ and $d_{A}=d_{\wz A}$, then given the boundary data, the absolute minimizers associated to $A$ and $\wz A$ coincide. 2. Associated to the diffusion matrix $A\notin\mathscr A_{\rm wusc} (\rn)$ given in Subsection 3.2, we show in Proposition \[c4.3\] that there is an absolute minimizer $u$ on $(0,\,1)^n$ which fails to be $C^1$. This example indicates that perhaps weak upper semicontinuity of $A$ is needed in order for the corresponding absolute minimizers to be of class $C^1$. 3. [We obtain in Theorem \[t5.1\] the linear approximation property of the absolute minimizer at all points of continuity of $A$, and hence at all points when $A$ is continuous on $\boz$.]{} The proof of Theorem \[t4.1\] relies on the (crurial) Lemma \[l2.1\] and Lemma \[l4.6\], which allows us to describe the absolute minimzer via the pointwise Lipschitz constant.Then the existence of the absolute minimizer follows from [@jn], while the uniqueness will be proved following the idea of [@as] (see [@pssw] for an earlier proof via the tug of war). Proposition \[c4.3\] follows from Theorem \[t3.1\] and properties of absolute minimizers. The proof of Theorem \[t5.1\] borrows the blow-up ideas of [@ceg], but due to the change of distance in the blow-up process, a detailed study is necessary. The $C^1$-regularity of the absolute minimizer is still open except for the case $n=2$ and $A=I_n$. Precisely, if $A=I_n$, Savin [@s05] obtained the $C^1$-regularity of the absolute minimizer when $n=2$ (see also [@wy] for a homogeneous norm and [@es]) while Evans-Smart [@es12] obtained the everywhere differentiability when $n\ge 3$. All the proofs in [@s05; @es; @es12; @wy] rely on the linear approximation property; indeed, controlling the convergence of different sequences appearing in the linear approximation. For an arbitrary continuous or even $C^1$-continuous $A$, we do not know if it is possible to obtain the everywhere differentiability by controlling the linear approximation process provided in Theorem \[t5.1\] as done in [@s05; @es; @es12; @wy]. Finally, we state some [*conventions*]{}. Throughout the paper, we denote by $C$ a [*positive constant*]{} which is independent of the main parameters, but which may vary from line to line. Constants with subscripts, such as $C_0$, do not change in different occurrences. The [*notation*]{} $A\ls B$ or $B\gs A$ means that $A\le CB$. If $A\ls B$ and $B\ls A$, we then write $A\sim B$. Denote by $\nn$ the [*set of positive integers*]{}. If $V$ is a bounded open set with $\overline V\subset U$, we simply write $V\Subset U$. We use $C(\boz)$ to denote the continuous function on $\boz$ while $C^1(\boz)$ the function with continuous gradient on $\boz$. For any locally integrable function $f$, we denote by $\bbint_E f\,d\mu$ the [*average of $f$ on $E$*]{}, namely, $\bbint_E f\,d\mu\equiv\frac 1{\mu(E)}\int_E f\,d\mu$. Case $n=1$ or $A\in\mathscr A_{\rm wusc}(\boz)$: $H(\cdot,\,\nabla u )=(\lip_{d_A}u )^2$ {#s2} ======================================================================================== We first show that if $n=1$, or if $n\ge2$ and $A\in\mathscr A_{\rm wusc}(\boz)$, then the intrinsic distance and differential structures always coincide in the sense that for all $u\in\lip(\boz)$, $(\lip _{d_A}u(x))^2=H(x,\,\nabla u(x))$ almost everywhere; see Theorems \[t2.1\] and \[t2.2\]. Then, for all $n\ge1$, we prove that $A\in\mathscr A_{\rm wusc}(\boz)$ if and only if the intrinsic differential and the local intrinsic distance structures coincide in the sense that for all $u\in C^1_\loc(\boz)$, $|Du|^2_{d_A}(x)=H(x,\,\nabla u(x))$ almost everywhere; see Theorem \[t2.3\]. \[t2.1\] If $n=1$, then for all $u\in\lip_{d_A}(\boz)$, $\lip_{d_A}u=\sqrt A|u'|$ almost everywhere. By the continuity of $\lambda$ associated with the ellipticity condition of $A$, we have $\text{Lip}_{d_A}(U)=\text{Lip}(U)$ for $U\Subset\Omega$. To prove that $\lip_{d_A}u(x)\le\sqrt{A(x)}|u'(x)|$ for almost all $x\in\Omega$, notice that $$\begin{aligned} \lip_{d_A}u(x)&&=\limsup_{y\to x}\frac{|u(y)-u(x)|}{d_A(x,\,y)}\\ &&\le \limsup_{y\to x}\frac{|u(y)-u(x)|}{|x-y|}\limsup_{y\to x}\frac{|x-y|} {d_A(x,\,y)}\\ &&=|u'(x)|\limsup_{y\to x}\frac{|x-y|} {d_A(x,\,y)}.\end{aligned}$$ Here we used the Rademacher theorem, according to which locally Lipschitz continuous functions on $\mathbb{R}$ are differentiable almost everywhere. Thus it suffices to check that for almost all $x\in\boz$, $$\label{e3.x2} \limsup_{y\to x}\frac{|x-y|} {d_A(x,\,y)}\le \sqrt{A(x)}.$$ This is reduced to showing that, for any $\ez>0$, there exists a constant $\dz>0$ and a Lipschitz continuous function $w$ such that $A(x)|w'(x)|^2\le1$ and for all $y\in(x-\dz,\,x+\dz)$, $$\label{e3.x3} |y-x|\le (1+\ez)\sqrt{A(x)}|w(y)-w(x)|.$$ Indeed, from this and the definition of $d_A$, we know that $$\sqrt{A(x)}\,d_A(x,\,y)\ge \sqrt{A(x)}\,|w(y)-w(x)|\ge \frac{1}{1+\ez}|y-x|,$$ which implies by the arbitrariness of $\ez$. Towards , take $$w(z)= \int_{x}^z\frac{1}{\sqrt{A(s)}}\,ds$$ for $z\in\boz$. Notice that the lower bound of $A$ guarantees that $\frac{1}{\sqrt{A}}\in L^1_\loc(\boz)$, and so $w^\prime(z)=A(z)^{-1/2}$ for almost all $z\in\mathbb{R}$. Let $I_{x,\,y}=[x,\,y]$ if $x<y$ ($[y,\,x]$ if $x>y$). By Lebesgue’s differentiation theorem, for almost all $x\in\boz$, we can find $\dz>0$ such that whenever $y\in(x-\dz,\,x+\dz)$, $$\frac{|w(y)-w(x)|}{|x-y|}=\bint_{I_{x,\,y}}\frac{1}{\sqrt{A(s)}}\,ds\ge\frac{1}{(1+\ez)\sqrt{A(x)}},$$ which implies . On the other hand, to prove $\sqrt{A(x)}|u'(x)|\le \lip_{d_A}u(x)$ for almost all $x\in\boz$, observe that at points $x$ of differentiability of $u$ (by the classical Rademacher’s theorem, almost every $x$ is such a point), $$\begin{aligned} |u'(x)| &&=\lim_{y\to x}\frac{|u(y)-u(x)|}{|x-y|}\\ &&\le \limsup_{y\to x}\frac{|u(y)-u(x)|}{d_A(x,\,y)}\limsup_{y\to x}\frac{d_A(x,\,y)}{|x-y|}\\ &&=\lip_{d_A}u(x)\limsup_{y\to x}\frac{d_A(x,\,y)}{|x-y|}.\end{aligned}$$ By the definition of $d_A$, for any $\ez>0$ and any fixed $y$, there exists a function $v$ such that $A(z)|v'(z)|^2\le1$ for almost all $z\in\boz$ and $d_A(x,\,y)\le(1+\ez)|v(x)-v(y)|$, which implies that $$\frac{d_A(x,\,y)}{|x-y|}\le(1+\ez) \frac{|v(x)-v(y)|}{|x-y|}\le \frac{(1+\ez)}{|x-y|} \int_{I_{x,\,y}}|v'(s)|\,ds \le \frac{(1+\ez)}{|x-y|} \int_{I_{x,\,y}}\frac1{\sqrt{A(s)}}\,ds .$$ If $x$ is a Lebesgue point of $\frac1{\sqrt{A}}$, there exists a $\dz>0$ such that whenever $y\in(x-\dz,\,x+\dz)$, $$\frac{d_A(x,\,y)}{|x-y|}\le (1+\ez) ^2\frac1{\sqrt{A(x)}},$$ which is as desired. \[t2.2\] If $n\ge2$ and $A\in\mathscr A_{\rm wusc}(\boz)$, then the intrinsic distance and differential structures coincide. That is, given Lipschitz function $u$ on $\boz$ [(]{}with respect to the Euclidean metric[)]{}, for almost every $x\in\boz$ we have $$(\text{Lip}_{d_A} u(x))^2=\langle A(x)\nabla u(x),\nabla u(x)\rangle.$$ To prove Theorem \[t2.2\], we first notice that the distance $d_A$ is locally comparable to the Euclidean distance, and hence $ (\boz,\,d_A,\,dx)$ satisfies the local doubling property in the sense that if $U$ is open and $U\Subset \boz$, there exists a constant depending on $U$ and $A$ such that for each $x\in U$ and $0<r<\min\{\text{diam}(U), d_A(x,\,\boz^\complement )\}/4$, $$\mu(B_{d_A}(x,\,2r))\le C(A,\,U)\mu(B_{d_A}(x,\, r)).$$ Here and in what follows, $d_A(x,\,K )=\inf_{x\in K}d_A(x,\,z)$ and if $d_A$ is the Euclidean distance, we use the notation $d_{\rn}(x,\,K )$. Therefore, applying [@kz Theorem 2.1] and its remark, we conclude with the following. \[l2.1\] For each $u\in\lip_{d_A}(\boz)$, $H(x,\,\nabla u(x))\le (\lip_{d_A}u(x))^2$ for almost all $x\in\boz$. To obtain the reverse relation, we need the following result. \[l2.2\] Assume that $n\ge2$. Let $x_0\in\boz$ and $0<r< d_\rn(x_0,\, \boz^\complement)$. If the diffusion matrix $\wz A$ is a constant positive definite symmetric matrix $A$ on the Euclidean ball ${B(x_0,\,r)}$, then, for the function $u(y)=|A^{1/2}\xi|^{-1}\langle \xi, y\rangle$ with $\xi\in S^{n-1}$, we have $ \lip_{d_{\wz A}}u \le 1$ on $B(x_0,\,r)$. It suffices to show that, for every $x\in B(x_0,\,r)$, there exists $\dz\in(0,\,r-|x-x_0|)$ such that for each fixed $y\in B(x,\,\dz)$, we can find a function $\wz u_{x,\,y}$ on $\boz$ satisfying \(i) $\wz u_{x,\,y}(z)=u(z)$ for all $z$ in the line segment joining $x$ and $y$, \(ii) $ \langle \wz A(z)\nabla\wz u_{x,\,y}(z),\,\nabla\wz u_{x,\,y}(z)\rangle\le1 $ for almost all $z\in\boz$. Indeed, from the definition of the intrinsic distance, the existence of such a function will lead to $|\wz u_{x,\,y}(z)-\wz u_{x,\,y}(w)|\le d_{\wz A}(z,\,w)$ for all $z,\,w\in\boz$, which gives the desired inequality $|u(x)- u (y)|\le d_{\wz A}(x,\,y)$ when choosing $z,\,w$ as $x,\,y$. Hence we have $\lip_{d_A}u(x)\le 1$ for all $x\in B(x_0,\,r)$. To this end, we first consider the case $A=\lz I_n$. Set $$\label{e3.1} \wz u_{x,\,y}(z)=\lf\{\begin{array}{ll} [u(y)-u(x)]\frac{|z-x|}{|y-x|}+u(x)&\quad if \quad |z-x|\le |y-x|\\ u(y)&\quad if \quad |z-x|\ge |y-x|. \end{array}\r.$$ Obviously, $\wz u_{x,\,y}$ satisfies (i). To see (ii), for $x\ne z\in B(x,\,|x-y|)\subset B(x,\,\dz)\subset B(x_0,\,r)$, we have $$|A^{1/2}\nabla \wz u_{x,\,y}(z)|= \frac{|u(y)-u(x)|}{|y-x|}\frac{|A^{1/2}(z-x)|}{|z-x|} = \frac{|\langle \xi, y-x\rangle|}{ |A^{1/2}\xi|} \frac{|A^{1/2}(z-x)|}{|y-x||z-x|}\le1;$$ while when $z\in \boz\setminus \overline{B}(x,\,|x-y|)$ we have $|\wz A^{1/2}\nabla \wz u_{x,\,y}(z)|= 0\le 1$. For a more general constant positive definite symmetric matrix $A$, we modify the above construction as follows, following the idea given above. Notice that there exist $\dz_1,\dz\in(0,\,r)$ such that $A^{1/2} B(0,\,\dz_1)\subset B(0,\,r )$ and $A^{-1/2}B(0,\,\dz)\subset B(0,\,\dz_1)$. Thus, for every $y\in B(x,\,\dz)$, we have $|A^{-1/2}(y-x)|<\dz_1$ and hence $$\{z\in \rn:\ |A^{-1/2}(z-x)|\le |A^{-1/2}(y-x)|\}\subset A^{1/2}B(0,\,\dz_1)+\{x\}\subset B(x_0,\,r).$$ For a given pair $x,\,y$, set $$\label{e3.2} \wz u_{x,\,y}(z)=\lf\{\begin{array}{ll} [u(y)-u(x)]\frac{|A^{-1/2}(z-x)|}{|A^{-1/2}(y-x)|}+u(x)&\quad if \quad |A^{-1/2}(z-x)|\le |A^{-1/2}(y-x)|,\\ u(y)&\quad if \quad |A^{-1/2}(z-x)|\ge |A^{-1/2}(y-z)|. \end{array}\r.$$ We still need to check that if $|A^{-1/2}(z-x)|\le |A^{-1/2}(y-x)|$, then $|A^{1/2}\nabla \wz u_{x,y}(z)|\le1$. Indeed, notice that for $y\in\mathbb{R}^n$, $$\langle A^{1/2}\xi, A^{-1/2}y\rangle = \langle A^{1/2}\xi,A^{1/2}A^{-1}y\rangle =\langle\xi, A\, A^{-1}y\rangle=\langle\xi,y\rangle,$$ and so $\langle \xi, y\rangle=\langle A^{1/2}\xi, A^{-1/2}y\rangle$. Furthermore, for $z\in S^{n-1}$, $$\nabla |A^{-1/2}z|=\frac{A^{-1}z}{|A^{-1/2}z|},$$ and so by the Cauchy-Schwarz inequality, we have $$|A^{1/2}\nabla \wz u_{x,y}(z)|= \frac{|\langle \xi, y-x\rangle|}{ |A^{1/2}\xi|} \frac{|A^{1/2}A^{-1}(z-x)|}{|A^{-1/2}(y-x)||A^{-1/2}(z-x)|} \le1,$$ as desired. \[comp-dist\] Given $A\in\mathscr{A}(\Omega)$ and $x\in\Omega$, we have $$\liminf_{x\ne y\to x}\frac{d_A(y,x)}{|y-x|}\ge \frac{1}{\sqrt{\lambda(x)}}.$$ Furthermore, $$\limsup _{x\ne y\to x}\frac{d_A(y,x)}{|y-x|}\le \sqrt{\lambda(x)}.$$ We fix $x\in\Omega$ and $r>0$ such that $\overline{B}(x,r)\subset\Omega$. Set $$\lambda_x(r)=\sup_{z\in B(x,r)}\lambda(z).$$ Notice that, by the continuity of $\lambda,$ we have $\lim_{r\to 0}\lambda_x(r)=\lambda(x)$. For the function $u_x$ given by $$u_x(z)=\frac{1}{\sqrt{\lambda_x(r)}}(r-|z-x|)_+,$$ we have that $\nabla u_x=0$ on $\Omega\setminus\overline{B}(x,r)$ and so $H(z,\nabla u_x(z))=0\le 1$ when $z\in\Omega\setminus\overline{B}(x,r)$. When $x\ne z\in B(x,r)$, we have $\nabla u_x(z)=\lambda_x(r)^{-1/2} |z-x|^{-1}(z-x)$. Therefore, by the ellipticity condition of $A$, $H(z,\nabla u_x(z))=\langle A(z)\nabla u_x(z),\nabla u_x(z)\rangle\le 1$. It follows that, by the definition of $d_A$, when $x\ne y\in B(x,r)$, $$d_A(x,y)\ge |u_x(y)-u_x(x)|=\frac{1}{\sqrt{\lambda_x(r)}}\, |y-x|,$$ from which the first part of the claim follows. For the second part, notice that if $x,y\in\Omega$, then there is a function $w$ on $\Omega$ with $d_A(x,y)\le |w(y)-w(x)|+\epsilon$ and $H(z,\nabla w(z))\le 1$ for almost every $z\in\Omega$. Let $E$ be the set of points at which this inequality fails. Then the Lebesgue measure of $E$ is zero. By the ellipticity property of $A,$ it follows that for almost every $z\in\Omega\setminus E$, $|\nabla w(z)|^2\le \lambda(z)$. By an argument using Fubini’s theorem, for each $\eta>0$ there is a point $y_\eta\in B(y,\eta)$ and a point $x_\eta\in B(x,\eta)$ such that the intersection of the Euclidean line segment $[x_\eta,y_\eta]$ connecting $x_\eta$ to $y_\eta$ with $E$ has $1$-dimensional Hausdorff measure zero. Thus $$|w(y_\eta)-w(x_\eta)|\le\int_{[x_\eta,y_\eta]}|\nabla w|\, ds \le \left[\sup_{p\in B(x,2{d_A}(x,y))}\sqrt{\lambda(p)}\right] |x_\eta-y_\eta|.$$ Letting $\eta\to 0$ and using the fact that $w$ is continuous, we obtain $$d_A(x,y)\le \left[\sup_{p\in B(x,2{d_A}(x,y))}\sqrt{\lambda(p)}\right]\, |x-y|\ + \epsilon.$$ Letting $\epsilon\to 0$ we obtain $$d_A(x,y)\le \left[\sup_{p\in B(x,2{d_A}(x,y))}\sqrt{\lambda(p)}\right]\, |x-y|,$$ from which the second part of the claim follows. Let $u\in\lip_{d_A}(\boz).$ Then, $u$ is also locally Lipschitz continuous with respect to the Euclidean metric on $\boz$. Notice that by Lemma \[l2.1\], we always have $H(x,\,\nabla u(x))\le (\lip_{d_A}u(x))^2$ for almost all $x\in\boz$. Now we will show that $(\lip_{d_A}u(x))^2\le H(x,\,\nabla u(x))$ for every $x\in\boz$ at which $A$ is weak upper semicontinuous and $u$ is differentiable. Fix such an $x\in\boz$. If $\nabla u(x)= 0$, then $|u(x)-u(y)|=o(|x-y|)$, which implies by Lemma \[comp-dist\] that $$\lip_{d_A} u(x)\le \lip\, u(x)\, \sqrt{\lambda(x)}=0=H(x,\nabla u(x)).$$ If $\nabla u(x)\ne0$, take $\xi=\frac{\nabla u(x)}{|A^{1/2}(x)\nabla u(x)|}$. Then, by Lemma \[comp-dist\] again, together with the fact that $u$ is differentiable at $x$, $$\begin{aligned} \label{e2.5} \lip_{d_A}u(x)&&=\limsup_{y\to x}\frac{|u(y)-u(x)|}{d_A(x,y)} \\ &&\le\limsup_{y\to x}\frac{|u(y)-u(x)-\langle \nabla u(x),\,y-x\rangle|}{d_A(x,y)}+ \limsup_{y\to x}\frac{|\langle \nabla u(x) ,\,y-x\rangle|}{d_A(x,y)}\nonumber\\ \le&& \sqrt{\lambda(x)}\, \lim_{y\to x}\frac{|u(y)-u(x)-\langle \nabla u(x),\,y-x\rangle|}{|x-y|}+ \limsup_{y\to x}\frac{|\langle \nabla u(x) ,\,y-x\rangle|}{d_A(x,y)}\nonumber\\ &&\le 0+| A^{1/2}(x)\nabla u(x)|\limsup_{y\to x}\frac{|\langle \xi,\,y-x\rangle|}{d_A(x,y)}.\nonumber\end{aligned}$$ Observe that $$| A^{1/2}(x)\nabla u(x)|^2=\langle A^{1/2}(x)\nabla u(x),\,A^{1/2}(x)\nabla u(x) \rangle =H(x,\, \nabla u(x) ).$$ Let $w(y)=\langle \xi,\,y\rangle$. It suffices to prove that $$\label{e3.x1} \limsup_{y\to x}\frac{|w(y)-w(x)|}{d_A(x,y)}\le 1.$$ To this end, notice that $\nabla w(y)=\xi$, and hence $H(y,\,\nabla w(y))=H(y,\, \xi )$ for all $y\in\boz$. By the weak upper semicontinuity of $A$ at $x$, there exists $\dz\in(0,\,r)$ such that for all $y\in B(x,\,\dz)$, $$H(y,\, \xi ) \le (1+\ez)H(x,\, \xi )=(1+\ez).$$ Set $\wz A(z)=(1+\ez)A(x)$ for $z\in B(x,\,\dz)$ and $\wz A(z)=A(z)$ for $z \notin B(x,\,\dz)$. It can be directly seen that $d_{\wz A}\le d_A$. We consider the function $v(y)=\frac{1}{\sqrt{1+\ez}}w(y)$ and $\eta=|\xi|^{-1}\xi\in S^{n-1}$; to this choice we apply Lemma \[l2.2\] to obtain $$\limsup_{y\to z}\frac{|w(y)-w(z)|}{d_A(z,y)}\le \limsup_{y\to z}\frac{|w(y)-w(z)|}{d_{\wz A}(z,y)}\le \sqrt{1+\ez}.$$ The arbitrariness of $\ez>0$ leads to . \[t2.3\] A diffusion matrix $A$ belongs to $\mathscr A_{\rm wusc}(\boz)$ if and only if $|Du|^2_{d_A} =H(\cdot,\,\nabla u )$ almost everywhere for all $u\in C^1(\boz)$. Suppose that whenever $u\in C^1(\boz)$ we have $|Du|_{d_A}^2(x)=H(x,\,\nabla u(x))$ almost everywhere. For each $\xi\in S^{n-1}$, taking $u(x)=\langle \xi,\,x\rangle$, we know that $H(x,\,\xi)=|Du|_{d_A}^2(x)$ almost everywhere, and hence is weak upper semicontinuous on $\boz$ because $x\mapsto |Du|_{d_A}(x)$ is upper semicontinuous. Suppose now that $A\in\mathscr A_{\rm wusc}(\boz)$. Then by Theorem \[t2.1\] and Theorem \[t2.2\], for all $u\in \lip_{d_A}(\boz)$ and almost all $x\in\boz$ we have $$H(x,\,\nabla u(x))\le (\lip_{d_A}u(x))^2\le |Du|^2_{d_A}(x).$$ To see that $ |Du|^2_{d_A}(x)\le H(x,\,\nabla u(x))$ almost everywhere for $u\in C^1(\boz)$, we give a 3-step argument. [*Step 1.* ]{} Let $\xi\in S^{n-1}$ and consider the function $u(y)=\langle\xi,\,y\rangle$. Then $\nabla u(x)=\xi$. To prove that $|Du|^2_{d_A}(x)\le H(x,\,\xi)$, it suffices to check that for almost every $x\in\boz$, $$\label{e2.x2} |Du|^2_{d_A}(x)\le (1+\ez) H(x,\,\xi)$$ for any $\ez>0$. The following argument is similar to that of Theorem \[t2.2\]. Let $x$ be a point of weak upper semicontinuity of $A$. For each fixed $\ez>0$, we know that there exists $r>0$ such that for almost all $y\in B(x,\,r)$, $H(y,\,\xi)\le (1+\ez)H(x,\,\xi)$. Let $$\wz A(y)=(1+\ez)A(x)1_{B(x,\,r)}(y) I_n+A(y)1_{\boz\setminus \overline {B(x,\,r)}}.$$ The corresponding intrinsic distance $d_{\wz A}$ is no more than $d_A$, and hence $|Du|_{d_A}\le |Du|_{d_{\wz A}}$ everywhere. By Lemma \[l2.2\], for any $y,\,z\in B(x,\,r/4)$, we have $$|u(y)-u(z)|\le d_{\wz A}(z,\,y)$$ and hence, $|Du|^2_{d_{\wz A}}(x)\le {\langle \wz A(x)\xi,\,\xi\rangle}$, which implies as desired. [*Step 2.* ]{} If $u\in C^1(\boz)$ and $\nabla u(x)=0$, then for any $\ez>0$, by the continuity of $\nabla u$, there exists a ball $B(x,\,r)$ such that $\|\nabla u\|_{L^\fz(B(x,\,r))}\le \ez$. With the aid of Lemma \[comp-dist\], we obtain $$|u(y)-u(z)|\le \ez|y-z|\ls \ez d_A(y,\,z)$$ which implies that $|Du|_{d_A}(x)\ls \ez$, and hence $|Du|_{d_A}(x)=0$ due to the arbitrariness of $\ez>0$. [*Step 3.* ]{} If $u\in C_\loc^1(\boz)$ with $\nabla u(x)\ne 0$, then let $$\wz u(y)=u(y)-\langle\nabla u(x),\,y\rangle$$ for $y\in\boz$. Then $\wz u$ is of class $C^1(\boz)$ with $\nabla\wz u(x)=0$, which implies that $|D\wz u|_{d_A}(x)=0$ by Step 2. Moreover, since $\langle A(y)\nabla u(x),\nabla u(x)\rangle$ is weak upper semicontinuous at $y=x$, by Step 1 we have $$|D u|_{d_A}(x)\le |D\wz u|_{d_A}(x)+|D(\langle \nabla u(x),\cdot\rangle)|_{d_A}(x) \le\sqrt{H(x,\,\nabla u(x))}$$ as desired. \[r2.1\] (i) We cannot replace the function class $C^1(\boz)$ by $\lip_\loc(\boz)$ in the above Theorem \[t2.3\]. Indeed, there exists a function $u\in\lip(\boz)$ such that $|\nabla u|^2$ is not weak upper semicontinuous on $\boz$, hence the above theorem fails for $A=I_n$. For example $$u(x_1,\,x_2)=\int_0^{x_1} 1_{C_{\bf a}}(z_1)\,dz_1,$$ where $C_{{\bf a}}\subset\mathbb{R}$ is a Cantor set of positive $1$-dimensional Lebesgue measure, and $1_{C_{\bf a}}:\mathbb{R}\to\mathbb{R}$ is the characteristic function of $C_{\bf a}$. For a construction of such a Cantor set $C_{\bf a}$ see Section 3. \(ii) Generally, for every open set $U$ with $\overline U \subset \boz$ and $u\in \lip(\boz)$, we have $|Du|_{d_A}\le C_U\lip_{d_A}u$ almost everywhere on $U$, where $C_U\ge 1$ is a constant. The proof of this is not trivial. Finally, we point out a relation between weak upper semicontinuity and the Eikonal equation. The Eikonal equation is necessary to obtain the coincidence of the intrinsic differential and distance structures. The Eikonal equation states that $$\langle A(\cdot)\nabla d_{A;\,x_0}(\cdot),\, \nabla d_{A;\,x_0} (\cdot)\rangle=1$$ almost everywhere for each $x_0\in\boz$, where $d_{A;\,x_0}(x)=d_A(x,\,x_0)$. When $A=I_n$ the statement of the Eikonal equation is that whenever $x_0\in\mathbb{R}^n$, the function ${d_A}(\cdot,x_0)$ satisfies $|\nabla {d_A}(\cdot,x_0)|=1$ almost everywhere in $\mathbb{R}^n$ (indeed, everywhere in $\mathbb{R}^n\setminus\{x_0\}$). \[p2.1\] For each $x_0\in\boz$, $H(x,\, \nabla d_{A;\,x_0}(x))=1$ almost everywhere if and only if $H(\cdot,\, \nabla d_{A;\,x_0} )$ is weak upper semicontinuous on $\boz$. If $H(x,\, \nabla d_{A;\,x_0}(x))=1$ almost everywhere, then obviously it is weak upper semicontinuous. Conversely, assume that $H(\cdot,\, \nabla d_{A;\,x_0} )$ is weak upper semicontinuous on $\boz$. It suffices to show that for each point $x\in \boz$ and all sufficient small $r>0$, $$\label{e2.x1} \lf\| H(\cdot,\, \nabla d_{A;\,x_0} )\r\|_{L^\fz(B_{d_A}(x,\,r))}=1.$$ Indeed, if this is true, then for almost all $x$, the weak upper semicontinuity leads to $$1\ge H(x,\, \nabla d_{A;\,x_0}(x) )\ge \limsup_{r\to 0}\lf\|H(\cdot,\, \nabla d_{A;\,x_0})\r\|_{L^\fz(B_{d_A}(x,\,r))}=1.$$ We prove by contradiction. Assume that fails for some $x_0\in\boz$ and some decreasing sequence $\{r_k\}$ which converges to $0$ as $k\to\fz$. By Lemma \[comp-dist\] and its proof, $d_A$ is comparable to the Euclidean distance. Hence for sufficiently large $k$ we have $B_{d_A}(x_0,\, r_k)\subset \boz$. Moreover, since we already know from Lemma \[l2.1\] applied to the function ${d_A}(\cdot,x_0)$ that $ \lf\|H(\cdot,\, \nabla d_{A;\,x_0} ) \r\|_{L^\fz(B_{d_A}(x,\,r_k))}\le1$, by our assumption there must be a positive number $\ez_k<1$ such that $$\lf\| H(\cdot,\, \nabla d_{A;\,x_0} )\r\|_{L^\fz(B_{d_A}(x,\,r_k))}\le 1-\ez_k.$$ Taking $$u_k(x)=\frac 1{\sqrt{1-\ez_k}}\min\{{d_A}(x_0,\,x),\,r_k\},$$ we have $u_k\in \lip(\boz)$ with $\lf\| H(\cdot,\,\nabla u_k)\r\|_{L^\fz( B_{d_A}(x_0,\,r_k) )}\le1 $ and $ H(z,\,\nabla u_k(z))=0 $ for $ z\in \boz\setminus B_{d_A}(x_0,\,r_k)$. Hence $u_k$ satisfies the conditions in the definition of $d_A(x,x_0)$, and so $$d_A(x_0,\,x)\ge u_k(x)-u_k(x_0)=\frac 1{\sqrt{1-\ez_k}}d_A(x_0,\,x),$$ which is a contradiction. \[r2.2\]As shown in [@kz Section 7], the Eikonal equation determines the asymptotic behavior of the gradient of heat kernel for a regular, strongly local Dirichlet form on a compact underlying space. We do not know if it is possible to deduce the coincidence of the intrinsic differential and distance structures from the Eikonal equation. Case $n\ge2$ and $A\notin\mathscr A_{\rm wusc}(\boz)$: $H(\cdot,\,\nabla u )=(\ne)(\lip_{d_A}u )^2$ {#s3} ==================================================================================================== In this section, we always assume that $n\ge 2$ and $\boz=\rn$. From Theorem \[t2.2\] we know that when $A\in\mathscr{A}_{\rm wusc}(\boz)$, for locally Lipschitz functions $u$ on $\boz$ we have $(\text{Lip}_{d_A}u)^2=H(x,\nabla u)$. In this section we show that when $A\notin\mathscr A_{\rm wusc}(\boz)$, the (non-)coincidence of the above intrinsic distance and differential structures depends on the geometry of the set where $A$ fails to be weak-upper semicontinuous. Indeed, we construct two examples based on a Cantor set and a Sierpinski carpet to show that both coincidence and noncoincidence may happen; see, respectively, Theorem \[t3.1\] and Proposition \[p3.1\]. We consider the simple $A\notin\mathscr A_{\rm wusc}(\boz)$ defined by $$A_{E,\,\dz}(x)= (1-\dz 1_{E})I_n,$$ where $\dz\in(0,\,1)$ and $E$ is a closed subset of $\rn$ with positive measure and empty interior. Obviously, $A_{E,\,\dz}$ fails to be weak upper semicontinuous at each $x\in E$, and hence $A\notin\mathscr A_{\rm wusc}(\rn)$. If $E$ is a suitable large Cantor set, then the intrinsic distance and differential structures never coincide. If $E$ is a suitable large Sierpinski carpet, then the intrinsic distance and differential structures do coincide. Recall that for $\dz\in(-\fz,\,0]$, $A_{E,\,\dz}= (1-\dz 1_{E})I_n\in\mathscr A_{\rm wusc}(\rn)$, and hence the associated intrinsic distance and differential structures always coincide by Theorem \[t2.2\]. The large Cantor set $C_{\bf a}$ -------------------------------- Let ${\bf a}=\{a_j\}$ with $0<a_j<1$. Then the associated Cantor set $C_{\bf a}$ is constructed as follows: $I_{i}$, $i=1,2$, are the two closed intervals obtained by removing the middle open interval with length $a_1$ from $I=[0,\,1]$ and are ordered from left to right; when $m\ge2$, the subintervals $I_{i_1\cdots i_m}$, $i_m=1,2$, are the two closed intervals obtained by removing the middle open interval with length $a_m|I_{ i_1\cdots i_{m-1}}|$ from $I_{ i_1\cdots i_{m-1}}$, and are ordered from left to right; finally set $$C_{\bf a} \equiv\bigcap_{m\in\nn}\ \bigcup_{i_1,\,\cdots,\,i_m\in\{1,2\}}I_{i_1\cdots i_m}.$$ and $C^{(n)}_{\bf a }\equiv C_{\bf a }\times\cdots\times C_{\bf a }$. Notice that $C^{(n)}_{\bf a}$ is closed and has empty interior, and that $C^{(n)}_{\bf a}$ has positive $n$-dimensional Lebesgue measure if and only if $C_{\bf a}$ has positive $1$-dimensional Lebesgue measure. Moreover, $$|C_{\bf a}|=\lim_{m\to\fz}(1-a_1)\cdots (1-a_m),$$ and by taking logarithms, $|C_{\bf a}|>0$ if and only if ${\bf a}\in\ell^1$. Thus, the $n$-dimensional Lebesgue measure of $C^{(n)}_{\bf a}$ is positive if and only if ${\bf a}\in\ell^1$. \[p3.1\] Assume that ${\bf a}\in \ell^1$ with $0<a_j<1$ for all $j\in\nn$. If $\dz\in(-\fz,\,0]$, then the associated intrinsic length and differential structure of $A_{C^{(n)}_{\bf a},\,\dz}$ do coincide; while if $\dz\in(0,\,1)$, then the associated intrinsic distance and differential structures never coincide. To prove Proposition \[p3.1\], we need the following (geometric) property of $C^{(n)}_{\bf a}$ that holds even if ${\bf a}\not\in\ell^1$. To simplify our notation, we set $d_{C^{(n)}_{\bf a},\,\dz}(x,\,y): =d_{A_{C^{(n)}_{\bf a}},\,\dz}(x,\,y).$ \[l3.1\] Let $\dz\in(0,\,1)$. Then for any $x\in C^{(n)}_{\bf a}$ and any $y\in x+\rr{\bf e_1}$, we have $d_{C^{(n)}_{\bf a},\,\dz}(x,\,y)=|x-y|$. Notice that, from the definition, we have $d_{C_{\bf a}^{(n)},\,\dz}(x ,\,y )\ge |x-y|$ for each pair $x,y\in\mathbb{R}^n$. Let $x\in C_{\bf a}^{(n)}$ and $y= x+r{\bf e_1}$ for some $r>0$. It suffices to show that $d_{C_{\bf a}^{(n)},\,\dz}(x ,\,y )\le |x-y|$. Recall that if $n=2$, it is already proved in [@kz Proposition 3.1] that for every pair $x,\,y\in \rn$, there exists a curve $\gz$ such that except for its endpoints, $\gz\subset\rn\setminus C_{\bf a}^{(2)}$, and with Euclidean length $\ell_{\rr^2}(\gz)\le C_{C^{(2)}_{\bf a}}|x-y|$. Hence $d_{C_{\bf a}^{(2)},\,\dz}(x,\,y)\le C_{C^{(2)}_{\bf a}}|x-y|$, where $C_{C_{\bf a}^{(2)}}$ is a constant determined by $C_{\bf a}^{(2)}$ and independent of $\dz$. If $n\ge2$, similar arguments still apply and hence for every pair $x,\,y\in \rn$, $d_{C_{\bf a}^{(n)},\,\dz}(x,\,y)\le C_{C^{(n)}_{\bf a}}|x-y|$. By the construction of $C_{\bf a}$, for each $k\in\nn$ we can find $x_k\in\rn\setminus C^{(n)}_{\bf a}$ such that $\langle x-x_k,{\bf e_1}\rangle=0$ and $$d_{C_{\bf a}^{(n)},\,\dz}(x,\,x_k)\le C_{C_{\bf a}^{(n)}}|x-x_k|\le \frac{1}{2k}|x-y|.$$ Take $y_k= y-(x-x_k)=x_k+r{\bf e_1}$. Then $y_k \in \rn\setminus C^{(n)}_{\bf a}$. Moreover, the line segment $x_k+[0,\,r]{\bf e_1}$ is contained in $\rn\setminus C^{(n)}_{\bf a}$, which implies that $$d_{C_{\bf a}^{(n)},\,\dz}(x_k,\,y_k)=|x_k-y_k|=|x-y|.$$ Therefore, $$d_{C_{\bf a}^{(n)},\,\dz}(x ,\,y )\le d_{C_{\bf a}^{(n)},\,\dz}(x_k,\,y_k)+d_{C_{\bf a}^{(n)},\,\dz}(x,\,x_k) +d_{C_{\bf a}^{(n)},\,\dz}(y,\,y_k)\le (1+\frac1k)|x-y|,$$ which implies that $d_{C_{\bf a}^{(n)},\,\dz}(x ,\,y )\le|x-y|$ by letting $k\to\fz$. Now we are ready to prove Proposition \[p3.1\]. Take $u(z)=\langle{\bf e_1}, z\rangle$ for $z\in\rn$. For each $\dz\in(0,\,1)$ and each $x\in C^{(n)}_{\bf a}$, by Lemma \[l3.1\], we have that $$\lip_{d_{C^{(n)}_{\bf a},\,\dz}}u(x)\ge \limsup_{y\in x+\rr\bf e_1}\frac{|u(x)-u(y)|}{d_{C^{(n)}_{\bf a},\,\dz}(x,\,y)} = \limsup_{y\in x+\rr\bf e_1}\frac{|u(x)-u(y)|}{|x-y|}=1> {\sqrt{1-\dz}}|\nabla u(x)|,$$ which is as desired because the Cantor set $C_{\bf a}^{(n)}$ has positive measure. From the above proof, we also conclude the following corollary. \[c3.1\] Let $E$ be a closed subset of $\rn$. Assume that $E$ has positive measure and empty interior. [(]{}i[)]{} If there is a constant $C_E$ such that for each pair $x,\,y\in \rn$ we can find a curve $\gz$ such that all of the curve except for perhaps countably many points lies in $\mathbb{R}^n\setminus E$ and $gz$ satisfies $\ell_\rn(\gz)\le C_E|x-y|$, then the intrinsic distance and differential sctructures associated to $A_{E,\,\dz}=(1-\dz1_E)I_n$ with $\dz\in(\frac1{C_E},\,1)$, do not coincide. [(]{}ii[)]{} If there exists $\xi\in S^{n-1}$ such that for all $x\in E$, we can find a sequence of $y\in x+\rr\xi$ satisfying $d_{E,\,\dz}(x,\,y)=|x-y|$, then the intrinsic distance and differential structures associated to $A_{E,\,\dz}=(1-\dz1_E)I_n$ with $\dz\in(0,\,1)$, do not coincide. The large Sierpinski carpet $S_{\bf a}$ --------------------------------------- Let ${\bf a}=\{a_j\}_{j\in\nn}$ with $a_j\in\{\frac13,\,\frac15,\,\frac17,\cdots\}$, that is, $a_j$ is the reciprocal of an odd integer strictly greater than one. A modified Sierpinski carpet $S_{\bf a}$ is constructed as follows. First, divide the unit cube $T= [0, 1]^n$ into $a_1^{-n}$ essentially disjoint closed congruent subcubes, and remove the interior of the central one; denote the central one by $T_{a_1^{-n}}$ and the others by $T_{k_1}$ with $1\le k_1\le a_1^{-n}-1$. When $m\ge2$, divide each $T_{k_1,\,\cdots,\,k_{m-1}}$ into $a_m^{-n}$ essentially disjoint closed congruent subcubes and remove the interior of the central one; denote the central one by $T_{k_1,\,\cdots,\,k_{m-1},\,a_m^{-n}}$ and the others by $T_{k_1,\,\cdots,\,k_m}$ with $1\le k_m\le a_m^{-n}-1$. For each $m\in\nn$, define the level $m$ precarpet by $$S_{{\bf a},\,m}= \bigcup_{k_1}\cdots\bigcup_{k_m} T_{k_1,\,\cdots,\,k_m}.$$ The modified Sierpinski carpet $S_{\bf a }$ is defined as the limit of precarpets $S_{{\bf a},\,m}$, that is, $S_{\bf a }=\cap_{m\in\nn}S_{{\bf a},\,m}.$ Obviously, $S_{\bf a }$ is closed, has empty interior, and $S_{\bf a }$ has positive $n$-dimensional Lebesgue measure if and only if ${\bf a}\in\ell^n$. Indeed, the $n$-dimensional Lebesgue measure of the precarpet $S_{{\bf a},\,m}$ is $$|S_{{\bf a},\,m}| =( 1-a_1^{n})\cdots(1-a^{n}_{m}).$$ Thus, by taking logarithms, $|S_{\bf a}|= \lim_{m\to\fz} |S_{{\bf a},\,m}|>0$ if and only if ${\bf a}\in\ell^n$. \[t3.1\] Let ${\bf a}=\{a_j\}_{j\in\nn}\in \ell^n$ with $a_j\in\{\frac13,\,\frac15,\,\frac17,\cdots\}$. Then for all $\dz \in(-\fz,\,1) $, the associated intrinsic distance and differential structures of $A_{S_{\bf a},\,\dz}$ do coincide. We employ the following geometric property of $S_{\bf a}$ to prove Theorem \[t3.1\]. We only need to consider the case $0<\delta<1$. \[l3.2\] Let $\dz\in(0,\,1)$ and ${\bf a}=\{a_j\}_{j\in\nn}\in \ell^n$ with $a_j\in\{\frac13,\,\frac15,\,\frac17,\cdots\}$. Then there exists a subset $E\subset S_{\bf a}$ with measure zero such that for any $\ez>0$ and each $x\in S_{\bf a}\setminus E$, we can find $r=r(x,\,\dz,\,\ez)>0$ which satisfies: for all $y\in B(x,\,r)$, $$\label{e3.x5} d_{S_{\bf a},\,\dz}(x,\,y)\ge (1-\ez)\frac1{\sqrt{1-\dz}}|x-y|.$$ With Lemma \[l3.2\], we can prove Theorem \[t3.1\] easily. Obviously, Lemma \[l2.1\] yields $H(x,\,\nabla u(x))\le (\lip_{d_{S_{\bf a},\,\dz}}u(x))^2$ for almost all $x\in\boz$. We now need to show that $(\lip_{d_{S_{\bf a},\,\dz}}u(x))^2\le H(x,\,\nabla u(x))$ almost everywhere. To this end, it suffices consider the cases $x\in\rr^n\setminus S_{\bf a}$ and $x\in E\subset S_{\bf a}$, where $E$ is as in Lemma \[l3.2\]. [*Case 1:*]{} $x\in\rr^n\setminus S_{\bf a}$. It suffices to show that if $r<d_{\rn}(x,\, S_{\bf a})/2$ and $y\in B(x,\,r)$ we have $$\label{e3.xx1} d_{S_{\bf a},\,\dz}(x,\,y) = |x-y|.$$ Indeed, will give $$H(x,\,\nabla u(x))=|\nabla u(x)|^2= (\lip\, u(x))^2 = (\lip_{d_{S_{\bf a},\,\dz}}u(x))^2$$ by the definition of the pointwise Lipschitz constant. The verification of is done as in the proof of Lemma \[comp-dist\], with $\lambda:\mathbb{R}^n\to[1,\infty)$ given as a continuous function that satisfies $\lambda(y)=1$ when $y\in B(x,3r/2)$ and $\lambda(y)=1/\sqrt{1-\delta}$ when $y\in S_{\bf a}$. [*Case 2:*]{} $x\in S_{\bf a}\setminus E$. In this case, implies that $$\limsup_{y\to x} \frac{|y-x|}{d_{S_{\bf a}}(x,y)}\le \sqrt{1-\delta}.$$ With this, if $u$ is differentiable at $x$, we have $$\begin{aligned} \text{Lip}_{d_{S_{\bf a}}}u(x)&= \limsup_{y\to x}\frac{|u(x)-u(y)|}{d_{S_{\bf a}}(x,y)}\\ &\le \limsup_{y\to x}\frac{|u(x)-u(y)-\langle \nabla u(x),y-x\rangle|}{d_{S_{\bf a}}(x,y)}+ \limsup_{y\to x}\frac{|\langle \nabla u(x),y-x\rangle|}{d_{S_{\bf a}}(x,y)}\\ & \le0\cdot\limsup_{y\to x} \frac{|y-x|}{d_{S_{\bf a}}(x,y)}+|\nabla u(x)|\limsup_{y\to x} \frac{|y-x|}{d_{S_{\bf a}}(x,y)}\\ &\le \sqrt{1-\delta}\, |\nabla u(x)|=\sqrt{H(x,\nabla u(x))}.\end{aligned}$$ This proves Theorem \[t3.1\]. Finally, we prove Lemma \[l3.2\]. Notice that Lemma \[l3.2\] is much stronger than Lemma \[comp-dist\]; see Remark \[r3.x1\] below. The proof of Lemma \[l3.2\] relies on the following approximation of distance established by Norris [@n97]. Let $\Phi\in C_c^\fz(\rn)$ be such that $\int_\rn \Phi(x)\,dx=1$, ${\rm supp}\,\Phi\subset B(0,\,2)$ and $0\le \Phi(x)\le1$ for all $x\in\rn$. For $t>0$, let $\Phi_t(x)=t^{-n}\Phi(t^{-1}x)$. Standard analysis arguments show that $\Phi_t\ast f \to f$ almost everywhere when $f\in L^1_\loc(\rn)$. The following lemma is due to Norris [@n97]. \[l3.3\] Let $A_{E,\,\dz,\,t}=[\Phi_t\ast (\frac{1}{1-\dz1_{E}})]^{-1}I_n$ and denote by $d_{E,\,\dz,\,t}$ the associated intrinsic distance. Then $d_{E,\,\dz,\,t}(x,\,y)\to d_{E,\dz}(x,\,y)$ as $t\to0$ for all $x,\,y\in\rn$. Moreover, $$(d_{E,\,\dz,\,t}(x,\,y))^2=\inf_{\gz}\int_0^1\Phi_t\ast \lf(\frac{1}{1-\dz 1_{E}}\r) (\gz(s))\lf|\frac d{ds}\gz(s)\r|^2\,ds.$$ We divide the proof into 6 steps. [*Step 1.*]{} Recall that for each $m$, $T_{k_1,\,\cdots,\,k_{m-1},\,a_m^{-n}}$ is the central cube whose interior has been removed from the cube $T_{k_1,\,\cdots,\,k_{m-1}}$ at step $m$ when constructing the Sierpinski Carpet $S_{\bf a}$. For each fixed $N\in\nn\cup\{0\}$, denote by $J _{N,\,m}$ the collection of all $(k_1,\,\cdots,\,k_{m-1},\,j)$ such that $T_{k_1,\,\cdots,\,k_{m-1},\,j}$ is $N$-close to the central cube $T_{k_1,\,\cdots,\,k_{m-1},\,a_m^{-n}}$ in the sense that there exists a sequence $i_0,\,i_1,\,\cdots,\,i_M$ with $1\le M\le N$ such that $i_0=j$, $i_M=a_m^{-n}$, $i_l\ne i_s$ if $i\ne s$, and for $0\le s<M-1$, $$T_{k_1,\,\cdots,\,k_{m-1},\,i_{s}}\bigcap T_{k_1,\,\cdots,\,k_{m-1},\,i_{s+1}}\ne\emptyset.$$ Let $$E _{N,\,m}=\bigcup_{(k_1,\,\cdots,\,k_{m-1},\,j)\in J_{N,\,m}}T_{k_1,\,\cdots,\,k_{m-1},\,j}.$$ If $N\ge a_m^{-1}$, then $E_{N,\,m}=T_{k_1,\,\cdots,\,k_{m-1}}$. Recall that we assume ${\bf a}\in\ell^n$. It follows that for sufficiently large $m$ we have $N<a_m^{-1}$. In this case, we see that $E_{N,\,m}$ is a cube centered at the center of $T_{k_1,\,\cdots,\,k_{m-1},a_m^{-n}}$ of edge length the $(2N+1)\,a_m$-fraction of the edge length of the cube $T_{k_1,\,\cdots,\,k_{m-1}}.$ Observe that this fraction tends to zero as $m\to\infty$. We set $$E_N=\bigcap_{m\in\nn}\ \bigcup_{\ell\ge m}E_{N,\,\ell}=\bigcap_{\nn\ni m>N}\ \bigcup_{\nn\ni \ell\ge m}E_{N,\,\ell},$$ Let $F$ be the union of all the $(n-1)$-dimensional faces of all the cubes that were removed in the construction of $S_{\bf a}$, and $$E=F\cup\left(\bigcup_{N\in\nn}E_N\right).$$ We claim that $|E|=0$. It is easy to see that $|F|=0$. >From the above discussion, $$|E_{N,\,m}|\le (2N+1)^n(1-a_1^n)\cdots(1-a_{m-1}^n)a_m^n.$$ >From this, it follows that $$\begin{aligned} \lf|\bigcup_{\ell\ge m}E_{N,\,\ell}\r| &&\le (2N+1)^n\sum_{\ell\ge m} (1-a_1^n)\cdots(1-a_{\ell-1}^n)a_\ell^n\le (2N+1)^n \sum_{\ell\ge m} a_\ell^n,\end{aligned}$$ which converges to zero as $m\to\fz$ because ${\bf a}\in\ell^n$. This implies that $E_N$ with $N\in\nn$, and hence $E$, has measure zero. [*Step 2.*]{} For any $\ez>0$, we choose $\wz N_\ez,\,N_\ez\in\nn$ such that $$\wz N_\ez\ge \frac {100^nn^{2n}}{(1-\dz)\ez}$$ and $N_\ez\ge(\wz N_\ez)^{n+1}$. For each fixed $x\in S_{\bf a}\setminus E$, recall that $x\in S_{\bf a}\setminus E_N$ for all $N\in\nn$. Since $$S_{\bf a}\setminus E_{N_\ez}= \lf [S_{\bf a}\setminus \lf(\bigcap_{m\in\nn}\bigcup_{\ell\ge m}E_{N_\ez,\,\ell}\r)\r] =\bigcup_{m\in\nn} \lf[S_{\bf a}\setminus \lf(\bigcup_{\ell\ge m}E_{N_\ez,\,\ell}\r)\r]$$ there exists an $m_x\in\nn$ such that $x\in S_{\bf a}\setminus (\bigcup_{\ell\ge m}E_{N_\ez,\,\ell})$ for all $m\ge m_x$. We also let $r_x>0$ be the Euclidean distance from $x$ to the union of all removed $T_{k_1,\,\cdots,\,k_{m-1},\,a_{m}^{-n}}$ with $m\le m_x-1$. Since $x\not\in F$, we see that $r_x>0$. Because ${\bf a}\in\ell^n$, we can further find $\wz m_x\ge m_x$ such that for all $m\ge \wz m_x$, $$\label{e3.x8} a_m\le (1-\dz)r_x/{2N^2_\ez}.$$ [*Step 3.*]{} For each $m> \wz m_x$ and $$y\in B(x,\,\wz N_\ez a_1\cdots a_m)\setminus \overline {B(x,\,\wz N_\ez a_1\cdots a_{m+1})},$$ we are going to estimate $d_{S_{\bf a},\,\dz}(x,\,y)$ from below. By Lemma \[l3.3\], we know that $d_{S_{\bf a},\,\dz,\,t}(x,\,y)$ converges to $d_{S_{\bf a},\,\dz}(x,\,y)$ as $t\to0$. So it suffices to estimate $d_{S_{\bf a},\,\dz,\,t}(x,\,y)$ (for simplicity, we denote this quantity $d_t(x,\,y)$) from below for all sufficiently small $t$. By Lemma \[l3.3\] again, we have $$(d_t(x,\,y))^2=\inf_{\gz}\int_0^1\Phi_t\ast \lf(\frac{1}{1-\dz 1_{S_{\bf a}}}\r) (\gz(s))\lf|\frac d{ds}\gz(s)\r|^2\,ds$$ and for each $t\in (0,\,1)$, we can find a rectifiable curve $\gz_{\{x,\,y,\,t\}}$ joining $x$ and $y$ such that the above infimum is reached, that is $$\begin{aligned} (d_t(x,\,y))^2 &&= \int_0^1\Phi_t\ast \lf(\frac1{1-\dz1_{S_{\bf a}}}\r)(\gz_{\{x,\,y,\,t\}}(s))\lf|\frac d{ds}\gz_{\{x,\,y,\,t\}}(s)\r|^2\,ds, \end{aligned}$$ and hence, by Hölder’s inequality, $$\begin{aligned} d_t(x,\,y) &&\ge \int_0^1\sqrt{\Phi_t\ast\lf(\frac1{1-\dz1_{S_{\bf a}}}\r)(\gz_{\{x,\,y,\,t\}}(s)) }\lf|\frac d{ds}\gz_{\{x,\,y,\,t\}}(s)\r|\,ds.\end{aligned}$$ Observe that for each $t\in(0,\,1)$ and every pair $z,\,w\in\rn$, $$|z-w|\le d_t(z,\,w)\le \frac1{1-\dz}|z-w|,$$ which follows from $$1\le \Phi_t\ast \lf(\frac1{1-\dz1_{S_{\bf a}}}\r)\le \frac1{1-\dz}.$$ Hence the curves $\gamma_{x,y,t}$ are Lipschitz with respect to the Euclidean metric under a suitable parametrization, and moreover, with a normalization, we can assume that for the Euclidean derivative, $\lf|\frac d{ds}\gz_{\{x,\,y,\,t\}}(s)\r|=1$ for almost all $s\in[0,\,\ell_{\rn}(\gz_{\{x,\,y,\,t\}})]$. Hence $$\begin{aligned} d_t(x,\,y) \ge \int_0^{\ell_{\rn}(\gz_{\{x,\,y,\,t\}})} \sqrt{\Phi_t\ast \lf(\frac1{1-\dz1_{S_{\bf a}}}\r)(\gz_{\{x,\,y,\,t\}}(s))}\,ds.\end{aligned}$$ [*Step 4.*]{} To estimate $d_t(x,\,y)$, we only need to know the length of the set $$L_t=\lf\{s\in[0,\,\ell_\rn(\gz_{\{x,\,y,\,t\}})]:\, \Phi_t\ast \lf(\frac1{1-\dz1_{S_{\bf a}}}\r)(\gz_{\{x,\,y,\,t\}}(s))\ge (1-\ez){\frac1{1-\dz}}\r\}.$$ To this end, observe that if $t=a_1\cdots a_\ell$ for any large $\ell >m$ and $z\in B(x,\, \frac {\wz N_\ez}{1-\dz} a_1\cdots a_m)$ but does not belong to the double enlargement of the (removed) cube $T_{k_1,\,\cdots,\,k_{i-1},\,a_i^{-n}}$ with $m\le i\le \ell$, by $N_\ez\ge 4\wz N_\ez\frac1{(1-\dz)}$, we have $$\label{e3.x7} B(z,\,2t)\subset B\lf(x,\, \frac {4\wz N_\ez}{1-\dz} a_1\cdots a_m\r)\subset B(x,\, N_\ez a_1\cdots a_m).$$ Hence $$\Phi_t\ast \lf(\frac1{1-\dz1_{S_{\bf a}}}\r)(z) \ge \frac1{1-\dz}\left[1- \frac{c_n}{|B(z,\,t)|}\lf|B(z,\,2t)\bigcap\lf(\bigcup_{j\ge\ell} T_{k_1,\,\cdots,\,k_{j-1},\,a_j^{-n}}\r) \r|\right].$$ Note that ${\bf a}\in\ell^n$ implies $|\bigcup_{j\ge\ell}T_{k_1,\,\cdots,\,k_{j-1},\,a_j^{-n}} |\to 0$ as $\ell\to\fz$. For every $\ez>0$ there exists $\ell_0\in\nn$ which depends only on $\ez$ such that for all $\ell\ge\ell_0$, $$\lf|\bigcup_{j\ge\ell}T_{k_1,\,\cdots,\,k_{j-1},\,a_j^{-n}} \r|\le \ez\, |B(z,\,t)|.$$ Therefore, if $\ell >\max\{\ell_0,\,m\}$, for the above $z$, we have $$\Phi_t\ast \lf(\frac1{1-\dz1_{S_{\bf a}}}\r)(z)\ge \frac{1-\ez}{1-\dz}.$$ On the other hand, by the choice of $r_x$ and $N_\ez$ at Step 2, when $t= a_1\cdots a_\ell\le a_\ell\le r_x/10$ we have $\ell_{\rn}(\gz_{\{x,\,y,\,t\}})\le r_x/10$. So for $i\le \wz m_x-1$, $$\text{dist}_{\mathbb{R}^n}(\gz_{\{x,y,t\}}, T_{k_1,\,\cdots,\,k_{i-1},\,a_i^{-n}})\ge \text{dist}_{\mathbb{R}^n}(x, T_{k_1,\,\cdots,\,k_{i-1},\,a_i^{-n}})\, -\, \ell_{\rn}(\gz_{\{x,\,y,\,t\}})\ge 2t.$$ Therefore $T_{k_1,\,\cdots,\,k_{i-1},\,a_i^{-n}}$ makes no contribution when we estimate $\Phi_t\ast \lf(\frac1{1-\dz1_{S_{\bf a}}}\r)(z)$ from below for $z\in\gz_{\{x,\,y,\,t\}}$. This also holds for $\wz m_x\le i\le m-1$ by a similar argument. Indeed, for $\wz m_x\le i\le m-1$, we also have $t= a_1\cdots a_\ell\le a_1\cdots a_i/10$ and $\ell_{\rn}(\gz_{\{x,\,y,\,t\}})\le a_1\cdots a_i/10$, and hence, in this case the Euclidean distance from $\gz_{\{x,\,y,\,t\}}$ to each $T_{k_1,\,\cdots,\,k_{i-1},\,a_i^{-n}}$ is at least $2t$. Based on the above argument, the lower bound estimate of the length of $L_t$ is transferred to the upper bound estimate of the length of $$\wz L_t=\lf\{s\in[0,\,\ell_\rn(\gz_{\{x,\,y,\,t\}})]\, :\, \gz_{\{x,\,y,\,t\}}(s)\in \bigcup_{m\le i\le \ell-1}\, \bigcup_{k_1,\,\cdots,\,k_i} 2T_{k_1,\,\cdots,\,k_{i-1},\,a_i^{-n}}\r\}.$$ Here, $\ell$ is the positive integer such that $t=a_1\cdots a_\ell$; keep in mind that $\ell>m$. [*Step 5.*]{} To estimate $\wz L_t$, we need the following key observations. \(i) Since $ |x-y|\le d_t(x,\,y)\le \frac1{1-\dz}|x-y|$, we have $$\label{e3.x6} \gz_{\{x,\,y,\,t\}}\subset B\left(x,\, \frac {\wz N_\ez}{1-\dz} a_1\cdots a_m\right).$$ Recall that $x$ is not in any $ N_\ez$-close cube of $T_{k_1,\,\cdots,\,k_{m-1},\,a_m^{-n}}$ whenever $m\ge m_x$. Since $N_\ez\ge 2n\wz N_\ez\frac 1{(1-\dz)^2}$, we have that $$2T_{k_1,\,\cdots,\,k_{m-1},\,a_m^{-n}}\cap \gz_{\{x,\,y,\,t\}}=\emptyset.$$ \(ii) If $|x-y|\le {N_\ez}a_1\cdots a_{m+1} $, then by , $|x-y|\le a_1\cdots a_m$, and hence there are at most $2^n$ many cubes $T_{k_1,\,\cdots,\,k_m}$ with $k_m<a_{m+1}^{-n}$ that overlaps with $\gz_{\{x,\,y,\,t\}}$, and hence, there are at most $2^n$ many $T_{k_1,\,\cdots,\,k_m,\,a_{m+1}^{-n}}$ such that its twice-enlargement overlapped with $\gz_{\{x,\,y,\,t\}}$. Moreover, up to a modification of the curve $\gz_{\{x,\,y,\,t\}}$ without increasing the $d_{t}$-length of $\gz_{\{x,\,y,\,t\}}$, we may assume that the Euclidean length of $\gz_{\{x,\,y,\,t\}}\cap 2T_{k_1,\,\cdots,\,k_m,\,a_{m+1}^{-n}}$ is less than $4\sqrt n a_1\cdots a_{m+1}$. Thus by $|x-y|\ge\wz N_\ez a_1\cdots a_{m+1} $, $$\begin{aligned} \wz L_{t,\,m}&&=\lf|\lf \{s\in[0,\,\ell_\rn(\gz_{\{x,\,y,\,t\}})],\, \gz_{\{x,\,y,\,t\}}(s)\in \bigcup_{k_1,\,\cdots,\,k_m} 2T_{k_1,\,\cdots,\,k_{m},\,a_{m+1}^{-n}}\r\}\r|\\ &&\le 4\sqrt n 2^n a_1\cdots a_{m+1} \le 4\sqrt n 2^n\frac1{\wz N_\ez}|x-y|\le\ez|x-y|\end{aligned}$$ If $ {N_\ez}a_1\cdots a_{m+1}\le |x-y|\le {\wz N_\ez}a_1\cdots a_{m}$, since $\ell_{\rn}(\gz_{\{x,\,y,\,t\}})\le \frac{\wz N_\ez}{1-\dz}a_1\cdots a_{m}$, there are at most $(2\frac {\wz N_\ez}{1-\dz})^n$ many $T_{k_1,\,\cdots,\,k_m}$ with $k_m<a_{m}^{-n}$ such that $$T_{k_1,\,\cdots,\,k_m}\cap \gz_{\{x,\,y,\,t\}}\ne\emptyset,$$ and hence, at most $(2\frac {\wz N_\ez}{1-\dz})^n$ many $T_{k_1,\,\cdots,\,k_m,\,a_{m+1}^{-n}}$ such that their twice-enlargement overlap with $\gz_{\{x,\,y,\,t\}}$. Notice that $4\sqrt n(2\frac {\wz N_\ez}{1-\dz})^n\le \ez N_\ez$ and $a_{m+1}\le (1-\dz)r_x/{2N^2_\ez}\le 1/{2N^2_\ez}$. With a similar argument on $\gz_{\{x,\,y,\,t\}}$ as above, we have $$\begin{aligned} \wz L_{t,\,m}&&=\lf|\lf \{s\in[0,\,\ell_\rn(\gz_{\{x,\,y,\,t\}})],\, \gz_{\{x,\,y,\,t\}}(s)\in \bigcup_{k_1,\,\cdots,\,k_m} 2T_{k_1,\,\cdots,\,k_{m},\,a_{m+1}^{-n}}\r\}\r|\\ &&\le 2\sqrt n (2\frac N{1-\dz})^n a_1\cdots a_{m+1} \le 2\sqrt n (2\frac N{1-\dz})^n \frac1{N_\ez}|x-y|\le\ez|x-y|\end{aligned}$$ \(iii) For each $i\ge m+1$, the numbers of $T_{k_1,\,\cdots,\,k_i,\,a_{i+1}^{-n}}$, whose twice-enlargement overlapped with $\gz$, is no more that the numbers of $T_{k_1,\,\cdots,\,k_{i}}$ with $k_{i}< a_{i}^{-n}$ which overlaps with $\gz$. By induction and similar argument as above, $$\begin{aligned} \wz L_{t,\,i}&&=\lf|\lf \{s\in[0,\,\ell_\rn(\gz_{\{x,\,y,\,t\}})],\, \gz_{\{x,\,y,\,t\}}(s)\in \bigcup_{k_1,\,\cdots,\,k_i} 2T_{k_1,\,\cdots,\,k_{i},\,a_{i+1}^{-n}}\r\}\r|\\ && \le 8\sqrt na_{i+1}\lf|\lf \{s\in[0,\,\ell_\rn(\gz_{\{x,\,y,\,t\}})],\, \gz_{\{x,\,y,\,t\}}(s)\in \bigcup_{k_1,\,\cdots,\,k_i} T_{k_1,\,\cdots,\,k_{i}}\r\}\r| \\ && \le (8\sqrt n)^{i-m }a_{i+1}\cdots a_{m+1}\ez|x-y|.\end{aligned}$$ [*Step 6.*]{} The three observations above yield that $$|\wz L_t|\le\sum_{i= m}^{\ell} \wz L_{t,\,i}\le \ez|x-y|+ \sum_{i\ge m+1}(8\sqrt n)^{i-m } a_{i+1}\cdots a_{m+1}\ez|x-y|\le 3\ez|x-y|,$$ and hence, $$|L_t|\ge \ell_\rn(\gz_{\{x,\,y,\,t\}})-|\wz L_t|\ge (1-3\ez)|x-y|.$$ Noticing that $\ell_\rn(\gz_{\{x,\,y,\,t\}})\ge|x-y|$, we have $$d_t(x,\,y) \ge \frac{\sqrt{1-\ez}}{\sqrt{1-\dz}}(1-3\ez)|x-y| \ge \frac{(1-4\ez)}{\sqrt{1-\dz}}|x-y| .$$ By the arbitrariness of $\ez$, we conclude . \[r3.x1\](i) Notice that Lemma \[l3.2\] is much stronger than Lemma \[comp-dist\]. To see this, let $\lz$ be a positive continuous on $\rn$ such that holds when $A=(1-\dz1_{S_{\bf a},\,\dz})I_n$, that is, $$\frac1{\lz(x)}|\xi|^2\le\langle A(x)\xi,\,\xi\rangle=(1-\dz1_{S_{\bf a},\,\dz})|\xi|^2\le\lz(x)|\xi|^2$$ for all $x\in\rn$ and $\xi\in\rn\setminus\{0\}$. From this, when $x\in S_{\bf a}$, it follows that $\frac1{\lz(x)}\le1-\dz\le \lz(x),$ which yields $\lz(x)\ge\frac1{1-\dz}\ge1. $ Without loss of generality, we may let that $\lz(x)=\frac1{1-\dz}$ for $x\in S_{\bf a}$. Now fix $x\in S_{\bf a}$. Then by Lemma \[comp-dist\], we always have that $$\liminf_{x\ne y\to x}\frac{d_{S_{\bf a},\,\dz}(y,x)}{|y-x|}\ge \frac{1}{\sqrt{\lambda(x)}}=\sqrt{1-\dz},$$ which is equivalent to that for any $\ez>0$, we can find $r>0$ such that for all $y \in B(x,\,r)$, $$\label{e3.xx2} d_{S_{\bf a},\,\dz}(x,\,y ) \ge (1-\ez) \sqrt{1-\dz}|x-y |;$$ and that $$\limsup_{x\ne y\to x}\frac{d_{S_{\bf a},\,\dz}(y,x)}{|y-x|}\le {\sqrt{\lambda(x)}}=\frac1{\sqrt{1-\dz}},$$ which is equivalent to that for any $\ez>0$, we can find $r>0$ such that for all $y\in B(x,\,r)$, $$\label{e3.xx3}d_{S_{\bf a},\,\dz}(x,\,y ) \le (1+\ez) \frac1{\sqrt{1-\dz}}|x-y |.$$ Obviously, we cannot obtain from and , and hence cannot obtain from Lemma \[comp-dist\]. Indeed, is much stronger than . \(ii) The reason why our Cantor set and Sierpinski carpet give entirely different outcomes is the different behavior of $d_{S_{\bf a},\,\dz}$ and $d_{C^n_{\bf a},\,\dz}$ when $\dz\in(0,\,1)$. Indeed, as the proof of Lemma \[l3.2\] shows, given almost every point $x\in S_{\bf a}$ and *every* close-by point $y$, any curve that connects $x$ to $y$ with length comparable to $|x-y|$ lives in $S_{\bf a}$ for a significant fraction of the time, and sees $x$ as a linear density point of $S_{\bf a}$. In comparison, almost every point $x$ in the Cantor set $C^n_{\bf a}$ can be connected to *some* near-by point by a curve of length comparable to the Euclidean distance between the two points while avoiding $C^n_{\bf a}$ for almost all of the time. \[r3.1\]Given an $A\in\mathscr A(\boz)$ with the intrinsic distance $d_A$, by Lemma \[l2.1\], for all $u\in\lip(\boz)$, we always have $$\langle A \nabla u,\,\nabla u\rangle\le(\lip_{d_A}u)^2\le |Du|_{d_A}^2$$ almost everywhere. If $A\in\mathscr A_{\rm wusc}(\boz)$, then the first $``\le"$ is actually $``="$, if $A\in\mathscr A_{\rm wusc}(\boz)$ and $u\in C^1_\loc(\boz)$, the second $``\le"$ is actually $``="$. However if $A\notin\mathscr A_{\rm wusc}(\boz)$, then the first $``\le"$ may be $``<"$ on some set with positive measure as shown by Proposition \[p3.1\]; the second $``\le"$ may be $``<"$ on some set with positive measure as shown by Theorem \[t3.1\] even for $u\in C^1_\loc(\boz)$. $L^\fz$-Variational problem for arbitrary $A\in\mathscr A(\boz)$ ================================================================ In this section, we assume that $n\ge2$. Let $A\in\mathscr A(\boz)$ and $U\Subset\boz$ be a bounded open subset. We obtain the following existence and uniqueness of the absolute minimizer given a boundary data (see Section 1 for the definition of absolute minimizers). \[t4.1\] [(]{}i[)]{} For every $f\in \lip(\partial U)$, there exists a unique absolutely minimizing Lipschitz extension. [(]{}ii[)]{} The absolute minimizer is completely determined by the intrinsic distance in the following sense: Let $A,\,\wz A\in\mathscr A(\boz)$ and denote by $d_A,\, d_{\wz A}$ [(]{}resp. $H,\,\wz H$[)]{} the corresponding intrinsic distance [(]{}resp. Hamiltonian[)]{}. If $$\label{e4.xx1}\lim_{x\ne y\to x}\frac{d_{ A}(x,\,y)}{d_{\wz A}(x,\,y)}=1$$ for almost all $x\in U$, then $u$ is an absolute minimizer on $U$ for the Hamiltonian $H $ if and only if $u$ is an absolute minimizer on $U$ for the Hamiltonian $\wz H $. A special case of is that for almost every $x\in U$, there exists $ r_x>0$ such that $d_{ A}(x,\,y)=d_{\wz A}(x,\,y)$ for all $y\in B_d(x,\,r_x)$. We do not know whether if weak upper semicontinuity of $A$ could guarantee $C^1$-regularity for the associated minimizers. However, we have the following negative result for the $C^1$-regularity of absolute minimizers. \[c4.3\] Let $A= 1-\dz 1_{S_{\bf a}}$ be as in Subsection 3.2, where ${\bf a} \in \ell^n$ with $a_j\in\{\frac13,\,\frac15,\,\frac17,\cdots\}$ and $\dz\in(0,\,1)$. Then there is an absolute minimizer on $U=(0,\,1)^n$ associated to a related $L^\fz$-variational problem that is not $C^1$-regular on $U$. Now we prove Theorem \[t4.1\] and Proposition \[c4.3\]. Observe that the relative compactness of $U$ implies that the function $\lz$ appearing is bounded from above on $U$. Without loss of generality, we may assume that $\boz=\rn$ and that the diffusion matrix $A$ satisfies $$\label{e4.1} \frac1{\lz}|\xi|^2\le \langle A(x)\xi,\,\xi\rangle\le \lz|\xi|^2$$ for almost all $x\in\boz$ and $\xi\in\rr^n$, where $\lz\ge1$ is a fixed constant. Observe that $(\rn,\,d_A)$ is a length space (see for example [@s10]), and hence a geodesic space due to its local compactness. Since we have no regularity of continuity assumption on the diffusion matrix, the approach of using the Aronsson equations is not applicable. Instead of this we characterize absolute minimizers via intrinsic distance; see for example [@gpp; @gwy; @cp; @dmv]. The following Lemma \[l4.5\] connects the absolute minimizer with a description via pointwise Lipschitz constants; its proof relies on (the key) Lemma \[l4.6\]. \[l4.5\] Let $u\in \lip(U)$. Then $u$ is an absolute minimizer on $U$ if and only if for each bounded open subset $V\Subset U$ and all $v\in \lip(V)\cap C(\overline V)$ with $u|_{\partial V}= v|_{\partial V}$, one (both) of the following holds: [(]{}i[)]{} $\esssup_{x\in V} \lip_{d_A}u(x) \le {\esssup}_{x\in V} \lip_{d_A}v(x);$ [(]{}ii[)]{} $\sup_{x\in V} \lip_{d_A}u(x) \le {\sup}_{x\in V} \lip_{d_A}v(x).$ \[l4.6\] For every bounded open set $V\subset \rn$ and every $u\in\lip_\loc(\rn)$, we have $$\label{e4.2} \esssup_{x\in V}\sqrt{H(x,\,\nabla u(x))}=\esssup_{x\in V} \lip_{d_A}u(x) = \sup_{x\in V} \lip_{d_A}u(x).$$ By Lemma \[l2.1\], we always have $$\sqrt {F(u,\,V)}:=\esssup_{x\in V}\sqrt{H(x,\,\nabla u(x))}\le \esssup_{x\in V} \lip_{d_A}u(x) \le\sup_{x\in V} \lip_{d_A}u(x).$$ It then suffices to show that $ \sup_{x\in V} \lip_{d_A}u(x)\le \sqrt {F(u,\,V)}$, which is further reduced to showing that for every $x\in V$, there exists $r_x<d_A(x,\,\partial V)$ such that for all $y\in B_{d_A}(x,\,r_x)$, $$\label{e4.xx2} |u(x)-u(y)|\le \sqrt {F(u,\,V)}d_A(x,\,y).$$ We divide the proof of into 4 steps. [*Step 1.*]{} Fix $x\in V$ and $0<r <\frac{1}{4}d_A(x,\,\partial V)$. Extend $u$ from $B_{d_A}(x,\,r)$ to $\rn$ via a McShane extension as follows: $$u_{x,\,r}(y)=\inf_{z\in B_{d_A}(x,\,r)}\{u(z)+\lip_{d_A}(u,\,B_{d_A}(x,\,r))d_A(z,\,y)\}.$$ Then $u_{x,\,r}=u$ on $B_{d_A}(x,\,r)$, and $$H(z,\,\nabla u_{x,\,r}(z))=H(z,\,\nabla u (z))\le F(u,\,B_{d_A}(x,\,r)) \le F(u,V)$$ for almost all $z\in B_{d_A}(x,\,r)$, and by Lemma \[l2.1\], $$\sqrt{H(z,\,\nabla u_{x,\,r}(z))}\le \lip_{d_A}u_{x,\,r}(z)\le \lip_{d_A}(u,\,B_{d_A}(x,\,r))$$ for almost all $z\notin B_{d_A}(x,\,r)$. [*Step 2.*]{} By the proof of Lemma \[comp-dist\] and the ellipticity condition , we have $d_A(x,y)\ge |x-y|/\sqrt{\lambda}$. Hence it follows from the last part of Step 1 above that for almost all $z\in\rn\setminus B_{d_A}(x,\,r)$, $$\begin{aligned} \sqrt{H(z,\,\nabla u_{x,\,r}(z))}\le \lip_{d_A}(u,\,B_{d_A}(x,\,r))&\le \sqrt{\lambda}\, \lip(u,\,B_{d_A}(x,\,r))\\ &= \sqrt{\lambda}\, \sup_{B_{d_A}(x,r)}|\nabla u|\le \lambda\, \sqrt{F(u,V)}. \end{aligned}$$ [*Step 3.*]{} Now we set $$\wz A=1_{B_{d_A}(x,\,r)}\, A+ \frac1{2\lambda} \,1_{\rn\setminus {B_{d_A}(x,\,r)}}\, A$$ and denote by $\wz H$ and $d_{\wz A}$ the corresponding Hamiltonian and intrinsic distance. Then for each $z\in B_{d_A}(x,\,r)$, there exists $0<r_z<r-d_A(z,x)$ such that whenever $d_{A}(z,\,y)<r_z$, we have $$\label{e4.xx4}d_{\wz A}(z,\,y)=d_A(z,\,y).$$ This is seen by modifying the proof of Lemma \[comp-dist\] by replacing the Euclidean metric with the metric $d_A.$ Indeed, notice that there exists a constant $\overline C\ge 1$ such that for all $z,\,y\in\rn$, $$\frac1{\overline C}d_{ A}(z,\,y)\le d_{\wz A}(z,\,y)\le \overline C d_{ A}(z,\,y).$$ For $r_z< \frac1{(\overline C)^2} (r-d_A(z,x))$, we have $$B_{d_{ A}}(z,\,r_z)\subset B_{d_{\wz A}}(z,\,\overline Cr_z)\subset B_{d_{ A}}(z,\,(\overline C)^2 r_z)\subset B_{d_{ A}}(x,\, r).$$ Set $$v_{z,\,r_z}(y)=\min\{d_{\wz A}(z,\,y),\,r_z\}.$$ We see that $$H(y,\,\nabla v_{z,\,r_z}(y))=\wz H(y,\,\nabla v_{z,\,r_z}(y))\le (\lip_{d_{\wz A}}v_{z,\,r_z}(y))^2\le 1$$ for almost all $y\in B_{d_{\wz A}}(z,\,\overline Cr_z)$ and $$H(y,\,\nabla v_{z,\,r_z}(y))=\wz H(y,\,\nabla v_{z,\,r_z}(y))=0$$ for almost all $y\notin B_{d_{\wz A}}(z,\,\overline Cr_z)$. Hence using $v_{z,\,r_z}$ in the definition of $d_A$, we have $d_{A}(z,\,y)\ge d_{\wz A}(z,\,y)$ for all $y\in B_{d_{\wz A}}(z,\,\overline Cr_z)$ and hence $y\in B_{d_{ A}}(z,\,r_z)$. Similar argument show to that $d_{A}(z,\,y)\ge d_{\wz A}(z,\,y)$ for all $y\in B_{d_{ A}}(z,\,r_z)$. We conclude from these inequalities. [*Step 4.*]{} From the discussion in Steps 1 and 2, $$\wz H(z,\,\nabla u_{x,\,r}(z))\le F(u,\,V)$$ for almost every $z$. Hence, using $\frac1{\sqrt{F(u,\,V)}}u_{x,\,r}$ in the definition of $ d_{\wz A}$, we see that for all $z,\,y\in\rn$, $$\frac1{\sqrt{F(u,\,V)}} |u_{x,\,r}(z)-u_{x,\,r}(y)|\le d_{\wz A}(z,\,y).$$ In particular, for all $z,\,y\in B_{d_A}(x,\,r)$, since $u(z)= u_{x,\,r}(z)$ and $u(y)= u_{x,\,r}(y)$, we have $$|u(z)-u(y)|\le\sqrt{F(u,\,V) }d_{\wz A}(z,\,y) =\sqrt{F(u,\,V) }d_{A}(z,\,y).$$ Applying this with $z=x$ and $y\in B_{d_A}(x,\,r_x)$, we obtain . \[r4.7\]By Lemma \[l2.1\] above, we always have $H(x,\,\nabla u(x))\le (\lip_{d_A}u(x))^2$ almost everywhere. But Proposition \[p3.1\] shows that it may happen that $H(x,\,\nabla u(x))<(\lip_{d_A}u(x))^2$ on a set with positive measure, and hence we can not expect $H(x,\,\nabla u(x))= (\lip_{d_A}u(x))^2$ almost everywhere. But as a compensation, Lemma \[l4.6\] provides a weak variant for this: $$\esup_{z\in B(x,\,r)}H(z,\,\nabla u(z))=\esup_{x\in B(x,\,r)} (\lip_{d_A}u(z))^2=\sup_{x\in B(x,\,r)} (\lip_{d_A}u(z))^2$$ for all $x$ and small $r$. This phenomenon persists in the setting of general regular, strongly local Dirichlet forms; see the companion paper [@ksz] of this paper. Notice that our concept of absolutely minimizing Lipschitz extension defined in Section 1 corresponds to the strongly absolutely minimizing Lipschitz extension in [@jn]. Recall that implies that $(\rn,\,d_A,\,dx)$ is a doubling metric measure space supporting a $(1,1)$-Poincaré inequality. By Lemma \[l4.5\] and [@jn Theorem 3.1], we have the following existence result. \[l4.8\] For every $f\in \lip(\partial U)$, there exists an absolutely minimizing Lipschitz extension. The uniqueness of an absolute minimizing Lipschitz extension will follow from the comparison formula. \[l4.9\] Let $u,\,v\in \lip(U)\cap C(\overline U)$ be absolute minimizers on $U$. Then $$\max_{x\in \overline U}[u(x)-v(x)]= \max_{x\in \partial U}[u(x)-v(x)].$$ To prove Lemma \[l4.9\], we need the following lemmas. First, as a consequence of Lemma \[l4.5\], we have the following result. \[l4.50\] If $u$ is an absolute minimizer on $U$, then for all open subsets $V\Subset U$, $\lip_{d_A}(u,V)=\lip_{d_A}(u,\partial V).$ Notice that for every pair $x,\,y\in\partial V$ with $x\ne y$, by the continuity of $d_A$ we can find $x_n,\,y_n\in V$ such that $x_n\to x$ and $y_n\to y$. By the continuity of $u$, $\frac{|u(x_n)-u(y_n)|}{d_A(x_n,\,y_n)}\to\frac{|u(x)-u(y)|}{d_A(x,\,y)}$ and hence $\lip_{d_A}(u,\,V)\ge \lip_{d_A}(u,\,\partial V)$. Thus it suffices to prove the converse. For $x\in\rn$, set $$w(x)=\sup_{z\in\partial V}[u(z)+\lip_{d_A}(u,\,\partial V) d_A(x,\,z)].$$ Then $\lip_{d_A}(w,\,\rn)=\lip_{d_A}(u,\,\partial V)$ and $w=u$ on $\partial V$. Applying Lemma \[l4.5\], we have $$\sup_{x\in V}\lip_{d_A} u(x)\le \sup_{x\in V}\lip_{d_A} w(x)\le \lip_{d_A}(u,\,\partial V).$$ Now, given a pair of points $x,\,y\in U$, let $\gz$ be a $d_A$-geodesic curve joining $x$ and $y$. The existence of $\gz$ is guaranteed by the fact that $(\rn,\,d_A)$ is a geodesic space [@s10]. If $\gz\subset V$, then $$|u(x)-u(y)|\le \int_\gz\lip\, u(z)\,d_Az\le d_A(x,\,y)\,\sup_{x\in V}\lip_{d_A} u(x) \le d_A(x,y)\, \lip_{d_A}(u,\,\partial V).$$ Here $d_Az$ denotes arc-length integral on $\gz$ with respect to the metric $d_A$. If $\gamma\not\subset V$, denote by $\hat x$ and $\hat y\in \gz\cap\partial V$ points that have shortest distance to $x$ and $y$, respectively. Then $$\begin{aligned} |u(x)-u(y)|&&\le |u(x)-u(\hat x)|+|u(\hat x)-u(\hat y)|+|u(\hat y)-u(y)|\\ &&\le [d_A( x,\,\hat x)+d_A( y,\,\hat y)]\sup_{x\in V}\lip_{d_A} u(x) +d_A( \hat x,\,\hat y)\lip_{d_A}(u,\,\partial V)\\ &&\le d_A( x,\, y)\lip_{d_A}(u,\,\partial V).\end{aligned}$$ In either case, we have the inequality $$\frac{|u(x)-u(y)|}{d_A(x,y)}\le \lip_{d_A}(u,\,\partial V).$$ This means that $\lip_{d_A}(u,\,V)\le \lip_{d_A}(u,\,\partial V)$. A function $u\in C(U)$ is said to satisfy the [*property of comparison with cones*]{} if for all each subset $V\Subset U$, and for all $a\ge0$, $b\in\rr$ and $x_0\in\rn\setminus V$, we have \(i) $\max_{x\in \partial V}[u(x)-C_{b,a,x_0}(x)]\le0$ implies $\max_{x\in V}[u(x)-C_{b,a,x_0}(x)]\le0;$ \(ii) $\max_{x\in \partial V}[u(x)-C_{b,-a,x_0}(x)]\ge0$ implies $\max_{x\in V}[u(x)-C_{b,-a,x_0}(x)]\ge0,$ where the cone function is defined by $C_{b,a,x_0}(x)=b+a\,d_A(x,\,x_0).$ It is known that an absolute minimizer satisfies the comparison property with cones; see [@ceg] for Euclidean case and [@acj; @jn; @gwy; @cp; @dmv] for the setting of metric spaces that are length spaces. For the sake of completeness, we sketch a proof below. \[l4.51\] An absolute minimizer satisfies the property of comparison with cones. We prove Condition (i), with the proof of Condition (ii) similar (and left to the interested reader). Let $u$ be an absolute minimizer and assume that $\max_{x\in \partial V}[u(x)-C_{b,a,x_0}(x)]\le0$. Suppose that the condition $\max_{x\in V}[u(x)-C_{b,a,x_0}(x)]\le0$ is *not* true. Denote by $W$ the open set of all $x\in V$ such that $u(x)>C_{b,a,x_0}(x)$. By the above supposition, $W$ is not empty. We can see that $u= C_{b,a,x_0}$ on $\partial W$. Since $W\subset V\Subset U$, by Corollary \[l4.50\] we have $\lip_{d_A}(u,\overline W)=\lip_{d_A}(u,W)=\lip_{d_A}(u,\partial W)=a$. For $x\in W$, let $\gz$ be the $d_A$-geodesic curve joining $x$ and $x_0$, and take $z\in\partial V\cap \gz$ be a closest point to $x$. Then $$u(x)-u(z)>C_{b,a,x_0}(x)-C_{b,a,x_0}(z)= ad_A(x_0,\,x)-a{d_A}(x_0,\,z)=ad_A(x,\,z),$$ which implies that $\lip_{d_A}(u,\,W)>a$. This is a contradiction. So $W$ must be empty. With the aid of Lemma \[l4.5\] and Lemma \[l4.51\], Lemma \[l4.9\] will be proved by following the procedure from [@as]. Since the proof in [@as] is for the case $A=I_n$, we write down the details below for the reader’s convenience. For $x\in U_r=\{z\in U:\ \overline{B_{d_A}(z,\,r)}\subset U\}$ with $r>0$, we set $u^r(x)= \sup_{d_A(z,\,x)\le r} u(z)$ and $u_r(x)= \inf_{d_A(z,\,x)\le r} u(z)$ and also $$S_r^+u(x)= \frac{u^r(x)-u(x)}{r},\quad S_r^-u(x)=\frac{u(x)-u_r(x)}{r}.$$ First we claim that for $x\in U_{2r}$, $$\label{e4.x5} S_r^-u^r(x)-S_r^+u^r(x)\le0\le S_r^-v_r(x)-S_r^+v_r(x).$$ Indeed, let $y\in \overline {B_{d_A}(x,\,r)}$ and $z\in \overline {B_{d_A}(x,\,2r)}$ such that $u^r(x)=u(y)$ and $(u^{r})^r(x)=u^{2r}(x)=u(z)$. Observe that $(u^r)_r(x)\ge u(x)$. We then have $$S_r^-u^r(x)-S_r^+u^r(x)=\frac1{r}[2u^r(x)-(u^r)^r(x)-(u^r)_r(x)] \le \frac1{r}[2u (y)-u(z)-u(x)].$$ For $w\in\boz$ such that $d_A(x,\,w)=2r$, we have $$u(w)\le u (z)=u(x)+ [u (z)-u(x)]= u(x)+\frac{[ u (z) -u(x)]}{2r}d_A(w,\,x).$$ Thus the comparison with cones property of $u$ implies that the inequality $$u(w)\le u(x)+\frac{[ u (z) -u(x)]}{2r}d_A(w,\,x)$$ holds for all $w\in\boz$ with $d_A(x,\,w)\le 2r$. In particular, taking $w=y$ and by $d_A(y,\,x)\le r$, we have $$u(y)\le u(x)+\frac{[ u (z) -u(x)]}{2r}d_A(y,\,x)\le u(x)+\frac12{[ u (z) -u(x)]}=\frac12{[ u (z)+u(x)]},$$ which implies the first inequality of . The second inequality of follows similarly. Notice that further implies $$\label{e4.xx5} \sup_{x\in U_r}[u^r(x)-v_r(x)]= \sup_{x\in U_r\setminus U_{2r}}[u^r(x)-v_r(x)].$$ Given the above, letting $r\to0$ in , we obtain Lemma \[l4.9\]. Thus it remains only to prove . Assume that is [*not*]{} true. Then there is some $r>0$ for which $$sup_{x\in U_r}[u^r(x)-v_r(x)] > \sup_{x\in U_r\setminus U_{2r}}[u^r(x)-v_r(x)].$$ By the continuity of $u^r -v_r $, there must exist some $y\in \overline {U}_{r}$ such that $[u^r(y)-v_r(y)]=\sup_{x\in U_{ r}}[u^r(x)-v_r(x)]$. Because fails, we know that $y\in U_{2r}$. Denote by $E$ all such $y$ and set $F=\{x\in E: \ u^r(x)=\max_{z\in E} u^r(z)\}$. Then $F$ is a closed subset of $U_{2r}$ by the continuity of $u^r$ again. Choose $x_0\in\partial F$. Then because $x_0\in E$, for every $x\in U$ we have $$u^r(x_0)-v_r(x_0)\ge u^r(x )-v_r(x ),$$ and it follows from the fact that $x_0\in U_{2r}$ and for every $x\in B_{d_A}(x_0,r)$, $$u^r(x_0)-v_r(x_0)\ge \inf_{z\in B_{d_A}(x_0,r)} u^r(z)-v_r(x)=(u^r)_r(x_0)-v_r(x).$$ Taking the infimum over $x\in B_{d_A}(x_0,r)$, we obtain $S_r^-v_r(x_0)\le S_r^-u^r(x_0)$. [*Case 1:*]{} $S^+_ru^r(x_0)=0$. Then by , we have $S_r^-u^r(x_0)\le0$ and hence $S_r^-u^r(x_0)=0$, which together with $S_r^-v_r(x_0)\le S_r^-u^r(x_0)$ implies that $S_r^-v_r(x_0)=0$. By again, we have $S_r^+v_r(x_0)\le0$ and hence $S_r^+v_r(x_0)=0$. So $u^r$ and $v_r$ are constant on $ B_{d_A}(x_0,\,r)$. This contradicts $x_0\in\partial F$. [*Case 2:*]{} $S^+_ru^r(x_0)>0$. Choose $z\in\overline B_{d_A}(x_0,\,r)$ such that $rS^+_ru^r(x_0)=u^r(z)-u^r(x_0)$. Since $u^r(z)>u^r(x_0)$ and $x_0\in F$, we know that $z\notin E$. Therefore $u^r(x_0)-v_r(x_0)> u^r(z)-v_r(z)$, and hence $$rS^+_rv_r(x_0)\ge v_r(z)-v_r(x_0)>u^r(z)-u^r(x_0)=rS^+_ru(x_0),$$ which together with $S_r^-v_r(x_0)\le S_r^-u^r(x_0)$ again yields that $$S^+_rv_r(x_0)-S_r^-v_r(x_0)> S^+_ru^r(x_0)-S_r^-u^r(x_0).$$ This is a contradiction of . So our assumption is not correct and hence is true. Now we are ready to prove Theorem \[t4.1\]. Theorem \[t4.1\] (i) follows from Lemmas \[l4.8\] and \[l4.9\]. Theorem \[t4.1\] (ii) follows from Lemma \[l4.5\] with the observation that under the assumption , $\lip_{d_A}u=\lip_{d_{ \wz A}}u$ almost everywhere for every $u\in \lip_\loc(\rn)$. Proposition \[c4.3\] will follow from Theorem \[t3.1\] and the following result; see [@jn Lemma 5.6] for the proof. \[l4.52\] Let $u\in\lip (U)$ be an absolute minimizer. Then for all $x\in U$, we have $$\lip_{d_A}u(x)=\lim_{r\to0} S^+_ru(x)=-\lim_{r\to0} S^-_ru(x).$$ Moreover, $S^+_ru(x)$ and $S^-_ru(x)$ are increasing function with respect to $r\in(0,\,d_A(x,\,\partial U))$. We prove Proposition \[c4.3\] on $U=[0,1]^n\supset S_{\bf a}$. The proof is in two steps. [*Step 1:*]{} In this step we show that each absolute minimizer on $U$ that is of class $C^1$ must satisfy $\nabla u=0$ on $S_{\bf a}$. Suppose that $u$ is an absolute minimizer on $U$ that is of class $C^1$. Observe that $\lip_{d_A}u$ is upper semicontinuous on $U$, that is, for any $x\in U$, we have $\lip_{d_A}u(x)\ge\limsup_{z\to x} \lip_{d_A}u(z).$ To see this, recall that the upper semicontinuity is equivalent to the property that for all $L>0$, $E_L=\{x\in U: \lip_{d_A}u(x)<L \}$ is open. Without loss of generality, we may assume that $E_L$ is not empty. Let $x\in E_L$. By Lemma \[l4.52\], we know that for all $z\in U$, $$\label{e4.xx6} \lip_{d_A}u(z)=\inf_{0<r<d_A(z,\,\partial U)} S^+_ru(z)=\inf_{0<r<d_A(z,\,\partial U)}\frac{u^r(z)-u(z)}{r}.$$ It is easy to see that for each $r>0$, $u^r$ and hence $S^+_ru$ is continuous on $U_r=\{y\in U: d_A(y,\,\partial U)>r\}$. Since $x\in E_L$, applying , we have $S_r^+u(x)<L$ for some $0<r<d_A(x,\,\partial U)/2$. By the continuity of $S_r^+u$ at $x\in U_r$, we know that there exists $r>\dz>0$ such that $B_{d_A}(x,\,\dz)\subset U_r$ and $S_r^+u(z)<L$ for all $z\in B_{d_A}(x,\,\dz)$. Since $d_A(z,\,\partial U)>r$, by again, we have $\lip_{d_A}u(z)\le S_r^+u(z)<L$. This means $E_L$ is open and hence gives the upper semicontinuity of $\lip_{d_A}u$ as desired. Applying Theorem \[t3.1\], we further obtain that $\lip_{d_A}u(x)=\sqrt{H(x,\,\nabla u(x))}$ for almost all $x\in U$, which yields that $x\mapsto H(x,\,\nabla u(x))$ is weak upper semicontinuous on $U$. In particular, for almost all $x\in K$, there exists a set $E$ (which may depend on $x$) with measure zero such that $$H(x,\,\nabla u(x))\ge\limsup_{y\in U\setminus E,\ y\to x} H(y,\,\nabla u(y)) \ge \limsup_{y\in U\setminus (S_{\bf a}\cup E),\ y\to x} H(y,\,\nabla u(y)).$$ [Note by the construction of $S_{\bf a}$ that whenever $x\in S_{\bf a}$ and $r>0$, the Lebesgue measure of $B(x,r)\setminus S_{\bf a}$ is positive. Therefore $x$ is a cluster point of $\mathbb{R}^n\setminus (S_{\bf a}\cup E)$, and hence the above limit supremum makes sense.]{} This, together with the continuity of $\nabla u$, implies that $$\begin{aligned} (1-\dz) |\nabla u(x)|^2\ge \limsup_{y\in U\setminus (S_{\bf a}\cup E),\ y\to x}|\nabla u(y)|^2=|\nabla u(x)|^2. \end{aligned}$$ This is a contradiction if $\nabla u(x)\ne 0$ and $\dz>0$. Hence it follows that each absolute minimizer $u$ on $U$ must satisfy $\nabla u=0$ on $S_{\bf a}$ if $\nabla u$ is continuous on $U$. [[*Step 2:*]{}]{} Now we show the existence of an absolute minimizer $u$ on $U$ which is either not of class $C^1$, or else satisfies $\nabla u\ne0$ on some set $K$ of $S_{\bf a}$ with positive measure. Consider the absolute minimizer $u$ on $U$ with boundary data $f(x)=x_1$. Assume that $u\in C^1(U)$. Due to the continuity of $\nabla u $, it suffices to show that $\nabla u(x)\ne 0 $ for some $x\in S_{\bf a}$. We prove this by contradiction. Assume that $\nabla u(x)= 0 $ for all $x\in S_{\bf a}$. Then for any $\ez>0$, there exists $0<\ez'<\ez$ such that for all $x\in U_\ez=\{y\in [\ez,\,1-\ez]\times[0,\,1]^{n-1}: \dist_\rn(y,\, S_{\bf a})<\ez'\}$ we have $|\nabla u(x)|\le\ez$. Fix $x'\in\mathbb{R}$ such that $|x'|<\ez'$, and choose $x,\,y\in \partial U$ such that $x=(0,\,x')$, $y=(1,\,x')$ and let $\gz$ be the line segment joining $x,\,y$. >From the construction of $S_{\bf a}$, we see that $\gz\cap[\ez,\,1-\ez]\times[0,\,1]^{n-1}\subset U_\ez$ when $\ez'$ is small enough and hence, $$\int_\ez^{1-\ez}|\nabla u((\gz(t)))|\,dt\le \ez (1-2\ez).$$ Moreover, since $$\begin{aligned} |\nabla u(z)|&&=\lip\, u(z)\le \frac1{\sqrt{1-\dz}} \lip_{d_{S_{\bf a},\,\dz}}(u,\,U)\\&&\le \frac1{\sqrt{1-\dz}}\lip_{d_{S_{\bf a},\,\dz}}(f,\,\partial U)\le \frac1{ 1-\dz}\lip (f,\,\partial U)=\frac1{ 1-\dz}\end{aligned}$$ for all $z\in U$, we have $$\lf(\int_0^\ez+\int_{1-\ez}^1\r) |\nabla u((\gz(t)))|\,dt\le 2\ez\frac1{ 1-\dz}.$$ Thus $$1=|u(x)-u(y)|=\lf |\int_\gz (u\circ\gz)'(t)\,dt\r|\le \int_0^1|\nabla u((\gz(t)))|\,dt\le 2\ez\frac1{ 1-\dz}+\ez (1-2\ez).$$ Taking $\ez$ small enough, the term $2\ez\frac1{ 1-\dz}+\ez (1-2\ez)<1$, which is a contradiction. So the assumption is not true and $\nabla u(x)\ne0$ for some $x\in S_{\bf a}$, which contradicts Step 1 above. Therefore $u$ is not of class $C^1$ on $U$. This proves Proposition \[c4.3\]. Finally, for later use, we list some more characterizations of absolute minimizers. \[l4.53\] The following conditions on $u$ are equivalent: \(i) $u$ is an absolute minimizer on $U$. \(ii) $u$ satisfies the property of comparison with cones. \(iii) for all open sets $V\Subset U$, $\lip_{d_A}(u,\,V)=\lip_{d_A}(u,\,\partial V)$. From Lemmas \[l4.50\] and \[l4.51\], it follows that (i)$\Rightarrow$(ii), (iii). To obtain (ii)$\Rightarrow$(i), we only need to notice that, with the help of Lemma \[l4.6\], the argument provided by the proof of [@jn Proposition 5.8] still works here, without the additional weak Fubini property required in [@jn]; see also [@acj]. The proof of (iii)$\Rightarrow$(ii) follows directly from the proof of Lemma \[l4.51\]. Linear approximation when $A$ is continuous on $\boz$ {#s5} ===================================================== In this section we only consider $n\ge2$. \[t5.1\] Let $A\in\mathscr A(\boz)$, $U\subset\boz$ and $u$ be an absolute minimizer on $U$. If $A$ is continuous at $x\in U$, then for every sequence $\{r_j\}_{j\in\nn}$ that converges to $0$, there exists a subsequence ${\bf r}=\{r_{j_k}\}_{k\in\nn}$ and a vector ${\bf e}_{x,\,\bf r}$ such that $$\label{e2.x5} \lim_{k\to\fz}\lf| \frac{u(x+r_{j_k}y)-u(x)}{r_{j_k}}-\langle {\bf e}_{x,\,\bf r},\, y\rangle\r|=0$$ and $H(x,\,{\bf e}_{x,\,\bf r})= \lip_{d_A} u(x)$. Consequently, if $A $ is continuous on $U$, then holds for all $x\in U$. To prove Theorem \[t5.1\], we need the following auxiliary lemmas. We first [ look]{} at the case $x=0\in U$, $u(0)=0$ and ${ \lip_{d_A}} u(0)\ne0$. For any $r_0\in(0,\,d_A(0,\,\partial U))$, we know that $u$ is an absolute minimizer on $B(0,\,r_0)\Subset U$. Moreover, $\nabla u\in L^\fz(B(0,\,r_0))$ and the ellipticity function $\lz$ of is bounded on $B(0,\,r_0)$. In what follows, we fix such a radius $r_0$, and without loss of generality, we write $U=B(0,\,r_0)$ and assume that $r_{j+1}<r_j<r_0$ for all $j$. For each $j\in\nn$ we scale the absolute minimizer $u$ by setting $$u_j(y)=\frac{u(r_j y)}{r_j}$$ for all $y\in \frac1{r_j} U=\{\frac1{r_j}x,\,x\in U\}$. For each $j\in\nn$, points $x\in\frac1{r_j}U$, and $\xi\in\rn$, set [ $A_j(x)=A(r_j x)$,]{} and also set [ $A_\infty(x)=A(0)$. Furthermore, for vectors $\xi\in S^{n-1}$, set]{} $H_\fz(\xi)=\langle A(0)\xi,\,\xi\rangle$. Denote by $d_j$ the intrinsic distance of [ $A_j $]{} for $j\in\nn\cup\{\fz\}$. There exists $u_\fz\in W^{1,\,\fz}(\rn)$ and a subsequence $\{r_{j_k}\}_{k\in\nn}$ of $\{r_j\}_{j\in\nn}$ such that $ u_{j_k}$ converges to $u_\fz $ locally uniformly and in weak $W^{1,\,\fz}(\rn)$. Since $\nabla u\in L^\fz(U)$ and $U=B(0,\,r_0)$ is convex, we know that $\lip (u,\,U)\le\|\nabla u\|_{L^\fz(U)}$. Extend $u$ to $\rn$ by the McShane extension, that is, set $$\wz u(x)=\sup_{z\in U}\{u(z)+ \lip (u,\,U)|x-z|\}$$ for all $x\in\rn$. Moreover, for each $j\in\nn$ and all $x\in\rn$, let $\wz u_j(x)=\frac{\wz u(r_jx)}{r_j}$ [ is such a McShane extension from $B(0,r_0/r_j)$ to $\mathbb{R}^n$.]{} On $\rn$ we have $\nabla \wz u_j(y)=(\nabla \wz u)(r_j y)$ and $\nabla \wz u\in L^\fz(\rn)$, [ so it follows that]{} $ \wz u_j \in W^{1,\,\fz}(\rn)$ with $\|\nabla\wz u_j \|_{L^\fz(\rn)} =\|\nabla\wz u \|_{L^\fz(\rn)}=\|\nabla u\|_{L^\infty(B(0,r_0))}<\fz$. Therefore, [ by the Arzela-Ascoli theorem,]{} there exists a subsequence $\{j_k\}_{k\in\nn}$ of $\nn$ and $u_\fz\in W^{1,\,\fz}(\rn)$ such that $ \wz u_{j_k}$ converges to $u_\fz$ locally uniformly and [in weak $W^{1,\,\fz}(\rn)$]{} [ This means that for each $(n+1)$-tuple of compactly supported continuous functions $(\phi_0,\phi_1,\cdots,\phi_n)$, we have $$\lim_k \int_{\mathbb{R}^n}\left[\wz u_{j_k}(x)\phi_0(x)+\sum_{i=1}^n\phi_i(x)\partial_i\wz u_{j_k}(x)\right]\, dx =\int_{\mathbb{R}^n}\left[u_\fz(x)\phi_0(x)+\sum_{i=1}^n\phi_i(x)\partial_iu_\fz(x)\right]\, dx.$$ This weak convergence (strictly, to be called weak-\* convergence), follows from the Banach-Alaouglu theorem upon noting that $W^{1,\infty}(\mathbb{R}^n)$ is a subset of the dual of the Banach space $(L^1(\mathbb{R}^n))^n$, together with Mazur’s lemma.]{} Notice that $u_j(x)=\wz u_j(x)$ whenever $x\in \frac1{r_j}U=B(0,r_0/r_j)$ for all $j\in \nn$. Given a compact set $K$, there exists a constant $j_K$ such that for all $j\ge j_K$, $K\subset\frac1{r_j}U$. Therefore $\wz u_j$ converges to $u_\fz$ on $K$ uniformly implies that $ u_j$ converges to $u_\fz$ uniformly as $j_K\le j\to\fz$. In what follows, for simplicity, we always write the subsequence $\{{j_k}\}_{k\in\nn}$ of $\nn$ obtained in above Lemma 5.2 as $\nn$ by abuse of notation. \[l5.2\] [(]{}i[)]{} For all $j\in\nn$, $u_j$ is an absolute minimizer on $\frac1{r_j}U$ associated to the Hamiltonian $H_j$ which corresponds to $A_j$. [(]{}ii[)]{} If $A$ is continuous at $0$, then $u_\fz$ is an absolute minimizer on $\rn$ associated to the Hamiltonian $H_\fz$. To prove this, we need two facts given in the following; the second one relies on the continuity of $A$ at $0$. We postpone the proof of Lemma \[l2.x2\] until after the proof of Lemma \[l5.2\]. \[l2.x2\] [(]{}i[)]{} For $j\in\nn$ and $x,\,y\in\rn$, $r_j d_j(x,\,y)= {d_A}(r_j x,\,r_j y)$. [(]{}ii[)]{} Assume that $A$ is continuous at $0$. Given a compact set $K$ and $x\in\rn$, for every $\ez>0$, there exists $j(x,\,\ez,\,K)\in\nn$ such that for all $j\ge j(x,\,\ez,\,K)$ and all $y\in K$, $$(1-\ez)d_\fz(x,\,y)\le {d_j(x,\,y)} \le(1+\ez )d_\fz(x,\,y).$$ [*Proof of [(]{}i[)]{}:*]{} Let $j\in\nn$. It suffices to show that for all open subsets $V\Subset \frac1{r_j}U$, $\lip_{d_j}(u_j,\,V)=\lip_{d_j}(u_j,\,\partial V)$. By Lemma \[l2.x2\] (i) and observing that $x,\,y\in V$ implies $r_jx,r_jy\in r_jV\Subset U$, we have $$\frac{u_j(x)-u_j(y)}{d_j(x,\,y)}= \frac{u (r_jx)-u(r_jy)}{{d_A}(r_j x,\,r_j y)} ,$$ which yields $\lip_{d_j}(u_j,\,V)= \lip_{d_A}(u,\, {r_j}V)$. Similarly, $\lip_{d_j}(u_j,\,\partial V)= \lip_{d_A}(u,\, \partial({r_j}V))$ with the help of $\partial{r_j}V=r_j\partial V$. Thus by $\lip_{d_A}(u,\, {r_j}V)=\lip_{d_A}(u,\, \partial({r_j}V))$, we obtain $\lip_{d_j}(u_j,\,V)= \lip_{d_j}(u_j,\,\partial V) $. [ Thus the claim follows from Lemma \[l4.53\].]{} [*Proof of [(]{}ii[)]{}:*]{} It suffices to show that $u_\fz$ satisfies the comparison property with cones. Let $V\Subset\rn$ and assume that for each $z\in\partial V$, $$\label{e5.xx1} u_\fz(z)\le b+ad_\fz(z_0,\,z)$$ for some $ z_0\notin V$, $b\in\rr$ and $a>0$ [ which are independent of $z$.]{} By Lemma \[l2.x2\] (ii), for every $\ez>0$, there exists $j_\ez$ such that whenever $j\ge j_\ez$ and $z\in \overline V $, we have $V\Subset \frac1{r_j}U$, $$(1-\ez) d_\fz(z_0,\,z)\le {d_j(z_0,\,z)} \le (1+\ez)d_\fz(z_0,\,z)$$ and [because $u_j\to u_\infty$ uniformly on the compact set $\overline{V}$, we also have]{} $$u_\fz(z)-\ez\le u_j(z)\le u_\fz(z)+\ez.$$ Thus by , $$u_j(z)\le (b+\ez)+{ \frac{a}{(1-\ez)}}d_j(z_0,\,z)$$ for all $z\in\partial V$. Since $u_j$ is an absolute minimizer on $\frac1{r_j}U$ associated to $H_j$ and $V\Subset \frac1{r_j}U$, we have $$u_j(z)\le (b+\ez)+{ \frac{a}{(1-\ez)}}d_j(z_0,\,z)$$ for all $z\in V$, which further implies that $$u_\fz(z)\le (b+2\ez)+{ \frac{a(1+\ez)}{(1-\ez)}}d_\fz(z_0,\,z)$$ for all $z\in V$. Due to the arbitrariness of $\ez$, we finally have $u_\fz(z)\le b+ad_\fz(z_0,\,z)$ for all $z\in V$. Similar argument also holds for $-u_\fz$. We omit the details. So, by Lemma \[l4.53\], $u_\fz$ is an absolute minimizer on $\frac1{r_j}U$ associated to the Hamiltonian $H_\fz$ [ for each $r_j$, and hence on $\mathbb{R}^n$.]{} \(i) Let [ $v$ be a locally Lipschitz function on $U$ such that $H(x,\nabla v(x))\le 1$ for almost every $x\in U$,]{} and let $v_j(z)=\frac1{r_j}v(r_jz)$. Since $H(z,\,\nabla v(z))\le 1$ for almost all $z\in\rn$, we have $$H_j(z,\,\nabla v_j(z))= H(r_j z,\,(\nabla v)(r_jz))\le 1$$ and hence $$d_j(x,\,y)\ge v_j(y)-v_j(x)$$ Taking the supremum over all such $v$, we see that $r_j d_j(x,\,y)\ge {d_A}(r_jx,\,r_jy)$. The inequality $r_j d_j(x,\,y)\le {d_A}(r_jx,\,r_jy)$ can be obtained similarly. \(ii) Given a compact set $K$ and $x\in\rn$, let $R>0$ and $j_x\in\nn$ be such that for all $j\ge j_x$, we have $K\cup\{x\}\subset B_{d_j}(0,\,R)\subset B_{d_j}(0,\,2R)\subset B (0,CR)\subset \frac1{r_j}U$, where $C>1$ is a constant depending on the lower and upper bounds of $\lz$ on $U$. We set $v_j(z)=\min\{d_j(x,\,z),\,R\}$ for all $z\in\rn$. Note that by Lemma \[l2.1\], $\langle A_j(z)\nabla v_j(z),\nabla v_j(z)\rangle\le 1$ for all $z\in\rn$, and that $ \nabla v_j(z) =0$ for $z\notin B(0,CR)$. Moreover, since $A$ is continuous at $0$, for sufficiently large $j_\ez>j_x$ we have that for all $z\in B (0,CR)$, $$|A_j(z)-A(0)|=|A(r_jz)-A(0)|<\ez,$$ where we consider the operator norm on $A_j(z)-A(0)$. So for almost every $z\in B(0,CR)$, $$\langle A(0)\nabla v_j(z),\nabla v_j(z)\rangle =\langle [A(0)-A_j(z)]\nabla v_j(z),\nabla v_j(z)\rangle +\langle\nabla A_j(z)\nabla v_j(z),\nabla v_j(z)\rangle\le L\ez+1,$$ where $L>0$ is a constant related to the bound of the ellipticity function $\lambda$ on $B(0,CR)$ such that $|\nabla v|\le L$ on $B(0,CR)$. It follows that $$w_j=\frac{1}{\sqrt{L\ez+1}}\, v_j$$ can be used to compute $d_\infty$ on $B(0,CR)$. Thus for $y\in K\subset B(0,CR)$, $$d_\infty(x,y)\ge w_j(x)-w_j(y)=\frac{v_j(x)-v_j(y)}{\sqrt{L\ez+1}},$$ that is $$d_\infty(x,y)\ge \frac{d_j(x,y)}{\sqrt{L\ez+1}}.$$ Now let $w(z)=\min\{d_\fz(x,\,z),\, R\}$ for $z\in\rn$. An argument similar to above yields that for $j\ge j_\ez$, $$\langle A_j(z)\nabla w(z),\nabla w(z)\rangle\le L\ez+1,$$ and so we obtain the reverse inequality $$d_j(x,y)\ge \frac{d_\infty(x,y)}{\sqrt{L\ez+1}}.$$ The conclusion of (ii) of the lemma follows. In what follows, $S^+_r u(x) $ is as in Section 4 and by Lemma \[l4.52\], when $u$ is an absolute minimizer [associated to the Hamiltonian $H$ that corresponds to $A$,]{} we know that $\lip_{d_A}u(x)=\lim_{r\to 0}S^+_ru(x)$. \[l5.3\]Assume that $A$ is continuous at $0$. Then [(]{}i[)]{} For all $r>0$, [ $S^+_r u_\fz(0)=\lip_{d_\fz}u_\fz(0) =\lip_{d_A}u(0)$ and $\sup_{x\in\rn}S^+_r u_\fz(x)\le \lip_{d_\fz}u_\fz(0)$.]{} [(]{}ii[)]{} $\sup_{x\in\rn}\lip_{d_\fz}u_\fz(x)=\lip_{d_\fz}(u_\fz,\,\rn)= \lip_{d_\fz}u_\fz(0).$ [ By Lemma \[l2.x2\], we know that $u_\fz$ is an absolute minimizer associated with $H_\fz$. Hence by Lemma \[l4.52\] and the claim (i) of this lemma, the claim (ii) will follow. Hence it suffices to prove the claim (i).]{} We first observe that $$\label{e5.x1} \lip_{d_\fz}(u_\fz,\,\rn)\le { \lip_{d_A}u(0)}.$$ Indeed, for all $x,\,y\in\rn$ with $x\ne y$, by $r_j d_j(x,\,y)= {d_A}(r_j x,\,r_j y)$, we have $$\begin{aligned} \label{eq:A} \frac{|u_\fz(x)-u_\fz(y)| }{d_\fz(x,\,y)} &&=\lim_{j\to\fz}\frac{| u_j(x)-u_j(y) |}{d_j(x,\,y)} = \lim_{j\to\fz}\frac{ |u (r_j x)-u (r_j y)|}{{d_A}(r_j x,\,r_j y)}.\end{aligned}$$ letting $\gz$ be the geodesic curve [ in the metric $d_j$ (and hence in the metric $d_A$)]{} joining $r_jx,\,r_jy$, (such $\gz$ exists when $j$ large enough because then $r_jx,r_jy\in B(0,R)$), we obtain $$|u (r_j x)-u (r_j y)|\le \int_\gz \lip_{d_A} u(z)|dz|\le\sup_{z\in\gz}{ \lip_{d_A}}u(z)\, {d_A}(r_jx,\,r_jy).$$ Thus $$\frac{|u_\fz(x)-u_\fz(y)|}{d_\fz(x,\,y)} \le\lim_{j\to\fz}\sup_{z\in B_{d_A}(0,\,{d_A}(r_j x,\,r_j y))}{ \lip_{d_A}u(z).}$$ Observing that [ $\lip_{d_A}u$]{} is upper semicontinuous (for details see the proof of Proposition \[c4.3\], [ in particular, ]{}), and by ${d_A}(r_jx,\,r_jy)\to0$ as $j\to\fz$, we arrive at $$\frac{|u_\fz(x)-u_\fz(y)|}{d_\fz(x,\,y)} { \le \lip_{d_A}} u(0).$$ [ This proves .]{} From and Lemma \[l4.52\], it also follows that ${ \lip_{d_\fz}} u_\fz(x)\le S^+_r u_\fz(x)\le { \lip_{d_A}}u( 0)$ for all $x\in\rn$ and $r>0$. Moreover, we [will show below that]{} $$\label{e5.xx9} %@@!!@@!! S^+_ru_\fz(0){ \ge \lip_{d_A}}u(0). %@@!!@@!!$$ [ From this, and applying the above discussion to $x=0$, by Lemma \[l4.52\] we have]{} $$S^+_ru_\fz(0)={ \lip_{d_\fz}} u_\fz(0)= { \lip_{d_A}}u(0)$$ for all $r>0$. Since we already have [ $\lip_{d_\fz}u_\fz(x)\le \lip_{d_\fz}(u_\fz,\mathbb{R}^n)$ for all $x\in\mathbb{R}^n$,]{} we obtain (i). This proves [ Lemma \[l5.3\]. ]{} Hence we end the proof of Lemma \[l5.3\] by establishing . By the continuity of [ $u_\fz$,]{} for every $\ez>0$ there exists $0<\dz_0<1/4$ such that whenever $\dz\in(0,\,\dz_0)$, $$\label{e2.x6} %S^+_ru_\fz(0)= \frac{\sup_{d_\fz(0,\,y)\le r}u_\fz(y)}{r}\ge \frac{\sup_{d_\fz(0,\,y)\le (1+\dz)r}u_\fz(y)}{(1+\dz)r} -\ez = S^+_{(1+\dz)r}u_\fz(0)-\ez;$$ and since $u_j\to u_\fz$ locally uniformly as $j\to\fz$, there exists $j_\ez\in\nn$ such that for all $j\ge j_\ez$ and $y\in B_{d_\fz}(0,\,2r)\setminus B_{d_\fz}(0,\,r/2)$, $$\label{e5.xx6} \frac{ u_\fz(y)-u_\fz(0)}{d_\fz(0,\,y)} \ge \frac{u_j(y)-u_j(0)}{ d_j(0,\,y)} -\ez = \frac{u(r_jy)-u (0)}{{d_A}(0,\,r_j y)}-\ez .$$ Moreover, by Lemma 5.4 (ii), for any $\dz\in(0,\,\dz_0)$, there exists $j_\dz$ such that such that for all $j\ge j_\dz$ and $y\in B_{d_\fz}(0,\,2r)$, $$\label{e5.xx7}(1-\dz){d_j}(0,\,y)\le d_\fz(0,\,y) \le (1+\dz){d_j}(0,\,y).$$ Let $z_j\in\rn$ such that $d_A(0,\, z_j)\le r_jr$ and $$\label{e5.xx8}\frac{u(z_j)-u (0)}{r_jr}=\frac{\max_{{d_A}(z,\,0)\le r_jr}u(z)-u(0)}{r_jr} =S^+_{r_jr}u(0)\ge { \lip_{d_A}}u(0).$$ By [the comparison Lemma \[l4.9\],]{} we know that $d_A(0,\, z_j)= r_jr$. Let $y_j=z_j/r_j$. Observe that whenever $j\ge j_\dz$, implies that $$d_\fz(0,\, y_j)\le (1+\dz)d_j(0,\, y_j)\le (1+\dz)\frac1{r_j}d_A(0,\, z_j)=(1+\dz) r$$ and similarly, $(1-\dz)r\le d_\fz(0,\,y_j).$ By this, the increasing property of $S^+_ru_\fz(0)$ with respect to $r$ given by Lemma \[l4.52\], , Lemma 5.4 (i) and , we have whenever $j\ge \max\{j_\dz,\,j_\ez\}$, $$\begin{aligned} S^+_{(1+\dz)r}u_\fz(0)&&\ge S^+_{d_\fz(0,\,y_j)}u_\fz(0) \ge \frac{ u_\fz(y_j)-u_\fz(0)}{d_\fz(0,\,y_j)}\\ && \ge \frac{u_j(y_j)-u_j(0)}{{d_j}(0,\,y_j )}-\ez = \frac{u(z_j)-u (0)}{{d_A}(0,\,z_j )}-\ez\ge { \lip_{d_A}}u(0)-\ez,\end{aligned}$$ which together with implies $S^+_{ r}u_\fz(0)\ge { \lip_{d_A}}u(0)-2\ez.$ From this, we conclude that $S^+_ru_\fz(0)\ge S^+u(0)$, and hence . \[l5.4\] Assume that $A$ is continuous at $0$. There exists ${\bf e}\in\rn$ such that $u_\fz(x)=\langle {\bf e},\,x\rangle$ for all $x\in\rn$ and [ $H_\fz(x,{\bf e})=\lip_{d_\fz}u_\fz(0)$.]{} Notice that by Lemma \[l5.2\], $u_\fz$ is an absolute minimizer on $\rn$ associated to the Hamiltonian $H_\fz$. Moreover $u_\fz$ satisfies Lemma \[l5.3\] (i) and (ii). If $A(0)=I_n$, then $H_\fz(\xi)=\langle \xi,\,\xi\rangle$ and hence Lemma \[l5.4\] follows from [@ceg]. Generally, Lemma \[l5.4\] follows from Lemma 3.4 of [@wy], where $H_\fz$ satisfies the conditions required there. Without loss of generality, we may assume that $x=0$, $u(x)=0$ and $\lip_{d_A}u(0)>0$. Indeed, set $\wz u(z)=u(x+z)-u(x)$ for $z\in\rn$, and $\wz H(z,\,\xi)=\langle A(x+z)\xi,\,\xi\rangle$. Then $\wz u$ is an absolute minimizer of $\wz H$ if and only if $ u$ is an absolute minimizer of $ H$; Theorem \[t5.1\] holds for $\wz u$ at $0$ if and only if Theorem \[t5.1\] holds for $ u$ at $x$. But $\wz u(0)=0$. We also notice that $\lip_{d_A}u(0)=0$ together with the equivalence of $d$ and the Euclidean distance yields that $\lip\, u(0)=0$, and hence, $u$ is differentiable at $0$ with $\nabla u(0)=0$. This means that holds with ${\bf e}=0$ and $ \lip_{d_A} u(0)=H(0,\,{\bf e})=0.$ Now we consider the scaling of the absolute minimizer $u$ by $u_j(y)=\frac{u(r_j y)}{r_j} $ as above. $u_\fz$ is the limit of some subsequence of $u_j$, which is still denoted by $u_j$ for simple. Then is reduced to showing $u_\fz(z)=\langle {\bf e},\,z\rangle$ for some vector ${\bf e}\in\rn$ and $H_\fz({\bf e})=\lip_{d_A}u(0)$. But this follows from Lemma \[l5.4\] and Lemma \[l5.3\]. \(i) In the above proof, we do need the continuity of $A$ at $x$ to conclude that $d_\fz$ is the intrinsic distance associated to $H_\fz$. 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Stollmann, A dual characterization of length spaces with application to Dirichlet metric spaces, Studia Math. 198 (2010), 221-233. K.-T. Sturm, Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and $L^p$-Liouville properties, J. Reine Angew. Math. 456 (1994), 173-196. K.-T. Sturm, Is a diffusion process determined by its intrinsic metric? Chaos Solitons Fractals 8 (1997), 1855-1860. C. Wang and Y. Yu, $C^1$-regularity of the Aronsson equation in ${\mathbf R}^2$, Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), 659-678. Pekka Koskela Department of Mathematics and Statistics, P. O. Box 35 (MaD), FI-40014, University of Jyväskylä, Finland [*E-mail* ]{}: `[email protected]` Nageswari Shanmugalingam Department of Mathematical Sciences, P.O.Box 210025, University of Cincinnati, Cincinnati, OH 45221-0025, U.S.A. [*E-mail*]{}: `[email protected]` Yuan Zhou Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China [*E-mail* ]{}: `[email protected]` | High | [
0.6652452025586351,
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--- author: - 'Vijai Jayadevan, Edward Delp, and Zygmunt Pizlo' bibliography: - 'bibliography.bib' title: Skeleton Extraction from 3D Point Clouds by Decomposing the Object into Parts --- [Jayadevan : Skeleton Extraction from 3D Point Clouds by Decomposing the Object into Parts]{} Decomposing a complex 3D shape into its components is an important problem that has applications in many fields including computer graphics and computer vision. Psychological studies have shown that human shape perception and recognition is based on decomposing complex shapes into simple primitives [@Biederman_1993_recognizing]. Therefore, characterization of a shape by its parts and the connections between them is only natural, especially for applications involving human interaction. A good example in this regard is the work by Funkhouser e. al [@funkhouser2004modeling], which aims at constructing detailed 3D models by assembling parts extracted from existing models. Part based approaches also have applications in other area like character animation [@baran2007automatic] and surface reconstruction [@li2010arterial; @chen2013_3sweep; @yin2014morfit]. To decompose a shape into its parts, we first need a good definition for a part. A good definition of a part would be general enough to capture the wide variety of part types available in the real world and at the same time be able to decompose a shape into meaningful units. In this context, generalized cylinders (GCs) introduced by Binford [@binford1971visual] would serve as a very good definition of a part. A wide variety of natural as well as man made objects have parts that can be well modeled by GCs. GCs are formed by sweeping a planar cross-section along a 3D axis, with uniform size scaling applied to the cross-section as it moves along the axis. An illustration of this is shown in Fig. \[fig:gc\_illustration\]. Translational symmetry is the fundamental property that defines a GC [@Pizlo_2014_Making]. In this work, we think of parts of a 3D shape as GCs and employ translational symmetry to extract them. [0.3]{} {width="\textwidth"} [0.3]{} {width="\textwidth"} [0.3]{} {width="\textwidth"} Decomposing a shape into its components can be thought of as an inverse problem which is often times also ill-posed. It is an inverse problem because the forming of a complex 3D shape by interconnecting parts can be thought of as the forward problem and the ill-posedness comes from the fact that there is no unique solution to the problem. Solution to ill-posed inverse problems are obtained by imposing additional constraints (aka priors). In this context, translational symmetry can be thought of as the prior we use to identify parts which eventually leads to the decomposition of shapes. Skeleton extraction methods often times lead to shape decomposition [@sharf2007fly; @au2008skeleton; @reniers2008computing]. But in our case it works in the opposite direction. The 3D-axis of a GC, which is integral to its definition, would serve as the skeleton of the part. Therefore, a GC based decomposition would naturally lead to skeletonization of the shape. There exist a method by Zhou et al. [@zhou2015generalized] which address the problem of decomposing shapes into GCs. As we point out later, though our method has similarities to their approach, there are significant differences stemming from the fact that our method works on unorganized point clouds and theirs on meshes. As shown in Fig. \[fig:overview\], the algorithm has three main steps. In the first step, a few candidate parts are generated. Not all candidate parts are ideal to represent the actual parts of the object, and there is often overlap between different candidate parts. Therefore, an optimal subset of parts are then selected from these candidate parts in the next step. Note that, every part has an axis associated with it, which serves as its skeletal representation. Therefore, in the final step, the individual skeletons of the selected parts are linked appropriately to form the complete skeleton. In order to generate candidate parts, we first detect the cross-section of parts and then grow parts starting from this initial cross-section to obtain complete parts. An interesting fact to notice here is that growth explains why many things in nature, like limbs of animals and tree trunks, exhibit translational symmetry [@Pizlo_2014_Making]. We employ translational symmetry to grow parts. Specifically, we start with a initial cross-sectional cluster (a small cluster of points representing a thin cross-section) and grow this cluster by identifying similar clusters in its neighborhood via 3D point set registration. By combining ideas from [@Myronenko_2010_CPD] and [@Billings_2015_GIMLOP] we present a new registration algorithm that is tailor made for our purpose of growing parts via registration. The proposed algorithm makes use of the orientation information of the point clouds (i.e., the point normals) and this, as we show in the results section, helps it to achieve greater accuracy in the registration process. In the results section, we also compare our method to two state of the art methods for skeleton extraction and point out the advantages of using a part based method. We also present a graphical user interface (GUI) to demostrate the advantage of using a part based approach to skeletonization. Specifically, we show the ease with which mistakes, if any, can be corrected with minimal user interaction using the GUI. In the next section we review the past literature relevant to our work. In section \[sec:generating\_candidate\_parts\], we explain the procedure to generate candidate parts. Method for selecting optimal subset of parts and the method for linking selected parts are explained in Sections \[sec:optimal\_part\_selection\] and \[sec:linking\_parts\] respectively. The GUI is described in section \[sec:GUI\_Skel\] and the results are presented in section \[sec:results\_skel\]. This is followed by sections on the implementation details and conclusion. [.63]{} {width="\textwidth"} [.33]{} {width="50.00000%"} {width="\textwidth"} Related Work ============ We organize the literature review into two sections. First, we discuss methods from the literature used for curve skeleton extraction. This is followed by a review of methods for shape decomposition. ### Skeleton Extraction {#sec:lit_review_skel .unnumbered} There is a vast body of prior work addressing the problem of curve skeleton extraction. Methods exist to extract curve skeletons from complete surface models, like polygonal meshes, as well as unorganized point clouds. Methods belonging to the latter category are the most relevant to our work and hence we focus on these methods for the review. The reader may refer to [@tagliasacchi_2016_skel_survey] or [@cornea2007curve] for a comprehensive review of the various skeleton extraction methods that are available. There exist a class of methods that rely on defining a field on the voxelized internal volume of shapes. In such methods, the ridges of the field are of particular interest when it comes to skeleton extraction. For example, in [@chuang2004potential], the authors identify valleys, in the generalized potential field, which connect several seed points, to derive the axis of the GC representation of the shape. In [@siddiqi1999hamilton], Siddiqi et al. extract skeletons by using the fact that the divergence of the euclidean distance transform would be zero everywhere except at the skeletal points. Song et al. [@song2018distance] improve upon the results obtained by Huang et al. [@huang2013L1] by using the distance field to guide the L1-median skeleton extraction. Note that the appropriate voxelization of unorganized point clouds is a non-trivial task. Apart from this, as we will demonstrate in the results section, these methods will not generalize well to certain shapes in comparison to a part-based approach. By defining an appropriate real valued function on a compact manifold and then tracking the evolution of its level sets, Reeb graphs, which capture the topology of the manifold, can be created. Methods described in [@hilaga2001topology; @natali2011graph; @bucksch2010skeltre] employ Reeb graphs to extract skeletons. Authors in [@dey2006defining; @ogniewicz1992voronoi] extract skeletons by employing Voronoi diagrams. Voronoi diagrams can be used to approximate medial surface of shapes and these can be further pruned to obtain curve skeletons. Tagliasacchi et al. [@tagliasacchi2009curve] proposed a method, based on the rotational symmetry axis, to extract skeletons from incomplete point clouds of generally cylindrical shapes. Sharf et al. [@sharf2007fly] proposed a method that is based on the evolution of a deformable model inside the point cloud. They obtain a first approximation to the skeleton by tracing the growing fronts and perform further filtering to obtain the final curve skeleton. Cao et al. [@cao2010point] extend the mesh contraction method of Au et al. [@au2008skeleton] to point clouds and use Laplacian based contraction followed by topological thinning to obtain curve skeletons. In the results section, we compare our method with that of Cao et al. and point out the drawbacks of using a contraction based approach for skeleton extraction. ### Shape Decomposition {#sec:lit_review_semantic .unnumbered} A variety of methods address the problem of segmentation and semantic labelling of point clouds [@nguyen20133d]. Skeleton extraction methods can some time lead to decomposition of shapes [@sharf2007fly; @au2008skeleton; @reniers2008computing]. But model fitting methods, which addresses the problem of shape decomposition, are the most relevant to our work. Most primitive detection and fitting methods employ simple primitives for the purpose. For instance, Schnabel et al. [@schnabel2007efficient] describe an efficient RANSAC based method capable of fitting simple primitives like planes, spheres, cylinders, cones and tori. Attene et al. [@attene2006hierarchical] present a method to fit simple primitives to triangle meshes using a hierarchical face clustering approach. GCs, compared to these simple primitives, can represent a much broader range of shapes. Lit et al. [@li2001decomposing] present an early work on decomposing polygonal meshes into parts that resemble GCs. They extract approximate curve skeletons by mesh edge contraction and then identify the critical points (points where the topology or geometry changes) by sweeping a plane, perpendicular to the skeleton branches, over the mesh. The parts of the mesh between consecutive critical points are then extracted as components. Though it is not stated explicitly, this method uses the notion of translational symmetry to identify components/parts. One of the two methods to grow parts that we describe later has similarities with this method. However, unlike this method we operate on unorganized point clouds and hence cannot employ their method of skeleton extraction. Moreover, the second method to grow parts that we describe later is more sophisticated as it is based on the very definition of a GC (i.e., based on translational symmetry), and is more suitable for point clouds. In [@chuang2004potential], the authors first derive a skeleton of the shape using a potential-based skeletonization approach and then generate the cross-sections with the help of seed points. But if the shape has to be decomposed into parts, each of which is a GC, the seed points have to be manually chosen. There are a number of automatic as well as interactive surface reconstruction methods that use a GC representation [@li2010arterial; @chen2013_3sweep; @yin2014morfit]. However, they do not explicitly aim at obtaining an optimal decomposition of the shape into GCs. With regards to obtaining a GC based decomposition, the work of Goyal et al. [@goyal2012towards] and Zhou et al. [@zhou2015generalized] are the most relevant to our work. Both these methods work on meshes unlike our method which takes unorganized point clouds as input. Goyal et al. obtain a direct parameterization of 3D meshes in terms of sets of locally prominent cross-sections (PCS). Each set of PCS represent a different sweep component. Zhou et al. propose a metric to measure cylindricity of a GC. They first extract an over-complete set of local cylinders using the method proposed by Tagliasacchi et al. [@tagliasacchi2009curve] and then combine these local cylinders to form longer candidate cylinders. The set of candidate cylinders is still over-complete and the partition of the shape into GCs is obtained by solving the exact cover problem. Our approach is similar to that of Zhou et al in the sense that we too first generate an overlapping set GCs and we choose the best subset of GCs that cover the shape. However, there are some significant differences between the two approaches. The most signifacnt difference being that our method operates on point clouds and not polygonal meshes. Our method to extract GCs is rooted in the very definition of a GC which is in turn based on translational symmetry. Their method of scoring the GCs is not applicable to us because we operate on point clouds. Therefore, we introduce metrics to score GCs based on factors like their self-similarity (i.e., based on how much one portion of the GC is similar to another portion of the same GC), length, straightness of axis etc. And finally, we frame the problem of choosing the final subset of GCs as a binary integer program. Generating Candidate Parts {#sec:generating_candidate_parts} ========================== As shown in Fig. \[fig:gc\_illustration\], a GC is formed by sweeping a planar cross-section along a 3D axis, with size scaling applied to the cross-section, as it moves along the axis. Such objects were referred to as generalized cones by Binford [@binford1971visual]. As per this definition, every part has an axis. This axis serves as the skeletal representation of the part. According to this definition of a part, there is a cross-sectional plane associated with each point on the axis. And as shown in Fig. \[fig:gc\_illustration\] (c), the normal of the cross-sectional plane associated with a point on the axis, is the tangent to the axis at that point. This important observation will be employed later in detecting local cross-sectional planes. Fig. \[fig:bloc\_diag\_gen\_parts\], shows the various steps involved in generating candidate parts. Given a point cloud, the first step in the algorithm is to estimate the point normals for each point in the cloud. The point normals are nothing but the local surface normals. At the end of this step, we would obtain an oriented set of points and the point normal orientations, as we show later, would play a very important role throughout the algorithm. In the next step, we derive local thresholds. The key idea here is that whenever thresholds are required to be applied (like estimating the closeness of a point in the cloud to some plane or deciding if two points in the point cloud can be considered as neighbors), locally adaptive thresholds need to be employed. For instance, the sparsity/density of the point clouds need not be uniform through out the cloud. To deal with this issue, we assign a number, which represent the local distance threshold, to each point in the cloud. In the next step, we detect what we call [“[initial cross-sections]{}”]{}. An initial cross-section is a cluster of points in the cloud that are likely to represent one of the cross-sections of a part. In Fig. \[fig:growing\_stages\], cluster 0, represents such an initial cross-section. Such clusters serve as the starting points to [“[grow]{}”]{} parts. Keep in mind that all points in the point cloud are assumed to come from parts which are generalized cylinders. Therefore, each point in the cloud corresponds to one of the cross-sectional planes (like the yellow planes in Fig. \[fig:gc\_illustration\] (c)) of one of the parts. Therefore, in this step, given any point in the cloud, we would like to be able to estimate the orientation of the cross-sectional plane, passing through that point. Provided, we can find the orientation of the cross-sectional plane corresponding to a given point in the cloud, all points sufficiently close (the notion of being sufficiently close will be made more concrete later) to this cross-sectional plane would constitute what we call an initial cross-section. Assume for a moment that given such an initial cross-section, we will be able to extract the part that the initial cross-section belongs to. For instance, in Fig. \[fig:growing\_stages\], given cluster 0, let’s assume we can grow the part and extract the torso of the dinosaur. We will explain how this can be done later. Since, we would like to extract all parts of an object we would need at least as many initial cross-sections as there are parts. In the example of the dinosaur (Fig. \[fig:growing\_stages\]), if we assume that the number of parts constituting the object is nine (i.e., four limbs, a tail, torso, neck, horn and face), we need at least nine initial cross-sections to extract all the parts. Hence, we cluster the point cloud into $M$ clusters and find the initial cross-section for each of these clusters. A large value is chosen for $M$ (close to hundred) to ensure that we detect initial cross-sections for all the parts. It is better to have some redundant parts than to miss out on extracting some parts. As shown in Fig. \[fig:bloc\_diag\_gen\_parts\], the next step is [“[growing]{}”]{} parts out of these initial cross-sections. To understand this process consider cluster 0, in Fig. \[fig:growing\_stages\], which represents an initial cluster. Once we have such a cluster of points, we search in the neighborhood, of that cluster, for a similar group of points which could represent the neighboring cross-section of the initial cluster. Cluster 1 in Fig. \[fig:growing\_stages\] represents such a matching cluster. Note, we will make the notion of similarity/match concrete later. If we find a matching cluster, we repeat this process of searching for matching clusters. For instance, cluster 2 is found to be a match for cluster 1. Keep in mind that our parts are defined by translational symmetry. Therefore, for each cross-sectional cluster, we will find similar clusters in its neighborhood. Or in other words, the procedure just described for growing parts from initial cross-sections is inspired by the definition of parts as generalized cylinders. This process of growing a part is repeated until there are no more matches to be found. Note, the parts are to be grown, from the initial cluster, in both directions. In Fig. \[fig:growing\_stages\] , the clusters in the two directions are represented by positive and negative cluster numbers respectively. The three fundamental components of a part is its 2D cross-sectional contour, the scaling function and the 3D Axis. Since we are dealing with point clouds, the concept of a 2D contour lying on a plane does not make sense. Hence, the initial cross-section is a cluster of points and these thin clusters play the role of the 2D cross-sectional contour. In the growing stage we are attempting to determine matches for the thin cross-sections. Finding such matches would give us an estimate of the scaling function and also the estimate of the axis of the part. The procedure of finding matches and how such matches would lead to estimates of the scaling function and the axis would be explained in the sections below. But the key point to keep in mind is that the part detection algorithm is attempting to identify parts by using its very definition. Each of the steps in Fig. \[fig:bloc\_diag\_gen\_parts\] are explained in greater detail in the sections below. ![Block diagram showing the different steps involved in generating candidate parts.[]{data-label="fig:bloc_diag_gen_parts"}](images/block_diagram_part_gen-eps-converted-to.pdf){width="50.00000%"} Estimating Point Normals {#sec:point_normal_estimation} ------------------------ Before extracting the candidate parts, we estimate the local surface normal of the points in the 3D point cloud. We use the software CloudCompare to do this [@cloud_compare_2019]. A quadratic surface is fit on to the local neighborhood to estimate the normal direction. But the orientation of these normals (i.e., whether it points towards the inside or outside of the object) is still ambiguous. To ensure that the normals are oriented in a consistent fashion, the normals are re-oriented by propagating the normal orientation starting from a random point with the help of a Minimum Spanning Tree (MST). We use $\mathbf{X} = \{\mathbf{x}^1,\mathbf{x}^2, \cdots, \mathbf{x}^N \}$ to represent the point cloud. Note, $\mathbf{x}^i = ({ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {p} }} } { {{{x}^ {i} }_{\hspace{-.045in} {p} }} } },{ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {n} }} } { {{{x}^ {i} }_{\hspace{-.045in} {n} }} } })$, where ${ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {p} }} } { {{{x}^ {i} }_{\hspace{-.045in} {p} }} } } \in \Re^3$ represents the position of the point and ${ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {n} }} } { {{{x}^ {i} }_{\hspace{-.045in} {n} }} } } \in \Re^3$ is a unit normal representing the orientation of the normal at the point. Deriving Locally-adaptive Thresholds {#sec:locally_adaptive_threshold} ------------------------------------ We use minimum spanning tree (MST) to derive local distance thresholds. The distance to neighboring points in an MST, constructed on the 3D point cloud, is a good indication of the local sparsity of the point cloud. Therefore, to derive a locally adaptive distance threshold for a point in the cloud, the distances of the point to its neighbors, as per the MST constructed on the cloud, can be used. To compute the MST, we must have an initial graph on the point cloud. Instead of considering a fully connected graph as input to MST, we construct a graph where every point is connected to its hundred nearest neighbors. Though a higher number of nearest neighbors could be considered, in practice, we found it be sufficient to just consider the nearest hundred neighbors. The reason for not considering a fully connected graph is to reduce the time for MST computation. The time complexity for MST is $\mathcal{O}(E\log{V})$, where $V$ is the number of nodes/vertices in the graph and $E$ is the number of edges. A fully connected graph would have a time complexity of $\mathcal{O}(V^2\log{V})$, whereas considering a fixed number of nearest neighbors, say hundred in our case, will only have a time complexity of $\mathcal{O}(V\log{V})$. We found that using a fixed, albeit large enough, neighborhood to create the input graph to MST produced considerable savings in computation time in practice. We use the k-d tree data structure to speed up neighborhood queries. Specifically , we use the k-d tree implementation from the Scikit-learn package [@scikit_learn]. Kruskal’s algorithm implemented in the SciPy package [@scipy_package] is used to compute MST. As mentioned before, the locally adaptive threshold for points in the cloud is employed, for various purposes, throughout the algorithm. One purpose of the locally adaptive threshold is to create a connectivity matrix on the point cloud. Or in other words, the locally adaptive threshold derived for a point in the cloud is used to determine its neighbours. Therefore, once the MST is computed, we assign a distance threshold for each individual point in the cloud. I.e., for each point $\mathbf{x}^i$ in the point cloud, we set a distance threshold ${ \ifthenelse{\equal{0}{1}} { {{\mathbf{\delta}^ {i}_ {cnct} }} } { {{{\delta}^ {i} }_{\hspace{-.045in} {cnct} }} } } =1.5 { \ifthenelse{\equal{0}{1}} { {{\mathbf{d}^ {i}_ {max} }} } { {{{d}^ {i} }_{\hspace{-.045in} {max} }} } }$, where ${ \ifthenelse{\equal{0}{1}} { {{\mathbf{d}^ {i}_ {max} }} } { {{{d}^ {i} }_{\hspace{-.045in} {max} }} } }$ is the maximum among the distances to all the neighbors the point $\mathbf{x}^i$ is connected to, in the MST. Two points $\mathbf{x}^i$ and $\mathbf{x}^j$ in the point cloud are considered to be connected if $d_{eucl}(\mathbf{x}^i,\mathbf{x}^j) \leq $ maximum$({ \ifthenelse{\equal{0}{1}} { {{\mathbf{\delta}^ {i}_ {cnct} }} } { {{{\delta}^ {i} }_{\hspace{-.045in} {cnct} }} } },{ \ifthenelse{\equal{0}{1}} { {{\mathbf{\delta}^ {j}_ {cnct} }} } { {{{\delta}^ {j} }_{\hspace{-.045in} {cnct} }} } })$, where $d_{eucl}(\mathbf{x}^i,\mathbf{x}^j)$ is the euclidean distance between the points. Based on this criterion a connectivity graph, $\mathbf{G}_{cnct}$, is constructed on the point cloud. ![Depiction of how a part is grown from an initial cross-sectional cluster (Cluster 0). Neighboring cross-sectional clusters are shown in alternating colors. The red curve represents the axis of the part.[]{data-label="fig:growing_stages"}](images/growing_stages_5-eps-converted-to.pdf){width="50.00000%"} [0.4]{} ![(a) The cross-sectional plane is shown in blue, the thin cross-section associated with the plane is shown in brown and seed point is shown in red. (b) All points close to the cross-sectional plane, but not necessarily connected to the seed point.[]{data-label="fig:cross_section_demo"}](images/Cross_section-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.44]{} ![(a) The cross-sectional plane is shown in blue, the thin cross-section associated with the plane is shown in brown and seed point is shown in red. (b) All points close to the cross-sectional plane, but not necessarily connected to the seed point.[]{data-label="fig:cross_section_demo"}](images/wrong_cross_section_eg-eps-converted-to.pdf "fig:"){width="\textwidth"} Detecting Initial Cross-sections {#sec:init_cross-sections} -------------------------------- As stated earlier, parts are formed by scaled versions of a 2D cross-sectional contour translated along an axis. And since thin cross-sectional clusters serve as an approximation to the 2D contour of a part in a point cloud, we would like to detect them and then use them to grow parts. Given any point in the cloud, we need an algorithm to detect a thin cross-sectional cluster corresponding to that point. For instance, in Fig. \[fig:cross\_section\_demo\] (a), given the red point, we need the algorithm to return the brown points. The red point is referred to as the seed point as it serves as the starting point for growing parts. As shown in Fig. \[fig:cross\_section\_demo\] (a), detecting the orientation of the cross-sectional plane (shown in blue) passing through the seed point would give us the thin cross-sectional cluster we are looking for. Because, once we estimate the orientation of the cross-sectional plane passing through the seed point, all points lying sufficiently close to that plane would represent the thin cross-sectional cluster. We need to consider only points lying close to the plane and at the same time connected to the seed point. As shown in Fig. \[fig:cross\_section\_demo\] (b), considering all points near the plane that are not necessarily connected to the seed point could lead to the inclusion of some wrong points as part of the cross-section. Note that the approach described above is similar to that of Tagliasacchi et al. [@tagliasacchi2009curve]. [0.36]{} {width="\textwidth"} [0.42]{} {width="\textwidth"} [0.21]{} {width="\textwidth"} We need to detect initial cross-sectional clusters at multiple locations on the point cloud to be able to extract all the parts. As mentioned before, in the example of the dinosaur in Fig. \[fig:growing\_stages\], we need at least nine initial cross-sections. Therefore, the point cloud is clustered into $M$ clusters using k-means clustering [@scikit_learn]. These clusters would determine the locations at which we would detect thin cross-sectional clusters from which candidate parts are grown. The idea is to pick one seed point per cluster and then find the thin cross-section to which the seed point belongs and finally grow parts out of this thin cross-section. For each cluster, we pick the point in the cluster which is closest to the k-means cluster center as the seed point. To find the cross-sectional plane that passes through a seed point, $\mathbf{s}^i$, we do an exhaustive search. Algorithm \[alg:cross-sectional\_plane\] shows the steps involved in searching for a cross-sectional plane that passes through a seed point. Note, the algorithm takes as input the connectivity matrix defined on the clusters, $\mathbf{G}_{clust}$. If any member of one cluster is connected to any member of the other cluster, according to $\mathbf{G}_{cnct}$, then two clusters are considered to be connected. Spherical coordinates are used to sample the unit sphere at regular angular intervals to obtain the normal directions for the planes. An angular interval of $\pi/6$ is used to sample both the zenith angle $\phi$ and the azimuthal angle $\theta$. Note, all the planes pass through the seed point, so picking a normal direction for the plane fully defines it. For each plane an inlier set, $\mathbf{B}$, is first computed. This inlier set, as shown in Fig. \[fig:cross\_section\_demo\] (a), contains all points that lie close to the plane and are connected to the seed point. A cluster dependent distance threshold, ${ \ifthenelse{\equal{0}{1}} { {{\mathbf{\delta}^ {i}_ {pd} }} } { {{{\delta}^ {i} }_{\hspace{-.045in} {pd} }} } } = median \big( \{ { \ifthenelse{\equal{0}{1}} { {{\mathbf{d}^ {j}_ {max} }} } { {{{d}^ {j} }_{\hspace{-.045in} {max} }} } } \mid \mathbf{x}^j \in \ $cluster$\ i \} \big)$, is used to determine if a point is considered close enough to a plane. We use the adaptive threshold derived earlier in section \[sec:locally\_adaptive\_threshold\] here to decide which points lie close to the plane. A cost is then assigned to each plane. The cost, represented by $c(\theta,\phi)$, is based on the defenition of the part and measures the average length of projection of the point normals of the points in $\mathbf{B}$ on to the normal of the plane. Ideally, the point normals will be perpendicular to the normal of the cross-sectional plane and therefore will have a zero length projection on the normal of the cross-sectional plane. As shown in Fig. \[fig:gc\_illustration\] (c), the cross-sectional plane (shown in yellow) contains the contour. The normals to the contour lie on the plane and hence are parallel to the plane and have projection length of zero on to the normal of the plane. This implies that the plane that minimizes this cost, for a given seed point, would be the best estimate for the cross-sectional plane for that seed point. After the costs associated with each plane is computed the plane that minimizes this cost is selected as the cross-sectional plane. The inlier set of that plane defines the thin cross-section. Point cloud : $\mathbf{X}$ Connectivity graph on $\mathbf{X}$: $\mathbf{G}_{cnct}$ Connectivity graph on the clusters: $\mathbf{G}_{clust}$ Distance Threshold: ${ \ifthenelse{\equal{0}{1}} { {{\mathbf{\delta}^ {i}_ {pd} }} } { {{{\delta}^ {i} }_{\hspace{-.045in} {pd} }} } }$ Seed point of $i^{th}$ cluster: $\mathbf{s}^i = ({ \ifthenelse{\equal{1}{1}} { {{\mathbf{s}^ {i}_ {p} }} } { {{{s}^ {i} }_{\hspace{-.045in} {p} }} } },{ \ifthenelse{\equal{1}{1}} { {{\mathbf{s}^ {i}_ {n} }} } { {{{s}^ {i} }_{\hspace{-.045in} {n} }} } })$ $\theta,\phi$ $d \gets \mathbf{\hat{n}} \boldsymbol{\cdot} { \ifthenelse{\equal{1}{1}} { {{\mathbf{s}^ {i}_ {p} }} } { {{{s}^ {i} }_{\hspace{-.045in} {p} }} } } $ $\mathbf{A}$ is the set of points close to the plane abs(): absolute value $\mathbf{A} \gets \{ \mathbf{x}^i \ \mid$ abs( $\mathbf{\hat{n}} \boldsymbol{\cdot} { \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {p} }} } { {{{x}^ {i} }_{\hspace{-.045in} {p} }} } } - d$ ) $\leq { \ifthenelse{\equal{0}{1}} { {{\mathbf{\delta}^ {i}_ {pd} }} } { {{{\delta}^ {i} }_{\hspace{-.045in} {pd} }} } } \} $ $\mathbf{B} \gets \{ \mathbf{x}^i \in \mathbf{A} \mid \mathbf{x}^i $ is connected to $\mathbf{s}$ as per $\mathbf{G}_{cnct} \}$ $\mathbf{H} \gets \{ \mathbf{s}^j \mid$ cluster $j$ neighbor of cluster $i$ as per $ \mathbf{G}_{clust} \}$ $\mathbf{\hat{n}} \gets [cos(\theta) sin(\phi), sin(\theta)sin(\phi), cos(\phi)]$ $\mathbf{B} \gets$ $c(\theta,\phi) \gets $mean$ \big( \{ $abs($ \mathbf{\hat{n}} \boldsymbol{\cdot} { \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {n} }} } { {{{x}^ {i} }_{\hspace{-.045in} {n} }} } } $)$ \ \mid \mathbf{x}^i \in \mathbf{B} \} \big)$ $\underset{\theta,\phi}{\arg\min} \ c(\theta,\phi) $ [0.36]{} {width="\textwidth"} [0.34]{} {width="\textwidth"} [0.28]{} {width="\textwidth"} Growing Parts {#sec:growing_parts} ------------- In the previous step, we identified $M$ initial cross-sectional clusters. Starting from these initial cross-sectional clusters, parts need to be grown. Two methods are used to grow parts from initial cross-sections. Both methods are again based on the definition of a part as a GC. We would refer to these methods as method 1 and method 2 for clarity. While method 1 is very simple, method 2 is much more sophisticated. Before we describe the methods, we would describe three assumptions that these methods make. The first assumption is that the scaling function of the GC is smooth and the second assumption is that the 3D axis of the GC is smooth. Note that we are looking for matching cross-sectional cluster for the initial cross-sectional cluster in its neighborhood to grow a part. In this context, the first assumption implies that there would not be a sudden jump in the scale of a cross-sectional cluster compared to its neighboring cross-sectional cluster. And the second assumption would mean that the orientation of the cross-sectional planes of neighboring cross-sectional clusters would be similar. As an example, in Fig. \[fig:gc\_illustration\] (c), the two yellow planes represent cross-sectional planes of two close-by cross-sections and therefore have similar orientation. Also, note that the scale function in Fig. \[fig:gc\_illustration\] (a) is smooth. The third assumption that both methods make is that the mean of all the points in a cross-sectional cluster of a part represents a point on the axis of the part. For instance, in Fig. \[fig:cross\_section\_demo\] (a), if we take the centre of mass of all brown points, we would obtain a point in the interior of the torso of the dinosaur. The torso of the dinosaur is a GC and the centre of mass of the points in the cross-sectional cluster (shown in brown) is assumed to lie on the axis of this GC. We refer to the centre of mass of points in the cluster as the cluster center. The axis of the torso, shown in red in Fig. \[fig:growing\_stages\], is obtained by joining the cluster centers of the blue and brown clusters. While this assumption is not generally true, we make such a simplifying assumption to estimate the axis points, given a cross-sectional cluster. We will demonstrate later that this assumption is a reasonable assumption for many real-world parts. The following sections will explain the two methods in detail. ### Method 1 As stated above, this is a simple method for growing parts from initial cross-sectional clusters. Keep in mind that, given an initial cross-sectional cluster, we are looking for the neighboring cross-sectional cluster to grow the part. For instance, in Fig. \[fig:growing\_stages\], we are looking for cluster 1, given the initial cluster, cluster 0. Fig. \[fig:method1\], shows the main steps in this method. As depicted in the figure, the first step is to obtain a rough estimate of the cluster center of the neighboring cluster, cluster 1. Let $\mathbf{C}_0$ denote the centre of cluster 0 and the normal of the cross-sectional plane corresponding to cluster 0 be denoted by $\hat{\mathbf{n}}_0$. By definition, the cross-sectional plane of cluster 0 is perpendicular to the axis of the GC (the torso of the dinosaur being the GC here) at $\mathbf{C}_0$. Or in other words, $\hat{\mathbf{n}}_0$ is the tangent to the axis of the GC at $\mathbf{C}_0$. Therefore, taking a small step along $\hat{\mathbf{n}}_0$ would give us a rough estimate of the axis point corresponding to cluster 1. Keep in mind that the tangent of a curve provides a linear approximation to the curve locally. Let this estimate of the neighboring axis point be denoted by $\widetilde{\mathbf{C}}_1$. I.e., $\widetilde{\mathbf{C}}_1 = \mathbf{C}_0 + \delta_{step} \hat{\mathbf{n}}_0$, where, $\delta_{step}$ represents a small step size. Fig. \[fig:method1\] (a), depicts this process. In the next step we estimate the orientation of the cross-sectional plane through $\widetilde{\mathbf{C}}_1$. An exhaustive, but local search is used to estimate the orientation of the cross-sectional plane. The exhaustive search is identical to the one described in algorithm \[alg:cross-sectional\_plane\], but here we only consider planes whose normal orientation is close to $\hat{\mathbf{n}}_0$. This is because, according to the second assumption, the orientation of the cross-sectional plane of cluster 1 is close to the orientation of the cross-sectional plane of cluster 0 (because the 3D axis is smooth). To obtain planes whose orientation is close to $\hat{\mathbf{n}}_0$, an angle range, $\Delta_{ang}$, and a step number, $k_{step}$, is first chosen. Let $\theta_0$ and $\phi_0$ represent the azimuth and the zenith angles corresponding to $\hat{\mathbf{n}}_0$. Let $\mathbf{A}_{\theta}$ represent $k_{step}$ equally spaced angles in the range $(\theta_0 - \Delta_{ang}, \theta_0 + \Delta_{ang} )$ and $\mathbf{A}_{\phi}$ represent $ k_{step}$ equally spaced angles in the range $(\phi_0 - \Delta_{ang}, \phi_0 + \Delta_{ang} )$. All planes represented by the cartesian product, $\mathbf{A}_{\theta} \bigtimes \mathbf{A}_{\phi}$, are considered. We use $\Delta_{ang} = 12.5$ and $k_{step} = 3$. This ensures that all the planes considered have normals which are similar in orientation to $\hat{\mathbf{n}}_0$. The best plane is chosen by using the same criterion as the one described in algorithm \[alg:cross-sectional\_plane\]. I.e., for each plane in the set $\mathbf{A}_{\theta} \bigtimes \mathbf{A}_{\phi}$, we compute its inlier set (see algorithm \[alg:cross-sectional\_plane\]) and then choose the plane which minimizes the average length of projection of the point normals of the points in its inlier set on to the normal of the plane. Considering all points lying close to a plane could lead to problems like the one shown in Fig. \[fig:nxt\_seed\_point\] (a). To avoid this issue, we need to only consider points lying close to the plane and connected to a seed point. As shown in Fig. \[fig:nxt\_seed\_point\] (b), the point closest to $\widetilde{\mathbf{C}}_1$, from amongst the points close to the plane (the green points), is chosen as the seed point. Choosing only those (green) points that are connected to the seed point would fix the issue of unwanted points being included in the cross-sectional cluster (Fig. \[fig:nxt\_seed\_point\] (c)). The steps described above can be used to find the neighboring cross-sectional cluster, cluster 1, given the initial cluster. This process can be repeated to obtain the neighboring cross-sectional cluster, cluster 2 in Fig. \[fig:growing\_stages\], of cluster 1. There needs to be a stopping criterion for this process. Or in other words, there needs to be some criterion that can be checked to see if we have reached the end cluster of a part. Here is where the first assumption, mentioned earlier, comes into play. Since, the scale function of a part is smooth, the two neighboring cross-sections would have similar scale factors. A sudden jump in the scale factor of a neighboring cross-section would indicate that we have reached a junction. For example, in Fig. \[fig:growing\_stages\], the search for the neighboring cross-sectional cluster for cluster 2 would fail as all the potential clusters considered would have a substantially different scale factor. A very simple metric is employed to measure the scale factor of a cross-sectional cluster. A local coordinate system is constructed, using PCA, for the cluster. Let the axes of this coordinate system be represented by $\mathbf{a}_1,\mathbf{a}_2$ and $\mathbf{a}_3$, with $\mathbf{a}_1$ representing the maximum variance direction and $\mathbf{a}_3$ representing the direction with the least variance. The axis $\mathbf{a}_3$, would have an orientation that is very close to the normal of the cross-sectional plane of the cross-sectional cluster because the cross-sectional cluster is thin and close to planar. Let the eigenvalues corresponding to axes $\mathbf{a}_1$ and $\mathbf{a}_2$ be $e_1$ and $e_2$ respectively. These eigenvalues serve as a good representation for the scale of the cluster. I.e., bigger cross-sectional clusters would have larger $e_1$ and $e_2$ values and vice-versa. Let $i$ and $j$ represent two neighboring cross-sections. We treat the combination of the two eigenvalues, $[e_1, e_2]$, as a vector. I.e., for cross-section $i$, we have a vector $[e^i_1, e^i_2]$ representing its scale. Similarly the vector $[e^j_1, e^j_2]$, represents the scale of cross-section $j$. We stop growing parts, if $ abs\big(1 - \frac{d_{eucl}( [e^i_1, e^i_2], [e^j_1, e^j_2])}{{\@ifstar{\norm*{\@}_2}supnormnostar}*{[e^i_1, e^i_2]} } \big) > \Delta_{eg} $, where $d_{eucl}( [e^i_1, e^i_2], [e^j_1, e^j_2])$ represents the euclidean distance between the vectors, $abs()$ represents the absolute value and $\Delta_{eg}$ represents an acceptable threshold for scale difference between neighboring clusters. The fraction is measuring the percentage change in the scale between the cross-sectional clusters. A value of one for the fraction would mean that the size of the cross-section did not change (according to our metric). If the percentage change in scale of the next cross-sectional cluster compared to the current cross-sectional cluster is greater than a threshold, it implies that we have reached a junction and the growing process stops. The growing process also terminates if there are no further points to be added to the part. For instance, the growing process of the tail of the dinosaur halts in one of the directions due to this reason. The growth of the tail stops in the other direction because the junction where the legs meet the tail is detected. As mentioned earlier, this method is a very simple one in which we depend on the smoothness of the scale function to grow parts. The termination criterion for the growth process as well as the metric to compute the scale of a cross-sectional cluster are also simple. In the next section, we describe a sophisticated method, which we refer to as method 2, to grow parts which directly takes inspiration from the process in which GCs are formed from its components (scale function, cross-sectional contour and 3D axis). Though we use method 2 as the primary method to grow parts, there are scenarios in which method 1 would be more suitable. Such scenarios will also be pointed out in the following sections. ### Method 2 {#sec:method_2} Given a scale function, cross-sectional contour and 3D axis, a GC is formed by a similarity transformation (i.e., rigid transformation and uniform scaling) of the contour. I.e., the action referred to as sweeping the 2D contour along an axis, consists of three transformations (translation, rotation and uniform scaling) applied to the 2D contour. This implies that the relationship between adjacent cross-sections is defined by a similarity transformation. In method 2, like in method 1, parts are grown, starting from an initial cross-sectional cluster (like cluster 0 in Fig. \[fig:growing\_stages\]), by finding its neighboring cross-sectional cluster. Since, the relationship between neighboring clusters is defined by a similarity transformation, one way to search for a similar cluster of points is to do registration between the initial cross-section and the points in its neighborhood. I.e., through registration, we can estimate the similarity transform that relates the two neighboring cross-sections. In Fig. \[fig:growing\_stages\], registration between cluster 0 and the points in its neighborhood would lead to the identification of cluster 1 as its neighbor. Similarly registration between cluster 1 and its neighborhood points would identify cluster 2 and so on. {width="\textwidth"} Fig. \[fig:why\_register\], demonstrates why method 2, which relies on registration to grow parts, is necessary to discover meaningful parts in the point cloud. The saffron colored portion represents the cross-section for which we seek to find a match. The plane shown in blue represents the actual cross-sectional plane of the neighboring cross-section.The points lying close to the cross-sectional plane, include many unwanted points as shown. Deriving a seed point (like in Fig. \[fig:nxt\_seed\_point\] (b)) and looking for the inlier set (alll points connected to the seed point) will help remove some unwanted points like the portions of the chair’s front legs. But portions of the chair’s hind legs still remain in the cluster. Performing a registration would tell us that these points belonging to hind legs have no match in the cluster for which we seek a match. Such points for which we fail to find a match can be removed to exactly identify points belonging to the neighboring cross-section. Point set 1: $\mathbf{X}$ Point set 2: $\mathbf{Y}$ $\mathbf{R},s$, $\mathbf{t}$, $\alpha$, $\sigma$ Set [$\mathbf{R} = \mathbf{I}_3, s=1$ and $\mathbf{t} = (0,0,0)^T$ ]{} Compute $\mathbf{P}$: $ p_{ji} = \frac{exp\big( - \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p^i - s \mathbf{R} \ { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } } - \mathbf{t}}^2 + \alpha ({\mathbf{x}_n^i})^T \mathbf{R} { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {n} }} } { {{{y}^ {j} }_{\hspace{-.045in} {n} }} } } \big)}{\sum\limits_{m=1}^M exp\big( - \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p^i - s \mathbf{R} \ { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {m}_ {p} }} } { {{{y}^ {m} }_{\hspace{-.045in} {p} }} } } - \mathbf{t}}^2 + \alpha ({\mathbf{x}_n^i})^T \mathbf{R} { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {m}_ {n} }} } { {{{y}^ {m} }_{\hspace{-.045in} {n} }} } } \big)} $ Estimate the parameter values, $\theta$, using the above value of $\mathbf{P}$: ${\hat{\mathbf{X}} = \mathbf{X}_p - \frac{1}{N} \mathbf{1} \big( {\mathbf{X}_p^T\mathbf{P}\mathbf{1}} \big)^T}$ ${\hat{\mathbf{Y}} = \mathbf{Y}_p - \frac{1}{N} \mathbf{1} \big( s\mathbf{R} {\mathbf{Y}_p^T\mathbf{P}\mathbf{1}} \big)^T}$ $\mathbf{A} = \hat{\mathbf{X}}^T \mathbf{P}^T \hat{\mathbf{Y}}$ $\mathbf{B} = \mathbf{X}_n^T \mathbf{P}^T \mathbf{Y}_n $ ${K_1 = tr \big ( \hat{\mathbf{Y}}^T d \big( \mathbf{P} \mathbf{1}\big) \hat{\mathbf{Y}} \big) }$ ${K_2 = tr \big ( \hat{\mathbf{X}}^T d \big( \mathbf{P} \mathbf{1}\big) \hat{\mathbf{X}} \big) }$ Use the BFGS algorithm with the gradient equations defined in equation \[eq:final\_gradients\], to compute optimal values for $\mathbf{R},s$, $\alpha$ and $\sigma$. $\mathbf{t} = \frac{1}{N} \big ( \mathbf{X}_p^T\mathbf{P}\mathbf{1} - s \mathbf{R} \mathbf{Y}_p^T\mathbf{P}\mathbf{1} \big )$ \ $\mathbf{R},s$, $\mathbf{t}$, $\alpha$, $\sigma$ In [@Myronenko_2010_CPD], Myronenko and Song present a solution to the registration problem by treating it as a probability density estimation problem. Note, though the authors call their method rigid registration, their method actually estimates the similarity transform that relates the two point clouds being registered. Myronenko and Song, however, only consider the location of the points being registered. In our case though, we have an oriented point set with each point having a position and an orientation (representing the local surface normal). As we demonstrate later, considering the orientation of the points is important in our case. Therefore, for the registration of two sets of oriented points, we modify the method in [@Myronenko_2010_CPD] by drawing in ideas from [@Billings_2015_GIMLOP]. We first introduce some additional notation and then explain the registration process between two oriented sets of points in the next section. Later sections explain how this registration process can be employed to grow parts. ### Registartion of Two Oriented Point Sets {#sec:generic_registration .unnumbered} Let $\mathbf{X} = \{\mathbf{x}^1,\mathbf{x}^2, \cdots, \mathbf{x}^N \}$ and $\mathbf{Y} = \{\mathbf{y}^1,\mathbf{y}^2, \cdots, \mathbf{y}^M \}$ represent the two point sets to be registered. As mentioned before, $\mathbf{x}^i = ({ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {p} }} } { {{{x}^ {i} }_{\hspace{-.045in} {p} }} } },{ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {n} }} } { {{{x}^ {i} }_{\hspace{-.045in} {n} }} } })$, where ${ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {p} }} } { {{{x}^ {i} }_{\hspace{-.045in} {p} }} } }$ represents the location and ${ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {i}_ {n} }} } { {{{x}^ {i} }_{\hspace{-.045in} {n} }} } }$ represent the point normal of $\mathbf{x}^i $. Similarly, $\mathbf{y}^i = ({ \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {i}_ {p} }} } { {{{y}^ {i} }_{\hspace{-.045in} {p} }} } },{ \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {i}_ {n} }} } { {{{y}^ {i} }_{\hspace{-.045in} {n} }} } })$. Let $\mathbf{X}_p = ({ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {1}_ {p} }} } { {{{x}^ {1} }_{\hspace{-.045in} {p} }} } },{ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {2}_ {p} }} } { {{{x}^ {2} }_{\hspace{-.045in} {p} }} } }, \cdots, { \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {N}_ {p} }} } { {{{x}^ {N} }_{\hspace{-.045in} {p} }} } } )^T$ be a $N \times 3$ matrix representing the positions and $\mathbf{X}_n = ({ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {1}_ {n} }} } { {{{x}^ {1} }_{\hspace{-.045in} {n} }} } },{ \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {2}_ {n} }} } { {{{x}^ {2} }_{\hspace{-.045in} {n} }} } }, \cdots, { \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {M}_ {n} }} } { {{{x}^ {M} }_{\hspace{-.045in} {n} }} } } )^T$ be a $M \times 3$ matrix representing the point normals of $\mathbf{X}$. Similarly, let $\mathbf{Y}_p$ and $\mathbf{Y}_n$ represent the positions and point normals of points in $\mathbf{Y}$ respectively. The diagonal matrix formed from a vector $\mathbf{v}$ is represented by $diag(\mathbf{v})$. A column vector of all ones is represented by $\mathbf{1}$ and a $P \times P$ identity matrix is represented by $\mathbf{I}_P$. The trace of a matrix $\mathbf{A}$ is represented by ${tr(\mathbf{A})}$. In [@Myronenko_2010_CPD], the authors consider $\mathbf{Y}$ as the centroids of a Gaussian mixture model (GMM) and $\mathbf{X}$ as the data points generated by the GMM. The probability density function for the GMM is then given by: $$\label{eq:prob_x} \begin{split} p(\mathbf{x}) = \sum\limits_{j = 1}^{M} P(j)p(\mathbf{x} \mid j) \end{split}$$ where $p(\mathbf{x} \mid j) = \frac{1}{{(2 \pi \sigma^2}) ^ {3/2}} exp\big(- \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p - { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } }}^2 \ \big)$ and $P(j) = \frac{1}{M}$. In our case, we need the density to also depend on the point normal orientations. Therefore, we modify $p(\mathbf{x} \mid j) $ with an additional term that depends on the orientation as shown below: $$\label{eq:xconditionaly} \begin{split} p(\mathbf{x} \mid j) = \frac{\alpha\ exp\big(\alpha { \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {T}_ {n} }} } { {{{x}^ {T} }_{\hspace{-.045in} {n} }} } } { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {n} }} } { {{{y}^ {j} }_{\hspace{-.045in} {n} }} } } \big)}{2 \pi (exp(\alpha) - exp(-\alpha))} \frac{exp\big(- \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p - { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } }}^2 \ \big)}{( {(2 \pi \sigma^2}) ^ {3/2} )} \end{split}$$ The above distribution is obtained by combining the original Gaussian distribution with another distribution, referred to as the Von Mises-Fisher distribution in directional statistics. The idea of combining these two distributions was first introduced by Billings and Taylor in [@Billings_2015_GIMLOP]. However, they do not involve a scaling parameter in their transformation. Since, our definition of a part involves uniform scaling, we cannot leave out the scale factor parameter from the formulation. Unlike [@Myronenko_2010_CPD], we do not include a uniform distribution to account for noise. Fig. \[fig:alpha\], shows the effect of the value of $\alpha$ on the distribution. We place an upper limit of ten on the value of $\alpha$ to maintain a good balance between the importance of position and orientation of points. The central idea behind this approach to registration is to parameterize the distribution defined by $\mathbf{Y}$ with a rotation matrix $\mathbf{R}$, uniform scale factor $s$ and a translation vector $\mathbf{t}$, and then estimate these parameters using maximum likelihood estimation (MLE) by treating the point set $\mathbf{X}$ as the observed data. After the parameterization, $p(\mathbf{x} \mid j) $ is given by: $$\label{eq:reparam_xconditionaly} \begin{split} p(\mathbf{x} \mid j) &= \frac{\alpha\ exp\big( - \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p - s \mathbf{R} \ { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } } - \mathbf{t}}^2 + \alpha { \ifthenelse{\equal{1}{1}} { {{\mathbf{x}^ {T}_ {n} }} } { {{{x}^ {T} }_{\hspace{-.045in} {n} }} } } \mathbf{R} { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {n} }} } { {{{y}^ {j} }_{\hspace{-.045in} {n} }} } } \big)}{2 \pi (exp(\alpha) - exp(-\alpha)) {(2 \pi \sigma^2}) ^ {3/2}} \end{split}$$ Like in [@Myronenko_2010_CPD], we define $P(j \mid \mathbf{x}^i) = \frac{ P(j) p(\mathbf{x}^i \mid j)}{p(\mathbf{x}^i)}$ as the correspondence probability between points $\mathbf{x}^i$ and $\mathbf{y}^j$. Using the i.i.d data assumption, the negative log-likelihood is given by: $$\label{eq:reparam_xconditionaly} \begin{split} \mathcal{L}(\theta) = \mathcal{L}(\mathbf{R},s,\mathbf{t},\sigma,\alpha) &= - \sum\limits_{i = 1}^N log \left( \sum\limits_{j = 1}^M P(j) p(\mathbf{x}^i \mid j) \right ) \end{split}$$ Where, $$\label{eq:xi_given_yj} p(\mathbf{x}^i \mid j) = \frac{\alpha\ exp\big( - \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p^i - s \mathbf{R} \ { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } } - \mathbf{t}}^2 + \alpha ({\mathbf{x}_n^i})^T \mathbf{R} { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {n} }} } { {{{y}^ {j} }_{\hspace{-.045in} {n} }} } } \big)}{2 \pi (exp(\alpha) - exp(-\alpha)) {(2 \pi \sigma^2}) ^ {3/2}}$$ [0.33]{} {width="\textwidth"} [0.33]{} {width="\textwidth"} [0.33]{} {width="\textwidth"} The Expectation Maximization (EM) algorithm is used to estimate the parameters that minimize the negative log-likelihood. The algorithm alternates between the E-step and the M-step until convergence. In the E-step, the posterior probability of the mixture components are computed as shown below: $$\label{eq:E-step} \resizebox{0.5\textwidth}{!}{$ P^{k}( j \mid \mathbf{x}^i) = \frac{exp\big( - \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p^i - \mathcal{T}_p({ \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } } ,\theta^{(k-1)} )}^2 + \alpha ({\mathbf{x}_n^i})^T \mathcal{T}_n({ \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {n} }} } { {{{y}^ {j} }_{\hspace{-.045in} {n} }} } } ,\theta^{(k-1)} ) \big) }{ \sum\limits_{m = 1}^M exp\big( - \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p^i - \mathcal{T}_p({ \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {m}_ {p} }} } { {{{y}^ {m} }_{\hspace{-.045in} {p} }} } } ,\theta^{(k-1)} )}^2 + \alpha ({\mathbf{x}_n^i})^T \mathcal{T}_n({ \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {m}_ {n} }} } { {{{y}^ {m} }_{\hspace{-.045in} {n} }} } } ,\theta^{(k-1)} ) \big)} $}$$ Where $\mathcal{T}_p({ \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } } ,\theta^{(k-1)} ) = s^{(k-1)} \mathbf{R}^{(k-1)} { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } } - \mathbf{t}^{(k-1)}$ and $\mathcal{T}_n({ \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {n} }} } { {{{y}^ {j} }_{\hspace{-.045in} {n} }} } } ,\theta^{(k-1)} ) = \mathbf{R}^{(k-1)} { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {n} }} } { {{{y}^ {j} }_{\hspace{-.045in} {n} }} } }$. The superscript $(k-1)$ indicates that the parameter values being used are the estimates from the previous iteration of the EM algorithm. In the M-step, the parameters need to be estimated by minimizing complete-data negative log-likelihood $Q$, which is given by: $$\label{eq:Q_theta} Q = - \sum\limits_{i=1}^N \sum\limits_{j=1}^M P^{k}( j \mid \mathbf{x}^i) log \big( P(j) p(\mathbf{x}^i \mid j) \big )$$ Considering only terms that depend on $\theta$, we can rewrite $Q$ as: $$\label{eq:E-step} \begin{split} Q(\theta) = \bigg( \sum\limits_{i=1}^N \sum\limits_{j=1}^M P^{k}( j \mid \mathbf{x}^i) \Big ( \frac{1}{2\sigma^2} {\@ifstar{\norm*{\@}_2}supnormnostar}*{\mathbf{x}_p^i - s \mathbf{R} \ { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {p} }} } { {{{y}^ {j} }_{\hspace{-.045in} {p} }} } } - \mathbf{t}}^2 - \\ \alpha ({\mathbf{x}_n^i})^T \mathbf{R} { \ifthenelse{\equal{1}{1}} { {{\mathbf{y}^ {j}_ {n} }} } { {{{y}^ {j} }_{\hspace{-.045in} {n} }} } } \Big ) \bigg)+ \frac{3N}{2} \log(\sigma^2) - N\log(\alpha) \ + \\ N\log \big( exp(\alpha) -exp(-\alpha) \big ) \end{split}$$ Like in [@Myronenko_2010_CPD], taking the partial derivative of $Q(\theta)$ with respect to $\mathbf{t}$ and setting it to zero gives: $$\mathbf{t} = \frac{1}{N} \big ( \mathbf{X}_p^T\mathbf{P}\mathbf{1} - s \mathbf{R} \mathbf{Y}_p^T\mathbf{P}\mathbf{1} \big ) \\$$ where $\mathbf{P}$ is a M $\times$ N matrix with elements $ {p_{ji} = P^{k}( j \mid \mathbf{x}^i) }$. Substituting $\mathbf{t}$ back into the equation (\[eq:Q\_theta\]) and setting ${\hat{\mathbf{X}} = \mathbf{X}_p - \frac{1}{N} \mathbf{1} \big( {\mathbf{X}_p^T\mathbf{P}\mathbf{1}} \big)^T}$ and ${\hat{\mathbf{Y}} = \mathbf{Y}_p - \frac{1}{N} \mathbf{1} \big( s\mathbf{R} {\mathbf{Y}_p^T\mathbf{P}\mathbf{1}} \big)^T}$, we get: $$\begin{split} Q(\theta) &= \frac{1}{2\sigma^2} \big [ tr \big ( \hat{\mathbf{X}}^T d \big( \mathbf{P}^T \mathbf{1}\big) \hat{\mathbf{X}} \big) - 2s\ tr \big( \hat{\mathbf{X}}^T \mathbf{P}^T \hat{\mathbf{Y}} \mathbf{R}^T\big) \\ &+ \ s^2 tr \big ( \hat{\mathbf{Y}}^T d \big( \mathbf{P} \mathbf{1}\big) \hat{\mathbf{Y}} \big)\big] + \alpha \ tr \big( \mathbf{X}_n^T \mathbf{P}^T \mathbf{Y}_n \mathbf{R}^T\big) \\ &+ \frac{3N}{2} \log(\sigma^2) - N\log(\alpha) + N\log \big( exp(\alpha) -exp(-\alpha) \big ) \end{split}$$ Let $\mathbf{A} = \hat{\mathbf{X}}^T \mathbf{P}^T \hat{\mathbf{Y}}$ and $\mathbf{B} = \mathbf{X}_n^T \mathbf{P}^T \mathbf{Y}_n $. Using the invariance of trace under cyclic matrix permutation, the fact that $\mathbf{R}$ is orthogonal, we can rewrite ${Q(\theta)}$ as: $$\label{eq:after_t} \begin{split} Q(\theta) &= \frac{1}{2\sigma^2} \big [ tr \big ( \hat{\mathbf{X}}^T d \big( \mathbf{P}^T \mathbf{1}\big) \hat{\mathbf{X}} \big) - 2s\ tr \big( \mathbf{A}^T \mathbf{R} \big ) \\ & + s^2 tr \big ( \hat{\mathbf{Y}}^T d \big( \mathbf{P} \mathbf{1}\big) \hat{\mathbf{Y}} \big)\big] + \alpha \ tr \big( \mathbf{B}^T \mathbf{R} \big) + \frac{3N}{2} \log(\sigma^2) \\ & - N\log(\alpha) + N\log \big( exp(\alpha) -exp(-\alpha) \big ) \end{split}$$ The form of equation (\[eq:after\_t\]) does not allow us to directly apply the method in [@Myronenko_2010_CPD] to estimate $\mathbf{R}$. Therefore, we use the BFGS algorithm to compute the parameters. For $\mathbf{R}$ to be a proper rotation matrix, it has to satisfy two constraints. I.e., $\mathbf{R}$ has to be an orthogonal matrix whose determinant is one. To avoid having to deal with these constraints during optimization, a reparameterization of $\mathbf{R}$ is necessary. We use the quaternion based parameterization of $\mathbf{R}$ based on [@terzakis2012recipe]. In [@terzakis2012recipe], the authors describe two different ways to parameterize a rotation matrix. We use the second method which stereographically projects a 3D hyperplane onto the 4D unit quaternion sphere. Such a parameterization not only removes the constraints but also provide rational expressions for the derivative of R, which becomes significant when iterative methods like BFGS are employed during optimization. The relevant equations from [@terzakis2012recipe] are provided below. The rotation matrix corresponding to an unit quaternion $\mathbf{q} = [q_0,q_1,q_2,q_3]$ is given by: $$\resizebox{0.5\textwidth}{!}{$\mathbf{R}(\mathbf{q}) = \begin{bmatrix} q_0^2 + q_1^2 - q_2^2 - q_3^2 & 2(q_1q_2 - q_0q_3) & 2(q_1q_3 + q_0q_2) \\ 2(q_1q_2 + q_0q_3) & q_0^2 - q_1^2 + q_2^2 - q_3^2 & 2(q_2q_3 - q_0q_1) \\ 2(q_1q_3 - q_0q_2) & 2(q_2q_3 + q_0q_1) & q_0^2 - q_1^2 - q_2^2 + q_3^2 \end{bmatrix} $}$$ The partial derivatives of the rotation matrix with respect to the components of the quaternion is given by: $$\begin{split} \frac{\partial \mathbf{R}(\mathbf{q})}{\partial q_0} &= 2\begin{bmatrix} q_0 & -q_3 & q_2 \\ q_3 & q_0 & -q_1 \\ -q_2 & q_1 & q_0 \end{bmatrix} \\ \frac{\partial \mathbf{R}(\mathbf{q})}{\partial q_1} &= 2\begin{bmatrix} q_1 & q_2 & q_3 \\ q_2 & -q_1 & -q_0 \\ q_3 & q_0 & -q_1 \end{bmatrix} \\ \frac{\partial \mathbf{R}(\mathbf{q})}{\partial q_2} &= 2\begin{bmatrix} -q_2 & q_1 & q_0 \\ q_1 & q_2 & q_3 \\ -q_0 & q_3 & -q_2 \end{bmatrix}\\ \frac{\partial \mathbf{R}(\mathbf{q})}{\partial q_3} &= 2\begin{bmatrix} -q_3 & -q_0 & q_1 \\ q_0 & -q_3 & q_2 \\ q_1 & q_2 & q_3 \end{bmatrix} \end{split}$$ As mentioned earlier, a stereographic projection is employed to project each point, $[x,y,z]$, on a 3D hyperplane onto a 4D unit quaternion sphere (see Figure 1 in [@terzakis2012recipe]). This mapping provides a way to represent a unit quaternion using a 3D vector. Given a point, $[x,y,z]$, on the hyperplane, the corresponding unit quaternion is given by: $$\begin{split} \beta^2 &= x^2 + y^2 + z^2 \\ \mathbf{q} &= \frac{1}{(\beta^2 + 1)} \bigg ( 2x,2y,2z,1-\beta^2 \bigg) \end{split}$$ The projection of a unit quaternion $\mathbf{q} = [q_0,q_1,q_2,q_3]$ onto the hyperplane is given by: $$\begin{split} \beta^2 &= \frac{1 - q_3}{1 + q_3} \\ \big ( x,y,z\big) &= \frac{\beta^2 + 1}{2} \big ( q_0, q_1, q_2\big ) \end{split}$$ The partial derivatives of the quaternions with respect to the point $\mathbf{\psi} = (x,y,z)$ is given by: $$\begin{split} \frac{\partial \mathbf{q}(\mathbf{\psi})}{\partial x} &= \frac{1}{(\beta^2 + 1)^2}\begin{bmatrix} 2(\beta^2 + 1) - 4x^2 \\ -4xy \\ -4xz \\ -4x \end{bmatrix} \\ \frac{\partial \mathbf{q}(\mathbf{\psi})}{\partial y} &= \frac{1}{(\beta^2 + 1)^2}\begin{bmatrix} -4xy \\ 2(\beta^2 + 1) - 4y^2 \\ -4yz \\ -4y \end{bmatrix} \\ \frac{\partial \mathbf{q}(\mathbf{\psi})}{\partial y} &= \frac{1}{(\beta^2 + 1)^2}\begin{bmatrix} -4xz \\ -4yz \\ 2(\beta^2 + 1) - 4z^2 \\ -4z \end{bmatrix} \\ \end{split}$$ The partial derivative of the rotation matrix, $\mathbf{R}$, with respect to $\mathbf{\psi}$ can now be written as: $$\begin{split} \frac{\partial \mathbf{R}(\mathbf{q}(\mathbf{\psi}))}{\partial x} &= \sum_{j = 0}^{3} \frac{\partial \mathbf{R}(\mathbf{q})}{\partial q_j} \frac{\partial q_j}{\partial x} \\ \frac{\partial \mathbf{R(}\mathbf{q}(\mathbf{\psi)})}{\partial y} &= \sum_{j = 0}^{3} \frac{\partial \mathbf{R}(\mathbf{q})}{\partial q_j} \frac{\partial q_j}{\partial y} \\ \frac{\partial \mathbf{R}(\mathbf{q}(\mathbf{\psi}))}{\partial z} &= \sum_{j = 0}^{3} \frac{\partial \mathbf{R}(\mathbf{q})}{\partial q_j} \frac{\partial q_j}{\partial z} \\ \end{split}$$ The partial derivatives required for optimizing $Q(\theta)$ using the BFGS algorithm are provided below: $$\begin{split} K_1 &= tr \big ( \hat{\mathbf{Y}}^T d \big( \mathbf{P} \mathbf{1}\big) \hat{\mathbf{Y}} \big) \\ K_2 &= tr \big ( \hat{\mathbf{X}}^T d \big( \mathbf{P}^T \mathbf{1}\big) \hat{\mathbf{X}} \big) \\ \frac{\partial Q(\theta)}{\partial \sigma} &= \frac{-1}{\sigma^3} \big ( K_2 - 2s \ tr(\mathbf{A}^T \mathbf{R} ) + s^2 K_1 \big) + \frac{3 N}{\sigma} \\ \frac{\partial Q(\theta)}{\partial s} &= \frac{-1}{\sigma^2} tr(\mathbf{A}^T \mathbf{R} ) + \frac{s}{\sigma^2} K_1 \\ \frac{\partial Q(\theta)}{\partial \alpha} &= -tr(\mathbf{B}^T \mathbf{R} ) - \frac{N}{\alpha} + N \frac{exp(\alpha) + exp(-\alpha)}{exp(\alpha) - exp(-\alpha)} \\ \frac{\partial Q(\theta)}{\partial x} &= \frac{-s}{\sigma^2} tr(\mathbf{A}^T \frac{ \partial \mathbf{R}}{\partial x} ) -\alpha \ tr(\mathbf{B}^T \frac{ \partial \mathbf{R}}{\partial x} ) \\ \frac{\partial Q(\theta)}{\partial y} &= \frac{-s}{\sigma^2} tr(\mathbf{A}^T \frac{ \partial \mathbf{R}}{\partial y} ) -\alpha \ tr(\mathbf{B}^T \frac{ \partial \mathbf{R}}{\partial y} ) \\ \frac{\partial Q(\theta)}{\partial z} &= \frac{-s}{\sigma^2} tr(\mathbf{A}^T \frac{ \partial \mathbf{R}}{\partial z} ) -\alpha \ tr(\mathbf{B}^T \frac{ \partial \mathbf{R}}{\partial z} ) \\ \label{eq:final_gradients} \end{split}$$ The steps involved in the registration algorithm are summarized in algorithm \[alg:estimate\_rst\]. [0.24]{} {width="\textwidth"} [0.24]{} {width="\textwidth"} [0.24]{} {width="\textwidth"} [0.24]{} {width="\textwidth"} ### Growing Parts Using Registration {#sec:specific_registration .unnumbered} In method 2, like in method 1, given an initial cross-sectional cluster, we grow parts by finding its neighboring cross-sectional cluster. Method 2 uses registration to find the neighboring cross-sectional cluster. From the definition of a part as a GC, we know that two cross-sectional clusters of a part are related to each other by a similarity transformation. In method 2, we use registration to estimate this transformation. For instance, there exists a rotation $\mathbf{R}$, uniform scale factor $s$ and a translation $\mathbf{t}$ that can transform cluster 0, in Fig. \[fig:growing\_stages\], to cluster 1. Looking at the two cross-sectional clusters, we can see that the rotation matrix in this case would be close to the identity matrix, the scale factor would be close to, but a little less than, one and the translation vector would point from the center of cluster 0, towards the center of cluster 1. The registration algorithm takes two point sets as its input. One of the point sets, $\mathbf{X}$, would be the cluster for which we are seeking a match. In our example, this would be cluster 0. The idea is to now provide points in the neighborhood of cluster 1 to the registration algorithm as the second point set, $\mathbf{Y}$. The registration algorithm would then find matches for points in cluster 0 in its neighborhood leading to the detection of cluster 1. In method 1, we did consider a group of planes whose orientation is close to the orientation of the cross-sectional plane of cluster 0. The second point set is formed by all points that are part of the inlier set of any of these planes (belonging to the set $\mathbf{A}_{\theta} \bigtimes \mathbf{A}_{\phi}$). As illustrated in Fig. \[fig:nxt\_seed\_point\] (b), these inlier points of various planes in set $\mathbf{A}_{\theta} \bigtimes \mathbf{A}_{\phi}$ will contain points in cluster 1. Some additional point, not part of cluster 1, are also contained in the inlier sets. But the registration algorithm is capable of dealing with the presence of some additional points. Given cluster 0 and the points in its neighborhood, the registration algorithm estimates the parameters, $\theta$. After registration, we still have to choose points from the second point set $\mathbf{Y}$ to form the neighboring cluster, cluster 1. Fig. \[fig:point\_selection\], illustrates the procedure of identifying points belonging to neighboring cluster, post registration. A 2D illustration is used for simplicity. As shown, the point $ \mathbf{y}^j \in \mathbf{Y}$ is chosen only if it has at least one point $\mathbf{x}^i \in \mathbf{X}$ sufficiently close to it and if the point normal orientations $ \mathbf{y}^j$ and $ \mathbf{x}^i $ are sufficiently close. Points $\mathbf{x}^i$ and $\mathbf{y^j}$ are considered sufficiently close if $d_{eucl}(\mathbf{x}^i_p, \mathbf{y^j_p}) \leq 1.5\sigma$, where $\sigma$ refers to the standard deviation of the GMM just estimated using the registration process. The point normal orientations are considered sufficiently close if the angle between them is less than $20^\circ$. As described above, the registration process can be used to detect cluster 1 given cluster 0. This process can be repeated to find a matching cross-sectional cluster for cluster 1, resulting in the detection of cluster 2. This process of growing a part stops when a good match cannot be found for a cross-sectional cluster. As mentioned above, $P(j \mid \mathbf{x}^i) $ is defined as the correspondence probability between points in the two point sets. For each point in $\mathbf{X}$, we can find the best match in $\mathbf{Y}$ using the correspondence probability, $P(j \mid \mathbf{x}^i) $. The average angular difference between the best matches is used to decide whether the growing process needs to be terminated. If the average angular difference between best matches is greater than $15^\circ$, the growing process terminates. As depicted in Fig. \[fig:why\_register\], method 2 is better equipped for dealing with junctions and therefore is the default method to grow parts. But when the cross-sectional cluster is sparse, the registration process cannot be relied on. The point normal estimation is itself unreliable in such a scenario. Therefore, method 1 is employed only when the cross-sectional cluster is sparse. In practice, if the cross-sectional cluster has less than hundred points in it, method 1 is employed. Optimal Part Selection {#sec:optimal_part_selection} ====================== In the previous section, methods to grow parts were described. The point cloud was clustered into $M$ clusters and one part per cluster was grown. Given these $M$ parts, we first assign costs to each part and then select the best subset of parts that cover the whole point cloud based on these scores. The overall cost has four components. Below, we first describe each of these components. The process of combining these components to obtain a single cost per part is then described. And finally we explain how the optimization process, which selects the best parts, is set up. Cost Components {#sec:cost_components} --------------- The first component is the registration cost. For a good part, the adjacent cross-sectional clusters would be a good match for each other. Remember, the relationship between adjacent cross-sectional clusters is defined by a similarity transform and via the registration process, we have estimated the best similarity transform parameters. After transformation (with the parameters estimated by the registration algorithm), the two point sets should be a good match to each other as illustrated in Fig. \[fig:point\_selection\] (b). Once we perform the registration between adjacent clusters of a part, for each point in the point set $\mathbf{X}$, we can find the best match in point set $\mathbf{Y}$ using the correspondence probability, $P(j \mid \mathbf{x}^i) $. The average angular difference between the best matches is used as the registration cost. Therefore, the registration cost would be low if the corresponding points in the two point sets have similar orientation. If a part is made up of $k$ cross-sectional clusters, we would obtain $k-1$ registration costs from pairs of adjacent clusters. To obtain the registration cost, we take the mean of these $k-1$ costs. The second component, referred to as the fit cost, measures the goodness of fit of the skeleton to the points that constitute the part. This cost is computed in the same manner as the cost, $c(\theta,\phi)$, in algorithm \[alg:cross-sectional\_plane\]. As explained before, and as depicted in Fig. \[fig:gc\_illustration\] (c), the point normals are expected to be perpendicular to the normal of the local cross-sectional plane. The fit cost is designed to penalize any deviations to this. To compute the fit cost, for a part with $k$ cross-sectional clusters, we compute the cost, $c(\theta,\phi)$, for each cross-sectional cluster and take their mean value. ![Skeletons are formed by joining cluster centers. The black lines represent the skeleton. The length of the skeleton is computed as the sum of the euclidean distances between cluster centers when traveling from one end ($C_0$) to the other end ($C_7$) of the part. The turning angles at cluster centers $C_1$ and $C_2$ are also shown.[]{data-label="fig:skel_cost_demo"}](images/skel_cost_demo-eps-converted-to.pdf){width="35.00000%"} The third component of the overall cost is the length of the part. The length here refers to the length of the skeleton. Since, skeletons are represented by cluster centers of the cross-sectional clusters, the length is computed as the sum of the euclidean distances between the centers as you travel from one end to the other end of the part. For instance, in Fig. \[fig:skel\_cost\_demo\], $ \sum\limits_{i=0}^6 d_{eucl}(C_i,C_{i+1})$ represents the length of the skeleton. Longer parts are preferred over shorter parts. Since, we prefer smooth curves as skeleton, the fourth component is the total turning angle of the skeleton. Fig. \[fig:skel\_cost\_demo\], shows how turning angles are computed. In the example shown, the total turning angle cost would be $ \frac{\sum\limits_{i=1}^6 \theta_i}{6}$. To obtain the overall cost, each individual cost component is first normalized separately by subtracting the mean and dividing by the standard deviation. Let $c_{reg}^i$, $c_{fit}^i$, $c_{len}^i $ and $c_{ang}^i $ represent the normalized registration, fit, length and turning angle costs of part $i$ respectively. The overall cost for part $i$ is then given by: $c_{ovr}^i = c_{reg}^i + c_{fit}^i - c_{len}^i + c_{ang}^i$. Note, during optimization we minimize the cost and since we prefer longer parts over short parts, we subtract the length component instead of adding it. Optimal Parts Selection ----------------------- Once we assign a cost to each part, the optimal subset of parts are chosen by minimizing the following constrained binary integer program. $$\begin{aligned} & minimize &\pmb{c}^T\pmb{x}\\ & \text{subject to} \end{aligned} \label{eq:optimization}$$ $$\begin{aligned} \pmb{x^{T} a} &\geq \left(\dfrac{k_1}{100}\right)\,N \tag{$C_1$}\label{cstr:c1}\\ \pmb{x^{T} Q\ x} &\leq \left(\dfrac{k_2}{100}\right)\,N \tag{$C_2$}\label{cstr:c2}\\\end{aligned}$$ $$\begin{aligned} & \text{where,} &\\ & \pmb{x} = (x^1,x^2, \cdots, x^M) \in \{0,1\}^{M \times 1}, \\ & \pmb{c} = (c_{ovr}^1,c_{ovr}^2, \cdots, c_{ovr}^M) \in {\mathbb{R}}^{M \times 1} \\ & \pmb{a} \in \mathbb{N}^{M \times 1} , \ \pmb{Q} \in \mathbb{N}^{M \times M} \\ \end{aligned}$$ [0.4]{} ![Linking all parts that can be potentially linked according to $G_{cnct}$ can lead to unnecessary additional connections. (a) The legs can potentially connect to both the torso and the tail parts. (b) The many links near the tail of the airplane are unnecessary.[]{data-label="fig:link_all"}](images/Link_all_1-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.44]{} ![Linking all parts that can be potentially linked according to $G_{cnct}$ can lead to unnecessary additional connections. (a) The legs can potentially connect to both the torso and the tail parts. (b) The many links near the tail of the airplane are unnecessary.[]{data-label="fig:link_all"}](images/Link_all_2-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.38]{} {width="\textwidth"} [0.38]{} {width="\textwidth"} [0.23]{} {width="\textwidth"} The optimization is carried out over the vector $\pmb{x}$, and individual components of $\pmb{x}$ indicate whether a particular part is selected or rejected. I.e., $x^i = 0$ implies that part $i$ is rejected and $x^i = 1$ implies that it is selected. Vector $\pmb{c}$ represents the costs associated with individual parts. Therefore, by minimizing $\pmb{c}^T\pmb{x}$, we are minimizing the overall cost. The trivial and uninteresting solution for $\pmb{x}$ is the vector of all zeros. But we are interested in solutions that cover almost all the points in the point cloud. Note, a point in the cloud is said to be covered if the optimization process selects a part, of which the point is a member. In order to force the optimization process to cover most of the points in the point cloud, we impose the constraint \[cstr:c1\]. The $i^{th}$ component of vector $\pmb{a}$ gives the number of points belonging to part $i$. Therefore, imposing constraint \[cstr:c1\] would ensure that at least $k1\%$ of the total number of points in the cloud are covered. The total number of points in the cloud is indicated by $N$. But if two of the selected parts share some points, these points would be counted twice. Note, a point in the point cloud can be a member of multiple parts. In Fig. \[fig:overview\] (a), for example, two parts (in the top-left corner) covering the tail portion have substantial overlap. If part $i$ covers $n_i$ points, part $j$ covers $n_j$ points and if the two parts share $n_s$ points, then the total number of points covered by selecting both parts $i$ and $j$ is $n_i + n_j - n_s$. To avoid too much overlap between parts, constraint \[cstr:c2\] is imposed. The element $q_{ij}$ of $\pmb{Q}$, represents the number of points that parts $i$ and $j$ share. Thus constraint \[cstr:c2\] ensures that the sum of pair-wise overlap (in terms of number of points) between parts is less than $k_2 \%$ of the total number of points in the cloud. To see this, note that, the element $q_{ij}$ is relevant only when both parts $i$ and $j$ are selected, i.e., when $x^i =1$ and $x^j = 1$. Note, the lower triangular part of $\pmb{Q}$ is zero to ensure that the pair-wise overlaps are not penalized twice. In short, the constraints ensure that most points in the point cloud are covered with little overlap between parts and the objective function ensures that this is done at a low cost (meaning the best parts are selected). The constrained binary integer program, described above, is solved using the Gurobi solver [@VJ-gurobi]. Since, the value of $M$, the number of candidate parts, is usually small (150 or less), the optimization algorithm converges fast, within a few seconds in most cases. The result of the optimization procedure is depicted in Fig. \[fig:overview\] (b). Once the individual parts that cover the point cloud are identified, the next step is to link them to obtain a skeletal representation of the shape. This procedure is explained in the next section. Linking Part Skeletons {#sec:linking_parts} ====================== The first step in linking skeletons is to determine potential connections among the various parts. For instance, the legs of the dinosaur in Fig. \[fig:overview\] (b) could be linked to the parts representing the torso or the tail but not to the parts representing the horn or neck of the dinosaur. I.e., a part can only be linked to a subset of other parts and the first step determines this subset of potential links for each part. To determine if two parts can be potentially linked to each other, a very simple observation is used. Two parts, say part A and part B, can be potentially linked only if there is at least one point in A who is the neighbor of some point in B. To determine if any two points in the point cloud are neighbors, the connectivity matrix $ G_{cnct} $, described in section \[sec:locally\_adaptive\_threshold\], is used. Linking all the parts that can be potentially linked would lead to strange additional connections like the one shown in Fig. \[fig:link\_all\]. Note, the parts extracted for the dinosaur and the airplane are shown in Fig. \[fig:overview\] (b) and Fig. \[fig:link\] (b) respectively. In the case of the dinosaur, the problem is that parts that could be combined, stay as separate parts. The skeletons for parts representing the tail and the torso of the dinosaur can be combined to form a single smooth curve. This process, of combining skeletal curve where it is possible, will be helpful later when we attempt to connect the legs of the dinosaur to the body. On the other hand if the tail and torso remain as separate parts, interconnecting the two legs, the torso and the tail could be confusing. Therefore, combining skeletons wherever it is possible would be a good first step. To decide if two parts can be combined, we check if the cross-sectional clusters at the end are a good match. This is done by registering the end cross-sectional clusters from the two parts. The end cross-sectional clusters for the torso and the tail of the dinosaur are shown in Fig. \[fig:link\] (a). After registering the two cross-sections, the registration cost (the same as the one defined in section \[sec:cost\_components\]) is computed. Keep in mind that a lower registration cost means that the points in one cross-sectional cluster, after registration, were able to find, near it, a similarly oriented match from the other cross-sectional cluster. If the registration cost, measured in terms of angular difference, is less than a threshold of $35^\circ$ and the scale factor difference from one is less than 0.5, it is decided to combine the two parts. These thresholds were chosen after experimenting with a few values. In the next step, we deal with parts that form connected components. If a part is only connected to one other part, there is no confusion as to how to link the parts. In Fig. \[fig:link\] (b), for example, part 5 has only part 1 as a potential link. Therefore, all that needs to be done is to connect par 5 to part 1. The case with part 6 is also the same. But when there are connected components, it is not immediately clear as to how to interconnect them. For instance, in Fig. \[fig:link\] (b), parts 1, 2, 3 and 4 form a connected component. The ideal way to interconnect them would be to find a junction point, and connect all parts to that single point forming one junction. To find the junction point, rays formed by extending the part skeletons are considered. Fig. \[fig:link\] (c), shows three part skeletons and the rays obtained by extending them. For each ray, the point that minimizes the sum of distances to the other rays is found. In the example in Fig. \[fig:link\] (c), for ray $\protect \overrightarrow{AB} $, we find the point on $\protect \overrightarrow{AB} $ that minimizes the sum of distances to rays $\protect \overrightarrow{ CD} $ and $\protect \overrightarrow{ EF} $. The same is done for rays $\protect \overrightarrow{CD} $ and $\protect \overrightarrow{EF} $. Among these points (we get one point per ray), the point with minimum sum of distances to the other rays is chosen as the junction point. ![An example of a clique of size three for which finding a junction point to interconnect the parts would not be appropriate. The key point is to see if it’s the same end point of a part that connects to all other parts in the clique.[]{data-label="fig:link_triangle_clique"}](images/Link_triangle_clique-eps-converted-to.pdf){width="25.00000%"} {width="95.00000%"} Finding a junction point to connect together all the members of the connected component would not be appropriate in the case when both end points of a part are involved in the clique formation. An example of such a scenario is shown in Fig \[fig:link\_triangle\_clique\]. Here, each end point of a part has only one potential link and therefore liking these parts together is straightforward. Hence, finding a junction point to link all the members of the connected component, is only appropriate when for each part involved, it is the same end point that connects to all the other parts in the component. Once, the issues depicted in Fig. \[fig:link\_all\] are addressed, all remaining potential connections are made to obtain the final skeleton. User Interface {#sec:GUI_Skel} ============== One significant advantage of a part based skeleton extraction algorithm is the ease with which users can interact with the algorithm. For point clouds that are not noisy, user interaction is unnecessary. But the part based algorithm can handle very noisy point clouds with little user interaction. To demonstrate the ease of interaction, a graphical user interface (GUI) was developed. Fig. \[fig:GUI\], shows the GUI with some annotations. Since the GUI is not the focus of this work, only a brief overview is provided and only the relevant features are explained. To begin the processing, the user can use the file browser to load the point cloud. Once the point cloud is loaded, the main display would show the rotating point cloud. Note, after each processing step the main display will update to show the corresponding results. The toolbar button labelled [“[Grow Parts]{}”]{} can be used to grow parts from initial cross-sections. I.e., this button executes steps described in sections \[sec:locally\_adaptive\_threshold\], \[sec:init\_cross-sections\] and \[sec:growing\_parts\]. The grown parts are then displayed on the two-by-two grid display on the right side of the main display. Note, all the displays (the main display and the grid displays) allow user interaction. I.e., the users can play/pause the rotation by double clicking on the display and also manually rotate the display using the mouse/touchpad. The button labelled [“[Part Selection]{}”]{}, can then be used to run the optimization routine that selects the optimal subset of parts. And finally, the [“[Link Part Skeletons]{}”]{} button can be used to link the individual part skeletons to obtain the final skeleton. The user may also choose to simply click the [“[Skeletonize]{}”]{} button to run all the steps (of generating parts, selecting optimal parts and linking selected parts) at once. The message box and the progress bar will provide the user with feedback on the status of the program execution. The two buttons labelled [“[Browse Parts]{}”]{}, can be used to browse through all the parts generated. The left and right arrows can be used to view the previous and next four parts respectively. After the parts are generated (by using the [“[Grow Parts]{}”]{} button), the users, instead of running the optimization routine, may choose to manually select the parts that they think are the best parts. For this purpose, each part shown in the grid display is accompanied with a checkbox that will allow the user to select that part. The users can instead run the optimization routine, which selects the best subset of parts, and then choose to correct mistakes, if any, made by the routine. For all parts that the optimization routine selects, the corresponding checkbox in the grid display would be checked. The user can browse through all the parts, after the optimization routine is run, and decide to reject the parts chosen by the routine by unchecking the corresponding checkbox. The user can also add to the currently selected list of parts by checking the checkbox corresponding to any unselected part. This procedure, allows the user to easily modify the selection of the optimizing routine with a few clicks. The user also has the option to permanently remove noisy parts from the available list of parts by clicking the [“[Remove]{}”]{} button. Results {#sec:results_skel} ======= ![ A synthetically generated GC.[]{data-label="fig:gc_pc"}](images/gc_pc_demo-eps-converted-to.pdf){width="45.00000%"} The results are divided into two sections. We first present the results for comparison of the our newly proposed registration algorithm with that of Myronenko and Song [@Myronenko_2010_CPD]. Next, the results of using the proposed algorithm for skeleton extraction are presented. Registration Results {#sec:reg_results} -------------------- As we described above, we use the registration algorithm to grow parts from initial cross-sectional clusters. Therefore, it is appropriate to use a similar setting to test the newly proposed registration algorithm. I.e., we first generate synthetic point clouds that represent GCs and then measure the accuracy of the registration algorithms in registering a random cross-sectional cluster with another randomly chosen neighborhood. For instance, in Fig. \[fig:gc\_pc\], the point cloud corresponding to a GC is shown. To measure the accuracy of the registration algorithms, we register the source cluster with the destination cluster. Since, the point cloud was generated by us, we can measure the accuracy by comparing the registration results with the ground truth. [0.255]{} ![ The random sampling of the point cloud could lead to inaccuracies in the registration if position alone is used to evaluate the fit.[]{data-label="fig:gc_contour_sampling"}](images/sampling_random-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.225]{} ![ The random sampling of the point cloud could lead to inaccuracies in the registration if position alone is used to evaluate the fit.[]{data-label="fig:gc_contour_sampling"}](images/sampling_regular-eps-converted-to.pdf "fig:"){width="\textwidth"} There are a couple of challenges that the registration algorithm has to overcome in order to accurately estimate the registration parameters. Understanding these challenges is important in understanding why it is appropriate to test the registration algorithms in the setting described above. One of the two challenges is related to the issue of random sampling. I.e., the points on a point cloud can be thought of as random samples from the surface of the shape. Or equivalently, they are random samples from a scaled rotated and translated 2D cross-sectional contour. Samples from two such contours from a point cloud are shown in Fig. \[fig:gc\_contour\_sampling\]. The point clouds are shown at the bottom with two contours highlighted, and the highlighted contours are shown at the top. The point cloud in Fig. \[fig:gc\_contour\_sampling\] (a) is obtained by transforming (i.e., scaling, rotating and translating) 2D contours which are sampled at random, while the point cloud in Fig. \[fig:gc\_contour\_sampling\] (b) is obtained by transforming 2D contours which are sampled at regular intervals. It is evident that, in the case of contours in Fig. \[fig:gc\_contour\_sampling\] (a), due to random sampling, a simple scaling of points in one of the contours would not produce the other point set exactly. Therefore, using just positional information to estimate the registration parameters would lead to inaccuracies in the estimate as we would demonstrate later. We would expect the registration algorithm to be able to handle point clouds like the one shown in Fig. \[fig:gc\_contour\_sampling\] (a). Adding the orientation information in such a scenario will make the registration process more robust and stable. To understand the second challenge, keep in mind the process of searching for a match, described in section \[sec:method\_2\]. Starting from an initial cross-sectional cluster, we search for a similar cluster in its neighborhood. The second cluster, therefore, is obtained from the neighborhood of the initial cluster and almost always has a lot more points than the initial cluster for which we seek a match. For example, in Fig. \[fig:gc\_pc\], the destination cluster is wider and has a lot more points than the source cluster. Looking just at the positional information of the points, to register the source cluster with the destination cluster, could lead to wrong estimates for the rotation parameter. Here again, penalizing large variations in point normal orientation, in addition to penalizing positional disparity, would significantly improve the estimates of the registration parameters. This is especially true if the neighborhood cluster has a lot more points than the initial cluster. Through experiments described below, we show that adding orientation information can effectively deal with these issues. Note, the random sampling issue and the issue of trying to find a match in a larger point cloud are issues encountered when registration is employed to grow parts. Since, the primary use of registration for us is in growing parts, it is only appropriate to test the registration algorithms in such a setting.The process of generating the point clouds is described next, followed by the description of the experiments and their results. ### Point Cloud Generation As shown in Fig. \[fig:gc\_illustration\], a scale function, a 2D cross-sectional contour and a 3D axis are the three components necessary to generate a GC. The following parametric equation is used to generate the 3D axis of the GC: $$( \ x(t),y(t),z(t) \ ) = ( \ C_1 cos(t), C_2 sin(t), C_3 t \ )$$ Where, $C_1, C_2$ and $C_3$ are random real numbers in the interval $(0,50)$. To obtain a smooth scale function, a sinusoidal curve with a random phase shift is used. Since scale values cannot be negative, a constant offset is added to the phase shifted sinusoid, to ensure that all the values are positive. In fact, the offset added is such that all values in the scale function are greater than or equal to one. To generate the 2D cross-sectional contour, we first generate a set of eight points as shown in Fig. \[fig:2D\_contour\]. The angular intervals between the points are equal and their distances to the origin is randomly chosen. We then fit a smooth, periodic, spline to these points to obtain the 2D cross-sectional contour. To obtain a GC, the 3D axis is sampled at regular intervals. In Fig. \[fig:gc\_illustration\], the red blobs on the 3D axis represent this discretization. The key idea in the construction of a GC is to place a rotated and scaled 2D cross-sectional contour at each sample point along the 3D axis. In fact, the 2D cross-sectional contour is translated in addition to rotation and scaling and the translation is determined by the 3D axis. The smooth scale function, defined above, is used to scale the cross-sectional contour along the 3D axis. To obtain a smooth rotation function along the axis, we employ the Frenet-Serret frame. I.e., at each point on the 3D axis, the tangent, normal, and binormal unit vectors of the axis, determines the rotation that needs to be applied at that point. Therefore, defining the 3D axis simultaneously defines the rotation that needs to be applied to the 2D cross-sectional contour along the 3D axis. Fig. \[fig:gc\_illustration\] (a) shows the GC generated when rotated and scaled 2D cross-sectional contours are placed at the sample points along the 3D axis. Since, we are interested in a point cloud representation of the GC, the 2D contour is sampled before applying the scaling, rotation and translation transformations. Note, the number of samples chosen for the 2D contour and the 3D axis would determine the sparsity/density of the point cloud. [0.24]{} ![Generating a random 2D cross-sectional contour. (a) Generate a set of points at equal angular interval of $\pi/4$ radians whose distance from the origin is random. (b) Fit a smooth closed contour (shown in red) to these points to obtain the 2D cross-sectional contour.[]{data-label="fig:2D_contour"}](images/2D_contour_points-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.24]{} ![Generating a random 2D cross-sectional contour. (a) Generate a set of points at equal angular interval of $\pi/4$ radians whose distance from the origin is random. (b) Fit a smooth closed contour (shown in red) to these points to obtain the 2D cross-sectional contour.[]{data-label="fig:2D_contour"}](images/2D_contour_curve-eps-converted-to.pdf "fig:"){width="\textwidth"} ### Experiments and Results [0.49]{} {width="\textwidth"} [0.49]{} {width="\textwidth"} [0.49]{} {width="\textwidth"} [0.49]{} {width="\textwidth"} As mentioned in section \[sec:reg\_results\] and as depicted in Fig. \[fig:gc\_pc\], to compare the registration algorithms, we register a randomly chosen source cluster with a randomly chosen destination cluster within the GC. We consider two different cases for comparing the registration accuracies. In one case we sample the 2D cross-sectional contour, before transforming it, randomly (as shown in Fig. \[fig:gc\_contour\_sampling\] (a)) and in the other case we sample the contour at regular intervals (as shown in Fig. \[fig:gc\_contour\_sampling\] (b)). Fig. \[fig:reg\_bar\_plots\], shows the results of comparing the two algorithms for both the cases. The results were obtained by performing five hundred registrations. I.e., a random GC point cloud was generated and a randomly chosen source cluster, within the GC, was registered with a randomly chosen destination cluster. This process was repeated five hundred times to obtain the results. Note, in the plots, [“[With Normals]{}”]{} refers to our method as it utilizes the point normal information. Similarly, the case in which the 2D contour is sampled at regular intervals is referred to as [“[Regular]{}”]{} and the other case is referred to as [“[Random]{}”]{}. In Fig. \[fig:reg\_bar\_plots\] (a), the mean error, from the five hundred registrations, in estimating the rotation matrix is shown. In [@huynh2009metrics], the author discusses various metrics employed to measure the difference between rotation matrices. We use the one based on the Frobenius norm which is given by: $$err_{rot}( \pmb{R}_1, \pmb{R}_2) \ = \ \| \pmb{I}_3 - \pmb{R}_1 \pmb{R}_2^T \|_F$$ where $\pmb{R}_1$ and $\pmb{R}_2$ are the two rotation matrices we want to compare. The value of this metric will be in the range $[0, 2\sqrt{2}]$. As shown in Fig. \[fig:reg\_bar\_plots\] (a), the proposed method that uses the normal information does better than the one in [@Myronenko_2010_CPD] in both cases. The difference is much higher in the random case. This is expected because an error function based just on positional information is less capable of dealing with the random sampling. Since, it is a little difficult to interpret the metric values for the rotation error, we also plot the error in the estimated orientation of the cross-sectional plane in Fig. \[fig:reg\_bar\_plots\] (b). These plots resemble the plots for the rotation error, but are easier to interpret as the error is measured in terms of the angle between the actual normal and the estimated normal of the cross-sectional plane and is expressed in degrees. In the context of growing parts, the accurate estimation of the cross-sectional plane orientation is crucial because an error in this estimate will accumulate as more registrations are performed to grow the part. The comparisons for the registration cost, defined in section \[sec:cost\_components\], are presented in Fig. \[fig:reg\_bar\_plots\] (c). Remember, the registration cost is mean difference in the point normal orientation between a point in the source cluster and its best match (found using the correspondence probability) in the destination cluster. Also keep in mind that, as described in section \[sec:specific\_registration\], if this cost is above the threshold of $15^\circ$, the part growth algorithm will decide that it is unable to find a good match in the neighborhood, and will terminate the growth process. Therefore, keeping this cost low is essential to obtain fully grown parts. As shown in Fig. \[fig:reg\_bar\_plots\] (c), proposed algorithm outperforms the other method in both the cases, significantly so in the case of random sampling. Also note that the rise in this cost, when comparing the regular case with the random case, is moderate for our registration method. The use of point normal information leads to a much more stable algorithm. Fig. \[fig:reg\_bar\_plots\] (d), shows the error in scale estimate. As it can be seen, the other method (i.e., the method in [@Myronenko_2010_CPD]) has a smaller scale error compared to our method. To understand this result better, keep in mind the observation that the estimated value of the parameter, $\sigma$, for our method is almost always much larger than the value estimated by the other method. For the other method, that only uses the positional information, to lower the cost, the points in the source cluster has to get as close as possible to the points in the destination cluster, and at the same time keep the value of $\sigma$ as small as possible. This can be done by tolerating bigger differences in point normal orientation. But for our method, since it uses both the orientation as well as positional information, getting closer to points in the destination cluster at the expense of larger differences in point normal orientation is not desirable. Moreover, the error in scale estimates is only about five percent on average in the worst case, which is not a significant error and does not have much consequences in the context of growing parts. This is true because the estimated parameters will decide which points in the neighborhood of a cross-sectional cluster would form the adjacent cluster. Therefore, the error is scale estimates is tolerable, as long as the error does not prevent the algorithm from picking the right neighboring points. Keep in mind that the value of the estimated $\sigma$ is used to determine the neighbors (see the explanation of method 2 in page ). This makes small errors in the scale estimate insignificant in the context of growing parts, especially because of the higher $\sigma$ value. As mentioned earlier, the error in rotation parameter estimates will accumulate as we perform multiple registrations to grow parts and therefore it is very significant to get it right. This again shows us why using the point normal orientation information is important in the context of using registrations to grow parts. And finally, to demonstrate the ability of our algorithm to handle the second challenge of registering the source cluster against a much larger destination cluster, mentioned in section \[sec:reg\_results\], we ran the following experiment. Like before, we performed five hundred random registration on synthetically generated GC point clouds. For each GC point cloud, we chose a random source cluster and two different neighboring destination cluster from within the GC. One of the neighboring cluster being much larger (more number of points included) than the other. We registered the source cluster against the two neighboring destination clusters for both methods. We then looked at the proportion of cases, from among the five hundred pairs of registrations for each method, where the registration with a larger destination cluster lead to larger errors in the estimated rotation parameter. For our registration method, in 16.2% of the cases, using a larger destination cluster (which is equivalent to looking for a match in a larger neighborhood in the context of growing parts) lead to larger errors in the estimation of the rotation parameter. This proportion was 72.2% in the case of the other method. This simply shows that our method is more robust to variations in the neighborhood size as we search for a matching cross-sectional cluster while growing parts. [ccccccc]{} {width="1.0\linewidth"} & {width="0.60\linewidth"} & {width="0.60\linewidth"} & {width="1.1\linewidth"} \ (a) & (b) & (c) & (d)\ \ {width="1.0\linewidth"} & {width="0.65\linewidth"} & {width="0.65\linewidth"} & {width="1.0\linewidth"} \ (e) & (f) & (g) & (h)\ \ {width="1.0\linewidth"} & {width="0.7\linewidth"} & {width="0.70\linewidth"} & {width="1.2\linewidth"} \ (i) & (j) & (k) & (l) \ Skeleton Extraction Results {#sec:skel_results} --------------------------- Skeleton extraction results for a variety of shapes are shown in Fig. \[fig:skeleton\_results\]. For each shape the individual skeletons for the parts identified by the algorithm are shown at the top and the linked skeleton is shown at the bottom. An extended gallery of results for skelton extraction, along with rotating 3D animations, is available at: <https://web.ics.purdue.edu/~vthottat/skel/>. The models were obtained mainly from the McGill 3D shape benchmark [@zhang2005retrieving] and from the 3D object recognition database, ObjectNet3D [@xiang2016objectnet3d]. As can be seen in Fig. \[fig:skeleton\_results\], the algorithm is capable of handling a wide variety of shapes. Both, flat objects like the circular table top (Fig. \[fig:skeleton\_results\] (f)) and spectacles (Fig. \[fig:skeleton\_results\] (i)), and rounder objects like the unicorn (Fig. \[fig:skeleton\_results\] (h)) or teddy bear (Fig. \[fig:skeleton\_results\] (j)) are handled well. [M[1.25cm]{} | M[2.0cm]{} M[2.0cm]{} M[2.0cm]{} M[2.0cm]{} M[2.0cm]{} M[2.0cm]{} M[2.0cm]{}]{}\ & (a) & (b) & (c) & (d) & (e) & (f) & (g)\ \ Cao et al. & {width="1.1\linewidth"} & {width="0.8\linewidth"} & {width="0.93\linewidth"} & {width="1.1\linewidth"} & {width="0.9\linewidth"} & {width="1.0\linewidth"} & {width="1.2\linewidth"} \ Our Results & {width="1.1\linewidth"} & {width="0.85\linewidth"} & {width="0.775\linewidth"} & {width="1.1\linewidth"} & {width="1\linewidth"} & {width="0.825\linewidth"} & {width="1.1\linewidth"} \ Huang et al. & {width="0.85\linewidth"} & {width="0.85\linewidth"} & {width="0.7\linewidth"} & {width="1.1\linewidth"} & {width="0.90\linewidth"} & {width="0.85\linewidth"} & {width="1.1\linewidth"} \ As shown in Fig. \[fig:GUI\], there are three parameters that can be tuned to obtain the desired results. The number of clusters from which candidate parts would be grown is one of the parameters. There should be at least as many clusters as there are parts. Remember, the final parts are selected from the candidate part list by the optimization algorithm (section \[sec:optimal\_part\_selection\]). Therefore, the number of clusters is usually set to a much higher value. In practice, depending on the shape, we use $50 n$ clusters, where, $1 \leq n \leq 4$. The parameters $k_1$ and $k_2$ are the optimization parameters that are defined in section \[sec:optimal\_part\_selection\]. The value of $k_2$, which determines the amount of overlap between parts in terms of the number of points they share, was set to $0.05$ for all the examples in Fig. \[fig:skeleton\_results\]. Keep in mind that it is possible for a point in the point cloud to be assigned to multiple parts. For example, a point at the intersection of multiple parts would be shared by all parts forming the junction. With $k_2 = 0.05$, less than five percent of all the points in the point cloud could be shared between various parts identified by the algorithm. The value of $k_1$ will decide the percentage of points covered by the parts chosen by the algorithm. Note that the optimization problem, described in section \[sec:optimal\_part\_selection\] may not be feasible for all values of $k_1$. For example, it might not be possible to cover 100% of the points in the cloud with only 5% overlap. Since, we would like the parts extracted to cover maximum number of points, the algorithm picks the maximum possible value of $k_1$. It does so by checking the feasibility, starting at 90% (i.e., $k_1$ = 0.90). If 90% is feasible then it tries a higher value, else it decreases the value of $k_1$. This process continues until, the maximum feasible value for $k_1$ is found. However, sometimes picking a value a little less than maximum feasible value for $k_1$ gives better results. Hence, the user has the option to modify this value through the user interface. We provide qualitative comparison of our results with the results from Cao et al. [@cao2010point], and Huang et al. [@huang2013L1] in Fig. \[fig:result\_comparison\]. We use the implementations provided by the authors themselves for the comparison. We found that using the default parameter settings for methods by Cao et al. and Huang et al., do not produce good results in most cases. Hence, we manually tuned the available parameters to obtain better results and the best results that were obtained are presented in Fig. \[fig:result\_comparison\]. Note, while we and Cao et al. use point normal information in our algorithms, Huang et al. do not use this information. However, keep in mind that the input to our algorithm is just a point cloud. As described in section \[sec:point\_normal\_estimation\], we estimate the point normals as a first step of our algorithm. Since the input to all the algorithms is the same, the algorithm of Huang et al. is not at any disadvantage. [0.24]{} ![The contracted points, at the end of the contraction step in the algorithm by Cao et al. [@cao2010point], is shown in red in (a) and (b). The final skeletons extracted by Cao et al., for point clouds shown in (a) and (b), are shown in (c) and (d) respectively.[]{data-label="fig:contraction"}](images/cao9_contraction-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.24]{} ![The contracted points, at the end of the contraction step in the algorithm by Cao et al. [@cao2010point], is shown in red in (a) and (b). The final skeletons extracted by Cao et al., for point clouds shown in (a) and (b), are shown in (c) and (d) respectively.[]{data-label="fig:contraction"}](images/cao2_contraction-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.24]{} ![The contracted points, at the end of the contraction step in the algorithm by Cao et al. [@cao2010point], is shown in red in (a) and (b). The final skeletons extracted by Cao et al., for point clouds shown in (a) and (b), are shown in (c) and (d) respectively.[]{data-label="fig:contraction"}](images/cao9-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.2]{} ![The contracted points, at the end of the contraction step in the algorithm by Cao et al. [@cao2010point], is shown in red in (a) and (b). The final skeletons extracted by Cao et al., for point clouds shown in (a) and (b), are shown in (c) and (d) respectively.[]{data-label="fig:contraction"}](images/compare/cao2-eps-converted-to.pdf "fig:"){width="\textwidth"} As shown in Fig. \[fig:result\_comparison\], the method by Huang et al. had difficulty in extracting skeletons for many of the point clouds shown. For the unicorn and the eagle ( Fig. \[fig:result\_comparison\] (g) and (f) respectively), parts of the skeleton were missing. For the hand (Fig. \[fig:result\_comparison\] (c)), the connection between the fingers are incorrect. Note, Huang et al. draws an initial set of samples from the point cloud to start their skeleton extraction process. We observed that even for the same set of parameters but different initial samples, the skeletons extracted varied widely. The method by Cao et al. did well on most point clouds except for the table (Fig. \[fig:result\_comparison\] (b)) and the suitcase (Fig. \[fig:result\_comparison\] (e)). In fact, these two cases demonstrate one of the drawbacks with their approach to skeleton extraction. As shown in Fig. \[fig:contraction\], when the contracted points closely represent the skeleton of the shape qualitatively, like in the case of the eight inter-connected toruses (Fig. \[fig:contraction\] (a)), the extracted skeleton (Fig. \[fig:contraction\] (c)) would correspondingly be good. But in Fig. \[fig:contraction\] (b), we can see that at the end of the contraction step, the contracted points do not resemble the skeleton of the round table top. Correspondingly, the extracted skeleton fails to provide a good representation for the skeleton of the table top. Note that distance field based approaches would also share this drawback. As shown in Fig. \[fig:result\_comparison\] (b), our method was able to extract a nice straight line skeleton for the table top, primarily because we are looking to extract part skeletons first. Similarly, our part based approach was able to extract centered skeletons for the point cloud shown in Fig. \[fig:result\_comparison\] (e). These examples show why decomposing objects into GCs to detect parts and part skeletons can effectively deal with a wide variety of shapes. Fig. \[fig:rocking\_chair\] compares the performance of our algorithm to that of Cao et al. in detecting skeletons from noisy point clouds. This point cloud represents a rough 3D shape reconstruction of a rocking chair. Notice that our algorithm successfully identifies the various parts within the noisy point cloud. For instance, it can be seen that our algorithm detected the seat of the rocking chair (shown in light green) as a GC. This demonstrates that using a very basic property like translational symmetry to detect GCs can be a powerful tool in identifying parts and thereby simplifying the skeleton extraction problem. This example also shows that our method can be used as the first step in denoising point clouds and in surface reconstruction. [0.24]{} ![Skeleton extraction with noisy point clouds. (a) Part skeletons extracted by our method with points belonging to different parts shown in different colors. (b) Skeleton extraction results from Cao et al.. []{data-label="fig:rocking_chair"}](images/rocking_chair_vj-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.21]{} ![Skeleton extraction with noisy point clouds. (a) Part skeletons extracted by our method with points belonging to different parts shown in different colors. (b) Skeleton extraction results from Cao et al.. []{data-label="fig:rocking_chair"}](images/rocking_chair_2_Cao_2-eps-converted-to.pdf "fig:"){width="\textwidth"} One of the limitations of our algorithm is that the method we use to link part skeletons, to form a complete skeleton of the shape, can sometimes lead to anomalies like the one shown in Fig. \[fig:torus\] (b). Keep in mind that we join individual part skeletons together using straight lines. The drawback of this can be clearly seen in Fig. . \[fig:torus\] (b), where this approach leads to an unnatural looking overall skeleton. The individual part skeletons of the parts detected by our algorithm shown in Fig. \[fig:torus\] (a). Ideally, the point cloud has to be segmented into eight toruses and each torus would be connected to two its neighbors. However, our algorithm does not succeed in extracting individual torus skeletons due to the presence of large number of junction regions where the translational symmetry of a torus breaks. In this case, the algorithm by Cao et al. succeeds in extracting a better skeletal representation of the shape as shown in Fig. \[fig:result\_comparison\] (c). As pointed out earlier, this is due to the fact that the point cloud at the end of the contraction step closely resembles the skeleton of the shape. [0.24]{} ![[]{data-label="fig:torus"}](images/vj9_parts-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.24]{} ![[]{data-label="fig:torus"}](images/vj9-eps-converted-to.pdf "fig:"){width="\textwidth"} We would like to point out an interesting observation regarding the ambiguity of part skeletons for the same part. The part skeleton extracted for the seat of the point cloud of a chair is shown in Fig. \[fig:ambiguity\] (a). This result was obtained when the number of clusters was set to 150 and using the maximum feasible value of $k_1 = 0.95$ (in equation \[eq:optimization\] , constrained \[cstr:c1\]) for this point cloud. Note that by setting $k_1 = 0.95$, we are asking the algorithm to cover at least 95% of the points in the cloud. In Fig. \[fig:ambiguity\] (b), the results obtained by setting $k_1 = 0.92$ is shown. Notice that the parts extracted are almost the same but the skeleton of the part representing the seat of the chair is now different. In fact, this result (i.e., Fig. \[fig:ambiguity\] (b)) is a qualitative better result than the one in Fig. \[fig:ambiguity\] (a). Also note that the points at the end cap region of the GC in Fig. \[fig:ambiguity\] (b) are not included by the algorithm as part of the seat. This shouldn’t be surprising because the translational symmetry based definition of a GC will not capture the end caps. However, the GC can capture the end caps if the skeleton is diagonal as is the case with Fig. \[fig:ambiguity\] (a). In short, very similar set of points representing the same part in a point cloud can be well represented by multiple skeletal curves due to the very general definition of a GC. Another example of such ambiguity can be seen by comparing the part skeletons in Fig. \[fig:ambiguity\] (a) and (c). Keep in mind that each part was assigned a cost which had four components. One of the components was length of the part skeleton. Longer part skeletons were given preference over shorter ones. Fig. \[fig:ambiguity\] (c) shows that removing the length component (i.e., not rewarding or penalizing length of parts) would result in a different set of part skeletons extracted. Note that the parts are almost the same, but the part skeletons are different. To summarize, the same part can be represented by multiple skeletal representations as per the definition of a GC. When such situations arise, there will be ambiguity in choosing the best skeletal representation. Since, our algorithm extracts parts and lists them as shown in Fig. \[fig:GUI\], it provides the user with the flexibility of manually choosing the best skeletal representation according to them. [0.15]{} ![Ambiguity in skeletal representation of parts. (a) The different parts identified, by our algorithm, are shown in different colors along with the skeleton shown as a red curve. (b) Parts identified and part skeletons extracted for a vale of $k_1$ (in equation \[eq:optimization\] , constrained \[cstr:c1\]) slighltly lesser than the maximum feasible value. (c) Part skeletons extracted when the length component is not part of the overall cost.[]{data-label="fig:ambiguity"}](images/ambiguity_diagonal-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.16]{} ![Ambiguity in skeletal representation of parts. (a) The different parts identified, by our algorithm, are shown in different colors along with the skeleton shown as a red curve. (b) Parts identified and part skeletons extracted for a vale of $k_1$ (in equation \[eq:optimization\] , constrained \[cstr:c1\]) slighltly lesser than the maximum feasible value. (c) Part skeletons extracted when the length component is not part of the overall cost.[]{data-label="fig:ambiguity"}](images/ambiguity_straight-eps-converted-to.pdf "fig:"){width="\textwidth"} [0.15]{} ![Ambiguity in skeletal representation of parts. (a) The different parts identified, by our algorithm, are shown in different colors along with the skeleton shown as a red curve. (b) Parts identified and part skeletons extracted for a vale of $k_1$ (in equation \[eq:optimization\] , constrained \[cstr:c1\]) slighltly lesser than the maximum feasible value. (c) Part skeletons extracted when the length component is not part of the overall cost.[]{data-label="fig:ambiguity"}](images/ambiguity_nolen-eps-converted-to.pdf "fig:"){width="\textwidth"} Implementation and Run Time =========================== The code is implemented in Python and takes about three minutes to run for a point cloud containing five thousand points with the number of clusters set to hundred on a 2.8 GHz Intel Core i7 processor with 16 GB RAM. We use Numba [@Lam_2015_numba] to accelerate the cost function evaluation and gradient calculations used for registering two 3D point clouds. Note that the registration function is called multiple times in order to grow a part. Even with a modest estimate of five calls to the registration function per cluster, the total number of calls would be around five hundred. Hence, it is essential to be able to quickly evaluate the cost function and compute gradients for the registration function. Growing parts is the most time consuming step in the algorithm. Since, two parts can be grown completely independently, this process is amenable to parallelization. Therefore, there is ample scope to speed up the computations by parallelizing the part growing stage. Conclusion ========== In this work we introduced a method to extract curve skeletons from unorganized point clouds by decomposing a shape into its parts. The parts are treated as generalized cylinders which are characterized by translational symmetry. Starting from the detection of thin cross-sectional clusters we grew parts by exploiting their fundamental property of translational symmetry. To do so, we introduced a point set registration method which is tailor made for the purpose of growing parts from thin cross-sections. By defining the parts as GCs and then relying primarily on the very definition of a GC to extract parts, we presented a very principled approach to 3D Point cloud decomposition. In the results section we demonstrated how the algorithm is capable of handling a wide variety of shapes. We pointed out the advantages of a part based approach over other state of the art methods. Another advantage of a part based approach is that it makes user interaction intuitive and easy. This was demonstrated with the help of a GUI. Acknowledgments {#acknowledgments .unnumbered} =============== Acknowledgment {#acknowledgment .unnumbered} ============== This research was supported by the National Eye Institute of the National Institutes of Health under award number 1R01EY024666-01. The content of this paper is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. | Mid | [
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Growing Plants to Save Lives Tucked behind old factory buildings on Penn’s South Bank campus stands a gleaming greenhouse. The $2 million structure, completed late last year, is state-of-the-art. Drip irrigation ensures each pot receives just the right amount of water. Humidity and temperature are precisely monitored and can be accessed and modified remotely. And if short winter days, snow cover, or cloudy skies prevent enough sunlight from entering the greenhouse, panels and lights on the ceiling adjust automatically to provide light that matches solar radiation. Such cutting-edge technology might seem over-the-top for a mere greenhouse. But the plants grown inside are not destined for a garden, farm, or windowsill; their intended fate is to save lives. The greenhouse is the domain of the School of Dental Medicine’s Henry Daniell, a professor in the departments of Biochemistry and Pathology and director of translational research. Daniell joined Penn’s faculty last year and has been working diligently to see his research move from the lab to the clinic. His life’s work centers on a unique means of delivering drugs and vaccinations to the human body. Instead of relying upon sterile injections to ferry the therapeutic protein of interest to the intended tissue, Daniell has used a humbler vehicle: lettuce leaves. His research has demonstrated the effectiveness of plant-based vaccines and therapeutics in treating nearly 30 conditions, from infectious diseases such as cholera, malaria, and anthrax, to autoimmune diseases such as diabetes and hemophilia. The way Daniell sees it, plant-based vaccines have a number of advantages over their traditional counterparts. They’re shelf-stable and don’t require refrigeration, they’re less likely than egg-based injections to provoke an allergy, they’re relatively easy to grow, and they’re safer because they only contain proteins from a pathogen, rather than the pathogen itself. Perhaps the greatest advantage of these vaccines and therapeutic agents, however, is their cost. “Interferon, a common cancer drug, for example, costs $30,000 to $40,000 for a four-month treatment, and a third of the global population earns $2 or less a day,” Daniell says. “To me, there is something morally not right about that. If you have something that saves lives, you have an obligation to make it available to everyone.” Manufacturing these so-called “green vaccines” does not require expensive purification equipment, and transporting and storing them doesn’t require a costly “cold chain” of refrigeration. Freed from these constraints, Daniell says the therapies could be produced and distributed relatively inexpensively, even to remote areas where refrigeration and electricity are rare commodities. In a soon-to-be published article that has attracted attention from pharmaceutical companies eager to scale up his techniques and make them available to patients, Daniell and colleagues have shown that his platform effectively counteracts one of the most dangerous complications of hemophilia treatment. And in the new greenhouse, he’s growing genetically modified tobacco and lettuce plants that could be used to vastly improve treatment for diabetes, HPV, polio, and hemophilia. Trials in humans could begin as early as next year. “This will be a paradigm shift in delivery of drugs,” Daniell says. “This will change the landscape and save lives.” Text by Katherine Unger Baillie Video by Rebecca Abboud Multimedia: Other Stories in Science & Technology Electric cars may be the future of driving, but first, the vehicles need to spark excitement among the general public. That’s why Penn students have been working hard for the past two years to build one of the world’s first electric racecars. | High | [
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Just another WordPress.com site Menu Broken Arm, Day Four It’s been brutal, let me tell you. Although I can’t say I know the pain Diane’s feeling, I can tell you that every time she gasps in pay, my poor little testicles get sucked right up into my abdominal cavity. It’s a very unpleasant feeling but serves to demonstrate the empathy I have for the pain she’s enduring. What makes it worse is the cast she received yesterday. When they first put it on it was OK, but by the time we got home se said it was loose, allowing her wrist to move. So, not being able to keep it entirely immobile, it hurts all the time. She wants her splint back because at least with that she got some respite from the pain once in a while. I suggested that we call the doctor now, and leave a message about the distress she’s in, but she’s my tough guy wife and plans to deal with it until Monday instead of interrupt her doctor’s weekend. What a gal, huh? That’s about all I have, except the Oregon Lady Ducks beat Baylor 7-4 in the loser bracket of the WCWS and will be playing again at 10 pm Eastern Time against LSU. One more loss in the tournament and they go home. That doesn’t have anything to do with a broken arm, I know, but we both enjoy watching the girls play. That brings me to one of my hot topics … Comcast, our cable provider, doesn’t deem it necessary to include female athletic events in the handy-dandy panel they provide for sporting events. For us, we push the “C” button on the remote (the one we can talk to) and the screen splits to show what’s currently playing on the channel we were watching, and a menu list of all current sporting events across the top: On Now (only man stuff), MLB, NBA, NHL, CFL, Soccer (men), and NASCAR. C’mon, Comcast. This is the Women’s College World Series, from criminy sakes. How about some respect for these Ladies? Don’t get me wrong, I like men’s sports, too, but I think it’s very unfair, maybe even sexist, to discriminate against the women in this way. Gotta quit and get off that soap box. I’ll end with a photo of Diane’s arm just before her purple case was applied. Maybe tomorrow will be better. I certainly hope so. I don’t know how many more times I can safely retract my testicles before it causes some sort of brain damage. | Mid | [
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Q: Why butane exist as a liquid in a lighter ? This is my go at explaining after researching ... Butane is light and normally would be a gas at standard atmospheric temperature and pressure due to Low boiling point (-1degrees) The butane gas is in liquid state in the lighter . This is because , when it is placed in the body of the lighter , it is placed there under very high pressure as compared to the open air in standard atmospheric temperature and pressure . Increasing the pressure of the butane gas forces the molecules closer together . This is because increase in pressure will also lead to increase in average kinetic energy meaning molecules need to 'hold' onto each other more to prevent themselves from breaking their bond. (LDF) With that theory, that means increase in pressure leads to increase in boiling point of the molecules because more heat is needed to break the bonds and move apart . Hence , When the butane gas are compressed at high pressures , (at a certain pressure for butane) , the alkane will undergo a phase change from gas to liquid. Now , am I right to say that the vapour pressure is equal to the pressure of the butane gases in the small container , That's why they undergo a phase change immediately ? A: Now, am I right to say that the vapour pressure is equal to the pressure of the butane gases in the small container, that's why they undergo a phase change immediately? You seem to have answered your own question. The pressure inside the lighter container is indeed the vapour pressure of the mixture of n-butane and iso-butane that it contains, at ambient pressure. Here is the pressure-temperature dependence for iso-butane: (Source) The high vapour pressure inside means that when you open the valve, a gaseous mixture of both isomers will come streaming out and some of the liquid mixture will spontaneously evaporate to replace it. | Mid | [
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Doctor Optics Red Dot on Glocks Thread Tools I have seen pictures here and on other sites that show some glocks with Dr. Optics Red Dot Sight Mounted to the top of the slide. But its not mounted to the slide via the dovetail its sunk into the gun. They Cut away material in the top back section of the slide and monted the sight down low ( I think it was on a Glock model 21). I have not been able to fnd these pictures again or the post on the website so I could ask the people who did the cutting? How is the sight mounted into that cut-away area? How hard was it to mount it. What holds the sight into the cut-away? Generally why and how does it work?? I guess it lowers the sight plane closer to the barrel for more accurracy. Thanks ill givem a call Monday. So I still will have to by a mount for the dovetailed rear sights on a glock or does that come with a standard model Doctor Red Dot. Ive heard some of the screws used to hold the dovetail down are kinda weak not very strong. Any Truth. I have no first hand experience with with Docter sights or J-Points, I have just been looking into them myself. I think the compliants about the screws are about the setscrews that hold the dovetail in place. They are quite small because of the small size of the dovetail itself. If you have a slide machined to accept the sight, the screws that hold it down are the ones that would hold the sight to the mount. I believe there are also positioning pins to help hold the sight in place. The mount is not used if you have the slide machined. I have a J Point mounted on my Glock 20. An old Tasco Optima 2000 on the the Glock 21. The mounts for both fit into the Dovetail on the slide. The J Point mount is better that the old Tasco mount, but they both work. I never had a set screw come loose yet and I only use the "Blue" loctite. The Red dot sights are very effective in all light conditions. Both of my dots art the 7 inch size. 50 yards shots are now easy. They also much faster and accurate that regular open sights. Glock Talk is the #1 site to discuss the world’s most popular pistol, chat about firearms, accessories and more. As our membership continues to grow we look forward to reading your stories and learning from your experiences. Membership is free and we welcome all types of shooters, whether you're a novice or a pro. Come for the info, stay and make some friends.. | Mid | [
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6 days ago 7 days ago 1 week ago 1 week ago Here’s hoping everyone had a safe and enjoyable Labor Day weekend, wherever you may have spent it. By now, most colleges are back in session, and the weeks leading up to Midnight Madness (October 12 this year) are often fraught with tales of players getting into all sorts of trouble as the combination of free time and warm weather results in a devilish concoction — let’s cross our fingers that the next six weeks are clean. One player who recently found himself unjustifiably in hot water to the point of school expulsion (at least according to an Ohio grand jury) is Xavier’s Dez Wells. The rising sophomore star spent his holiday weekend flying around and visiting potential new schools — specifically, Oregon, Memphis and Maryland — according to several published reports. Earlier contenders Louisville, Ohio State and Kentucky had been removed from his list for various reasons, and it now appears that Mark Turgeon’s program may be the clubhouse leader as Wells is expected to make his decision in coming days. According to the Washington Post, Wells’ trip to College Park seemed to produce a level of excitement that he didn’t experience (or at least, share) while touring the others. Regardless of where he ends up, that program will receive an unexpected yet instant infusion of talent into its backcourt. This UCLA situation involving its top recruiting class remains interesting. We mentioned in yesterday’s M5 that the big news over the weekend involved the NCAA investigating potential violations in the recruitments of Shabazz Muhammad, Kyle Anderson and Tony Parker. Athletic director Dan Guerrero fired back at this report on Monday, suggesting that such an investigation is “misleading and inaccurate” but offering little in the way of specific details beyond the simple statement that two Bruin players had yet to receive their amateur certification. A separate Monday report from Peter Yoon at ESPNLosAngeles stated that the two players not yet certified are Muhammad and Anderson (interestingly, Parker has been cleared, according to his source). Whether something substantive actually sticks to one or both of these elite recruits certainly must have UCLA fans nervous right now — the program’s resurgence depends almost entirely on the NBA-quality talent that these two are bringing to Westwood. If they are not available in 2012-13, UCLA likely drops from a top five team to a top 35 team, and Ben Howland’s job would correspondingly be in jeopardy. No doubt Howland’s blood pressure has risen over the last few days, and with good reason — acting as CEO of a major college basketball program is a stressful job. This is especially true in the midst of a crisis, such as the strong likelihood of a player mutiny that could threaten one’s reputation as well as his employment. Billy Gillispie, as we all now, has been hospitalized since Friday in a Lubbock hospital, and he is not expected to leave the premises soon as he receives ongoing treatment for high blood pressure. An early-morning episode Friday where his BP spiked to “dangerous” levels left the second-year head coach feeling the “worst” he’s ever felt. Presumably aware of what faces him once he returns to campus — to be certain, nothing short of a serious inquiry into how he runs his program — the salve for his long-term health might be to stay in the hospital for as long as possible. We certainly wish him the best in recovery on both his medical and professional counts. Some vacant assistant coaching positions were filled over the holiday weekend on both coasts, as Arizona State added two new members to Herb Sendek’s staff and Steve Lavin brought on a former one of his players to assist him at St. John’s. As Andy Katz notes on ESPN.com regarding ASU’s new hires, Sendek is clearly trying to make a bold statement in bringing former Sacramento Kings and Golden State Warriors head coach Eric Musselman in addition to Portland Trail Blazers assistant coach Larry Greer into his program. Three thousand miles away in Queens, Lavin hired former UCLA point guard Darrick Martin to help him with recruiting and coaching up their backcourt. Martin played under Lavin — then an assistant to Jim Harrick at UCLA — in the early 90s, leaving the program as the then-all-time leader in assists and steals before moving on to the NBA for 15 years. He also has ties to the NYC area, having played prep basketball across the Hudson River at Bob Hurley’s famed St. Anthony’s program in the mid-1980s. It’s not often that the media publishes an in-depth report essentially stating that nothing happened, but that appears to be the case with the bizarre yet compelling story that San Diego State‘s best-ever 34-3 season in 2010-11 was targeted by those involved with the University of San Diego point-shaving scandal as another viable option. FBI agents who at the time were monitoring the key individuals associated with the USD case were also keeping a very close eye on a number of SDSU players — and when we write “close eye,” try this on for size — several players were subjected to “physical and electronic surveillance, GPS tracking devices on cars, phone logs, infiltration of the team by an undercover agent, even recruitment of a player to be a confidential informant.” Uh, yeah — that’s serious stuff. Thankfully, the outcome of all of this surveillance was the aforementioned ‘nothing’ — whether because SDSU players from that illustrious season were never actually approached by point-shavers, or because they were smart enough to turn down those doing the asking — we’re not sure. Still, the FBI never accused any Aztec players of wrongdoing, and the school has been adamant in stating that none of its players were involved in any of the shenanigans that went on across town. Crazy story. | Mid | [
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Q: How can I select a PHP variable that relates to a specific percentage chance? I'm trying hard to wrap my head around what I'm doing here, but having some difficulty... Any help or direction would be greatly appreciated. So I have some values in a table I've extracted according to an array (brilliantly named $array) I've predefined. This is how I did it: foreach ($array as $value) { $query = "SELECT * FROM b_table WHERE levelname='$value'"; $result = runquery($query); $num = mysql_numrows($result); $i=0; while ($i < 1) { $evochance=@mysql_result($result,$i,"evochance"); // These values are integers that will add up to 100. So in one example, $evochance would be 60, 15 and 25 if there were 3 values for the 3 $value that were returned. $i++; } Now I can't figure out where to go from here. $evochance represent percentage chances that are linked to each $value. Say the the favourable 60% one is selected via some function, it will then insert the $value it's linked with into a different table. I know it won't help, but the most I came up with was: if (mt_rand(1,100)<$evochance) { $valid = "True"; } else { $valid = "False"; } echo "$value chance: $evochance ($valid)<br />\n"; // Added just to see the output. Well this is obviously not what I'm looking for. And I can't really have a dynamic amount of percentages with this method. Plus, this sometimes outputs a False on both and other times a True on both. So, I'm an amateur learning the ropes and I've had a go at it. Any direction is welcome. Thanks =) **Edit 3 (cleaned up): @cdburgess I'm sorry for my weak explanations; I'm in the process of trying to grasp this too. Hope you can make sense of it. Example of what's in my array: $array = array('one', 'two', 'three') Well let's say there are 3 values in $array like above (Though it won't always be 3 every time this script is run). I'm grabbing all records from a table that contain those values in a specific field (called 'levelname'). Since those values are unique to each record, it will only ever pull as many records as there are values. Now each record in that table has a field called evochance. Within that field is a single number between 1 and 100. The 3 records that I queried earlier (Within a foreach ()) will have evochance numbers that sum up to 100. The function I need decides which record I will use based on the 'evochance' number it contains. If it's 99, then I want that to be used 99% of the time this script is run. HOWEVER... I don't want a simple weighted chance function for a single number. I want it to select which percentage = true out of n percentages (when n = the number of values in the array). This way, the percentage that returns as true will relate to the levelname so that I can select it (Or at least that's what I'm trying to do). Also, for clarification: The record that's selected will contain unique information in one of its fields (This is one of the unique values from $array that I queried the table with earlier). I then want to UPDATE another table (a_table) with that value. So you see, the only thing I can't wrap my head around is the percentage chance selection function... It's quite complicated to me, and I might be going about it in a really round-about way, so if there's an alternative way, I'd surely give it a try. To the answer I've received: I'm giving that a go now and seeing what I can do. Thanks for your input =)** A: I think I understand what you are asking. If I understand correctly, the "percentage chance" is how often the record should be selected. In order to determine that, you must actually track when a record is selected by incrementing a value each time the record is used. There is nothing "random" about what you are doing, so a mt_rand() or rand() function is not in order. Here is what I suggest, if I understood correctly. I will simplify the code for readability: <?php $value = 'one'; // this can be turned into an array and looped through $query1 = "SELECT sum(times_chosen) FROM `b_table` WHERE `levelname` = '$value'"; $count = /* result from $query1 */ $count = $count + 1; // increment the value for this selection // get the list of items by order of percentage chance highest to lowest $query2 = "SELECT id, percentage_chance, times_chosen, name FROM `b_table` WHERE `levelname` = '$value' ORDER BY percentage_chance DESC"; $records = /* results from query 2 */ // percentage_chance INT (.01 to 1) 10% to 100% foreach($records as $row) { if(ceil($row['percentage_chance'] * $count) > $row['times_chosen']) { // chose this record to use and increment times_chosen $selected_record = $row['name']; $update_query = "UPDATE `b_table` SET times_chosen = times_chosen + 1 WHERE id = $row['id']"; /* run query against DB */ // exit foreach (stop processing records because the selection is made) break 1; } } // check here to make sure a record was selected, if not, then take record 1 and use it but // don't forget to increment times_chosen ?> This should explain itself, but in a nutshell, you are telling the routine to order the database records by the percentage chance highest chance first. Then, if percentage chance is greater than total, skip it and go to the next record. UPDATE: So, given this set of records: $records = array( 1 => array( 'id' => 1001, 'percentage_chance' => .67, 'name' => 'Function A', 'times_chosen' => 0, ), 2 => array( 'id' => 1002, 'percentage_chance' => .21, 'name' => 'Function A', 'times_chosen' => 0, ), 3 => array( 'id' => 1003, 'percentage_chance' => .12, 'name' => 'Function A', 'times_chosen' => 0, ) ); Record 1 will be chosen 67% of the time, record 2 21% of the time, and record 3 12% of the time. | Mid | [
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--- abstract: | Data obtained over the last three solar cycles have been analysed to reveal the relationships between theintensity of the photospheric field measured along the line of sight by the WSO group at heliolatitudes from -75 to 75 degrees and the intensity of the interplanetary magnetic field and absolute values of the perturbations of the different characteristics of the solar wind at the Earth orbit, and geomagnetic parameters. provided by the OMNI team. The heliospheric and geomagnetic data are found to be divided into two groups characterized by their response to variability of the solar magnetic field latitudinal structures on short and on long time scales. --- Title: To the question about perturbations of solar-terrestrial characteristics. Authors: E. A. Gavryuseva (Institute for Nuclear Research RAS) Comments: 14 pages, 6 Postscript figures *Keywords*: Sun; solar variability; magnetic field; interplanetary magnetic field; solar wind; geomagnetic perturbations; solar cycles Introduction ============ Solar magnetic field plays the main role in the heliosphere. It has to be study carefully the relations between the solar wind, the perturbations of geosphere and global structure of the photosperic magnetic field. WSO and OMNI data were used for comparison of 30 years long data sets (see referenses in Gavryuseva 2018c) on a long and short time scale. This paper is concentrated on the study the relations of between absolute values of these characteristics. This approach led to the conclusion that all solar wind data and geomagnetic perturbations that were examined divided into two groups characterized by sensitivity to the variability of the interplanetary magnetic field and photospheric field at different latitudes. We use Wilcox Solar Observatory data for the photospheric magnetic fields http://wso.stanford.edu/synopticl.html, (Scherrer et al., 1977), OMNI data for solar wind parameters at the Earth’s orbit, and indices of geomagnetic activity for the period 1976-2004, to study the relations between the solar wind, geomagnetic disturbances and solar drivers at different solar latitudes. In order to understand from which latitudinal zone the solar wind is originated and how it depends on the activity cycle it is necessary to know the latitudinal $SMF$ structure over at least 22 years. The latitudinal structure of the $SMF$ has been deduced for the last 29 years since May 27, 1976 from the Wilcox Solar Observatory (WSO) data (Scherrer et al., 1977; Gavryuseva & Kroussanova, 2003, Gavryuseva & Gogoli, 2006, Gavryuseva, 2005, 2006, 2006a,b, 2008a,b, 2018 and references there). The structure in latitude and time of the 1-year running mean of the solar magnetic field with 1 Bartels Rotation (BR, 1 BR = 27 days) step is shown on the upper plot in Fig. 1 Gavryuseva, 2018c. The solar wind and geomagnetic data were taken from the OMNI directory (http://nssdc.gsfc.nasa.gov/omniweb) which contains the Bartels mean values of the interplanetary magnetic field (IMF) and solar wind plasma parameters measured by various space-crafts near the Earth’s orbit, as well as geomagnetic and solar activity indices). First, daily averages are deduced from OMNI’s basic hourly values, and then the 27-day Bartels averages are deduced from the daily averages. The corresponding standard deviations are related to only these averages and do not include the variances in the higher resolution data. The $IMF$ and solar wind parameters taken into account are the following:\ $B_x$, $B_y$, $B_z$ and $B = (B_x^2+B_y^2+B_z^2)^{1/2}$ are the components and magnitude of the interplanetary magnetic field, in nT;\ Proton density, $N_p$, in $N/cm^3$;\ Proton temperature, $T_p$, in degrees $K$;\ Plasma speed, $V_p$, in $km/s$;\ Electric field, in mV/m;\ Plasma beta, $N_{\beta}= [(T*4.16/10^5) + 5.34] * N_p/B^2$;\ Ratio $N_{\alpha}/N_{p}$;\ Flow Pressure, $P$ proportional to $N_p*V^2$, in nPa;\ Alfven Mach number, $M_a = (V*N_p^{0.5})/20*B$.\ The geomagnetic parameters taken into account are the following:\ $AE$-index;\ Planetary Geomagnetic Activity Index, $K_p-$ index;\ $DST$-index, in nT.\ Sunspot number ($SSN$) was used, as well, for a further comparison. The $X$ axis directed along the intersection line of the ecliptic and solar equatorial planes to the Sun, the Z axis is directed perpendicular and north-ward from the solar equator, and the $Y$ axis completes the right-handed set. The solar wind parameters analysed cover the same period as the WSO solar data with one Bartels rotation resolution. We call the set of these 16 parameters taken from the OMNI data base as “solar wind” ($SW$) data; they include the interplanetary magnetic field, solar wind and geomagnetic parameters and sun spot number ($SSN$). Relationships between the Solar Magnetic Field Intensity/ and the Absolute Values of the OMNI Data/ on Long- and Short-Term Scales ================================================================================================================================== Physical connections between the Sun and the interplanetary parameters could be attributed to the influence of the intensity of the solar magnetic field without taking into account its polarity ($|MF|$). The corresponding correlation coefficients between the 1-year mean values of the $SMF$ intensity and absolute values of the $SW$ data ($|SW|$) as functions of time delay in years and in latitude are shown in Fig. 1. The $K_{cor}(|MF|, |SW|)$ have an 11-year periodicity for all the $SW$ data except the $IMF$ intensity $B$, and this periodicity is slightly visible in the $K_{cor}$ for the absolute values of the $B_y$: $|B_y|$ and $AE$: $|AE|$. There is a remarkable particularity of the latitudinal dependence of the\ $K_{cor}(|MF|, |SW|)$: the change of sign and a phase shift of the correlation coefficients at the heliographic latitude of about 50-55 degrees. This result can be interpreted as an evidence that the photospheric magnetic fields originated at the heliographic latitudes up to $\pm 55$ degrees propagate in the heliosphere and contribute to the perturbations of the solar wind and magnetosphere. The solar magnetic fields originated above $\pm 55$ degrees do not appear close to the Earth’s orbit (see also Gavryuseva, 2006c,f; 2008b; Gavryuseva & Gondoli, 2006). The $K_{cor}(|MF|, |SW|)$ are symmetric respect to the equator. This is well illustrated in Fig. 2 for the latitudinal dependence of the $K_{cor}(|MF|, |SW|)$ for the fixed optimum delay between the $SMF$ intensity and the absolute values of the $SW$ data. Thise figures are analogous to Fig. 11, 12 for the original (not absolute) $SMF$ (Gavryuseva, 2018c) and $SW$ values where the $K_{cor}(MF, SW)$ are antisymmetric to the equator. There is a clear anti-correlation between the intensity of the photospheric field of the activity belts and $B$, $V_p$, $P$, $N_p$, $N_{\beta}$ and $M_a$. This confirms that during high activity periods the slow solar wind prevails. Positive correlations of the $|MF|$ with the absolute values of the $AE$, $K_p$ and $DST$ indices correspond to the statement that most of the geomagnetic perturbations are originated from the low and middle latitudes when the intensity of the magnetic field is high. Figure 3 shows the latitudinal dependence of the $K_{cor}$ for the fixed optimum delay between the absolute values of the $SMF$ and $SW$ data after the filtering of the variabilities longer than 4 years and shorter than 1 year. The $K_{cor}$ for -$B_y$, $T_p$, $V_p$, $P$, $N_p$, $AE$, $K_p$ and $-DST$ have very similar latitudinal dependence, and the strongest correlation with the $SMF$ intensity takes place at about 40 degrees in the southern hemisphere. Owing to the symmetry of the solar magnetic field intensity $|MF|$ the latitudinal dependences of the $K_{cor}(|MF|, |SW|)$ and $K_{cor}(F|MF|, F|SW|)$ are also symmetric respect to the equator. These correlation coefficients are plotted in Fig. 4 together for all the $|SW|$ data for the long-term variability (on the left side) and for the short-term variability (on the right side). Figure 4 for the $K_{cor}$ of the absolute values of the $SMF$ and $SW$ data is analogous to the corresponding Figs. 14 and 15 for the original values of the $SMF$ and $SW$ data (Gavryuseva, 2018c). The difference between them permits to investigate the sensitivity of the $SW$ parameters to the $SMF$ polarity (and not only to the intensity of the SMF) and to the basic topology of the solar magnetic field. Cross-Correlation between the OMNI Data ======================================= The cross-correlation coefficients between the OMNI data provide an information limited to the relationships between them and could be useful for understanding why the $SW$ parameters are subdivided into two groups only. The parameters of the interplanetary field, solar wind and geomagnetic activity have been numbered as follows:\ 1: $B$, 2: $B_x$, 3: $B_y$, 4: $B_z$, 5: $T_p$, 6: $V_p$, 7: $E$, 8: $N_{\alpha}/N_p$, 9: $N_p$, 10: $P$, 11: $N_{\beta}$, 12: $M_a$, 13: $AE$, 14: $K_p$, 15: $DST$, 16: $SSN$.\ The cross-correlation was calculated and the corresponding correlation coefficients are plotted in Fig. 5. The corresponding numbers and short names of the parameters are shown along the $X$ and $Y$ axis. Asterisks correspond to the positive values of $K_{cor}$, and diamonds correspond to the negative values of $K_{cor}$. The size of the symbols is proportional to their values. On the top there are $K_{cor}$ for the original values of the $SW$ data (on the left side), and for their absolute values (on the right side). This makes difference for the $IMF$ components $B_x$, $B_y$ and $B_z$, for $E$ and for $DST$. On the bottom there are $K_{cor}$ for the residuals of the original values of the $FSW$ data (on the left side), and for the residuals of their absolute values (on the right side). From the first plot on the left top strong correlations between the parameters No 9, 10, 11, 12, 13 and between No 5, 6, 14 are deduced. Not very strong, but significant correlations take place between No 5, 6, 9, 13. Strong anti-correlations take place between No 4 and 7; No 14 and 15; No 5, 6 and 15, etc. Then there are anti-correlations between No 8 and 9, 10, 11, 12, 13, etc. Comparison between the other plots of Fig. 5 and the groups of the $SW$ data connected with the $B$ and $B_z$ (or $B_x$, $B_y$) permits to verify and to understand the existence of such groups. The study of such cross-relationships is very informative, but it does not provide a sufficient support to predict the $SW$ connection with the solar magnetic field while it helps to understand which of $SW$ parameters could respond in a similar way to the solar perturbations. Direct comparison of the $SW$ data with the basic topology of the $SMF$ permits to study SMF – SW relationships. An influence of the solar activity (or solar magnetic field intensity) on the $SW$ parameters was investigated by the analysis of their correlation on short subsequent intervals of time. Fig. 6 shows the correlation through solar cycles between the 3-year long sub-sets of the data corresponding to the absolute values of the photospheric field and to the absolute values of the solar wind and geomagnetic parameters. It is clearly visible that the main source of geomagnetic perturbations is concentrated in the helio-latitudinal zone from -55 to 55 degrees about Some summary remarks ==================== Southward-directed interplanetary magnetic field is considered a primary cause of geomagnetic perturbations (Durney, 1961; Gonzales et al., 1994, 1999). As a consequence the orientation of the interplanetary magnetic field (Axford and McKenzie, 1997; Low, 1996; Parker, 1997; Smith, 1997) plays an important role. The solar activity phenomena depend on the sunspot cycle, which can be characterized by the variability of the $SMF$ intensity in time and along the latitudes. The topology of the solar magnetic field influences the geomagnetic perturbations through the intensity and orientation of the interplanetary magnetic field and/or through other parameters of the solar wind. In this approach we could understand the presence of two groups of the OMNI data similarly sensitive to the basic topology of the magnetic field of the Sun (from the point of view of the dependence on latitude and phase-shift of the correlation of the coefficients with the mean latitudinal magnetic field). The formal and complete study of the problem of solar-terrestrial relations has been performed and the connections between the processes on the way from the Sun to the Earth have been revealed. A useful information was deduced from the temporal behaviour and dependence of the correlation of the photospheric magnetic field and different parameters of interplanetary space and geomagnetosphere. It was revealed directly from the experimental data that there are two groups of $SW$ parameter which respond in a similar way to the behaviour of solar characteristics. We found that the photospheric field influences the magnitude of the interplanetary field and, in the same way, the proton density, flow pressure, Alfven Mach number and plasma $\beta$ respond to the $SMF$. Moreover the $AE$-index behaves in a similar way as the above mentioned solar wind parameters. On the contrary, regarding the planetary geomagnetic activity index $K_p$ we can deduce that solar activity events (CME, magnetic field intensity, sunspots, etc.) through perturbations of the $B_z$ component ($B_x$, $B_y$ components) of the $IMF$, the proton temperature $T_p$, plasma speed $V_p$, $N_{\alpha}/N_{p}$ ratio influence the $K_p$ index. The variations of the $-B_z$ ($B_y$) component produce the perturbations of the $DST$ index, and they are of opposite sign of the $K_p$ and $B_x$ time dependence. It was also revealed from the experimental data that the solar magnetic fields and solar activity processes originated bellow $\pm 55$ degrees propagate up to the Earth orbit and produce the perturbations of the magnetosphere (Gavryuseva, 2006 c,f; 2008b, Gavryuseva & Godoli, 2006). These results are useful for understanding the origin of solar wind and geomagnetic perturbations and for long-term predictions. Acknowledgments {#acknowledgments .unnumbered} =============== I thank the WSO and OMNI teams for making available data of measurements of the solar magnetic field, solar wind and geomagnetic quantities. I am grateful to Prof. G. Godoli for his stimulating interest in these results and Profs. B. Draine, L. Paterno and E. Tikhomolov for help in polishing this paper and useful advises. Axford, W.L. and McKenzie J.F. (1997), The solar wind, in Cosmic winds and the heliosphere, ed. by J.R. Jokipii, C.P. Sonett & M.S. Giampapa, 31. Clua de Gonzalez, W. D. Gonzalez, S. L. G. Dutra, B. 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(2006b), Basic topology and dynamics of magnetic field leading activity the Sun Solar Activity and its Magnetic Origin, Proc. of the 233rd Symposium of the IAU, Cairo, Egypt, March 31 - April 4, 2006, Ed. V. Bothmer; A. A. Hady. Cambridge: Cambridge University Press, 67. Gavryuseva, E. (2006c), Variability of the differential rotation of the photospheric magnetic field through solar cycles Solar Activity and its Magnetic Origin, Proc. of the 233rd Symposium of the IAU, Cairo, Egypt, March 31 - April 4, 2006, Ed. V. Bothmer; A. A. Hady. Cambridge: Cambridge University Press, 65. Gavryuseva, E. (2006d), North-South asymmetry of the photospheric magnetic field Solar Activity and its Magnetic Origin, Proc. of the 233rd Symposium of the IAU, Cairo, Egypt, March 31 - April 4, 2006, Ed. V. Bothmer; A. A. Hady. Cambridge: Cambridge University Press, 63. Gavryuseva, E. (2006e), Longitudinal structure of the photospheric magnetic field Solar Activity and its Magnetic Origin, Proc. of the 233rd Symposium of the IAU, Cairo, Egypt, March 31 - April 4, 2006, Ed. V. Bothmer; A. A. Hady. Cambridge: Cambridge University Press, 61. Gavryuseva, E. (2006f), Relationships between photospheric magnetic field, solar wind and geomagnetic perturbations over last 30 years Solar Activity and its Magnetic Origin, Proc. of the 233rd Symposium of the IAU, Cairo, Egypt, March 31 - April 4, 2006, Ed. V. Bothmer; A. A. Hady. Cambridge: Cambridge University Press, 291. Gavryuseva, E. (2008a), In search of the origin of the latitudinal structure of the photospheric magnetic field, ASP Conf. Ser., v. 383, Proc. of “Subsurface and atmospheric influence on solar activity”, held at NSO, Sacramento Peak, Sunspot, New Mexico, USA 16-20 April 2007, Ed. R. Howe, R. W. Komm, K. S. Balasubramaniam & G. J. D. Petrie, 99. Gavryuseva, E. (2008b), Longitudinal structure originated in the tachocline zone of the Sun, ASP Conf. Ser., v. 383, Proc. of “Subsurface and atmospheric influence on solar activity”, held at NSO, Sacramento Peak, Sunspot, New Mexico, USA 16-20 April 2007, Ed. R. Howe, R. W. Komm, K. S. Balasubramaniam & G. J. D. Petrie, 381. Gavryuseva, E. (2018), Latitudinal structure and dynamic of the photospheric magnetic field, arXiv:1802.02450. Relations between variability of solar and interplanetary characteristics To the connection between intensity of the solar and geomagnetic perturbations, arXiv:1802.NNNN(N) Gavryuseva, E. (2018), Latitudinal structure and dynamic of the photospheric magnetic field, arXiv:1802.02450 Gavryuseva, E. (2018b), Longitudinal structure of the photospheric magnetic field in Carrington system, arXiv:1802.02461 Gavryuseva, E.; Godoli, G. 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(2005b), Short-term periodicities in solar indices, Solar Phys., 227, 155. Li, Y., Luhmann, J. G., Arge, C. N., Ulrich, R., How do solar magnetic fields influence the long term changes of some geomagnetic indexes?, American Geophysical Union, Spring Meeting 2001, abstract SH52A-02, 2001. Pizzo, V. J., A three-dimensional model of corotating streams in the solar wind. III Magnetohydrodynamic streams, J. Geophys. Res., 87, 4374, 1982. Wang, Y.-M., J. Lean, and N. R. Sheeley, The long-term variation of the Sun’s open magnetic flux, Geophys. Res. Lett., 27, 505, 2000. Low, B.C. (1996), Solar activity and the corona, Solar Phys., 167, 217. Luhmann, J. G., Li, Y., Arge, C. N., Gazis, P. R., Ulrich, R., Solar cycle changes in coronal holes and space weather cycles, J. Geophys. Res., 107(A8), 1154, pp. SMP 3-1, 2002. Makarov, V. I., Tlatov, A. G., Callebaut, D. K., Obridko, V. N., Increase of the Magnetic Flux From Polar Zones of the sun in the Last 120 Years, Solar Physics, v. 206, Issue 2, p. 383-399 (2002). Parker, E.N., (1997), Mass ejection and a brief history of the solar wind concept, in Cosmic winds and the heliosphere, ed. by J.R. Jokipii, C.P. Sonett and M.S. Giampapa, p.3. Rivin, Yu.R. (1989), Cycles of the Earth and of the Sun, Nauka, IZMIRAN, p.36. Smith, E.J., (1997), Solar wind magnetic field, in Cosmic winds and the heliosphere, ed. by J.R. Jokipii, C.P. Sonett and M.S. Giampapa, p.425. Stamper E.J., (1997), Solar wind magnetic field, in Cosmic winds and the heliosphere, ed. by J.R. Jokipii, C.P. Sonett and M.S. Giampapa, p.425. Stamper, R., Lockwood, Wild, M.N., Clark, T.D.G., (1999), Solar causes of the long-term increase of the geomagnetic activity, J. Geophys. Res., 104, Issue A12, pp.28,325. Pizzo, V. J. (1982), A three-dimensional model of corotating streams in the solar wind. III Magnetohydrodynamic streams, J. Geophys. Res., 87, 4374. Scherrer, P.H., J.M. Wilcox, L.Svalgaard, T.L. Duvall, Ph.H. Dittmer and E.K. Gustafson (1977), The mean magnetic field of the Sun: observations at Stanford. Solar Phys., 54, 353. Wang, Y.-M., J. Lean, and N. R. Sheeley (2000), The long-term variation of the Sun’s open magnetic flux, Geophys. Res. Lett., 27, 505. {width="39pc"} {width="39pc"} {width="39pc"} {width="39pc"} {width="39pc"} {width="39pc"} | Mid | [
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The present invention concerns security protection within a secure device and pertains particularly to a method and apparatus for performing a secure operation. In order to protect against theft or misuse, security devices are utilized to protect property. The property can be tangible or intangible. An example of intangible property that often requires protection is information stored within an integrated circuit memory. One solution is to include security features on the integrated circuit upon which the information is stored. In this way, the information may be encrypted and access to the encrypted information can be limited. For some applications, however, implementation of a security system on a single integrated circuit may not be feasible. For example, a security system may be implemented using two integrated circuits. A first integrated circuit is a security device and a second integrated circuit is a non-volatile memory such as an erasable programmable read-only memory (EPROM) or a flash memory. The security device encrypts information using a security key, unique to the security device, before storing the information on the non-volatile memory. This protects the information from being read by other devices. One problem with this approach is that there can be susceptibility to a "replay" attack. In a replay attack the data stored in the non-volatile memory is copied. Later the copied data can be used to restore the information within the non-volatile memory to a previous value. For example, suppose the security system is used to keep track of an amount of money. Further, suppose the security system initially has $50 to spend in an "off-line" system. If the security system is implemented using two integrated circuits, the security device encrypts the amount "$50" using a security key and places the encoded value in the non-volatile memory. Without the security key, the encrypted amount is safe from decryption. Further, without the security key it would be extremely difficult to replace the encrypted amount of $50 with another valid dollar amount. However, now suppose that the contents of the non-volatile memory is copied. This copy of the contents includes the encrypted amount of $50. The $50 now may be spent by the user of the security system. After all the money has been spent, the security device encrypts the amount "$0" using the security key and places the encoded value in the non-volatile memory. However, the copy of the contents the non-volatile memory can now be copied back to the non-volatile memory and replace the current contents. Since the copy of the contents was made when the encrypted amount was $50, the copy back from the previous contents of the non-volatile memory results in restoration of the encrypted amount to $50. Thus, when the replacement of the contents of the non-volatile memory is not detectable to the security device, it can allow the security system to be circumvented. | Low | [
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Q: What is SOA, Microservices, REST and Web Services "in plain English"? Could somebody explain SOA, Microservices, REST and Web Services in simple terms. It is really fascinating and confusing me. Any help would be appreciated. A: SOA (Service oriented architecture) as the name suggests that it is combination of services. These services are loosly coupled and interacts with each other to provide a solution. Services may be RESTful web service to carry out some function. Microservices - Again as the name suggests micro services. The idea behind microservices is that it becomes easier to build and maintain some type of services when they are broken down into smaller, composable pieces that work together. Webservices - A service (some functionality like checking seat availability in a train) available on web is known as web service. Such services communicate over the WWW using HTTP. REST - It is just an architectural style for designing webservices. We can think like this:- SOA is having some services. These services are combination of microservices. Those microservices are exposed as webservices and the webservices are build on REST. | High | [
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NEW DELHI: Delhi’s reputation as a city on short fuse was again reinforced on Saturday night, when the son of an Army man shot at a youth outside a west Delhi eatery because he was “speaking too loudly”. The attack came five days after a man was stabbed to death at a food stall in south-east Delhi’s Okhla wholesale market for not paying a bill of Rs 200. In east Delhi’s Sunlight Colony the same day, a customer poured boiling oil on a momo stall owner when asked to pay for a plate of momo. On Saturday night, the assailant, Nitesh Yadav, who was having dinner inside a car, lost his cool and allegedly shot at a young man with his father’s pistol for arguing too loudly with the food stall owner. A youth, Jagat, was shot at for “speaking too loudly” outside an eatery near the main Janakpuri market. The Jagat, and his friends had arrived for dinner and were refused food as the stall owner had shut shop for the day. The youths got into an argument demanding dinner, saying other customers were still having their dinner. During the exchange of words, another customer, Nitesh Yadav, who was having food with his friend Lakshay inside a Maruti Swift car parked nearby, called Jagat and asked him to keep quite. Nitesh even offered to sort out the dispute. When Jagat turned down the offer, Nitesh pulled out a pistol and shot at him but missed. Police said Nitesh has been arrested. Hearing the gunshot, the other customers fled but Jagat managed to call the cops, who arrived from the Janakpuri police station. They arrested Nitesh and Lakshay from the spot and recovered the pistol along with three live cartridges. During interrogation, Nitesh said the gun belonged to his father, Lal Singh Yadav, a non-commissioned officer with the Army. He had taken the gun from his father as a retainer. He claimed to have a B Tech degrees and said he ran a transport agency in Janakpuri. Nitesh told police that he had shot Jagat as he was angry with him for speaking too loudly and refusing to take his help in sorting out the matter with the restaurant owner. A case of attempt to murder under section 307 IPC and the arms Act was registered against him. | Mid | [
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Exposure assessment and risk characterisation of ethyl carbamate from Korean traditional fermented rice wine, Takju and Yakju. Ethyl carbamate is one of the most hazardous chemicals naturally occurring in food, and is present in alcoholic beverages. Korean traditional rice wine, Takju and Yakju, is frequently consumed in Korea, but there have been no studies characterising the risks of ethyl carbamate in these products. In order to assess and characterise the exposure risk of ethyl carbamate in Korean traditional rice wines, ethyl carbamate was investigated by means of GC-MS. The analytical methods were optimised and validated through determining linearity, detection limit, quantification limit, recovery and precision. A total of 283 traditional Korean rice wines, including 175 Takju and 108 Yakju samples, were analysed. Exposure assessment was performed by factoring in ethyl carbamate content, daily consumption and body weight. Daily exposures of ethyl carbamate were estimated for adults in four age groups, and risks of ethyl carbamate were characterised by the margin of exposure, which is more than 10 000. Based on this study, the risks of ethyl carbamate in Korean traditional rice wine were shown to be of low concern. | Mid | [
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In recent years, it is strongly demanded that internal combustion engines such as automotive internal combustion engines address low power consumptions and regulate carbon dioxide emissions and unburned gas emissions from the viewpoint of global environmental protection. In order to meet such a demand, new types of internal combustion engines such as lean-burn engines, direct-injection engines and low-emission engines have been developed. For ignition of air-fuel mixtures in these developed internal combustion engines and for efficient ignition of air-fuel mixtures in the conventional internal combustion engines, there is a need for spark plugs that have higher ignition performance than conventional ones. As one type of such a high-ignition-performance spark plug, a spark plug is known which includes a center electrode, a noble metal tip welded to a front end of the center electrode, a ground electrode and a noble metal tip welded to a front end of the ground electrode facing the center electrode so as to generate a spark discharge between the noble metal tips. Patent Document 1 discloses a spark plug that includes a center electrode (30) and a ground electrode (40) arranged facing each other, with a spark gap (50) left between the center and ground electrodes, and a noble metal tip (45) joined at one end thereof by laser welding to a spark-gap-side surface (43) of the ground electrode, wherein the cross sectional area of the other end of the noble metal tip is in the range of 0.12 mm2 to 1.55 mm2; wherein the length (L) of protrusion of the noble metal tip from the ground electrode is in the range of 0.3 mm to 1.5 mm; and wherein there is formed a fused part (47) in which the ground electrode and the noble metal tip are fused together so that the outer surface (47a) of the fused part linking the circumferential surface (45a) of the noble metal tip with the surface (43) of the ground electrode to which the noble metal tip is joined has a concave curved shape with a radius (R) of curvature of 0.1 mm to 1.0 mm. The noble metal tips of the respective electrodes are formed of alloys containing noble metals such as platinum and iridium as main components. As these alloys are expensive, there is a problem that the spark plugs with the noble metal tips increase in cost. Another type of spark plug in which the electrode has a protrusion formed by processing the ground electrode itself in place of the noble metal tip has also been proposed. For example, there is proposed a technique of forming a protrusion on one side of the ground electrode by extruding the opposite side of the ground electrode. More specifically, Non-Patent Document 1 mentions as follows: “This feature enables it to be pushed-out directly from top towards center electrode as shown in FIG. 16. By conducting this process, new fine-wired portion was achieved with smaller material cost and a more simple production way when compared to the conventional fine-fired electrode.”, that is, teaches that the ground electrode can be produced at low cost by extrusion process. | Mid | [
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Games National Service (NS) is one amongst the key foundations, along side philosophy and spiritual harmony, in Singapore's distinctive social material. each male of the fashionable generation has saw the rites of NS, together with our easiest athletes. These athletes leave their faculties as future sports champions of our nation, however only a few of them truly fulfill their potential to try to to Singapore proud in international competitions. What happened to those potential sports stars? Did NS hinder their passion and motivation to stand out in their sports? Why do thus few stick with it in their sports when college and NS? In our national go after a lot of sporting excellence and glories, maybe it's time to re-look at our NS policy and see however we are able to really support and encourage the journeys of those potential sports stars while not essentially compromising the safety of the state. The argument that NS is prejudicial to the event and continuous journey of our budding athletes from college isn't new. Athletes WHO area unit affected are fighting for years to induce the Ministry of Defence (MINDEF) to form special concessions and arrangements for them to continue with their coaching programs with their sports coaches. In most cases, MINDEF has adopted a general guide line that athletes will still continue with their sports career as long as their obligations with their various NS units don't seem to be compromised. This primarily implies that athletes can need to calculate the nice graces of their commanding officers to form special arrangements for them to continue reebok women's princess sneaker coaching, and at a similar time fulfill their coaching and duties with their units. A most troublesome task at the best. Any category|premium|top|best|top rate|quality} jock can tell you that so as to achieve success and be competitive with the remainder of the opposite world class athletes, coaching double each day, seven day every week, with full nutritionary and physiological support is common follow. NS coaching by itself is already robust, and asking our athletes to pay time in NS and train at a similar time is simply unacceptable. once visaged with this example, most of our athletes don't have any selection however to drop out. solely a few, with smart lucky and determination are able to realize the time to balance the NS commitments and coaching to the impact that some live of success is feasible. Even these athletes don't compare well once competitory against different sportsmen from round the world. however do sportsmen in countries while not obligatory NS fair? allow us to investigate a small amount additional. In the Olympic Games, the same old powerhouses that garner the foremost medals embody countries like China, USA, Russia, Australia, Britain, Germany, and to an explicit extend Asian country and Japan. Do these countries have obligatory military service? the solution isn't any. A logical conclusion here is that their athletes have unobstructed ways towards their sporting ambitions and peak performance in sports. in fact some would possibly argue that these countries area unit massive in terms of their population size. China features a population of one.3 billion. Surely, from these mass of individuals, champions for numerous sports is found. that's true. allow us to currently examine countries with similar population as Singapore and compare their sport achievements. A search on the web can reveal that the subsequent countries have comparable population size as Singapore (5m); Noreg (4.8m), Ireland (4.5m), Croatia (4.4m), New Seeland (4.3m), Finland (5.3m) and Danmark (5.5m). What strikes you as you read this list? These area unit all countries with documented sports achievements despite their restricted population size. The 3 Scandinavian Countries listed higher than have won in access of 350 Gold Medals all told athletic competition Games, and that they also are well painted in World Sports Events. Noreg and Danmark has featured in several soccer World Cups. European nation is consistent in manufacturing NHL skilled ice-hockey players. As for eire and Republic of Croatia, they need won eight and three Olympic Gold medals severally in their history. however allow us to not forget these 2 countries also are power homes in different sports. eire options extremely in tourney soccer, rugby football and even golf. Republic of Croatia produces the most effective water-polo and handball groups often on the planet Stage. would like we are saying a lot of regarding New Zealand? except for the All Blacks, New Seeland has additionally created thirty six Olympic Gold in their history. These countries didn't have immense population bases like China and Russia, however nevertheless they need been systematically no-hit in peak performance in sports. By the way, did I mention that these countries don't have any obligatory military service for his or her citizens? | Mid | [
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# $NetBSD: Makefile,v 1.72 2020/08/17 20:19:13 leot Exp $ DISTNAME= gpredict-2.2.1 PKGREVISION= 3 CATEGORIES= ham MASTER_SITES= ${MASTER_SITE_GITHUB:=csete/} GITHUB_RELEASE= v${PKGVERSION_NOREV} EXTRACT_SUFX= .tar.bz2 MAINTAINER= [email protected] HOMEPAGE= https://sourceforge.net/projects/gpredict/ COMMENT= Gnome satellite tracking program LICENSE= gnu-gpl-v2 # runtime dependency only DEPENDS+= hamlib-[0-9]*:../../ham/hamlib USE_LANGUAGES= c c++ USE_TOOLS+= gmake msgfmt pkg-config intltool USE_PKGLOCALEDIR= yes GNU_CONFIGURE= yes .include "../../devel/gettext-lib/buildlink3.mk" .include "../../devel/glib2/buildlink3.mk" .include "../../x11/gtk3/buildlink3.mk" .include "../../www/curl/buildlink3.mk" .include "../../graphics/goocanvas2/buildlink3.mk" .include "../../mk/bsd.pkg.mk" | Mid | [
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Grad Plus loan problems cooleylawstudent I am on the 3 year plan which the stafford loan falls a few grand short of fully covering, I can probally come up with that much and for books/gas on my own, but for rent and utilities I needed the gradplus loan. I signed up for it and was denied due to credit issue which I understand since I fell beyond on payments awhile back and its still on my report. Here's the thing, I offered to get a cosigner for it but they told me that Gradplus loans cant use a cosigner only private loans can(which are MUCH higher fees) does anyone know of a bank that allows cosigners for gradplus loans? Also, I heard that I can only work 20 hours if "fulltime" per week. Is that true? Has anyone else faced this problem? How'd you fix it? Wrong. 20 hours is for all law students regardless of year. The only way around this is if you are enrolled part-time and then they can't stop you from working 20 hours a day if you wanted. But yeah, I agree with armyjag that they don't go around and ask for your timesheets, but it could be seen as an honor code violation if you do it, and if you plan on doing legal work most employers, knowing that you are in school, won't let you work more than 20 hours anyway Is your school a FFELP school or a Direct Loans school? If it is a FFELP school you can use any lender for the GradPlus you want. You may have to make special arrangements to get your loans disbursed and really stay on top of things to use a lender that isn't on your school's preferred list but it is totally possible. In years past, many lenders offered the option of getting a cosigner or endorser if you couldn't qualify on your own. Some companies may have ditched that due to the financial crisis. I would just start calling lenders and ask them. Make sure you ask if they will lend a borrower attending your school before you do anything else though. Here is a list of lenders I found online. It's probably not comprehensive but should get you started: Make sure your cosigner or endorser understand that they will have to pay back the loan if you can't and make sure they have good credit. If they don't have good credit, you will not get a loan. Also, keep in mind this person will have to re-authorize and sign off each year for your loans. If they decide not to during 2L and 3L, you could be screwed. In general, I would try to clear up any credit issues before going to law school. Even if you can get a grad plus loan somehow for all 3 years, you may have trouble with the character and fitness portion of your state's bar exam. Logged cooleylawstudent I ended up getting one that accepted a cosigner(my wife even though we have the same house and household income) You mentioned the same cosigner each year? In theory couldnt someone get a different cosigner each year if needed? WHy would it need to be the same one?(I probally will keep useing her I am just curious) You will need a co-signer each year. Who it is doesn't matter. What I was trying to say is that it's good to have someone you can rely on or multiple people who can cosign, in case the first person changes their mind and doesn't want to cosign for 2L and 3L. Out of curiosity, were you able to get a GradPlus loan? Or did you have to get a private loan? | Mid | [
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286 So.2d 271 (1973) Samuel KIPNIS, Petitioner, v. William L. TAUB and Tom Ogburn, Respondents. No. 73-1082. District Court of Appeal of Florida, Third District. December 11, 1973. Kovner, Mannheimer, Greenfield & Cutler and Steven J. Rose, Miami, for petitioner. Talianoff & Bader, Miami Beach, for respondents. Before PEARSON, CARROLL and HAVERFIELD, JJ. PER CURIAM. We are presented with a petition for certiorari and a cross-petition for certiorari; each petition seeks review of a portion of an order entered by the trial court in a proceeding in garnishment. The cross-petition for certiorari is denied and, in view of our custom of not writing opinions upon denial of petitions for certiorari, the cross-petition will not be discussed further. The petition for certiorari filed by the petitioner, Samuel Kipnis, is granted and a portion of the order hereafter delineated is quashed. Petitioner Kipnis secured the issuance of a writ of garnishment against the Jefferson National Bank of Miami Beach garnishing the assets of respondent, William L. Taub. Respondent immediately filed a motion to dissolve garnishment and secured an early appointment for hearing thereon. At the hearing, the trial court denied the motion to dissolve garnishment but rendered the writ ineffective as to certain items. The order provided as follows: * * * * * * "2. Effective September 5, 1973 the Garnishee, JEFFERSON NATIONAL BANK OF MIAMI BEACH, is authorized and directed to pay checks drawn on the garnished account of WILLIAM L. TAUB bearing a date on or prior to August 17, 1973, which may have been issued to the following named persons in the approximate amounts as set forth after their names. A.B. Cheylac $ 2,500.00 c/o Clair Jourdan Claire Jourdan 215.00 Claire Jourdan 685.00 Peter Smillie and/or Harriet Smith 100.00 Ron Howie 200.00 663-5th Ave. Corp. 50.00 So. Bell T & T 150.00 New York Telephone Co. 75.00 Hampshire House 570.00 Howard Kurman 500.00 New York Athletic Club 129.31 Bank of America 650.00 Master Charge 200.00 "Any of the above checks and all other items bearing a date subsequent to August 17, 1973 shall be returned with directions to redeposit the same within 15 days." *272 * * * * * * We know of no statute or rule of law which permits the type of exception here carved into the effectiveness of a writ of garnishment. The respondent Taub has likewise been unable to present us with any authority for this action of the trial court. The rule is that once a bank account has been garnished, the bank is obligated to retain funds of the depositor in obedience to the writ. See Fla. Stat. § 77.06(2), F.S.A. See also Fla. Stat. § 673.3-409, F.S.A. Cf. Poland v. Love, 164 F. 186 (8th Cir.1908). Accordingly, the court's order dated the fourth day of September and appearing in case # 73-16201 of the Circuit Court of the Eleventh Judicial Circuit, be and same is hereby quashed as to the second paragraph thereof and shall remain in full force and effect as to all other portions thereof. It is so ordered. | Mid | [
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Q: Simplest way to check edge set for transitivity I'm playing around with tournaments and currently have the problem that I need to check whether a given subset of the edges of a tournament is transitive (it need not be acyclic). I'm aware that I can always take the transitive closure of the edge set and see whether it terminates without adding a single edge or not, but I was wondering if there might be a simpler way than that. Note that I'm specifically going for simplicity, not efficiency; the tournaments I want to check are over a maximum of $7$ vertices, so complexity really isn't an issue. I would prefer simple, easy to implement ways. The simplest I could find so far is Floyd-Warshall, but maybe someone knows anything that's simpler still. A: There's a very simple algorithm for this: for each edge (u,v) in the graph: for each edge (v,w) in the graph: if (u,w) is not in the graph, return "Not transitive" return "Transitive" Basically, if the graph is not transitive, then you can always find some path of length two $u\to v \to w$ such that the edge $u \to w$ is not present in the graph. If the graph is transitive, there won't be any such path of length 2. So, just check this condition. | Mid | [
0.6453333333333331,
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WikiLeaks' founder Julian Assange will head to London's High Court on Tuesday to try to reverse an extradition order that would send him to Sweden for questioning about sexual assault allegations. In February, a district judge ruled that Sweden's extradition request was valid despite arguments from Assange's legal team that, if charged, he would face an unfair trial since press and the public are excluded from portions of sexual assault trials. Assange, 40, of Australia, has not been charged by Swedish prosecutors, who say they want to question Assange about sexual encounters with two women in Sweden last August. Sweden filed a European Arrest Warrant and Assange voluntarily turned himself into U.K. police on Dec. 7. His attorneys argued at the February hearing that an extradition request should only be filed when a person is charged and not for questioning. But Sweden's legal representative, Clare Montgomery, argued that the country intends to charge him. Since the hearing in February, Assange has changed his legal team and will now be represented well-known human rights lawyers Gareth Peirce and Ben Emmerson. Neither had a comment on Monday on the appeals hearing, which is scheduled to last two days. At its conclusion, the judges will likely returning a ruling at a later date. Assange has sought to connect his personal legal problems as retribution for the work of WikiLeaks, which angered the U.S. government when it began releasing more than 250,000 secret U.S. diplomatic dispatches leaked to the website last November. The U.S. has not charged Assange with a crime, however, although he has been under investigation. If Assange is sent to Sweden, both Sweden and the U.K. would have to give their approval if the U.S. tried to extradite him. So far the only person charged in connection with the release of the cables is U.S. Army Private First Class Bradley E. Manning. He is charged with mishandling and transferring classified information and awaiting trial at the U.S. Army's detention facility in Fort Leavenworth, Kansas. WikiLeaks continues to release the diplomatic cables, although the documents are not generating the massive media coverage as when the site first began posting the documents. Just 16,068 of 251,287 cables have been released so far, according to the site on Monday, and cables continue to trickle out daily. WikiLeaks' main site, however, has not been taking new submissions "due to re-engineering improvements the site to make it both more secure and more user-friendly." "We anticipate reopening the electronic drop box and live chat support in the near future," according to a note on its submissions page. WikiLeaks has also been struggling with accepting donations since Visa, MasterCard, PayPal, Western Union and the Bank of America cut off payment links due to the cables release, costing what the organization claims US$15 million. It has since set up alternative ways to accept money. Assange has been free on bail since December is staying in Norfolk, England, at the manor of Vaughan Smith, who founded the journalism organization the Frontline Club. Send news tips and comments to [email protected] | Mid | [
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