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Studies on the optimal immunization schedule of experimental animals. V. The effects of the route of injection, the content of Mycobacteria in Freund's adjuvant and the emulsifying antigen. The effects of several conditions for the immunization of mice was studied using an aliquot of a viomycin (VM) protein conjugate as the common primary or booster antigen. Responses of the mice were assessed by measuring mouse serum levels of total immunoglobulin G (IgG) and anti-VM antibody responses using the newly improved two assay methods. The choice of route was found to be a very important factor in immunization and intraperitoneal injection was the most optimal among the four routes studied. The effect of the concentration of Mycobacteria in Freund's complete adjuvant (FCA) was also studied, and it was found that a diluted FCA was more effective than a commercial FCA. The effect of the controlled release of the antigen was studied and three important phenomena were observed: The mice immunized by the mini-osmotic pump-aided controlled release of the antigen responded with similar small amounts of both total IgG and anti-VM antibody regardless of the presence or absence of FCA in the antigen; emulsifying the antigen with FCA was a very important condition for the effective elicitation of the specific antibody; a mixture of antigen and FCA without emulsifying produced little specific antibody and a large amount of total IgG. The more effectively immunized mice responded with a larger decrease in body weight soon after the primary injection. | High | [
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package com.browseengine.bobo.facets.attribute; import java.util.Iterator; import java.util.List; import com.browseengine.bobo.api.BrowseFacet; import com.browseengine.bobo.api.FacetIterator; public class AttributesFacetIterator extends FacetIterator { private final Iterator<BrowseFacet> iterator; public AttributesFacetIterator(List<BrowseFacet> facets) { iterator = facets.iterator(); } @Override public boolean hasNext() { // TODO Auto-generated method stub return iterator.hasNext(); } @Override public void remove() { throw new UnsupportedOperationException(); } @Override public Comparable<?> next() { count = 0; BrowseFacet next = iterator.next(); if (next == null) { return null; } count = next.getFacetValueHitCount(); facet = next.getValue(); return next.getValue(); } @Override public Comparable<?> next(int minHits) { while (iterator.hasNext()) { BrowseFacet next = iterator.next(); count = next.getFacetValueHitCount(); facet = next.getValue(); if (next.getFacetValueHitCount() >= minHits) { return next.getValue(); } } return null; } @Override public String format(Object val) { return val != null ? val.toString() : null; } } | Mid | [
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Eight Graphically Forward Pairs of Socks for Summer Colors, patterns, flourishes and beyond—all for your feet With seasonal change, we are quick to transform our wardrobe to match the weather—or, most of it. Shirts and pants get swapped out. Some items are stowed, while others are retrieved. But what about socks? Summer in the northern hemisphere makes for a greater opportunity to show off what you've got going on at ankle level, and there's no better time to ramp up your style with personality to match the season. There are options out there (from the excellent Strolling Wild, for example) for an entire sock drawer makeover, but if you'd like to go pair by pair or with smaller sets, here are eight options below that take the sock game to the next level. Nice Laundry Get your summer sock update done in one go with Nice Laundry's Envoy sock set ($49). Six pairs of graphically charged socks, crafted from premium cotton blends, make for a vibrant, nuanced offering. And while they're fun, they also happen to dress up nicely. Jimmy Lion Another master of fanciful sock sets, Jimmy Lion offers customizable (or recommended) boxes for all genders. While we were smitten with both, their array of ladies' socks ($14 each or $42 for a set of four) vary from cute and kitschy to prim and proper. This are soft combed cotton socks, produced in Portugal, and durability is guaranteed. Cav Empt These ribbed tube socks from Cav Empt have just enough flair to draw the eye to your ankles, without looking gaudy. Mostly white and taupe, with a splash of indigo, the Japanese streetwear brand’s Waste Sock (£20), thanks to the 100% cotton composition, offer breathability on hot summer days. Henrik Vibskov Purveyor of all things graphic and fun, CH favorite Henrik Vibskov has plenty of delightful socks to choose from every season. This time though, we picked the Water Hole Socks ($26) which come in white or black. Depicting a landscape with palm trees and bright sun (or moon) these intarsia woven socks really spell out summer. Pair of Thieves The somewhat mysteriously named Bowie Socks ($10) from Pair of Thieves boast the brand’s “sneaky performance,” meaning they are moisture-wicking, breathable and super-comfy. With an abstract design resembling leaves or butterflies, the socks come in a delightfully fresh blue/green colorway. Gorman From Gorman come these playful, cutesy sheer polka dot socks ($16 AUD), perfect for jazzing up your sneakers or to wear under sandals if you’re feeling kitsch (or simply toe-phobic). With a white sheer layer and mint green spots, they are bright and breezy and will probably carry you through summer and into fall. Hansel from Basel Made in collaboration with artist and musician Kyle Field, Hansel from Basel's 3:33 Crew socks ($30) are made in Japan from breathable combed cotton. These dark charcoal colored socks feature a series of "3:33" graphics, and there's a story behind them. Field thought up the visuals at 3:33AM after jet lag from a trip to Japan. Summer's an ideal time for wanderlusting and maybe these high-quality pieces might inspire more than dreaming. Mack Weldon As a brand rethinking basics, especially underwear, Mack Weldon impresses with their comfort and quality-driven "Everyday" socks—especially with their padded footbed. The Grey Heather Diamond pair ($12.50) with its seamless toe promises to keep up with your long summer walks and bar crawls. Lead image courtesy of Strolling Wild, all other images courtesy of respective brands | Mid | [
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What To Expect From A Physical Therapy A person in pain needs nothing but a way that can get him rid off his discomfort caused by the pain. The physical therapy proves to be one of the beneficial ways to treat your chronic pain. It makes you feel stronger by bringing back the strength in the muscles. You should always consult your physiotherapist before you start with your set of physiotherapy sessions. He will guide you about the sessions that would be needed to attain remarkable results. How does Physical Therapy Works? Physical therapy does not aim at reducing calories. It is a highly focused type of a workout that targets the muscles that are highly affected by pain. In a physiotherapy session you focus on a lot of things: Stretching: The first thing to start a physiotherapy session is to begin with a workout. The therapist provides you a set of warm up exercises. The therapist gives you instructions on how often you should do them. Exercises that give you strength: These set of exercises involves the use of machines like resistance bands. It is essential to manage your body weight by practicing exercises like squats and lunges. Aerobic training: These set of exercises works as cardio exercises. It begins with walking and then jogging. It increases the heartbeat rate, pumps in more oxygen but still works on the joints. Exercise that relieve pain: It targets the areas most affected by chronic pain. It brings back the strength and flexibility of your body. There are certain procedures other than the set of exercises that your physiotherapist may ask you to do: Heat and ice packs: There are times when burning sensation arises due to pain. Ice helps in reducing this burning sensation. To let your muscles move in much better way heat is required. It involves the use of heat belts. Stimulation in the spinal cord: A device is implanted in the spine that blocks pain by delivering low voltage electricity. It is important to have a trial of this process before getting it implanted permanently into the body. Massage: The massage sessions are not the ones that would make you feel extremely relaxed like a spa, but the physiotherapist makes sure he focusses on the right parts of the body suffering from pain. He gives assurance that the massage is extremely safe and helpful in reducing pain. Benefits of Physical Therapy: Improves the body balance: The initial session of physical therapy requires a screening of the patient as to how much is he prone to fall risk. If you have a poor body balance, the therapist provides you with real life situations so as to make your body used to those moves. Eliminates pain: Treatments like stimulation in the spine by electrical implants relieves pain. Manage diseases: Patients who have undergone heart surgeries after the completion of their cardiac rehabilitation are advised to go for physical therapy if they are unable to return to their daily routine. Avoid Surgery: Physical therapy heals your pain in an effective manner thereby avoiding surgeries. However, if there is an urgent need for a surgery, some pre-surgery exercises are suggested by the therapist. Keeps a check on diabetes: Physical therapy can control blood sugar by making a unique plan that includes both the strengthening and stretching exercises. Physical therapy is challenging and needs hard work by the patient to help him reduce the pain as it uses all the parts of the body that are hurt but, it is safe and helpful. Consult your therapist as he may have a plan based on your needs.The daily activity, the type of body you have and age are certain factors that might affect your plan. Stick with what your therapist say and you will get benefits soon. | High | [
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Q: Can Cython code be compiled to a dll so C++ application can call it? I have a C++ program and it has sort of plugin structure: when program starts up, it's looking for dll in the plugin folder with certain exported function signatures, such as: void InitPlugin(FuncTable* funcTable); Then the program will call the function in the dll to initialize and pass function pointers to the dll. From that time on, the dll can talk to the program. I know Cython let you call C function in Python, but I'm not sure can I write a Cython code and compile it to a dll so my C++ program can initialize with it. An example code would be great. A: Using cython-module in a dll is not unlike using a cython-module in an embeded python interpreter. The first step would be to mark cdef-function which should be used from external C-code with public, for example: #cyfun.pyx: #doesn't need python interpreter cdef public int double_me(int me): return 2*me; #needs initialized python interpreter cdef public void print_me(int me): print("I'm", me); cyfun.c and cyfun.h can be generated with cython -3 cyfun.pyx These files will be used for building of the dll. The dll will need one function to initialize the python interpreter and another to finalize it, which should be called only once before double_me and print_me can be used (Ok, double_me would work also without interpreter, but this is an implementation detail). The header-file for the dll would look like following: //cyfun_dll.h #ifdef BUILDING_DLL #define DLL_PUBLIC __declspec(dllexport) #else #define DLL_PUBLIC __declspec(dllimport) #endif //return 0 if everything ok DLL_PUBLIC int cyfun_init(); DLL_PUBLIC void cyfun_finalize(); DLL_PUBLIC int cyfun_double_me(int me); DLL_PUBLIC void cyfun_print_me(int me); So there are the necessary init/finalize-functions and the symbols are exported via DLL_PUBLIC (which needs to be done see this SO-post) so it can be used outside of the dll. The implementation follows in cyfun_dll.c-file: //cyfun_dll.c #define BUILDING_DLL #include "cyfun_dll.h" #define PY_SSIZE_T_CLEAN #include <Python.h> #include "cyfun.h" DLL_PUBLIC int cyfun_init(){ int status=PyImport_AppendInittab("cyfun", PyInit_cyfun); if(status==-1){ return -1;//error } Py_Initialize(); PyObject *module = PyImport_ImportModule("cyfun"); if(module==NULL){ Py_Finalize(); return -1;//error } return 0; } DLL_PUBLIC void cyfun_finalize(){ Py_Finalize(); } DLL_PUBLIC int cyfun_double_me(int me){ return double_me(me); } DLL_PUBLIC void cyfun_print_me(int me){ print_me(me); } Noteworthy details: we define BUILDING_DLL so DLL_PUBLIC becomes __declspec(dllexport). we use cyfun.h generated by cython from cyfun.pyx. cyfun_init inizializes python interpreter and imports the built-in module cyfun. The somewhat complicated code is because since Cython-0.29 PEP-489 is default. More information can be found in this SO-post. cyfun_double_me just wraps double_me so it becomes visible outside of the dll. Now we can build the dll! :: set up tool chain call "<path_to_vcvarsall>\vcvarsall.bat" x64 :: build cyfun.c generated by cython cl /Tccyfun.c /Focyfun.obj /c <other_coptions> -I<path_to_python_include> :: build dll-wrapper cl /Tccyfun_dll.c /Focyfun_dll.obj /c <other_coptions> -I<path_to_python_include> :: link both obj-files into a dll link cyfun.obj cyfun_dll.obj /OUT:cyfun.dll /IMPLIB:cyfun.lib /DLL <other_loptions> -L<path_to_python_dll> The dll is now built, but the following details are noteworthy: <other_coptions> and <other_loptions> can vary from installation to installation. An easy way is to see them is to runcythonize some_file.pyx` and to inspect the log. we don't need to pass python-dll, because it will be linked automatically, but we need to set the right library-path. we have the dependency on the python-dll, so later on it must be somewhere where it can be found. Were you go from here depends on your task, we test our dll with a simple main: //test.c #include "cyfun_dll.h" int main(){ if(0!=cyfun_init()){ return -1; } cyfun_print_me(cyfun_double_me(2)); cyfun_finalize(); return 0; } which can be build via ... :: build main-program cl /Tctest.c /Focytest.obj /c <other_coptions> -I<path_to_python_include> :: link the exe link test.obj cyfun.lib /OUT:test_prog.exe <other_loptions> -L<path_to_python_dll> And now calling test_prog.exe leads to the expected output "I'm 4". Depending on your installation, following things must be considered: test_prog.exe depends on pythonX.Y.dll which should be somewhere in the path so it can be found (the easiest way is to copy it next to the exe) The embeded python interpreter needs an installation, see this and/or this SO-posts. IIRC, it is not a great idea to initialize, then to finalize and then to initialize the Python-interpreter again (that might work for some scenarios, but not all , see for example this) - the interpreter should be initialized only once and stay alive until the programs ends. So if your C/C++-program already has an initialized Python-interpreter it would make sense to offer a function which only imports the module cyfun and doesn't initialize. In this case I would define CYTHON_PEP489_MULTI_PHASE_INIT=0, because PyImport_AppendInittab must be called before Py_Initialize, which might be already too late when the dll is loaded. | High | [
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The candy pink sports bra offered by the top online fitness apparel brand is specifically designed to meet your fitness needs. Buy online at best prices. Visit: http://www.alanic.com/shopping/women-clothing/sports-bra/candy-pink-sports-bra/ | Low | [
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China hacking Hong Kong protesters’ smartphones, says security firm By IAN ALLEN | intelNews.org A mobile telephone security company has said the government of China is probably behind a sophisticated malware designed to compromise the smartphones of protesters in Hong Kong. Ever since the Hong Kong ‘umbrella revolution’ began to unfold, countless reports have referred to the use of smartphone applications as organizing tools by the protesters. According to one account, an application called FireChat was downloaded by more than 100,000 smartphone users in Hong Kong in less than 24 hours. FireChat is said to allow protesters to continue communicating with each other even when their individual devices are unable to connect to a mobile network. But a California-based mobile telephone security firm has warned that the Chinese government could be using such enabling applications to compromise the smartphones of pro-democracy protesters in the former British colony. Lacoon Mobile Security, which specializes in assessing and mitigating mobile security threats, said on Tuesday that it had detected several types of malware camouflaged as mobile phone applications designed to help the protesters organize. In a statement posted on its website, the security firm said that, once downloaded by a smartphone user, the malware gives an outsider access to the address book, communication logs and other private data stored on the unsuspecting user’s device. Lacoon added that what made the malware unusual was that it came in two different versions; one appears to target smartphones that run Apple’s iOS operating system, while the other is designed to compromise phones using Google’s Android software. The company noted that the types of malware that are circulating among Hong Kong protesters were some of the most sophisticated it had ever seen. They made use of a method called mRAT, which stands for multidimensional requirements analysis tool. Among other things, mRAT allows a hacker to take surreptitious pictures using the phone camera of a compromised smartphone. According to Lacoon, the design of the malware in question is so advanced that it is “undoubtedly backed by a nation state”. The company added that the identities of the victims, as well as the details of the servers used to direct the malware, led its engineers to “believe that the Chinese government is behind the attacks”. However, the reputable technology review Ars Technica cautioned on Thursday that it was unclear whether the detected malware was part of a state-sponsored attack. It could be “merely hackers taking advantage of a huge social engineering opportunity” to spread their malicious product, it said. But it concluded that whoever is behind the hacking is both “well-funded and sophisticated”. | Mid | [
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Delhi Metro begins phase-3 trials on Kalindi Kunj-Okhla line Delhi Metro Rail Corporation (DMRC) has started trial runs on a 3.5-km stretch between the Kalindi Kunj Depot and Okhla Vihar Metro stations of the Janakpuri West-Botanical Garden line -- the first in phase 3 Delhi Metro Rail Corporation (DMRC) has started trial runs on a 3.5-km stretch between the Kalindi Kunj Depot and Okhla Vihar Metro stations of the Janakpuri West-Botanical Garden line -- the first in phase 3(Hindustan Times file) Delhi Metro Rail Corporation (DMRC) has started trial runs on a 3.5-km stretch between the Kalindi Kunj Depot and Okhla Vihar Metro stations of the Janakpuri West-Botanical Garden line -- the first in phase 3. During the trials, the interface of the metro train will be checked to ensure there is no physical infringement with civil infrastructure during its movement on the track. The subsystems of the coaches will also be tested. “Later on, in stages, the new signaling technology to be implemented on this corridor and the communication-based train control (CBTC) will undergo rigorous testing,” said a DMRC spokesperson. The response of the train at different speeds, braking and the interconnection with the operations control centre (OCC) will be monitored. The behaviour of the track system and the overhead electrification (OHE), where snags are often reported, will be checked repeatedly. The total length of the corridor, called the magenta line, is 38 km (including the Kalindi Kunj–Botanical Garden part of 3.494 km). There will be 25 stations, of which 10 will be elevated and 15 underground. According to DMRC, the estimated ridership is 3, 61,356 from Janakpuri West to Kalindi Kunj and 46,054 from Kalindi Kunj to Botanical Garden. | High | [
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#! /bin/sh set -e #--------------------------------------------------------------------- # pre-remove # # Executed before the package is removed. # # http://code.google.com/p/fwtemplates/wiki/PackageHooks #--------------------------------------------------------------------- case "$1" in upgrade) # defer to newer package's script exit 1 ;; failed-upgrade) # actually handle the upgrade here # old-version is $2 ;; remove) ;; *) ;; esac exit 0 | Low | [
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Director Nick Broomfield documents the love story between musician Leonard Cohen and his lover, Marianne Ihlen, in Marianne & Leonard: Words of Love. Aviva Layton / Roadside Attractions Originally published on July 5, 2019 9:48 am Marianne & Leonard: Words of Love, a warmly absorbing new documentary by British filmmaker Nick Broomfield, opens with an image of a beautiful young Norwegian woman steering a sailboat off the sun-soaked Greek island of Hydra. The footage, which was shot by famed documentarian and Broomfield mentor D.A. Pennebaker on a visit to the island in the 1960s, recurs from slightly different angles throughout the film. But Marianne Ihlen — an early lover of Leonard Cohen and the subject of several of his most famous songs including "So Long Marianne" — doesn't steer this moving, sympathetic, but ultimately frustrating tribute. Perhaps inevitably, Cohen does, via Broomfield's fascination with the singer's tortured relations with the many women he romanced. Ihlen and Cohen met in 1960 on Hydra, which at that time was forming as a hub of literary hippies with full subscriptions to the sexual revolution. The two had in common uncommon physical beauty and a sense of themselves as refugees, she from an abusive partner, he from the Orthodox Jewish family that both confined and inspired him. They became lovers, and Ihlen sustained Cohen through the writing of his early novel Beautiful Losers. Juggling a deftly edited mix of footage, the voices of Cohen and Ihlen, and well-chosen testimony from friends of both, Broomfield covers the often excruciating bouts of parting and reconnecting that marked their relationship. Theirs was a love match, everyone agrees, but a brief one with a long tail of grief for Marianne, who repeatedly put her own life (and, tragically, that of her son Axel) on hold to be there for Cohen. Once he found his voice and his fortune as a singer, Marianne gradually got left behind, though he supported her financially, and their liaison sputtered on between Greece, Norway, Montreal and New York as Cohen got fully on board for free love. With his trademark blithe disregard for the boundaries between narrative and non-fiction, Broomfield has cheerfully inserted himself into a bunch of impish but keenly observed and compassionate portraits of, respectively, Hollywood madam Heidi Fleiss, rocker Courtney Love, serial killer Aileen Wuornos and Sarah Palin. Depending on how you feel about his resolutely non-ideological approach, Marianne & Leonard is either the best thing he's done or uncharacteristically circumspect, almost self-effacing. I say almost because Broomfield casually admits up front that he was, briefly, Marianne's lover on Hydra, and the two remained friends until her death from leukemia in 2016. The film is his least transgressive, but also most mature portrait of a woman who, by her own admission, suffered from crippling insecurities exacerbated by the claims to artistry of those she hung out with. Counterculture enclaves were rife with such women, and though Cohen waxes ecstatic onscreen about the movement's gender parity, Broomfield (a bit of an Apollo in his youth too) gives the hippie moment its due while remaining admirably clear-eyed about the emotional wreckage and broken families that the sexual revolution left in its wake. Marianne & Leonard founders, though, in sticking Ihlen within the vexing label of muse, which in its mostly male iteration functions as code for a passive beauty who makes the meals and clears the terrain, makes no demands and sits — in Marianne's case, quite literally — at the feet of genius. (She'd have needed heroic reserves of forbearance to cope with choice cuts of early Cohen-speak like this one: "When I got up in the morning I had to decide whether I was in a state of grace.") Genius, in return, is full of worship until the muse wears out her welcome. We see Marianne only through the attenuating fog of her beauty and her equable nature, where she languishes as a placeholder for all the women Cohen loved (or at least obsessed over) and left. Late in life Cohen is heard regretting his own heedlessness. It's not that Broomfield has cooked the books of Marianne's history with Cohen. Indeed to the degree that he ever takes sides he's with her and, probably correctly, identifies her as a somewhat tragic casualty. But though his focus keeps veering away to Cohen, he allows another woman, the vivacious and psychologically astute Aviva Layton (who was married to Cohen's friend and fellow writer Irving Layton and knows the price of taking up with a congenital escape artist) to provide crucial insight into Marianne's plight, as well as the reasons why she was so widely beloved of men and women alike. Layton is perceptive, too, about Cohen's symbiotic bond with his intense mother, from whom he inherited a lifelong struggle with depression, and about her influence on his inability to sustain relationships with women. As she lay dying in a hospital, Ihlen asked a friend to contact Cohen. Close to death himself, he wrote her a widely publicized letter of farewell, only this time minus the grandiloquence. "So Long, Marianne" is a beautiful melody, but willy-nilly, Broomfield's sensitive tribute to its subject — and object — makes crystal-clear why it was never her favorite of his songs. | Mid | [
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This invention relates to high frequency transistor test fixtures used in testing RF transistors in microwave frequencies (see ref. 1, 2). Active RF components (transistors—DUT) need to be thoroughly tested at the operation frequencies before used in amplifier and other circuit designs. “Load pull” and “Source pull” (see ref. 3) are test methods which use impedance tuners to systematically characterize the DUTs under various load and source impedance conditions. Load pull or source pull are automated measurement techniques used to measure Gain, Power, Efficiency and other characteristics of the DUT, employing, beyond source and load impedance tuners, also other test equipment, such as signal sources, directional couplers, test fixtures to house the DUT and input and output power meters (FIG. 1), see ref. 3. Typical test fixtures used are based on micro-strip (FIG. 2) or coaxial (FIG. 3) transmission line structure. Microstrip test fixtures (FIG. 2) include grounded input (22, 213) and output (28, 215) body sections and a DUT INSERT (214). The DUT (210) is mounted on the INSERT (214) using screws (26) or other securing mechanism. The fixture has input (20) and output (27) connectors and microstrip lines (29, 212) between the connectors. The microstrip lines comprise a dielectric layer on which a thin copper conductor layer is etched using photolithographic process. The DUT (210) package has leads (24, 211) which can be soldered or pressed on the microstrip (29, 212). A coaxial test fixture (FIG. 3) has two slabline sections made of the blocks (25), the cover (10) and the center conductors (31) which lead from the coaxial connectors, which are mounted on the vertical walls (11), to the DUT, which is mounted on the INSERT (21) using vertical studs or screws. The DUT leads are inserted in slots of the center conductors. | High | [
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--- abstract: 'We study the time taken by a language learner to correctly identify the meaning of all words in a lexicon under conditions where many plausible meanings can be inferred whenever a word is uttered. We show that the most basic form of *cross-situational learning*—whereby information from multiple episodes is combined to eliminate incorrect meanings—can perform badly when words are learned independently and meanings are drawn from a nonuniform distribution. If learners further assume that no two words share a common meaning, we find a phase transition between a *maximally efficient* learning regime, where the learning time is reduced to the shortest it can possibly be, and a *partially-efficient* regime where incorrect candidate meanings for words persist at late times. We obtain exact results for the word-learning process through an equivalence to a statistical mechanical problem of enumerating loops in the space of word-meaning mappings.' author: - Rainer Reisenauer - Kenny Smith - 'Richard A. Blythe' date: 'May 31, 2013' title: Stochastic dynamics of lexicon learning in an uncertain and nonuniform world --- On average, children learn ten words a day, thereby amassing a lexicon of 60,000 words by adulthood [@Bloom00]. This speed of learning is remarkable given that every time a speaker says a word, a hearer cannot be certain of its intended meaning [@Quine60]. Our aim is to identify which of the many proposed mechanisms for eliminating uncertainty can actually deliver such rapid word learning. In this work, we pursue this aim in the long tradition of applying quantitative methods from statistical mechanics to problems in learning [@Watkin93; @Hopfield82; @Amit85a; @Amit85b] and communication [@Sourlas89; @Kabashima00; @Nishimori01]. Empirical research suggests that two basic types of learning mechanism are involved in word learning. First, a learner can apply various *heuristics*—e.g., attention to gaze direction [@Baldwin91] or prior experience of language structure —at the moment a word is produced to hypothesize a set of plausible meanings. However, these heuristics may leave some residual uncertainty as to a word’s intended meaning in a single instance of use. If the heuristics are weak, the set of candidate meanings could be very large. This residual uncertainty can be eliminated by comparing separate instances of a word’s use: if only one meaning is plausible across all such instances, it is a very strong candidate for the word’s intended meaning. This second mechanism is referred to as *cross-situational learning* [@Pinker89; @Siskind96]. Formally, it can be couched as a process whereby associations between words and meanings are strengthened when they co-occur [@Siskind96; @Vogt04; @Tilles12a; @Yu12], as in neural network models for learning [@Watkin93; @Hopfield82; @Amit85a; @Amit85b; @Pulvermuller99]. It can also be viewed as an error-correction process [@Sourlas89; @Kabashima00; @Nishimori01] where a target set of associations is reconstructed from noisy data. There is little consensus as to which word-learning mechanisms are most important in a real-world setting [@Gleitman90; @Pinker94; @Yu07; @Frank09; @Medina11]. In part this is because word-learning experiments (e.g. [@Yu07; @Smith08; @Smith11]) are necessarily confined to small lexicons. A major question is whether strategies observed in experiments allow realistically large lexicons to be learned rapidly: this can be fruitfully addressed through stochastic dynamical models of word learning [@SSBV06; @BSS10; @Tilles12a; @Tilles12b]. In these models, a key control parameter is the *context size*: the number of plausible, but unintended, meanings that typically accompany a single word’s true meaning. Even when contexts are large, the rapid rate of learning seen in children is reproduced in models where words are learned independently by cross-situational learning [@SSBV06; @BSS10; @Tilles12a; @Tilles12b]. This suggests that powerful heuristics, capable of filtering out large numbers of spurious meanings, are not required. However, a recent simulation study [@Vogt12] shows that this conclusion relies on the assumption that these unintended meanings are uniformly distributed. In the more realistic scenario where different meanings are inferred with different probabilities, word learning rates can decrease dramatically as context sizes increase. Powerful heuristics may be necessary after all. One heuristic, of great interest to empiricists (e.g. [@Markman88; @golinkoff_94_young; @halberda_03_development; @Markman03]) and modelers (e.g. [@Frank07; @BSS10; @Tilles12a; @Tilles12b; @Vogt12]), is a *mutual exclusivity constraint* [@Markman88]. Here, a learner assumes that no two words may have the same meaning. This generates nontrivial interactions between words which makes analysis of the corresponding models difficult. For example, if one begins with a master equation, as in [@SSBV06; @BSS10; @Tilles12a], the expressions become unwieldy to write down, let alone solve. Here, we adopt a fundamentally different approach which entails identifying the criteria that must be satisfied for a lexicon to be learned. This allows existing results for the simple case of independently-learned words and uniform meaning distributions [@BSS10] to be generalized to arbitrary meaning distributions *and* exactly solves the interacting problem to boot. Our main result is that mutual exclusivity induces a dynamical phase transition at a critical context size, below which the lexicon is learned at the *fastest* possible rate (i.e., the time needed to encounter each word once). As far as we are aware, the ability of a single heuristic to deliver such fast learning has not been anticipated in earlier work. ![\[XSL\] Acquisition of a three-word lexicon. Solid shapes are meanings that have appeared in every episode alongside a word; open shapes are therefore excluded as candidate meanings. (a) In the noninteracting case, only the meaning of the word ‘’square’’ is learned. (b) In the interacting case, mutual exclusivity further removes meanings (shown hatched) of learned words, both prospectively and retrospectively (shown by arrows). All three words are learned in this example.](xsl){width="\linewidth"} We begin by defining our model for lexicon learning. The lexicon comprises $W$ words, and each word $i$ is uttered as a Poisson process with rate $\phi_i$. In all cases, we take words to be produced according to the Zipf distribution, $\phi_i = 1/(\mu i)$, that applies for the ${\sim}10^4$ most frequent words in English [@Zipf49; @Cancho01; @Petersen12]. Here, $\mu=\sum_{i=1}^{W} (1/i)$ so that one word appears on average per unit time. Each time a word $i$ is presented, the intended *target* meaning is assumed always to be inferred by the learner by applying some heuristics. At the same time, a set of non-target *confounding* meanings, called the *context*, is also inferred. In the purest version of cross-situational learning [@Siskind96; @BSS10], a learner assumes that all meanings that have appeared every time a word has been uttered are plausible candidate meanings for that word. The word becomes *learned* when the target is the only meaning to have appeared in each episode. In the *noninteracting* case, each word is learned independently—see Fig. \[XSL\]a. In the *interacting* case, mutual exclusivity acts to further exclude the meanings of learned words as candidates for other words. We take this exclusion to occur at the instant a word is learned, which means a single learning event may trigger an avalanche of other learning events by repeated application of mutual exclusivity. An example of this nontrivial effect that is hard to handle within standard approaches [@BSS10; @Tilles12a] is shown in Fig. \[XSL\]b. Here, learning “square” causes “circle” to be learned at the same time. We consider the noninteracting case first both to introduce our more powerful analytical approach and to pinpoint the origin of the catastrophic increase in learning times noted in [@Vogt12]. Two conditions must be satisfied for the lexicon to be learned by a given time: (C1) all words must have been exposed at least once; and (C2) no confounding meaning may have appeared in every episode that any given word was uttered. To express these conditions mathematically, we introduce two stochastic indicator variables. We take $E_i(t)=1$ if word $i$ has been uttered before time $t$, and zero otherwise; and $A_{i,j}(t)=1$ if confounding meaning $j$ has appeared in every context alongside word $i$ up to time $t$ (or if word $i$ has never been presented), and zero otherwise. Conditions (C1) and (C2) then imply that the probability that the lexicon has been learned by time $t$ is $$\label{Lni} L(t) = \Big\langle \prod_{i} E_i(t) \prod_{j\ne i} [1 - A_{i,j}(t)] \Big\rangle = \Big\langle \prod_{i\ne j} [1 - A_{i,j}(t)] \Big\rangle$$ where the angle brackets denote an average over all sequences of episodes that may occur up to time $t$. The second equality holds because $A_{i,j}(t) = 1 \forall j\ne i$ if $E_i(t)=0$. This expression is valid for any distribution over contexts. For brevity, we consider a single, highly illustrative construction that we call *resampled Zipf* (RZ). It is based on the idea that meaning frequencies should follow a similar distribution to word forms [@Vogt12]. It works by associating an ordered set, ${\cal M}_i$, of $M$ confounding meanings with each word $i$. The $k^{\rm th}$ meaning in each set has an *a priori* statistical weight $1/k$. Whenever word $i$ appears, meanings are repeatedly sampled from ${\cal M}_i$ with their *a priori* weights, and added to the context if they are not already present until a context of $C$ distinct meanings has been constructed. When words are learned independently, the learning time depends only on $M$, $W$ and $C$, and not on which meanings are present in any given set ${\cal M}_i$ [@BSS10]. We seek the time, $t^\ast$, at which the lexicon is learned with some high probability $1-\epsilon$. In the RZ model, each context is an independent sample from a fixed distribution. Hence, the correlation functions $\langle A_{i_1,j_1} A_{i_2,j_2} \cdots \rangle$ in (\[Lni\]) all decay exponentially in time. To find $t^\ast$ to good accuracy in the small-$\epsilon$ limit, only the slowest decay mode for each word $i$ is needed. Higher-order correlation functions depend on many meanings co-occurring, and so decay more rapidly than lower-order correlation functions. As shown in Appendix \[app:a\], we find that at late times (\[Lni\]) is well approximated by $$\label{Lnia} L(t) \sim \prod_{i} \big[ 1 - {\rm e}^{-\phi_i (1-a_i^\ast) t} \big]$$ where $a_i^\ast$ is the fraction of episodes in which word $i$’s most frequent confounder appears alongside the target. This expression generalizes results for independently-learned words [@SSBV06; @BSS10; @Tilles12a] from uniform to *arbitrary* nonuniform confounder distributions. The RZ model has the further simplification that $a_i^\ast$ has a common value, $a^\ast$, for all words $i$. Then, it is known from previous calculations [@BSS10] for Zipf-distributed word frequencies that the learning time is $$\label{tast1} t^\ast \sim \frac{\mu W}{1-a^\ast} {\ensuremath{{\cal W}}}_0\left( \frac{W}{-\ln(1-\epsilon)} \right)$$ where ${\ensuremath{{\cal W}}}_0(z)$ is the principal branch of the Lambert W function [@Corless96]. For large argument, this function behaves as a logarithm. In Fig. \[RZ1\], we compare the analytical result (\[tast1\]) with learning times obtained from direct Monte Carlo simulations, conducted as detailed in [@BSS10]. The only complication is that we unfortunately have no analytic expression for $a^\ast$ arising from the RZ procedure. We therefore obtain the frequency of the most common confounder for given $C$ and $M$ from independent Monte Carlo samples. The agreement between (\[tast1\]) and simulation is very good. ![\[RZ1\] Time to learn a lexicon of $W$ words independently to a residual probability $\epsilon=0.01$ with $C$ of $M$ confounders present in each episode. Points: data from Monte Carlo simulations (over $10,000$ sampled lexicons in each case). Lines: the analytical result, Eq. (\[tast1\]).](lex-rainer-nomutex){width="\linewidth"} Fig. \[RZ1\] also shows that the learning time increases super-exponentially with the context size. We have found that the probability the $k^{\rm th}$ most confounder appears in a context of size $C$ fits the form $p_k \approx 1-(1-w_k)^{C{\rm e}^{\lambda C}}$ where $w_k$ is the *a priori* probability and $\lambda$ is a fitting parameter that depends on $M$ and $k$. As noted by Vogt [@Vogt12], the repeated sampling without replacement implies that $p_k \ge 1-(1-w_k)^C$. Our analysis further reveals that the learning time is *entirely* determined by the frequency of the most common confounder, $a^\ast$ through (\[tast1\]). We note that this is true even when other confounders have comparable appearance frequencies ($C \le 5$). We now turn to the case where the mutual exclusivity constraint serves to exclude the meanings of learned words as possible meanings for other words. In this case, it is important to distinguish between *labeled* and *unlabeled* meanings: an unlabeled meaning is not the target meaning of any word in the lexicon, and hence cannot be excluded using the mutual exclusivity constraint. To generalize Eq. (\[Lni\]) to this problem, we must identify the conditions for the lexicon to be learned. Condition (C1) still applies: each word must be uttered at least once for a learner to be able to learn it. Condition (C2) now applies only to unlabeled confounding meanings: these can only be excluded if they fail to appear in a context, as before. When these two conditions are satisfied, there is a third—necessary and sufficient—condition for the lexicon to be learned that takes into account all the interactions and avalanches generated by the mutual exclusivity constraint. This is condition (C3): no *candidate loops* exist at time $t$. A candidate loop, $\ell=(i_1, i_2, \ldots, i_n)$, is a subset of distinct, labeled meanings whereby each meaning $i_{k}$ has appeared alongside the word associated with meaning $i_{k-1}$ (or $i_{n}$ if $k=1$) every time it has been uttered. Inspection of Fig. \[XSL\]b shows that the one candidate loop (,$\bullet$) that exists after the third episode is destroyed in the fourth. Then, in the fifth episode, the final word appears, and since no unlabeled meaning is a candidate for any word, the entire three-word lexicon is learned. To see why condition (C3) is necessary and sufficient in general when (C1) and (C2) hold, we first show that a candidate loop must exist if the lexicon has not been learned. Suppose word $i_1$ has not been learned. Then, at least one meaning, $i_2$, must confound word $i_1$. Word $i_2$ must also not have been learned, otherwise meaning $i_2$ would not confound word $i_1$. Hence, word $i_2$ must be confounded by a meaning, $i_3$, and so on. As there is a finite set of words, this sequence of meanings must eventually form a loop. We now show the lexicon cannot have been learned if a candidate loop exists by first assuming that it *has* been learned under these conditions. Then, if word $i_1$ was learned at time $t$, word $i_2$ must have been learned before time $t$ for mutual exclusivity to act (even if words $i_1$ and $i_2$ are learned as part of the same avalanche). Iterating this argument around the loop, one finds that word $i_1$ can only have become learned at time $t$ if it had already been learned at some earlier time. This contradiction therefore implies that the absence of candidate loops and a learned lexicon are equivalent. We again use indicator variables to translate conditions (C1)–(C3) into an exact expression for the learning probability. Introducing $C_{\ell}(t) = A_{i_1,i_2}(t) A_{i_2,i_3}(t) \cdots A_{i_n,i_1}(t)$ that equals $1$ if the loop $\ell$ persists at time $t$, we have $$\label{lme} L(t) = \left\langle \prod_{i=1}^{W} E_i(t) \prod_{j>W} \left[ 1 - A_{i,j}(t) \right] \prod_{\ell} \left[ 1 - C_{\ell}(t) \right] \right\rangle \;,$$ again valid for any distribution of confounding meanings. Here, meanings $1$ to $W$ correspond to words $1$ to $M$, and so meanings with an index $j>W$ are unlabeled. The product over $\ell$ is over all possible candidate loops. This expression has the remarkable property that it is expressed concisely in terms of the word and confounder appearance frequencies alone: the avalanche dynamics triggered by mutual exclusivity do not enter explicitly. This property, reminiscent of the avalanche dynamics of Abelian sandpile models [@Dhar90], reduces analysis of the learning probability to the statistical mechanical problem of enumerating candidate loops. In the interacting problem, the structure of each candidate set ${\cal M}_i$ is important, as this determines which words interact. We consider a model which has no unlabeled meanings and where each set ${\cal M}_i$ is a sample of $M$ non-target meanings obtained via the RZ prescription. Then, in each episode, $C$ meanings are drawn from the relevant candidate set using RZ again, but with an *a priori* weight $1/k$ where $k$ is the rank of a meaning within the set ${\cal M}_i$ when ordered by the frequency of the corresponding words. Thus meanings of high-frequency words are high-frequency confounders. Learning times from Monte Carlo simulations are shown in Fig. \[RZL\]. ![\[RZL\] As Fig. \[RZ1\] but with the mutual exclusivity constraint. Points: data from Monte Carlo simulations (100,000 lexicons for $C \le 20$, at least 2,500 lexicons for larger $C$). Dotted lines: time for the entire lexicon to have been exposed with residual probability $\epsilon=0.01$. Dashed lines: time for the slowest decaying candidate loop to remain with probability $\epsilon$. Solid line: time to learn lexicon independently, Eq. (\[tast1\]), for comparison.](lex-rainer-crude){width="\linewidth"} We observe two distinct learning-time regimes. At small $C$, the learning time is constant, and close to the time it takes for all words in the lexicon to appear at least once. (This time is given by Eq. (\[tast1\]) with $a^\ast=0$). In this regime, learning is as fast as it can possibly be: mutual exclusivity is *maximally efficient* and reverses the undesirable increase in learning times that arises from nonuniform confounder distributions. Above a critical context size, the learning time rises, but remains much smaller than when words are learned independently: mutual exclusivity is *partially efficient* in this regime. Our exact result (\[lme\]) can be used to explain these observations, details of which appear in Appendix \[app:b\]. For the RZ model as described above, it turns out that only one confounder loop $\ell=(1,2)$ is relevant at late times. Consequently, the learning probability $L(t)$ is asymptotically given as the product of two factors. The first gives the probability that all words have been encountered by time $t$, and approaches unity exponentially with rate $1/\mu W$. The second is the probability that the loop $\ell=(1,2)$ has not decayed away: this approaches unity with rate $3(1-a^\ast)/2\mu$. The appearance frequency of the most frequent confounder, $a^\ast$, increases with context size. When $a^\ast < 1-\frac{2}{3W}$, the slowest relaxational mode of the learning probability is associated with each word being uttered at least once, whereas for larger values, the slowest mode comes from eliminating the confounder loop. In this latter partially-efficient regime, the lexicon learning time is predicted as $t^\ast = - \frac{2\mu \ln\epsilon}{3(1-a^\ast)}$ for small $\epsilon$, in very good agreement with simulation data (see Fig. \[RZL\]). We describe the sudden change in the dominant relaxational behavior—a phenomenon seen also in driven diffusive systems [@deGier05]—as a *dynamical phase transition*. It is broadly reminiscent of transitions exhibited by combinatorial optimization problems, whereby the number of unsatisfied constraints increases from zero above a critical difficulty threshold [@Mezard02]. In the present case the learning problem remains solvable in both regimes, but there is a transition from a regime where it is solved in constant time to one where the time grows super-exponentially in the difficulty of the problem (here, the context size). To summarize, we have found that mutual exclusivity is an extremely powerful word-learning heuristic. It can yield lexicon learning times in the presence of uncertainty that coincide with the time taken for each word to be heard at least once. Empirical data (summarized in [@BSS10]) suggests that this is easily fast enough for realistic lexicons of $W=60,000$ words to be learned. To enter the partially-efficient regime, each word’s most frequent confounder would need to be present in at least $99.99\%$ of all episodes: even then, learning is over $W$ times faster than when mutual exclusivity is not applied. The dynamical transition between a maximally- and partially-efficient regime also appears to be present in a variety of word-learning models we have investigated, e.g., those in which confounder frequencies are uncorrelated with their corresponding word frequencies, or using less memory-intensive learning strategies [@RSSBip]. We also expect the transition to be evident in models where the target meaning does not always appear, at least in the regime where learning is possible [@Tilles12a; @Tilles12b]. We believe the analytical methods introduced in this work should allow more detailed quantities to be calculated, e.g., the distribution of learning times for a given word, which would shed light on such phenomena as the childhood vocabulary explosion at around 18 months [@McMurray07]. Similar thinking may also allow analysis of other nonequilibrium dynamical systems whose master equations are hard to solve directly. Finally, our results suggest new empirical questions, such as whether high-frequency confounders correlate with high-frequency words, and the extent to which learners are able to apply the mutual-exclusivity constraint retroactively. We therefore contend that statistical physicists can contribute much to the understanding of how children learn the meaning of words. *Acknowledgments* — We thank Mike Cates and Cait MacPhee for comments on the manuscript. Learning time in the noninteracting case {#app:a} ======================================== In the main text, we derived a formula—given there as Eq. (1)—for the probability $L(t)$ that a lexicon of words is learned by time $t$ if they are learned independently by cross-situational learning. This read $$L(t) = \Big\langle \prod_{i} E_i(t) \prod_{j\ne i} [1 - A_{i,j}(t)] \Big\rangle$$ where $E_i(t) = 1$ only if word $i$ has been presented by time $t$, and $A_{i,j}(t)$ is $1$ if word $i$ has never been presented, or, if in every presentation up to time $t$, the confounding meaning $j\ne i$ has always appeared alongside. The angle brackets denote an average over all possible exposure sequences. Under all other conditions, these indicator variables are zero. This equation was first of all presented in an alternative form which follows from the fact that $E_i(t)=0$ implies that $A_{i,j}(t)=1$ for all $j \ne i$. Hence, for all allowed combinations of $E_i(t)$ and $A_{i,j}(t)$, we have the identity $[1-E_i(t)] A_{i,j}(t) = [1-E_i(t)]$ which can be rearranged to obtain $E_i(t)[1-A_{i,j}(t)] = [1-A_{i,j}(t)]$. Assuming that there is at least one confounding meaning for each word, the $E_i(t)$ variables in the above equation are then redundant, and the more concise form $$L(t) = \Big\langle \prod_i \prod_{j\ne i} [1 - A_{i,j}(t)] \Big\rangle$$ then applies. In the main text, we discussed models where contexts of confounding meanings were independently sampled from distributions that may be word-dependent, but remain fixed over time. In particular, this implies that the contexts appearing against different words are independent, and we have factorization of the average into word-dependent factors: $$\label{factor} L(t) = \prod_i \Big\langle \prod_{j\ne i} [1 - A_{i,j}(t)] \Big\rangle \;.$$ Since the confounder distributions are fixed, we find after $n_i$ presentations of word $i$ that $$A_{i,j_1} \cdots A_{i,j_k} = \left\{ \begin{array}{ll} 1 & \mbox{with prob. $a_i(j_1, \ldots, j_k)^{n_i}$} \\ 0 & \mbox{otherwise} \end{array} \right.$$ where $a_i(j_1, \ldots, j_k)$ is the joint probability that all $k$ meanings $j_1, j_2, j_3, \ldots, j_k$ appear in a single episode. Since word $i$ is presented as a Poisson process with frequency $\phi_i$, we find that $$\begin{aligned} \big\langle A_{i,j_1} A_{i,j_2} \cdots A_{i,j_k} \big\rangle &= \sum_{n_i=0}^{\infty} \frac{(\phi_i t)^{n_i}}{n_i!} a_i(j_1, \ldots, j_k)^{n_i} {\rm e}^{-\phi_i t} \nonumber\\ &= {\rm e}^{-\phi_i [1 - a_i(j_1, \ldots, j_k)] t}\end{aligned}$$ Therefore, on multiplying out the average in (\[factor\]), we find a sum of exponential decays. We are interested in the slowest decay mode, which corresponds to the highest possible value of $a_i(j_1, \ldots, j_k)$ among all possible sets of confounding meanings. As noted in the main text, any combination of meanings $j_1, j_2, \ldots, j_k$ cannot appear more frequently than the least frequent meaning among that subset. If, for each word, the individual meaning frequencies $a_i(j)$ are distinct for different $j$, there will be a unique maximum appearance frequency, and the slowest decay is given by $a_i^\ast = \max_j \{ a_i(j) \}$. Multiplying the factors for each word $i$ together yields Eq. (2) of the main text. We note that in the special case where the most frequent meaning is $r$-fold degenerate, we acquire a prefactor $r$ in front of the dominant exponential decay. For the case where $a_i^\ast$ is the same for all words $i$, Eq. (3) in the main text is obtained by taking the logarithm of $L(t)$, replacing the sum with an integral, and expanding the logarithm to first order. For a Zipf distribution of word frequencies, $\phi_i = 1/(\mu i)$, $\mu = \sum_{i=1}^{W} (1/i)$, this procedure yields [@BSS10] $$\begin{aligned} \label{lgzipf} \ln L(t) &\approx - \int_1^{W} {\rm d} x \exp\left( - \frac{(1-a^\ast) t}{\mu x} \right) \nonumber \\ &\approx -\frac{\mu W^2 }{(1-a^\ast) t} \exp\left( -\frac{(1-a^\ast) t}{\mu W} \right) \;,\end{aligned}$$ where we have used the asymptotics of the exponential integral [@AS65] to obtain the second approximate equality. The solution of the equation $\ln L(t^\ast) = \ln(1-\epsilon)$ yields the learning time given by Eq. (3). This involves the Lambert W function which is defined by solutions of the equation $ {\cal W}(z){\rm e}^{{\cal W}(z)} = z$ [@Corless96]. Learning time for the interacting RZ model {#app:b} ========================================== In the interacting RZ model described in the main text, it is assumed that all meanings are labeled and so Eq. (4) for the learning probability simplifies to $$L(t) = \left\langle \prod_{i=1}^{W} E_i(t) \prod_{\ell} \left[ 1 - C_{\ell}(t) \right] \right\rangle \;,$$ where here $C_{\ell}(t) = A_{i_1,i_2}(t) A_{i_2,i_3}(t) \cdots A_{i_n,i_1}(t)$ for an ordered subset $\ell=(i_1, i_2, \ldots, i_n)$ of the $W$ meanings. Numerical investigations of the RZ sampling procedure reveal that, when the context size is large, the most frequent confounders are all very likely to appear ($a_{i,j} \approx 1$ for the lowest $j$), while the relative frequencies of *non-appearance* diverge with $C$, i.e., that $(1-a_{i,j+1})/(1-a_{i,j}) \to \infty$ as $C$ is increased. Since it is these non-appearance probabilities, $1-a_{i,j}$, that enter into the decay rates of correlation functions (see above), it follows that the slowest-decaying confounder loops are those that are (a) short; and (b) comprise only the most frequent meanings. The slowest decay of all loops therefore comes from $\ell=(1,2)$. We have found that a good match between theory and numerical data is obtained by assuming this is the *only* loop that contributes to the late-time behavior of $L(t)$. To obtain the theoretical prediction, we first make this single-loop approximation: $$\begin{aligned} \label{Eaa} L(t) &= \left\langle \prod_{i=1}^{W} E_i(t) \left[ 1 - A_{1,2}(t) A_{2,1}(t) \right] \right\rangle \nonumber\\ &= \prod_{i=1}^{W} \langle E_i(t) \rangle \left[ 1 - \frac{ \langle E_1(t)A_{1,2}(t) \rangle \langle E_2(t)A_{2,1}(t) \rangle }{ \langle E_1(t) \rangle \langle E_2(t) \rangle } \right]\;,\end{aligned}$$ where we have used the fact that the contexts presented alongside different words are uncorrelated. $\langle E_i(t) \rangle$ is the probability that an event governed by a Poisson process with frequency $\phi_i$ has occurred at least once by time $t$. Hence, $$\prod_{i=1}^{W} \langle E_i(t) \rangle = \prod_{i=1}^{W} \left[1 - {\rm e}^{-\phi_i t}\right] \;.$$ This is of the same form as Eq. (3) of the main text, but with $a^\ast=0$, and so from (\[lgzipf\]) we have that $$\label{fm} \prod_{i=1}^{W} \langle E_i(t) \rangle \approx \exp\left( - \frac{\mu W^2}{t} {\rm e}^{-t/\mu W} \right) \;.$$ Turning now to the second term in (\[Eaa\]), we use again the identity $[1-E_i(t)] A_{i,j}(t) = [1-E_i(t)]$ from the previous section, to find that $E_i(t) A_{i,j}(t) = 1 - A_{i,j}(t) - E_i(t)$. Hence, $$\Lambda_{i,j} = \frac{\langle E_i(t) A_{i,j}(t) \rangle}{\langle E_i(t) \rangle} = \frac{{\rm e}^{-\phi_i[1-a_{i}(j)]t} - {\rm e}^{-\phi_i t}}{1 - {\rm e}^{-\phi_i t}} \;.$$ If $a_{i}(j)$ is close to unity, as is the case for the high-frequency meanings in the RZ model, we have at late times that $$\Lambda_{i,j} \sim {\rm e}^{-\phi_i[1-a_{i}(j)]t} \;.$$ Combining this result with (\[fm\]) in (\[Eaa\]), and noting that $\phi_i = 1/(\mu i)$, we arrive at $$\label{Ltpt} L(t) \sim \exp\left( - \frac{\mu W^2 {\rm e}^{-\frac{t}{\mu W}} }{t} \right) \left( 1 - \exp\left[ -\frac{3(1-a^\ast)t}{2\mu} \right] \right)$$ which gives an asymptotic expression for the learning probability as a function of time. To convert this into a learning time, we need to solve the equation $L(t^\ast)=1-\epsilon$. Unfortunately, we have not been able to do this exactly. It is however straightforward now to identify the slowest decay mode of $L(t)$ by expanding out: $$\label{Lexp} L(t) \approx 1 - \frac{\mu W^2}{t} \exp\left({-\frac{t}{\mu W}}\right) - \exp\left(-\frac{3(1-a^\ast)t}{2\mu}\right) + \cdots \;.$$ Thus, as stated in the main text, we find that the mode associated with exposure of the entire lexicon decays at a rate $1/\mu W$, and that the mode associated with elimination of the confounder loop decays at rate $3(1-a^\ast)t / 2 \mu$. Now, as $\epsilon\to0$, the learning time $t$ must diverge towards infinity. Hence, as $\epsilon$ is reduced, the subleading term in (\[Lexp\]) can be made arbitrarily small, and the solution of $$\epsilon = \left\{ \begin{array}{ll} \frac{\mu W^2}{t^\ast} \exp\left({-\frac{t^\ast}{\mu W}}\right) & \mbox{for $a^\ast < 1-\frac{2}{3W}$} \\ \exp\left(-\frac{3(1-a^\ast)t^\ast}{2\mu}\right) & \mbox{for $a^\ast > 1-\frac{2}{3W}$} \end{array}\right.$$ yields the learning time $t^\ast$ to better and better accuracy in the limit $\epsilon\to0$. Formally, as $\epsilon\to0$, the function $\phi(a^\ast) = t^\ast / \ln\epsilon$ exhibits a nonanalyticity at $a^\ast=1-\frac{2}{3W}$. It is in this sense that we regard this model to exhibit a dynamical phase transition. For more general models, in which more than one candidate loop enters at large times, we have found that including only loops of length 2 in the product in (\[lme\]) yields very good agreement with simulation data. More precisely, numerically-determined roots of $L(t) = 1-\epsilon$ with $L(t)$ given by the approximate expression $$L(t) \approx \prod_{i=1}^{W} \left[ 1 - {\rm e}^{-\phi_i t} \right] \prod_{\langle i,j \rangle} \left[ 1 - \Lambda_{i,j} \Lambda_{j,i} \right]$$ correspond well with simulation data, and furthermore provides evidence for our claim that the dynamical phase transition reported is not a peculiarity of the specific model discussed in the main text. 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Ask HN: What's the best software for communities to co-ordinate? - nns Hi All,<p>We are organizing a Mutual Aid group for our community to help any elderly or families who have to self-isolate due to the ongoing COVID-19 outbreak. We are using WhatsApp to communicate, but I wonder if anyone has any suggestions for how a group of individual volunteers can co-ordinate with each other. ====== thepete2 some quick ideas \- telegram group (you can pin messages and some other features that whatsapp doesn't have) \- mumble server with push-to-talk \- trello board \- etherpad / google docs \- possibly syncthing (if you're dealing with files and don't change them too much, be careful with conflicts) | High | [
0.661807580174927,
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253 Cal.App.2d 16 (1967) CALIFORNIA WATER & TELEPHONE COMPANY et al., Plaintiffs and Respondents, v. THE COUNTY OF LOS ANGELES et al., Defendants and Appellants. Civ. No. 29880. California Court of Appeals. Second Dist., Div. Five. July 31, 1967. Burris & Lagerlof and H. Jess Senecal for Plaintiffs and Respondents. Harold W. Kennedy, County Counsel, and Edward H. Gaylord, Assistant County Counsel, for Defendants and Appellants. HUFSTEDLER, J. The County of Los Angeles and the county engineer appeal from a judgment declaring that the county "Water Ordinance," ordinance No. 7834, cannot constitutionally apply to investor-owned public utilities and enjoining the county and the county engineer from enforcing the ordinance against the public utilities. *20 Statement of the Case The action was brought by the public utilities and the California Water Association, an organization to which each of the respondent public utilities belongs, [fn. 1] on behalf of the respondents and all other investor-owned public utilities serving water within the unincorporated area of the County of Los Angeles, to test the constitutionality of the Water Ordinance and certain related ordinances as applied to them. Respondents averred that the appellants could attempt to compel them to comply with the Water Ordinance and certain related ordinances, that the challenged ordinances could not constitutionally apply to them because the state has fully occupied the field of public utilities regulation by adopting article XII, section 23 of the California Constitution and the state Public Utilities Code, and that appellants were entitled to a declaration that the ordinances as applied to them were unconstitutional and an injunction restraining their enforcement against respondents. At the trial respondents withdrew their request for relief in respect of all ordinances other than the Water Ordinance. Appellants countered with the alternative contentions that there was no justiciable controversy, that the ordinance could constitutionally apply to respondents, and that even if some of the ordinance could not apply, one section of it was constitutionally applicable to respondents. The facts are not disputed. Respondents are private corporations which own and operate plants and equipment for the production, transmission and delivery of water. Each of the respondents furnishes water within the unincorporated sections of the County of Los Angeles. On August 2, 1960, the board of supervisors adopted the Water Ordinance (No. 7834). For the recited purpose of promoting a minimum level of fire protection performance for water supply facilities the Water Ordinance requires that all persons who supply domestic water to more than one customer [fn. 2] must obtain either a *21 "Water Utility Certificate of Registration" or a "Water Utility Authorization" as a condition precedent to the construction of any portion of a water system. [fn. 3] The water utility certificate of registration is a form filed with the county engineer containing an agreement to abide by the terms of the Water Ordinance. [fn. 4] The water utility authorization is obtained by filing an application with the Water Works and Utility Division of the office of the engineer which includes the plans and specifications of the water facility. If the engineer approves the plans and specifications, he issues the authorization. The county engineer is delegated authority to require revisions of plans and specifications and to promulgate standards of materials and construction to be published in a utility manual, to which standards the applicant must adhere. [fn. 5] The Water Ordinance sets detailed requirements for service, design and construction of water facilities. [fn. 6] Section 152 of the Water Ordinance requires plans and specifications for water service to new subdivisions to be submitted to the county engineer "as required by Section 196 of Ordinance No. 4478, entitled 'Subdivision Ordinance' " and further requires that there shall be included with such plans and specifications "a certificate from a water utility that the proposed system can be operated by the water utility, and that the system will in every particular, meet the requirements of this ordinance." Section 153 provides that "[a] water utility ... shall supply to the applicant for a building permit the certificate, if any, required by Section 307 of said Ordinance No. 2225, the Building Code, [fn. 7] if the facts are such *22 that such water utility ... truthfully can execute such a certificate." [fn. 8] A violation of any of the provisions of the Water Ordinance constitutes a misdemeanor. (Section 17.) Following the passage of the Water Ordinance, the county engineer notified respondents and other water purveyors of the adoption of the Water Ordinance and transmitted copies of the utility manual promulgated pursuant to the Water Ordinance. In December of 1960 the county engineer advised respondents of the registration requirements and urged them to comply with the Water Ordinance. Respondents registered as required by the county engineer. At all times respondents have complied with the provisions of the Water Ordinance, and there has been no prosecution of any of the respondents. Justiciable Controversy Presented [1a] Appellants principally contend that respondents are not entitled to either declaratory or injunctive relief because the cause was never justiciable. Under the encompassing label of nonjusticiability, appellants present a clutch of arguments variously challenging the existence of any ground to invoke the judicial process, the propriety of the trial court's exercising its discretion in granting declaratory relief, the merits of the declaration issued, and the basis for issuing the injunction. The principle that courts will not entertain an action which is not founded on an actual controversy is a tenet of common law jurisprudence, the precise content of which is difficult to define and hard to apply. [2] The concept of justiciability involves the intertwined criteria of ripeness and standing. A controversy is "ripe" when it has reached, but has not passed, the point that the facts have sufficiently congealed to permit an intelligent and useful decision to be made. [fn. 9] One *23 who invokes the judicial process does not have "standing" if he, or those whom he properly represents, does not have a real interest in the ultimate adjudication because the actor has neither suffered nor is about to suffer any injury of sufficient magnitude reasonably to assure that all of the relevant facts and issues will be adequately presented. [fn. 10] [3] When justiciability in a jurisdictional sense exists, [fn. 11] the ripeness and standing concepts are metamorphosed in a declaratory relief action into guides for the exercise of judicial discretion in granting or withholding that remedy, and the trial court's exercise of discretion will not be disturbed on appeal unless its discretion has been abused. (Columbia Pictures Corp. v. DeToth (1945) 26 Cal.2d 753, 762 [161 P.2d 217, 162 A.L.R. 747]; Bess v. Park (1955) 132 Cal.App.2d 49, 52 [281 P.2d 556]; Mefford v. City of Tulare (1951) 102 Cal.App.2d 919, 922 [223 P.2d 847].) The present controversy was within the judicial ken. The factors which appellants say destroy justiciability are not in the nature of jurisdictional facts. They are merely factors which are properly considered in exercising discretion committed to the court by section 1061 of the Code of Civil Procedure: "The court may refuse to exercise the power granted by this chapter in any case where its declaration or *24 determination is not necessary or proper at the time under all the circumstances." [4] Among the factors affecting exercise of judicial discretion are these: the penal character of the ordinance attacked, the need for now determining the validity of the ordinance, the character of the respondents' interest and that of the public in the subject matter, and the existence of alternative remedies, if any, to test the validity of the ordinance. [5] Declaratory relief is not foreclosed simply because the subject matter of the action is a penal statute or ordinance. (Charles L. Harney, Inc. v. Contractors' etc. Board (1952) 39 Cal.2d 561 [247 P.2d 913]; LaFranchi v. City of Santa Rosa (1937) 8 Cal.2d 331 [65 P.2d 1301, 110 A.L.R. 639]; Sandelin v. Collins (1934) 1 Cal.2d 147 [33 P.2d 1009, 93 A.L.R. 956]; Katzev v. County of Los Angeles (1959) 52 Cal.2d 360 [341 P.2d 310] (passim). See also Abbott v. City of Los Angeles (1960) 53 Cal.2d 674, 678 [3 Cal.Rptr. 158, 349 P.2d 974]; Portnoy v. Superior Court (1942) 20 Cal.2d 375, 378 [125 P.2d 487].) But this does not mean that declaratory relief is always appropriate to challenge the validity of a penal statute or to obtain a construction of it for a plaintiff's benefit. Declaratory relief is properly denied, for example, if the factual matrix is insufficiently set to permit a useful and intelligent adjudication to be made (Witschner v. City of Atchison (1941) 154 Kan. 212 [117 P.2d 570]), or if the issues can be better decided in a criminal proceeding (People v. Ray (1960) 181 Cal.App.2d 64, 67 [5 Cal.Rptr. 113]; see also Nathan H. Schur, Inc. v. City of Santa Monica (1956) 47 Cal.2d 11, 17 [300 P.2d 831]; Manchel v. County of Los Angeles (1966) 245 Cal.App.2d 501, 507 [54 Cal.Rptr. 53]). The character of the challenged statute or ordinance is merely one factor to be considered with all the other facts and circumstances to determine the propriety of granting declaratory relief. [6] A person need not violate or plan to violate a penal ordinance before he can obtain a declaration construing it and deciding its application to him. (Cf. Charles L. Harney, Inc. v. Contractors' etc. Board, supra, 39 Cal.2d 561; Mefford v. City of Tulare, supra, 102 Cal.App.2d 919, 922; see also Zeitlin v. Arnebergh (1963) 59 Cal.2d 901, 906 [31 Cal.Rptr. 800, 383 P.2d 152, 10 A.L.R.3d 707].) To hold otherwise is like "telling the prospective victim that the only way to determine whether the suspect is a mushroom or a toadstool is to eat *25 it." (Abbott v. City of Los Angeles, supra, 53 Cal.2d 674, 678, n. 2.) The remark of the court in County of Colusa v. Strain (1963) 215 Cal.App.2d 472, 477 [30 Cal.Rptr. 415], that "[i]t must be clear that the citizen intends to perform the disputed act" to justify declaratory relief, does not mean that intent to violate an ordinance is a condition precedent to declaratory relief. In the context of the case all that was meant is that one seeking such relief must demonstrate the reality of his interest in a present adjudication. (Charles L. Harney, Inc. v. Contractors' etc. Board, supra, 39 Cal.2d 561, 564.) [7] A prosecution based on violation of a challenged ordinance is relevant in determining the availability of declaratory relief to test the validity of that ordinance, but it is not a condition precedent to declaratory relief nor necessarily a bar to such relief. If a person seeking declaratory relief is actually being prosecuted, it is obvious that the controversy is ripe and that he is interested in the outcome. But even though both criteria are present, declaratory relief may not be appropriate if the very determination he seeks can be just as well or better made in the pending criminal proceeding. (See People v. Ray, supra, 181 Cal.App.2d 64, 67.) [8] If the criminal prosecution has concluded, declaratory relief may be unavailable because the controversy is over. But if the same defendant may be subjected to future prosecution based upon different violations of the same or similar ordinances, the prior criminal prosecution does not foreclose declaratory relief. (County of Colusa v. Strain, supra, 215 Cal.App.2d 472, 476-477; see also Zeitlin v. Arnebergh, supra, 59 Cal.2d 901, 907.) A threat to prosecute is at best some evidence of a dispute between the parties. If a person seeking declaratory relief has never violated the ordinance he seeks to have construed, a threat of prosecution is meaningless. If he has actually violated the ordinance, those who are charged with enforcing it are obliged to do their duty, and threats to perform a legal duty add nothing. [fn. 12] [9] The existence of a penal statute or ordinance apparently applicable to the existing *26 conduct of a person who seeks declaratory relief is itself a "threat" to impending prosecution. [1b] Respondents' interest in obtaining a declaration respecting the validity of the Water Ordinance is neither academic or remote. The constitutional amenability of the public utilities to the local regulations prescribed by the Water Ordinance has a continuing effect upon the conduct of respondents' business. That the impact of the ordinance is not necessarily immediate does not make respondents' interest in the adjudication remote. Respondents' business requires a continuity of development and planning which extends well into the future. Water facilities and equipment must be planned substantially in advance of consumer demand. In order intelligently to plan such facilities, utilities must know whether they are required to comply with the specifications of the Water Ordinance and the utility manual or whether they must comply solely with the specifications promulgated by the Public Utilities Commission. To say that respondents have no present interest in the subject matter is rather like saying that law students have no real interest in the subjects to be covered on the bar examination until they start taking the examination. However, even aside from the interest which respondents have in a determination of the validity of the Water Ordinance, the public interest requires that there be an adjudication to settle the constitutional question here presented. Both the respondents and appellants are well aware that the amenability of water utilities to local control is a matter of substantial public concern. Were there any doubt about the justiciability of the controversy, that doubt would be resolved in favor of present adjudication, because the public is interested in the settlement of the dispute. (California Physicians' Service v. Garrison (1946) 28 Cal.2d 790, 801 [172 P.2d 4, 167 A.L.R. 306]; Golden Gate Bridge etc. Dist. v. Felt (1931) 214 Cal. 308 [5 P.2d 585]; Collier v. Lindley (1928) 203 Cal. 641, 645 [266 P. 526]; County of Colusa v. Strain, supra, 215 Cal.App.2d 472, 477-478.) The trial court did not abuse its discretion in deciding that declaratory relief was warranted. Water Ordinance Unconstitutional [10a] Respondents contend that the state has fully occupied the field of regulation of water utilities, thereby depriving the county of any power to legislate in that field. Appellants *27 urge that the Water Ordinance is a valid exercise of its police power and that the ordinance does not extend into an area fully occupied by general law and that it does not conflict with existing general law. Appellants further argue that even if some of the provisions of the Water Ordinance are invalid as applied to the respondents, at least the provision of the Water Ordinance requiring respondents to furnish certificates to building permit applicants falls outside the preempted area. [11] Local legislation in conflict with general law is void. [fn. 13] Conflicts exist if the ordinance duplicates, [fn. 14] contradicts, [fn. 15] or enters an area fully occupied by general law, either expressly or by legislative implication. [fn. 16] [12] If the subject matter or field of the legislation has been fully occupied by the state, there is no room for supplementary or complementary local legislation, even if the subject were otherwise one properly characterized as a "municipal affair." [fn. 17] No exact formula exists upon which to forecast precisely the application of implied legislative preemption. One of the clouds in the crystal ball is the definition of the field which may be ultimately adopted in any particular case. If the definition is narrow, preemption is circumscribed; if it is *28 broad, the sweep of preemption is expanded. For example, the Supreme Court defined the subject matter of the legislation considered in the Hubbard case, [fn. 18] not as "all gambling," but only as those forms of gambling expressly enumerated by section 330 of the Penal Code, thus permitting local supplementary legislation in respect of other forms of gaming. But in the Lane case, [fn. 19] the field was broadly defined as "the criminal aspects of sexual activity," thus encompassing a very wide range of legislation previously assumed to be outside the area covered by general law. [10b] The litigants, well knowing what kind of crop will grow from the seeds of definition, have characterized the field accordingly: Respondents say that the field, both of the general and local law, is "regulation of investor-owned public utilities;" appellants say that the field of the ordinance is "fire protection," a local affair the subject matter of which has not been enveloped by the state. It is unnecessary for us to nurture either of these seeds. [13] If the local legislation conflicts with general law or is a matter of state-wide rather than strictly local concern, the Water Ordinance is void whether or not the general law totally occupies the "field," however defined. [10c] The Water Ordinance as applied to the respondents conflicts with the general law and relates to matters which are of state-wide rather than local concern. Section 23 of article XII of the California Constitution provides in part that the Railroad Commission (now the Public Utilities Commission) "shall have and exercise such power and jurisdiction to supervise and regulate public utilities ... or services rendered by public utilities as shall be conferred upon it by the Legislature, and the right of the Legislature to confer powers upon the Railroad Commission respecting public utilities is hereby declared to be plenary and to be unlimited by any provision of this Constitution. From and after the passage by the Legislature of laws conferring powers upon the Railroad Commission respecting public utilities, all powers respecting such public utilities vested in boards of supervisors ... or other governing bodies of the several counties ... shall cease so far as such powers shall conflict with the powers so conferred upon the Railroad Commission; provided, however, that this section shall not affect such powers of control over *29 public utilities as relate to the making and enforcement of local, police, sanitary and other regulations ... vested in any city and county or incorporated city or town as, at an election ..., a majority of the qualified electors ... shall vote to retain. ..." [fn. 20] Pursuant to section 23 of article XII the Legislature adopted the Public Utilities Act, in which it delegated to the Public Utilities Commission the power to "supervise and regulate every public utility in the State and [to] do all things, whether specifically designated in this part or in addition thereto, which are necessary and convenient in the exercise of such power and jurisdiction." (Pub. Util. Code, 701.) Article III of division 1 of the Public Utilities Act (Pub. Util. Code, 761-773) contains detailed provisions relating to the equipment and facilities of public utilities: Section 761 requires the commission to "fix the rules, practices, equipment, appliances, facilities, service, or methods to be observed, furnished, constructed, enforced, or employed. The commission shall prescribe rules for the performance of any service or the furnishing of any commodity of the character furnished or supplied by any public utility, and, on proper demand and tender of rates, such public utility shall furnish such commodity or render such service within the time and upon the conditions provided in such rules." Section 762 requires the commission to issue orders for such extensions, repairs, improvements or changes in the "existing plant, equipment, apparatus, facilities, or other physical property of any public utility" as the commission finds ought reasonably to be made "to promote the security or convenience of its employees or the public, or in any other way to secure adequate service or facilities." Section 768 empowers the commission to promulgate orders to require every public utility to "construct, maintain, and operate its line, plant, system, equipment ... and premises in such manner as to promote and safeguard the health and safety of its employees ... customers, and the public ... and require the performance of any other act which the health or safety of its employees ... customers or the public may demand." *30 Section 770 gives the commission power to ascertain and fix standards, regulations, practices, or service to be furnished, imposed, observed, and followed by all utilities furnishing water. Section 1001 provides that no water corporation shall begin the construction of a water system or any extension thereof "without having first obtained from the commission a certificate that the present or future public convenience and necessity require or will require such construction." The commission has promulgated rules governing water service, including standards for design and construction, as for example, General Order No. 103, adopted June 12, 1956, containing comprehensive specifications for water systems and facilities. Section III of General Order No. 103, following a recitation that the system "shall be adequate to deliver the water requirements of all customers," provides for minimum pipe sizes and minimum pressures and provides "specifications, location, installation, and the responsibility for the maintenance of fire hydrants, public and private fire protection facilities, connecting mains, and their ownership may be subject to negotiation between the utility and the applicant. Fire hydrants and public and private fire protection facilities shall be installed to the requirements of the utility and when owned by the utility shall be subject to such conditions as the Commission may determine based upon the compensation received for this service." The same section of General Order No. 103 further provides: "The quantity of water delivered to the distribution system from all source facilities should be sufficient to supply adequately, dependably and safely the total requirements of all customers under maximum consumption, and should be determined so as to maintain the specified pressures as required by paragraph II 3 a." No profound exegesis of the contents of the Water Ordinance and the utilities manual and of the contents of the cited sections of the Public Utilities Code and the commission's regulations promulgated pursuant thereto is necessary to conclude that the Water Ordinance as applied to respondents conflicts with general law. Although the wording of both sets of legislation is not identical, the subject matter which is covered by each is substantially identical. Moreover, the construction, design, operation and maintenance of public water utilities is a matter of state-wide concern. Of course, the county is vitally interested in the *31 adequacy of the water supply available for fire protection. But the interest is not so parochial. All of the citizens of the complex of communities within the County of Los Angeles and in the neighboring counties are affected by the adequacy of water supply, not only for fire protection but also for other domestic and industrial uses. Under such circumstances, the control of these aspects of water utilities is not a municipal affair subject to a checkerboard of regulations by local governments. " 'Neither the public nor the service corporation could tolerate as many standards and policies as there were towns, cities, or boroughs through which they operated ... [R]egulations not exclusively local, those affecting the [public utilities] business as a whole, or affecting the public as a whole, and those which the nature of the business and the character of the regulation require should be under the single agency of the state, are by our act committed to the exclusive jurisdiction of the Public Utilities Commission. The subject matter of this ordinance clearly falls within the exclusive jurisdiction of the commission.' " [fn. 21] (Los Angeles Ry. Corp. v. Los Angeles (1940) 16 Cal.2d 779, 787 [108 P.2d 430].) We find no basis for distinguishing section 153 of the Water Ordinance from the remainder of the Water Ordinance as it applies to respondents. Section 153 of the Water Ordinance states in pertinent part: "A water utility ... shall supply to the applicant for a building permit the certificate, if any, required by Section 307 of said Ordinance No. 2225, the Building Code, if the facts are such that such water utility ... truthfully can execute such a certificate." Section 307 of the Building Code Ordinance, which is incorporated into section 153 of the Water Ordinance, states in part: "Except as otherwise provided by this section, every application for a building permit shall be accompanied by: (a) A certificate from a water utility that it can supply water to the proposed structure in compliance with Ordinance No. 7834, entitled 'Water Ordinance,' adopted August 2, 1960, ..." [14] Respondents cannot be required to issue a certificate that they *32 will supply water to the proposed structure "in compliance with ... [the] 'Water Ordinance' " because the ordinance cannot be constitutionally applied to them. The purpose of section 153 is to coerce a water utility which has the ability to conform to the Water Ordinance to supply the certificate. The condition that the water utility need not supply the certificate "if the facts are such" that the water utility cannot truthfully execute the certificate was not intended to excuse a utility from furnishing a certificate simply because it is not disposed to submit to the requirements of the Water Ordinance. As used in the proviso, the word "facts" relates to the ability of the utility to furnish water in conformance with the Water Ordinance; a utility cannot "truthfully" say that such "facts" do not exist if it has that ability, even though it has no intention of complying with the Water Ordinance. To read section 153 as leaving it up to the utility to execute the certificate or not, depending upon its disposition voluntarily to comply with the ordinance is to read the section right out of the ordinance. We assume for the purposes of this opinion that the Water Ordinance can be properly applied to building permit applicants. We hold only that the Water Ordinance cannot be constitutionally applied to the respondents. Issuance of Injunction Improper The issuance of an injunction to restrain enforcement of an ordinance declared unconstitutional is not invariably appropriate. [15] An ancillary injunction should not issue as a concomitant to a declaratory judgment unless the pleading and proof demonstrate that the traditional requisites of injunctive relief have been met. [16] When the plaintiff has failed to prove any facts which would entitle him to any affirmative relief beyond a declaration of his rights, the issuance of an injunction is error. (City of San Diego v. Cuyamaca Water Co. (1930) 209 Cal. 105, 150-151 [287 P. 475]; Sunset Scavenger Corp. v. Oddou (1936) 11 Cal.App.2d 92, 97 [53 P.2d 188].) Nothing in the record indicates that respondents have any need for an ancillary injunction. There is no reason to suppose that either the county or the county engineer is in the least disposed to enforce the Water Ordinance against the respondents in the teeth of a declaration of its unconstitutionality as applied to them. No affirmative act is required of the appellants fully to effectuate the declaration. *33 Accordingly, the judgment is modified by striking the provision therefrom enjoining appellants from enforcing the Water Ordinance against respondents. [fn. 22] In all other respects the judgment is affirmed. Respondents shall recover their costs on appeal. Kaus, P. J., and Stephens, J., concurred. Section 154 of the same ordinance provides: "A person legally required to comply with this Ordinance and not having a water utility certificate of registration shall not construct any portion of a water system, subject to the provisions of this Ordinance without first having obtained a Water Utility Authorization." NOTES [fn. 1] 1. California Water Association, a nonprofit organization, is not a public utility. The trial court refused relief to the California Water Association on the apparent ground that the association had no standing to challenge the Water Ordinance. No appeal has been taken by California Water Association. [fn. 2] 2. Section 82 of the Water Ordinance defining "water utility" states: "The term 'Water Utility' shall mean any person, firm, private, quasi-public or public agency supplying or purporting to supply other than at wholesale water for any purpose other than irrigation or water replenishment to more than one retail customer or stockholder. ..." [fn. 3] 3. Section 151 of the Water Ordinance provides in part: "A person to whom constitutionally this ordinance can apply shall not construct any portion of a water system which is subject to the provisions of this ordinance without first having obtained a Water Utility Certificate of Registration." [fn. 4] 4. Section 151 of the Water Ordinance. [fn. 5] 5. Water Ordinance, sections 8, 155, 252. The county engineer accordingly published a utility manual setting forth the standard specifications establishing minimum standards of the County of Los Angeles for water mains and water systems, materials and construction. [fn. 6] 6. Water Ordinance, sections 201-266. [fn. 7] 7. Ordinance No. 2225, as amended by ordinance No. 7835, added section 307, which requires that application for a building permit shall be accompanied by "(a) a certificate from a water utility that it can supply water to the proposed structure in compliance with Ordinance No. 7834, entitled 'Water Ordinance', adopted August 2, 1960, ..." [fn. 8] 8. Concurrently with the amendment of the Building Code by ordinance No. 7835 zoning ordinance No. 1494 was amended by ordinance No. 7874 to require as a condition precedent to obtaining a zoning change the filing of a certificate "from the person who is to supply water that he can supply water as required by said Ordinance No. 7834, also stating the amount and pressure, which certificate also shall be signed by the Forester and Fire Warden, or a certificate from the County Engineer that such water will be available." Ordinance No. 4478 was also amended by ordinance No. 7875 requiring compliance with the provisions of the Water Ordinance as a condition to approval of a subdivision. [fn. 9] 9. It is easier to illustrate ripeness than it is to define it. For example, in Silva v. City & County of San Francisco (1948) 87 Cal.App.2d 784 [198 P.2d 78], the landowner could not obtain an adjudication of the value of his property which might be subjected to future condemnation proceedings where no taking had yet occurred. In Pittenger v. Home Sav. & Loan Assn. (1958) 166 Cal.App.2d 32 [332 P.2d 399], the controversy was overripe or moot. No justiciable controversy was presented against the holder of plaintiff's note and deed of trust where the holder, who refused the tender of a required fire insurance policy, sold the note and security after suit was filed to a third person and the latter accepted the policy. Merkley v. Merkley (1939) 12 Cal.2d 543 [86 P.2d 89], held non-justiciable a claim primarily upon the ground that the controversy was not ripe, but the case also involves a lack of standing to sue. There a former wife sought to establish her ex-husband's interest in property on the theory that she might wish to resort to that property if in the future he might default in paying alimony and support to her. [fn. 10] 10. E.g., Jennings v. Strathmore Public Utility Dist. (1951) 102 Cal.App.2d 548 [227 P.2d 838] (plaintiff had no standing to challenge validity of contracts for construction of sewage system where his only interest was as a citizen and a potential worker on the project). See also Note, Judicial Determinations in Nonadversary Proceedings, 72 Harv. L. Rev. 723, 724 (1959); 1 Witkin, Cal. Procedure (1954) 10, p. 497. [fn. 11] 11. When the controversy is one which is outside the jurisdictional purview, it cannot be litigated even if the party seeking relief is intensely interested and even if the dispute is fully ripened. (In re McGee (1951) 36 Cal.2d 592, 599 (wholly political issue, nonjusticiable); Erickson v. Gospel Foundation of Cal. (1954) 43 Cal.2d 581, 585 [275 P.2d 474] (ecclesiastical controversy outside court's temporal realm).) [fn. 12] 12. The conversation in some of the decisions about threatened prosecution usually relates to the availability of injunctive relief. The language of threat is a legal cliche in equity proceedings to obtain an injunction. For examples of decisions using the threat terminology, see City of Santa Monica v. Superior Court (1964) 231 Cal.App.2d 223 [41 Cal.Rptr. 824], and Golden Gate Sightseeing Tours, Inc. v. City & County of San Francisco (1937) 21 Cal.App.2d 582 [69 P.2d 899], cited by appellants. [fn. 13] 13. Section 11 of article XI of the California Constitution is both a grant and a limitation upon the power of cities and counties to enact legislation: "Any county, city, town, or township may make and enforce within its limits all such local, police, sanitary and other regulations as are not in conflict with general laws." [fn. 14] 14. Chavez v. Sargent (1959) 52 Cal.2d 162, 176 [339 P.2d 801]; In re Portnoy (1942) 21 Cal.2d 237, 240 [131 P.2d 1]; Pipoly v. Benson (1942) 20 Cal.2d 366, 370 [125 P.2d 482, 147 A.L.R. 515]. [fn. 15] 15. Ex parte Daniels (1920) 183 Cal. 636, 642-645 [192 P. 442, 21 A.L.R. 1172]. [fn. 16] 16. E.g., Abbott v. City of Los Angeles (1960) 53 Cal.2d 674, 682-688 [3 Cal.Rptr. 158, 349 P.2d 974]; Chavez v. Sargent, supra, 52 Cal.2d 162, 176-178; In re Lane (1962) 58 Cal.2d 99 [22 Cal.Rptr. 857, 372 P.2d 897]; People v. Moore (1964) 229 Cal.App.2d 221, 226-227 [40 Cal.Rptr. 121]; Baldwin Park County Water Dist. v. County of Los Angeles (1962) 208 Cal.App.2d 87 [25 Cal.Rptr. 167] (holding the Water Ordinance void as applied to certain public water and irrigation districts). [fn. 17] 17. In re Hubbard (1964) 62 Cal.2d 119, 125 [41 Cal.Rptr. 393, 396 P.2d 809]; In re Loretizo (1963) 59 Cal.2d 445 [30 Cal.Rptr. 16, 380 P.2d 656]; In re Koehne (1963) 59 Cal.2d 646 [30 Cal.Rptr. 809, 381 P.2d 633]; In re Zorn (1963) 59 Cal.2d 650 [30 Cal.Rptr. 811, 381 P.2d 635]; People v. Lopez (1963) 59 Cal.2d 653 [30 Cal.Rptr. 813, 381 P.2d 637]; Whitney v. Municipal Court (1962) 58 Cal.2d 907 [27 Cal.Rptr. 16, 377 P.2d 80]; In re Lane, supra, 58 Cal.2d 99; In re Moss (1962) 58 Cal.2d 117 [23 Cal.Rptr. 361, 373 P.2d 425]; Abbott v. City of Los Angeles, supra, 53 Cal.2d 674. [fn. 18] 18. In re Hubbard, supra, 62 Cal.2d 119, 123-126. [fn. 19] 19. In re Lane, supra, 58 Cal.2d 99. [fn. 20] 20. The proviso last quoted applies solely to certain freeholders' charter cities. (Pacific Tel. & Tel. Co. v. City of Los Angeles (1955) 44 Cal.2d 272, 281 [282 P.2d 36]; City of San Mateo v. Railroad Com. (1937) 9 Cal.2d 1, 7 [68 P.2d 713].) [fn. 21] 21. Lewis v. People's Water Co. (1913) 3 C.R.C. 416, and City of Alameda v. People's Water Co. (1916) 9 C.R.C. 234, cited by appellants for the principle that the Public Utilities Commission does not have jurisdiction to regulate the design and size of water utility equipment for the purpose of fire protection, are not in point. The commission recognized its jurisdiction of the subject matter, but declined to require extension of mains for fire protection purposes when the utility had no duty to supply water to the applicants for fire protection. (City of San Leandro v. Railroad Com. (1920) 183 Cal. 229, 234 [191 P. 1].) [fn. 22] 22. "2. That defendants are restrained and enjoined from enforcing Ordinance No. 7834 of the County of Los Angeles against plaintiffs, California Water & Telephone Company, Diamond Bar Water Company, Dominguez Water Corporation, East Pasadena Water Co., Palos Verdes Water Company, San Gabriel Valley Water Company, Southern California Water Company, Southwest Water Company, Suburban Water Systems, and Vallecito Water Company, and all other public utilities in the County of Los Angeles similarly situated." | Low | [
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The S region of the murine histocompatibility complex (H-2) was defined almost 25 years ago as a genetic locus controlling the quantity of Ss (serum substance) in mouse serum. Subsequent work from a number of laboratories established that Ss is composed of two distinct proteins: C4, the murine fourth component of complement, and sex-limited protein (Slp), a protein that shares extensive structural and biochemical identity with C4 but which lacks C4 activity. Slp is notable in that its expression is testosterone-dependent and hence limited to males in some strains while in other strains expression is either independent of testosterone or conversely completely undetectable. Recent nucleic acid cloning and sequencing studies in our laboratory and others have demonstrated that C4 and Slp are encoded by distinct structural genes that lie in the S region and are doubtless the products of gene duplication. The goals of the proposed program are (a) to determine and compare the structural organization of the C4 and Slp genes; (b) to understand the structural and evolutionary relationships between these genes and other genes, in particular the class I and class II genes of the H-2 complex and the genes for the related complement proteins C3 and C5; and (c) to characterize the molecular mechanisms controlling sex-, tissue-, and strain- specific expression of the C4 and Slp genes. We propose to use recombinant DNA cloning and sequencing methods (a) to sequence the entire transcribed regions of the C4 and Slp genes; (b) to extend our study of upstream regions of the C4 and Slp genes by mapping restriction enzyme cleavage sites and by DNA sequencing; (c) to sequence regions upstream of the transcription initiation sites of C4 and Slp genes from mouse strains that exhibit varied C4 and Slp expression phenotypes; and (d) to use site-specific mutation and DNA reconstruction methods, together with methods for expression in cell culture to identify the gene segments responsible for regulating C4 and Slp expression. | High | [
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Self-reconstruction property of fractional Bessel beams: comment. An expression for the complex amplitude of a fractional Bessel beam [J. Opt. Soc. Am. A21, 1192 (2004)] is not a proper solution of the Helmholtz equation. | Low | [
0.522727272727272,
31.625,
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Warning: mysql_select_db() [function.mysql-select-db]: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2) in /var/www/common/store_header.php on line 21 Warning: mysql_select_db() [function.mysql-select-db]: A link to the server could not be established in /var/www/common/store_header.php on line 21 Warning: mysql_query() [function.mysql-query]: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2) in /var/www/common/_get_cur.php on line 5 Warning: mysql_query() [function.mysql-query]: A link to the server could not be established in /var/www/common/_get_cur.php on line 5 Warning: mysql_query() [function.mysql-query]: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2) in /var/www/common/_get_store_mfr.php on line 59 Warning: mysql_query() [function.mysql-query]: A link to the server could not be established in /var/www/common/_get_store_mfr.php on line 59 Warning: Cannot modify header information - headers already sent by (output started at /var/www/common/make_db_connection.php:4) in /var/www/common/_get_store_mfr.php on line 71 Warning: mysql_query() [function.mysql-query]: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2) in /var/www/common/_get_features.php on line 67 Warning: mysql_query() [function.mysql-query]: A link to the server could not be established in /var/www/common/_get_features.php on line 67 Warning: Cannot modify header information - headers already sent by (output started at /var/www/common/make_db_connection.php:4) in /var/www/common/_get_cart_contents.php on line 7 Warning: mysql_select_db(): supplied argument is not a valid MySQL-Link resource in /var/www/common/_get_cart_contents.php on line 17 Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2) | Low | [
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Current handheld plasma cutting systems use a power supply coupled to a handheld cutting torch that has a trigger mechanism for initiating or stopping the cutting operation. However, this trigger mechanism is simply an “on/off” mechanism and when it is engaged the power supply activates to its set output. In many instances, users of handheld cutting systems “overuse” the system to cut workpieces of a thinner or weaker material than the system is designed for. For example, users would use a 100 amp cutting system to cut thin sheet metal, or thin aluminum but do not bother to reduce the output of the power supply. This usage typically results in very poor quality cuts, as the cutting energy is too high. Further limitations and disadvantages of conventional, traditional, and proposed approaches will become apparent to one of skill in the art, through comparison of such approaches with embodiments of the present invention as set forth in the remainder of the present application with reference to the drawings. | Mid | [
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MIPTV: Henson Seeks Partners for ‘ImaginOcean’ The Jim Henson Company is hard at work developing a new animated children’s series, ImaginOcean, based on the acclaimed Off-Broadway musical John Tartaglia’s ImaginOcean. The musical underwater adventure series (52 x 11) will utilized the company’s Emmy-winning proprietary Henson Digital Puppetry Studio which blend real time puppeteering and CG characters. The show stars an eccentric and charming young fish named Dorsel, performed by Tartaglia (Johnny and the Sprites). The character driven stories will blend comedy, friendship and music with a social-emotional curriculum that will engage young viewers and Dorsel and his pals learn how one small ripple can create a wave. ImaginOcean will be executive produced by TJHC CEO Lisa Henson and Halle Stanford, with Tartaglia, Jill Shinderman and Michael Shawn Lewis exec producing for Jellyfish Jive Productions, LLC. The Jim Henson Company will be meeting with potential co-production partners at the MIPTV market in Cannes next week. | Mid | [
0.613043478260869,
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Introduction {#s1} ============ Sensory feedback is widely accepted as an integral component of vertebrate locomotor control ([@bib15]; [@bib25]; [@bib37]; [@bib67]; [@bib74]). Proprioception from muscle mechanoreceptors contributes to 1) short-latency reflexes via spinal mono- and polysynaptic pathways to regulate the ongoing activity and muscle mechanical output (force, stiffness, impedance and work) and 2) longer-latency responses to coordinate and maintain task-level goals for balance and movement ([@bib37]; [@bib47]; [@bib33]; [@bib67]; [@bib68]; [@bib74]; [@bib76]; [@bib80]; [@bib79]). Proprioceptive reflexes can occur through *autogenic* (self-generated) pathways arising from the same muscle, and through *heterogenic* pathways arising from other muscles via spinal interneurons ([@bib1]; [@bib33]; [@bib47]; [@bib58]; [@bib73]). Thus, the relationship between a specific sensory signal and its resulting effects is complex and dynamic. Despite recognized functions of proprioception, the relative contribution of feedback control in high-speed locomotion remains unclear. Sensorimotor delay constrains how quickly an animal can sense and respond to a stimulus using feedback control ([@bib55]; [@bib54]). The fastest possible feedback loop occurs through mono-synaptic reflexes, which involve a delay that increases in proportion to nerve transmission distance. This reflex delay becomes a larger fraction of the stride cycle with increasing speed, limiting time available for reflex-mediated correction. The challenges of long delays relative to stride cycle times likely necessitates greater reliance on feedforward control strategies at higher speeds. Here we use feedforward to refer to the contributions to motor output arising from the motor cortex, descending pathways and rhythmic spinal networks ([@bib33]; [@bib62]; [@bib86]). Rhythmic spinal networks can generate the basic flexion and extension motor pattern for gait, even when proprioceptive feedback is removed (e.g., [@bib63]; [@bib78]). Normally, however, descending networks act in concert with spinal networks and feedback, using multimodal and distributed sensory inputs to update state estimates, regulate rhythm and control foot placement ([@bib15]; [@bib27]; [@bib53]; [@bib62]; [@bib75]; [@bib83]; [@bib66]; [@bib85]). Consequently, there is no 'pure' feedfoward control within vertebrate systems. We use the term here as a pragmatic distinction, where *feedforward* refers to anticipatory 'look-ahead' control over one or more stride cycles, and *feedback* refers to reflex-mediated reactive responses to perturbations. Although feedforward networks normally act in concert with feedback, feedforward motor activation coupled to intrinsic muscle properties can be sufficient to produce stable gait ([@bib86]). Consistent with this, the lateral gastrocnemius (LG) of guinea fowl (*Numida meleagris*) rapidly absorbs energy in response to unexpected drop perturbations ([@bib18]), stabilizing high speed running without a reflex response. The rapid perturbation response arises from the intrinsic mechanical properties of the muscle-tendon tissues and musculoskeletal system ([@bib9]; [@bib48]; [@bib44]; [@bib4]). Intrinsic mechanical responses can be actively tuned by the specific feedforward pattern of muscle activation. For example, humans hopping on surfaces with randomized, sudden increases in ground stiffness show a feedforward increase in muscle co-activation and knee flexion, increasing mechanical stability ([@bib56]). However, many perturbation responses involve multiple control mechanisms that overlap in time. Guinea fowl running over obstacles use a combination of feedforward, intrinsic mechanical and reflex-mediated mechanisms, with a delay of \~40 ms for reflex-mediated increases in muscle force (6ms reflex latency + 34ms force development delay: [@bib18]; [@bib21]). Considering that the feedforward and intrinsic mechanical contributions alter ongoing muscle dynamics *before* the reflex-mediated response, it is difficult to disentangle the specific contributions of proprioceptive reflexes to the observed perturbation responses ([@bib21]; [@bib35]). Investigating the role of proprioception through self-reinnervation {#s1-1} ------------------------------------------------------------------- Here we probe the integration of feedforward, feedback and intrinsic mechanical control by eliciting a proprioceptive deficit in the lateral gastrocnemius muscle (LG) of the guinea fowl (*Numida meleagris*) using bilateral self-reinnervation ([Figure 1](#fig1){ref-type="fig"}). Self-reinnervation involves peripheral nerve branch transection and immediate repair, resulting in recovery of motor output with long-term, local loss of autogenic muscle proprioception ([@bib16]; [@bib10]). Self-reinnervation occurs through axonal regrowth and reconnection with denervated tissues over a recovery period of 4-8 weeks ([@bib11]; [@bib16]; [@bib36]; [@bib84]). Reinnervated muscles retain a deficit in the monosynaptic stretch reflex due to synaptic retraction of primary muscle spindle afferents and disconnection from parent motoneuron populations ([@bib2]; [@bib8]). However, intermuscular force and length feedback networks may remain partially intact ([@bib49]). Cats and rats with reinnervated muscles maintain whole-limb function by adjusting inter-joint coordination and muscle co-activation to compensate for loss of reflex-mediated ankle stiffness ([@bib1]; [@bib51]; [@bib12]; [@bib7]). These findings highlight the ability of animals to flexibly exploit musculoskeletal plasticity to maintain function and suggest self-reinnervation as a promising tool to investigate sensorimotor control mechanisms. {#fig1} Studying neuromuscular control in the guinea fowl, a bipedal animal model, provides insight into similarities and differences among vertebrates that may relate to locomotor modality, evolutionary history, or both. Birds share features of sensorimotor structure and function with mammals, including muscle tissue properties ([@bib57]; [@bib65]) and muscle proprioception through muscle spindle and Golgi tendon organs ([@bib26]; [@bib38]; [@bib52]). Ground birds use bipedal walking and running gaits with mechanics and energetics similar to human locomotion ([@bib39]; [@bib82]; [@bib34]; [@bib70]; [@bib22]). Bipedal gaits involve substantial periods of single-limb contact, which limits the redundancy of balance mechanisms and poses a challenge for stability ([@bib18]; [@bib13]; [@bib21]). Whereas a quadrupedal cat or rat might be able to compensate for deficits by shifting weight bearing among legs, a biped with a bilateral proprioceptive deficit cannot. Accordingly, one goal of the current study is to explore whether or not guinea fowl exhibit a similar response to proprioceptive deficit as observed in quadrupedal vertebrates ([@bib1]; [@bib51]; [@bib12]; [@bib7]). We hypothesize that autogenic proprioceptive deficit will lead to increased reliance on feedforward control mechanisms and intrinsic muscle mechanics to maintain stable locomotion. To test for shifts in stability and control mechanisms, we measured ankle kinematics and in vivo LG muscle dynamics (length, force and activation) during treadmill running on level and obstacle terrain. There are several potential mechanisms to compensate for autogenic proprioceptive deficit: 1) Birds might compensate for proprioceptive deficit by increasing feedforward muscle activation before obstacle contact, as observed in birds negotiating high-contrast obstacles ([@bib35]). 2) Alternatively, if feedback regulation of LG is essential for stability in fast locomotion, loss of autogenic proprioception may necessitate increased reliance on heterogenic reflex pathways from synergists, with a slight delay compared to intact animals, as suggested by work in cats and rats ([@bib7]; [@bib49]). 3) Finally, if intrinsic mechanics are mainly responsible for the modulation of muscle force and work, we might expect minimal change in muscle activity patterns (EMG), as observed in birds subjected to unexpected drop perturbations ([@bib18]). We expect birds to compensate for proprioceptive deficit by tuning gait and feedforward muscle activity to maintain a stable response to obstacle perturbations, as observed in reinnervated rats and cats walking on slopes ([@bib1]; [@bib51]; [@bib12]; [@bib7]). If stability is impaired following reinnervation, this should be evident from increased variance and longer time to recover from obstacles. By investigating the shifts in guinea fowl LG muscle force, length and activation dynamics following reinnervation, we hope to gain insight into the mechanisms of sensorimotor integration and plasticity that enable robustly stable and agile bipedal locomotion. Results {#s2} ======= Mechanical function of intact *versus* reinnervated LG {#s2-1} ------------------------------------------------------ We find that many features of the steady-state in vivo mechanical function of the guinea fowl reinnervated lateral gastrocnemius (rLG) are similar to that previously measured in the intact LG (iLG) ([Table 1](#table1){ref-type="table"}). In [Figure 2](#fig2){ref-type="fig"}, average trajectories (mean±95% confidence interval) are shown for muscle strain, force and electromyographic activity (iLG at top, rLG below), with the average for steady level running in grey. During the swing phase of the stride cycle, both iLG and rLG exhibit a period of passive stretch, followed by rapid shortening. Activation and force development begin in late swing around the time of the transition from stretch to shortening, initiating rapid active shortening until foot contact ([Figure 2](#fig2){ref-type="fig"}, triangles). At the time of foot contact, force increases rapidly to a peak before midstance, then declines more slowly. Typically, in level running both iLG and rLG show a near-isometric phase in early stance, followed by shortening in late stance, which produces net positive work, as indicated by counter-clockwise force-length work loops ([Figure 3](#fig3){ref-type="fig"}). The average magnitude of work output (W~net~) during steady level running is similar between the iLG and rLG, with similar spread of the distribution around the mean ([Figure 4](#fig4){ref-type="fig"}). However, rLG shows faster shortening velocity at peak force (V~pkF~) compared to the iLG across both level and obstacle terrains ([Figure 4](#fig4){ref-type="fig"}), indicating a difference in steady state contraction dynamics. ![Muscle trajectories during obstacle negotiation for intact and reinnervated lateral gastrocnemius (iLG: blue, top, rLG: orange, bottom).\ Stride cycle averages are shown, from mid-swing to mid-swing (mean ± 95% ci) for a 4-stride sequence in obstacle terrain, with steady level terrain means as a reference, in grey. The shaded box is an obstacle encounter (S 0). Obstacle terrain strides are coded as in [@bib21], for strides preceding (S −1), on (S 0) and following obstacle contact (S +1), with S +2 including all other strides between obstacles. Trajectories are fractional muscle fascicle length (top), muscle-tendon force (middle) and rectified myoelectric activity (EMG). Triangles indicate the timing of foot-ground contact (grey: level terrain, black: obstacle terrain). Example data is shown from one individual in each treatment cohort. See [Figure 2---figure supplement 1](#fig2s1){ref-type="fig"} for details on stride-cycle cutting and categorization in an example stride sequence in obstacle terrain.](elife-53908-fig2){#fig2} {ref-type="fig"}, where the shaded box is an obstacle encounter (S 0). Triangles indicate the timing of foot-ground contact and arrows indicate the direction of the work loop, with a counter-clockwise loop corresponding to net positive muscle work.](elife-53908-fig3){#fig3} {ref-type="table"} and [2](#table2){ref-type="table"} for full statistics results and summary data.](elife-53908-fig4){#fig4} ###### Statistical results. F-statistics for linear mixed effect model ANOVA with fixed effects of treatment cohort (*treatment*: intact, reinnervated) and stride category (*stride ID*) and the interaction *treatment* x *stride ID* on measures of muscle contraction mechanics and activation. Bolding indicates statistical significance using FDR corrected threshold (p\<=0.0263, see Methods). Degrees of freedom for fixed effects were *treatment* = 1, *stride ID* = 4, *interaction* = 4, and error = 2529. See [Table 1---source data 1](#table1sdata1){ref-type="supplementary-material"} for p-values. Table 1---source data 1.P-values linear mixed effect model ANOVA with fixed effects of treatment cohort (*treatment*: intact, reinnervated) and stride category (*stride ID*) and the interaction *treatment* x *stride ID.* F-statistic ----------- ------------- ------------ ----------- W~net~ 2.44 **172.04** **7.44** F~pk~ 0.52 **30.12** **61.73** L~pkF~ 1.52 **238.03** **39.52** V~pkF~ **11.43** **28.09** **8.73** T~force~ 0.27 **99.09** **18.32** T~stride~ 0.10 **12.17** **17.82** E~tot~ 0.01 **49.05** **3.51** E~freq~ 3.93 **8.71** 1.85 E~phase~ **5.72** 2.34 **7.64** E~dur~ **10.02** **8.86** **10.69** Force-length dynamics and work output during obstacle negotiation {#s2-2} ----------------------------------------------------------------- In obstacle encounters ([Figure 2](#fig2){ref-type="fig"}, S 0), foot contact with the obstacle occurs earlier in the stride cycle compared to level terrain, altering force-length dynamics during the obstacle stance period. During obstacle contact, both iLG and rLG remain at longer lengths, force increases rapidly to reach a higher peak force, and the muscle shortens throughout force development, producing positive work ([Figure 2](#fig2){ref-type="fig"}, S 0). Both iLG and rLG exhibit increased force and work output in obstacle strides compared to level strides ([Figure 3](#fig3){ref-type="fig"}, S 0). The magnitude of the shift in work output (W~net~) in obstacle strides (S 0) is similar between intact and reinnervated cohorts, increasing by 3.60±0.57 Jkg^−1^ in iLG and 3.88±0.60 Jkg^−1^ in rLG (mean±95% ci, [Figure 4B](#fig4){ref-type="fig"}, [Table 2](#table2){ref-type="table"} ). ###### Pairwise posthoc comparisons. Pairwise mean differences (mean ± 95% ci) between intact and reinnervated treatment cohorts (left), and between obstacle stride categories compared to level stride means, within treatment cohorts (intact/reinnervated). Bolding indicates statistical significance using FDR corrected threshold (p \<= 0.0263). See [Table 2---source data 1](#table2sdata1){ref-type="supplementary-material"} for p-values. Table 2---source data 1.P-values for posthoc pairwise mean differences between intact and reinnervated treatment cohorts (left column) and between obstacle stride categories compared to the level terrain means, within treatment cohorts (intact/reinnervated). Variable Treatment cohort Intact Reinnervated ----------- ------------------ ------------------ ------------------- ------------------ ------------------ ------------------ ------------------- ------------------ ------------------ W~net~ −0.47 ± 0.59 **−0.91 ± 0.60** **3.60 ± 0.57** 0.00 ± 0.59 **−0.86 ± 0.34** 0.34 ± 0.55 **3.88 ± 0.60** 0.49 ± 0.70 −0.19 ± 0.46 F~pk~ −0.02 ± 0.06 −0.04 ± 0.07 **0.17 ± 0.06** 0.04 ± 0.07 −0.04 ± 0.04 **0.09 ± 0.06** **0.62 ± 0.07** **0.10 ± 0.08** 0.05 ± 0.05 L~pkF~ −0.02 ± 0.04 **−0.02 ± 0.01** **0.10 ± 0.01** −0.01 ± 0.01 **−0.02 ± 0.01** **−0.05 ± 0.01** **0.14 ± 0.01** **−0.06 ± 0.02** **−0.04 ± 0.01** V~pkF~ **−1.89 ± 1.10** 0.07 ± 0.45 **−1.26 ± 0.43** 0.00 ± 0.45 0.11 ± 0.26 **0.60 ± 0.42** −0.39 ± 0.46 **0.63 ± 0.53** **0.81 ± 0.35** T~force~ 0.02 ± 0.07 −0.01 ± 0.02 **0.11 ± 0.02** −0.01 ± 0.02 −0.01 ± 0.01 **−0.07 ± 0.02** **0.07 ± 0.02** **−0.06 ± 0.02** **−0.06 ± 0.02** T~stride~ 0.00 ± 0.02 −0.01 ± 0.02 **0.03 ± 0.02** **−0.02 ± 0.02** 0.01 ± 0.01 **−0.07 ± 0.02** **0.04 ± 0.02** **−0.04 ± 0.03** **−0.03 ± 0.02** E~tot~ 0.01 ± 0.22 0.12 ± 0.18 **0.76 ± 0.18** 0.11 ± 0.18 **0.12 ± 0.11** 0.16 ± 0.17 **0.74 ± 0.19** **0.39 ± 0.22** 0.09 ± 0.14 E~freq~ 55.70 ± 55.12 3.05 ± 9.44 **−15.05 ± 9.04** −1.46 ± 9.34 −0.46 ± 5.43 −2.86 ± 8.75 **−22.06 ± 9.52** −6.81 ± 11.04 **−7.68 ± 7.28** E~phase~ **−0.06 ± 0.05** −0.01 ± 0.02 0.00 ± 0.02 0.00 ± 0.02 −0.01 ± 0.01 0.01 ± 0.02 **0.04 ± 0.02** −0.01 ± 0.02 0.00 ± 0.01 E~dur~ **0.08 ± 0.05** 0.00 ± 0.03 **0.04 ± 0.02** −0.01 ± 0.02 0.00 ± 0.01 **−0.04 ± 0.02** −0.01 ± 0.03 0.00 ± 0.03 **−0.03 ± 0.02** Although the magnitude of the shifts in work output are similar between iLG and rLG, the mechanisms underlying the shift in work output differ between them ([Figure 4)](#fig4){ref-type="fig"}. In iLG, increased work upon obstacle contact occurs through modest increases in both peak force (F~pk~) and shortening velocity (V~pkF~), compared to level strides. In contrast, rLG exhibits a substantially larger increase in F~pk~ on obstacle strides and maintains similar V~pkF~ between level and obstacle terrain strides (S 0, [Figure 4B](#fig4){ref-type="fig"}, [Table 2](#table2){ref-type="table"}). Reinnervated LG also exhibits small but significant increases in F~pk~ in the strides preceding and following obstacle contact (S-1 and S+1, respectively), compared to level terrain. Shifts in activation patterns between intact and reinnervated LG {#s2-3} ---------------------------------------------------------------- Despite deficits in LG monosynaptic reflex following reinnervation, rLG and iLG show similar increases in total muscle activation intensity (E~tot~, integral of EMG) in obstacle strides compared to steady level strides (S 0, [Figure 5](#fig5){ref-type="fig"}). Intact LG exhibits a 4% increase in duration in obstacle strides (S 0) compared to level; however, there is no significant increase in EMG duration for rLG in S 0 ([Figure 5B](#fig5){ref-type="fig"}, [Table 2](#table2){ref-type="table"}). This suggest that the observed increase in E~tot~ in rLG obstacle strides occurs through increased activation amplitude, not increased duration. {ref-type="fig"}. See [Tables 1](#table1){ref-type="table"} and [2](#table2){ref-type="table"} for full statistics results and summary data.](elife-53908-fig5){#fig5} Several results suggest a shift in central drive and feedforward activation pattern in rLG compared to iLG. Reinnervated LG exhibits longer steady-state duration of activity (E~dur~) compared to iLG across all level and obstacle terrain strides, averaging 37% of the stride cycle in rLG compared to 29% in iLG ([Figure 5B](#fig5){ref-type="fig"}, [Table 2](#table2){ref-type="table"}). Additionally, rLG exhibits higher average frequency of EMG activity across all strides compared to the intact cohort ([Figure 5](#fig5){ref-type="fig"}, [Table 2](#table2){ref-type="table"}, [Figure 5---figure supplement 1](#fig5s1){ref-type="fig"}). Finally, the steady-state timing of rLG activation is phase-shifted to 6% (23ms) earlier in the stride cycle relative to the length trajectory, quantified by the variable 'E~phase~' ([Figure 6](#fig6){ref-type="fig"}, [Tables 1](#table1){ref-type="table"}--[2](#table2){ref-type="table"}). Earlier activation onset may help explain the higher rate of shortening in rLG compared to iLG, reported above. {#fig6} Timing of obstacle-induced changes in EMG activity in iLG and rLG {#s2-4} ----------------------------------------------------------------- To explore the timing of obstacle-induced shifts in EMG activity relative to perturbations in force and length, we calculated a difference trajectory between the steady-state level and obstacle perturbed stride cycles (S 0 -- Lev) for each individual, and then calculated the mean and 95% confidence interval across individuals ([Figure 7](#fig7){ref-type="fig"}). Increased EMG activity begins \~30-40 ms *before* obstacle-induced increases in length and force, for both iLG and rLG, suggesting an anticipatory (feedforward) contribution to increases in E~tot~ ([Figure 7](#fig7){ref-type="fig"}, arrows indicating 'anticipatory increase'). In iLG, the anticipatory increase in EMG starts \~25% of stride period (asterisk in EMG trace and vertical dashed line in [Figure 7A](#fig7){ref-type="fig"}). Starting around 58% of stride period, there is another distinct burst of increased activity, suggesting reflex-mediated contribution to increased EMG in obstacle strides ([Figure 7](#fig7){ref-type="fig"}, arrow indicating 'reflex'). In rLG, the 'anticipatory increase' in EMG starts around 21% of stride (asterisk and vertical dashed line in 7B); however activity in the latter half of stance is highly variable and idiosyncratic among individuals ([Figure 7---figure supplement 1](#fig7s1){ref-type="fig"}), as indicated by the wide 95% confidence intervals spanning the region of time where the iLG shows a distinct reflex response (compare [Figure 7B](#fig7){ref-type="fig"} versus 7A lower panels). Cross-correlation between the obstacle perturbation trajectories for iLG reveals a correlation of 0.82 between length and EMG deviations, and a correlation of 0.85 between force and EMG deviations. For rLG, the cross-correlations are reduced to 0.53 between length and EMG deviations, and 0.57 between force and EMG deviations, respectively. The reduced correlations suggest a disrupted reflex-mediated response to muscle load and strain in the latter half of stance in rLG, but which is present in iLG ([Figure 7](#fig7){ref-type="fig"}). Considering that the changes in muscle length and force are strongly correlated with each other during obstacle encounters in both intact and reinnervated conditions ([Figure 7](#fig7){ref-type="fig"}), it is difficult to distinguish the specific sensory signal eliciting reflex responses. {ref-type="fig"}. A black asterisk (\*) indicates the first timepoint in each trajectory that differs significantly from the level mean. The dashed vertical line and arrow indicating 'anticipatory increase' highlights a significant increase in EMG that starts *before* deviations length and force in S 0. In (**A**) (iLG), solid vertical lines and yellow fill indicates a 2nd period of significantly increased EMG in late stance that correlates with increased fascicle length and force, suggesting a reflex response. In (**B**) (rLG), the anticipatory increase in EMG is present; however, wide confidence intervals for EMG in late stance indicates inconsistent patterns of activity across individuals, despite similar increases in length and force as iLG. This suggests disrupted autogenic feedback and idiosyncratic heterogenic feedback patterns across individuals ([Figure 7---figure supplement 1](#fig7s1){ref-type="fig"}).](elife-53908-fig7){#fig7} Stability and kinematic changes during obstacle negotiation in intact vs reinnervated birds {#s2-5} ------------------------------------------------------------------------------------------- Compared to the intact cohort, birds with rLG exhibit more pronounced shifts in gait dynamics in obstacle terrain relative to level terrain. Obstacle-induced increases in peak force (F~pk~) are larger for rLG compared to iLG (S 0 [Figure 4](#fig4){ref-type="fig"}, [Table 2](#table2){ref-type="table"}), reflecting larger deviations from steady state in response to the same obstacle. Additionally, rLG shows small but significant increases in peak force (F~pk~) in the strides preceding and following obstacle contact (S -1, S +1) compared to steady level strides ([Figure 4B](#fig4){ref-type="fig"}, [Table 2](#table2){ref-type="table"}). Multiple significant differences from level strides occur for rLG in S +1, including a 39±22% increase in E~tot~, a 6±2% decrease in force duration and a 4±3% decrease in stride duration (mean±95% ci, [Table 2](#table2){ref-type="table"}). In contrast, most variables for iLG have recovered to steady state in S +1 ([Table 2](#table2){ref-type="table"}). Both iLG and rLG rapidly increase work output during obstacle encounters and face increased activation costs for locomotion in obstacle terrain. However, rLG shows larger deviations from steady state, and a slower recovery to steady state mechanics and activation level compared to iLG, indicating reduced stability. Reinnervated birds also show differences in running kinematics in obstacle terrain compared to the intact cohort, undergoing a more pronounced increase in ankle flexion in obstacle encounters ([Figure 8](#fig8){ref-type="fig"}). Reinnervated birds also use a shorter stride duration immediately preceding the obstacle encounter (S -1), suggesting anticipatory preparation that is not observed in intact birds ([Figure 8](#fig8){ref-type="fig"}). These observations suggest reduced ankle stiffness and increased anticipatory preparation for obstacle encounters in the reinnervated birds. {ref-type="supplementary-material"} for statistical results on ankle angle at the time of foot contact).\ Figure 8---source data 1.ANOVA results for ankle angle at time of foot contact.F-statistics, p-values and posthoc pairwise comparisons for linear mixed effect model ANOVA with fixed effects of treatment cohort (*treatment*: intact, reinnervated) and stride category (*stride ID*) and the interaction *treatment* x *stride ID.* Posthoc pairwise mean differences (mean ±95% ci) are shown between intact and reinnervated treatment cohorts (left), and between obstacle stride categories compared to level stride means, within treatment cohorts (intact/reinnervated).](elife-53908-fig8){#fig8} Discussion {#s3} ========== What is the role of proprioception in the control of high-speed locomotion? {#s3-1} --------------------------------------------------------------------------- We investigated the role of reflexes in the sensorimotor control of running by examining the effects of proprioceptive deficit on the mechanical function of the lateral gastrocnemius muscle (LG) of guinea fowl. Long sensorimotor delays relative to limb cycling times necessitate that animals use a combination of feedforward, feedback and intrinsic mechanical control mechanisms to achieve stable locomotion at high speeds ([@bib9]; [@bib44]; [@bib6]; [@bib21]; [@bib18]; [@bib33]; [@bib37]; [@bib47]; [@bib55]; [@bib64]; [@bib67]). We hypothesized that an autogenic proprioceptive deficit will lead to increased reliance on feedforward tuning of muscle activity to achieve stable muscle dynamics in obstacle terrain. In birds with intact LG proprioception, the timing of muscle activity in obstacle-perturbed strides is consistent with combined feedforward and feedback control ([@bib21]; [@bib35]). Birds with reinnervated LG (rLG) exhibit a consistent phase shift in EMG onset relative to muscle length, with activation starting 6% earlier (23 ms) in the steady state contraction cycle, in both level and obstacle terrain ([Figure 6](#fig6){ref-type="fig"}, [Table 2](#table2){ref-type="table"}). This is consistent with a feedforward tuning of rLG activation timing to enable rapid force development and high muscle stiffness during stance, in the absence of monosynaptic reflexes. Regulation of EMG duration in obstacle strides (S 0) is absent in rLG ([Figure 5](#fig5){ref-type="fig"}), suggesting that proprioceptive feedback in late stance normally regulates force duration, which is disrupted following reinnervation. A stable intrinsic mechanical response with neither feedforward- nor feedback-mediated changes in neural drive can occur when a perturbation is encountered at high running speeds ([@bib18]). Rapid changes in muscle length and velocity in response to perturbations can decouple activation and force development ([@bib18]; [@bib21]). In our previous work on intact in vivo muscle dynamics, variation in LG muscle strain during initial foot contact and limb loading explained 60% of the variation in force developed in obstacle encounters, while variation in LG muscle activation explained only 9%. This clearly demonstrates the decoupling between activation and force development that can occur in vivo ([@bib21]). These intrinsic mechanical effects minimize the disturbances in body dynamics that arise from terrain height perturbations, enabling rapid recovery to steady gait. Similar intrinsic mechanical stabilizing responses have been demonstrated in the distal hindlimb joints of hopping and running humans subjected to unexpected changes in terrain height and stiffness ([@bib24]; [@bib32]; [@bib56]). In concert with the stabilizing contributions of the intrinsic muscle-tendon dynamics, guinea fowl with intact proprioception also use feedforward and feedback regulation of muscle activity to maintain stability in obstacle terrain, with greater feedforward contributions when obstacles are visible and high contrast ([@bib21]; [@bib35]). We find that guinea fowl with LG proprioceptive deficit achieve similar increases in total EMG activity during obstacle strides; however, the increases in activity occur early in the stride, before obstacle-induced changes in muscle force and length ([Figure 7](#fig7){ref-type="fig"}). This is consistent with anticipatory, feedforward increases in neural drive to the muscle, as observed in birds running over high-contrast visible obstacles ([@bib35]), and humans hopping on randomized but expected increases in surface stiffness ([@bib56]). These findings are consistent with a hybrid feedforward/feedback control model as conceptualized by [@bib46] in which feedforward and feedback gains are balanced to enable accurate state estimation and robust cyclical dynamics in the presence of both disturbances and sensory error. Although the reinnervated LG contributes to an effective obstacle negotiation response, it requires a longer recovery time and increased muscle activity following obstacle contact ([Figure 5B](#fig5){ref-type="fig"}). This suggests that the integrated response of the intact neuromuscular system enables robust stability with lower muscle activation costs. Several features of the kinematics and muscle dynamics suggests coordinated plasticity and tuning of feedfoward control to compensate for reflex deficit following recovery from nerve injury ([Figure 9](#fig9){ref-type="fig"}). We observe similar increases in work output in response to obstacle encounters in rLG and iLG ([Figure 4B](#fig4){ref-type="fig"}). This finding is consistent with the idea that muscle work modulation is an important feature of task-level control for stability in uneven terrain ([@bib18]; [@bib21]). However, work modulation is achieved through different underlying mechanisms in rLG and iLG. Earlier steady state activation in rLG (lacking autogenic proprioceptive feedback) enables higher muscle force development in early stance to resist the external load applied at foot contact, which likely contributes to the higher rate of shortening throughout stance. Additionally, rLG exhibits larger increases in peak force in obstacle encounters compared to iLG ([Figure 4B](#fig4){ref-type="fig"}). This increase in peak force likely involves both active and passive components: an active contribution from increased feedforward drive and EMG amplitude ([Figure 5B](#fig5){ref-type="fig"}), and a passive contribution from increased stretch of connective tissues associated with a more flexed ankle posture at foot contact ([Figure 8](#fig8){ref-type="fig"}). Finally, Birds with rLG also show an anticipatory shift in stride duration before obstacle encounters, which is not observed in the intact cohort ([Figure 8B](#fig8){ref-type="fig"}) and may help control landing conditions for obstacle encounters ([@bib35]). These findings suggest that reinnervated birds achieve effective muscle work modulation and stable obstacle negotiation through feedforward tuning of muscle activation and gait to compensate for loss of autogenic proprioception. {#fig9} A recent study by [@bib77] found that earlier onset of activation was associated with a shift to energy absorption in cyclical muscle contractions with a sinusoidal MTU length trajectory. We find here that earlier onset is associated with greater shortening and work production. The specific response of a muscle to a shift in activation phase is likely to be highly sensitive to the specific steady-state length trajectory of the muscle. Muscle force capacity and the activation and deactivation kinetics are substantially influenced by velocity and recent strain history, as demonstrated in controlled studies of in vitro muscle force-length work loops ([@bib3]; [@bib45]). Further work is needed to understand how in vivo muscle fascicle length dynamics interact with neural activation patterns and MTU compliance to enable tuning of muscle contraction dynamics to the mechanical demands of cyclical locomotor tasks. We do observe shifts in muscle activity in late stance in some reinnervated individuals in response to obstacle encounters, which suggests heterogenic reflex responses in reinnervated LG ([Figure 2](#fig2){ref-type="fig"}). However, these responses are variable and idiosyncratic, with some birds showing increased EMG in late stance in obstacle strides, and others showing a decrease ([Figure 7---figure supplement 1](#fig7s1){ref-type="fig"}). The variable and idiosyncratic reflex responses result in wide confidence intervals for the obstacle-induced EMG response in the latter half of stance, despite consistent force-length trajectories over the same time-period ([Figure 7](#fig7){ref-type="fig"}). Idiosyncratic use of heterogenic reflex modulation across individuals following nerve injury recovery is consistent with findings in cats ([@bib49]; [@bib50]). Guinea fowl have several agonist muscles to the LG that could contribute to heterogenic feedback modulation, including the medial gastrocnemius and digital flexors ([@bib21]; [@bib35]). However, no muscle is an exact synergist of the LG, because each has a unique combination of moment arms, fiber length, pennation angle and connective tissue compliance ([@bib20]; [@bib17]). Consequently, it is unlikely that proprioception from agonists can completely restore accurate sensing to regulate LG force and work output. Additionally, in the presence of increased sensory error and noise, birds may learn over time to compensate through sensory integration in higher CNS pathways, leading to updated central coordination and feedforward drive to rhythm generating networks. It was previously unknown whether guinea fowl would respond to reinnervation and proprioceptive deficit in a manner similar to quadrupedal mammals. We find that our results are consistent with the findings on rats and cats. Reinnervated cats and rats exhibit shifts in feedforward muscle activity and inter-joint coordination during slope walking, to compensate for loss of reflex-mediated ankle stiffness ([@bib1]; [@bib51]; [@bib12]; [@bib7]). Cats and rats also preserve task level features of gait, such as leg length and body motions, despite variance in muscle and joint dynamics ([@bib12]; [@bib7]). These findings suggest performance of task-level goals as a target of sensorimotor optimization. Also similar to cats, guinea fowl exhibit variation among individuals in heterogenic compensation for loss of the autogenic stretch reflex, as suggested by the variable tendon tap responses and variation in late-stance EMG activity in obstacle perturbed steps ([Figure 7](#fig7){ref-type="fig"}; [Figure 7---figure supplement 1](#fig7s1){ref-type="fig"}). Work on cats suggests complex intermuscular feedback connectivity, which can recovery to varying degrees following reinnervation ([@bib16]; [@bib62]; [@bib49]; [@bib50]). This complexity and variability among individuals following recovery from nerve injury reflects the complexity and plasticity of proprioceptive feedback networks. Nonetheless, the recovery of consistent task-level mechanical function supports the idea that sensorimotor control is optimized to maintain task-level performance goals such as stable body dynamics ([@bib12]; [@bib76]). Limitations and future directions {#s3-2} --------------------------------- One of the major limitations in the current study is the potential for multiple differences between the intact and reinnervated cohorts that were not controlled, because the experiments on the two cohorts were conducted over different periods of time. The self-reinnervation procedure requires a long-term recovery period and results in a chronic sensory deficit, which is likely to lead to a complex array of changes in the musculoskeletal tissues and the sensorimotor networks. The current study did not include a sham-surgery experimental control, and we did not strictly monitor the ages of the original intact cohort at the time of the in vivo muscle-tendon surgeries. Nonetheless, it is reassuring that our findings are consistent with similar studies in cats and rats, suggesting feedforward tuning of muscle activation and ankle kinematics to maintain stability following loss of proprioception. In future experiments, it will be important to control the timing and amount of exercise training in intact and reinnervated experimental groups, considering the potential for exercise to influence the recovery process ([@bib7]; [@bib8]). The recovery process almost certainly involves coupled changes across multiple systems, including connective tissue compliance, muscle activation kinetics, fiber type distribution, motor unit size and distribution, spinal intraneuronal connectivity, and sensory integration in higher CNS centers for state estimation and movement planning. Due to the complex nature of these adaptations, it is challenging to fully tease apart individual contributions and mechanisms from in vivo experimental measures alone. In future studies, the coordinated mechanisms of sensorimotor adaptation and plasticity could be systematically explored through a combination of integrative experimental and computational approaches. These approaches could include 1) closed loop neuromechanical simulations to enable predictive hypothesis testing ([@bib43]; [@bib75]), 2) combined use of in vivo measures of muscle dynamics with in vitro testing of muscle contractile dynamics, to replicate biologically realistic force-length contraction dynamics, 3) histological studies to examine changes in muscle fiber type distribution and connective tissue characteristics following reinnervation, and 4) perturbation approaches that probe both short and long term adaptation processes. It remains unclear how the specific length trajectory and velocity features of in vivo muscle dynamics contribute to the intrinsic stability and control of movement. Dynamic measurement techniques are needed to address this challenge and to develop realistic models for in vivo muscle-tendon function. In addition to widely recognized force-length and force-velocity 'Hill-type' properties, muscle exhibits short and long-term history-dependent changes in force capacity in response to stretch and shortening ([@bib28]; [@bib29]; [@bib30]; [@bib45]; [@bib40]; [@bib31]; [@bib41]; [@bib72]; [@bib60]; [@bib87]; [@bib61]). Recent developments in biorobotic platforms that enable controlled muscle experiments with realistic loading and length trajectories are promising tools for advancing our understanding of the role of intrinsic muscle dynamics in the control of movement ([@bib14]; [@bib69]; [@bib71]). Integrative neuromechanical studies using multiple techniques will be essential for unravelling mechanisms of muscle function, sensorimotor integration and plasticity. Findings from these studies have important implications for many human health conditions, including acute nerve injury, diabetic neuropathy, neurodegenerative disorders, cerebral palsy, and muscular dystrophies. Materials and methods {#s4} ===================== Animals and treadmill training {#s4-1} ------------------------------ We obtained and reared six hatchling guinea fowl keets (*Numida meleagris*) from a breeder (Hidden Hollow Acres, Whitehouse Station, NJ), to allow re-innervation surgeries in juveniles with at least 12 weeks for recovery before in vivo muscle procedures (see below). At the time of the in vivo muscle measurements, the guinea fowl had reached adult size, averaging 1.81±0.28 kg body mass (mean±S.D.). Birds had primary feathers clipped and were trained to run on a level motorized treadmill (Woodway, Waukesha, WI, USA). Training sessions were 15-20 minutes in duration, with breaks for 2 minutes as needed. All experiments were undertaken at the Concord Field Station of Harvard University, in Boston (MA, USA), and all procedures were licensed and approved by the Harvard Institutional Animal Care and Use Committee (AEP \#20-09) in accordance with the guidelines of the National Institutes of Health and the regulations of the United States Department of Agriculture. We also include data previously reported in [@bib21] from intact individuals (n=6, 1.77±0.63 kg body mass) to serve as a control group for statistical comparison to the new dataset (n=6 reinnervated individuals). We re-analyzed the intact cohort dataset alongside the reinnervated cohort, to ensure consistency in data processing and statistics. The intact data includes a larger sample than reported in [@bib21], because the analysis here includes all strides in the level and obstacle terrain collected for running speeds between 1.3-2.0 ms^−1^. Trials were recorded only for speeds that each bird could comfortably maintain on the treadmill belt for at least 30 seconds, allowing for 10-minute rest periods between trials with access to food and water. We focus on running speeds (\>1.3ms^−1^), to avoid the confounding effect of different sensorimotor control strategies in walking *versus* running ([@bib35]). Due to variation among individuals in the successful trials recorded, the intact cohort dataset includes a wider speed range (1.3-2.0 ms^−1^) than the reinnervated cohort dataset (1.7-2.0 ms^−1^). However, the analysis is focused on obstacle perturbations compared to steady gait at the same speed, and the datasets include comparable samples of obstacle encounters between the two cohorts: 128 for intact and 133 for reinnervated birds, respectively. In total, the dataset includes 1027 strides for reinnervated and 1512 strides for intact individuals and excludes 81 strides as outliers that were non-obstacle encounter strides with Z-score \> 4. No obstacle encounter strides were excluded as outliers. The complete datasets for reinnervated and intact cohorts are available through [DataDryad.org](https://datadryad.org/stash), including metadata and Matlab processing scripts ([@bib19], <https://doi.org/10.7280/D11H49>). Anesthesia and post-operative care {#s4-2} ---------------------------------- Birds were induced and maintained on a mid-plane of anesthesia using isoflurane (2 - 3%, mask/intubation delivery). We administered perioperative enrofloxacin and flunixin intramuscularly for analgesia after induction and continued for three days after each surgery. Birds recovered to bilateral weight bearing within 20 minutes following completion of surgical procedures. Reinnervation surgery {#s4-3} --------------------- The timing of surgeries was planned based on a pilot study, which found full recovery of LG motor activity by 6 weeks following reinnervation surgeries, and continued absence of calcaneal tendon reflex one year later, indicating continued absence of autogenic stretch reflexes ([@bib11]). We bilaterally transected and immediately repaired the peripheral nerve branch supplying the LG muscle in maturing guinea fowl between 7-12 weeks of age. We allowed time for full reinnervation recovery of motor output and growth to adult size before a subsequent surgery to implant muscle transducers ([Figure 1](#fig1){ref-type="fig"}). In the reinnervation surgery, a lateral incision was made posterior-distal to the knee to expose the underlying muscle. Blunt dissection enabled exposure and identification of relevant nerve branches, and the identity of the correct nerve branch was confirmed using an isolated nerve stimulator (SD48, Grass Instruments, Warwick, RI) to visualize contraction in the LG. After pre-placement of single longitudinal throw of 6-0 braided non-absorbable silk (Silk, Ethicon, Somerville, NJ, USA) through a 3 mm nerve section, we transected the nerve branch and sutured to appose the cut nerve endings. Fibrin glue (bovine thrombin in CaCl~2~, fibrinogen, fibronectin from bovine plasma) was applied over the apposed nerve endings as an additional repair scaffold ([@bib11]; [@bib81]). We closed the fascia and skin with 3-0 braided absorbable polyglactin (Vicryl, Ethicon,Somerville, NJ, USA). In the immediate post-operative period, bilateral limb posture was visibly more crouched compared to 'intact' birds and Achilles tendon tap revealed no stretch reflex response. LG atrophy was qualitatively observed during the first 2 weeks of the recovery period. Within 1 week of surgery, bird activity levels appeared comparable to intact conspecifics, with limb posture partially recovered. From 2-3 weeks onwards, differentiating reinnervated from 'intact' birds was not possible from grossly observable limb morphology, posture and gait. We conducted regular treadmill training from 7 weeks after reinnervation surgery. Exercise was started at 7 weeks to ensure synaptic withdrawal of primary afferents before recovery, eliciting a proprioceptive deficit in the self-reinnervated LG. In rats, synaptic withdrawal and resulting proprioceptive deficit is minimized if training is initiated on the 3^rd^ day after nerve injury ([@bib7]; [@bib8]). During training and experiments, birds did not stumble or fall with noticeably greater frequency than observed in intact birds and were able to maintain treadmill position over a similar speed range. At the time of muscle recordings, Achilles tendon tap revealed variable latencies of 49±43ms (mean±S.D., range 10.3-91.5ms). This may reflect variable recovery of intermuscular reflex connectivity, consistent with observations in cats and rats ([@bib7]; [@bib8]; [@bib49]). In comparison, the Achilles tendon tap reflex latency in intact birds was 6.1±1.2ms (mean±S.D), consistent with the mono-synaptic stretch reflex ([@bib59]; [@bib21]). Transducer implantation surgery {#s4-4} ------------------------------- When the birds were 23-28 weeks old (13-16 weeks following bilateral reinnervation surgeries), we performed a 2nd surgery for transducer placement, following similar procedures as [@bib20]. The surgical field was plucked of feathers and gently cleaned with antiseptic solution (Prepodyne, West Argo, Kansas City, MO, USA). We tunneled transducer leads subcutaneously from a 1--2 cm incision over the synsacrum to a second 4--5 cm incision over the lateral left shank. Sonomicrometry crystals (2.0 mm; Sonometrics Inc, London, Canada) were implanted into the lateral head of the gastrocnemius (LG) along the fascicle axis in the middle 1/3rd of the muscle belly. Crystals were placed in small openings using fine forceps, approximately 3--4 mm deep and 15 mm apart. We verified signal quality using an oscilloscope and secured the crystals by closing the overlying muscle fascia and lead wires with separate 4-0 silk sutures (Silk, Ethicon, Somerville, NJ, USA). Next to the crystal pair, we implanted bipolar EMG electrodes constructed from two strands of 38-gauge Teflon-coated stainless steel (AS 632, Cooner Wire Co., California, USA) with staggered 1 mm exposed regions spaced 1.5 mm apart. Electrodes were placed using sew-through methods and surface silicon anchors (3 x 3 x 2 mm) positioned with a single square knot at the muscle surface-electrode interface ([@bib23]). An "E"-type stainless-steel tendon buckle force transducer insulated with a polyurethane coating (Micro-Measurements, Raleigh NC) was implanted on the common gastrocnemius tendon, equipped with a metal foil strain gauge (type FLA-1, Tokyo Sokki Kenkyujo). We connected transducers to a micro-connector plug (15-way Micro-D, Farnell Ltd, Leeds, UK) sutured to the bird's dorsal synsacrum. Transducer recordings {#s4-5} --------------------- A lightweight shielded cable was used to connect the microconnector to data acquisition systems. Sonomicrometry data were collected via a Sonometrics TRX analog data-acquisition device and PC interface (TRX Series 8, Sonometrics, Ontario, Canada). Crystals were tested before surgery in a saline bath to confirm distances measured by digital caliper matched those measured by the software. Occasional drop-outs and level-shift artifacts in the sonomicrometry length signal (arising from variation in signal-to-noise characteristics) were corrected within the Sonometrics software where possible and smoothed using cubic smoothing spline with a tolerance of 0.1 in MATLAB ('spaps' function, Mathworks, Inc; Natick, MA, USA). Tendon buckle signals were fed through a bridge amplifier (Vishay 2120, Micro-Measurements, Raleigh, NC), and EMG signals were amplified and bandpass filtered (10Hz and 3kHz) using GRASS pre-amplifiers (P511, Grass Instruments, Warwick, RI). Signals were recorded at 10kHz using a 16-channel, 16-bit Biopac A/D acquisition device (MP150, BIOPAC systems, Gotleta, CA, USA). Following experiments, birds were euthanized using an intravenous injection of sodium pentobarbital (100 mg kg^−1^) while under deep isoflurane anesthesia (4%, mask delivery). Muscle morphology {#s4-6} ----------------- Postmortem, we recorded the morphology of the muscle and the location of transducers to confirm muscle fascicle and tendon alignment. In the reinnervated cohort (this study) LG mass was 10.7±2.7 g and total gastrocnemius mass was 26.5±5.1 g. In the intact cohort ([@bib21]), LG mass was 10.2±4.3 g, and total gastrocnemius mass was 23.5±7.4 g. These muscle masses are a comparable to those measured from intact guinea fowl in previous studies, representing approximately 0.5% body mass for LG and 1.3% body mass for total gastrocnemius mass ([@bib20]; [@bib42]). This suggests full recovery from denervation-induced muscle atrophy in the reinnervated cohort. Fascicle lengths for were 17 ±1 mm and 18±2 mm and pennation angles were 25±5° and 24±5° for reinnervated and intact LG, respectively. Crystal alignment relative to the fascicle axis (*α*) was within 2°, indicating that errors due to misalignment were *\<*0.1%. We calibrated the tendon force buckle in situ p*ost mortem* by applying a series of known cyclical loads using a force transducer (model 9203, Kistler, Amherst, MA), which yielded linear least-squares calibration slopes with R^2^ \> 0.97. Level and obstacle terrain conditions {#s4-7} ------------------------------------- We recorded trials on i) uniform level terrain and ii) terrain with repeating 5 cm obstacles, at the same treadmill speeds, as in [@bib21]. The treadmill belt (Woodway, Waukesha WI) was slatted black rubber-coated steel with running surface 55.8 cm x 172.7 cm with clearance for obstacles beneath. Obstacles were constructed from styrofoam reinforced with cardboard covered with black neoprene to form a light, stiff surface. Waterproof glue (Shoe Goo, Eugene, OR, USA) secured heavy-duty fabric hook and loop fastener (Velcro, Cheshire, UK) to the obstacle and treadmill surface. Four sequential slats of obstacles produced a 20 cm^2^ continuous obstacle surface. Obstacles were encountered approximately every 4-5 strides, with some variation due to varied stride length and treadmill station keeping. We recorded high-speed video at 250 Hz (Photron, San Diego, CA, USA) for analysis of ankle kinematics, detection of stride timing and statistical coding of strides in relation to obstacle encounters. Data processing {#s4-8} --------------- We assigned strides categories in relation to the obstacle encounters, using the approach in [@bib21], based on the stride sequence of the instrumented leg: the stride prior to an obstacle contact (S −1), obstacle contact strides (S 0), the stride following obstacle contact (S +1), and strides in flat terrain between obstacles (S +2). All level terrain strides were assigned the same stride category (L). Note, this is simpler stride coding than presented in [@bib35], which also considered the timing of obstacle encounters by the contralateral leg. Strides in which the contralateral limb had made contact with the obstacle in the previous step are grouped here into the (S +2) category, for simplicity. This does not substantially alter the findings, because the coding was similar between intact and reinnervated birds, and the current analysis is focused on the shifts in LG force-length dynamics related to a direct obstacle encounter by the instrumented leg. Features of LG activation, force-length dynamics and work output were measured, similar to [@bib21]. Raw EMG signals were used to calculate myoelectric intensity in time and frequency domains using wavelet decomposition ([@bib18]; [@bib35]). This was used to calculate total myoelectric intensity per stride (E~tot~) and mean frequency of muscle activation (E~freq~). We calculated fractional fascicle length (L) from sonomicrometry data using mean length in level terrain as a reference length (L~o~). Note, however, that L~o~ is not directly related to sarcomere length or optimal length for the isometric force-length curve, which were not measured. Fractional fascicle length was differentiated to obtain fascicle velocity (V, in lengths per second, Ls^−1^). Shortening strains are negative. We multiplied fascicle velocity (in ms^−1^) by tendon force (in Newtons, N) to calculate muscle power (Watts), which was integrated through time to calculate total work per stride (Joules, J; with shortening work being positive), and then normalized by muscle mass to obtain mass-specific muscle work (Jkg^−1^). We also recorded muscle (fascicle) length, velocity and force at specified times to evaluate how strain and activation factors influence muscle force and work output. All data processing was completed using MATLAB (Mathworks, Inc; Natick, MA, USA). Statistics {#s4-9} ---------- The statistical analysis approach is similar to that used in [@bib35] to investigate obstacle perturbation responses relative to steady state level terrain strides. We used a linear mixed-effects model ANOVA to test for significant effects of *treatment* (intact/reinnervated cohorts) and stride category (*stride ID*: Level, S -1, S 0, S +1, S +2) as fixed categorical factors, with individual (*ind*) included as a random effect. Statistical analysis was completed in Matlab using 'fitlme' and associated functions in the Statistics and Machine Learning Toolbox (Mathworks, Inc; Natick, MA, USA). Several linear mixed effects models were evaluated: 1. \'Y \~ 1 + (1\|ind)\' 2. \'Y \~ 1 + treatment + (1\|ind)\' 3. \'Y \~ 1 + stride_ID + (1\|ind)\' 4. \'Y \~ 1 + stride_ID + treatment + (1\|ind)\' 5. \'Y \~ 1 + stride_ID \*treatment + (1\|ind)\' Model 5 (with the interaction term between fixed effects) was used as the final model, because it had the lowest AIC for 13 of 14 of the variables analyzed (AIC, Akaike, 1976). Model 4 had the lowest AIC for mean EMG frequency (E~freq~), but the difference between Models 4 and 5 was not significant according to a likelihood ratio test. Therefore, for consistency, Model 5 was used for all variables. Posthoc pairwise comparisons were calculated for the mean difference ± 95% confidence interval between intact and reinnervated treatment cohorts and for the mean differences between level and obstacle strides categories within each treatment cohort. Pairwise comparisons were calculated after removing the random effect of individual, because the intact and reinnervated datasets came from different cohorts of individuals. We used False Discovery Rate to calculate an adjusted p-value threshold to maintain a 5% false positive rate across all statistical tests, including fixed effects tests and post-hoc pairwise comparisons ([@bib5]). Funding Information =================== This paper was supported by the following grants: - http://dx.doi.org/10.13039/100000002National Institutes of Health NIAMS 5R01AR055648 to Andrew Biewener. - http://dx.doi.org/10.13039/501100000268Biotechnology and Biological Sciences Research Council BB/H005838/1 to Monica A Daley. - http://dx.doi.org/10.13039/501100000268Biotechnology and Biological Sciences Research Council Doctoral training studentship to Joanne C Gordon, Monica A Daley. This research was supported by NIH grant NIAMS 5R01AR055648 to AAB, grant BB/H005838/1 to MAD from the Biotechnology and Biological Sciences Research Council (BBSRC), and a doctoral training studentship from the BBSRC to JCG supervised by MAD. Thanks to Jennifer A Carr for assistance in the experiments. Thanks to Reviewers N Cowan and L Ting and Reviewing Editor K VijayRaghavan for thoughtful and constructive feedback. Additional information {#s5} ====================== No competing interests declared. Formal analysis, Investigation, Methodology, Writing - original draft. Investigation, Writing - review and editing. Conceptualization, Resources, Supervision, Funding acquisition, Writing - review and editing. Conceptualization, Resources, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Visualization, Methodology, Writing - original draft, Writing - review and editing. Animal experimentation: All experiments were undertaken at the Concord Field Station of Harvard University, in Boston (MA, USA), and all procedures were licensed and approved by the Harvard Institutional Animal Care and Use Committee (AEP \#20-09) in accordance with the guidelines of the National Institutes of Health and the regulations of the United States Department of Agriculture. Surgery was performed under isoflurane anesthesia, and every effort was made to minimize suffering. Additional files {#s6} ================ Data availability {#s7} ================= The full dataset including raw data, metadata files and processing code have been deposited to Dryad (<https://doi.org/10.7280/D11H49>). The following dataset was generated: DaleyMAGordonJCHoltNCBiewenerA2020Dataset for \'Tuning of feedforward control enables stable muscle force-length dynamics after loss of autogenic proprioceptive feedback\'Dryad Digital Repository10.7280/D11H49 10.7554/eLife.53908.sa1 Decision letter VijayRaghavan K Reviewing Editor National Centre for Biological Sciences, Tata Institute of Fundamental Research India Cowan Noah J Reviewer Johns Hopkins University United States Ting Lena H Reviewer Emory University United States In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses. **Acceptance summary:** Gordon et al. use bilateral reinnervation of a leg muscle to deduce reflex contributions to muscle activity, kinematics, and muscle force-length trajectories during walking and obstacle crossing in bipedal birds, consistent with prior work in quadrupedal locomotion. Not only does the work advance our understanding, but the paper is very well-written with an extensive analysis that is of broad interest to those interested in complex sensorimotor integration. The work described in this paper is novel and its impact would be considerable in understanding the complexities of sensorimotor reflexes in bipedal locomotion. **Decision letter after peer review:** Thank you for submitting your article \"Tuning of feedforward control enables stable muscle dynamics after loss of autogenic proprioceptive feedback\" for consideration by *eLife*. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by K VijayRaghavan as the Senior Editor and Reviewing Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Noah J Cowan (Reviewer \#1); Lena H Ting (Reviewer \#2). The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission. Summary: This paper studies the mechanism of sensorimotor integration of guinea fowl as an example of bipedal locomotion. Sensorimotor integration consists of neuronal feedforward, neuronal feedback and intrinsic muscle mechanics. Authors have studied how lateral gastrocnemius muscle (LG) and nervous system respond to the rapid perturbation when the proprioceptive sense as the fast feedback response is lost. Statistical comparison has been conducted between two groups (reinnervated and intact birds) through the recorded running trials at the same speed for both level and obstacle terrain. From the collected data of muscle force and length (intrinsic mechanics) and EMG (feedforward) signals, the authors have found that despite deficits in LG monosynaptic reflex following reinnervation, the general pattern of muscle dynamics of the reinnervated LG (rLG) is qualitatively similar to that of previously measured intact birds (iLG). However, the steady-state timing of EMG activation of rLG, as the feedforward, is phase-shifted earlier in the stride cycle. This earlier onset enables rapid force development and higher muscle stiffness at the time of foot contact and likely helps compensate for the loss of proprioceptive feedback. Additionally, regulation of force duration in obstacle strides is disrupted following reinnervation, suggesting that proprioceptive feedback in late stance normally regulates force duration. The authors have concluded that the autogenic proprioceptive deficit will lead to increased reliance on feedforward tuning of muscle activity to achieve stable muscle dynamics in obstacle terrain. In general, this is a very well-written paper, with an extensive analysis that is of broad interest to those interested in complex sensorimotor integration. Also, in general, the figures and methods were very clear. The work described in this paper is novel and its impact would be considerable in understanding complexities of sensorimotor in bipedal locomotion. There are some important concerns that, however, need to be addressed. In the main, these require: A\) Presenting the data more clearly. B\) A clear qualitative description of the differences between cohorts. C\) Redo the statistical analysis in a more interpretable manner. D\) Improve clarity of figures. E\) Reproducing data from the previous manuscript in order to make side-by-side comparisons will be convenient. Essential revisions: 1\) Suggestions: Figure 2: To avoid confusion, it\'s better to use different colors since blue and orange are used extensively in this paper for iLG and rLG. Figure 5: Figure is really busy and it\'s hard to visually see the differences between iLG and rLG. The difference between iLG and rLG looks negligible. It might be useful to show the mean and standard deviation of the difference between rLG and iLG. 2\) A major weakness is the lack of discussion about potentially profound differences across the two groups, and inconsistent comparison across different cohorts of bird. While the authors do acknowledge that different birds were sampled in the intact and reinnervated groups in the Materials and methods, this point may easily be missed by the reader and should be re-stated as a limitation in the Discussion (perhaps starting at the seventh paragraph of the subsection "What is the role of proprioception in the control of high-speed locomotion?"). Considering that the nerves were injured while the birds were juveniles and testing was performed in adults means the normal maturation process may have impacted adaptation to proprioceptive loss and may limit applicability to understanding the roles of feedback and feedforward control, or effects of nerve injury, in adults. In general, similarities among groups are stated to be \"comparable\" without supporting quantification from the intact group (e.g. in the Materials and methods, body and muscle masses, muscle lengths, gait speed etc.; in Results, Figure 2. While is it also reported that tendon tap reflexes were absent, no quantification was provided. How are potentially different levels of recovery accounted for? Was exercise begun 7 weeks after injury to avoid regeneration associated with immediate training? (Brandt et al., 2015). 3\) Despite the assertion in the Results (first paragraph), there are clearly differences in the level- and obstacle-terrain gait kinematics and kinetics between groups (c.f. Figures 2, 3, 6, 8). 4\) Differences across S-1, S-0, and S+1 are interesting but not discussed. Why is it that S+1 has a greater advance in EMG than S-0 and S^-1^? This could be compared to downslope walking? 5\) In general, figures were difficult to digest without careful parsing of the legends and could use better in-figure descriptors. For example, Figures 3 and 4 are not readable in black and white, the upper and lower rows could be labeled as \"intact\" and \"reinnervated\", while a dark line indicating \"level terrain\" with the colors indicating \"obstacle\". Foot contact lines could also be labeled, as the legends are hard to follow. Figure 3 legend \"for a single individual from each condition\" it is not clear whether \"condition\" refers to level vs. obstacle or intact vs. reinnervated. 6\) The mixed model ANOVA results were difficult to follow, and it may be better to present specific individual findings based on the hypothesis, e.g. earlier LG activation, evidence of later reflex, There is also concern over the number of variables in the model and the potential for false positives (Tables 1, 2 and Figure 5). A select number of tests should be done in alignment with specific hypotheses posed. Mean effects should be reported using ANOVA and post hoc tests. The coefficients reported are not interpretable in terms of differences across conditions/steps (e.g. Figure 6B). Bar charts with the main effect would be easier to understand. 7\) The implication for broader audiences could be enhanced, and the differences between bipedal and quadrupedal locomotor impairments are not clearly discussed. It is not clear that the shift to bipedal gait added significant insight into the role of proprioception in movement, as similar deficits occur in both. 10.7554/eLife.53908.sa2 Author response > In general, this is a very well-written paper, with an extensive analysis that is of broad interest to those interested in complex sensorimotor integration. Also, in general, the figures and methods were very clear. The work described in this paper is novel and its impact would be considerable in understanding complexities of sensorimotor in bipedal locomotion. > > There are some important concerns that, however, need to be addressed. In the main, these require: > > A\) Presenting the data more clearly. We have reformatted the figures to present data distributions and pairwise mean differences for the fixed effect categories. The figures, tables and text have been updated to allow direct comparison between the intact and reinnervated cohorts for all results. > B\) A clear qualitative description of the differences between cohorts. We have added text to the Materials and methods, Results and Discussion to provide clear descriptions of how the two cohorts compare in terms of experimental conditions (subsection "Animals and treadmill training"), reflex latency (subsection "Reinnervation surgery"), muscle morphology (subsection "Muscle morphology"), muscle function (subsections "Mechanical function of intact versus reinnervated LG", "Force-length dynamics and work output during obstacle negotiation" and "Shifts in activation patterns between intact and reinnervated LG") and gait kinematics (subsection "Stability and kinematic changes during obstacle negotiation in intact vs. reinnervated birds"). We revisit the differences between the cohorts in the limitations section of the Discussion (subsection "Limitations and future directions"). Throughout the text, we avoid stating that the two cohorts were 'qualitatively similar' or 'comparable' and instead state the specific similarities and differences between them. All figures provide direct comparison between the iLG and rLG cohorts, and we also provide the full datasets for both cohorts on DataDryad (https://doi.org/10.7280/D11H49). > C\) Redo the statistical analysis in a more interpretable manner. We revised the statistics as suggested to present pairwise mean differences between fixed effect categories in the figures and tables, with correction for multiple tests to maintain a 5% false discovery rate. We have also added a more detailed description of the statistical methods (subsection "Statistics"). > D\) Improve clarity of figures. We have modified the formatting of the figures as suggested by the reviewers, to consistently show the intact and reinnervated cohort datasets in direct comparison, with half-violin plots to show distributions, and bar plots with the mean and 95% confidence interval for pairwise comparison between fixed effect categories. We have added annotations to the figures to aid interpretation, as suggested by the reviewers. > E\) Reproducing data from the previous manuscript in order to make side-by-side comparisons will be convenient. All figures and analyses include the data from Daley and Biewener, 2011, alongside the new experimental data. We have provided the complete datasets (and processing code) for both cohorts through DataDryad as noted above. > Essential revisions: > > 1\) Suggestions: > > Figure 2: To avoid confusion, it\'s better to use different colors since blue and orange are used extensively in this paper for iLG and rLG. Figure 2 has been revised to provide a direct comparison of average stride cycles for the intact and reinnervated birds. Annotations have been added to make the figure easier to read, and the color scheme is consistent with all other figures in the paper, with blue for intact gastrocnemius (iLG) and orange for reinnervated lateral gastrocnemius (rLG). (The current Figure 2 is a revised version of former Figure 4. The original Figure 2 has been updated and now provided as Figure 2---figure supplement 1). > Figure 5: Figure is really busy and it\'s hard to visually see the differences between iLG and rLG. The difference between iLG and rLG looks negligible. It might be useful to show the mean and standard deviation of the difference between rLG and iLG. The original Figure 5 has been replaced with two separate figures (Figures 4 and 5) to allow clearer visual interpretation of the differences between iLG and rLG and to aid interpretation with respect to the hypotheses stated in the Introduction. Figure 4 contains half-violin distributions and bar plots for mean differences for variables relating to *muscle mechanical function*. Figure 5 contains half-violin distributions and bar plots for variables relating to *muscle activation*. Annotations have been added to aid the reader. The bar plots provide the mean and 95% CI for differences between the iLG and rLG treatment cohorts, and between level and obstacle terrain stride categories within treatment cohorts. > 2\) A major weakness is the lack of discussion about potentially profound differences across the two groups, and inconsistent comparison across different cohorts of bird. While the authors do acknowledge that different birds were sampled in the intact and reinnervated groups in the Materials and methods, this point may easily be missed by the reader and should be re-stated as a limitation in the Discussion (perhaps starting at the seventh paragraph of the subsection "What is the role of proprioception in the control of high-speed locomotion?"). Considering that the nerves were injured while the birds were juveniles and testing was performed in adults means the normal maturation process may have impacted adaptation to proprioceptive loss and may limit applicability to understanding the roles of feedback and feedforward control, or effects of nerve injury, in adults. In general, similarities among groups are stated to be \"comparable\" without supporting quantification from the intact group (e.g. in Materials and methods, body and muscle masses, muscle lengths, gait speed etc.; in Results, Figure 2. While is it also reported that tendon tap reflexes were absent, no quantification was provided. How are potentially different levels of recovery accounted for? Was exercise begun 7 weeks after injury to avoid regeneration associated with immediate training? (Brandt et al., 2015). We have added text to the Materials and methods, Results and Discussion to provide clear descriptions of how the two cohorts compare in terms of experimental conditions (subsection "Animals and treadmill training"), reflex latency (subsection "Reinnervation surgery"), muscle morphology (subsection "Muscle morphology"), muscle function (subsections "Mechanical function of intact versus reinnervated LG", "Force-length dynamics and work output during obstacle negotiation" and "Shifts in activation patterns between intact and reinnervated LG") and gait kinematics (subsection "Stability and kinematic changes during obstacle negotiation in intact vs. reinnervated birds"). We revisit the differences between the cohorts in the limitations section of the Discussion (subsection "Limitations and future directions". Throughout the text, we avoid stating that the two cohorts were 'qualitatively similar' or 'comparable' and instead state the specific similarities and differences between them. We have also added additional text on the methods rationale and relevant citations to the literature on cats and rats. All figures provide direct comparison between the iLG and rLG cohorts, and we also provide the full datasets for both cohorts on DataDryad (https://doi.org/10.7280/D11H49). > 3\) Despite the assertion in the Results (first paragraph), there are clearly differences in the level- and obstacle-terrain gait kinematics and kinetics between groups (c.f. Figures 2, 3, 6, 8). The Results and Discussion have been updated to more clearly state the differences in gait kinematics between the intact and reinnervated cohorts (subsections "Stability and kinematic changes during obstacle negotiation in intact vs. reinnervated birds", and "What is the role of proprioception in the control of high-speed locomotion?"). > 4\) Differences across S^-1^, S-0, and S+1 are interesting but not discussed. Why is it that S+1 has a greater advance in EMG than S-0 and S^-1^? This could be compared to downslope walking? We summarize these differences between stride categories in the Results (subsection "Stability and kinematic changes during obstacle negotiation in intact vs. reinnervated birds") and Discussion in the context of interpreting stability and neuromuscular control strategies (subsection "What is the role of proprioception in the control of high-speed locomotion?"). Although S +1 has slightly greater phase advance in activation, the difference is not statistically significant (Figure 6, Table 2). The main difference in S +1 for rLG is a 39% increase in total EMG activity, at 6% decrease in force duration and 4% decrease in stride duration, compared to steady state level strides (reported in the subsection "Stability and kinematic changes during obstacle negotiation in intact vs. reinnervated birds"). We have added a paragraph to the Discussion to address how our findings relate to similar work on cats and rats (subsection "What is the role of proprioception in the control of high-speed locomotion?"). > 5\) In general, figures were difficult to digest without careful parsing of the legends and could use better in-figure descriptors. For example, Figures 3 and 4 are not readable in black and white, the upper and lower rows could be labeled as \"intact\" and \"reinnervated\", while a dark line indicating \"level terrain\" with the colors indicating \"obstacle\". Foot contact lines could also be labeled, as the legends are hard to follow. Figure 3 legend \"for a single individual from each condition\" it is not clear whether \"condition\" refers to level vs. obstacle or intact vs. reinnervated. We have revised the figures as suggested, including added annotations to indicate 'intact' and 'reinnervated' cohorts, arrows indicating level and obstacle terrain strides, triangles for foot contact with an annotation arrow. We have revised the phrasing to refer to intact and reinnervated '*cohorts'* and level and obstacle terrain '*conditions'*. > 6\) The mixed model ANOVA results were difficult to follow, and it may be better to present specific individual findings based on the hypothesis, e.g. earlier LG activation, evidence of later reflex, There is also concern over the number of variables in the model and the potential for false positives (Tables 1, 2 and Figure 5). A select number of tests should be done in alignment with specific hypotheses posed. Mean effects should be reported using ANOVA and post hoc tests. The coefficients reported are not interpretable in terms of differences across conditions/steps (e.g. Figure 6B). Bar charts with the main effect would be easier to understand. The figures have been revised to focus on specific variables relating to muscle mechanical function in Figure 4 and muscle activation in Figure 5, to make the link to the specific hypotheses clearer. (The hypotheses are stated in Introduction in the subsection "Investigating the role of proprioception through self-reinnervation"). The results have been re-sequenced to follow the revised figure sequence. The statistics have been updated to provide post hoc pairwise mean differences between fixed effect categories from the ANOVA, with correction for multiple tests to maintain a 5% false positive rate. The figures include bar charts of the pairwise mean differences, with 95% confidence intervals. Comparisons are made between the intact and reinnervated cohorts (in grey) and between level and obstacle stride categories within treatment cohorts (in blue for iLG and orange for rLG). > 7\) The implication for broader audiences could be enhanced, and the differences between bipedal and quadrupedal locomotor impairments are not clearly discussed. It is not clear that the shift to bipedal gait added significant insight into the role of proprioception in movement, as similar deficits occur in both. We have added a paragraph discussing the findings in the context of previous work in cats and rats (subsection "What is the role of proprioception in the control of high-speed locomotion?"). In general, our findings are consistent with the studies of quadrupeds. However, the studies of rats and cats have focused more on muscle activity patterns in relation to kinematics, without detailed analysis of in vivo muscle mechanical function (direct measures of muscle force and work). The current study provides insight into how shifts in muscle activation relate to shifts in muscle mechanical function to compensate for loss of reflex-mediated ankle stiffness. | High | [
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m/5 + 486/5. -2*(m - 9)*(m + 27)/5 Solve 4*w**5 + 16*w**4 - 84*w**3 - 208*w**2 + 80*w + 192 = 0 for w. -6, -2, -1, 1, 4 Factor -2*v**3/3 - 16*v**2/3 + 440*v/3 - 800/3. -2*(v - 10)*(v - 2)*(v + 20)/3 Factor -4*w**3 + 312*w**2 + 988*w - 1296. -4*(w - 81)*(w - 1)*(w + 4) Suppose -b**3 - 146*b**2 + b + 146 = 0. What is b? -146, -1, 1 Find c, given that 5*c**2 - 1810*c + 14160 = 0. 8, 354 Factor -2*a**2 - 6*a + 8. -2*(a - 1)*(a + 4) Find d such that -4*d**2 - 40*d - 64 = 0. -8, -2 Factor 2*p**4 - 8*p**3 - 24*p**2 + 128*p - 128. 2*(p - 4)*(p - 2)**2*(p + 4) Factor -w**3/2 - 13*w**2 - 111*w/2 - 63. -(w + 2)*(w + 3)*(w + 21)/2 Factor -4*q**2 + 920*q - 52900. -4*(q - 115)**2 What is d in d**4 + 9*d**3 + 2*d**2 - 84*d + 72 = 0? -6, 1, 2 Factor -5*o**4/3 + 13*o**3/3. -o**3*(5*o - 13)/3 Let 5*n**3 - 10*n**2 - 45*n + 90 = 0. What is n? -3, 2, 3 What is l in -2*l**5/9 - 8*l**4/9 + 8*l**3/9 + 44*l**2/9 - 2*l/3 - 4 = 0? -3, -1, 1, 2 Determine j, given that -4*j**5/3 + 196*j**4/3 + 140*j**3 - 596*j**2/3 - 832*j/3 + 272 = 0. -2, 1, 51 Find s, given that 175*s**5 + 60*s**4 - 107*s**3 + 12*s**2 + 4*s = 0. -1, -1/7, 0, 2/5 Let -20*r**2 + 296*r + 60 = 0. Calculate r. -1/5, 15 Factor -2*k**2/3 - 286*k/3 - 804. -2*(k + 9)*(k + 134)/3 Factor 5*z**2 + 29*z + 20. (z + 5)*(5*z + 4) Factor h**4 + 408*h**3 + 35046*h**2 - 1340280*h + 10791225. (h - 15)**2*(h + 219)**2 Let 3*o**2/2 + 3*o/2 - 18 = 0. What is o? -4, 3 Let -3*k**2/4 - 33*k/4 - 15/2 = 0. Calculate k. -10, -1 Solve 4*s**4 - 4792*s**3 + 1425588*s**2 + 5759984*s + 5779216 = 0 for s. -2, 601 Solve -2*c**5/3 - 4*c**4 - 16*c**3/3 + 4*c**2/3 + 6*c + 8/3 = 0. -4, -1, 1 Let 2*r**2/3 - 1000*r/3 + 125000/3 = 0. What is r? 250 Solve -2*f**2/3 - 352*f/3 - 350/3 = 0. -175, -1 Factor 3*x**2 - 27*x - 66. 3*(x - 11)*(x + 2) Factor 289*x**3/6 - 357*x**2/2 + 108*x - 18. (x - 3)*(17*x - 6)**2/6 Find j such that -5*j**2 + 435*j + 440 = 0. -1, 88 What is l in 21*l**3 + 15*l**2 - 6*l = 0? -1, 0, 2/7 Factor 54*j**2/5 - 114*j/5 + 12. 6*(j - 1)*(9*j - 10)/5 Factor -2*u**4/9 + 14*u**2/9 - 4*u/3. -2*u*(u - 2)*(u - 1)*(u + 3)/9 Factor 2*j**2/7 + 44*j/7 + 80/7. 2*(j + 2)*(j + 20)/7 What is m in 5*m**3 + 28380*m**2 + 53694960*m + 33863621440 = 0? -1892 Suppose -5*b**3 - 535*b**2 - 1050*b = 0. Calculate b. -105, -2, 0 Factor j**2/4 - 96*j + 9216. (j - 192)**2/4 Factor 5*i**3 - 90*i**2 - 5*i + 90. 5*(i - 18)*(i - 1)*(i + 1) Factor -l**3/2 + l**2 + 21*l/2 + 9. -(l - 6)*(l + 1)*(l + 3)/2 Suppose d**4 - 181*d**3 - 183*d**2 + 181*d + 182 = 0. What is d? -1, 1, 182 Factor p**2 - 1944*p + 944784. (p - 972)**2 Solve -f**3/8 - 37*f**2/8 + 105*f/4 = 0 for f. -42, 0, 5 Determine t so that 2*t**5/5 - 134*t**4/5 + 2308*t**3/5 - 2044*t**2/5 - 462*t + 2178/5 = 0. -1, 1, 33 Factor 5*c**2 - 2460*c + 302580. 5*(c - 246)**2 Determine w so that w**4 - 6*w**3 + 4*w**2 + 24*w - 32 = 0. -2, 2, 4 Suppose -j**2 + 34*j - 33 = 0. What is j? 1, 33 Suppose -5*n**2/4 + 170*n - 2400 = 0. Calculate n. 16, 120 Determine n so that 4*n**2 - 492*n - 496 = 0. -1, 124 Let 25*d**3 + 5*d**2 - 180*d - 180 = 0. Calculate d. -2, -6/5, 3 Factor -11*m**5/4 + 149*m**4/4 + 513*m**3/4 + 535*m**2/4 + 91*m/2. -m*(m + 1)**3*(11*m - 182)/4 Let -3*k**2/2 - 21*k/2 + 12 = 0. What is k? -8, 1 Factor -2*j**3 - 82*j**2 + 88*j + 168. -2*(j - 2)*(j + 1)*(j + 42) Determine r, given that 146*r**4 - 2*r**3 - 146*r**2 + 2*r = 0. -1, 0, 1/73, 1 Solve -o**5 - 30*o**4 + 31*o**3 = 0. -31, 0, 1 Factor -q**2/2 + 93*q/2 + 47. -(q - 94)*(q + 1)/2 Find s, given that 2*s**3/7 - 220*s**2/7 + 6466*s/7 - 22472/7 = 0. 4, 53 Factor 54*m**3 + 5160*m**2 - 6904*m/3 + 256. 2*(m + 96)*(9*m - 2)**2/3 Factor -q**4/6 - 101*q**3/6 - 2497*q**2/6 + 935*q/2 + 867. -(q - 2)*(q + 1)*(q + 51)**2/6 Factor -5*k**4 - 10*k**3 + 15*k**2 + 20*k - 20. -5*(k - 1)**2*(k + 2)**2 Suppose 25*o**2 + 13660*o + 5460 = 0. What is o? -546, -2/5 Factor n**3 - 348*n**2 + 40368*n - 1560896. (n - 116)**3 What is n in -3*n**2/5 + 9*n/5 - 6/5 = 0? 1, 2 Determine o, given that 3*o**2 + 33*o = 0. -11, 0 Factor -8*d**2/13 + 150*d/13 - 108/13. -2*(d - 18)*(4*d - 3)/13 Factor -3*w**2 - 9150*w - 9147. -3*(w + 1)*(w + 3049) Determine n, given that 3*n**2/2 - 84*n + 1176 = 0. 28 Let -28*w**5/5 - 214*w**4/5 - 366*w**3/5 + 176*w**2/5 + 32*w/5 = 0. Calculate w. -4, -1/7, 0, 1/2 Factor 3*f**5 - 150*f**4 + 1548*f**3 + 21546*f**2 - 313551*f - 333396. 3*(f - 21)**3*(f + 1)*(f + 12) Find h such that 2*h**2/7 - 6*h = 0. 0, 21 Factor -2*r**2 + 1514*r + 3036. -2*(r - 759)*(r + 2) Let -d**5/2 + 7*d**4/2 + 11*d**3/2 - 19*d**2/2 - 19*d - 8 = 0. What is d? -1, 2, 8 What is t in -5*t**2 - 110*t + 375 = 0? -25, 3 Determine o, given that 2*o**4/21 + 372*o**3/7 + 52632*o**2/7 + 617156*o/21 + 153458/7 = 0. -277, -3, -1 Factor -5*g**4 + 60*g**2 + 80*g. -5*g*(g - 4)*(g + 2)**2 Solve s**3/2 - 3*s**2 - 7*s/2 = 0 for s. -1, 0, 7 Factor -3*b**2/2 + 507*b - 85683/2. -3*(b - 169)**2/2 Let 5*h**5 + 20*h**4 + 5*h**3 - 30*h**2 = 0. What is h? -3, -2, 0, 1 Factor -729*a**3 + 1566*a**2 - 220*a + 8. -(a - 2)*(27*a - 2)**2 Find c such that 196*c**3/3 - 51520*c**2 + 29424*c - 12608/3 = 0. 2/7, 788 Factor m**3 + 19*m**2 - 413*m + 1617. (m - 7)**2*(m + 33) Determine l, given that -2*l**5/9 + 4*l**4/3 + 14*l**3 - 712*l**2/9 + 64*l = 0. -8, 0, 1, 4, 9 Find y, given that y**4/10 - 23*y**3/10 + 41*y**2/10 + 23*y/10 - 21/5 = 0. -1, 1, 2, 21 Find r, given that -2*r**4/5 - 118*r**3/5 - 10*r**2 + 3702*r/5 - 7308/5 = 0. -58, -7, 3 Factor -l**4/2 + 7*l**3/2 - 7*l**2/2 - 15*l/2. -l*(l - 5)*(l - 3)*(l + 1)/2 Let -4*g**2 - 11604*g = 0. What is g? -2901, 0 Factor x**3/6 + 13*x**2/6 - 29*x/6 + 5/2. (x - 1)**2*(x + 15)/6 Let 3*i**2/2 + 126*i = 0. Calculate i. -84, 0 Factor 2*w**5 + 10*w**4 + 4*w**3 - 16*w**2. 2*w**2*(w - 1)*(w + 2)*(w + 4) Factor -c**2 - 66*c - 1089. -(c + 33)**2 Solve 2*v**4 + 402*v**3 - 2484*v**2 + 64*v + 13248 = 0 for v. -207, -2, 4 Solve -g**2/5 + 387*g/5 + 388/5 = 0 for g. -1, 388 Factor -f**2 + 231*f. -f*(f - 231) Suppose -2*g**3 - 428*g**2 - 15928*g - 164560 = 0. What is g? -170, -22 Factor -r**4/3 + 47*r**3 - 1584*r**2 - 5184*r. -r*(r - 72)**2*(r + 3)/3 Factor 2*j**2/19 - 220*j/19 + 6050/19. 2*(j - 55)**2/19 Find o, given that -3*o**3/5 + 39*o**2/5 - 24*o + 108/5 = 0. 2, 9 Factor -m**2/4 - 131*m/4 + 33. -(m - 1)*(m + 132)/4 Factor -7*p**2 + 276*p + 283. -(p + 1)*(7*p - 283) Factor -4*u**3 - 116*u**2 + 1040*u + 1152. -4*(u - 8)*(u + 1)*(u + 36) Find z, given that 2*z**2/9 + 22*z/9 + 16/3 = 0. -8, -3 Suppose 3*s**3/7 - 6*s**2/7 - 3*s/7 + 6/7 = 0. What is s? -1, 1, 2 What is m in 2*m**4/7 + 106*m**3/21 - 134*m**2/7 + 374*m/21 - 4 = 0? -21, 1/3, 1, 2 Suppose 10*v**5 + 45*v**4 - 580*v**3 - 300*v**2 = 0. What is v? -10, -1/2, 0, 6 Solve -18*j**5/5 - 10*j**4 + 246*j**3/5 + 218*j**2/5 - 12*j = 0 for j. -5, -1, 0, 2/9, 3 Determine x, given that 72*x**2/7 - 8040*x/7 + 224450/7 = 0. 335/6 Find v such that v**2/2 + v/2 = 0. -1, 0 Find v such that v**3/2 + 3*v**2/2 - 9*v/2 - 27/2 = 0. -3, 3 Let 2*x**5/13 - 4*x**4/13 - 32*x**3/13 + 28*x**2/13 + 126*x/13 + 72/13 = 0. What is x? -3, -1, 3, 4 Solve 4*u**2 - 64*u + 256 = 0. 8 Factor c**2/6 - 140*c/3 - 2009/6. (c - 287)*(c + 7)/6 Suppose -v**4/2 + 17*v**3/2 + 37*v**2/2 + 19*v/2 = 0. What is v? -1, 0, 19 Factor -9*v**3 + 12*v**2 + 27*v - 30. -3*(v - 2)*(v - 1)*(3*v + 5) Solve -o**3/3 + 5*o**2/3 + o/3 - 5/3 = 0. -1, 1, 5 Factor -2*z**2/9 + 32*z/3 + 200/9. -2*(z - 50)*(z + 2)/9 Factor -2*v**4/9 + 20*v**3/9 + 2*v**2/3 - 280*v/9 - 392/9. -2*(v - 7)**2*(v + 2)**2/9 Solve -60*r**3/11 + 186*r**2/11 - 6*r/11 - 36/11 = 0. -2/5, 1/2, 3 Let m**2/6 - 10*m/3 + 6 = 0. What is m? 2, 18 Suppose 3*j**2/2 + 123*j/2 - 3348 = 0. Calculate j. -72, 31 Find u such that 196*u**5/3 + 168*u**4 - 2896*u**3/3 - 8032*u**2/3 - 1280*u - 512/3 = 0. -4, -2, -2/7, 4 Suppose -h**4 + 12*h**3 - 27*h**2 - 40*h = 0. What is h? -1, 0, 5, 8 Factor 3*b**4 + 72*b**3 + 519*b**2 + 1494*b + 1512. 3*(b + 3)**2*(b + 4)*(b + 14) Determine x so that -x**3/4 + 5*x**2/4 + x - 5 = 0. -2, 2, 5 Factor 3*h**2 - 12*h - 15. 3*(h - 5)*(h + 1) Determine s so that 55*s**2/6 - 475*s/6 - 30 = 0. -4/11, 9 Suppose -5*c**5 + 5*c**4 + 130*c**3 + 120*c**2 = 0. What is c? -4, -1, 0, 6 Factor -2*l**2 + 688*l + 1384. -2*(l - 346)*(l + 2) Determine z so that z**3/3 + 32*z**2/3 + 95*z + 150 = 0. -15, -2 Factor i**4/2 - 5*i**3/2 + | Low | [
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In this Wednesday, Aug. 1, 2018 photo, Ronnie Anderson, an African-American man charged with possession of a firearm by a convicted felon, poses for a photo in front of a confederate statue on the lawn of the East Feliciana Parish Courthouse, where he is facing the charge, in Clinton, La. The statue of the unnamed Confederate soldier has stood since 1909 in front of the courthouse in East Feliciana Parish, hands resting on his rifle looking down on the flow of lawyers, jurors and defendants going into the white columned building. (AP Photo/Gerald Herbert) In this Wednesday, Aug. 1, 2018 photo, Ronnie Anderson, an African-American man charged with possession of a firearm by a convicted felon, poses for a photo in front of a confederate statue on the lawn of the East Feliciana Parish Courthouse, where he is facing the charge, in Clinton, La. The statue of the unnamed Confederate soldier has stood since 1909 in front of the courthouse in East Feliciana Parish, hands resting on his rifle looking down on the flow of lawyers, jurors and defendants going into the white columned building. (AP Photo/Gerald Herbert) CLINTON, La. (AP) — The statue of the unnamed Confederate soldier has stood since 1909 in front of the courthouse in Louisiana’s East Feliciana Parish, hands resting on his rifle looking down on the flow of lawyers, jurors and defendants going into the white columned building. Ronnie Anderson, an African-American man charged with possession of a firearm by a convicted felon, illegal possession of a stolen firearm, and speeding, was one such defendant and the statue gave him cause for concern. ADVERTISEMENT “It’s just intimidating to walk into a courthouse that’s supposed to be a place of equality, fair justice and to see this monument that made me feel like ... I don’t stand a chance,” Anderson said. Anderson wants his case to be moved to another parish without such a memorial; his motion to change venue argues he can’t get a fair trial in the same place where a “symbol of oppression and racial intolerance” stands. Confederate flags and monuments — long a part of the Southern landscape — have come under renewed scrutiny following the 2015 shooting by Dylann Roof of nine black churchgoers in South Carolina and the 2017 deadly white nationalist rally in Charlottesville, Virginia. Supporters say the statues are a part of history honoring their ancestors; detractors say they, in effect, honor slavery and in many cases were erected during the Jim Crow era to intimidate black people and bolster white supremacy. Confederate monuments dot the lawns of many Southern courthouses. In addition to the one in East Feliciana, a database compiled by the Southern Poverty Law Center lists 11 more in front of Louisiana courthouses. Ben Cohen, a lawyer with the New Orleans-based Promise of Justice Initiative that advocates for reforming Louisiana’s criminal justice system, says so far it’s rare for defendants to use the legal argument Anderson is making. Cohen represented a defendant appealing a conviction in a Caddo Parish murder case in which a prospective juror objected to the Confederate flag in front of the courthouse. The state Supreme Court ultimately upheld the conviction but Cohen said he anticipates this argument being used more often. “I think people are looking at these monuments in a new light,” he said. Officials in Caddo Parish voted last October to remove theirs. They concluded that citizens would be better served if it was not in front of the courthouse “where justice is to be administered fairly and impartially.” A lawsuit stalled the move, but was recently dismissed by a federal judge. ADVERTISEMENT The East Feliciana Parish District Attorney, Sam D’Aquilla says its “ridiculous” to think a statue would affect the fairness of Anderson’s trial and questions why an out-of-town defendant and lawyer are stirring up trouble in the primarily rural parish, located about 30 miles (48 kilometers) north of Baton Rouge. Anderson is from Plaquemines Parish to the southeast and was driving through when he was pulled over. His lawyer, Niles Haymer is based in Baton Rouge. D’Aquilla said he doesn’t have an opinion on the statue but regardless of whether it’s there the people inside strive for colorblind justice. He also points out the racial diversity of the elected officials across the parish. “All the elected officials that I know of, your judges, your clerk of court, your sheriff, we all strive for racial equality. And we work hard for that,” he said. This is not the first time the East Feliciana Parish statue has come under scrutiny. In 2016, retired physician Paul Jackson Jr. asked the parish to move the statue to a local Confederate cemetery. He says having the statue on the courthouse grounds signals that the Confederacy was for justice: “But it wasn’t. They’re for slavery obviously.” His suggestion was debated during a parish meeting and ultimately rejected. Jackson said he lost two friends over the issue. He said he supports Anderson’s change-of-venue motion. Lataya Johnson, who lives and works in the parish, sympathized with Anderson’s argument and dismissed the idea that most people don’t pay attention to the statue. “You walk by and you think about it. Because if you’re African-American do you look at it and say, ‘My fate is already destined because of this statue ... Judgment has already been made because of this statue,’” she said. But parish president Louis Kent said Anderson is “very mistaken” in believing he will not get a fair trial in East Feliciana. “I have been in this parish all my life. We don’t have a race problem. We never have and we’re not going to create one,” he said. Anderson’s lawyer, Niles Haymer, says he’s already heard from other lawyers interested in filing similar motions, and he may be filing the same motion for another client. For him, this case could become a catalyst for change. A hearing on the motion is expected Tuesday. “I feel like if we flood the criminal justice system with these motions, they’re going to have to deal with this monument issue,” he said. ___ Associated Press researcher Jennifer Farrar contributed to this report. ___ Follow Santana on Twitter at https://twitter.com/ruskygal . | Low | [
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For me, the turning point in watching HBO's Silicon Valley can be traced back to the Burger King subplot in the third episode. That's when the broad caricature of Peter Thiel transforms from a smug, aspy(er)-than-thou venture capitalist—hates college, loves profit, take it or leave on human beings—into something exquisitely specific: delicious in its weirdness, but almost in awe of his intellect. Based on this article about Bill Gates and pea shortages in North America, Mike Judge's satirical take might not be that far from reality. The sesame seed scene hinges on Peter Gregory, the lead investor behind Pied Piper, the compression software startup at the heart of the show. Gregory is maybe 75 percent Thiel, 15 percent Paul Graham, and 10 percent Quora questions. Another promising startup in his portfolio begs Gregory for an "emergency capital injection" of $15 million in order to avoid shutting down. However Gregory, played by the late great Christopher Evan Welch, is more consumed by a sudden curiosity about fast food. "Have many of you ever eaten at Bur-gur King? Well, I was just driven past one. And while I know that their market cap is $7 billion plus, I realize I am unfamiliar with their offerings. Is it popular among your peers? Is it. . . enjoyed? And their selection consists solely of these bur-gurs of which they are presumably king [tiny laugh]?" Only later in the episode do we see how Gregory's circuitous neural pathways lead him from hamburger buns to cicadas to Indonesian sesame futures, which will make him a tidy $70 million, enough for a $15 million bridge loan to keep the startup alive and save its employees. [There was a video here] In the real world, it's peas not sesame seeds and the investor is Bill Gates, judging by this Bloomberg report: Because General Mills was early to recognize the potential of plant protein, the Betty Crocker owner has stocked up from suppliers like Canada's Alliance Grain Traders Inc. (AGT), creating a shortage that's left rivals rushing to catch up. How hot is this trend? Enough to attract investment from billionaires Bill Gates, Li Ka-Shing and Tom Steyer. Gates being Gates, he's leveraging the "fashionable scarcity" of pulses (a branch of the legume family) to reduce climate change and improve animal welfare. One of his investments is Beyond Meat, a company that wants to produce "mass-market solutions that perfectly replace animal protein with plant protein." But that's what makes Silicon Valley so promising. Of course the venture capitalist would see an unexpected windfall as a chance to make a bridge loan. To contact the author of the post, please email [email protected]. [Image and video via HBO] | Mid | [
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It is the highly anticipated climax of a fiercely fought competition, and will no doubt have avid viewers shouting at their screens. But tonight's University Challenge final between Wolfson, Cambridge and Balliol, Oxford has sparked outrage over the lack of any female contestants. Student equality campaigners have blasted the show's production company, ITV Studios, for allowing all-male teams into the competition, with a third of this year's teams having no women. Indeed, only 22 per cent of the contestants on this series are women and just five per cent of the finalists in the last five years have been women. Tonight's University Challenge final between Wolfson, Cambridge (pictured) and Balliol, Oxford has sparked outrage over the lack of any female contestants. Student equality campaigners have blasted the show's production company, ITV Studios, for allowing all-male teams into the competition, with a third of this year's teams having no women. Pictured above, Oxford's Balliol team Azita Chellappoo, equality and diversity officer at Wolfson College, told the Daily Mail that university quizzing societies can be 'very hostile to women'. She also noted that many female students are discouraged from signing up to take part in University Challenge because of the social media trolling or unwanted attention to which contestants - particularly female ones - are often subjected. She said: 'The underrepresentation of women on University Challenge is a big problem. 'I think partly it is because the quizzing community [such as university quizzing societies] can often be quite hostile to women, or at the very least not particularly welcoming spaces. 'Also, the women that do appear on the show often face a lot of sexist commentary on social media. There's often a lot of discussion about their looks, for example.' This year, Emma Johnson from Corpus Christi College, was described as the 'perfect woman' by viewers after her appearance on the show. And last year, Hannah Woods received thousands of messages online about her eyebrows. This year, Emma Johnson from Corpus Christi College, was described as the 'perfect woman' by viewers after her appearance on the show And last year, Hannah Woods, from Peterhouse, Cambridge, received thousands of messages online about her eyebrows Asked whether she thought the competition should have any rules in place regarding the diversity of teams, Miss Chellappoo said: 'I think quotas would be a really good idea, or if not formal quotas, guidelines at the very least. I don't think all-male teams should be allowed on the show. 'Greater representation on University Challenge is an important part of encouraging more women to join the quizzing scene, and to showcase the intellectual capacities of women at UK universities.' Whilst universities, or individual colleges in the case of Oxbridge, are responsible for selecting their own teams, ITV Studios only selects 28 teams to take part, and therefore a vetting process does take place. Viewers have threatened to boycott the show over the final being an all-male contest for the third time in five years. The Balliol team declined a request for comment, and Wolfson's hugely popular captain Eric Monkman said he had 'no comments' on the matter. A University Challenge spokesperson said: 'Each team is determined by the universities themselves and whilst we do encourage them to reflect the diversity of their student population ultimately each university has their own team selection process.' University Challenge airs tonight on BBC Two at 8pm. | Mid | [
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Ask HN: did hordes of hackers swoop in the first hours (minutes) of Heartbleed? - hoodoof I have this idea that there are hordes of hackers who create a hitlist of target websites that they want to hack.<p>They then just wait until the next exploit comes along.<p>And within hours (or minutes) of the new exploit becoming public, they swoop, own their target site and rootkit it.<p>Does anyone else think this is true?<p>And if it is true, then has half the Internet been rootkitted long before the sites owner could update SSL?<p>AND......so you updated your website - good on you. Do you think you had already been rootkitted? ====== adrianoconnor Heartbleed wasn't a remote execution vulnerability. I am not a security expert, but I'm pretty sure that Heartbleed in and of itself wouldn't allow hackers to install a root kit. In answer to your question, I have no idea how long it takes the bad guys to exploit newly revealed exploits. Probably a day or two on average (for the tools to be developed and then distributed). Also, different people have different agendas and motivations -- there are no doubt people out there desperate to jump on to certain high-profile sites at the first chance (Apple, Amazon, with their credit card data would be an obvious target, for instance), but I suspect most hackers just cast their net far and wide and take whatever they can. Mostly it'll be unpatched servers from years ago that aren't managed by a proper ops team, using exploits that should have been patched a long time ago. ------ ryanthejuggler The exploit only works on whatever data's in memory. If someone had started attacking servers when Heartbleed started being publicized, they'd be getting passwords and data from users who were active at that point in time. Unfortunately (perhaps interestingly) right after the announcement I would imagine that much of this activity would be changing passwords. I'd like to think that they were good about telling people not to change passwords until the hole was patched, but presumably some people would still start to change their passwords. Ironically this hurts more than helps. | Low | [
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373 B.R. 19 (2007) In re Bryan Duane PANKEY and Jo Ann Pankey, Debtors. Gene R. Kohut, Trustee, Plaintiff, v. Wells Fargo Bank, N.A., Defendant. Bankruptcy No. 05-67427. Adversary No. 06-5628. United States Bankruptcy Court, E.D. Michigan, Southern Division. July 25, 2007. *20 Terri Weik, Weik and Associates, P.C., Warren, MI, for Debtors. Donna J. Lehl, Southfield, MI, for Plaintiff. Christopher Gregory Bovid, Brighton, MI, for Defendant. *21 Opinion Regarding Motion for Summary Judgment STEVEN W. RHODES, Chief Bankruptcy Judge. Gene Kohut, the chapter 7 trustee, filed this adversary proceeding to avoid a mortgage on the debtors' real property. He seeks to avoid the mortgage as a preferential transfer pursuant to 11 U.S.C. § 547(b), asserting that the mortgage was perfected during the 90 days prior to the debtors' bankruptcy. Wells Fargo has filed a motion for summary judgment, asserting that the mortgage was recorded prior to the preference period and is therefore not avoidable. The debtors refinanced their residential real property on February 11, 2005, granting two mortgages to New Century Mortgage Corporation. On February 22, 2005, New Century assigned the mortgages to Wells Fargo. The first mortgage, for $192,000, is the subject of this adversary proceeding. Kohut filed a second adversary proceeding to avoid the second mortgage. The debtors filed this bankruptcy case on August 26, 2005. In this adversary proceeding, Kohut asserts that the first mortgage should be deemed recorded June 20, 2005, which is the date appearing in the liber and page stamp on the mortgage and is also the date of the cashier's receipt for the payment of the recording fees. The receipt shows that the filing fee for this mortgage was paid in a batch payment by check no. 60291. The back of the check from the title company has an Oakland County Register of Deeds date stamp of June 20, 2005. It appears to have been deposited the following day and paid by the bank on June 22, 2005. Wells Fargo asserts the mortgage was recorded on March 24, 2005, before the 90 day preference period. The mortgage document is stamped with a received stamp from the Oakland County Register of Deeds dated March 24, 2005. Additionally, Deputy Register Laura Thierbach testified that the mortgage was received that day. Further, Thierbach testified that the mortgage was in recordable form. Wells Fargo asserts that it was "ready willing and able" to pay on March 24, 2005, but that it was prevented from doing so based on a written policy of the Oakland County Register of Deeds. I. Under Rule 56(c) of the Federal Rules of Civil Procedure, summary judgment may be granted "if the pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits, if any, show that there is no genuine issue as to any material fact and that the moving party is entitled to judgment as a matter of law." "A fact is `material' and precludes grant of summary judgment if proof of that fact would have [the] effect of establishing or refuting one of the essential elements of the cause of action or defense asserted by the parties, and would necessarily affect [the] application of appropriate principle[s] of law to the rights and obligations of the parties." The court must view the evidence in a light most favorable to the nonmovant as well as draw all reasonable inferences in the nonmovant's favor. United States v. Certain Real Prop., 800 F.Supp. 547, 549-50 (E.D.Mich.1992). Kohut does not dispute that the Oakland County Register of Deeds received the mortgage on March 24, 2005. The recorded mortgage is stamped with a received stamp dated March 24, 2005, and Thierbach testified in her deposition that it was received that day. *22 Kohut also does not dispute that the mortgage was submitted in recordable form. Thierbach so testified because the received stamp was not crossed out; this would have indicated that the mortgage had been rejected and re-submitted. The parties' disagreement over when the mortgage should be deemed to have been recorded arises from the payment of the recording fees. Wells Fargo asserts that the only reason that it did not pay the fee at the time the mortgage was presented for recording is that Oakland County Register of Deeds had a policy of refusing to accept payment for recording a batch of documents until it determined that all of the documents in the batch were in recordable form. Wells Fargo presented Thierbach's deposition testimony and a policy memorandum from Oakland County Register of Deeds to establish the existence of this policy. Accordingly, Wells Fargo asserts that the delay in payment is attributable to Oakland County Register of Deeds and that Wells Fargo should not be penalized for the delay in payment. Kohut asserts that Thierbach's testimony also indicated that if a title company wanted to wait for verification that a document is in recordable form, the process could be accomplished in one day. Moreover, Kohut argues that Thierbach testified that according to their records, it appears that the mortgage at issue was verified before the preference period and that payment could have been made much earlier than was actually done in this case. Accordingly, Kohut argues that since it was possible for payment to be made when the mortgage was submitted for recording, the delay in payment is not attributable to the Oakland County Register of Deeds. II. This case involves a legal issue which has arisen with some frequency in this district. The issue is this: When is a mortgage deemed "recorded" if the county register of deeds does not maintain an "entry book" as required by Michigan law? This Court has adopted the result and reasoning of Gold v. Interstate Fin. Corp. (In re Schmiel), 362 B.R. 802 (Bankr. E.D.Mich.2007). See In re Ammar, 368 B.R. 629 (Bankr.E.D.Mich.2007). In Schmiel, Judge Shefferly determined that pursuant to Michigan law, there are three specific requirements for recording a mortgage. 1. The mortgage must be received by the register of deeds under Mich. Comp. Laws Ann. § 565.25(1). 2. The mortgage must meet the technical requirements of Mich. Comp. Laws Ann. § 565.201. 3. The recording fee must be paid when the mortgage is left for record, under Mich. Comp. Laws Ann. § 600.2567(1)(a). Id., 362 B.R. at 817. In the absence of the required mortgage entry book, a mortgage is deemed recorded at the moment when the last of three requirements is met. As Judge Shefferly stated: If a mortgagee has done all that the law requires or permits it to do by presenting a mortgage in recordable form and paying the proper filing fee, no useful purpose is served by penalizing the mortgagee for the failure of a register of deeds to perform its statutory duties, over which the mortgagee has no control. Id. at 818. This case presents an issue not addressed in Schmiel. That issue is this: When the register of deeds refuses payment of the recording fee at the time a mortgage is submitted in recordable form, is it then deemed recorded? Indeed, Judge Shefferly specifically noted that it *23 was beyond the scope of Schmiel to determine whether such a delay in payment of recording fees world impact the date that a mortgage would be deemed recorded. Id. at 819, n. 5. The law regarding the timing of the payment of a filing fee for recording a mortgage is quite clear. Mich. Comp. Laws Arm. § 600.2567(1)(a) explicitly requires the filing fee to be paid when a mortgage is left for recording. Moreover, the entry book for recording a mortgage is also required to record the payment of the fee. Mich. Comp. Laws Ann. § 565.24 states, "Every register of deeds shall keep an entry book of deeds and an entry book of mortgages, each page of which shall be divided into 6 columns, with title or heads to the respective columns, in the following form. . . ." The heading for the sixth column is "Fee (Fees) Received." Section 565.201 lists the requirements that an instrument must meet in order to be recorded by a register of deeds. Any instrument "shall not be received for record by the register of deeds . . . unless that instrument complies with each" requirement. Mich. Comp. Laws Ann. § 565.25(1). Section 565.25 specifies what a register of deeds must enter in an entry book, when an instrument complies with the statutory requirements. It provides as follows: In the entry book of deeds, the register shall enter all deeds of conveyance absolute in their terms, and not intended as mortgages or securities, and all copies left as cautions. In the entry book of mortgages the register shall enter all mortgages and other deeds intended as securities, and all assignments of any mortgages or securities. In the entry book of levies the register shall enter all levies, attachments, liens, notices of lis pendens, sheriffs' certificates of sale, United States marshals' certificates of sale, other instruments of encumbrances, and documentation required under subsection (2), noting in the books, the day, hour, and minute of receipt, and other particulars, in the appropriate columns in the order in which the instruments are respectively received. Mich. Comp. Laws Ann. § 565.25(1). Accordingly, Michigan law establishes that the entry book must have columns for both the time received and the payment received. This further establishes that the legislature intended for the recording fees to be paid at the time that a mortgage is presented for recordation. The Court must conclude that nothing in law allows the Register of Deeds to refuse payment pending its validation of the documents. It is the duty of the Register of Deeds to accept payment of the recording fees at the time the mortgage is submitted for recordation. The evidence establishes that during the time that this mortgage was submitted for recordation, the Register of Deeds violated that duty as a matter of practice and policy. The affidavit of Laura Thierbach, the Chief Deputy Register at the Oakland County Register of Deeds, describes the process for mortgage recordation that was in place in August and September 2004. Thierbach states that it was the policy of the Oakland County Register of Deeds to require title companies that were batch filing multiple documents to leave the documents in a folder at the register of deeds office for review and validation. Documents were validated in the order of their receipt. Once validated, the documents were placed in the same folder in a file drawer for pick-up by the title company representative according to that representative's schedule. The title company representative would bring the validated documents to the cashier for the register of *24 deeds, who would then accept the proper fee and assign liber and page numbers. According to Thierbach, "rush" processing, a procedure in which an instrument could be validated, paid for and affixed with a record date stamp all in one day, was not available for large groups of multiple filings. (Thierbach Affidavit, November 13, 2006). Thierbach's affidavit is consistent with a "Memo" from the Oakland County Register of Deeds addressed to "All Title Companies" dated May 5, 2005. Thierbach's deposition indicates that the same process was in place at the time the present mortgage was presented for recordation. (Thierbach Dep. at p. 8.) Wells Fargo has established that Oakland County Register of Deeds had a policy of refusing payment at the time this mortgage was presented for recordation. Michigan "law does not require a useless formality. A formal tender is not necessary where a party has shown by act or word that it would not be accepted, if made." Hanesworth v. Hendrickson, 320 Mich. 577, 31 N.W.2d 726 (1948). The Court concludes that the policy of the Oakland County Register of Deeds excused Wells Fargo from making payment on March 24, 2005, when it submitted this mortgage, as any such tender of payment would have been futile.[1] Ultimately, as in Schmiel, the issue is how to interpret the statute defining recordation when the local authority charged with the duty to apply the requirements for recordation violates that duty. Schmiel concluded that a filing party should not be prejudiced by the authority's failure to maintain the statutorily required entry book. This Court now concludes for similar reasons that a filing party must not be prejudiced by the authority's refusal to accept the statutorily required recording fee. Accordingly, the Court holds that the mortgage in this case is deemed recorded on March 24, 2005. Because that was outside the 90 day preference period, the mortgage is not avoidable as a preference and Wells Fargo is entitled to summary judgment. III. Wells Fargo also seeks summary judgment on the grounds that § 547(b)(1) is not applicable in the present case because the mortgage was not the transfer of an interest of the debtor in property due to the earmarking doctrine. Wells Fargo asserts because this mortgage involved a refinancing, the mortgage merely substituted one secured creditor for another and did not involve a transfer of an interest of a debtor in property. This Court has previously rejected Wells Fargo's position. In Chase Manhattan Mortgage Corp. v. Shapiro (In re Lee), this Court held that when a mortgage is recorded outside of the 20-day safe harbor, it involves two transfers, the second of which is not protected by the earmarking doctrine. On appeal in that case, the district court reversed this Court's decision. *25 339 B.R. 165, 170 (E.D.Mich.2006). That case is currently on appeal to the Sixth Circuit Court of Appeals. In its motion for summary judgment in this case, Wells Fargo relies on the district court decision. However, the district court's decision in Lee is not binding upon this Court in this case. Upon review, this Court stands by its decision in Lee in this case. See also Gold v. Interstate Fin. Corp. (In re Schmiel), 319 B.R. 520, 528-29 (Bankr.E.D.Mich.2005); Shapiro v. Homecomings Fin. Network, Inc. (In re Davis), 319 B.R. 532, 534 (Bankr. E.D.Mich.2005); Scaffidi v. Kenosha City Credit Union (In re Moeri), 300 B.R. 326 (Bankr.E.D.Wis.2003); Sheehan v. Valley Nat'l Bank (In re Shreves), 272 B.R. 614 (Bankr.N.D.W.Va.2001); Vieira v. Anna Nat'l Bank (In re Messamore), 250 B.R. 913, 916 (Bankr.S.D.Ill.2000). The Court will enter an appropriate order. NOTES [1] The Court further concludes that any factual issues about the dates on the check are not material, and do not preclude summary judgment. The objection to the motion for summary judgment included two copies of Progressive Check # 60291. Ex. 2 is a Copy of Progressive Check # 60291 faxed by Prestige Mtg. Service on November 9, 2006. Ex. 3 is a copy of Progressive Check # 60291 faxed by Progressive Title on February 19, 2007. There are a few differences between the copies. Ex. 2 is dated March 24, 2005, payable to Oakland County Register of Deeds, with Wayne crossed out and Oakland substituted by handwritten notation. Ex. 3 is dated March 28, 2005, but otherwise appears the same. The parties were unable to provide any explanation for these discrepancies, but, as noted, they are not material to the issues before the Court. | Mid | [
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Day: November 11, 2019 With the entire environment’s toxicity, as well as the wrong lifestyle choices that we make, there is a tendency that we are destroying our overall health unintentionally. Sometimes, even if we thought we are regularly exercising, eating healthy foods, and taking our time to rest,… | Low | [
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Q: Do Network Services support Multimodal Networks (ArcGIS 10.1, Network Analyst Extension)? Do Network Services support Multimodal Networks (ArcGIS 10.1)? I'm assuming that multimodal networks are supported, but I am troubleshooting and just want to be sure. A: Yes, Network Services (map services published with the Network Analysis capability on) support multi-modal networks. I am able to perform routing on a such service published locally from a simple JS application. | High | [
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Thursday, October 16, 2008 The day after I posted my first entry, I had a "teensy accident" and broke bones in both hands, amongst other things. However, before I left on the road trip that led to my eventual ambulance ride I went out and took some photos of several places which will end up here, including the former home of the former mica factory. Soon to be posted (once I am a bit more healed), the old Chinese laundry in New Edinburgh, the city-run outdoor pool, at Flatrock, again in New Edinburgh, and Laroque's Department Store at Rideau and Dalhousie. 1 comment: Today May 8th, 2017, i was trying to find info on the city run pool at Flatrock I read what you wrote below back in 2008 THURSDAY, OCTOBER 16, 2008 - The best laid plans...The day after I posted my first entry, I had a "teensy accident" and broke bones in both hands...Soon to be posted (once I am a bit more healed), the old Chinese laundry in New Edinburgh, the city-run outdoor pool, at Flatrock, again in New Edinburgh, and Laroque's Department Store at Rideau and Dalhousie. - POSTED BY MUDHOOKS AT 11:37 PM and was wondering if you ever managed to get any more info on the city run pool at Flatrocks located in the Rideau River in New Edinburgh just east of the Cummings Bridge? I used to swim there back in 1966/1967 and was fascinated by this pool. It was 3 pools in one - all different depths - you could swim over the walls into the other pools - in the deepest pool if you went over the wall you were in the river itself. Could you let me know if you found any pictures or articles about this pool. | Mid | [
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Learn about 5 multi-talented useful herbs you must grow in your garden. They are all perennials which look beautiful, and have several other talents too. If you are new to gardening, one of the best types of plants to grow are herbs. This top five is not only pretty to look at, they are all perennials, which means they will come back year after year. You are probably familiar with all of them, as they are all often used in cooking. However, you many not know that they have several other great uses, making them multi-talented and very useful herbs to grow in your garden. This post contains some affiliate links (that means if you make a purchase after clicking a link, there's no additional cost to you, but I will earn a very small commission.) Click here to read my full disclosure policy. Lavender looks gorgeous in the garden. There are so many different varieties you can grow, allowing most people the ability to find one that works best in their area. If you subscribe to this blog you know I have written about this herb a few times already. Cooking with Lavender, the difference between English and French Lavender and how Lavender will help you sleep. One use for lavender that I haven't written about is a really fun craft; Lavender wands, made with stalks of lavender and ribbons, are super fun to make and a nice embellishment to packages, or alone as a gift. Stick them in your clothes drawers, or set they out on display. I love this great graphic tutorial from PreparednessMama that shows you how to make them, along with four more ideas for using your lavender harvest. Thyme is a wonderful herb. There are hundreds of varieties varying in size, texture and scent. My favorite culinary thyme is lemon thyme. I use it in dips, vinaigrette and marinades. However, have you ever seen thyme used as a lawn instead of grass? Many thymes, especially woolly thyme make great ground covers as seen here at Drought Smart Plants. If an entire lawn seems like too much, consider planting it between pavers, or stones in the walkway. Thyme is also the perfect plant for miniature gardens, fairy gardens and shallow planters like this bird bath planter created by The Empress of Dirt. There's even a variety called 'Elfin' thyme. The tiny leaves and little flowers are just the right size for these dainty projects. Sage is one of those herbs that is very savory and strong-tasting. Great for soups and stews but, have you every tried fried sage leaves? Here's a great post at Saveur on how to make fried sage leaves. They're fun treat for the foodie, a unique garnish, and will impress your guests. Another great use for sage is to make a smudge stick. Smudge sticks are a Native American custom in which you light a bundle of dried of sage and wave the smoke into all the corners of you home, to rid it of negative energy. A fun idea I think, but be careful, I had a friend who smudged her apartment once, and her neighbors called the police thinking she was smoking an illegal substance. Mint is known to all and is probably the most utilized of this useful herbs list. Mint is used to flavor a myriad of products, and is so eager to grow in the garden that many will tell you to plant it in a pot, before placing it in the garden. A great garnish in all kinds of drinks, mint also makes a wonderful simple syrup by combining 1 part sugar to 2 parts water and a large handful of mint leaves, simmered on low for 20 minutes. Allow to cool and add to sparkling water, iced tea or lemonade. Also great for making Mojitos and Mint Juleps. Mint is also said to be a great moth chaser. Who can stand those stinky moth balls anyway? Just pick some mint and allow it to dry naturally, or dry it on low in the oven, and make little sachets of mint to place with your sweaters. Guaranteed to smell better than moth balls. Rosemary is the last of this useful herbs list. “There's rosemary, that's for remembrance. Pray you, love, remember.” Shakespeare's Hamlet famous quote. Rosemary is a wonderful gift to give to someone who has had a loved one pass away. They make beautiful topiary that you can train yourself, or simply purchase one. Rosemary is considered a tender perennial which means you will need to bring it indoors for the winter. However, in warmer climates, rosemary can get quite large and if so, the stems make very nice and fragrant skewers for vegetables, shrimp or scallops on the grill. Rosemary's flexible younger branches make wonderful tiny wreaths. Great for place settings and accents in the table. Even simple rosemary sprigs on a white napkin can look pretty chic, or how about adding one to a cocktail. That's the last of my list today but there are really so many useful herbs to grow. Ok, here are a couple more tips; later in the summer you can make a pretty harvest wreath or unique firestarters with your herbs and give them to your family and friends. If you enjoy creating your own crafts and homemade products with herbs I highly recommend this new book written by my friend Jan Berry, titled, 101 Easy Homemade Products for your Skin, Health and Home. This book is loaded with great ideas and easy to follow recipes that will keep you happily busy for a long time. | Mid | [
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Utilization and effectiveness of medical rehabilitation in foreign nationals residing in Germany. In Germany, the proportion of foreign national residents receiving an invalidity pension is higher than that of Germans. Lower utilization and effectiveness of medical rehabilitation are presumed to be the main reasons. We aimed to examine whether differences in utilization and effectiveness of medical rehabilitation between Germans and foreign nationals are attributable to differences in socio-demography, socio-economic background and health status. Utilization of rehabilitation was analyzed for household members aged 18 years or above enrolled in the German Socio-Economic Panel in 2002-2004 (n = 19,521). Effectiveness of rehabilitation was defined by the occupational performance at the end of rehabilitation. It was examined by using an 80% random sample of all completed medical rehabilitations in the year 2006 funded by the German Statutory Pension Insurance Scheme (n = 634,529). Our study shows that foreign nationals utilize medical rehabilitation less often than Germans (OR = 0.68; 95%-CI = 0.50; 0.91). For those who do, medical rehabilitation is less effective (OR for low occupational performance = 1.50; 95%-CI = 1.46; 1.55). Both findings are only partially attributable to socio-demographic, socio-economic and health characteristics: After adjusting for these factors, ORs for utilization and low occupational performance were 0.66 (95%-CI = 0.49; 0.90) and 1.20 (95%-CI = 1.16; 1.24), respectively. It can be concluded that differences in the utilization and effectiveness of medical rehabilitation between Germans and foreign nationals cannot be explained only by socio-economic differences or poorer health before rehabilitation. In addition, factors such as the ability of the rehabilitative care system to accommodate clients with differing expectations, and migrant-specific characteristics such as cultural differences, seem to play a role. | High | [
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IAMK Climax Scene – Leaked Video Watch the Video Below, Iruttu Araiyil Murattu Kuththu is an upcoming Indian Tamil language adult comedy horror film written and directed by Santhosh P. Jayakumar and produced by K. E. Gnanavel Raja. The film is based on incidents happen in Thailand. The film’s concept is partially inspired by the trailer of a concept film ‘Handjob Cabin’ available on YouTube. The film marks director Santhosh P Jayakumar’s second venture after Hara Hara Mahadevaki. The film is based on incidents that happen in a house in Thailand The film has extensively been shot there in Chennai, and other foreign locations. The ghost in the film is a virgin and how it attacks boys to fulfil its desires. Watch the Video Below | Low | [
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Instructor Name SCORE: 790 Education:BS, UC Berkeley | JD, USC | MBA, UCLA Ravi Sreeramahas seen his share of Pac-12 universities, having graduated from UC Berkeley (BS), USC (JD), and UCLA (MBA). He’s an experienced teacher who’s been selected as Veritas’ Instructor of the Year, and is currently the single highest-rated GMAT instructor in the world on GMAT Club (yes, you read that correctly). His “99th Percentile or Bust” teaching philosophy has empowered countless students (both in person, and online), and his methods are beloved for combining a rigorous classroom environment with personalized attention. But it’s his deep passion for “making a difference” that motivates him. “Sometimes it's big, sometimes it's small. But in the end, you're always making a difference. And when you see your students achieve that success, you can't help but feel proud that you played a part in that process.” Oh - and did we mention that he’s the highest-rated GMAT instructor in the world? Schedule 1 Foundations of GMAT Logic Tuesday 12/12 2 Arithmetic Tuesday 12/12 3 Critical Reasoning Tuesday 12/12 4 Algebra Tuesday 12/12 5 Sentence Correction Tuesday 12/12 6 Geometry Tuesday 12/12 1 Foundations of GMAT Logic Tuesday 12/12 2 Arithmetic Tuesday 12/12 3 Critical Reasoning Tuesday 12/12 4 Algebra Tuesday 12/12 5 Sentence Correction Tuesday 12/12 6 Geometry Tuesday 12/12 Live Online™ No matter where you are, you have access to one of the industry's most accomplished GMAT instructors. Veritas Prep conducts all of its Live Online™ classes in real time, allowing students to directly interact with their instructor and fellow classmates through a two-way communication system built into the Live Online™ interface. Students and instructors collaborate using an interactive whiteboard and instant messaging utility, making note-taking fast and easy. Many students actually find these online GMAT courses to be more interactive than even traditional in-person courses. Each Live Online™ course is conducted by one of Veritas Prep's highest-rated instructors. Real reviews Apart from his great teaching style, he kept the class motivated. No matter where you are, you have access to one of the industry's most accomplished GMAT instructors. Veritas Prep conducts all of its Live Online™ classes in real time, allowing students to directly interact with their instructor and fellow classmates through a two-way communication system built into the Live Online™ interface. Students and instructors collaborate using an interactive whiteboard and instant messaging utility, making note-taking fast and easy. Many students actually find these online GMAT courses to be more interactive than even traditional in-person courses. Each Live Online™ course is conducted by one of Veritas Prep's highest-rated instructors. Apart from his great teaching style, he kept the class motivated. No matter where you are, you have access to one of the industry's most accomplished GMAT instructors. Veritas Prep conducts all of its Live Online™ classes in real time, allowing students to directly interact with their instructor and fellow classmates through a two-way communication system built into the Live Online™ interface. Students and instructors collaborate using an interactive whiteboard and instant messaging utility, making note-taking fast and easy. Many students actually find these online GMAT courses to be more interactive than even traditional in-person courses. Each Live Online™ course is conducted by one of Veritas Prep's highest-rated instructors. Apart from his great teaching style, he kept the class motivated. No matter where you are, you have access to one of the industry's most accomplished GMAT instructors. Veritas Prep conducts all of its Live Online™ classes in real time, allowing students to directly interact with their instructor and fellow classmates through a two-way communication system built into the Live Online™ interface. Students and instructors collaborate using an interactive whiteboard and instant messaging utility, making note-taking fast and easy. Many students actually find these online GMAT courses to be more interactive than even traditional in-person courses. Each Live Online™ course is conducted by one of Veritas Prep's highest-rated instructors. | High | [
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Q: Trigger hover effect over another element when hovering an element I am having issues with this: I want to force a hover function over the image when infact hovering over the h3 element html: <p><a><img class="size-full wp-image-1236 alignleft" alt="phone-icon-red" src="..." width="50" height="50" /></a></p> <h3>Contact Us</h3> CSS: img:hover{ margin-left: 10px; } js: $('h3').hover(function(e){ e.preventDefault(); $(this).prev('p').find('img').trigger('mouseover'); }); See my fiddle A: I have workaround for your issue. Add img class same as hover pseudo class: img:hover, img.hover{ margin-left: 10px; } Bind mouseover and mouseout events to h3 element: $('h3').on({ 'mouseover': function() { $(this).prev('p').find('img').addClass('hover'); }, 'mouseout': function() { $(this).prev('p').find('img').removeClass('hover'); } }); fiddle | Mid | [
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Q: Count users, not enough memory error Hi I have like 2000 users in my system. I would like to get a count of the active ones, so I did it like this: {{craft.users.group('member').count()}} but this returns the count with the limit of 100, so when I remove the limit {{craft.users.group('member').limit(null).count()}} I got this error Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 32 bytes) in /Users/alex/git/website/craft/app/models/BaseModel.php on line 280 A: Use .total() instead of .count() .count() will query the db and fetch all fields for all items relating to your criteria and then count them. .total() only counts the number of items your criteria returns without all of their fields. | Low | [
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--- abstract: 'We define a generalization of the classical four-point cross ratio of hyperbolic geometry on the unit circle given by invariant functions on Shilov boundaries of arbitrary bounded symmetric domains of tube type. This generalization is functorial and well-behaved under products. In fact, these two properties determine our extension uniquely. Any maximal representation of a closed surface group can be used to pull back our generalized cross ratios to functions on the circle; these pullbacks turn out to be strict cross ratios in the sense of Labourie and can be used to estimate the translation length of an element under the corresponding representation. The corresponding estimates show that maximal representations are well-displacing. This implies in particular that the action of the mapping class group on the moduli space of maximal representations into a Hermitian Lie group is proper.' author: - Tobias Hartnick and Tobias Strubel bibliography: - 'Bibliography.bib' title: Cross ratios associated with maximal representations --- Introduction ============ Let $\Gamma$ be the fundamental group of a closed surface $\Sigma$ of genus $g \geq 2$ and $\Gamma \hookrightarrow PU(1,1)$ a fixed hyperbolization of $\Sigma$, i.e. an isometric action of $\Gamma$ on the Poincare disc $\mathbb D$ with $\Sigma = \Gamma \backslash \mathbb D$. Every $\gamma \in \Gamma$ is hyperbolic, i.e. fixes a unique unit speed geodesic $\sigma_\gamma$. We have $$\gamma.\sigma_\gamma(t) = \sigma_{\gamma}(t+\tau_{\mathbb D}(\gamma)),$$ where $$\tau_{\mathbb D}(\gamma) := \inf_{x \in \mathbb D} d(x, \gamma.x)$$ denotes the *translation length* of $\gamma$. The action of $\Gamma$ on $\mathbb D$ extends to its boundary $S^1$, and it turns out that the translation length of each $\gamma \in \Gamma$ can be recovered from the boundary action: Indeed, denote by $$[a:b:c:d] := \frac{(a-d)(c-b)}{(c-d)(a-b)}$$ the four point cross ration on $\mathbb{CP}^1$ and abbreviate $\gamma^{\pm} := \sigma_{\gamma}(\pm \infty) \in S^1$. Then for any $\xi \in S^1\setminus \{\gamma^\pm\}$ we have $$\tau_{\mathbb D}(\gamma) = \tau^\infty_{\mathbb D}(\gamma) := \log [\gamma^-:\xi:\gamma^+:\gamma.\xi].$$ In particular, $\tau^\infty_{\mathbb D}(\gamma)$ does not depend on the choice of $\xi \in S^1\setminus \{\gamma^\pm\}$. We refer to $\tau^\infty_{\mathbb D}(\gamma)$ as the *virtual translation length* of $\gamma$.\ Now consider the case of a representation $\rho: \Gamma \to G$ into a semisimple Lie group (always assumed without compact factors and with finite center) with associated symmetric space ${{\mathcal{X}}}$. Although $\rho(\Gamma)$ need not consist of hyperbolic elements anymore, the translation length $$\tau_{{{\mathcal{X}}}}(\rho(\gamma)) := \inf_{x \in {{\mathcal{X}}}} d(x, \rho(\gamma).x)$$ can still be defined for every $\gamma \in \Gamma$. We can thus ask the similar question, whether $\tau_{{{\mathcal{X}}}}(\rho(\gamma))$ can be computed from the action of $\rho(\Gamma)$ on some suitable limit set in some boundary of ${{\mathcal{X}}}$. In this article we deal with the case, where the associated symmetric space of $G$ is isomorphic to a bounded symmetric domain of tube type and $\rho: \Gamma \to G$ is a representation with maximal Toledo invariant, or *maximal representation* for short. In this case we denote by $\check S$ the Shilov boundary of the bounded symmetric domain $\mathcal D$ isomorphic to ${{\mathcal{X}}}$. We then need to define a generalized cross ratio on $\check S$ in order to define a virtual translation length for the $\Gamma$ action. Such generalized cross ratios have been defined by various people in various degrees of generality. In the symplectic case the construction is quite classical (see e.g. [@Lab05 Subsec. 4.2.6]). Beyond that case there does not seem to be a consensus about the definition. Our key observation is that there is actually only one real-valued extension of the classical cross ratio to higher rank Shilov boundaries, provided one insists on the right kind of functoriality. (On the contrary, there are various natural generalizations to vector valued or operator valued cross ratios, see e.g. [@CRSiegel], [@CRBraun] and [@CRBiallas]). This is the content of the following theorem: \[Main\] For each bounded symmetric domain $\mathcal D$ of tube type with Shilov boundary $\check S$ there exists a subset $\check S^{(4+)}$ of $\check S^4$ (defined in Definition \[DefExtremal\] below) and a function $B_{\check S}:\check S^{(4+)} \to {\mathbb{R}}^\times$ called the *generalized cross ratio* of $\mathcal D$, such that the family of functions $\{B_{\check S}\}$ is characterized uniquely by the following properties: - $B_{\check S}$ is invariant under the group of orientation-preserving biholomorphic automorphisms of $\mathcal D$. - If $f: \mathcal D_1 \to \mathcal D_2$ is an affine holomorphic map of symmetric spaces which is induced from a balanced Jordan algebra homomorphism (see Definition \[DefBalanced\] below), then the corresponding generalized cross ratios $B_{\check S_1}$, $B_{\check S_2}$ satisfy $$B_{\check S_2}(\bar f(v_1), \dots, \bar f(v_4)) = B_{\check S_1}(v_1, \dots, v_4),$$ where $(v_1, \dots, v_4) \in \check S_1^{(4+)}$ and $\bar f$ is the boundary extension of $f$. - If $\mathcal D = \mathcal D_1 \times \mathcal D_2$ is a direct product of symmetric spaces of ranks $r_1, r_2$ with projections $p_j: \mathcal D \to \mathcal D_j$ then $$B_{\check S}(v_1, \dots, v_4)^{r_1+r_2} = B_{\check S_1}(p_1(v_1), \dots, p_1(v_4))^{r_1}B_{\check S_2}(p_2(v_1), \dots, p_2(v_4))^{r_2}.$$ - $B_{S^1}$ is the restriction of the classical four point cross ratio. (Theorem \[Main\] will be proved in Subsection \[SubsecProofMain\] below.)\ Generalizing the classical cross ratio we will define $$B_{\check S}(a,b,c,d) := \frac{k(d,a)k(b,c)}{k(d,c)k(b,a)}$$ for a kernel function $k: \check S \times \check S \to {\mathbb{C}}$ (see Section \[SecKernels\]). Returning to our maximal representation $\rho: \Gamma \to G$, the limit set of $\Gamma$ in $\check S$ is homeomorphic to a circle and can be parameterized by a continuous limit curve ${\varphi}: S^1 \to \check S$. For $\gamma \in \Gamma$ we may thus define the *virtual translation length* of $\rho(\gamma)$ to be $$\tau^\infty_{{\mathcal{D}}}(\rho(\gamma)) := \log B_{\check S}({\varphi}(\gamma^-),{\varphi}(\xi),{\varphi}(\gamma^+),\rho(\gamma).{\varphi}(\xi)),$$ where $\xi \in S^1 \setminus \{\gamma^\pm\}$ is arbitrary. Again, this does not depend on the choice of the basepoint $\xi$. It is not quite true that the translation length and the virtual translation length of $\rho(\gamma)$ always coincide. However, at least the virtual translation length can be used to bound the actual translation length from below. More precisely, if $\operatorname{rk}\mathcal D$ denotes the rank of the bounded symmetric domain $\mathcal D$ and $\dim_{\mathbb{C}}\mathcal D$ its complex dimension, then we obtain for all $\gamma \in \Gamma$ the estimate $$\begin{aligned} \label{MainEstimate}\tau_{{\mathcal{D}}}(\rho(\gamma)) \geq \frac{\operatorname{rk}\mathcal D}{\dim_{\mathbb{C}}\mathcal D} \cdot \tau^\infty_{{\mathcal{D}}}(\rho(\gamma)).\end{aligned}$$ In order to apply this fact we observe that the pullback of a generalized cross ratios $B_{\check S}:\check S^{(4+)} \to {\mathbb{R}}^\times$ to $S^1$ under a limit curve of a maximal representation happens to be a strict cross ratio in the sense of Labourie [@Lab05]. As a consequence, any two virtual translation length functions are at bounded distance. This together with the estimate then implies the following results: \[ThmResults\] Let $\rho: \Gamma \to G$ be a maximal representation. - For any finite generating set $S$ of $\Gamma$ there exist $A,B>0$ such that $$\tau_{\mathcal D}(\rho(\gamma))\geq A \cdot l_S(\gamma)-B$$ for all $\gamma\in \Gamma$. - For every $x \in \mathcal D$ and every finite generating set $S$ of $\Gamma$ the map $$(\Gamma, d_S) \to (\mathcal D, d_{\mathcal D}), \quad \gamma \mapsto \gamma.x$$ is a quasi-isometric embedding. (Theorem \[ThmResults\] will be proved in Theorem \[WD\] and Theorem \[QI\] below.) In the language of [@DGLM] the first part of the theorem says that maximal representations are *well-displacing*. This has the following well-known consequence: \[CorProperness\] Let $G$ be a semisimple Lie group without compact factors and with finite center and assume that the symmetric space of $G$ is a bounded symmetric space of tube type. Let $\Gamma$ be the fundamental group of a closed surface $\Sigma_g$ of genus $g \geq 2$ and denote by ${\rm Mod}_g$ the corresponding mapping class group. Finally, write $\mathcal M_{\max}(\Gamma, G)$ for the space of maximal representations of $\Gamma$ into $G$ up to conjugation. Then the action of ${\rm Mod}_g$ on $\mathcal M_{\max}(\Gamma, G)$ is proper. (Corollary \[CorProperness\] will be proved in Subsection \[SubsecProper\] below.)\ For symplectic, respectively, classical simple groups Corollary \[CorProperness\] was proved by Labourie [@Lab05] and Wienhard [@AnnaMCG]. Since $\mathcal M_{\max}(\Gamma, {\rm PSL}_2({\mathbb{R}}))$ is canonically identified with the Teichmüller space of $\Sigma$, we can think of the spaces $\mathcal M_{\max}(\Gamma, G)$ as *higher Teichmüller spaces*. The quotients ${\rm Mod}_g \backslash \mathcal M_{\max}(\Gamma, G)$ should then be considered as higher analoga of the moduli space of hyperbolic structures on $\Sigma$. Our results imply that these spaces are orbifolds.\ Let us briefly summarize the structure of this article; for a more detailed overview over its content see also the introductions to the individual sections. The generalized cross ratios, whose existence is claimed in Theorem \[Main\], are constructed in *Section \[SecGenCR\]*, where it is also proved that these functions have the desired properties. The preceding two sections contain preparatory material, which is needed for the construction of these cross ratios. We suggest to the hasty reader to start from Section \[SecGenCR\] and to refer backwards as necessary. In order to support this approach let us briefly summarize the content of the preparatory sections:\ *Section \[Prelims\]* contains mostly well-known material, albeit sometimes in a somewhat reorganized form. In the first subsection we relate bounded symmetric domains to Lie groups on the one hand and Jordan algebras on the other hand; in particular, we introduce notations for the various groups and spaces occurring in the context of bounded symmetric domains. We also provide a short dictionary on how to translate between the different pictures. The second subsection has the more specific purpose to relate maximal polydiscs to Jordan frames; the main result here is Proposition \[PolydiscAlgebraic\]. The final subsection is devoted to orbits of pairwise transverse triples and quadruples. The Maslov index and the corresponding notion of maximality are introduced; these are important tools throughout. The most important result in this subsection is Proposition \[Quadruples\].\ The purpose of *Section \[SecKernels\]* is to establish the existence of suitable kernel functions on boundaries of bounded symmetric domains of tube types. These kernel functions are a crucial ingredient in our construction of the generalized cross ratios and their construction is probably one of the most technical parts in the whole article. Their main properties are summarized in Theorem \[BalancingTheorem\] and Corollary \[KernelPolydisc\]. The reader who is willing to take these results on faith can skip the whole section on first reading. The Section is divided into four subsections, the first of which explains the relation between kernel functions and transversality. Based on this, the normalized kernel functions are then constructed in two steps, first for simple Jordan algebras and then in the general case. Finally, we compare our normalized kernel to the Bergman kernel of the underlying complex domain.\ The final two sections provide applications of the results of Section \[SecGenCR\]: In the first subsection of *Section \[SecMaxRep\]* it is explained how our generalized cross ratios can be used in order to associate a strict cross ratios in the sense of [@Lab05] to any maximal representation. The second subsection is devoted to the proof of the crucial Proposition \[PropLab\], which allows one to compare to arbitrary strict cross ratios. This result is implicitly contained in [@Lab05], but unfortunately not stated in the present generality. For the convenience of the reader we included a full proof. *Section \[SecWellDisp\]* is finally devoted to the proof of Inequality and its consequences. We first deal with a simple special case, which demonstrates the power of our functorial approach. The next two subsections establish our main inequality by first estimating the translation length from below and then estimating the virtual translation length from above. The final three subsections establish Theorem \[ThmResults\] and Corollary \[CorProperness\]. In fact, both follow easily once is established. **Acknowledgements** We would like to thank Marc Burger and Alessandra Iozzi for their interest in our work and for many useful conversations and Anna Wienhard for helpful comments. We would like to thank Kloster Mariastein for their hospitality. The algebraic structure of bounded symmetric domains of tube type {#Prelims} ================================================================= Bounded symmetric domains can be studied using geometric, Lie theoretic and Jordan algebraic methods. While our point of view in this article is mostly Jordan algebraic, we still need to be able to translate between the various approaches and in particular to express geometric notions in algebraic terms. The purpose of this section is to provide all the basic definitions and notations related to either of the three approaches and to sketch the relations between them. We will need this relations for example for the proof of Theorem \[Main\] (ii). With the exception of Proposition \[Quadruples\] we do not present any new results here, but only collect and reformulate various foundational material for ease of later reference. We thus recommend readers familiar with the structure theory of bounded symmetric domains to skip this section and to return to it when required.\ In the first subsection we recall the equivalence of categories between Euclidean Jordan algebras and *marked* bounded symmetric domains. The main reference for this is [@Bertram]. We use this opportunity to fix our notations. The main result of this subsection is Proposition \[Levi\], which provides a linear action for the Levi factor of a certain maximal parabolic. The second subsection relates the geometric notion of a maximal polydisc to the algebraic notion of a Jordan frame. This correspondence can be deduced from the results in [@FK] quite easily; lacking a suitable reference, we decided to include the proofs to keep the exposition self-contained. In the last subsection we recall the classification of pairwise transverse triples in the Shilov boundary of a bounded symmetric domain of tube type due to Clerc and Ørsted [@CO2]. Besides being important in their own right, these results finally allows us to prove Proposition \[Quadruples\], which provides sufficient conditions for quadruples to be contained in the boundary of a maximal polydisc, and is the main result of this section. Algebraic categories related to bounded symmetric domains {#SubsecNonsense} --------------------------------------------------------- A *bounded symmetric domain* (or *bsd* for short) is a connected bounded open subset $\mathcal D$ of a complex vector space together with a family of biholomorphic involutions $\{\sigma_x: \mathcal D \to \mathcal D\,|\,x\in \mathcal D\}$ such that $x$ is an isolated fix point of $\sigma_x$. We denote by $G: = G(\mathcal D)_0$ denotes the group of orientation preserving biholomorphic automorphisms of $\mathcal D$. It is well-known that $G$ is transitive on $\mathcal D$, in particular any bsd is homogeneous. A *tube* in ${\mathbb{C}}^n$ is a subset of the form ${\mathbb{R}}^n + i \Omega$, where $\Omega$ is an open convex cone in ${\mathbb{R}}^n$ and a bsd is *of tube type* if it is biholomorphic to a tube. A *pointed bounded symmetric domain* is a triple $(\mathcal D, \{\sigma_x\}, o)$, where $(\mathcal D, \{\sigma_x\})$ is a bsd and $o \in \mathcal D$ is a fixed basepoint. The topological boundary $\overline{\mathcal D}\setminus \mathcal D$ of a bounded symmetric domain contains a unique closed $G$-orbit $\check S$ referred to as the *Shilov-boundary* of $\mathcal D$. A *marked bounded symmetric domain* is a quadruple $(\mathcal D, \{\sigma_x\}, o, \xi)$, where $(\mathcal D, \{\sigma_x\}, o)$ is a pointed bsd and $\xi \in \check S$ is a point in the Shilov boundary. Together with the obvious morphisms, i.e. holomorphic maps preserving the pointwise involutions and fixing both base points, marked bsds form a category, which we denote by $\mathfrak{mBSD}$. The full subcategory of marked bsds of tube type is denoted $\mathfrak{mBSD}_T$. The purpose of this subsection is to exhibit algebraic categories which are equivalent to $\mathfrak{mBSD}_T$. This will allow us to reduce geometric statements on bounded symmetric domains to algebraic problems.\ Let $G$ be a connected semisimple Lie group with universal cover $\widetilde{G}$, Lie algebra ${\mathfrak}g$ and Killing form $\kappa$. An involution $\sigma: \widetilde{G} \to \widetilde{G}$ is called a *Cartan involution* if $-\kappa(\cdot, d\sigma(\cdot))$ is positive-definite. In this case $(\widetilde{G}, \sigma)$ and $({\mathfrak}g, d\sigma)$ are called *globally symmetric* and *infinitesimally symmetric pair* respectively. Every globally symmetric pair defines a homogeneous space ${{\mathcal{X}}}= \widetilde{G}/\widetilde{G}^\sigma$, which can be equipped with the structure of a Riemannian symmetric space. If there exists a $\widetilde{G}$-invariant complex structure $\mathcal J$ on ${{\mathcal{X}}}$, then the triple $(\widetilde{G}, \sigma, \mathcal J)$ is called a *global Hermitian symmetric triple*. In this case, a theorem of Harish-Chandra ensures that $({{\mathcal{X}}}, J)$ can be realized as a bsd $\mathcal D$; the triple $(\widetilde{G}, \sigma, \mathcal J)$ is called *of tube type*, if $\mathcal D$ is. The action of $\widetilde{G}$ extends to the Shilov boundary $\check S$ of $\mathcal D$. This action is in fact transitive and the point stabilizers form a conjugacy class of maximal parabolic subgroups of $\widetilde{G}$. A maximal parabolic in this conjugacy class will be referred to a s a *Shilov parabolic* for $\widetilde{G}$. A *marked global Hermitian symmetric triple* is a quadruple $(\widetilde{G}, \sigma, \mathcal J, \widetilde{Q_+})$ consisting of a global Hermitian symmetric triple together with a Shilov parabolic. Morphisms of such triples are smooth group homomorphisms preserving the additional structure involved. We denote by $\mathfrak{mHST}$ and $\mathfrak{mHST}_{T}$ the categories of all marked global Hermitian symmetric triples respectively those of tube types. Every marked global Hermitian symmetric triple defines a *marked infinitesimal Hermitian symmetric triple* $({\mathfrak}g, d\sigma, J, {\mathfrak}q_+)$, where $J = \mathcal J_{e\widetilde{G}^\sigma}$ and ${\mathfrak}q_+$ is the Lie algebra of $\widetilde{Q_+}$. We denote by $\mathfrak{mhst}_{T}$ the category of all marked infinitesimal Hermitian symmetric triples of tube type.\ Let $V$ be a finite-dimensional (real or complex) vector space, equipped with a (real- or complex-) bilinear mapping $$m: V \times V \to V, \quad (x,y) \mapsto xy.$$ We call $V$ (or rather the pair $(V,m)$) a (real or complex) *Jordan algebra* if the following three axioms are satisfied: - $m$ is commutative, i.e. $xy = yx$ - There exists a unit element $e \in V$ with $ex = xe = x$ for all $x \in V$. - For all $x,y \in V$ we have $x((xx)y) = (xx)(xy)$. A real Jordan algebra is called *Euclidean* if there exists a Euclidean inner product $(\cdot, \cdot)$ on $V$ such that left multiplication by elements of $V$ defines a self-adjoint operator, i.e. $$\forall x,y,z \in V: \quad (xy, z) = (y, xz).$$ In fact, the inner product can always be chosen to be $(x,y) = \operatorname{tr}(xy)$, where $\operatorname{tr}$ is the Jordan algebra trace in the sense of [@FK p. 29]. Moreover [@FK Prop. VIII.4.2], $V$ is Euclidean iff it is formally real, i.e. $$\forall x,y \in V: \quad x^2 + y^2 = 0 \Rightarrow x=y=0.$$ A *morphism* of Jordan algebras is a (real or complex) linear map preserving both the Jordan product and the unit element. We denote by $\mathfrak{Jor}_+$ the category of Euclidean Jordan algebras. Then we have: \[CategoryEquivalence\] There are equivalences of categories $$\mathfrak{mBSD}_T \cong \mathfrak{mHST}_{T} \cong \mathfrak{mhst}_{T} \cong \mathfrak{Jor}_+.$$ This follows immediately from the results in [@Bertram]. Since we need the explicit correspondences in the sequel, let us briefly recall them: Let us start from a Euclidean Jordan algebra $V$ and denote by $V^{\mathbb{C}}:= V \otimes {\mathbb{C}}$ its complexification. The interior of the set $\{x^2\,|\, x\in V\}$ in $V$ is an open cone $\Omega$ and thus $T_\Omega := V + i \Omega \subset V^{\mathbb{C}}$ is a tube. We refer to $\Omega$ as the *symmetric cone associated* with $V$. Put $$D(c) := \{w \in V^{\mathbb{C}}\,|\,e-w\,{\rm invertible}\}, \quad D(p):= \{z \in V^{\mathbb{C}}\,|\,z + ie\,{\rm invertible}\}.$$ Then the *Cayley transform* $$c: D(c) \to D(p), \quad c(w) = i(e+w)(e-w)^{-1}$$ is biholomorphic with inverse $$p: D(p)\to D(c), \quad p(z) = (z-ie)(z+ie)^{-1}.$$ By [@FK Theorem X.1.1], we have $T_\Omega \subset D(p)$ and hence we obtain a bounded domain $\mathcal D_V := p(T_\Omega)$ of tube type. This bounded domain is in fact symmetric; since we do not need the symmetric structure $\{\sigma_x\}$ explicitly, we refer the reader to [@Bertram Thm. X.3.2] for a proof of this fact. A marking of $\mathcal D_V$ is obtained by $0 \in \mathcal D_V$ and $e \in \check S$. Since $0$ and $e$ are preserved by Jordan algebra homomorphisms, the assignment $$\mathfrak{Jor}_+ \to \mathfrak{mBSD}_T, \quad V \mapsto \mathcal (\mathcal D_V, \{\sigma_x\}, 0, e)$$ is functorial. Now, given a marked bsd $(\mathcal D, \{\sigma_x\}, o, \xi)$ we define $G = G(\mathcal D)_0$, $K := {\rm Stab}_o(G)$, $Q_+ := {\rm Stab}_\xi(G)$ and denote by ${\mathfrak}g, {\mathfrak}k, {\mathfrak}q_+$ the respective Lie algebras. Denote by ${\mathfrak}p$ a Killing-orthogonal complement of ${\mathfrak}k$ in ${\mathfrak}g$. Then the *Cartan decomposition* ${\mathfrak}g= {\mathfrak}k \oplus {\mathfrak}p$ defines a Cartan involution $d\sigma$ with $\pm 1$-eigenspaces ${\mathfrak}k, {\mathfrak}p$. Denoting by $J$ the restriction of the complex structure of $\mathcal D$ to ${\mathfrak}p = T_o\mathcal D$ we obtain an assignment $$\mathfrak{mBSD} \to \mathfrak{mhst}, \quad (\mathcal D, \{\sigma_x\}, o, \xi) \to ({\mathfrak}g, d\sigma, J, {\mathfrak}q_+),$$ which clearly preserves tube type. For a proof that this assignment is functorial and defines in fact an equivalence of categories one uses [@Bertram Thm. V.1.9]. On the other hand, the equivalence of categories $\mathfrak{mHST}_{T} \cong \mathfrak{mhst}_{T}$ is given simply by integration. It thus remains to prove the equivalence of categories $\mathfrak{mhst}_{T} \equiv \mathfrak{Jor}_+$. Given any infinitesimal Hermitian symmetric triple $({\mathfrak}g, d\sigma, J)$ (not necessarily of tube type) we define a Lie triple product $[\cdot, \cdot, \cdot]: {\mathfrak}p \to {\mathfrak}p$ by $$[X, Y, Z] := [[X,Y],Z] \quad (X,Y,Z \in {\mathfrak}p).$$ The invariance of the complex structure $J$ then yields $$[JX, Y, Z] = -[X, JY, Z],$$ i.e. the triple $({\mathfrak}p, [\cdot, \cdot, \cdot], J)$ is a *twisted complex Lie triple system* in the sense of [@Bertram Def. III.2.1]. Its associated *Hermitian Jordan triple system* $({\mathfrak}p, \{\cdot, \cdot, \cdot\}, J)$ is given by $$\{X, Y, Z\} := \frac 1 2 ([X,Y,Z] - [JX, Y, JZ]).$$ Since the Lie triple product can be reconstructed from the Jordan triple product by the formula $$[X, Y, Z] = \{X,Y,Z\} - \{Z,X,Y\},$$ the categories of twisted complex Lie triple system and Hermitian Jordan triple products (morphisms being complex linear maps preserving the respective triple product) are equivalent. (This is a special case of Bertram’s Jordan-Lie functor, see [@Bertram Prop. III.2.7]). Moreover, by [@Bertram Thm. V.1.9] both categories are equivalent to the category $\mathfrak{hst}$ of *unmarked* Hermitian symmetric triples. Now assume that the Jordan triple system $({\mathfrak}p, \{\cdot, \cdot, \cdot\}, J)$ arises from a marked Hermitian symmetric triple system of tube type. Then there exists a *unitary tripotent*, i.e. an element an element $e \in {\mathfrak}p$ such that $\{e,e,v\} = v$ for all $v \in {\mathfrak}p$. Any such tripotent define a Jordan algebra structure on ${\mathfrak}p$ via $$\begin{aligned} \label{ProdFromTripel}v\cdot w := \{v,e,w\}.\end{aligned}$$ Now the set of unitary tripotents in ${\mathfrak}p$ can be canonically identified with the Shilov boundary $\check S$ considered before. The marking therefore determines a unique unitary tripotent $e$ by demanding ${\mathfrak}q_+ = {\rm Stab}_e({\mathfrak}g)$. This choice of unitary tripotent then determines a specific Jordan algebra structure on ${\mathfrak}p$ via . It remains to find the correct Euclidean real form $V$ of the complex Jordan algebra ${\mathfrak}p$. For this we define an involution $z \mapsto \bar{z}$ of ${\mathfrak}p$ by $$\bar z = \{e,z,e\}.$$ Then $V := \{z \in {\mathfrak}p\,|\, z = \bar z\}$ is the desired real form and the assignment $$\mathfrak{mhst} \to \mathfrak{Jor}_+, \quad ({\mathfrak}g, d\sigma, J, {\mathfrak}q_+) \to V$$ provides the last functor in the circle $$\mathfrak{Jor}_+ \to \mathfrak{mBSD}_T \to \mathfrak{mHST}_{T} \to \mathfrak{mhst}_{T} \to \mathfrak{Jor}_+.$$ Given a Euclidean Jordan algebra $V$ we will denote by $\mathcal D_V$ the associated bounded symmetric domain. We also abbreviate $G := G(\mathcal D_V)_0$ and $Q_+ = {\rm Stab}_e(G)$ as above. The explicit form of the equivalence $\mathfrak{mHST}_{T} \cong \mathfrak{Jor}_+$ exhibits a close relation between the Shilov parabolic $Q_+$ and the symmetric cone $\Omega$ associated with $V$: Write $$G(\Omega) := \{g \in GL(V)\,|\,g \Omega \subset \Omega\}$$ for the group of linear transformations preserving $\Omega$ and denote by $$L := G(\Omega)_0$$ its identity component. (We warn the reader that in the literature on Hermitian Jordan algebras including [@FK] this group is often denoted $G$, which conflicts with our notation for $G(\mathcal D)_0$.) $L$ is reductive with one-dimensional center and the maximal compact subgroup of $L$ is $$M := {\rm Stab}_{L}(e).$$ Now we have: \[Levi\] Denote by $L(Q_+)$ the Levi factor of $Q_+$. Then the Cayley transform $c$ defines an isomorphism $$L(Q_+)_0 \xrightarrow{\cong} L, \quad h \mapsto c \circ h \circ p.$$ We denote by $Q_-$ the stabilizer of $-e$ in $G$. Then $Q_\pm$ are opposite maximal parabolics and thus $L(Q_+) = Q_+ \cap Q_-$. Now let $g \in L$ and consider $h := p\circ g\circ c \in G$. Since $g$ is linear, it fixes $0$, whence $h$ fixes $p(0) = -e$. Moreover, since $g$ acts linearly we obtain $$\begin{aligned} h.e &=& \lim_{\epsilon \to 0} h.((1-\epsilon)e)\\ &= & \lim_{\epsilon \to 0} (p\circ g)((2-\epsilon)ie)(\epsilon e)^{-1}) = \lim_{\epsilon \to 0}(p\circ g)\left(\frac {2 -\epsilon}{\epsilon} \cdot ie \right)\\ &=& \lim_{\epsilon \to 0} p\left(\frac {2 -\epsilon}{\epsilon} \cdot ig.e \right) = \lim_{\epsilon \to 0} \left(g.e - \frac{\epsilon}{2 -\epsilon}e\right)\left(g.e + \frac{\epsilon}{2 -\epsilon}e\right)^{-1}\\ &=& (g.e)(g.e)^{-1} = e.\end{aligned}$$ Thus $h$ fixes $\pm e$ and since $g \in L$ was arbitrary we obtain the inclusion $p\circ L \circ c \subset (Q_+ \cap Q_-)_0$. It remains to show that both groups have the same real dimension. For this we observe that by [@FK Thm. III.5.1] we have $M = {\rm Aut}(V)_0$ and by [@FK Prop. X.3.1 and Thm. X.5.3] we have $K/M = \check S$, whence $$\begin{aligned} \dim \check S = \dim K - \dim M.\end{aligned}$$ Since $L/M = \Omega$ is open in $V$ and $V$ is homeomorphic to an open subset of $\check S$ we also have $$\begin{aligned} \dim \check S = \dim V = \dim \Omega = \dim L - \dim M,\end{aligned}$$ whence $$\begin{aligned} \label{LeviDim1}\dim L = \dim K.\end{aligned}$$ On the other hand, since $G/Q_{\pm} = \check S$ and $G/K = \mathcal D$ we have $$\dim G - \dim K = \dim \mathcal D = 2 \dim V = 2 \dim \check S= 2(\dim G - \dim Q_{\pm}),$$ i.e. $$\dim Q_{\pm} = \frac{1}{2}(\dim G - \dim K).$$ Using and the fact that $Q_+Q_-$ is open in $G$ we obtain $$\dim(Q_+ \cap Q_-) = \dim Q_{+} + \dim Q_{-} -\dim(G) = \dim K = \dim L,$$ finishing the proof. The first part of the proof of the Proposition above actually shows that $$\begin{aligned} \label{Levi2}c\circ L(Q_+)\circ p\supset G(\Omega).\end{aligned}$$ Since $L(Q_+)$ need not be connected, the opposite inclusion is not obvious. However, since $L(Q_+)$ is algebraic, the possible failure of this opposite inclusion can easily be corrected: \[LeviConvenient\] There exists $M \in \mathbb N$ (depending only on $G$) such that for all $g \in c\circ L(Q_+)\circ p$ the power $g^M$ is contained in $G(\Omega)$. Since $L(Q_+)$ is algebraic and irreducible, $\pi_0(L(Q_+))$ is finite. Denote by $M$ the order of this quotient. Now let $g \in c\circ L(Q_+)\circ p$, say $g = c \circ h \circ p$ with $h \in L(Q_+)$. Then we have $h^M \in L(Q_+)_0$ and thus $g^M = c\circ h^M \circ p \in L$ by Proposition \[Levi\]. Another application of Proposition \[Levi\] concerns the following result: Let $\alpha: V_1 \to V_2$ be a morphism of Euclidean Jordan algebras and $\alpha^{\mathbb{C}}: V_1^{\mathbb{C}}\to V_2^{\mathbb{C}}$ its complexification. Then the following hold: - The corresponding bounded symmetric domains satisfy $\alpha^{\mathbb{C}}(\mathcal D_1) \subset \mathcal D_2$. - The corresponding Shilov boundaries satisfy $\alpha^{\mathbb{C}}(\check S_1) \subset \check S_2$. - The corresponding symmetric cones satisfy $\alpha(\Omega_1) \subset \Omega_2$. \(i) is an immediate consequence of Proposition \[CategoryEquivalence\]. (ii) follows from the fact that $$\begin{aligned} \label{Shilov}\check S = \{z \in V^{\mathbb{C}}\,|\, z \,{\rm invertible}, z^{-1} = \bar z\}.\end{aligned}$$ (iii) Denote by $\alpha^\dagger: ({\mathfrak}g_1, \sigma_1, J_1, {\mathfrak}q_{+,1}) \to ({\mathfrak}g_2, \sigma_2, J_2, {\mathfrak}q_{+,2})$ the image of $\alpha$ under the equivalence of categories $\mathfrak{Jor}_+ \to \mathfrak{mhst}_{T}$. Then $\alpha^\dagger$ maps the Levi factor of ${\mathfrak}q_{+,1}$ to the Levi factor of ${\mathfrak}q_{+,2}$.Since Jordan algebra homomorphisms preserve the Cayley transform, we derive from Proposition \[Levi\] that $\alpha^\dagger$ maps the Lie algebra of $L_1 := G(\Omega_1)_0$ to that of $L_2$. Since $\Omega_j = L_j.e$ and $\alpha(e) = e$ the result follows. We will use the notations $G, K, L, M, Q_\pm$ throughout this article. If we want to stress the corresponding Euclidean Jordan algebra $V$ then we will add a subscript ${-}_V$, e.g. writing $G_V$ instead of $G$. We will use the corresponding small gothic letters to denote the associated Lie algebras. Idempotents, Jordan frames and maximal polydiscs ------------------------------------------------ Throughout this subsection $V$ denotes a Euclidean Jordan algebra. A basic reference on such Jordan algebras suitable for our purposes is [@FK]. In view of the equivalence of categories provided by Proposition \[CategoryEquivalence\] all geometric properties of bsds of tube type are reflected by algebraic properties of the corresponding Euclidean Jordan algebras. Here we shall provide an algebraic description of maximal polydiscs. We start from the observation that a Jordan algebra while not associative in general, is always power-associative in the sense that the subalgebra of $V$ generated by a single element $x$ is associative (see [@FK II.1.2]). In particular, the powers $x^n$ of an element are well-defined. An element $x \in V^{\mathbb{C}}$ with $x^2 = x$ is called *idempotent*. The following definition is fundamental for the whole theory of Euclidean Jordan algebras: \[defjordanframe\] A *Jordan frame* of a Euclidean Jordan algebra $V$ is a family $(c_1,\ldots,c_r)$ of non-zero idempotents satisfying the following conditions: - each $c_i$ is primitive, i.e. it cannot be written as the sum of two non-zero idempotents, - the idempotents are orthogonal, i.e. $c_ic_j=0$ for $i\neq j$, - $\sum_{i=1}^r c_i=e$, where $e$ is the unit of $V$. The cardinality $r$ of a Jordan frame is independent of the choice of Jordan frame and called the *rank* of the Jordan algebra $V$; it coincides with the rank of the associated bsd. The following well-known result is a version of the spectral theorem for Euclidean Jordan algebras: ([@FK III.1.2])\[spectralthm\] Suppose $V$ has rank $r$. Then for $x$ in $V$ there exists a Jordan frame $(c_1,\ldots,c_r)$ and real numbers $\lambda_1,\ldots,\lambda_r$ such that $$x=\sum_{i=1}^r \lambda_i c_i.$$ The following lemma will be used in Section \[SecKernels\] below: \[JordanCompletion\] Let $d_1, \dots, d_m$ be a collection of pairwise orthogonal idempotents in an Euclidean Jordan algebra $V$ with $d_1 + \dots + d_m = e$. Then there exists a Jordan frame $c_1, \dots, c_r$ of $V$ and numbers $i_1 < \dots < i_m < i_{m+1} = r$ such that $$d_j = \sum_{i_j+1}^{i_{j+1}} c_j.$$ If each $d_i$ is primitive, then we are done. Otherwise, there is at least one non-primitive idempotent among the $d_j$, say $d_1$. We can then write $d_1 = f_1 + f_2$ with $f_1, f_2$ idempotents. Then $f_1 + f_2 + d_2 + \dots + d_m = e$. Moreover we have $$f_1 + f_2 = d_1 = d_1^2 = (f_1 + f_2)^2 = f_1^2 + 2f_1f_2 + f_2^2 = f_1 + f_2 + 2f_1f_2,$$ whence $f_1f_2 = 0$. This implies in particular that $$d_1f_j = (f_1 + f_2)f_j = f_j^2 = f_j,$$ whence $f_1, f_2$ are in the $1$-eigenspace of $d_1$, while $d_2, \dots, d_m$ are in the $0$-eigenspace of $d_1$. We deduce from [@BraunKoecher Satz I.12.3 a)] that $f_1, f_2, d_2, \dots, d_m$ is a collection of pairwise orthogonal idempotents whose sum equals $e$. Proceeding inductively, we either end up with a Jordan frame or produce larger and larger systems of pairwise orthogonal idempotents. By finite-dimensionality of $V$, the latter is impossible. We now relate the notion of Jordan frame to the following geometric notion: \[defpolydisc\] Let ${\mathcal{D}}$ be a bounded symmetric domain of rank $r$. An isometrically embedded copy of ${\mathbb{D}}^s$ in ${\mathcal{D}}$ with $s\leq r$ is called *polydisc*. If $r=s$ it is called *maximal*. A maximal polydisc is called *centered*, if it contains $0 \in V^{\mathbb{C}}$. Since the embedding is isometric, every polydisc contains a flat of dimension $r$. In fact, every polydisc is the complexification of a maximal flat. There are lots of maximal polydiscs in $\mathcal D$: Let $x,y\in {\mathcal{D}}$. Then there exists a maximal polydisc containing them. There exists a geodesic joining $x$ and $y$. This geodesic is a flat and lies therefore in a maximal flat. The complexification of this maximal flat is a maximal polydisc. Now the relation between Jordan frames and polydiscs is provided by the following proposition: \[PolydiscAlgebraic\] - If $c=(c_1,\ldots,c_r)$ is a Jordan frame, then the map $$\varphi_c:\begin{cases} {\mathbb{D}}^r\rightarrow {\mathcal{D}}\\ (\lambda_1,\ldots,\lambda_r)\mapsto \sum_{i=1}^r\lambda_ic_i \end{cases}$$ defines a centered maximal polydisc in ${\mathcal{D}}$. - For any polydisc $P$ and any Jordan frame $(c_1,\ldots,c_r)$ there exists $g\in G$ such that $$g\cdot P=\{\sum \lambda_i c_i|\lambda_i\in {\mathbb{D}}\}.$$ \(i) The map which maps $(\mu_1,\ldots,\mu_r)\in {\mathbb{C}}^r$ to $\sum \mu_i c_i$ is an injective Jordan algebra morphism $\alpha: {\mathbb{R}}^r \to V$ and thus induces $\alpha_0: \mathbb D^r \to \mathcal D$. The metric structures on both sides come from the Jordan algebra structures. Since they are equal on the image of this map, $\varphi$ is an isometry. It is clearly injective, hence it defines an isometric copy of ${\mathbb{D}}^r$ in ${\mathcal{D}}$. \(ii) Let $A\subset P$ be a maximal flat and $\sigma$ a regular geodesic in $A$. Then $A$ is the only flat containing $\sigma$. There exists $h\in G({\mathcal{D}})$ such that $0=h\cdot \sigma(0)$. The point $h\cdot \sigma(1)$ can be written in the form $u\cdot \sum \lambda_i c_i$ for some $u \in K$ (see [@FK X.3.2]). Now put $g:=u^{-1}h$. The geodesic $g\cdot \sigma$ is contained in the flats $g\cdot A$ and $\{\sum \lambda_i c_i| \lambda_i\in (-1,1)\}$. But being regular, $g\cdot \sigma$ lies in only one unique flat, hence these two flats have to be equal. Therefore their complexifications have to be equal and we obtain (ii). Notice that the image of the Shilov boundary under the maximal polydisc embedding associated to the Jordan frame $(c_1, \dots, c_r)$ is given by $$\begin{aligned} \{\sum_{j=1}^r \lambda_j c_j\,|\, |\lambda_j| = 1\}.\end{aligned}$$ \[shilovpoints\] Let $z$ be in the Shilov boundary. Then there exists a Jordan frame $(c_1,\ldots,c_r)$ and complex numbers $\lambda_i$ with $|\lambda_i|=1$ such that $$z=\sum_{i=1}^z \lambda_i c_i.$$ Write $z = x+iy$ with $x, y \in V$. By [@FK Proposition X.2.3] we have $$\begin{aligned} \label{SquareCondition} x^2 + y^2 = e\end{aligned}$$ and $[L(x), L(y)] = 0$. In view of [@FK Lemma X.2.2] the latter yields the existence of a Jordan frame $(c_1, \dots, c_r)$ and real numbers $\mu_1, \dots, \mu_r$, $\nu_1, \dots, \nu_r$ such that $$x = \sum_{j=1}^r \mu_jc_j, \quad y = \sum_{j=1}^r \nu_jc_j$$ and hence $$z = \sum_{j=1}^r \lambda_jc_j,$$ where $\lambda_j = \mu_j + i\nu_j$. Now implies $|\lambda_j| = \mu_j^2 + \nu_j^2 = 1$. Hence $z$ is contained in the Shilov boundary of the polydisc embedding $\iota: \mathbb D^r \to \mathcal D$ associated with the Jordan frame $(c_1, \dots, c_r)$. Orbits of transverse triples and quadruples ------------------------------------------- Let $V$ be a Euclidean Jordan algebra, $\mathcal D$ its bounded symmetric domain and $\check S$ the corresponding Shilov boundary. We use the notations $G, K, L, M, Q_\pm$ for the associated groups as introduced in Subsection \[SubsecNonsense\]. Since $Q_+$ is a maximal parabolic in $G$, the Shilov boundary $\check S = G(\mathcal D)_0/Q_+$ carries the structure of a generalized flag manifold. In particular, we can define transversality for points in $\check S$: $gQ_+, hQ_+ \in \check S$ are *transverse*, denoted $z \pitchfork w$, if $Q_+g^{-1}hQ_+$ coincides with the unique cell of maximal dimension in the Bruhat decomposition of $\check S$ with respect to $Q_+$. For the definition of Bruhat decomposition see e.g. [@Knapp Thm. 7.40]. We write $$\check S^{(n)} := \{(z_1, \dots, z_n) \in \check S^n\,|\, \forall {i \neq j}: \; z_i \pitchfork z_j\}$$ for the set of pairwise transversal $n$-tuples in $\check S$. Since the $G$-action preserves transversality, each $\check S^{(n)}$ is a union of $G$-orbits. For $n=2$ we see from the definition that $\check S^{(2)}$ is the unique $G$-orbit in $\check S^2$ of maximal dimension This characterization can be used to identify $\check S^{(2)}$ in concrete examples. In the case of $G = {\rm Sp}(2n, {\mathbb{R}})$ the Shilov boundary is identified with the set $\mathcal L({\mathbb{R}}^{2n})$ of Lagrangian subspaces of ${\mathbb{R}}^{2n}$. Classically, two Lagrangian subspaces $V,W$ of ${\mathbb{R}}^{2n}$ are called transverse if $V \oplus W = {\mathbb{R}}^{2n}$. Clearly, $$\mathcal L({\mathbb{R}}^{2n})^{(2)} = \{(V,W) \in \mathcal L({\mathbb{R}}^{2n})^2\,|\, V \oplus W = {\mathbb{R}}^{2n}\}$$ is an open ${\rm Sp}(2n, {\mathbb{R}})$-orbit, hence $\check S^{(2)} = \mathcal L({\mathbb{R}}^{2n})^{(2)}$ in this case.\ For $n=3$ orbits in $\check S^{(3)}$ can be classified in terms of the Maslov index $\mu_{\check S}$ of $\check S$ as defined in [@CO2]. Rather than repeating the definition, we explain a simple way to compute the Maslov index based on the following result: \[Triples\] Any triple $(z_1, z_2, z_3) \in \check S^3$ is contained in the Shilov boundary of an embedded maximal polydisc. Combining Proposition \[Triples\] and Proposition \[PolydiscAlgebraic\] we find for every $(z_1, z_2, z_3) \in \check S^3$ a Jordan frame $(c_1, \cdots, c_r)$ and $g\in G({\mathcal{D}})$ such that $$g\cdot z_i = \sum_{j=1}^r \lambda_{ij}c_j\quad (i = 1,2,3)$$ for some $\lambda_{ij} \in S^1$. If $(z_1, z_2, z_3) \in \check S^{(3)}$ then all the triples $(\lambda_{1j}, \lambda_{2j}, \lambda_{3j})$ are pairwise transverse, hence contained in the domain of the orientation cocycle $o: (S^1)^{(3)} \to \{\pm 1\}$, which takes value $\pm 1$ depending on whether the given triple is positively or negatively oriented. The results of Clerc and Ørsted in [@CO2] then imply that $$\mu_{\check S}(z_1, z_2, z_3) = \mu_{\check S}(g\cdot z_1, g\cdot z_2,g\cdot z_3) =\sum_{j=1}^r o(\lambda_{1j}, \lambda_{2j}, \lambda_{3j}).$$ From this description we see immediately that $$\mu_{\check S}(\check S^{(3)}) = \{-r, -r+2, \dots, r-2, r\}.$$ A triple $(z_1, z_2, z_3) \in \check S^{(3)}$ with $\mu_{\check S}(z_1, z_2, z_3) = r$ is hence called *maximal*. As mentioned above, the Maslov index classifies triples of pairwise transverse points: \[TransverseTriples\] Two triples $(z_1, z_2, z_3)$, $(w_1, w_2, w_3) \in \check S^{(3)}$ lie in the same $G(\mathcal D)_0$ orbit iff $$\mu_{\check S}(z_1, z_2, z_3) = \mu_{\check S}(w_1, w_2, w_3).$$ The classification of orbits in $\check S^3$ is much more involved; see [@ClercNeeb]. Here we are interested in generalized cross ratios, which are defined on a subset of $\check S^4$. Unfortunately, the analog of Proposition \[Triples\] fails in this case, i.e. not every orbit $\check S^{(4)}$ contains a representative in the boundary of a maximal polydisc. We shall use the following proposition as a substitute: \[Quadruples\] Let $(z_1, \dots, z_4) \in \check S^{(4)}$, and suppose $(z_i, z_j, z_k)$ is maximal for some $\{i,j,k\} \subset \{1, \dots, 4\}$. Then $z_1, \dots, z_4$ are contained in the boundary of a common maximal polydisc. We may assume w.l.o.g. that $(z_1, z_2, z_3)$ is maximal. Since $$\mu_{\check S}(z_1,z_2,z_3) = r = \mu_{\check S}(-e, -ie,e),$$ it follows from Proposition \[TransverseTriples\] that there exists $g \in G$ with $g.(z_1,z_2,z_3) = (-e, -ie,e)$. Let $z = g.z_4$. By Proposition \[shilovpoints\] there exists a Jordan frame $(c_1,\ldots,c_r)$ and $\lambda_i\in {\mathbb{C}}$ with $|\lambda_i|=1$ such that $$z=\sum_{i=1}^r\lambda_i c_i.$$ We deduce that $$g.(z_1, \dots, z_4) = (\sum (-1) \cdot c_j, \sum(- i) \cdot c_j, \sum 1 \cdot c_j, \sum \lambda_j c_j)$$ is contained in the Shilov boundary of the polydisc embedding $\iota: \mathbb D^r \to \mathcal D$ associated with the Jordan frame $(c_1, \dots, c_r)$. Correspondingly, $(z_1, \dots, z_4)$ is contained in the Shilov boundary of the embedded maximal polydisc $g^{-1} \circ \iota$. Normalized kernels of Euclidean Jordan algebras {#SecKernels} =============================================== After the preliminary results in Section \[Prelims\] we now turn to the construction of generalized cross ratios. In view of the above equivalence of categories, we will work with Jordan algebras rather than bounded symmetric domains. Thus our problem is to construct a generalized cross ratio $B_V$ on $4$-tuples on the Shilov boundary $\check S_V$ associated with a Euclidean Jordan algebra $V$. In view of the various cocycle relations expected from a generalized cross ratio, a natural *ansatz* is to define $$B_V(a,b,c,d) := \frac{k_V(d,a)k_V(b,c)}{k_V(d,c)k_V(b,a)}$$ for some function $k_V: \check S \times \check S \to {\mathbb{C}}$. In order to obtain $G$-invariance this function should have some nice equivariance properties. If $B_V$ is supposed to be functorial, then also the normalization of $k_V$ has to be chosen carefully. Since this is a delicate issue we devote a whole section to the construction of the kernels $k_V$ and their basic properties. The actual study of the corresponding cross ratios will then be undertaken in the next section. The reader willing to take the main properties of the kernels $k_V$ on faith can skip this section except for the definition of balanced Jordan algebra homomorphisms (Definition \[DefBalanced\]) which will be used throughout.\ The first subsection introduces automorphy kernels and their relation to various notions of transversality. Based on this notion we construct in subsequent subsections the kernels $k_V$ first for simple Euclidean Jordan algebras, and then for general Euclidean Jordan algebras. Finally, we compare the our normalized kernels $k_V$ to the Bergman kernels of the corresponding bounded symmetric domains. The automorphy kernel and transversality ---------------------------------------- Let $V$ be a Euclidean Jordan algebra. Given $z \in V^{\mathbb{C}}$ we denote by $L(z)$ the left-multiplication by $z$. Then for all $z,w \in V^{\mathbb{C}}$ the *box operator* and the *quadratic representation* are defined by $$z \square w := L(zw) + [L(z), L(w)],$$ and $$P(z) := 2L(z)^2 - L(z^2)$$ respectively. Following [@CO2] (see also [@FK] and [@Satake]) we define the *automorphy kernel* $$K: V^{\mathbb{C}}\times V^{\mathbb{C}}\to {\rm End}(V^{\mathbb{C}}),$$ by $$K(z,w) := I - 2z\square \overline{w} + P(z) P(\overline{w}).$$ \[exampleR\] Let $V={\mathbb{R}}$ so that $V^{\mathbb{C}}={\mathbb{R}}^{\mathbb{C}}={\mathbb{C}}$. For $x,w,z\in {\mathbb{C}}$ we then have $$(z\square w)x=L(zw)x+[L(z),L(w)]x=(zw)x,$$ whence $z\square w$ is multiplication with $zw$. Similarly, $$P(z)x=(2L(z)^2-L(z^2))x=z^2x,$$ hence $P(z)$ is multiplication by $z^2$. Combining these two observations we can calculate $K(z,w)$: We obtain $$K(z,w)x=x-2z\bar w x+z^2\bar w^2=(1-z\bar w)^2x$$ and thus $K(z,w)$ is multiplication by $(1-z\bar w)^2$. We also use the quadratic representation to define the *structure group* of $V^{\mathbb{C}}$ to be $${\rm Str}(V^{\mathbb{C}}) := \{g \in GL(V^{\mathbb{C}})\,|\,P(gx) = gP(x)g^{\top}\}.$$ If $z,w \in \mathcal D$ then $K(z,w) \in {\rm Str}(V^{\mathbb{C}})$ [@CO2 p. 315]. Let us briefly describe the behavior of $K$ under automorphisms. Since we do not want to digress to deeply into the structure theory of bounded symmetric domain, we refer the reader to [@Satake Chapter II, Section 5] for the definition of the canonical automorphy factor $J$ of a bounded symmetric domain $\mathcal D$. All we have to know at this place is that $J$ restricts to a map $J: \overline{\mathcal D} \times V^{\mathbb{C}}\to {\rm Str}(V^{\mathbb{C}})$ satisfying $$\begin{aligned} \label{AutomorphyI}K(gz, gw) = J(g,z)K(z,w)J(g,w)^*\end{aligned}$$ for $g \in G(\mathcal D)_0$, $z,w \in \overline{\mathcal D}$. The automorphy kernel allows us to detect transversality on the Shilov boundary $\check S$: \[TransMain\] Let $V$ be a Euclidean Jordan algebra, $\mathcal D$ the associated bounded symmetric domain and $\check S$ its Shilov boundary. Then $z,w \in \check S$ are transverse iff one of the following conditions holds true: - $\det(z-w) \neq 0$. - $K(z,w)$ is invertible. - $K(z,w) \in {\rm Str}(V^{\mathbb{C}})$. - $\det K(z,w) \neq 0$. Let us first prove that $z,w$ are transverse iff (iv) holds. Indeed, it follows from that $$\{(z,w) \in \check S\,|\, \det K(z,w) \neq 0\}$$ is a $G$-orbit. By continuity of $\det K(\cdot, \cdot)$ this orbit is open, hence coincides with $\check S^{(2)}$. It thus remains to prove equivalence of (i)-(iv).The implication (i) $\Rightarrow$ (ii) is provided in [@CO2 Lemma 5.1]. The implication (ii) $\Rightarrow$ (iii) follows from the fact that $K(z_0,w_0) \in {\rm Str}(V^{\mathbb{C}})$ for $z_0, w_0 \in \mathcal D$ together with the continuity of $K$ and the fact that ${\rm Str}(V^{\mathbb{C}})$ is closed in ${\rm GL}(V^{\mathbb{C}})$. Finally, the implication (iii) $\Rightarrow$ (iv) is obvious. Thus it remains to show (iv) $\Rightarrow$ (i). Thus let $w,z \in \check S$ be arbitrary and assume $\det K(z,w) \neq 0$. We first claim that there exists $g \in G$ such that $e-g\cdot w$ and $e-g\cdot z$ are invertible. Indeed, if $\mathcal D$ is a polydisc with $w=(w_1,\ldots,w_r)$ and $z=(z_1,\ldots,z_r)$, then one can clearly find an element $g=(g_1,\ldots,g_r)\in SO(2)^r\subset G$ such that $g_i\cdot w_i$ and $g_i\cdot z_i$ are both not equal to $1$. The general case is reduced to this case by applying Proposition \[Triples\] to the triple $(e,w,z)$, thereby finishing the proof of the claim. Next observe that implies $$\det K(gz,gw)=\underbrace{\det(J(g,z))}_{\neq 0}\det K(z,w)\underbrace{\overline{\det(J(g,w))}}_{\neq 0},$$ and thus our assumption yields $\det K(gz, gw) \neq 0$. Now note that with $e-gw$ also $e-\overline{gw} = \overline{e-gw}$ is invertible , hence [@FK Lemma X.4.4 ii)] applies and yields $$K(gz,gw)=P(e-gz)P(c(gz)+c(\overline{gw}))P(e-\overline{gw}),$$ whence $$\det(P(c(gz)+c(\overline{gw})))\neq 0.$$ A simple calculation shows that $c(\overline{gw}))=-\overline{c(gw)}$. Since $gw \in \check S\cap D(c)$, the image $c(gw)$ is contained in $V$, whence $\overline{c(gw)}=c(gw)$. We thus obtain $$\det(P(c(gz)-c(gw)))\neq 0.$$ Using the definition of the Cayley transform and [@FK p.190] we obtain $$\begin{aligned} c(gz)-c(gw)=& i\big((e+gz)(e-zg)^{-1}-(e+gw)(e-gw)^{-1}\big)\\ =& i\big(-ie+2i(e-gz)^{-1}+ie-2i(e-gw)^{-1}\big)\\ =&-2\big((e-gz)^{-1}-(e-gw)^{-1}\big). \end{aligned}$$ We thus obtain $$\begin{aligned} \label{Transv2} \det P(-2((e-gz)^{-1}-(e-gw)^{-1}))\neq 0. \end{aligned}$$ Now we can apply Hua’s formula [@FK Lemma X.4.4] to obtain $$\begin{aligned} &P(-2((e-gz)^{-1}-(e-gw)^{-1}))\\=&P(e-gz)^{-1}P(-2((e-gz)-(e-gw)))P(e-gw)^{-1}\\ =&P(e-gz)^{-1}P(-2(gw-gz)))P(e-gw)^{-1}. \end{aligned}$$ Combinining this with and using that $P(e-gz)^{-1}$ and $P(e-gw)^{-1}$ are invertible, we obtain $$\det P(-2(gw-gz))) \neq 0.$$ Thus $P(-2(gw-gz))$ is invertible. By [@FK Prop. II.3.1] this implies that $-2(gw-gz)$ and hence $gz-gw$ is invertible. Thus $\det(gz-gw) \neq 0$, which by [@CO2 Prop. 3.2] implies $\det(z-w) \neq 0$. This finishes the proof of Proposition \[TransMain\]. Proposition \[TransMain\] implies immediately: The image $p(V)$ of $V$ under the inverse Cayley transform is precisely the subset of points in $\check S$, which are transverse to $e$. The normalized kernel function I: The simple case ------------------------------------------------- The aim of this subsection is to define a suitably normalized kernel functions on the bounded symmetric domain $\mathcal D$ of a given simple Euclidean Jordan algebra $V$, whose extension to the Shilov boundary reflects transversality. We have seen in Proposition \[TransMain\] that transversality is characterized by non-singularity of the automorphy kernel $K: V^{\mathbb{C}}\times V^{\mathbb{C}}\to {\rm End}(V^{\mathbb{C}})$, which when restricted to $\overline{D}^{(2)} := \mathcal D \cup \check S^{(2)}$ takes values in the structure group ${\rm Str}(V^{\mathbb{C}})$. In order to obtain a numerical kernel function, one can compose $K$ with an arbitrary character $\chi$ of ${\rm Str}(V^{\mathbb{C}})$. We denote the resulting function by $$k_\chi: \overline{{\mathcal{D}}}^{(2)} \to {\mathbb{C}}^\times, \quad (z,w) \mapsto \chi(K(z,w)).$$ Since we would like our kernel functions to be compatible under (certain) Jordan algebra homomorphisms, we will have to choose the character $\chi$ carefully. Recall our assumption that $V$ is supposed to be simple and denote by $n := \dim V$ its dimension. We then choose $\chi := \det^{\frac 1 {2n}}$ and denote the associated kernel function by $k_V := k_{\det^{\frac 1 {2n}}}$. Here, the fractional exponent has to be interpreted as follows: If $k_{\det}: \overline{D}^{(2)} \to {\mathbb{C}}^\times$ denotes the kernel function $\det(K(z,w))$, then $k_V$ is defined as the unique function $\overline{D}^{(2)} \to {\mathbb{C}}^\times$ satisfying $k_V^{2n} = k_{\det}$ and $k_V(0,0) = 1$. The kernel $k_V$ extends in fact continuously to all of $\check S^2$ due to the following general lemma: \[Branching\] Let $X$ be a manifold, $f: X \to {\mathbb{C}}$ be a continuous function, $X' := f^{-1}({\mathbb{C}}\setminus\{0\})$. Let $\widetilde{f}: X' \to {\mathbb{C}}\setminus \{0\}$ be any continuous function with $\widetilde{f}^n = f|_{X'}$. Then $\widetilde{f}$ extends continuously by $0$ to all of $X$. Extend $\widetilde{f}$ to all of $X$ by $0$. We show that this extension is continuous. For this let $x_k \in X'$ with $x_k \to x$, where $x \in X\setminus X'$. Then $f(x_k) \to f(x) = 0$ by continuity of $f$, hence $\widetilde{f}(x_k)^n \to 0$. This, however, implies already $\widetilde{f}(x_k) \to 0 = \widetilde{f}(x)$, which yields continuity of the extended function. Applying this to the continuous function $k_{\det}$ we obtain the desired extension of $k_V$ to $\check S^2$. In view of Proposition \[TransMain\] and this extension has the following properties: \[ExtendKernelTransv\] Let $V$ be a simple Euclidean Jordan algebra. Then the normalized kernel $k_V: \check S^2 \to {\mathbb{C}}$ satisfies $$k_V(z,w) \neq 0 \Leftrightarrow z \pitchfork w$$ and $$k_V(gz, gw) = j_V(g,z)k_V(z,w)\overline{j_V(g,w)}, \quad(g \in G, z,w \in \check S),$$ where $j_V := \det^{\frac 1 {2n}} \circ J$. The factor $\frac 1 2$ in the normalization exponent $\frac 1 {2n}$ was added to achieve the following normalization: \[KernelDisc\] Let $V = ({\mathbb{R}}, \cdot)$ so that $\mathcal D = \mathbb D$ is the unit disc. Since $\dim V = {\rm rk}(V) = 1$ it follows from Example \[exampleR\] that $k_{\det}(z,w) = (1-z \overline{w})^2$. Now our normalization is chosen in such a way that $$k_{\mathbb{R}}(z, w) = 1-z \overline{w}.$$ This additional normalization factor does not affect the proof of the following desired invariance property: \[UniversalitySimpleCase\]Let $\alpha: V_1 \to V_2$ be an injective morphism of simple Jordan algebras. Denote by $\mathcal D_1$ and $\mathcal D_2$ respectively the corresponding bounded symmetric domains and by $\check S_1$ and $\check S_2$ the respective Shilov boundaries. Then for all $z,w \in\mathcal D_1 \cup \check S_1$ we have $$\begin{aligned} \label{UniversalityKernel1} k_{V_2}(\alpha^{\mathbb{C}}(z), \alpha^{\mathbb{C}}(w)) = k_{V_1}(z,w).\end{aligned}$$ By continuity it suffices to prove for $z, w \in \mathcal D$. We would like to apply [@CO2 Prop. 6.2]; for this we have to translate this proposition into our language. Define a character $\chi_j$ of ${\rm Str}(V_j^{\mathbb{C}})$ by $$\det(gz) = \chi_j(g) \det(z) \quad (g \in {\rm Str}(V_j^{\mathbb{C}}), z \in \mathcal D_j),$$ where $\det$ is the Jordan algebra determinant. Denote by $r_j$ and $n_j$ respectively the rank and dimension of $V_j$. Then the proposition of Clerc and [Ø]{}rsted states that $$k_{\chi_2}(\alpha^{\mathbb{C}}(z), \alpha^{\mathbb{C}}(w)) = k_{\chi_1}(z,w)^{\frac{r_2}{r_1}}.$$ On the other hand, since the $V_j$ are simple, [@FK Prop. III.4.3] applies and shows $$\chi_j = \det{}^{\frac{r_j}{n_j}}.$$ We thus obtain $$\begin{aligned} k_{V_2}(\alpha^{\mathbb{C}}(z), \alpha^{\mathbb{C}}(w)) &=& \det{}^{\frac{1}{2n_2}}(K(\alpha^{\mathbb{C}}(z), \alpha^{\mathbb{C}}(w)))\\ &=& \left[\det{}^{\frac{r_2}{n_2}}(K(\alpha^{\mathbb{C}}(z), \alpha^{\mathbb{C}}(w)))\right]^{\frac{1}{2r_2}}\\ &=&\left[k_{\chi_2}(\alpha^{\mathbb{C}}(z), \alpha^{\mathbb{C}}(w))\right]^{\frac{1}{2r_2}}\\ &=&\left[k_{\chi_1}(z,w)^{\frac{r_2}{r_1}}\right]^{\frac{1}{2r_2}}\\ &=&\left[\det{}^{\frac{r_1}{n_1}}K(z,w)\right]^{\frac{1}{2r_1}}\\ &=&\det{}^{\frac{1}{2n_1}}K(z,w)\\ &=& k_{V_1}(z,w).\end{aligned}$$ We have been slightly sloppy here by not specifying the arc of the various roots. Still, it is easy to make the above argument precise. Strictly speaking we have only shown that $$k_{V_2}(\alpha^{\mathbb{C}}(z), \alpha^{\mathbb{C}}(w))^{2n_1} = k_{V_1}(z,w)^{2n_1}$$ rather than $$k_{V_2}(\alpha^{\mathbb{C}}(z), \alpha^{\mathbb{C}}(w)) = k_{V_1}(z,w).$$ However, since $k_{V_2}(\alpha^{\mathbb{C}}(0), \alpha^{\mathbb{C}}(0)) = k_{V_1}(0,0)$ the former implies the latter by uniqueness. We will allow ourselves this kind of sloppyness regarding roots, whenever it is clear how to make the arguments precise.\ The normalized kernel function II: The general case --------------------------------------------------- We would like to define a normalized kernel with invariance properties generalizing those of Lemma \[UniversalitySimpleCase\] also in the case where the involved Jordan algebras are not simple. For this we first observe that any Euclidean Jordan algebra $V$ is semisimple ([@FK Prop. III.4.4]) and thus decomposes into simple ideals, say $V = V_1 \oplus \dots \oplus V_n$. Accordingly we identify elements $z \in V$ with vectors $z = (z_1, \dots, z_n)^\top$ with $z_j \in V_j$ and define $k_V: {\mathcal D}^{2} \to {\mathbb{C}}^\times$ by the formula $$\begin{aligned} \label{ProductFormula}k_V(z,w) = \prod_{i=1}^n (k_{V_i}(z_i, w_i))^{\frac{\operatorname{rk}V_i}{\operatorname{rk}V}}.\end{aligned}$$ More precisely, if $\widetilde{k_V}:\mathcal D^{2} \to {\mathbb{C}}^\times$ is given by the formula $$\widetilde{k_V}(z,w) := \prod_{i=1}^n (k_{V_i}(z_i, w_i))^{\operatorname{rk}V_i}.$$ then $k_V$ is defined to be the unique function satisfying $$k_V(z,w)^{{\rm rk}(V)} = \widetilde{k_V}(z,w), \quad k_V(0,0) = 1.$$ As before Lemma \[Branching\] implies that $k_V$ extends to a function $\mathcal D^2 \cup \check S^2 \to {\mathbb{C}}$, which vanishes precisely on non-transversal pairs. Observe that for $V$ simple the function $k_V$ coincides with the normalized kernel $k_V$ defined earlier so that there it is justified to use the same notation and to refer to $k_V$ in general as the *normalized kernel function* of $V$. Moreover, the following property follows right from the definition: \[kVProjection\] Let $V$ be a Euclidean Jordan algebra. If $V = V_1 \oplus V_2$ is the sum of two (not necessarily simple) ideals of ranks $r_1, r_2$ with projections $p_j: V \to V_j$ then $$k_V(z,w)^{r_1+r_2} = k_{V_1}(p_1(z),p_1(w))^{r_1}k_{V_2}(p_2(z),p_2(w))^{r_2}.$$ Let us spell this out in the case of a polydisc: Let $V = ({\mathbb{R}}, \cdot)^r$ so that $\mathcal D = \mathbb D^r$ is the standard polydisc. In our sloppy notation the normalized kernel function $k_{{\mathbb{R}}^r}$ of the polydisc $\mathbb D^r$ is $$\begin{aligned} k_{{\mathbb{R}}^r}((z_1, \dots, z_r), (w_1, \dots, w_r)) = \prod_{j=1}^r (1-z_j\overline{w_j})^{\frac 1 r}.\end{aligned}$$ We can see already from the case of polydiscs that our normalized kernel is *not* invariant under arbitrary Jordan algebra homomorphisms: \[BalancedCounterexample\] Consider the Jordan algebra embedding $\alpha: {\mathbb{R}}^2 \to {\mathbb{R}}^3$ given by $(\lambda_1, \lambda_2) \mapsto (\lambda_1, \lambda_1, \lambda_2)$. Then $$\begin{aligned} k_{{\mathbb{R}}^2}(\lambda, \mu) &=& (1 - \lambda_1 \overline{\mu_1})^{\frac 1 2}(1 - \lambda_2 \overline{\mu_2})^{\frac 1 2}\\ &\neq& (1 - \lambda_1 \overline{\mu_1})^{\frac 2 3}(1 - \lambda_2 \overline{\mu_2})^{\frac 1 3} =k_{{\mathbb{R}}^3}(\alpha^{\mathbb{C}}(\lambda),\alpha^{\mathbb{C}}(\mu)).\end{aligned}$$ We want to exclude bad behavior as in the last example. Denote by $\operatorname{tr}_V$ the Jordan algebra trace of $V$. Thus if $(c_1, \dots, c_r)$ is a Jordan frame for $V$ then $$x = \sum_{j=1}^r \lambda_jc_j \Rightarrow \operatorname{tr}_V(x) = \sum_{j=1}^r \lambda_j.$$ Now we define: \[DefBalanced\] A Jordan algebra homomorphism $\alpha_V: V \to W$ is called *balanced* if for all $v \in V$ $$\frac{1}{\operatorname{rk}V}\operatorname{tr}_V(v) = \frac{1}{\operatorname{rk}W} \operatorname{tr}_W(\alpha(v)).$$ The notion is clearly invariant under complexification. Moreover, we have the following characterization of balanced Jordan algebra homomorphisms: Let $(c_1, \dots, c_r)$ be a Jordan frame in $V$ and $\alpha: V \to W$ a Jordan algebra homomorphism. Then $\alpha(c_1), \dots, \alpha(c_r)$ is a family of idempotents with $\alpha(c_i)\alpha(c_j) = 0$ and $\sum \alpha(c_i) = e$. Thus Proposition \[JordanCompletion\] applies and there exists a Jordan frame $(c_{11}, \dots, c_{1l_1}, \dots, c_{r1}, \dots, c_{rl_r})$ of $W$ such that $$\alpha(c_j) = \sum_{k=1}^{l_j} c_{jk}.$$ We have $\operatorname{tr}_W(\alpha(c_j)) = l_j$ and thus $\alpha$ is balanced if and only if $$l_1 = \dots = l_r.$$ Conversely, if the latter condition is true for any Jordan frame $(c_1, \dots, c_r)$ of $V$, then $\alpha$ is balanced. Note that we obtain in particular $$\operatorname{rk}W = l_j \cdot \operatorname{rk}V \quad (j = 1, \dots, r),$$ so that $\operatorname{rk}W$ is divisible by $\operatorname{rk}V$. In particular, the morphism in Example \[BalancedCounterexample\] is not balanced. Also note that a balanced Jordan algebra homomorphism is injective unless it is trivial. In our attempts to prove an invariance theorem we will restrict attention to balanced Jordan algebra homomorphisms. Even in this case we cannot quite obtain the same kind of invariance as in Lemma \[UniversalitySimpleCase\]. In order to formulate our (slightly weaker) result, we introduce the following terminology: Two elements $v_1, v_2$ are called *co-diagonalizable* if there exists a Jordan frame $(c_1, \dots, c_r)$ and elements $\lambda_j \in \mathbb D$, $\mu_j \in \mathbb D$ such that $$v_1 = \sum_{j=1}^r \lambda_jc_j \in \mathcal D_{V}, \quad v_2 = \sum_{j=1}^r \mu_jc_j\in \mathcal D_{V}.$$ Then we have: \[BalancingTheorem\] Let $\alpha: V \to W$ be a non-trivial Jordan algebra homomorphism. If $\alpha$ is balanced, then for every pair of co-diagonalizable elements $v_1, v_2 \in \mathcal D$ we have $$\begin{aligned} \label{BalancingDream} k_W(\alpha^{\mathbb{C}}(v_1),\alpha^{\mathbb{C}}(v_2)) = k_{V}(v_1,v_2).\end{aligned}$$ Conversely, if holds for all co-diagonalizable $v_1, v_2 \in \mathcal D_V$, then $\alpha$ is balanced. For the proof we consider first the case, where $V$ is a maximal polydisc in $W$. In this case we have the following version of Theorem \[BalancingTheorem\], which is a slight extension of the results of Clerc and [Ø]{}rsted in [@CO2]: \[FrameFormulaKernel\] If $(c_1, \dots, c_r)$ is a Jordan frame in a Jordan algebra $W$ and $\lambda_j \in {\mathbb D}$, $\mu_j \in {\mathbb D}$, then $$\begin{aligned} k_{W}(\sum_{j=1}^r \lambda_jc_j, \sum_{j=1}^r \mu_jc_j) = \prod_{j=1}^r(1- \lambda_j\overline{\mu_j})^{\frac 1 r}.\end{aligned}$$ Assume first that $W$ is simple. Then [@CO2 Lemma 5.4] applies directly and we obtain $$k_{\chi_W}(\sum_{j=1}^r \lambda_jc_j, \sum_{j=1}^r \mu_jc_j) = \prod_{j=1}^r(1-\lambda_j\overline{\mu_j})^2,$$ whence $$k_{\chi_W}(\sum_{j=1}^r \lambda_jc_j, \sum_{j=1}^r \mu_jc_j)^r = \left(\prod_{j=1}^r(1-\lambda_j\overline{\mu_j})\right)^{2r}.$$ Since $$\prod_{j=1}^r(1-0 \cdot \overline{0}) = 1$$ this settles the simple case. For the general case, consider a decomposition $W = W_1 \oplus \dots \oplus W_n$ into simple ideals. Let $r_l := {\rm rk}(W_l)$ and $(c_{l1}, \dots, c_{lr_l})$ be a Jordan frame for $W_l$. Then $(c_{11},\dots, c_{nr_n})$ is a Jordan frame for $W$ and, in fact, any Jordan frame for $W$ is of this form (as follows e.g. from [@FK Prop. X.3.2]). Let $$z := \sum_{l=1}^n \sum_{j=1}^{r_l}\lambda_{lj}c_{lj}, \quad w:= \sum_{l=1}^n \sum_{j=1}^{r_l}\mu_{lj}c_{lj}.$$ By definition we have $$k_W(z,w)^{{\operatorname{rk}W}} = \prod_{l=1}^n (k_{W_l}(z_l, w_l))^{\operatorname{rk}W_l},$$ where $$z_l = \sum_{j=1}^{r_l}\lambda_{lj}c_{jl}, \quad w_l := \sum_{j=1}^{r_l}\mu_{lj}c_{lj}.$$ By the simple case we have $$(k_{W_l}(z_l, w_l))^{\operatorname{rk}W_l} = \prod_{j=1}^{r_l}(1- \lambda_{lj}\overline{\mu_j}),$$ and thus $$k_W(z,w)^{{\operatorname{rk}W}} = \prod_{l=1}^n \prod_{j=1}^{r_l}(1- \lambda_{lj}\overline{\mu_j}).$$ From this the general case follows easily: If $\alpha$ is balanced, then $r_V := {\rm rk}(V)$ and $r_W := {\rm rk}(W)$ are related by $r_W = \mu_{\alpha}r_V$ for some constant $\mu_\alpha$. Given a Jordan frame $(c_1, \dots, c_r)$ in $V$ and elements $$v_1 = \sum_{j=1}^r \lambda_jc_j \in \mathcal D_{V}, \quad v_2 = \sum_{j=1}^r \mu_jc_j\in \mathcal D_{V}$$ with $\lambda_j \in \mathbb D$, $\mu_j \in \mathbb D$ we have $$\alpha^{\mathbb{C}}(v_1) = \sum_{j=1}^r \lambda_j\alpha(c_j), \quad \alpha^{\mathbb{C}}(v_2)= \sum_{j=1}^r \mu_j\alpha(c_j).$$ Now each $\alpha(c_j)$ decomposes as $$\alpha(c_j) = d_{j1} + \dots + d_{j\mu_{\alpha}},$$ where the $d_{jl}$ are primitive idempotents. Now we obtain $$k_{V}(v_1,v_2)^{r_V} = \prod_{j=1}^r(1- \lambda_j\overline{\mu_j}),$$ whence $$k_{V}(v_1,v_2)^{r_W} = \left(\prod_{j=1}^r(1- \lambda_j\overline{\mu_j})\right)^{\mu_{\alpha}} = \prod_{j=1}^r(1- \lambda_j\overline{\mu_j})^{\mu_{\alpha}}.$$ Similarly, $$k_W(\alpha^{\mathbb{C}}(v_1),\alpha^{\mathbb{C}}(v_2))^{r_W} = \prod_{j=1}^r(1- \lambda_j\overline{\mu_j})^{\mu_{\alpha}}.$$ As $k_{V}(0,0) = k_W(\alpha^{\mathbb{C}}(0),\alpha^{\mathbb{C}}(0))^{r_W}$, this implies . On the other hand, if $\alpha$ is not balanced and $v_1, v_2$ are as above, then $$\begin{aligned} k_{V}(v_1,v_2) &=& \prod_{j=1}^r(1- \lambda_j\overline{\mu_j})^{\frac 1 r_V}\\ &\neq&\prod_{j=1}^r(1- \lambda_j\overline{\mu_j})^{\frac{\mu_{\alpha}(c_j)}{r_W}}\\ &=& k_W(\alpha^{\mathbb{C}}(v_1),\alpha^{\mathbb{C}}(v_2)).\end{aligned}$$ \[ExamplesBalanced\] The following are examples of balanced Jordan algebra homomorphisms: - Jordan algebra homomorphisms $\alpha: V \to W$ between simple Jordan algebras are balanced by Lemma \[UniversalitySimpleCase\]. - If ${\rm rk}(V) = {\rm rk}(W)$ then every injective Jordan algebra homomorphism $\alpha: V \to W$ is balanced. - In particular, maximal polydisc embeddings are balanced. - Any Jordan algebra homomorphism $\alpha: {\mathbb{R}}\to W$ is balanced. - Compositions of balanced Jordan algebra homomorphisms are balanced. So far we have been working on the interior of a bounded symmetric domain. Of course, by continuity our discussion extends the Shilov boundary. In particular we have: \[KernelPolydisc\] Let $V$ be a Euclidean Jordan algebra and $k_V: (\mathcal D \cup \check S)^2 \to {\mathbb{C}}$ the associated normalized kernel. Then - If $z,w \in \check S$, then $k_V(z,w) \neq 0 \Leftrightarrow z \pitchfork w$. - There exists a continuous function $j_V: G \times V \to {\mathbb{C}}^\times$ such that $$k_V(gz, gw) = j_V(g,z)k_V(z,w)\overline{j_V(g,w)}, \quad(g \in G, z,w \in \check S).$$ - If $(c_1, \dots, c_r)$ is a Jordan frame for $V$ and $\lambda_1, \dots, \lambda_r, \mu_1, \dots, \mu_r \in \overline{\mathbb D}$, then $$\begin{aligned} \label{KernelPolydiscFormula}k_V(\sum_{j=1}^r \lambda_jc_j, \sum_{j=1}^r \mu_jc_j) = \prod_{j=1}^r (1-\lambda_j\overline{\mu_j})^{\frac 1 r}.\end{aligned}$$ Comparison to the Bergman kernel -------------------------------- Given a Euclidean Jordan algebra $V$ with associated bounded symmetric domain $\mathcal D$, we can forget about the algebraic structure of $V$ and consider $\mathcal D \subset V$ simply as a bounded domain. From this data we can then define the Bergman kernel $$K_{\mathcal D}: \mathcal D \times \mathcal D \to {\mathbb{C}}^\times$$ as the reproducting kernel of the Bergman space $\mathcal H^2(\mathcal D)$. It turns out that our normalized kernel $k_V$ is uniquely determined by $K_{\mathcal D}$. More precisely we have: \[BergmanComparison\] The restriction $k_V: \mathcal D \times \mathcal D \to {\mathbb{C}}^\times$ of the normalized kernel and the Bergman kernel $K_{\mathcal D}$ are related by the formula $$k_V(z,w)^r = C\cdot K_{\mathcal D}(z,w)^{-1},$$ where $C$ is some constant depending only on the domain $\mathcal D$. By [@FK Prop. X.4.5] the Bergman kernel on $\mathcal D$ is of the form $$K_{\mathcal D}(z,w) = \frac{1}{{\rm Vol}(D)} \cdot \det(K(z,w))^{-1} .$$ Let us first assume that $V$ is simple of rank $r$. Then $$k_V(z,w) = \det(K(z,w))^{\frac 1 r} = {\rm Vol}(D) \cdot K_{\mathcal D}(z,w)^{-\frac 1 r}.$$ In the general case we decompose $V = V_1 \oplus \dots \oplus V_n$ into simple ideals with $r_i := {\rm rk}(V_i)$ so that $r := {\rm rk}(V) = \sum r_i$. Now the Bergman kernel is multiplicative, i.e. we have $$K_{\mathcal D} = \prod_{i=1}^n K_{\mathcal D_i}.$$ Now the simple case yields $$k_{V_i}^{r_i} = {\rm Vol}(D_i)^{r_i} \cdot K_{\mathcal D_i}^{-1},$$ and thus by definition of $k_V$ we have $$\begin{aligned} k_V &=& \prod_{i=1}^n k_{V_i}^{\frac{r_i}{r}} = \left(\prod_{i=1}^n k_{V_i}^{r_i}\right)^{\frac{1}{r}}\\ &=& \left(\prod_{i=1}^n {\rm Vol}(D_i)^{r_i} \cdot K_{\mathcal D_i}^{-1} \right)^{\frac{1}{r}}\\ &=& \left(\prod_{i=1}^n {\rm Vol}(D_i)^{\frac{r_i}{r}}\right) \cdot K_{\mathcal D}^{-\frac 1 r}.\end{aligned}$$ Note that the relation to the Bergman kernel together with the normalization $k_V(0,0) = 1$ determines $k_V$ uniquely. Thus, while the definition of $k_V$ involves the Jordan algebra $V$ and thus the structure of $\mathcal D$ as a marked bounded symmetric domain, the above proposition shows that the result depends only on $\mathcal D$ as a bounded domain. Generalized cross ratios on Shilov boundaries {#SecGenCR} ============================================= In this section we use the normalized kernel functions defined in the last section in order to construct a family of generalized cross ratios on Shilov boundaries of bounded symmetric domains of tube type. In the first subsection we provide an axiomatic characterization of these generalized cross ratios. In the second subsection we give an explicit construction and show that this construction satisfies the desired axioms. The third subsection explains how to compute generalized cross ratios using maximal polydiscs. In the fourth subsection we deduce a number of cocycle properties of the generalized cross ratios. In the final subsection we express the generalized cross ratio in terms of Bergman kernels, thereby showing that it is independent of the marking of the bounded symmetric domain. The axiomatic approach ---------------------- Before we can define generalized cross ratios, we have to clarify, which properties these functions should have. We will thus collect in this subsection a number of axioms that our functions are supposed to satisfy. We will then see in the subsequent subsections that such functions exist and are in fact uniquely determined by the axioms. The object that we want to generalize is the classical four point cross ratio of hyperbolic geometry. Recall that the latter is defined on quadruples of mutually distinct points in ${\mathbb{C}}\mathbb P^1$ by the formula $$\begin{aligned} \label{ClassicalCR}[a:b:c:d] := \frac{(a-d)(c-b)}{(c-d)(a-b)}.\end{aligned}$$ This cross ratio restricts to a real-valued function on $(S^1)^{(4)}$, which is invariant under $PU(1,1)$. We would like to generalize this cross ratio from $S^1$ to the Shilov boundary $\check S_V$ of an arbitrary Euclidean Jordan algebra, that is, we would like to define a family of functions $$B_V: \check S_V^{(4)} \to {\mathbb{R}}^\times,$$ which are invariant under the respective groups $G_V$. Moreover, these generalized cross ratios should be related to each other. E.g. it would be nice to have $$\begin{aligned} \label{InvarianceB}B_W(\alpha(v_1),\alpha(v_2),\alpha(v_3) , \alpha(v_4)) = B_V(v_1, v_2,v_3, v_4)\end{aligned}$$ for any Jordan algebra homomorphism $\alpha: V \to W$ and $v_1, v_2,v_3, v_4 \in \check S_V$. This, however, is too much of wishful thinking. Firstly, we should not ask for arbitrary Jordan algebra homomorphism $\alpha: V \to W$ since these can be rather badly behaved, as we have seen before. Rather, as suggested by Theorem \[BalancingTheorem\], we should restrict to balanced homomorphism. Secondly, if we insist that our generalized cross ratio should be real-valued then we cannot define it on all of $\check S_V^{(4)}$. A posteriori, the following domain turns out to be the correct one: \[DefExtremal\] Let $V$ be a Euclidean Jordan algebra, $\mathcal D$ its bounded symmetric domain and $\check S$ the associated Shilov boundary. A quadruple $(a,b,c,d) \in \check S^{(4)}$ is called *extremal* if any triple $(x,y,z) \ \in \check S^3$ of pairwise distinct points with $x,y,z \in \{a,b,c,d\}$ is either maximal or minimal. We denote the set of extremal quadruples in $\check S^4$ by $\check S^{(4+)}$. Note that an extremal quadruple is contained in the Shilov boundary of a maximal polydisc by Proposition \[Quadruples\]. Now we can formulate the axioms, which the desired extension of the classical cross ratio should satisfy: \[UniversalCrossRatio\] There exists a unique system of functions $$\{B_V: \check S_{V}^{(4+)} \to {\mathbb{R}}^\times\,|\, V \text{ Euclidean Jordan algebra}\}$$ with the following properties: - If $\mathcal D_V$ is the bounded domain associated with $V$, then $B_V$ is $G(\mathcal D_V)_0$-invariant. - If $\alpha: V \to W$ is a balanced Jordan algebra homomorphism, $(v_1, \dots, v_4) \in \check S_{V}^{(4+)}$ and $(\alpha(v_1), \dots, \alpha(v_4)) \in \check S_{W}^{(4+)}$, then $$B_W(\alpha(v_1), \dots, \alpha(v_4)) = B_V(v_1, \dots, v_4).$$ - If $V = V_1 \oplus V_2$ is the sum of two ideals of ranks $r_1, r_2$ with projections $p_j: V \to V_j$ then $$B_V(v_1, \dots, v_4)^{r_1+r_2} = B_{V_1}(p_1(v_1), \dots, p_1(v_4))^{r_1}B_{V_2}(p_2(v_1), \dots, p_2(v_4))^{r_2}.$$ - $B_{{\mathbb{R}}}$ is the restriction of the classical four point cross ratio. Condition (iii) was added here, to rigidify the situation and to obtain uniqueness. It is unclear to us, whether it follows from the other three axioms. Explicit construction of generalized cross ratios ------------------------------------------------- The proof of Theorem \[UniversalCrossRatio\] is constructive, i.e. we will construct the functions $B_V$ explicitly. The functions $B_V$ extend to all of $\check S^{(4)}$ and these extensions are given as follows: \[LieJordanCrossRatio\] Let $V$ be a Euclidean Jordan algebra. Then the *cross ratio* of $V$ is the function $$B_V: \check S^{(4)} \to {\mathbb{C}}^\times$$ given by $$B_V(a,b,c,d) := \frac{k_V(d,a)k_V(b,c)}{k_V(d,c)k_V(b,a)}.$$ We claim that the cross ratios satisfy the conditions of Theorem \[UniversalCrossRatio\]. The proof of this fact will occupy the remainder of this section. We start by checking condition (iv): \[CRClassic\] Let $V = ({\mathbb{R}}, \cdot)$ so that $\check S = S^1$. By Example \[KernelDisc\] we have $k_{\mathbb{R}}(a,b)=1-a\bar b$. Then for four mutually distinct points $a,b,c,d \in S^1$ we have $$B_{\mathbb{R}}(a,b,c,d) = \frac{(1-d\bar a)(1-b\bar c)}{(1-d\bar c)(1-b\bar a)} = \frac{(a-d)(c-b)}{(c-d)(a-b)} = [a:b:c:d]$$ Condition (iii) follows directly from Proposition \[kVProjection\]. For the proofs of the remaining properties it will be useful to extend $B_V$ to a continuous function $$\begin{aligned} \label{BTilde}\widetilde{B}_V:\overline{\mathcal D}^{(4)} \to {\mathbb{C}}^\times, \quad (a,b,c,d) \mapsto \frac{k_V(d,a)k_V(b,c)}{k_V(d,c)k_V(b,a)},\end{aligned}$$ where $\overline{\mathcal D}^{(4)} := \mathcal D^4\cup \check S^{(4)}$. If $V$ is simple then by definition $\widetilde{B}_V$ is the unique continuous function satisfying $$\begin{aligned} \label{BTilde2}\widetilde{B}_V(a,b,c,d)^{2\dim V} = B_{V,\det}(a,b,c,d), \quad \widetilde{B}_V(0,0,0,0) = 1,\end{aligned}$$ where $$B_{V, \det}:\overline{\mathcal D}^{(4)} \to {\mathbb{C}}^\times, \quad (a,b,c,d) \mapsto \frac{k_{\det}(d,a)k_{\det}(b,c)}{k_{\det}(d,c)k_{\det}(b,a)}.$$ This characterized $\widetilde{B}_V$ and hence the restriction $B_V$ in the simple case, and the general case can be reduced to this situation using property (iii). Using this characterization we now prove: \[GInvariance\] Let $V$ be a Euclidean Jordan algebra. Then the cross ratio $B_V$ is $G$-invariant, i.e. for all $(a,b,c,d) \in \check S^{(4)}$ we have $$B_V(a,b,c,d) = B_V(ga,gb,gc,gd)\quad (g \in G).$$ Let us first assume that $V$ is simple. By Corollary \[ExtendKernelTransv\] we have $$k_{\det}(gz, gw) = j_{\det}(g,z)k_{\det}(z,w)\overline{j_{\det}(g,w)}$$ for all $g \in G$, $w,z \in \overline{\mathcal D}^{(2)}$. From this we obtain for all $g \in G$ and $(a,b,c,d) \in \mathcal D^4 \cup \check S^{(4)}$ the following relation: $$\begin{aligned} B_{V,\det}(ga,gb,gc,gd) &=& \frac{k_{\det}(gd,ga)k_{\det}(gb,gc)}{k_{\det}(gd,gc)k_{\det}(gb,ga)}\\ &=& \frac{j_{\det}(g,d)k_{\det}(d,a)\overline{j_{\det}(g,a)}j_{\det}(g,b)k_{\det}(b,c)\overline{j_{\det}(g,c)}}{j_{\det}(g,d)k_{\det}(d,c)\overline{j_{\det}(g,c)}j_{\det}(g,b)k_{\det}(b,a)\overline{j_{\det}(g,a)}}\\ &=& \frac{k_{\det}(d,a)k_{\det}(b,c)}{k_{\det}(d,c)k_{\det}(b,a)}\\ &=& B_{V,\det}(a,b,c,d).\end{aligned}$$ This shows $G$-invariance of $B_{V,\det}$. As a consequence, we obtain for all $g\in G$ $$\widetilde{B}_V(ga,gb,gc,gd)^{2 \dim V} = B_{V,\det}(ga,gb,gc,gd) = B_{V,\det}(a,b,c,d)$$ Since $\widetilde{B}_V(g.0, g.0, g.0, g.0) = 1$ and $\widetilde{B}_V$ is uniquely determined by , this implies $\widetilde{B}(ga,gb,gc,gd) = \widetilde{B}(a,b,c,d)$. Restricting to the Shilov boundary, we obtain the statement of the proposition for simple $V$. The general case is easily reduced to the simple case using Condition (iii). In order to deduce condition (ii) we make use of the equivalence of categories observed in Proposition \[CategoryEquivalence\]: Given a Jordan algebra homomorphisms $\alpha: V\to W$, there exists a group homomorphism $\alpha^\dagger: \widetilde{G}_V \to \widetilde{G}_W$ which is equivariant with respect to $\alpha^{\mathbb{C}}: \mathcal D_V \to \mathcal D_W$. (Here $\widetilde{G}_V, \widetilde{G}_W$ denote the universal coverings of $G_V$ and $G_W$.) In particular, given $g \in \widetilde{G}_V$ there exists $h \in \widetilde{G}_W$ such that for all $v \in \mathcal D_V$ $$\begin{aligned} \label{Equivariance1}\alpha^{\mathbb{C}}(gv) = h\alpha^{\mathbb{C}}(v).\end{aligned}$$ Since the actions of $\widetilde{G}_V, \widetilde{G}_W$ factor through the actions of $G_V$ and $G_W$ respectively that for every $g \in G_V$ there exists $h \in G_W$ such that holds for all $v \in V$. Now we can prove Condition (ii): If $(v_1, \dots, v_4)$ is extremal then by Proposition \[Quadruples\] we find $g \in G_V$ such that $gv_1, \dots, gv_4$ are diagonalized by a common Jordan frame $(c_1, \dots, c_r)$. Let $h \in G_W$ be an element such that holds for all $v \in V$. Using Proposition \[GInvariance\] and Theorem \[BalancingTheorem\] we now obtain $$\begin{aligned} B_V(v_1, \dots, v_4) &=& B_V(gv_1, \dots, gv_4)\\ &=& \frac{k_V(gv_4,gv_1)k_V(gv_2,gv_3)}{k_V(gv_4,gv_3)k_V(gv_2,gv_1)}\\ &=& \frac{k_W(\alpha^{\mathbb{C}}(gv_4),\alpha^{\mathbb{C}}(gv_1))k_W(\alpha^{\mathbb{C}}(gv_2),\alpha^{\mathbb{C}}(gv_3))}{k_W(\alpha^{\mathbb{C}}(gv_4),\alpha^{\mathbb{C}}(gv_3))k_W(\alpha^{\mathbb{C}}(gv_2),\alpha^{\mathbb{C}}(gv_1))}\\ &=& \frac{k_W(h\alpha^{\mathbb{C}}(v_4),h\alpha^{\mathbb{C}}(v_1))k_W(h\alpha^{\mathbb{C}}(v_2),h\alpha^{\mathbb{C}}(v_3))}{k_W(h\alpha^{\mathbb{C}}(v_4),h\alpha^{\mathbb{C}}(v_3))k_W(h\alpha^{\mathbb{C}}(v_2),h\alpha^{\mathbb{C}}(v_1))}\\ &=&B_W(h\alpha(v_1), \dots, h\alpha(v_4))\\ &=& B_W(\alpha(v_1), \dots, \alpha(v_4)).\end{aligned}$$ This shows that the cross ratios satisfy Conditions (i) - (iv) of Theorem \[UniversalCrossRatio\]. Conversely, these conditions determine the family $\{B_V\}$: Any $(a,b,c,d) \in \check S^{(4+)}$ is contained in the boundary of a maximal polydisc by Proposition \[Quadruples\]. Since the embedding of a maximal polydisc is balanced, the family $\{B_V\}$ is uniquely determined by the family $\{B_{{\mathbb{R}}^r}\}$. Finally, condition (iii) implies that $$B_{{\mathbb{R}}^r}(a,b,c,d)^r = \prod B_{\mathbb{R}}(a_j, b_j, c_j, d_j).$$ The right hand side is uniquely determined by (iv). If we denote by $\alpha: {\mathbb{R}}\to {\mathbb{R}}^r$ the diagonal embedding, then $\alpha$ is balancing and therefore $$B_{{\mathbb{R}}^r}(0,0,0,0) = B_{{\mathbb{R}}^r}(\alpha(0), \dots, \alpha(0))= B_{\mathbb{R}}(0,0,0,0),$$ and again the latter is determined by (iv). The last two equations determine $\{B_{{\mathbb{R}}^r}\}$ uniquely. The uniqueness of the whole system $\{B_V\}$ follows.\ Thus we have proved Theorem \[UniversalCrossRatio\] up to the claim that the cross ratio is real-valued on $\check S^{(4+)}$. This latter fact will be proved in the next subsection, where we also provide techniques to compute the cross ratio effectively. Computation of generalized cross ratios --------------------------------------- Let $V$ be a Euclidean Jordan algebra and $(a,b,c,d) \in \check S^{(4+)}$. The aim of this subsection is to provide an effective way to compute $B_V(a,b,c,d)$. As a byproduct we will see that $B_V(a,b,c,d) \in {\mathbb{R}}$, thereby finishing the proof of Theorem \[UniversalCrossRatio\]. As a first step we apply Proposition \[Quadruples\] in order to find a polydisc whose Shilov boundary contains $(a,b,c,d)$. Actually, the proof of the proposition shows slightly more: Let us assume that $(a,b,c)$ is maximal. Then we can find $g \in G$ and a Jordan frame $(c_1, \dots, c_r)$ of $V$ such that $$g.(a,b,c,d) = (-e,-ie,e, \sum_{j=1}^r\lambda_j c_j).$$ By Property (iii) of Theorem \[UniversalCrossRatio\] we thus have $$B_V(a,b,c,d) = B_{{\mathbb{R}}^r}(-e,-ie,e, \lambda).$$ We may therefore assume $V = {\mathbb{R}}^r$ and $(a,b,c) = (-e,-ie, e)$ provided $(a,b,c)$ is maximal. If $(a,b,c)$ is minimal rather than maximal, then we may assume $(a,b,c) = (e, -ie,-e)$ by the same argument. In the remainder of this section we will always assume $(a,b,c) = (-e,-ie,e)$; the minimal case can be treated accordingly. Since $(-e,-ie, e, \lambda)$ is assumed extremal, the possible values of $\lambda$ are seriously restricted: Indeed, $(-1, \lambda_j, 1)$ is positive iff $\lambda_j$ is contained in the lower half-circle and negative, iff $\lambda_j$ is contained in the upper half-circle. Since $(-e, \lambda, e)$ is either maximal or minimal we see that either $\lambda_j$ is contained in the lower half-circle for all $j = 1, \dots, r$ or in the upper half-circle for all $j = 1, \dots, r$. Correspondingly, let us call $\lambda$ *positive* or *negative*. In the positive case, all the $\lambda_j$ are contained in a fixed quarter circle. This special position of $\lambda$ allows us now to compute $B_{V}(-e,-ie, e, \lambda)$ as follows: Let $\tilde B_V$ as in . Given $a \in \overline{\mathbb D^r}$ we write $a_j$ for its $j$-th component. Now let $(a, b,c, d) \in \overline{\mathbb D^r}^{(4)}$. We have $$\begin{aligned} \label{PdCrossPower}\widetilde{B}_V(a, b, c, d)^r = \frac{k_V(d,a)^r k_V(b,c)^r}{k_V(d,c)^r k_V(b,a)^r} = \prod_{j=1}^r [a_j:b_j: c_j: d_j]\end{aligned}$$ and $$\begin{aligned} \label{PdCrossNormalization}\widetilde{B}_V(0,0,0,0) = 1.\end{aligned}$$ Moreover, $\widetilde{B}_V$ is uniquely determined by and . From this we obtain the following result almost immediately: \[DullRoot\] If $\lambda_1 = \dots = \lambda_r$, then $$B_{{\mathbb{R}}^r}(-e, -ie,e, \lambda) = [-1:-i:1:\lambda_1].$$ The curve ${\varphi}(t) := (-te, -ite,te, t\lambda)$ connects $(0,0,0,0)$ and $(-e, -ie,e, \lambda)$. Since $$\widetilde{B}_{V}({\varphi}(t))^r = B_{\mathbb{R}}(-t:-it:t:\lambda_1t)^r$$ and both functions agree at $0$, we see that $$B_{V}(-e, -ie,e, \lambda) =\widetilde{B}_{V}({\varphi}(1)) = B_{\mathbb{R}}(-1:-i:1:\lambda_1) = [-1:-i:1:\lambda_1].$$ Although the situation of Lemma \[DullRoot\] is very special, the general case can now be reduced to it. Indeed we have: The cross-ratio $B_{{\mathbb{R}}^r}$ is real-valued on $((S^1)^r)^{(4+)}$. More precisely, $B_{{\mathbb{R}}^r}(-e, -ie,e, \lambda)$ is positive/negative iff $\lambda$ is positive/negative. Consider the function $f: (S^1 \setminus\{-1,-i,1\})^r \to S^1$ given by $$f(\lambda) :=\frac{B_{{\mathbb{R}}^r}(-e, -ie,e, \lambda)}{|B_{{\mathbb{R}}^r}(-e, -ie,e, \lambda)|}.$$ We have $f(\lambda)^r \in {\mathbb{R}}\cap S^1 = \{\pm 1\}$, hence $f$ takes values in the set $R_{2r}$ of $2r$-th roots of unity. Since $R_{2r}$ is discrete and $f$ is continuous, $f$ must be locally constant. In particular, if $\lambda$ and $\mu$ are contained in the same connected component of $(S^1 \setminus\{-1,-i,1\})^r$ and $B_{{\mathbb{R}}^r}(-e, -ie,e, \mu)$ is a positive/negative real number, then the same is true for $B_{{\mathbb{R}}^r}(-e, -ie,e, \lambda)$. Combining this with Lemma \[DullRoot\] we obtain the proposition. Since admits precisely one positive/negative $r$-th real root, this determines the cross ratio. To summarize our discussion, let us call an extremal quadruple $(a,b,c,d)$ *positive/negative* if it is conjugate to $B_{{\mathbb{R}}^r}(-e, -ie,e, \lambda)$ for some positive/negative $\lambda$. Then we obtain the following formula for $B_{{\mathbb{R}}^r}$: \[TrueRoot\] Suppose $(a,b,c)$ is maximal and $(a,b,c,d) \in ((S^1)^r)^{(4+)}$. Then $$B_{{\mathbb{R}}^r}(a,b,c,d) = \epsilon(a,b,c,d) \cdot \sqrt[r]{\left|\prod_{j=1}^r [a_j:b_j: c_j: d_j]\right|},$$ where $$\epsilon(a,b,c,d) = \left\{\begin{array}{ll}+1 & (a,b,c,d)\text{ positive}\\ -1 & (a,b,c,d)\text{ negative}\end{array}\right.$$ In the case, where $(a,b,c,d)$ is positive, there are two possibilities for $d$: Either, each $d_j$ lies in between $a_j$ and $b_j$ or between $b_j$ and $c_j$. This corresponds to the cases of $(a,d,b)$ or $(b,d,c)$ being maximal. These two cases can be distinguished by the cross ratio as follows: If $(a,b,c)$ and $(a,d,b)$ are maximal, then $0 < B_{{\mathbb{R}}^r}(a,b,c,d) < 1$. If $(a,b,c)$ and $(b,d,c)$ are maximal, then $B_{{\mathbb{R}}^r}(a,b,c,d) > 1$. The assumptions imply $0 < [a_j: b_j: c_j: d_j] < 1$, respectively $[a_j: b_j: c_j: d_j] >1$ for each $j$, hence the lemma follows from the explicit formula in Corollary \[TrueRoot\]. In particular we obtain: \[RangeofCR\] For every Euclidean Jordan algebra $V$ with associated Shilov boundary $\check S$ we have $B_V(\check S^{(4+)}) = {\mathbb{R}}\setminus \{0,1\}$. Let $(a,b,c,d) \in \check S^{(4+)}$. If $(a,b,c)$ is maximal, then depending on $d$ we have either $B_{{\mathbb{R}}^r}(a,b,c,d) < 0$ (if $(a,b,c,d)$ is negative) or $B_{{\mathbb{R}}^r}(a,b,c,d) < 1$ (if $(a,d,b)$ is maximal) or $B_{{\mathbb{R}}^r}(a,b,c,d) > 1$ (if $(b,d,c)$ is maximal). If $(a,b,c)$ is minimal one may argue similarly (or reduce to the former case by means of the cocycle properties to be proved below). This shows the inclusion $\subset$. For the converse inclusion, it suffices to see that $B_{\mathbb{R}}$ is onto ${\mathbb{R}}\setminus \{0,1\}$ and ${\mathbb{R}}$ has a balanced embedding into every Euclidean Jordan algebra. The reason that the cross ratio is not onto ${\mathbb{R}}$ is due to our choice of domain. In fact, we can extend $B_V$ continuously to the slightly larger domain $\check S^{4*}$ which is defined as follows: $\check S^{4*}$ contains $\check S^{(4+)}$ and $(a,b,c,d)$ is contained in $\check S^{4*} \setminus \check S^{(4+)}$ iff $$(a = c) \vee (b=d) \vee (b=a) \vee(c=b)$$ and moreover $\{a,b,c,d\}$ contains a maximal triple. This implies in particular that at most two of $a,b,c,d$ coincide and the non-coinciding pairs are transverse. Recall that the normalized kernel function $k_V$ extends to all of $\check S$ and satisfies $k_V(a,b ) \neq 0$ iff $a \pitchfork b$. Thus $$B_V(a,b,c,d) := \frac{k_V(d,a)k_V(b,c)}{k_V(d,c)k_V(b,a)}$$ is well-defined as long as $d \pitchfork c$ and $b \pitchfork a$. In particular, $B_V$ extends continuously to $\check S^{4*}$. We denote this extension by the same letter. Then we have: \[Special01\] The cross ratio $B_V: \check S^{4*} \to {\mathbb{R}}$ is onto. Moreover, $$\begin{aligned} x=z \text{ or } y=t &\Leftrightarrow& B_V(x,y,z,t)=1\\ t=x \text{ or } z=y &\Leftrightarrow& B_V(x,y,z,t)=0.\end{aligned}$$ If $x=z$ or $y=t$ then enumerator and denominator coincide, whence $B_V(x,y,z,t)=1$. If $y=x$ or $z=t$ then one of the two terms in the enumerator vanishes. In any other case we have $(x,y,z,t) \in \check S^{(4+)}$, hence $B_V(x,y,z,t) \not \in \{0,1\}$. This proves the converse direction. Cocycle properties ------------------ Generalized cross ratios satisfy various cocycle properties. The key observation for the proof of this fact is the following lemma: \[CocycLemma\] If $X$ is a set and $k: X^2 \to {\mathbb{C}}^*$ is an arbitrary function then $$b:\begin{cases} X^4\rightarrow {\mathbb{C}}^*\\ (a,b,c,d) \mapsto\frac{k(d,a)k(b,c)}{k(d,c)k(b,a)} \end{cases}$$ has the following properties: $$\begin{aligned} b(a,b,c,d)&=&b(c,d,a,b) \label{b1}\\ b(a,b,c,d)&=&b(a,b,c,e)b(a,e,c,d) \label{b2}\\ b(a,b,c,d)&=&b(a,b,e,d)b(e,b,c,d) \label{b3}\end{aligned}$$ We have $$\begin{aligned} b(c,d,a,b) &=& \frac{k(b,c)k(d,a)}{k(b,a)k(d,c)}\\ &=&\frac{k(d,a)k(b,c)}{k(d,c)k(b,a)}\\ &=& b(a,b,c,d).\end{aligned}$$ Moreover, $$\begin{aligned} b(a,b,c,e)b(a,e,c,d)&=&\frac{k(e,a)k(b,c)}{k(e,c)k(b,a)}\frac{k(d,a)k(e,c)}{k(d,c)k(e,a)}\\ &=& \frac{k(d,a)k(b,c)}{k(d,c)k(b,a)}\\ &=&b(a,b,c,d)\end{aligned}$$ and $$\begin{aligned} b(a,b,e,d)b(e,b,c,d)&=&\frac{k(d,a)k(b,e)}{k(d,e)k(b,a)}\frac{k(d,e)k(b,c)}{k(d,c)k(b,e)}\\ &=& \frac{k(d,a)k(b,c)}{k(d,c)k(b,a)}\\ &=&b(a,b,c,d).\end{aligned}$$ Since the normalized kernel $k$ is only partially defined, this does not directly apply. Still we have: \[BVCocyc\] The cross ratio $B_V: \check S^{4*} \to {\mathbb{R}}$ satisfies - above, whenever both sides of the equation are well-defined. Again we can easily reduce to the case, where $V$ is simple. In this case we can apply Lemma \[CocycLemma\] to the function $k_V|_{\mathcal D^2}$. By continuity, the relations extend to $\check S^{(4)}$. We also have the following property: \[StrangeCocycle\] For all $(a,b,c,d) \in \check S^{(4*)}$ we have $$B_V(a,b,c,d) = B_V(b,a,d,c).$$ We first do a number of reduction steps. Since $B_V(a,b,c,d) \in {\mathbb{R}}$ for $(a,b,c,d) \in \check S^{(4*)}$ it suffices to show that $$\overline{B_V(a,b,c,d)} = B_V(b,a,d,c).$$ We shall prove the latter statement for $\widetilde{B}_V$ and $(a,b,c,d) \in \mathcal D^4$. The statement for $(a,b,c,d) \in \check S^{(4+)}$ will then follow by continuity. Using Property (iii) of Theorem \[UniversalCrossRatio\] we may assume that $V$ is simple. Moreover, since the desired symmetry is preserved by passing to a power, it suffices to show that $$\overline{B_{V, \det}(a,b,c,d)} = B_{V, \det}(b,a,d,c)\quad((a,b,c,d) \in \mathcal D^4),$$ By [@CO2] we have $$K^*(z,w) = K(w,z)$$ and thus $$\overline{k_{\det}(z,w)} = k_{\det}(w,z)$$ for all $w, z \in \mathcal D$. In particular, for $(a,b,c,d) \in \mathcal D^4$ we deduce $$\begin{aligned} \overline{B_{V, \det}(a,b,c,d)} &=& \frac{\overline{k_{\det}(d,a)}\cdot\overline{k_{\det}(b,c)}}{\overline{k_{\det}(d,c)}\cdot\overline{k_{\det}(b,a)}}\\ &=& \frac{k_{\det}(a,d)k_{\det}(c,b)}{k_{\det}(c,d)k_{\det}(a,b)}\\ &=& \frac{k_{\det}(c,b)k_{\det}(a,d)}{k_{\det}(c,d)k_{\det}(a,b)}\\ &=& B_{V, \det}(a,b,c,d).\end{aligned}$$ The Bergman cross ratio and the proof of Theorem \[Main\] {#SubsecProofMain} --------------------------------------------------------- Given any bounded symmetric domain we can find a Euclidean Jordan algebra $V$ such that $\mathcal D = \mathcal D_V$. We then obtain a generalized cross ratio $B_V$ on the Shilov boundary $\check S$ of $\mathcal D$. The Jordan algebra $V$, however, is not unique; it corresponds to a choice of a marking on the bounded symmetric domain $\mathcal D$. In order to deduce Theorem \[Main\] from Theorem \[UniversalCrossRatio\] we need to show that $B_V$ is actually independent of this choice and depends only on $\mathcal D$. Now for any complex domain $\mathcal C$ the corresponding Bergman kernel $K_{\mathcal C}$ can be used in order to define a Bergman cross ratio $$B_{\mathcal C}: \mathcal C^4 \to {\mathbb{C}}^\times, \quad (x,y,z,t)\mapsto\frac{K_\mathcal C(t,x)^{-1}K_\mathcal C(y,z)^{-1}}{K_\mathcal C(t,z)^{-1}K_\mathcal C(y,x)^{-1}} = \frac{K_\mathcal C(t,z)K_\mathcal C(y,x)}{K_\mathcal C(t,x)K_\mathcal C(y,z);}$$ in the case of a bounded symmetric domain $\mathcal D$ associated with a Euclidean Jordan algebra $V$ Proposition \[BergmanComparison\] yields $\widetilde{B_V}^{\operatorname{rk}V} = B_{\mathcal D}$, where $\widetilde{B_V}$ is the extension of $B_V$ as in . In particular, $B_{\mathcal D}$ determines $\widetilde{B_V}$ on $\mathcal D^4$, and thus by continuity also $B_V$. This shows that $B_V$ depends only on $\mathcal D$ and thus proves Theorem \[Main\]. We can also use the above description of $\widetilde{B_V}$ in terms of the Bergman kernel in order to obtain the following invariance property of $\widetilde{B_V}$: \[BergmanCrossInvariance\] Let $\mathcal C$ be a complex domain and $c: \mathcal D \to C$ be a biholomorphism. Then for all $(x,y,z,t) \in \mathcal D^{4}$ we have $$\widetilde{B_V}(x,y,z,t)^{\operatorname{rk}V} = B_{\mathcal C}(c(x), c(y), c(z), c(t)).$$ Since $\widetilde{B_V}(x,y,z,t)^{\operatorname{rk}V} = B_{\mathcal D}(x,y,z,t)$ it suffices to show that $$B_{\mathcal D}(x,y,z,t) = B_{\mathcal C}(c(x), c(y), c(z), c(t)).$$ For this we apply [@FK Prop. IX.2.4] in order to relate the Bergman kernels on $\mathcal D$ and $\mathcal C$. Denote by $J_c$ the complex Jacobi matrix of $c$. Then $$K_{\mathcal D}(z,w) = K_{\mathcal C}(c(z), c(w))\det{}_{\mathbb{C}}(J_c(z))\overline{\det{}_{\mathbb{C}}(J_c(w))}.$$ Hence $$\begin{aligned} B_{\mathcal D}(x,y,z,t) &=& \frac{K_\mathcal D(t,z)K_\mathcal D(y,x)}{K_\mathcal D(t,x)K_\mathcal D(y,z)}\\ &=& \frac{K_{\mathcal C}(c(t),c(z))\det{}_{\mathbb{C}}(J_c(t))\overline{\det{}_{\mathbb{C}}(J_c(z))}}{K_{\mathcal C}(c(t),c(x))\det{}_{\mathbb{C}}(J_c(t))\overline{\det{}_{\mathbb{C}}(J_c(x))}}\\ && \cdot \frac{K_{\mathcal C}(c(y),c(x))\det{}_{\mathbb{C}}(J_c(y))\overline{\det{}_{\mathbb{C}}(J_c(x))}}{K_{\mathcal C}(c(y),c(z))\det{}_{\mathbb{C}}(J_c(y))\overline{\det{}_{\mathbb{C}}(J_c(z))}}\\ &=& \frac{K_{\mathcal C}(c(t),c(z))K_{\mathcal C}(c(y),c(x))}{K_{\mathcal C}(c(t),c(x))K_{\mathcal C}(c(y),c(z))}\\ &=& B_{\mathcal C}(c(x), c(y), c(z), c(t)).\end{aligned}$$ Maximal representations, limit curves and strict cross ratios {#SecMaxRep} ============================================================= In this section we explain how the generalized cross ratio functions defined above can be used to associate with any maximal representation into a Hermitian group of tube type a strict cross ratio in the sense of [@Lab05]. We then prove that all strict cross ratios are equivalent in a sense made precise in Proposition \[PropLab\]. The latter result is essentially contained, but not stated in [@Lab05], where it is presented in the context of a more general theory of adapted flows. The proof we give here avoids this machinery and tries to be more elementary. The cross ratio of a maximal representation ------------------------------------------- Returning to the problem of the introduction, let $\Sigma$ be a closed, oriented surface of genus $g\geq 2$ with fundamental group $\Gamma$. We fix a hyperbolization of $\Sigma$, i.e. a faithful homomorphism $\Gamma \to PU(1,1)$ with discrete image so that $\Sigma = \Gamma\backslash \mathbb D$. We also fix a Euclidean Jordan algebra $V$ and denote by $\mathcal D$ and $\check S$, respectively the associated bounded symmetric domain and Shilov boundary. The groups $G, K, L, Q_+$ are defined as before. The aim of this section is to construct an invariant associated with a maximal representation $\varrho:\Gamma \rightarrow G$. Our basic references concerning maximal representations are [@Surface] and [@Anosov]. Let us briefly recall the main definitions: Denote by $\omega_{\mathcal D}$ the Kähler form on $\mathcal D$ associated with the metric of minimal holomorphic sectional curvature $-1$. Given an arbitrary $\rho$-equivariant map $f: \mathbb D \to \mathcal D$ we define the *Toledo invariant* $T_{\varrho}$ of $\rho$ by $$T_\varrho:=\frac{1}{2\pi} \int_{\Sigma}f^*\omega_{\mathcal{D}}.$$ This does not depend on the choice of $f$. The Toledo invariant satisfies a generalized Milnor-Wood inequality, in the present normalization given by $$\begin{aligned} \label{MW}|T_\varrho|\leq |\chi(\Sigma)|\cdot \operatorname{rk}(V).\end{aligned}$$ Accordingly, the representation $\varrho$ is called *maximal* if $T_\varrho = |\chi(\Sigma)|\cdot \operatorname{rk}(V)$. Every maximal representation $\varrho:\Gamma\rightarrow G$ defines a canonical *limit curve*, i.e. an injective continuous $\varrho$-equivariant map $\varphi: S^1 \to \check S$. Since these limit curves play a crucial role in our construction and for lack of suitable references, we briefly digress to explain their construction:\ First consider a maximal representation $\varrho:\Gamma\rightarrow G$ with Zariski-dense image. In this case, a $\varrho$-equivariant injective map ${\varphi}: S^1 \to \check S$ is constructed in [@Rigidity Ch.7], and by [@Anosov] this map is continuous. We claim that ${\varphi}$ is in fact the unique limit curve ${\varphi}: S^1 \to \check S$ for $\varrho$. Indeed, $S^1$ is the closure of any of its $\Gamma$-orbit, and since $\varphi$ is continuous and $\varrho$-equivariant, this implies that $\varphi(S^1)$ is a minimal closed $\Gamma$-invariant subset of $\check S$. Now the first lemma in Section 3.6 of [@Benoist] applies to show that $\varphi(S^1) = \Lambda_\Gamma$, where the latter denotes is the limit set of $\Gamma$ in $\check S$. This implies in particular, that any other limit curve $S^1 \to \check S$ has to intersect ${\varphi}$. The uniqueness of ${\varphi}$ then follows from the following lemma: Let $\varphi_1, \varphi_2: S^1\rightarrow \check S$ be two limit curves for the same maximal representation $\varrho$ with $\varphi_1(S^1) \cap \varphi_2(S^1) \neq \emptyset$. Then $\varphi_1 = \varphi_2$. By equivariance of the $\varphi_j$ the intersection contains a $\Gamma$-orbits, but since the $\Gamma$-action on $S^1$ is minimal this implies that this preimage is the full circle and thus $\varphi_1(S^1) = \varphi_2(S^1)$. Every $\gamma \in \Gamma$ has a unique attractive fixed point $\gamma^+$ in $S^1$. By equivariance, this is mapped under both $\varphi_j$ to the unique attractive fixed point of $\rho(\gamma)$ in $\varphi_1(S^1) = \varphi_2(S^1)$. We deduce $\varphi_1(\gamma^+) = \varphi_2(\gamma^+)$ for all $\gamma \in \Gamma$ and since $\{\gamma^+\,|\, \gamma \in \Gamma\}$ is dense in $S^1$ we deduce that $\varphi_1 = \varphi_2$. Thus we have proved: \[LCZariskiUnique\] If $\varrho:\Gamma\rightarrow G$ is a Zariski-dense maximal representation, then there exists a unique limit curve $\varphi: S^1 \to \check S$ for $\varrho$. If we drop the assumption of Zariski-dense image, then Corollary \[LCZariskiUnique\] fails. Indeed, if $\varphi$ is a limit curve for $\varrho$ and $g \in C_G(\varrho(\Gamma))$, then $g\varphi$ is again a limit curve for $\varrho$. We therefore cannot hope for a unique limit curve in general. Still, there is an explicit construction for a canonical limit curve, which we now describe: For this let $\varrho:\Gamma \rightarrow G$ be an arbitrary maximal representation, and denote by $H$ the Zariski-closure of $\varrho(\Gamma)$ in $G$. It follows from [@Surface Thm. 5] that $H$ is of tube type. Then $\varrho$ factors as $\varrho=\iota \circ \varrho'$, where $\iota: H \to G$ is the inclusion and $\varrho': \Gamma \to H$ is a maximal representation with Zariski dense image. In particular, there is a unique limit curve $\varphi': S^1 \to \check S_H$ for $\varrho'$. In order to extend this limit curve to a limit curve for $\varrho$ we observe that by the general structure theory of maximal representations developed in [@Surface], the embedding $\iota$ is *tight* in the sense of [@Tight]. Then [@Tight Thm 4.1] implies that a $\iota$-equivariant map $\widehat{\iota}: \check S_H \to \check S_G$ can be constructed as follows: Denote by ${\mathcal{D}}_H$ and ${\mathcal{D}}_G$ the symmetric spaces of $H$ and $G$ respectively and choose a basepoint $p \in {\mathcal{D}}_G$. Then ${\rm Stab}_H(p)$ and hence $\iota({\rm Stab}_H(p))$ are compact, whence $\iota({\rm Stab}_H(p))$ is contained in a maximal compact subgroup of $G$. We thus find $x \in G$ with ${\rm Stab}_G(x)\supset \iota {\rm Stab}_H(p)$. Given $p$ and $x$ we define a $\iota$-equivariant continuous, totally geodesic map $$\begin{aligned} \label{fLC}f: {\mathcal{D}}_H \to {\mathcal{D}}_G, \quad g\cdot p\mapsto \iota(g)x.\end{aligned}$$ Now every point $\xi \in \check S_H$ can be represented uniquely by a geodesic ray $\sigma$ emanating from $p$. Then $f\circ \sigma$ is a geodesic ray in ${\mathcal{D}}_G$, which by the results in [@Tight Chapter 4] ends in some point $\widehat{\iota}(\xi) \in \check S_G$. This yields the desired continuous $\iota$-equivariant embedding $\widehat{\iota}: \check S_H \to \check S_G$, and we can define the limit curve $\varphi$ of $\varrho$ by $\varphi := \widehat{\iota} \circ \varphi'$.\ A priori the above construction of $\widehat{\iota}$ depends on the choices of basepoints $p$ and $x$. In order to obtain a canonical limit curve $\varphi$ we have to show that $\widehat{\iota}$ is *a posteriori* independent of these choices. We show the independence of $x$ first: Suppose $y \in {\mathcal{D}}_G$ is another base point with ${\rm Stab}_G(y)\supset \iota {\rm Stab}_H(p)$. Then for any $g \in G$ we have $$d(\iota(g)x,\iota(g)y)=d(x,y).$$ Since the geodesics through $p$ in ${\mathcal{D}}_H$ are of the form $\sigma(t) = \exp(tX)p$ this implies that the images of a geodesic in ${\mathcal{D}}_H$ under the two maps $f_x$ and $f_y$ corresponding to $x$ and $y$ respectively are at bounded distance, hence define the same point in the Shilov boundary. This shows that $\widehat{\iota}$ is independent of the choice of $x$ once $p$ is given. Now let us prove independence of $p$: For this we suppose that two points $p, p' \in {\mathcal{D}}_H$ are given. We then find $h_0 \in H$ such that $p' = h_0p$. Now let $x \in {\mathcal{D}}_G$ such that ${\rm Stab}_G(x)\supset \iota({\rm Stab}_H(p))$. Then $p$ and $x$ determine a map $f: {\mathcal{D}}_H \to {\mathcal{D}}_G$ by . Similarly, given $x' \in {\mathcal{D}}_G$ with ${\rm Stab}_G(x')\supset \iota({\rm Stab}_H(p'))$ we obtain a map $f': {\mathcal{D}}_H \to {\mathcal{D}}_G$ by $f'(hp') := hx'$. We have to show that $f$ and $f'$ induce the same map $\widehat{\iota}$ of Shilov boundaries. By the previous considerations we may choose $x' \in {\mathcal{D}}_G$ arbitrary subject to the condition ${\rm Stab}_G(x')\supset \iota({\rm Stab}_H(p'))$; in particular we may chose $x' = \rho(h_0).x$. But with this choice of $x'$ the maps $f$ and $f'$ coincide. This proves that $\widehat{\iota}$ and consequently $\varphi$ do not depend on any of the choices made to define them. We may thus refer to $\varphi$ as the *canonical* limit curve of $\varrho$. This canonical limit curve has the following key property: \[LCExistence\] Let $\varrho: \Gamma \to G$ be a maximal representation and $$\varphi:S^1\rightarrow \check S$$ the canonical limit curve of $\varrho$. Then for every positively/negatively oriented triple $(x,y,z)\in (S^1)^{(3)}$, the triple $(\varphi(x),\varphi(y),\varphi(z))$ is maximal/minimal. We deduce from the proposition that two distinct points $x\neq y\in S^1$ are mapped to transverse points under every limit curve. As another consequence of Proposition \[LCExistence\] we deduce that $\varphi$ induces an injective map $${\varphi}^{(4)}: (S^1)^{4*} \to \check S_{V}^{4*}, \quad (x,y,z,t) \mapsto ({\varphi}(x),{\varphi}(y),{\varphi}(z),{\varphi}(t)),$$ where $$(S^1)^{4*} := \{(x,y,z,t) \in (S^1)^4\,|\, x\neq t, y\neq z\}.$$ \[DefCR\] Let $\rho: \Gamma \to G$ be a maximal representation and $\varphi: S^1 \to \check S$ the associated canonical limit curve. Then the function $$\begin{aligned} b_\rho := ({\varphi}^{(4)})^*B_V: (S^1)^{4*} \to {\mathbb{R}}, \quad (x,y,z,t) \mapsto B_V({\varphi}(x),{\varphi}(y),{\varphi}(z),{\varphi}(t)).\end{aligned}$$ is called the *cross ratio of the maximal representation $\varrho$*. The main properties of cross ratios of maximal representations are collected in the following theorem: \[CRStrict\] The cross ratio $b_\rho: (S^1)^{4*} \to {\mathbb{R}}$ is a continuous $\Gamma$-invariant function satisfying the following properties: $$\begin{aligned} b_{\rho}(x,y,z,t)&=&b_{\rho}(z,t,x,y) \label{a1}\\ b_{\rho}(x,y,z,t)&=&b_{\rho}(x,y,z,w)b_{\rho}(x,w,z,t) \label{a2}\\ b_{\rho}(x,y,z,t)&=&b_{\rho}(x,y,w,t)b_{\rho}(w,y,z,t) \label{a3}\\ x=z \text{ or } y=t &\Leftrightarrow& b_{\rho}(x,y,z,t)=1 \label{a4}\\ t=x \text{ or } z=y &\Leftrightarrow& b_{\rho}(x,y,z,t)=0 \label{a5}\end{aligned}$$ $\Gamma$-invariance on $(S^1)^{(4)}$ follows from $G$-invariance of $B_V$ on $S^{(4+)}$ (i.e. Property (i) of Theorem \[UniversalCrossRatio\]). By continuity we obtain $\Gamma$-invariance on all of $(S^1)^{4*}$. By a similar extension argument, Properties - follow from Corollary \[BVCocyc\]. Finally, Properties - follow from Proposition \[Special01\]. In fact, it follows from Corollary \[StrangeCocycle\] that $b_\rho$ also satisfies $$b_\rho(x,y,z,t) = b_\rho(y,x,t,z).$$ However, we are not going to use this property in the sequel. Instead let us focus on the properties mentioned in Theorem \[CRStrict\]. In the language of [@Lab05] the theorem says precisely that $b_\rho$ is a *strict cross ratio*. In the next subsection we shall recall some general properties of such strict cross ratios. Strict cross ratios ------------------- In this subsection we collect basic properties of strict cross ratios, i.e. continuous $\Gamma$-invariant functions on $(S^1)^{4*}$ satisfying - above. The material is adapted from [@Lab05]. Let $b: (S^1)^{4*} \to {\mathbb{R}}$ be any strict cross ratio. We will ocassionally use the following two cocycle identities: $$\begin{aligned} \label{p1} b(x,y,x,t)&=&b(x,y,z,t)b(z,y,x,t)=1\\ \label{p2} \log b(x,y,z,t)&=&-\log b(z,y,x,t)\end{aligned}$$ The former is an immediate consequence of and and the latter follows by applying the logarithm. We will usually consider $x,y,z$ fixed and study $g(t)=b(x,y,z,t)$ as a function of $t$. Let us assume that $(x,y,z)$ is positively oriented. We then divide the circle into three open disjoint intervals $I_1=(x,y)$, $I_2=(y,z)$ and $I_3=(z,x)$ so that $$S^1 = \{x\} \cup I_1 \cup \{y\} \cup I_2 \cup\{z\} \cup I_3.$$ The function $g$ is then defined on $S^1 \setminus \{z\}$. By Axiom , $x$ is the only zero of $g$. Since $g(y)=1$ is positive, $g$ is positive on $I_u:=I_1\cup \{y\} \cup I_2$. Let $a,b\in I_u$ such that $g(a)=g(b)$. Then we have: $$1=g(a)g(b)^{-1}=b(x,y,z,a)b(x,y,z,b)^{-1}=b(-1,a,1,b),$$ but by Axiom this can only be the case if $a=b$. Hence $g|_{I_u}$ is injective. Furthermore, by Axiom and we have $$\underset{t \in I_u}{\lim_{t\rightarrow z}} g(t)=\underset{t \in I_u}{\lim_{t\rightarrow z}}b(z,y,x,t)^{-1}= +\infty.$$ Since $g(x) = 0$ the intermediate value theorem implies that $g|_{I_u}$ is surjective and therefore defines a homeomorphism between $I_u$ and $(0,\infty)$. Now consider the case $t\in I_3$. We claim that $g(t)$ is negative on $I_3$. For this we first observe that as above $$\underset{t \in I_u}{\lim_{t\rightarrow z}} g(t) \in \{\pm \infty\}.$$ Again, since $g(x) = 0$ the intermediate value theorem implies that $g$ maps $I_3$ homeomorphically to either $(0, \infty)$ or $(-\infty,0)$. However, the former would imply the existence of $t_0 \in I_3$ with $g(t_0) = 1$, which contradicts Axiom . Hence $$\underset{t \in I_u}{\lim_{t\rightarrow z}} g(t) = -\infty$$ and $g$ maps $I_3$ homeomorphically to $(-\infty,0)$. We have proved: \[StrictCrHomeo\] If $(x,y,z)$ is a positively oriented triple on $S^1$ and $b: (S^1)^{4*} \to {\mathbb{R}}$ is a strict cross ratio, then $$g: S^1 \setminus\{z\} \to {\mathbb{R}}, \quad t\mapsto b(x,y,z,t)$$ is a homeomorphism with $g(x) = 0$. Notice that as a homeomorphism $S^1 \setminus \{z\} \to {\mathbb{R}}$ the function $g$ is automatically monotonous. In the sequel we denote by $$(S^1)^{3+} := \{(x,y,z) \in (S^1)^{(3)}\,|\, (x,y,z) \text{ positively ordered}\}$$ the set of positively ordered triples. \[FlowOfACr\] For every strict cross ratio there exists a $\Gamma$-equivariant continuous map $$\psi:{\mathbb{R}}\times (S^1)^{3+}\rightarrow S^1$$ such that $\log b(x,y,z,\psi_s(x,y,z))=s$. Put $\psi_s(x,y,z):=(\log g)^{-1}(s)$. \[PropLab\] Let $b_1$ and $b_2$ be strict cross ratios. Then there exists a $C>0$ such that $$C^{-1} \leq \frac{|\log b_1|}{|\log b_2|} \leq C$$ We adapt an argument of Labourie [@Lab05], Chapter 2: Let $\psi^1_s$ and $\psi^2_s$ be maps associated to $b_1$ and $b_2$ by means of Corollary \[FlowOfACr\]. Define a function $T:(S^1)^{3+} \rightarrow {\mathbb{R}}$ by $$T(x,y,z):=b_1(x,y,z,\psi^2_1(x,y,z))$$ This map is positive and continuous. Since $ \psi^2_s$ is $\Gamma$-equivariant, T is $\Gamma$-invariant. Furthermore it satisfies $ \psi_1^2(x,y,z)=\psi^1_{T(x,y,z)}(x,y,z)$. Since $(S^1)^{3+}/\Gamma$ is compact, $T$ has a global maximum $A$. For $t\in S^1$ there exists $s,\tilde s\in {\mathbb{R}}$ such that $$t= \psi^1_{\tilde s}(x,y,z)= \psi^2_{s}(x,y,z).$$ If $|s|\in [n,n+1)$ for $n\in {\mathbb{N}}$, then we have by definition of $A$ that $|\tilde s|\in (0,A(n+1))\subset (0,2A|s|)$., hence $|\tilde s|\leq 2A|s|$. We can calculate: $$\begin{aligned} |\log b_1(x,y,z,t)|=&|\log b_1(x,y,z, \psi_{\tilde s}^1(x,y,z))| =|\tilde s|\\ \leq & 2A|s|=2A|\log b_2(x,y,z,\psi_s^2(x,y,z))|=2A|\log b_2(x,y,z,t)|. \end{aligned}$$ This proves the upper bound for $(x,y,z)\in (S^1)^{3+}$. If $(x,y,z)$ is negatively oriented, then $(z,y,x)$ is in $(S^1)^{3+}$. The upper bound for this case follows from the fact that: $$|\log b(x,y,z,t)|=|\log b(z,y,x,t)|.$$ The lower bound is obtained by reversing the roles of $b_1$ and $b_2$. We will apply this in the following form: \[CREq\] Let $\rho: \Gamma \to G$ be a maximal representation with associated cross ratio $b_\rho$. Then there exists $C>0$ such that for all $(x,y,z,t) \in (S^1)^{(4)}$, $$|\log b_\rho(x,y,z,t)| \geq C \cdot |\log[x:y:z:t]|.$$ Well-displacing and quasi-isometry property {#SecWellDisp} =========================================== We keep the notation introduced in the last section. In particular, $\Sigma$ denotes a closed, oriented surface of genus $g\geq 2$ with fundamental group $\Gamma$ and fixed hyperbolization $\Gamma \to PU(1,1)$, while $V$ denotes a Euclidean Jordan algebra with bounded symmetric domain $\mathcal D$, Shilov boundary $\check S$ and associated group $G$. We fix a maximal representation $\varrho: \Gamma \to G$ and denote by ${\varphi}: S^1 \to \check S$ its canonical limit curve. Recall from the introduction that for $\gamma \in \Gamma$ the translation length of $\rho(\gamma)$ is defined by $$\tau_{\mathcal D}(\rho(\gamma)) = \inf_{x \in \mathcal D}d(\rho(\gamma)x, x).$$ Since $\Sigma$ is smooth and closed, $\gamma$ cannot be elliptic or parabolic respectively, hence must be hyperbolic. We denote by $\gamma^+ \in S^1$ the attractive, and by $\gamma^-$ the repulsive fixed point of $\gamma$ in $S^1$. The *virtual translation length* of $\rho(\gamma)$ is defined by $$\tau_{\mathcal D}^\infty(\rho(\gamma)) = \log b_\rho(\gamma^-, \xi, \gamma^+, \gamma \xi)$$ for $\xi \in S^1 \setminus \{\gamma^\pm\}$. We will see below that this does not depend on the choice of $\xi$. The main result in this section is Theorem \[CRTransl\] which says that there exists a constant $C>0$ such that $$\label{CompareTransLength} \tau_{\mathcal{D}}(\varrho(\gamma))\geq C\tau_{\mathcal{D}}^\infty(\varrho(\gamma)).$$ From the resulting inequality we deduce that $\rho$ is well-displacing and that the corresponding action on $\mathcal D$ is quasi-isometric. This implies in particular the desired properness of the mapping class group on Hermitian higher Teichmüller spaces. Before we prove Inequality we discuss a special case, where we have equality and $C=1$. Fuchsian representations ------------------------ A maximal representation $\varrho: \Gamma \to G$ is called *Fuchsian* if it factors as $$\varrho: \Gamma \xrightarrow{\widehat{\varrho}} PU(1,1) \xrightarrow{t} G,$$ where $\widehat{\varrho}: \Gamma \to PU(1,1)$ is some fixed hyperbolization and $t: PU(1,1) \to G$ is some embedding. It then follows automatically from maximality of $\varrho$ that the embedding $t$ is tight in the sense of [@Tight]. Now we claim: If $\varrho: \Gamma \to G$ is a Fuchsian representation then $$\tau^\infty_{\mathcal{D}}(\varrho(\gamma))=\tau_{\mathcal{D}}(\varrho(\gamma)).$$ The proposition will be an immediate consequence of the following three lemmas: \[LowerBoundDisc\] For all $\gamma \in \Gamma$ we have $$\tau_{\mathbb D}(\gamma) = \tau^\infty_{\mathbb D}(\gamma).$$ Observe that both sides of the claimed equality are invariant under $PSL_2({\mathbb{R}})$ and Cayley transform. Conjugating $\gamma$ with the Cayley transform and some $g\in PSL(2,{\mathbb{R}})$, we can transform the whole situation to the upper half plane model $\overline{\mathbb{H}}$ and we may assume without loss of generality that $\gamma$ acts by translation on the imaginary axis, i.e. the attractive fixpoint $\gamma^+$ is $\infty$, while the repulsive fix point $\gamma^-$ is $0$. Then $\gamma$ can be written as $$\gamma=\left(\begin{array}{cc} a&0\\0&a^{-1}\end{array}\right)$$ with $a>1$ and we have $$\tau_{\mathbb{D}}(\gamma)=d(i,\gamma i).$$ Using the relation between the hyperbolic distance and the classical cross ratio on $\overline{\mathbb{H}}$ we obtain $$\tau_{\mathbb{D}}(\gamma)=d(i,\gamma i)=\log[i:0:\gamma i:\infty]=\log \frac{\gamma i-0}{i-0}=\log \frac{ia^2}{i}=\log a^2.$$ Now consider the geodesic $\sigma$ through $i$ which is orthogonal to the imaginary axis. It is a half circle with endpoints $1$ and $-1$ on the real axis. The geodesic $\gamma \cdot \sigma$ goes through $\gamma i$ and intersects the real axis in the points $\gamma(1)=a^2$ and $\gamma (-1)=-a^2$. Now we have a quadruple of points in ${\mathbb{R}}\cup \{\infty\}$ and we calculate their cross ratio: $$\tau^\infty_{\mathbb D}(\gamma) = \log[0:1:\infty: \gamma 1]=\log\frac{a^2}{1}= \log a^2 = \tau_{\mathbb{D}}(\gamma).$$ For all $\gamma \in \Gamma$ we have $$\tau^\infty_{\mathcal{D}}(\varrho(\gamma))=\tau^\infty_{\mathbb{D}}(\widehat{\varrho}(\gamma))$$ The Lie group homomorphism $t: PU(1,1) \to G$ corresponds to a morphism $\alpha: {\mathbb{R}}\to V$ of the associated Jordan algebras. By Example \[ExamplesBalanced\], this morphism is balanced. Now denote by $\varphi$ and $\widehat{\varphi}$ the canonical limit curves of $\varrho$ and $\widehat{\varrho}$ respectively. Then $\varrho = \alpha_{\mathbb{C}}\circ \widehat{\varrho}$ and thus Property (ii) of Theorem \[UniversalCrossRatio\] implies that the generalized cross ratios associated to $\varrho$ and $\widehat{\varrho}$ are the same. This in turn shows that the corresponding virtual translation lengths are the same. For all $\gamma \in \Gamma$ we have $$\tau_{\mathcal{D}}(\varrho(\gamma))=\tau_{\mathbb{D}}(\widehat{\varrho}(\gamma))$$ Let $\gamma \in \Gamma$. Then $\gamma$ is hyperbolic and thus there exists a geodesic $\sigma$ in ${\mathbb{D}}$ such that $\gamma$ fixes $\sigma$ and $$\widehat{\varrho}(\gamma).\sigma(s) = \sigma(s + \tau_{\mathbb{D}}(\widehat{\varrho}(\gamma)))\quad(s \in {\mathbb{R}}).$$ Now there exists a $t$-equivariant totally geodesic embedding $t^\dagger: {\mathbb{D}}\to {\mathcal{D}}$. If $\sigma^\dagger$ denotes the image of $\sigma$ under $t^\dagger$ then $\varrho(\gamma)$ fixes $\sigma^\dagger$ and $$\varrho(\gamma).\sigma^\dagger(s) = \sigma^\dagger(s + \tau_{\mathbb{D}}(\widehat{\varrho}(\gamma)))\quad (s \in {\mathbb{R}}).$$ By [@BrHa Thm II.6.8] this implies the lemma. Bounding the translation length from below ------------------------------------------ In this subsection we return to the general case of an arbitrary maximal representation $\varrho: \Gamma \to G$ of $\Gamma$ into a Hermitian group of tube type. As a first step towards our main inequality we will bounded the translation length of $\rho(\gamma)$ from below in terms of some auxiliary data. This auxiliary data will then be related to the virtual translation length in the next subsection. We will use the fact that for $\gamma \in \Gamma$ the element $\varrho(\gamma)$ is contained in the Levi factor of a certain Shilov parabolic. We will transport the whole situation into the Levi factor $L$, which has a linear action on the symmetric cone $\Omega$ of the underlying Jordan algebra $V$. Using this linear action, we can estimate the dynamics of $\varrho(\gamma)$ using the reductive symmetric space of $GL(V)$.\ We introduce the notations $g_0 := \rho(\gamma)$ and $g_0^{\pm} := {\varphi}(\gamma^\pm)$. Since $G$ is transitive on $\check S^{(2)}$, there exists $h_1 \in G$ such that $h_1g_0^{\pm} = \pm e$. Set $g_1 := h_1g_0h_1^{-1}$. Since $g_0$ fixes $g_0^{\pm} \in \check S$, we see that $g_1$ fixes $\pm e$, whence Corollary \[LeviConvenient\] applies and we find $M \in \mathbb N$ such that $g_2:=(c\circ g_1\circ c^{-1})^M\in G(\Omega)$. We will use $g_2$ to estimate $\tau_{\mathcal{D}}(\varrho(\gamma))$; for this we need the following lemma: \[translengthpower\] Let $X$ be a metric space and $g\in Is(X)$ an isometry. Then for any $M\in {\mathbb{N}}$: $$\tau_X(g)\geq \frac{1}{M}\tau_X(g^M).$$ We have: $$d(g^Mx,x)\leq \sum_{i=1}^Md(g^ix,g^{i-1}x)=M \cdot d(gx,x).$$ Taking the infimum on both sides finishes the proof. Since the Cayley transform is isometric we obtain $$\begin{aligned} \tau_{\mathcal D}(\rho(\gamma)) &=& \tau_{\mathcal D}(g_0) = \inf_{x \in \mathcal D}d(g_0x,x) = \inf_{x \in \mathcal D}d(g_0h_1^{-1}x, h_1^{-1}x)\\ &=& \inf_{x \in \mathcal D}d(h_1g_0h_1^{-1}x, x) = \tau_{\mathcal D}(g_1)=\tau_{T_\Omega}(c\circ g_1\circ c^{-1})\\ &\geq & \frac{1}{M}\tau_{T_\Omega}(g_2).\end{aligned}$$ and thus $$\begin{aligned} \label{g2vsg0} \tau_{\mathcal D}(\rho(\gamma))\geq \frac{1}{M} \cdot \tau_{\mathcal T_\Omega}(g_2).\end{aligned}$$ Let $h \in L$. Then for all $z \in T_{\Omega}$ we have $$d(z,hz) \geq d(i{\rm Im}(z), h(i{\rm Im}(z))).$$ Since $T_\Omega$ is an open subset of $V^{\mathbb{C}}$, we can identify the tangent space of $T_\Omega$ at any point $z \in T_\Omega$ canonically with $V^{\mathbb{C}}$. Using this identification, the Hermitian metric $H$ on $T_\Omega$ admits the following description (see [@FK Prop. X.1.3]): Let $n := \dim V$, $r := {\rm rk}(V)$. Then given $z \in T_\Omega$ and $a,b \in V^{\mathbb{C}}$ we have $$H_z(a, b) = \left.\left(\frac{2n}{r}P\left(\frac{z-\bar z}{i}\right)^{-1}a \,\right|\, b\right) = \left.\left(\frac{2n}{r}P\left(2{\rm Im}(z)\right)^{-1}a\,\right|\,b\right) = H_{{\rm Im}(z)}(a,b).$$ In other words, translation in the direction of the real axis is isometric for $H$. We have $H = g + i \omega$, where $g$ is the Riemannian metric on $T_\Omega$ and $\omega$ is the Kähler form. In particular, since $\omega$ is skew-symmetric, we have for all $z \in T_\Omega$ and all $a \in V^{\mathbb{C}}$ the equality $$\begin{aligned} g_z(a,a) = H_z(a,a) &=& H_z({\rm Re}(a),{\rm Re}(a)) + H_z(i{\rm Im}(a),i{\rm Im}(a))\\ &=& g_z({\rm Re}(a),{\rm Re}(a)) + g_z(i{\rm Im}(a),i{\rm Im}(a)).\end{aligned}$$ In particular, $$g_z(a,a) \geq g_z(i{\rm Im}(a),i{\rm Im}(a)) = g_{i{\rm Im}(z)}(i{\rm Im}(a),i{\rm Im}(a)).$$ Thus, given any path $\sigma:[0,1] \to T_\Omega$ with $\sigma(0) = z$, $\sigma(1) = hz$ we have $$\begin{aligned} l(\sigma) &=& \int_{0}^1\sqrt{g_{\sigma(t)}(\dot\sigma(t),\dot\sigma(t) )}dt\\ &\geq& \int_{0}^1\sqrt{g_{i{\rm Im}(\sigma(t))}(i{\rm Im}(\dot\sigma(t)),i{\rm Im}(\dot\sigma(t)))}dt\\ &=& l(i{\rm Im}(\sigma(t))).\end{aligned}$$ Observe that $i{\rm Im}(\sigma(t))$ is a path joining $i{\rm Im}(z)$ and $i{\rm Im}(hz)) = h(i{\rm Im}(z)))$. (The latter equality is the only place where we use the special form of $h \in L$.) Passing to the infimum over all $\sigma$, we obtain the lemma. Specializing to $h = g_2$ and passing to the infimum over all $z \in T_\Omega$ we deduce: \[g2Cone\] Let $g_2 \in G(\Omega)$. Then $$\tau_{\mathcal T_\Omega}(g_2) = \tau_{\Omega}(g_2).$$ Observe that $\Omega$ is the reductive symmetric space associated with $L$. In particular, the inclusion $L \to GL(V)$ induces an isometric embedding of $\Omega$ into the reductive symmetric space $\mathcal P(V)$ of $GL(V)$, which happens to be the space of all positive definite symmetric matrices of size $\dim(V)$. A detailed exposition of $\mathcal P(V)$ is provided in [@BrHa Ch. II.10]. We will use the results described therein without further reference. We will need the following result concerning $\mathcal P(V)$: \[PVEstimate\] Let $g \in GL(V)$. Then $$\tau_{\mathcal P(V)}(g) \geq \frac{1}{\sqrt{\dim V} }|\log \det(g)^2|.$$ Let $p \in \mathcal P(V)$ and $c: [0, d(p, gp)] \to \mathcal P(V)$ a unit speed geodesic joining $p$ with $gp$. Then there exists $h \in GL(V)$ such that $p = hh^{\top}$ and an element $X$ of norm $1$ in the Lie algebra of $GL(V)$ such that $c(t) = h\exp(tX)h^{\top}$. Moreover, $gp= ghh^\top g^\top$. Since the $d(p,gp)=gp$ we have $$\begin{aligned} &&h\exp(d(p, gp) \cdot X)h^{\top} = ghh^\top g^\top\\ &\Rightarrow& \det(h\exp(d(p, gp) \cdot X)h^{\top}) = \det(ghh^\top g^\top)\\ &\Rightarrow& \exp(d(p, gp) \cdot\operatorname{tr}(X)) = \det(g)^2\\ &\Rightarrow& \exp(d(p, gp) \cdot\operatorname{tr}(X)) = \exp(\log \det(g)^2)\\\end{aligned}$$ Since both $d(p, gp) \cdot \operatorname{tr}(X)$ and $\log \det(g)^2$ are real this implies $$d(p, gp) \cdot\operatorname{tr}(X) = \log \det(g)^2,$$ whence $$\begin{aligned} \label{LengthInPd} d(p, gp) \cdot |\operatorname{tr}(X)| = |\log \det(g)^2|.\end{aligned}$$ Now observe that $$|\operatorname{tr}(X)| = |(X|{{\textbf}1})| \leq \|X\|\|{{\textbf}1}\| = 1 \cdot \sqrt{\dim V} = \sqrt{\dim V}.$$ Inserting into we obtain $$d(p, gp) \geq \frac{1}{\sqrt{\dim V} }|\log \det(g)^2|.$$ Passing to the infimum over all $p \in \mathcal P(V)$ we obtain the lemma. \[noabsolutevalue\] We want to apply Lemma \[PVEstimate\] to the element $g_2$ defined above. We recall that by construction $g_2$ has $0$ as a repulsive fixed point (since $g_1$ has $-e$ as a repulsive fixed point) at the boundary at infinity. This implies that $\det(g_2) \geq 1$ and hence $\log \det(g)^2 \geq 0$. In particular, the estimate in Lemma \[PVEstimate\] becomes $$\tau_{\mathcal P(V)}(g_2) \geq \frac{1}{\sqrt{\dim V} }\log \det(g_2)^2,$$ when specialized to $g_2$. \[LowerBound\] For all $\gamma \in \Gamma$, $$\tau_{\mathcal D}(\rho(\gamma)) \geq \frac{1}{M \cdot \sqrt{\dim V}} \cdot \log \det(g_2)^2.$$ Combining , Corollary \[g2Cone\] and Lemma \[PVEstimate\] (in combination with Remark \[noabsolutevalue\]) we obtain $$\begin{aligned} \tau_{\mathcal D}(\rho(\gamma)) &=& \tau_{\mathcal D}(g_0) \geq \frac{1}{M}\tau_{T_\Omega}(g_2) = \frac{1}{M}\tau_{\Omega}(g_2)\\ &\geq& \frac{1}{M}\tau_{\mathcal P(V)}(g_2) \geq \frac{1}{M \cdot \sqrt{\dim V}} \cdot \log \det(g_2)^2 .\end{aligned}$$ Bounding the virtual translation length from above -------------------------------------------------- We keep the notations from the last subsection. In particular, given $\gamma \in \Gamma$ the elements $g_0, g_1, g_2, h_1, h_2$ are defined as before. In order to prove the desired inequality between translation length and virtual translation length (Theorem \[CRTransl\]) we have to estimate $\tau_{\mathcal{D}}^\infty(\varrho(\gamma))$ from above. As before we denote $g_0^\pm := {\varphi}(\gamma^\pm)$. \[logbgammapositiv\] We have $\tau_{\mathcal D}^\infty(\rho(\gamma)) > 0$. By definition $\tau_{\mathcal{D}}^\infty(\varrho(\gamma))=\log b_\varrho(\gamma^-,\xi,\gamma^+,\gamma \xi)$, where $\xi\neq \gamma^\pm$. Since $\gamma^+$ is the attractive fixed point of $\gamma$, the point $\gamma \xi$ is between $\xi$ and $\gamma^+$. More precisely: $(\gamma^-,\xi,\gamma^+)$ and $(\xi,\gamma \xi,\gamma^+)$ are either both positive or both negative. In both cases $\tau_{\mathcal{D}}^\infty(\varrho(\gamma))$ is positive. Our next observation is that $\tau^\infty(\varrho(\gamma))$ does not depend on the choice of $\xi$. We shall prove a slightly more general statement: Given $x,z \in \check S$ we define $$\check S^{(4)}_{x,z} = \{(y,t) \in \check S^2\,|\, (x,y,z,t) \in \check S^{(4)}\}.$$ With this notation we have $$({\varphi}(\xi), {\varphi}(\gamma \xi)) = ({\varphi}(\xi), g_0.{\varphi}(\xi)) \in \check S^{(4)}_{g_0^+, g_0^-}$$ for all $\xi \in S^1 \setminus \{\gamma^\pm\}$. Now we claim: \[ArbitraryPoint\] Suppose that $y \in \check S \setminus\{g_0^\pm\}$ and $(y, g_0.y) \in \check S^{(4)}_{g_0^-, g_0^+}$ then $$\tau_{\mathcal D}^\infty(\rho(\gamma)) = \log B_V(g_0^-, y, g_0^+, g_0y)$$ Let $F(y) := B_V(g_0^-, y, g_0^+, g_0y)$. We have to show that $F(y) = F(z)$ for all $y,z \in \check S$ satisfying the conditions of the lemma. If $(y,z) \in \check S^{(4)}_{g_0^+, g_0^-}$. Then we can compute $$\begin{aligned} F(z) = B_V(g_0^-, z, g_0^+, g_0z) &=& B_V(g_0^-, z, g_0^+, y) \cdot B_V(g_0^-, y, g_0^+, g_0z)\\ &=& B_V(g_0g_0^-, g_0z, g_0g_0^+, g_0y) \cdot B_V(g_0^-, y, g_0^+, g_0z)\\ &=& B_V(g_0^-, y, g_0^+, g_0z) \cdot B_V(g_0^-, g_0z, g_0^+, g_0y)\\ &=& B_V(g_0^-, y, g_0^+, g_0y) = F(y).\end{aligned}$$ Otherwise we can find $w \in \check S$ satisfying the conditions of the lemma such that both $(y,w)\in \check S^{(4)}_{g_0^+, g_0^-}$ and $(z,w)\in \check S^{(4)}_{g_0^+, g_0^-}$. Then $F(y) = F(w) = F(z)$, finishing the proof of the lemma in the general case. \[CorBGammaFormula\] Suppose that $z \in \check S \setminus\{\pm e\}$ and that $(z, g_1.z) \in \check S^{(4)}_{-e, e}$. Then $$\tau_{\mathcal D}^\infty(\rho(\gamma)) = \log B_V(-e, z, e, g_1z).$$ Apply Lemma \[ArbitraryPoint\] to $y := h_1^{-1}z$ and use $G$-invariance of $B_V$. Recall that $g_2=(c\circ g_1\circ p)^M$. We thus need the following lemma: \[inftranslengthpower\] If $g \in G$ and $g^\pm$ are fixed points of $g$, then for all $M \in \mathbb N$, $$\log B_V(g^-,x,g^+,g^Mx) = M \cdot \log B_V(g^-,x,g^+,gx)$$ We have $$\begin{aligned} \log B_V(g^-,x,g^+,g^Mx)&=&\sum_{i=1}^M \log B_V(g^-,g^ix,g^+,g^{i+1}x)\\ &=&M \cdot \log B_V(g^-,x,g^+,gx). \end{aligned}$$ For the next step we observe that by Proposition \[BergmanComparison\] and the transfomrmation behavior of the Bergman kernel under biholomophic maps [@FK Prop. IX.2.4] that the Bergman kernel $\mathcal K_{T_{\Omega}}$ of the tube $T_\Omega$ extends continuously to transversal pairs on $V$. Denoting this extension by the same letter $T_\Omega$ we prove: \[VTLugly\] Let $w \in V$ such that $0, w$ and $g_2w$ are pairwise transversal. Then $$\begin{aligned} \tau_{\mathcal D}^\infty(\rho(\gamma)) &=&\frac{1}{M \cdot {\operatorname{rk}V}} \cdot \log\left( \frac{K_{T_\Omega}(w,0)}{K_{T_\Omega}(g_2w, 0)} \cdot \lim_{n \to \infty} \frac{K_{T_\Omega}(g_2w, c(x_n))}{K_{T_\Omega}(w, c(x_n))}\right),\end{aligned}$$ where $x_n$ is a sequence in $\mathcal D$ converging to $e$. Combinge Corollary \[CorBGammaFormula\] and Lemma \[inftranslengthpower\] with Proposition \[BergmanCrossInvariance\] applied to the Cayley transform $c: \mathcal D \to \mathcal T_{\Omega}$. Now the right hand side can be computed explicitly: \[VTL\] $$\begin{aligned} \tau_{\mathcal D}^\infty(\rho(\gamma)) &=&\frac{1}{M \cdot {\operatorname{rk}V}} \cdot \log \det(g_2)^2\end{aligned}$$ We first show that $$\lim_{n \to \infty} \frac{K_{T_\Omega}(g_2w, c(x_n))}{K_{T_\Omega}(w, c(x_n))} = 1.$$ Indeed, let $\lambda\in [0,1)$. Then $$c(\lambda \cdot e )=-\frac{1+\lambda}{1-\lambda}e.$$ Using [@FK X.1.3] we obtain $$\begin{aligned} \lim_{n \to \infty} \frac{K_{T_\Omega}(g_2w,c(x_n))}{K_{T_\Omega}(w,c(x_n))} &=&\lim_{\lambda \rightarrow 1} \left(\frac{\det(g_2w-\frac{1+\lambda}{1-\lambda}e)}{\det(w-\frac{1+\lambda}{1-\lambda}e)}\right)^{-\frac{2n}{r}}\\ &=& \lim_{\lambda \rightarrow 1}\left(\frac{\det(\frac{1-\lambda}{1+\lambda}g_2w-e)}{\det(\frac{1-\lambda}{1+\lambda}w-e)}\right)^{-\frac{2n}{r}} =1.\end{aligned}$$ In view of Proposition \[VTLugly\] it now suffices to show that $\frac{K_{T_\Omega}(w,0)}{K_{T_\Omega}(g_2w, 0)} = \det(g_2)^2$. Since $g_2: T_\Omega \to T_\Omega$ is biholomorphic, we see from [@FK Prop. IX.2.4] that $$K_{T_\Omega}(w, 0) = K_{T_\Omega}(g_2w, g_20)\det{}_{{\mathbb{C}}}J_{g_2}(w) \overline{\det{}_{{\mathbb{C}}}J_{g_2}(0)},$$ where $J_{g_2}$ denotes the complex Jacobi matrix of $g_2$. Note that $g_2$ is a real matrix, because it is in $G(\Omega)_0\subset GL(V)$. Since it is linear, we have $J_{g_2} \equiv g_2$ and $g_20=0$, whence $$K_{T_\Omega}(w, 0) = K_{T_\Omega}(g_2w, g_20)\det{}_{{\mathbb{C}}}J_{g_2}(w) \overline{\det{}_{{\mathbb{C}}}J_{g_2}(0)} = K_{T_\Omega}(g_2w, 0)\det(g_2)^2.$$ Dividing both sides by $K_{T_\Omega}(g_2w, 0)$ the proposition follows. Comparing with we ultimately obtain: \[CRTransl\] For all $\gamma \in \Gamma$ and all $\xi \in S^1 \setminus \{\gamma^\pm\}$ the inequality $$\tau_{\mathcal D}(\rho(\gamma)) \geq \frac{\operatorname{rk}V}{\sqrt{\dim V}}\cdot \tau_{\mathcal D}^\infty(\rho(\gamma))$$ holds. By Corollary \[LowerBound\] and Proposition \[VTL\] we have $$\begin{aligned} \tau_{\mathcal D}(\rho(\gamma)) &\geq& \frac{1}{M \cdot \sqrt{\dim V}} \log \det(g_2)^2\\ &=&\frac{\operatorname{rk}V}{\sqrt{\dim V}} \cdot \left(\frac{1}{M \cdot {\operatorname{rk}V}} \cdot \log \det(g_2)^2\right)\\ &=& \frac{\operatorname{rk}V}{\sqrt{\dim V}} \cdot \tau_{\mathcal D}^\infty(\rho(\gamma)).\end{aligned}$$ Well-displacing --------------- Before we can deduce well-displacing of maximal representations from our main inequality, we need one more ingredient: If $\Gamma$ is a finitely generated group and $S$ a finite set of generators, then we denote by $\|\,\cdot \,\|_S$ the word length with respect to $S$. We then define the word metric $d_S$ by $$d_S(\gamma_1, \gamma_2) = l_S(\gamma_2^{-1}\gamma_1),$$ where $$l_S(\gamma_1):=\inf_{\eta\in \gamma}\|\eta \gamma \eta^{-1}\|_S.$$ Then the Švarc-Milnor lemma reads as follows: \[MilSva\] Let $(X,d)$ be a length space. If a group $\Gamma$ acts properly and cocompactly by isometries on $X$, then $\Gamma$ is finitely generated and for every finite generating set $S$ with associated word metric $l_S$ on $\Gamma$ and every basepoint $x_0 \in X$ the map $$(\Gamma, d_S) \to (X,d), \quad \gamma \mapsto \gamma.x_0$$ is a quasi-isometry. Note that the constants appearing in the quasi-isometry inequality may depend on $x_0$. Nevertheless, applying this to the $\Gamma$ action on the disc chosen in the introduction, we obtain: \[DiscTranslationLength\] Let $S$ be an arbitrary finite generating set for $\Gamma$ and $l_S$ the associated word length. Then there exist constants $A, B > 0$ such that for every $\gamma \in \Gamma$ $$\tau_{\mathbb D}(\gamma) \geq A \cdot l_S(\gamma) - B.$$ We fix a compact fundamental domain $F$ for the $\Gamma$-action on $\mathbb{D}$. We know that every $\gamma\in \Gamma$ is hyperbolic, i.e. there exists a geodesic $\sigma$ on which $\gamma$ acts by translation and we have $\gamma\cdot \sigma(t)=\sigma(t+\tau_\mathbb{D}(\gamma))$ for all $t$. There exists $\eta\in \Gamma$ such that $\eta \sigma$ intersects $F$, say $y:=\eta \sigma(t_0)\in F$. Then we have for any $x\in F$: $$d(x,\eta\gamma\eta^{-1}x)\leq d(x,y)+d(y,\eta\gamma\eta^{-1}y)+d(\eta\gamma\eta^{-1}y,\eta\gamma\eta^{-1}x)\leq 2\text{diam}(F)+\tau_\mathbb{D}(\eta\gamma\eta^{-1}).$$ Now we fix $x\in F$ and apply the Švarc-Milnor lemma with $x = x_0$ to find positive constants $A, B'$ satisfying $$d(x, \gamma x) = d(e x, \gamma x) \geq A \cdot d_S(e, \gamma) - B' = A \cdot l_S(\gamma) - B'$$ for all $\gamma \in \Gamma$. We deduce $$\begin{aligned} \tau_\mathbb{D}(\gamma)&=&\tau_\mathbb{D}(\eta\gamma\eta^{-1})\geq d(x,\eta\gamma\eta^{-1}x)-2\text{diam}(F)\\ &\geq &A\cdot l_S(\eta\gamma\eta^{-1})-B'-2\text{diam}(F)=A \cdot l_S(\gamma)-(B'+2\text{diam}(F)). \end{aligned}$$ Now we can finally prove: \[WD\] For any finite generating set $S$ of $\Gamma$ there exist $A,B>0$ such that $$\tau_{\mathcal D}(\rho(\gamma))\geq A \cdot l_S(\gamma)-B$$ for all $\gamma\in \Gamma$. Using Corollary \[CREq\], Theorem \[CRTransl\], Lemma \[LowerBoundDisc\] and Corollary \[DiscTranslationLength\] we find positive constants $C_1, \cdots, C_4$ such that $$\begin{aligned} \tau_{\mathcal D}(\rho(\gamma)) &\geq& C_1 \cdot \tau^\infty_{\mathcal D}(\rho(\gamma)) \\ &=& C_1 \cdot \log b_\rho(\gamma^-, \xi, \gamma^+, \gamma \xi)\\ &\geq& C_2\cdot \log [\gamma^-: \xi: \gamma^+: \gamma \xi]\\ &=& C_2 \cdot \tau_{\mathbb D}^\infty(\gamma)\\ &=& C_2 \cdot \tau_{\mathbb D}(\gamma) \\ &=& C_2C_3 \ell_S(\gamma)-C_2C_4.\end{aligned}$$ Quasi-isometry property ----------------------- As a simple consequence of Theorem \[WD\] we obtain the following result: \[QI\] Let $\rho: \Gamma \to G$ be a maximal representation. Then for every $x \in \mathcal D$ and every finite generating set $S$ of $\Gamma$ the map $$(\Gamma, d_S) \to (\mathcal D, d_{\mathcal D}), \quad \gamma \mapsto \gamma.x$$ is a quasi-isometric embedding. Since for $\gamma_1, \gamma_2 \in \Gamma$ we have both $d_S(\gamma_1, \gamma_2) = l_S(\gamma_2^{-1}\gamma_1)$ and $d_{\mathcal D}(\gamma_1.x, \gamma_2.x) = d(\gamma_2^{-1}\gamma_1x,x)$ it suffices to show that there exist $A,B>0$ such that for all $\gamma \in \Gamma$ $$A^{-1}\cdot l_S(\gamma)-B\leq d_{\mathcal D}(\gamma x,x)\leq A \cdot l_S(\gamma)+B.$$ The left inequality follows immediately from Theorem \[WD\]: Indeed, we have $$d_{\mathcal D}(\gamma x, x)\geq \tau_{\mathcal{D}}(\gamma) {\geq} A\cdot l_S(\gamma)-B$$ for some constants $A,B > 0$ independent of $\gamma$. On the other hand, the right inequality is elementary: Write $\gamma=s_1\cdots s_{l_S(\gamma)}$ with $s_i \in S$. Then $$\begin{aligned} d(x,\gamma x)\leq &d(x,s_1x)+d(s_1x,s_1s_2x)+\ldots+d(s_1\cdots s_{l_S(\gamma)-1}x,\gamma x)\\ =& d(x,s_1x)+d(x,s_2x)+\ldots+d(x,s_{l_S(\gamma)}x)\\ \leq&\max_{s\in S}d(x,sx) \cdot l_S(\gamma).\end{aligned}$$ Properness of the mapping class group {#SubsecProper} ------------------------------------- It is now easy to deduce Corollary \[CorProperness\] from the introduction. Indeed, it suffices to establish Inequality (2.1) of [@AnnaMCG Prop. 2.4]. Now the upper bound is already established in [@AnnaMCG Lemma 2.7], and the lower bound was established within the proof of Theorem \[WD\]. | Mid | [
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Postoperative issues of sacral nerve stimulation for fecal incontinence and constipation: a systematic literature review and treatment guideline. There is a lack of knowledge on the incidence and management of suboptimal therapeutic effect and the complications associated with sacral nerve stimulation for fecal incontinence and constipation. This study aimed to review current literature on postoperative issues and to propose a treatment algorithm. PubMed, MEDLINE, and EMBASE were searched using the keywords "sacral nerve stimulation," "sacral neuromodulation," "fecal incontinence," and "constipation" for English-language articles published from January 1980 to August 2010. A further search was conducted on a wider literature using the keywords "complication," "adverse effect," "treatment failure," "equipment failure," "infection," "foreign-body migration," "reoperation," "pain," and "algorithm." Four hundred sixty-one titles were identified, and after a title and abstract review, 135 were subjected to full article review; 89 were finally included in this review. Five articles were added by manual search and consensus. Forty-eight studies were identified as cohort studies reporting on postoperative issues, including 1661 patients who underwent percutaneous nerve evaluation and 1600 patients who proceeded to sacral nerve stimulation therapy. Pooled data showed that the most common problem during percutaneous nerve evaluation was lead displacement (5.3%). The incidence of suboptimal outcome, pain, and infection after implantation was 12.1%, 13.0%, and 3.9%. There was significant underreporting of untoward events, because 60% of the studies did not report complications during percutaneous nerve evaluation, and suboptimal outcome after implantation was not disclosed in 44% of the studies. The incidence of untoward events associated with sacral nerve stimulation appears to be low. However, there is a significant underreporting of the incidence. Using the information from the structured and systematic literature review, we formulated a clinically relevant guideline for reporting and managing postoperative issues. The guideline can provide a framework for clinical practice. | High | [
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Q: Uniqueness for ODE systems, what do we need besides Lipschitz? The ODE system I'm interested is: $$ x^\prime(t)= (1-x(t))/y(t)$$ $$ y^\prime(t)=(1-y(t))/x(t)$$ with initial condition $$ (x(0),y(0))=(1,1).$$ Let $F(x,y)=((1-x)/y, (1-y)/x)$ then the Jacobian of $F$ is $$ JF=\left(\begin{array}{cc}\partial_x F_1 & \partial_y F_1 \\\partial_x F_2& \partial_y F_2 \end{array}\right)=\left(\begin{array}{cc}-\frac{1}{y} & -\frac{1-x}{y^2} \\ -\frac{1}{x} & -\frac{1-y}{x^2} \end{array}\right), $$ which is continuous and bounded in some convex neighborhood of $(1,1)$, say the ball with radius 1/2 and center on $(1,1)$, $D=B_{1/2}(1,1)$. Hence, $F$ is uniformly Lipschitz on $D$. Accordingly to the book that I'm using, this should be enough to guarantee the uniqueness of the solution of the ODE system. But if we use the fact this is an autonomous system, we can write it as: $$ \frac{d}{dx}y=\frac{(1-y)y}{(1-x)x}$$ and any of its infinite solutions, $y=\frac{x}{1-c+cx}$, satisfies the initial condition $x=1$, $y=1$. I'm probably missing something very trivial but I can't see what. A: The right side of your equation for $dy/dx$ is undefined when $x=1$, so it's not quite true to say $y = x/(1-c+cx)$ is a a solution of this differential equation with initial condition $x=1,y=1$. The system will have trajectories along these curves, but they will not reach $x=1,y=1$ at any finite time, only in a limit as $t \to \infty$. | Mid | [
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prime factors of 786333. 3, 262111 What are the prime factors of 301546? 2, 7, 17, 181 List the prime factors of 149514. 2, 3, 24919 What are the prime factors of 4872922? 2, 487, 5003 What are the prime factors of 11501719? 29, 613, 647 List the prime factors of 295062. 2, 3, 49177 What are the prime factors of 1358004? 2, 3, 113167 List the prime factors of 3303964. 2, 825991 List the prime factors of 13774401. 3, 23, 41, 541 What are the prime factors of 193728? 2, 3, 1009 List the prime factors of 9469121. 9469121 List the prime factors of 8348140. 2, 5, 47, 83, 107 List the prime factors of 731205. 3, 5, 16249 List the prime factors of 98417. 11, 23, 389 List the prime factors of 4230336. 2, 3, 11, 2003 List the prime factors of 13686796. 2, 3421699 What are the prime factors of 244141? 244141 List the prime factors of 1341049. 461, 2909 What are the prime factors of 192687? 3, 11, 5839 What are the prime factors of 440894? 2, 220447 What are the prime factors of 192654? 2, 3, 7, 11, 139 List the prime factors of 205252. 2, 23, 97 What are the prime factors of 320664? 2, 3, 31, 431 What are the prime factors of 25401349? 17, 1494197 List the prime factors of 4851163. 4851163 What are the prime factors of 11334780? 2, 3, 5, 62971 What are the prime factors of 1928419? 1928419 List the prime factors of 6131246. 2, 11, 229, 1217 What are the prime factors of 22039277? 13, 1695329 What are the prime factors of 2884058? 2, 263, 5483 List the prime factors of 804219. 3, 13, 17, 1213 List the prime factors of 2904309. 3, 263, 409 What are the prime factors of 1692861? 3, 37, 101, 151 What are the prime factors of 2446406? 2, 1223203 List the prime factors of 660101. 13, 50777 List the prime factors of 581944. 2, 11, 17, 389 List the prime factors of 1185113. 1185113 List the prime factors of 229247. 229247 List the prime factors of 5497375. 5, 13, 17, 199 What are the prime factors of 6299803? 6299803 List the prime factors of 35185. 5, 31, 227 List the prime factors of 1537502. 2, 768751 What are the prime factors of 44660? 2, 5, 7, 11, 29 What are the prime factors of 121416? 2, 3, 5059 What are the prime factors of 4921508? 2, 1230377 List the prime factors of 84859. 84859 What are the prime factors of 29166? 2, 3, 4861 What are the prime factors of 408555? 3, 5, 7, 1297 List the prime factors of 558828. 2, 3, 19, 43 List the prime factors of 2100351. 3, 11, 63647 What are the prime factors of 586509? 3, 7, 11, 2539 What are the prime factors of 7833434? 2, 7, 19, 601 List the prime factors of 179990. 2, 5, 41, 439 List the prime factors of 934130. 2, 5, 109, 857 What are the prime factors of 30400407? 3, 1125941 What are the prime factors of 7050326? 2, 1511, 2333 List the prime factors of 133064. 2, 16633 What are the prime factors of 2143611? 3, 79393 List the prime factors of 372971. 372971 List the prime factors of 91271. 107, 853 What are the prime factors of 1369721? 47, 151, 193 List the prime factors of 4952621. 431, 11491 List the prime factors of 18101141. 17, 59, 18047 List the prime factors of 16386282. 2, 3, 11, 82759 What are the prime factors of 11998595? 5, 7, 19, 18043 What are the prime factors of 4991990? 2, 5, 59, 8461 What are the prime factors of 1651861? 1651861 What are the prime factors of 3117043? 3117043 What are the prime factors of 121043? 13, 9311 What are the prime factors of 14313164? 2, 59, 60649 List the prime factors of 15910. 2, 5, 37, 43 List the prime factors of 322749. 3, 7, 47, 109 What are the prime factors of 2954095? 5, 590819 What are the prime factors of 6987205? 5, 1397441 List the prime factors of 95411. 73, 1307 List the prime factors of 525473. 13, 83, 487 What are the prime factors of 2369153? 53, 44701 List the prime factors of 5197753. 11, 472523 What are the prime factors of 28008640? 2, 5, 11, 73, 109 List the prime factors of 542195. 5, 108439 What are the prime factors of 346742? 2, 11, 15761 What are the prime factors of 7291536? 2, 3, 7, 21701 List the prime factors of 439720. 2, 5, 10993 What are the prime factors of 4868510? 2, 5, 439, 1109 What are the prime factors of 493613? 31, 15923 What are the prime factors of 83558? 2, 41, 1019 List the prime factors of 460844. 2, 115211 List the prime factors of 19124. 2, 7, 683 List the prime factors of 175669. 13, 13513 List the prime factors of 654177. 3, 17, 101, 127 List the prime factors of 158176. 2, 4943 What are the prime factors of 281199? 3, 67, 1399 List the prime factors of 6328831. 6328831 List the prime factors of 283303. 283303 List the prime factors of 291662. 2, 7, 83, 251 What are the prime factors of 55093? 37, 1489 What are the prime factors of 1519399? 7, 217057 List the prime factors of 169165. 5, 23, 1471 What are the prime factors of 4836018? 2, 3, 11, 47, 1559 What are the prime factors of 2947127? 2947127 List the prime factors of 11512403. 7, 234947 List the prime factors of 30275953. 37, 151, 5419 What are the prime factors of 391512? 2, 3, 11, 1483 What are the prime factors of 6382867? 6382867 List the prime factors of 12096476. 2, 7, 41, 257 List the prime factors of 24841. 24841 List the prime factors of 1140949. 1140949 List the prime factors of 1120242. 2, 3, 186707 What are the prime factors of 936410? 2, 5, 29, 3229 List the prime factors of 100769. 100769 List the prime factors of 7306696. 2, 913337 List the prime factors of 5259077. 103, 51059 What are the prime factors of 236724? 2, 3, 19727 List the prime factors of 3231821. 3231821 List the prime factors of 1032410. 2, 5, 17, 6073 What are the prime factors of 2864724? 2, 3, 238727 List the prime factors of 682212. 2, 3, 139, 409 List the prime factors of 871985. 5, 73, 2389 List the prime factors of 7461768. 2, 3, 73, 4259 What are the prime factors of 384715? 5, 76943 List the prime factors of 441715. 5, 23, 167 What are the prime factors of 387187? 387187 List the prime factors of 2103642. 2, 3, 19, 6151 List the prime factors of 949614. 2, 3, 158269 What are the prime factors of 295586? 2, 147793 List the prime factors of 25546. 2, 53, 241 What are the prime factors of 20694024? 2, 3, 13, 22109 What are the prime factors of 5558589? 3, 719, 859 List the prime factors of 23179498. 2, 11589749 What are the prime factors of 13495785? 3, 5, 899719 What are the prime factors of 328? 2, 41 List the prime factors of 15638438. 2, 7819219 What are the prime factors of 7964532? 2, 3, 23, 9619 What are the prime factors of 47685? 3, 5, 11, 17 What are the prime factors of 11601463? 17, 682439 List the prime factors of 1215767. 7, 29, 53, 113 What are the prime factors of 3562215? 3, 5, 19, 29, 431 What are the prime factors of 551819? 41, 43, 313 List the prime factors of 32919187. 7, 23, 41, 4987 What are the prime factors of 126208? 2, 17, 29 What are the prime factors of 416424? 2, 3, 17351 List the prime factors of 16938143. 23, 736441 List the prime factors of 11918588. 2, 11, 37, 7321 What are the prime factors of 373705? 5, 31, 2411 What are the prime factors of 177713? 71, 2503 List the prime factors of 320524. 2, 227, 353 List the prime factors of 224728. 2, 7, 4013 What are the prime factors of 55552? 2, 7, 31 What are the prime factors of 69494? 2, 34747 What are the prime factors of 7373344? 2, 11, 20947 List the prime factors of 14513526. 2, 3, 397, 677 List the prime factors of 602257. 602257 List the prime factors of 91157. 11, 8287 What are the prime factors of 16957189? 16957189 What are the prime factors of 232831? 157, 1483 What are the prime factors of 30182606? 2, 15091303 What are the prime factors of 149467? 137, 1091 List the prime factors of 128230. 2, 5, 12823 What are the prime factors of 1455939? 3, 161771 List the prime factors of 640130. 2, 5, 64013 What are the prime factors of 2569997? 19, 23, 5881 List the prime factors of 545935. 5, 13, 37, 227 What are the prime factors of 28677220? 2, 5, 11, 13, 37, 271 What are the prime factors of 735093? 3, 81677 List the prime factors of 38462. 2, 19231 What are the prime factors of 6857464? 2, 71, 12073 What are the prime factors of 1612236? 2, 3, 134353 List the prime factors of 2852402. 2, 7, 73, 2791 List the prime factors of 319785. 3, 5, 21319 What are the prime factors of | Mid | [
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Carrying knives on Lancashire’s streets is unacceptable – and police are encouraging residents to hand in the weapons as part of a national knife surrender campaign. From next Tuesday to Monday, September 24, Lancashire Police is hosting a knife amnesty for members of the public to dispose of knives anonymously at stations across the county. Clive Grunshaw, Lancashires Police and Crime Commissioner The week-long surrender is part of Operation Sceptre, a move to remove dangerous weapons from the street, reduce knife crime and raise awareness of the dangers and consequences of carrying a knife. Chief Insp Mark Baines, Lancashire Police’s co-ordinator for the knife surrender, said: “While knife crime is not a major problem in the county, a knife is a lethal weapon – even one on Lancashire’s streets is one too many. “During our last campaign in February, 106 knives were surrendered to police. Among the weapons given up were combat knives, kitchen knives and large blades. “I hope that our communities will again help us to remove such items and help to keep everyone safe. “If anyone is in possession of a knife and is unsure what to do about it, I would urge them to take this opportunity to dispose of it anonymously and safely. “In particular, I want to appeal to youngsters who may be tempted to carry a knife because they believe it offers them protection. Having a knife in a public place is a criminal offence, with young people more likely to be stabbed and seriously injured with their own weapon. “I would also ask people to provide us with information about knife crime in their area. “If you know your partner regularly carries or uses such weapons, please encourage them to hand these weapons in over the next week without fear of prosecution. “Don’t run the risk of ending up with a criminal record, a life-changing or even worse a potentially fatal injury.” There will be special bins at five designated police stations countywide. Anyone will be able to anonymously dispose of a weapon, whether it belongs to them, a friend or a relative. Knife bins will be available at the following designated police stations: Further bins will be in place in Skelmersdale at the Tanhouse and Digmoor Community Stations. Any knives or offensive weapons which are too large for the bins can be handed in at the front counters at the designated police stations, and residents are asked to ensure the knives are wrapped in newspaper, cardboard or tape before they are dropped in the bins or handed in. Clive Grunshaw, Lancashire’s Police and Crime Commissioner added: “Knives are deadly weapons and you will be arrested and prosecuted if you are caught carrying one. If you own a dangerous knife I’d urge you to protect both yourself and those around you by handing it in safely and anonymously. “Campaigns such as this play an important role in reducing crime and re-offending, a key priority in my Police and Crime Plan. I’m committed to making our neighbourhoods safer and anything that helps to achieve this can only be a good thing.” Trending Legal process under way to evict Travellers from Chorley town centre car park Missing Chorley school girl Ellie Ogden found 'safe' Chorley Little Theatre reveals name change as part of a major rebranding project | Mid | [
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According to LIPA, many of the customers could go as long as until 9 p.m. until power is restored. Story: Lightning struck a utility pole in Wading River as thunderstorms began rolling through the area about 12:40 p.m. Friday, dumping heavy rains with rates of 2 inches per hour, police and weather officials said. “I saw the lines get hit,” said Jo Anne Freeborn Armstrong of Aquebogue, who then called 911. “It was the scariest thing I’ve ever seen. “I’m still shaking.” LIPA had been reporting 42 customers without power at about 1 p.m., with one or two traffic lights knocked out along 25A by the storms. The power outage figure dropped to about 5 a half hour later, as electric was quickly restored to the area. In an urban flood advisory issued about 1 p.m., the National Weather Service said it was tracking a series of storms “moving slowly eastward along and north of Route 25A in Suffolk County, between Smithtown and Riverhead.” As of 1:20 p.m., Ms. Freeborn Armstrong said she was still stuck in her car in a parking lot in Rocky Point. “The thunder, lightning, rain and hail are still fierce right now!” she wrote in a Facebook message. She later reported the rain had stopped about 1:30 p.m., then picked up again about 2 p.m. | Low | [
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Selectively enhanced red upconversion luminescence and phase/size manipulation via Fe(3+) doping in NaYF4:Yb,Er nanocrystals. Red upconversion luminescence (UCL) is selectively enhanced by about 7 times via Fe(3+) codoping into a NaYF4:Yb,Er nanocrystalline lattice. The maximum red-to-green ratio (R/G) as well as the overall integrated UCL intensity features at an Fe(3+) content of 20 mol%. The size and phase of nanocrystals are simultaneously manipulated via Fe(3+) doping with various concentrations by a facile hydrothermal method. Contrary to the literature, the pure hexagonal phase appears when Fe(3+) concentrations are from 5 to 20 mol%, meanwhile, the size of NaYF4:Yb,Er nanocrystals reaches its maximum at 10 mol%. The intensified visible UCL especially the dominant red emission is mainly ascribed to the energy transfer (ET) from |(2)F7/2, (4)T1g > (Yb(3+)-Fe(3+) dimer) to (4)F9/2 (Er(3+)) states as well as the distortion of the crystalline field symmetry upon Fe(3+) codoping. Dynamic investigation of (4)S3/2 and (4)F9/2 states under the pulsed laser excitation of 980 nm along with the diffuse reflectance data further supports the proposed mechanism of UC processes. The results show the remarkable promise of Fe(3+)-codoped NaYF4:Yb,Er nanocrystals as upconverting nanoprobes with high sensitivity and penetrability in deeper tissue for multimodal biomedical imaging. | High | [
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Hyaluronidases in Loxosceles intermedia (Brown spider) venom are endo-beta-N-acetyl-d-hexosaminidases hydrolases. In studying Loxosceles venom, we detected degradation of purified hyaluronic acid (HA) and hydrolysis of purified chondroitin sulphate (CS) while neither dermatan sulphate, heparin or heparan sulphate were affected. In addition, with HA-degrading kinetic assays, we show that a hydrolase enzyme was involved in the HA cleavage. By use of the Reissig colorimetric reaction, we found that venom hyaluronidase is an endo-beta-N-acetyl-d-hexosaminidase that generates terminal N-acetylglucosamine residues upon cleavage of HA. Zymogram analysis of L. intermedia venom showed HA lytic activities at 41 and 43kDa, and, when CS was used as a substrate, zymograph experiments resulted in 41 and 43kDa lytic zones. Thus, these results support the hypothesis that the same molecules are involved in cleaving HA and CS residues. Experiments to compare L. intermedia electrostimulated venom and venom gland extract also demonstrated very similar HA lytic activity, suggesting again that hyaluronidases are self-components of Loxosceles spider venom instead of oral egesta contamination. HA degradation as a function of pH in these hydrolase enzymes showed no apparent activities at low or high pH, with optimal activity at 6.0-8.0 pH. Finally, we confirmed the cleaving action of the venom hyaluronidases on HA in the extracellular matrix of the dermis of rabbit by fluorescence reaction to HA and confocal microscope analysis. Thus, hyaluronidases type hydrolases endo-beta-N-acetyl-d-hexosaminidase are implicated as self-components of Loxosceles spider venom and can be involved in venom effects as spreading factors. | High | [
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By By Andrew Moran Nov 2, 2012 in World Calgary - Canadian universities received a failing grade in the annual Campus Freedom Index by the Justice Centre for Constitutional Freedoms (JCCF). The report claims that these post-secondary institutions have desecrated free speech. It also looks at security fees to see if these can be utilized by officials as an indirect method from banning certain speech that they don’t approve of. The Calgary-based centre noted that “actions speak louder than words,” which is why it only awarded three top “A” grades. At the other end of the scale, 28 “F” grades were given to 12 universities and 26 student unions for their policies and actions. “Universities justify their censorship on grounds of safety and security, believing that people have a right not to be offended by what they see or hear on university campus, and believing that would-be violent protests must be appeased by censoring unpopular messages,” said John Carpay, study co-author and president of the JCCF, in a What universities received an “F” grade? The universities of McMaster, McGill, York, Carleton, Simon Fraser, Western Ontario, Concordia, Dalhousie, University of Toronto, Saint Mary’s and others were given “F” grades for these actions: - Threatened Ann Coulter with civil and criminal penalties if she iterates her views incorrectly and did not provide proper security for, which forced the organizers to cancel the event (University of Ottawa). - Cancelled campus events for Jared Taylor and British Member of Parliament George Galloway, who were deemed “too controversial.” (Dalhousie University). - Prohibited the issue of a campus newspaper that featured images of the Prophet Mohammed (University of Prince Edward Island). - Banned the expression “Israeli Apartheid” (McMaster University and Wilfrid Laurier University). - Ordered a pro-life club to hold their activities in an isolated room so they would not offend anyone (University of Toronto, University of Western Ontario and Carleton University). Meanwhile, student unions at Carleton University, Memorial University, McGill University, Lakehead University, University of Calgary and others were provided with an “F” grade for either banning campus pro-life groups or not certifying them. Also, the Students’ Society of McGill University Equity Committee can end funding for a club if it is in violation of its Equity Policy. The University of Toronto did get an “A” for its policies and principles, while St. Thomas University got an “A” for its actions and policies and Mount Allison University’s Students’ Administrative Council was given an “A” for its student union actions and practices. The 2012 Campus Freedom Index looks at the state of free speech at Canadian universities. This year’s study assigned grades to 35 universities and student unions. Grades are given based on human rights and anti-discrimination policies. Higher grades are given if there is a clear anti-disruption policy, which prohibits students and other people from obstructing, blocking, suppressing or interrupting speech that these individuals disagree with.It also looks at security fees to see if these can be utilized by officials as an indirect method from banning certain speech that they don’t approve of.The Calgary-based centre noted that “actions speak louder than words,” which is why it only awarded three top “A” grades. At the other end of the scale, 28 “F” grades were given to 12 universities and 26 student unions for their policies and actions.“Universities justify their censorship on grounds of safety and security, believing that people have a right not to be offended by what they see or hear on university campus, and believing that would-be violent protests must be appeased by censoring unpopular messages,” said John Carpay, study co-author and president of the JCCF, in a news release What universities received an “F” grade? The universities of McMaster, McGill, York, Carleton, Simon Fraser, Western Ontario, Concordia, Dalhousie, University of Toronto, Saint Mary’s and others were given “F” grades for these actions:- Threatened Ann Coulter with civil and criminal penalties if she iterates her views incorrectly and did not provide proper security for, which forced the organizers to cancel the event (University of Ottawa).- Cancelled campus events for Jared Taylor and British Member of Parliament George Galloway, who were deemed “too controversial.” (Dalhousie University).- Prohibited the issue of a campus newspaper that featured images of the Prophet Mohammed (University of Prince Edward Island).- Banned the expression “Israeli Apartheid” (McMaster University and Wilfrid Laurier University).- Ordered a pro-life club to hold their activities in an isolated room so they would not offend anyone (University of Toronto, University of Western Ontario and Carleton University).Meanwhile, student unions at Carleton University, Memorial University, McGill University, Lakehead University, University of Calgary and others were provided with an “F” grade for either banning campus pro-life groups or not certifying them. Also, the Students’ Society of McGill University Equity Committee can end funding for a club if it is in violation of its Equity Policy.The University of Toronto did get an “A” for its policies and principles, while St. Thomas University got an “A” for its actions and policies and Mount Allison University’s Students’ Administrative Council was given an “A” for its student union actions and practices. More about 2012 Campus Freedom Index, Justice Centre for Constitutional Freedoms, Canada, Universities, Free speech More news from 2012 Campus Freedom ... Justice Centre for C... Canada Universities Free speech | Low | [
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Pages Thursday, May 26, 2011 Half Sleeve Tattoos Half sleeve tattoos generally start at the very top of the shoulder and run down below the bicep, often to the elbow. However some people refer to half sleeves as starting at the elbow and running down to the wrist. Then again, i suppose there is two halves to every arm, so both estimations would be correct.This picture gallery showcases some very beautiful and quite colorful sleeve tattoos which | Mid | [
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Contemporary, flash memory-based Solid State Drives/Disks (SSDs) have grown enormously both in data storage capacity and popularity as a design feature of many electronic devices (“hosts”). Indeed, NAND flash-based storage devices (“NAND devices”) are current available in multiple Terabytes (TBs) and the future promises greater data storage capacity and higher performance. Current market trends indicate that PCIe based NAND devices are in great demand in enterprise as well as data center applications. In certain enterprise applications, storage domain multi-path and virtualization are two important features of storage devices. That is, a storage device should be useable (or accessible) by multiple host entities capable of using the storage device for different purposes. The term Quality of Service (“QoS”) is used to characterize the operating performance of a storage device in relation to one or more hosts. For example, QoS may be expressed as a minimum time within which the storage device responds to a request received from a host. For multi-function storage devices being accessed by multiple hosts, this minimum time should ideally be fixed and consistent across the range of hosts, regardless of the type of requests being issued by the respective hosts. In this context, each host may be understood as creating a virtual environment within which the storage device is accessed. This virtual environment may define, sequence and execute a number of “tasks” respectively corresponding to requests received from one or more hosts. Certain hosts (e.g., hosts running one or more multimedia applications) may generate a large number of data I/O operations, while other hosts may run Online Transaction Processing (OLTP) or even a full blown database. If the storage device is unaware of the number and type of tasks being generated by each host, the QoS relative to different hosts may vary dynamically, dramatically, and in an unpredictable manner. Under such conditions, the storage device manufacturer will be unable to ensure a fixed and acceptable QoS for each host request. However, a predictable and reliable QoS is very important to the proper execution of OLTP and similar operations. Accordingly, there is need to provide methods and systems capable of providing a fixed QoS across a range of hosts accessing a storage device using protocols and approaches specified by the PCIe. | High | [
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Here is a call to holistic Christianity: A challenge to be thinkers, engaged and serious about knowing God. And to be feelers, pulsing with passion for Jesus and his gospel. And to be doers, endeavoring great acts of love for others. Our Savior himself shows us that holistic Christianity is comprised of mind, heart, and hands. And he shows us that the Christian life is multidimensional—irreducibly and inseparably thinking, loving, and doing. With contributions from Francis Chan, Rick Warren, Albert Mohler, R. C. Sproul, and Thabiti Anyabwile, Thinking. Loving. Doing. extends a thorough and compelling invitation to experience the fullness of the Christian life. | High | [
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What is Tor? Tor is a system intended to enable online anonymity, composed of client software and a network of servers which can hide information about users' locations and other factors which might identify them. Imagine a message being wrapped in several layers of protection: every server needs to take off one layer, thereby immediately deleting the sender information of the previous server. Use of this system makes it more difficult to trace internet traffic to the user, including visits to Web sites, online posts, instant messages, and other communication forms. It is intended to protect users' personal freedom, privacy, and ability to conduct confidential business, by keeping their internet activities from being monitored. The software is open-source and the network is free of charge to use. Like all current low latency anonymity networks, Tor cannot and does not attempt to protect against monitoring of traffic at the boundaries of the Tor network, i.e., the traffic entering and exiting the network. While Tor does provide protection against traffic analysis, it cannot prevent traffic confirmation (also called end-to-end correlation) Caution: As Tor does not, and by design cannot, encrypt the traffic between an exit node and the target server, any exit node is in a position to capture any traffic passing through it which does not use end-to-end encryption such as TLS. (If your postman is corrupt he might still open the envelope and read the content). While this may or may not inherently violate the anonymity of the source, if users mistake Tor's anonymity for end-to-end encryption they may be subject to additional risk of data interception by third parties. So: the location of the user remains hidden; however, in some cases content is vulnerable for analysis through which also information about the user may be gained. Using Tor Browser Bundle The Tor Browser Bundle lets you use Tor on Windows, OSX and/or Linux without requiring you to configure a Web browser. Even better, it's also a portable application that can be run from a USB flash drive, allowing you to carry it to any PC without installing it on each computer's hard drive. Downloading Tor Browser Bundle You can download the Tor Browser Bundle from the torproject.org Web site (https://www.torproject.org), either as a single file (13MB) or a split version that is multiple files of 1.4 MB each which may proof easier to download on slow connections. If the torproject.org Web site is filtered from where you are, type "tor mirrors" in your favorite Web search engine: The results probably include some alternative addresses to download the Tor Browser Bundle. Caution: When you download Tor Bundle (plain or split versions), you should check the signatures of the files, especially if you are downloading the files from a mirror site. This step ensures that the files have not been tampered with. To learn more about signature files and how to check them, read https://wiki.torproject.org/noreply/TheOnionRouter/VerifyingSignatures Click each file to download it (one ending in ".exe" and nine others ending in ".rar"), one after the other, and save them all in one folder on your hard- or USB-drive. Double-click the first part (the file whose name ends in ".exe"). This runs a program to gather all the parts together. Choose a folder where you want to install the files, and click "Install". The program displays messages about its progress while it's running, and then quits. When the extraction is completed, open the folder and check that the contents match the image below: To clean up, delete all the files you originally downloaded. Using Tor Browser Before you start: Close Firefox. If Firefox is installed on your computer, make sure it is not currently running. Close Tor. If Tor is already installed on your computer, make sure it is not currently running. Launch Tor Browser: In the "Tor Browser" folder, double-click "Start Tor Browser". The Tor control panel ("Vidalia") opens and Tor starts to connect to the Tor network. When a connection is established, Firefox automatically connects to the TorCheck page and then confirms if you are connected to the Tor network. This may take some time, depending on the quality of your Internet connection. If you are connected to the Tor network, a green onion icon appears in the System Tray on the lower-right-hand corner of your screen: Browsing the Web using Tor Browser Try viewing a few Web sites, and see whether they display. The sites are likely to load more slowly than usual because your connection is being routed through several relays. If this does not work If the onion in the Vidalia Control Panel never turns green or if Firefox opened, but displayed a page saying "Sorry. You are not using Tor", as in the image below, then you are not using Tor. If you see this message, close Firefox and Tor Browser and then repeat the steps above. You can perform this check to ensure that you are using tor, at any time by clicking the bookmark button labelled "TorCheck at Xenobite..." in the Firefox toolbar. If Firefox browser does not launch, another instance of the browser may be interfering with Tor Browser. To fix this: Open the Windows Task Manager. How you do this depends on how your computer is set up. On most systems, you can right-click in the Task Bar and then click "Task Manager". Click the "Processes" tab. Look for a process in the list named "firefox.exe". If you find one, select the entry and click "End Process". Repeat the steps above to launch Tor Browser. If Tor Browser still doesn't work after two or three tries, Tor may be partly blocked by your ISP and you should try using the bridge feature of Tor. | Mid | [
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A clinician's guide to the assessment and management of nonadherence in glaucoma. To apply lessons learned in the treatment of systemic hypertension to the problem of nonadherence in glaucoma medical therapy. Although physicians recognize that nonadherence with glaucoma medication is a problem, most lack the skill set to identify nonadherent patients, to identify the causes of nonadherence, and to provide solutions to address nonadherence. A PubMed search was conducted using the terms "adherence" OR "compliance" AND "hypertension," with the following limitations: title, English language, humans, from 2000 through 2009. Other studies identified outside of the PubMed search were included if relevant. Studies from the systemic hypertension literature suggest that simplifying medication regimens, lowering costs, and patient education about the disease and the importance of taking medications are successful strategies for improving adherence. In addition, good family or social support, frequent physician visits, and pairing medication administration with specific activities (such as meals or brushing one's teeth) can help improve adherence. The body of literature on adherence interventions in chronic diseases such as systemic hypertension shows that although many interventions have been tested and evaluated, only some are successful. Paradigms derived from behavioral medicine and nursing offer valuable lessons on how to motivate patients to change behavior, but these activities require skill sets not traditionally taught in medical school. Just as there are myriad causes of nonadherence, the interventions most likely will need to be multifaceted and tailored to the individual patient. Proprietary or commercial disclosure may be found after the references. | Mid | [
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Q: flex 4: while in a vgroup, how can i add a moveable element that won't be part of the vgroup? I created several components that are placed inside a VGroup. in one of the components code, i want to add an image and to move it. i don't want the image to be part of the vgroup and to be bound to the vgroup area, i want it to be like float in css. how can I do that? update I want to be able to move the element in the entire area of the application. not to move it within the vgroup. i don't want this object to be attached to any container besides the main application window in order for me not to have limits how much can i move it and where. example. If i created a new mxml component called test that extends a VGroup component. inside that vgroup i want to be able to do something like Main_Application_Window.addElement(myElement) which will allow me create animate that will move the element through the entire screen. thanks! A: Having the VGroup control things outside of its boundaries seems like a violation of OO principles to me. A more common approach would be to have your custom VGroup dispatch a custom event, which your main application would be listening for, and have the main application handle creating/placing/moving the element around. Hope that helps. | Mid | [
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#include "llvm/IR/Instructions.h" #include "libcpu.h" #include "libcpu_llvm.h" #include "frontend.h" #include "m88k_internal.h" #include "m88k_insn.h" #include <inttypes.h> using namespace llvm; #define ptr_PSR ptr_xr[0] #define ptr_TRAPNO ptr_xr[1] #define ptr_C ((Value *)cpu->feptr) ////////////////////////////////////////////////////////////////////// // TAGGING ////////////////////////////////////////////////////////////////////// #include "tag.h" static bool arch_m88k_fix_return_pc(m88k_insn const &insn, addr_t *next_pc) { if (insn.rd() != 1 || insn.rs1() != 1 || insn.format() != M88K_IFMT_REG) return false; //assert(insn.rs1() == 1 && "only r1 as source is supported"); //assert(insn.format() == M88K_IFMT_REG && "only immediate format is supported"); switch (insn.opcode()) { case M88K_OPC_ADD: case M88K_OPC_ADDU: *next_pc += insn.immediate(); return true; case M88K_OPC_SUB: case M88K_OPC_SUBU: *next_pc -= insn.immediate(); return true; default: //assert(0 && "the opcode alters r1 but it is not handled"); return false; } } int arch_m88k_tag_instr(cpu_t *cpu, addr_t pc, tag_t *tag, addr_t *new_pc, addr_t *next_pc) { m88k_insn instr = INSTR(pc); switch (instr.opcode()) { case M88K_OPC_ILLEGAL: *tag = TAG_TRAP; break; case M88K_OPC_JMP: case M88K_OPC_JMP_N: *tag = TAG_RET; break; case M88K_OPC_JSR: case M88K_OPC_JSR_N: *tag = TAG_CALL; *new_pc = NEW_PC_NONE; break; case M88K_OPC_BR: case M88K_OPC_BR_N: *new_pc = pc + (instr.branch26() << 2); *tag = TAG_BRANCH; break; case M88K_OPC_BSR: case M88K_OPC_BSR_N: *new_pc = pc + (instr.branch26() << 2); *tag = TAG_CALL; break; case M88K_OPC_BB0: case M88K_OPC_BB0_N: case M88K_OPC_BB1: case M88K_OPC_BB1_N: *new_pc = pc + (instr.branch16() << 2); *tag = TAG_COND_BRANCH; break; case M88K_OPC_BCND: case M88K_OPC_BCND_N: if (instr.mb() == M88K_BCND_NEVER) *tag = TAG_CONTINUE; else { *new_pc = pc + (instr.branch16() << 2); if (instr.mb() == M88K_BCND_ALWAYS) *tag = TAG_BRANCH; else *tag = TAG_COND_BRANCH; } break; case M88K_OPC_TB1: if (instr.rs1() == 0) { *tag = TAG_CONTINUE; break; } case M88K_OPC_TB0: case M88K_OPC_TBND: case M88K_OPC_TCND: *tag = TAG_TRAP; //XXX COND_TRAP break; default: *tag = TAG_CONTINUE; break; } if (instr.is_delaying()) { *tag |= TAG_DELAY_SLOT; *next_pc = pc + 8; // // In case of subroutine call, check // the instruction in the delay slot // modifes the return addess. // switch (instr.opcode()) { case M88K_OPC_BSR_N: case M88K_OPC_JSR_N: arch_m88k_fix_return_pc(INSTR(pc+4), next_pc); break; default: break; } } else { *next_pc = pc + 4; } return 4; } ////////////////////////////////////////////////////////////////////// enum { I_SEXT = 1, I_UPPER = 2, I_BS = 4 }; static Value * arch_m88k_get_imm(cpu_t *cpu, m88k_insn const &instr, uint32_t bits, unsigned flags, BasicBlock *bb) { uint64_t imm; if (flags & I_SEXT) imm = (uint64_t)instr.immediate(); else imm = (uint64_t)(uint16_t)instr.immediate(); if (flags & I_UPPER) { imm <<= 16; if (flags & I_BS) imm |= 0xffff; } else if (flags & I_BS) imm |= 0xffff0000; return ConstantInt::get(getIntegerType(bits ? bits : cpu->info.word_size), imm); } #define IMM arch_m88k_get_imm(cpu, instr, 0, I_SEXT, bb) #define UIMM arch_m88k_get_imm(cpu, instr, 0, 0, bb) #define IMM_U arch_m88k_get_imm(cpu, instr, 0, I_UPPER, bb) #define IMM_B arch_m88k_get_imm(cpu, instr, 0, I_BS, bb) #define IMM_UB arch_m88k_get_imm(cpu, instr, 0, I_UPPER | I_BS, bb) #define IMM32 arch_m88k_get_imm(cpu, instr, 32, I_SEXT, bb) ////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////// #define LET_PC(v) new StoreInst(v, cpu->ptr_PC, bb) #define LET_TRAPNO(v) new StoreInst(v, cpu->ptr_TRAPNO, bb) #define TRAP(n) do { \ LET_TRAPNO(CONST32(instr.vec9())); \ LET_PC(CONST(pc + 4)); \ } while(0) #define JMP_BB(b) BranchInst::Create(b, bb) #define LINKr(i, d) LET(i, CONST((uint64_t)(int64_t)(int32_t)pc+(4<<(d)))) #define LINK(d) LINKr(1, d) ////////////////////////////////////////////////////////////////////// #define GET_CARRY() (SEXT32(new LoadInst(ptr_C, "", false, bb))) #define SET_CARRY(v) (new StoreInst(v, ptr_C, bb)) ////////////////////////////////////////////////////////////////////// // FLOATING POINT ////////////////////////////////////////////////////////////////////// static Value * arch_m88k_get_fpr(cpu_t *cpu, bool xfr, m88k_reg_t r, uint32_t t, BasicBlock *bb) { if (xfr) { switch (t) { case 0: return FPBITCAST32(FR80(r)); case 1: return FPBITCAST64(FR80(r)); case 2: return FR80(r); } } else { switch (t) { case 0: return FPBITCAST32(R32(r)); case 1: if (r < 2) return FPCONST64(0); else return FPBITCAST64(OR(SHL(ZEXT64(R32(r & ~1)), CONST64(32)), ZEXT64(R32(r | 1)))); case 2: abort(); // can't happen } } abort(); // can't happen return NULL; } static void arch_m88k_set_fpr(cpu_t *cpu, bool xfr, m88k_reg_t r, uint32_t t, Value *v, BasicBlock *bb) { if (xfr) { switch(t) { case 0: LETFP(r, FPBITCAST80(FPBITCAST32(v))); break; case 1: LETFP(r, FPBITCAST80(FPBITCAST64(v))); break; case 2: LETFP(r, FPBITCAST80(v)); break; } } else { Value *iv; switch (t) { case 0: LET32(r, IBITCAST32(FPBITCAST32(v))); break; case 1: iv = IBITCAST64(FPBITCAST64(v)); LET32(r & ~1, TRUNC32(LSHR(iv, CONST64(32)))); LET32(r | 1, TRUNC32(iv)); break; case 2: abort(); // can't happen } } } static Value * arch_m88k_load_fp32(cpu_t *cpu, Value *address, BasicBlock *bb) { return FPBITCAST80(arch_load32_aligned(cpu, address, bb)); } static void arch_m88k_store_fp32(cpu_t *cpu, Value *value, Value *address, BasicBlock *bb) { arch_store32_aligned(cpu, address, IBITCAST32(FPBITCAST32(value)), bb); } static Value * arch_m88k_load_fp64(cpu_t *cpu, Value *address, BasicBlock *bb) { Value *hi = arch_load32_aligned(cpu, address, bb); Value *lo = arch_load32_aligned(cpu, ADD(address, CONST(4)), bb); return FPBITCAST80(OR(SHL(ZEXT64(hi), CONST64(32)), ZEXT64(lo))); } static void arch_m88k_store_fp64(cpu_t *cpu, Value *value, Value *address, BasicBlock *bb) { Value *v = IBITCAST64(FPBITCAST64(value)); Value *hi = TRUNC32(LSHR(v, CONST64(32))); Value *lo = TRUNC32(v); arch_store32_aligned(cpu, address, hi, bb); arch_store32_aligned(cpu, ADD(address, CONST32(4)), lo, bb); } static Value * arch_m88k_load_fp80(cpu_t *cpu, Value *address, BasicBlock *bb) { return FPCONST80(0); } static void arch_m88k_store_fp80(cpu_t *cpu, Value *value, Value *address, BasicBlock *bb) { } #define GET_FPR(x,r,t) arch_m88k_get_fpr(cpu, x, r, t, bb) #define SET_FPR(x,r,t,v) arch_m88k_set_fpr(cpu, x, r, t, v, bb) enum { FP_OP_CMP, FP_OP_ADD, FP_OP_SUB, FP_OP_MUL, FP_OP_DIV, FP_OP_REM, FP_OP_CMP_ORD, FP_OP_CMP_OEQ, FP_OP_CMP_OGE, FP_OP_CMP_OGT, FP_OP_CMP_UEQ, FP_OP_CMP_UGE, FP_OP_CMP_UGT }; /* * The Motorola 88K can operate on three different * types of floating point using the same register set, * and can mix them in a single instruction so that, * for example, you can add a double to a single and * put the result in an extended float. * * LLVM mandates both operands of a binary operation * shall be the same size. This function overrides * frontend.h macros and extends the operation to * the biggest of the two operands. */ static Value * arch_m88k_fp_op(cpu_t *cpu, unsigned op, Value *a, Value *b, BasicBlock *bb) { Type::TypeID typeid_a, typeid_b; Type *type_a = a->getType(); Type *type_b = b->getType(); typeid_a = type_a->getTypeID(); typeid_b = type_b->getTypeID(); // Both a and b shall be of the same size, // extend to the biggest. if (typeid_a != typeid_b) { if (typeid_a > typeid_b) b = new FPExtInst(b, type_a, "", bb); else a = new FPExtInst(a, type_b, "", bb); } switch (op) { case FP_OP_ADD: return FPADD(a, b); case FP_OP_SUB: return FPSUB(a, b); case FP_OP_MUL: return FPMUL(a, b); case FP_OP_DIV: return FPDIV(a, b); case FP_OP_REM: return FPREM(a, b); case FP_OP_CMP_ORD: return FPCMP_ORD(a, b); case FP_OP_CMP_OEQ: return FPCMP_OEQ(a, b); case FP_OP_CMP_OGE: return FPCMP_OGE(a, b); case FP_OP_CMP_OGT: return FPCMP_OGT(a, b); case FP_OP_CMP_UEQ: return FPCMP_UEQ(a, b); case FP_OP_CMP_UGE: return FPCMP_UGE(a, b); case FP_OP_CMP_UGT: return FPCMP_UGT(a, b); default: assert(0 && "Invalid FP operation"); return NULL; } } #undef FPADD #undef FPSUB #undef FPMUL #undef FPDIV #undef FPREM #undef FPCMP_ORD #undef FPCMP_OEQ #undef FPCMP_OGE #undef FPCMP_OGT #undef FPCMP_OLT #undef FPCMP_UEQ #undef FPCMP_UGE #undef FPCMP_UGT #define FPADD(a, b) arch_m88k_fp_op(cpu, FP_OP_ADD, a, b, bb) #define FPSUB(a, b) arch_m88k_fp_op(cpu, FP_OP_SUB, a, b, bb) #define FPMUL(a, b) arch_m88k_fp_op(cpu, FP_OP_MUL, a, b, bb) #define FPDIV(a, b) arch_m88k_fp_op(cpu, FP_OP_DIV, a, b, bb) #define FPREM(a, b) arch_m88k_fp_op(cpu, FP_OP_REM, a, b, bb) #define FPCMP_ORD(a, b) arch_m88k_fp_op(cpu, FP_OP_CMP_ORD, a, b, bb) #define FPCMP_OEQ(a, b) arch_m88k_fp_op(cpu, FP_OP_CMP_OEQ, a, b, bb) #define FPCMP_OGE(a, b) arch_m88k_fp_op(cpu, FP_OP_CMP_OGE, a, b, bb) #define FPCMP_OGT(a, b) arch_m88k_fp_op(cpu, FP_OP_CMP_OGT, a, b, bb) #define FPCMP_OLT(a, b) NOT(FPCMP_OGE(a, b)) #define FPCMP_UEQ(a, b) arch_m88k_fp_op(cpu, FP_OP_CMP_UEQ, a, b, bb) #define FPCMP_UGE(a, b) arch_m88k_fp_op(cpu, FP_OP_CMP_UGE, a, b, bb) #define FPCMP_UGT(a, b) arch_m88k_fp_op(cpu, FP_OP_CMP_UGT, a, b, bb) ////////////////////////////////////////////////////////////////////// // CONDITIONAL EXECUTION ////////////////////////////////////////////////////////////////////// static Value * arch_m88k_bcnd_cond(cpu_t *cpu, Value *src1, m88k_bcnd_t cond, BasicBlock *bb) { switch (cond) { case M88K_BCND_EQ0: return ICMP_EQ(src1, CONST32(0)); case M88K_BCND_NE0: return ICMP_NE(src1, CONST32(0)); case M88K_BCND_GT0: return ICMP_SGT(src1, CONST32(0)); case M88K_BCND_LT0: return ICMP_SLT(src1, CONST32(0)); case M88K_BCND_LE0: return ICMP_SLE(src1, CONST32(0)); case M88K_BCND_GE0: return ICMP_SGE(src1, CONST32(0)); case M88K_BCND_4: // rs1 != 0x80000000 && rs1 < 0 return AND(ICMP_NE(src1, CONST32(0x80000000)), ICMP_SLT(src1, CONST32(0))); case M88K_BCND_5: // (rs1 & 0x7fffffff) != 0 return ICMP_NE(AND(src1, CONST32(0x7fffffff)), CONST32(0)); case M88K_BCND_6: // rs != 0x80000000 && rs <= 0 return AND(ICMP_NE(src1, CONST32(0x80000000)), ICMP_SLE(src1, CONST32(0))); case M88K_BCND_7: // rs != 0x80000000 return ICMP_NE(src1, CONST32(0x80000000)); case M88K_BCND_8: // rs == 0x80000000 return ICMP_EQ(src1, CONST32(0x80000000)); case M88K_BCND_9: // rs > 0 || rs == 0x80000000 return OR(ICMP_SGT(src1, CONST(0)), ICMP_EQ(src1, CONST32(0x80000000))); case M88K_BCND_10: // (rs1 & 0x7fffffff) == 0 return ICMP_EQ(AND(src1, CONST32(0x7fffffff)), CONST32(0)); case M88K_BCND_11: // rs1 >= 0 || rs1 == 0x80000000 return OR(ICMP_SGE(src1, CONST(0)), ICMP_EQ(src1, CONST32(0x80000000))); case M88K_BCND_NEVER: case M88K_BCND_ALWAYS: return NULL; default: assert(0 && "Cannot happen"); return NULL; } } Value * arch_m88k_translate_cond(cpu_t *cpu, addr_t pc, BasicBlock *bb) { m88k_insn insn(INSTR(pc)); uint8_t bit = insn.mb(); switch (insn.opcode()) { case M88K_OPC_BCND: case M88K_OPC_BCND_N: return arch_m88k_bcnd_cond(cpu, R32(insn.rs1()), (m88k_bcnd_t)(bit & 0xf), bb); case M88K_OPC_BB0: case M88K_OPC_BB0_N: return ICMP_EQ(AND(R32(insn.rs1()), CONST32(1 << bit)), CONST(0)); case M88K_OPC_BB1: case M88K_OPC_BB1_N: return ICMP_NE(AND(R32(insn.rs1()), CONST32(1 << bit)), CONST(0)); default: return NULL; } } ////////////////////////////////////////////////////////////////////// // COMPLEX INSTRUCTIONS ////////////////////////////////////////////////////////////////////// #define COMPUTE_CARRY(src1, src2, result) \ (AND(ICMP_NE(src2, CONST(0)), ICMP_ULT(result, src1))) #define COMPUTE_BORROW(src1, src2, result) \ (AND(ICMP_NE(src2, CONST(0)), ICMP_UGT(result, src1))) static void arch_m88k_addsub(cpu_t *cpu, addr_t pc, m88k_reg_t dst, Value *src1, Value *src2, bool sub, unsigned carry, bool overflow_trap, BasicBlock *bb) { Value *result; if (sub) result = SUB(src1, src2); else result = ADD(src1, src2); if (overflow_trap) { //XXX trap on overflow! } if (carry & M88K_CARRY_IN) { if (sub) result = SUB(result, GET_CARRY()); else result = ADD(result, GET_CARRY()); } if (carry & M88K_CARRY_OUT) { if (sub) SET_CARRY(COMPUTE_BORROW(src1, src2, result)); else SET_CARRY(COMPUTE_CARRY(src1, src2, result)); } LET32(dst, result); } static void arch_m88k_shift(cpu_t *cpu, m88k_opcode_t opc, m88k_reg_t rd, Value *src1, Value *src2, uint32_t width, uint32_t offset, bool ifmt, BasicBlock *bb) { uint32_t wmask = (width != 0) ? (1 << width) - 1 : (-1U); switch (opc) { case M88K_OPC_ROT: // (rs1 >> bits)|(rs1 << (32-bits)) if (ifmt) LET32(rd, OR(LSHR(src1, CONST32(offset)), SHL(src1, CONST32(32 - offset)))); else LET32(rd, OR(LSHR(src1, AND(src2, CONST32(0x1f))), SHL(src1, SUB(CONST32(32), AND(src2, CONST32(0x1f)))))); break; case M88K_OPC_MAK: // (rs1 & wmask) << offset if (ifmt) LET32(rd, SHL(AND(src1, CONST32(wmask)), CONST32(offset))); else LET32(rd, SHL(src1, src2)); break; case M88K_OPC_SET: // rs1 | (wmask << n) if (ifmt) LET32(rd, OR(src1, CONST32(wmask << offset))); else LET32(rd, OR(src1, SHL(CONST32(wmask), AND(src2, CONST32(0x1f))))); break; case M88K_OPC_CLR: // rs1 & ~(wmask << n) if (ifmt) LET32(rd, AND(src1, CONST32(~(wmask << offset)))); else LET32(rd, AND(src1, COM(SHL(CONST32(wmask), AND(src2, CONST32(0x1f)))))); break; case M88K_OPC_EXT: // ((int)rs1 >> n) & wmask if (ifmt) { if (width == 0) { LET32(rd, ASHR(src1, CONST32(offset))); } else { unsigned nb = 32 - (offset + width); LET32(rd, ASHR(SHL(src1, CONST32(nb & 0x1f)), CONST32((offset + nb) & 0x1f))); } } else LET32(rd, ASHR(src1, AND(src2, CONST32(0x1f)))); break; case M88K_OPC_EXTU: // (rs1 >> n) & wmask if (ifmt) LET32(rd, AND(LSHR(src1, CONST32(offset)), CONST32(wmask))); else LET32(rd, LSHR(src1, AND(src2, CONST32(0x1f)))); break; default: abort(); } } /* * Motorola 88000 optimized cmp: * * if (s1 == s2) * dst = 0x5aa4; * else { * dst = 0xa008; * if ((u)s1 > (u)s2) dst |= 0x900; else dst |= 0x600; * if ((s)s1 > (s)s2) dst |= 0x90; else dst |= 0x60; * } * * bit name meaning/pseudo-code * 2 eq s1 == s2 * 3 ne s1 != s2 * 4 gt (s)s1 > (s)s2 * 5 le (s)s1 <= (s)s2 * 6 lt (s)s1 < (s)s2 * 7 ge (s)s1 >= (s)s2 * 8 hi (u)s1 > (u)s2 * 9 ls (u)s1 <= (u)s2 * 10 lo (u)s1 < (u)s2 * 11 hs (u)s1 >= (u)s2 * 12 be any_byte_eq(s1, s2) (supported partially) * 13 nb !any_byte_eq(s1, s2) (supported partially) * 14 he any_half_eq(s1, s2) (supported partially) * 15 nh !any_half_eq(s1, s2) (supported partially) */ static void arch_m88k_cmp(cpu_t *cpu, m88k_reg_t dst, Value *src1, Value *src2, BasicBlock *bb) { LET32(dst, SELECT(ICMP_EQ(src1, src2), CONST32(0x5aa4), // EQ | LE | GE | LS | HS | BE | HE OR(CONST(0xa008), // NE | NB | NH // (((-X) ^ 6) & 0xf) << Y will do the trick. OR(SHL(AND(XOR(SEXT32(ICMP_UGT(src1, src2)), CONST32(6)), CONST32(0xf)), CONST32(8)), SHL(AND(XOR(SEXT32(ICMP_SGT(src1, src2)), CONST32(6)), CONST32(0xf)), CONST32(4)))))); } /* Small inline optimization for always true case (reg1 == reg2). */ static inline void arch_m88k_cmp_reg(cpu_t *cpu, m88k_reg_t dst, m88k_reg_t src1, m88k_reg_t src2, BasicBlock *bb) { if (src1 == src2) LET32(dst, CONST32(0x5aa4)); else arch_m88k_cmp(cpu, dst, R32(src1), R32(src2), bb); } /* * Motorola 88000 fcmp(u): * * bit name meaning/pseudo-code * 0 un is_unordered(s1) || is_unordered(s2) * 1 leg !(is_unordered(s1) || is_unordered(s2)) * 2 eq s1 == s2 * 3 ne s1 != s2 * 4 gt s1 > s2 * 5 le s1 <= s2 * 6 lt s1 < s2 * 7 ge s1 >= s2 * 8 ou (s2 >= 0.0) && (is_unordered(s1 - s2) || (s1 < 0 || s1 > s2)) * 9 ib (s2 >= 0.0) && is_ordered(s1 - s2) && (s1 >= 0 && s1 <= s2) * 11 in (s2 >= 0.0) && is_ordered(s1 - s2) && (s1 >= 0 && s1 <= s2) * 12 ob (s2 >= 0.0) && (is_unordered(s1 - s2) || (s1 < 0 || s1 > s2)) * 13 ue is_unordered(s1 - s2) || (s1 == s2) * 14 lg is_ordered(s1 - s2) && (s1 < s2 || s1 > s2) * 15 ug is_unordered(s1 - s2) || (s1 > s2) * 16 ule is_unordered(s1 - s2) || (s1 <= s2) * 17 ul is_unordered(s1 - s2) || (s1 < s2) * 18 uge is_unordered(s1 - s2) || (s1 >= s2) * * TBD If an operand is either signalling or quiet NaN, * set the FINV bit in the FPSR; if using fcmp, * raise also FPE. */ enum { F_UN = (1 << 0), F_LEG = (1 << 1), F_EQ = (1 << 2), F_NE = (1 << 3), F_GT = (1 << 4), F_LE = (1 << 5), F_LT = (1 << 6), F_GE = (1 << 7), F_OU = (1 << 8), F_IB = (1 << 9), F_IN = (1 << 11), F_OB = (1 << 12), F_UE = (1 << 13), F_LG = (1 << 14), F_UG = (1 << 15), F_ULE = (1 << 16), F_UL = (1 << 17), F_UGE = (1 << 18) }; static void arch_m88k_fcmp(cpu_t *cpu, m88k_reg_t rdst, Value *src1, Value *src2, BasicBlock *bb) { Value *zero = FPCONST80(0); Value *ord = FPCMP_ORD(src1, src2); Value *uno = NOT(ord); Value *d = FPSUB(src1, src2); Value *dord = FPCMP_ORD(d, d); Value *duno = NOT(dord); Value *neg2 = AND(FPCMP_ORD(src2, src2), FPCMP_OLT(src2, zero)); Value *dst = R32(rdst); // UN | LEG LET32(rdst, ZEXT32(uno)); LET32(rdst, OR(dst, SHL(ZEXT32(ord), CONST32(1)))); // EQ | NE | GT | LE | LT | GE LET32(rdst, OR(dst, SELECT(FPCMP_OEQ(src1, src2), // EQ | LE | GE CONST32(F_EQ | F_LE | F_GE), // NE | LT | GT OR(CONST(F_NE), SELECT(FPCMP_OGT(src1, src2), CONST32(F_GT), CONST32(F_LT)))))); // OU | IB | IN | OB LET32(rdst, OR(dst, SELECT(neg2, CONST32(0), SELECT(OR(duno, OR(FPCMP_OLT(src1, zero), FPCMP_OGT(src1, src2))), CONST32(F_OU | F_OB), CONST32(F_IN | F_IB))))); // LG LET32(rdst, OR(dst, SELECT(OR(dord, OR(FPCMP_OLT(src1, src2), FPCMP_OGT(src1, src2))), CONST32(F_LG), CONST32(0)))); // UE | UG | ULE | UL | UGE LET32(rdst, OR(dst, SELECT(dord, CONST32(0), // UE | ULE | UGE SELECT(FPCMP_UEQ(src1, src2), CONST32(F_UE | F_ULE | F_UGE), SELECT(FPCMP_UGT(src1, src2), CONST32(F_GT), CONST32(F_LT)))))); } /* * Exchange Register/Memory (Word/Byte) * * NOTE: This operation locks the bus, so when we'll go system * emulation, this operation must be atomic. */ static void arch_m88k_xmem(cpu_t *cpu, bool byte, m88k_reg_t rd, Value *src1, Value *src2, BasicBlock *bb) { Value *reg_value; Value *mem_value; Value *address; reg_value = R32(rd); if (byte) { address = ADD(src1, src2); mem_value = arch_load8(cpu, address, bb); } else { address = ADD(src1, SHL(src2, CONST32(2))); mem_value = arch_load32_aligned(cpu, address, bb); } LET32(rd, mem_value); if (byte) STORE8(reg_value, address); else STORE32(reg_value, address); } ////////////////////////////////////////////////////////////////////// // TRANSLATOR ////////////////////////////////////////////////////////////////////// int arch_m88k_translate_instr(cpu_t *cpu, addr_t pc, BasicBlock *bb) { #define BAD do { printf("%s:%u: BAD INSTRUCTION AT PC %" PRIu64 "\n", __func__, __LINE__, pc); exit(1); } while(0) #define LOGX LOG("%s:%d PC=%llx\n", __func__, __LINE__, pc); m88k_insn instr = INSTR(pc); m88k_opcode_t opc = instr.opcode(); m88k_insnfmt_t fmt = instr.format(); switch (opc) { case M88K_OPC_ILLEGAL: BAD; break; case M88K_OPC_ADD: case M88K_OPC_ADDU: if (fmt == M88K_IFMT_REG) arch_m88k_addsub(cpu, pc, instr.rd(), R32(instr.rs1()), (opc == M88K_OPC_ADD) ? IMM : UIMM, false, instr.carry(), (opc == M88K_OPC_ADD), bb); else arch_m88k_addsub(cpu, pc, instr.rd(), R32(instr.rs1()), R32(instr.rs2()), false, instr.carry(), (opc == M88K_OPC_ADD), bb); break; case M88K_OPC_SUB: case M88K_OPC_SUBU: if (fmt == M88K_IFMT_REG) arch_m88k_addsub(cpu, pc, instr.rd(), R32(instr.rs1()), (opc == M88K_OPC_SUB) ? IMM : UIMM, true, instr.carry(), (opc == M88K_OPC_SUB), bb); else arch_m88k_addsub(cpu, pc, instr.rd(), R32(instr.rs1()), R32(instr.rs2()), true, instr.carry(), (opc == M88K_OPC_SUB), bb); break; case M88K_OPC_MULS: LET32(instr.rd(), MUL(R32(instr.rs1()), R32(instr.rs2()))); break; case M88K_OPC_MULU: if (fmt == M88K_IFMT_REG) LET32(instr.rd(), MUL(R32(instr.rs1()), UIMM)); else LET32(instr.rd(), MUL(R32(instr.rs1()), R32(instr.rs2()))); break; case M88K_OPC_DIVS: if (fmt == M88K_IFMT_REG) LET32(instr.rd(), SDIV(R32(instr.rs1()), IMM)); else LET32(instr.rd(), SDIV(R32(instr.rs1()), R32(instr.rs2()))); break; // DIVU doesn't fault on div by zero. case M88K_OPC_DIVU: { Value *divisor; if (fmt == M88K_IFMT_REG) divisor = UIMM; else divisor = R32(instr.rs2()); LET32(instr.rd(), SELECT(ICMP_EQ(divisor, CONST32(0)), CONST32(0), UDIV(R32(instr.rs1()), divisor))); break; } case M88K_OPC_MASK: LET32(instr.rd(), AND(R32(instr.rs1()), UIMM)); break; case M88K_OPC_MASK_U: LET32(instr.rd(), AND(R32(instr.rs1()), IMM_U)); break; case M88K_OPC_AND: if (fmt == M88K_IFMT_REG) LET32(instr.rd(), AND(R32(instr.rs1()), IMM_B)); else LET32(instr.rd(), AND(R32(instr.rs1()), R32(instr.rs2()))); break; case M88K_OPC_AND_C: LET32(instr.rd(), AND(R32(instr.rs1()), COM(R32(instr.rs2())))); break; case M88K_OPC_AND_U: LET32(instr.rd(), AND(R32(instr.rs1()), IMM_UB)); break; case M88K_OPC_OR: if (fmt == M88K_IFMT_REG) LET32(instr.rd(), OR(R32(instr.rs1()), UIMM)); else LET32(instr.rd(), OR(R32(instr.rs1()), R32(instr.rs2()))); break; case M88K_OPC_OR_C: LET32(instr.rd(), OR(R32(instr.rs1()), COM(R32(instr.rs2())))); break; case M88K_OPC_OR_U: LET32(instr.rd(), OR(R32(instr.rs1()), IMM_U)); break; case M88K_OPC_XOR: if (fmt == M88K_IFMT_REG) LET32(instr.rd(), XOR(R32(instr.rs1()), UIMM)); else LET32(instr.rd(), XOR(R32(instr.rs1()), R32(instr.rs2()))); break; case M88K_OPC_XOR_C: LET32(instr.rd(), XOR(R32(instr.rs1()), COM(R32(instr.rs2())))); break; case M88K_OPC_XOR_U: LET32(instr.rd(), XOR(R32(instr.rs1()), IMM_U)); break; case M88K_OPC_ROT: case M88K_OPC_MAK: case M88K_OPC_SET: case M88K_OPC_CLR: case M88K_OPC_EXT: case M88K_OPC_EXTU: arch_m88k_shift(cpu, opc, instr.rd(), R32(instr.rs1()), (fmt == M88K_BFMT_REG) ? NULL : R32(instr.rs2()), instr.bit_width(), instr.bit_offset(), (fmt == M88K_BFMT_REG), bb); break; case M88K_OPC_FF0: LET32(instr.rd(), FFC32(R32(instr.rs2()))); break; case M88K_OPC_FF1: LET32(instr.rd(), FFS32(R32(instr.rs2()))); break; case M88K_OPC_CMP: if (fmt == M88K_IFMT_REG) arch_m88k_cmp(cpu, instr.rd(), R32(instr.rs1()), UIMM, bb); else arch_m88k_cmp_reg(cpu, instr.rd(), instr.rs1(), instr.rs2(), bb); break; case M88K_OPC_LDA: LET32(instr.rd(), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(2)))); break; case M88K_OPC_LDA_H: LET32(instr.rd(), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(1)))); break; case M88K_OPC_LDA_D: LET32(instr.rd(), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(3)))); break; case M88K_OPC_LDA_X: LET32(instr.rd(), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(4)))); break; case M88K_OPC_LD: if (fmt == M88K_IFMT_MEM) LOAD32(instr.rd(), ADD(R32(instr.rs1()), UIMM)); else if (fmt == M88K_IFMT_XMEM) { LETFP(instr.rd(), arch_m88k_load_fp32(cpu, ADD(R32(instr.rs1()), UIMM), bb)); } else if (fmt == M88K_TFMT_REG) { LOAD32(instr.rd(), ADD(R32(instr.rs1()), R32(instr.rs2()))); } else if (fmt == M88K_TFMT_REGS) { LOAD32(instr.rd(), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(2)))); } else { BAD; } break; case M88K_OPC_LD_B: if (fmt == M88K_IFMT_MEM) LOAD8S(instr.rd(), ADD(R32(instr.rs1()), UIMM)); else LOAD8S(instr.rd(), ADD(R32(instr.rs1()), R32(instr.rs2()))); break; case M88K_OPC_LD_BU: if (fmt == M88K_IFMT_MEM) LOAD8(instr.rd(), ADD(R32(instr.rs1()), UIMM)); else LOAD8(instr.rd(), ADD(R32(instr.rs1()), R32(instr.rs2()))); break; case M88K_OPC_LD_H: if (fmt == M88K_IFMT_MEM) { LOAD16S(instr.rd(), ADD(R32(instr.rs1()), UIMM)); } else if (fmt == M88K_TFMT_REG) { LOAD16S(instr.rd(), ADD(R32(instr.rs1()), R32(instr.rs2()))); } else if (fmt == M88K_TFMT_REGS) { LOAD16S(instr.rd(), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(1)))); } else { BAD; } break; case M88K_OPC_LD_HU: if (fmt == M88K_IFMT_MEM) { LOAD16(instr.rd(), ADD(R32(instr.rs1()), UIMM)); } else if (fmt == M88K_TFMT_REG) { LOAD16(instr.rd(), ADD(R32(instr.rs1()), R32(instr.rs2()))); } else if (fmt == M88K_TFMT_REGS) { LOAD16(instr.rd(), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(1)))); } else { BAD; } break; case M88K_OPC_LD_D: if (fmt == M88K_IFMT_MEM) { LOAD32(instr.rd() & ~1, ADD(R32(instr.rs1()), UIMM)); LOAD32(instr.rd() | 1, ADD(ADD(R32(instr.rs1()), UIMM), CONST32(4))); } else if (fmt == M88K_IFMT_XMEM) { LETFP(instr.rd(), arch_m88k_load_fp64(cpu, ADD(R32(instr.rs1()), UIMM), bb)); } else if (fmt == M88K_TFMT_REG) { LOAD32(instr.rd() & ~1, ADD(R32(instr.rs1()), R32(instr.rs2()))); LOAD32(instr.rd() | 1, ADD(R32(instr.rs1()), ADD(R32(instr.rs2()), CONST32(4)))); } else if (fmt == M88K_TFMT_REGS) { LOAD32(instr.rd() & ~1, ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(3)))); LOAD32(instr.rd() | 1, ADD(R32(instr.rs1()), ADD(SHL(R32(instr.rs2()), CONST32(3)), CONST32(4)))); } else { BAD; } break; case M88K_OPC_LD_X: LETFP(instr.rd(), arch_m88k_load_fp80(cpu, ADD(R32(instr.rs1()), UIMM), bb)); break; case M88K_OPC_ST: if (fmt == M88K_IFMT_MEM) STORE32(R(instr.rd()), ADD(R32(instr.rs1()), UIMM)); else if (fmt == M88K_IFMT_XMEM) { arch_m88k_store_fp32(cpu, GET_FPR(true, instr.rd(), 2), ADD(R32(instr.rs1()), UIMM), bb); } else if (fmt == M88K_TFMT_REG) { STORE32(R(instr.rd()), ADD(R32(instr.rs1()), R32(instr.rs2()))); } else if (fmt == M88K_TFMT_REGS) { STORE32(R(instr.rd()), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(2)))); } else { BAD; } break; case M88K_OPC_ST_B: if (fmt == M88K_IFMT_MEM) STORE8(R(instr.rd()), ADD(R32(instr.rs1()), UIMM)); else STORE8(R(instr.rd()), ADD(R32(instr.rs1()), R32(instr.rs2()))); break; case M88K_OPC_ST_H: if (fmt == M88K_IFMT_MEM) STORE16(R(instr.rd()), ADD(R32(instr.rs1()), UIMM)); else if (fmt == M88K_TFMT_REG) STORE16(R(instr.rd()), ADD(R32(instr.rs1()), R32(instr.rs2()))); else if (fmt == M88K_TFMT_REGS) STORE16(R(instr.rd()), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(1)))); else { BAD; } break; case M88K_OPC_ST_D: if (fmt == M88K_IFMT_MEM) { STORE32(R(instr.rd() & ~1), ADD(R32(instr.rs1()), UIMM)); STORE32(R(instr.rd() | 1), ADD(ADD(R32(instr.rs1()), UIMM), CONST32(4))); } else if (fmt == M88K_IFMT_XMEM) { arch_m88k_store_fp64(cpu, GET_FPR(true, instr.rd(), 2), ADD(R32(instr.rs1()), UIMM), bb); } else if (fmt == M88K_TFMT_REG) { STORE32(R(instr.rd() & ~1), ADD(R32(instr.rs1()), R32(instr.rs2()))); STORE32(R(instr.rd() | 1), ADD(R32(instr.rs1()), ADD(R32(instr.rs2()), CONST32(4)))); } else if (fmt == M88K_TFMT_REGS) { STORE32(R(instr.rd() & ~1), ADD(R32(instr.rs1()), SHL(R32(instr.rs2()), CONST32(3)))); STORE32(R(instr.rd() | 1), ADD(R32(instr.rs1()), ADD(SHL(R32(instr.rs2()), CONST32(3)), CONST32(4)))); } break; case M88K_OPC_ST_X: arch_m88k_store_fp80(cpu, GET_FPR(true, instr.rd(), 2), ADD(R32(instr.rs1()), UIMM), bb); break; case M88K_OPC_XMEM: case M88K_OPC_XMEM_BU: arch_m88k_xmem(cpu, (opc == M88K_OPC_XMEM_BU), instr.rd(), R32(instr.rs1()), R32(instr.rs2()), bb); break; case M88K_OPC_JSR: LINK(0); case M88K_OPC_JMP: LET_PC(R(instr.rs2())); break; case M88K_OPC_JSR_N: LINK(1); case M88K_OPC_JMP_N: LET_PC(R(instr.rs2())); break; case M88K_OPC_BSR: LINK(0); case M88K_OPC_BR: break; case M88K_OPC_BSR_N: LINK(1); case M88K_OPC_BR_N: break; // jump pc + disp IF !(rS & (1 << bit)) case M88K_OPC_BB0: case M88K_OPC_BB0_N: // jump pc + disp IF (rS & (1 << bit)) case M88K_OPC_BB1: case M88K_OPC_BB1_N: // jump pc + disp IF rS <cc> 0 case M88K_OPC_BCND: case M88K_OPC_BCND_N: break; case M88K_OPC_TB1: if (instr.rs1() == 0) break; case M88K_OPC_TB0: case M88K_OPC_TBND: case M88K_OPC_TCND: TRAP(CONST32(instr.vec9())); break; //////////////////// FPU /////////////////// case M88K_OPC_FADD: SET_FPR(fmt == M88K_TFMT_XFR, instr.rd(), instr.td(), FPADD(GET_FPR(fmt == M88K_TFMT_XFR, instr.rs1(), instr.t1()), GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2()))); break; case M88K_OPC_FSUB: SET_FPR(fmt == M88K_TFMT_XFR, instr.rd(), instr.td(), FPSUB(GET_FPR(fmt == M88K_TFMT_XFR, instr.rs1(), instr.t1()), GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2()))); break; case M88K_OPC_FMUL: SET_FPR(fmt == M88K_TFMT_XFR, instr.rd(), instr.td(), FPMUL(GET_FPR(fmt == M88K_TFMT_XFR, instr.rs1(), instr.t1()), GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2()))); break; case M88K_OPC_FDIV: SET_FPR(fmt == M88K_TFMT_XFR, instr.rd(), instr.td(), FPDIV(GET_FPR(fmt == M88K_TFMT_XFR, instr.rs1(), instr.t1()), GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2()))); break; case M88K_OPC_FCVT: SET_FPR(fmt == M88K_TFMT_XFR, instr.rd(), instr.td(), GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2())); break; case M88K_OPC_INT: // round-to-zero LET32(instr.rd(), FPTOSI(32, GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2()))); break; case M88K_OPC_NINT: // round-to-nearest LET32(instr.rd(), FPTOSI(32, GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2()))); break; case M88K_OPC_TRNC: // truncation LET32(instr.rd(), FPTOSI(32, GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2()))); break; case M88K_OPC_FLT: // flt <- int SET_FPR(fmt == M88K_TFMT_XFR, instr.rd(), instr.td(), SITOFP(32, R32(instr.rs2()))); break; case M88K_OPC_FSQRT: SET_FPR(fmt == M88K_TFMT_XFR, instr.rd(), instr.td(), FPSQRT(FPBITCAST64(GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2())))); break; case M88K_OPC_FCMP: case M88K_OPC_FCMPU: arch_m88k_fcmp(cpu, instr.rd(), GET_FPR(fmt == M88K_TFMT_XFR, instr.rs1(), instr.t1()), GET_FPR(fmt == M88K_TFMT_XFR, instr.rs2(), instr.t2()), bb); break; case M88K_OPC_MOV: switch(fmt) { case M88K_TFMT_XREG: // xfr <- gpr SET_FPR(true, instr.rd(), 2, GET_FPR(false, instr.rs2(), instr.t2())); break; case M88K_TFMT_REGX: // gpr/xfr <- xfr if (instr & 0x200) SET_FPR(true, instr.rd(), 2, GET_FPR(true, instr.rs2(), 2)); else SET_FPR(false, instr.rd(), instr.td(), GET_FPR(true, instr.rs2(), 2)); break; default: assert(0 && "Cannot happen"); } break; case M88K_OPC_DIVU_D: case M88K_OPC_MULU_D: // XXX TODO break; case M88K_OPC_FLDCR: // XXX TODO LET32(instr.rd(), CONST32(0)); case M88K_OPC_FSTCR: // XXX TODO break; default: LOG("INVALID %s:%d\n", __func__, __LINE__); exit(1); break; } return 4; } | Low | [
0.521829521829521,
31.375,
28.75
]
|
Finding the Depth in Brevity Oikawa Blooms Oikawa Blooms (A Haikyuu!! Character Analysis) With the conclusion to Oikawa’s first (and hopefully not last!) major arc as a character coming in Episode 25 of Haikyuu!!’s second season, I wanted to analyze his character thus far. Oikawa’s a goofy ladykiller, and easily the most developed of the non-Karasuno players. Haikyuu!! is filled with foil and complementary characters, and Oikawa is the most important of them all. Despite Hinata’s apparent role as main protagonist, Oikawa’s foil with Kageyama is perhaps the most important relationship in the series, and the competition between these two setters is really the focal point of the new Karasuno-Seijoh rivalry—not to mention the story of the entire first two seasons. Let’s figure out how he got there and what makes him such an essential character. A defining feature of Oikawa’s character is his hate for “geniuses”—which can really just be interpreted as ‘the highly talented’—but what’s interesting is that Oikawa was once genius-esque himself. He comes into junior high with a physical edge on other kids his age. Because of his initial advantage, coming into contact with players with even more natural talent than him (that ‘true’ genius level) frustrates him even more than if he had been a talentless player from the start. At first, Oikawa gets to experience an advantage in volleyball. When he meets Ushijima, an even more advantaged player, it negates Oikawa’s abilities and leaves him helpless. The arrival of Kageyama is a thorn in Oikawa’s back, as Kageyama’s talent threatens to outshine Oikawa on his own team. As Iwaizumi tells us, this sends Oikawa into a “panic”, leading him to overwork himself and lose focus during matches. Geniuses like Kageyama are demons that Oikawa doesn’t believe he can overcome on the court. Iwaizumi points out the selfishness of Oikawa thinking it’s “I” vs. geniuses with a nice headbutt before presenting one of the most pervasive motifs of the series: “The team with the strong six players is the stronger team.” You don’t need to be a genius player, you simply need make sure you and your team score enough points to win. This gives Oikawa the focus he needs to return to leading his team, and even to take a set off Shiratorizawa. However, it isn’t enough to overcome the wall that is a genius. He loses to Shiratorizawa. The words that motivate him to continue fighting and to believe he can eventually overcome that wall come from his junior high coach: nothing can ever increase the amount of raw talent you have, but have you really discovered just how much talent you have? Have you really perfected everything else about your play? Can you really not go any higher? The chunk of raw talent inside Oikawa may not be as powerful as Kageyama’s or Ushijima’s, but that doesn’t mean Oikawa can’t make it bloom bigger. He resolves to do everything he can to increase his chances of winning. After junior high (and presumably the first two years of high school), Oikawa solidifies his vendetta against geniuses and works to perfect his playstyle. Really, he has an agenda against talented people, and wants them to throw all their best attacks at him so he can overcome it all and beat them knowing nothing was left in reserve. His playstyle becomes an echo of Iwaizumi’s words in junior high—make a team of the strongest six. If this includes practicing his own technique, studying the matches of his opponents, or meditating for focus—he’ll do it. Although he may appear to be joking around (as he is want to do), most of what Oikawa says is super-calculated. Actually, the show does a good job of cluing us in on when he isn’t being serious at all by animating his face in expressive ways. But, when his spikers are warming up before the Inter High match against Karasuno, his comments (even the ones to Iwaizumi) are meant to reassure his teammates. He means to reassure and to make his teammates aware he knows how/what they’re thinking. To Oikawa, a setter is a tool for the spiker to use. By speaking what the spikers are thinking, he lets them know he’s aware of their needs and implies they can control his tosses from inside their heads. This is a big reason his teammates have ultimate trust in him. With that, Oikawa becomes the egoless egoist. Egoless because he tosses the balls up for his spikers, always thinking of them and how he can help them play their best. Egoist because he plays this way out of his own obsession with proving he can beat geniuses. This shines through in his serves/dumps that are reliable enough to put his team at ease, but flashy enough to give him satisfaction. The same can be said for his opening line of “I believe in all of you”—both a complete reassurance and a complete threat. This all works because the stronger six players are the stronger team. By losing his ego, his team reaches a total understanding of each other (the reassurance). By understanding each other, they can play as a strong enough six to satisfy Oikawa’s ego (the threat). This idea shows up all over Oikawa’s playstyle and leadership. Honestly, there are too many examples to name in this essay—any line out of Oikawa’s mouth during a match would work. Let’s just look at a couple specific moments. Oikawa both attempts to break down the solidarity of the six players on his opposing team, as well as boost the solidarity of his own six. At the Inter High, he originally attempts to ruin Karasuno’s morale by getting a service ace off of their libero, Nishinoya (this would also boost his team’s morale). Once that fails, he switches to targeting a weaker receiver and important attacker, Tanaka. If he can spawn doubt or fear in Tanaka’s mind, he’ll have weakened one of Karasuno’s six. As for his own team, Oikawa is a machine gun of encouragement and focus. When Karasuno subs in Sugawara, Oikawa quickly analyzes his setting style and tactics and then delivers appropriate encouragement and strategy to his team. He tells them that Karasuno has a solid offense, but that they’ve “played a number of teams like that,” so there’s nothing to worry about. This positivity and forward-thinking is the essence of Oikawa’s on-court attitude. Of course, there are numerous on-court actions he takes as well, such as setting more to Kunimi at the end of the Inter High match to fully utilize his reserves of energy. Kageyama adopts those same actions in Season 2. Oikawa’s whole philosophy towards geniuses at this point can be summed up by his line, “Tobio, I might actually lose to you, considering how quickly you evolve. But that won’t be today!” As his coach told him, he will always have less talent than some people, but so long as he can make himself and his team stronger in some way, he can win. The team that scores enough points wins. At the same time, he recognizes that the genius talent of Kageyama and those like him will eventually lead them to greater heights. At the end of the match, he reflects on Kageyama’s “troublesome” improvement, dreading that the day he loses might soon come. The mental advantage he had is fast disappearing. But that philosophy turns against him in the finals against Shiratorizawa. Volleyball works both ways. If you are talented enough, and just smart enough, you can break through a weaker opponent’s hard work. In the end, it doesn’t matter if you’re a genius, but it doesn’t necessarily matter if you’ve improved yourself either. The team that scores enough points wins. The game is as simple as that when it comes to who wins and who loses. “All of [their] practices, experience, and strategies are being broken by force,” and that’s enough. Oikawa has yet to surrender, though. Although we don’t know exactly what happened between the Inter High and the Spring Tournament, we learn that Aoba Johsai has tightened their trust in each other even further. Before the match against Karasuno, the team has so much trust in one another that Oikawa’s teammates turn his “I believe in you” line backwards on him. They all recognize what he’s done as a setter. Although they joke about what ramen they want him to buy if he misses his serve, they admit they know he won’t miss. I said we don’t know what happened, but based on the flashback to Oikawa practicing with Kindaichi, we get a sense. Instead of switching up the type of toss or the spiker’s approach entirely, Oikawa just tells Kindaichi to stay how he is, and then adjusts his toss to match. This is Oikawa developing his skills as the egoless, but also leaning towards Kageyama’s initial mindset of having the spiker think less about matching the toss. It’s just an interesting moment that gives us something to point to when we wonder if Oikawa is different or better than before. Speaking of developments as a player, we finally meet a spiker that Oikawa has a hard time forming trust with. The Mad Dog should really be Oikawa’s worst nightmare—he gets in the way of other player’s spikes, he’s a self-centered player, and he’s hard to understand and utilize. Admittedly, the Kyotani does help resolve those issues on his own, but Oikawa handles a troublesome teammate adeptly. He learns how to use Kyotani as a decoy on the fly, making “[his] fangs even sharper.” Just like with any other player, if they hit a rough spot, Oikawa looks for a way to bail them out. I would argue that Kyotani is able to become a team player because Oikawa puts absolute trust in Kyotani by tossing to him after the Mad Dog is subbed back in. Unfortunately, Oikawa is not our main protagonist. Oikawa Toru is not a genius. Seeing Kageyama’s improvement, Oikawa repeats his/Iwaizumi’s mantra: the team with six strong players is stronger. That’s true—just like how ‘the team that scores enough points wins’ is true. And that’s the beginning of the end for Aoba Johsai in this tournament. Kageyama, the genius, dumping the toss at such an important moment with so many potential spikers is like the ultimate insult to Oikawa. It’s like rubbing Kageyama’s genius in Oikawa’s face (which sounds a lot like some doujins, I’m sure). Anyway, the flashbacks to low angle shots of Ushijima and younger Kageyama really cement the idea that the dump took a serious toll on Oikawa’s attitude. Oikawa fights back with all that he’s learned and practiced. “Talent is something you make bloom. Instinct is something you polish,” is a reaffirmation of what’s driven Oikawa this far. Give your raw talent the best chance to flourish on the court by training hard. Make up for whatever you lack by strategy, teamwork, and composure. This is also reflective of Oikawa’s style as a setter. He tries to make the talent of his spikers bloom as best he can. He operates based on game sense, analysis, and instinct. During the final volley of the match, all six players on Karasuno’s side of the court get a chance to shine. With a crazed face, Oikawa remembers his mantra: “Six who are strong are stronger.” He realizes that Karasuno has indeed become a team of six (plus some) strong players. They’re a team with a genius, but they’re also a team of six. This match, and Oikawa’s dream for high school volleyball, all ride on the last attack from Kageyama and Hinata. “Come at me with your ultimate weapon,” he thinks. Play your best. Be a genius, be a team of six strong players, be all of that—I want to beat you without any excuses. This is the epitome of Oikawa’s ego and pride. This is why he applies to Aoba Johsai and not Shiratorizawa. This is his moment to prove to himself and geniuses everywhere that he can win. The ball hits the court and, at this moment, Oikawa could not win. The team that scores enough points wins. Six who are strong are stronger. These are the truths. These are the reasons a team wins or loses. This is what Oikawa represents in Haikyuu!!: the struggle of competition, and the truths that decide that struggle. Oikawa will have to end his high school volleyball career by accepting these truths and looking Kageyama and Ushijima in the eye, acknowledging that those truths dictated who was stronger today. Yet, Oikawa is a player who won’t stop until he’s reached his absolute limit. Post navigation 7 thoughts on “Oikawa Blooms” That was beautifully analyzed and described. I always wondered why Oikawa is one of the more popular characters in Haikyuu! and you really opened my eyes as to why. I honestly thought Oikawa was just another pretty boy character whom Kageyama has to overcome. But hey, this is Furudate-sensei we’re talking about here. He makes you care for the rival team which makes it very conflicting who to cheer for. Thanks, I appreciate it! As for popularity, I have to admit I think his looks and charm have a lot to do with it lol. He’s still fantastically developed and serves a crucial purpose in Haikyuu’s narrative, but he’s smooth on top of all that 😛 I really enjoyed your post. The last two episodes left quite the impression on me. I am yearning for the next season. The Kageyama – Oikawa dynamic feels really balanced, Oikawa acknowledges that Kageyama is a genius but Kageyama himself considers Oikawa a genius and a inspiring model. Normally i don’t really like when the word genius is used in anime (this is in general, not about your use of it). It is a shallow word and i think it mostly cheapens the characters achievements and motivations. It is not that someone is a genius but there is always someone better. By better i mean that circumstances and motivations of one person led to a better position than you have in something. But i understand why genius is used, it is way easier to convey but it gets often lost in the anime-ness of it all. Leaving that aside and going back to the anime, these last episodes really surprised me by the amount of depth given to Oikawa and his team. Although the first season loss pretty much sets up this win by the main character team, in the end it feels the opposite result could have happened again. I really like those scenes where he speaks to his past(?) coach and gets advice on how to improve himself shaping how he views the world. It shows it is not just about anime special techniques and raw effort. It is believable that an high level player would ask for this kind of advice. I also like that the advice given to him feels somewhat realistic, you just have to endure the facts and move on the best you can. As for the whole “genius” thing, I think it’s a matter of oversimplification, but also a case of meaning lost in translation. I’m the furthest thing from a native speaker, but from the context of lots of Japanese media, genius/tensai doesn’t really have the same connotations as it does in English. The word as it’s used in the show leans more towards “high aptitude/highly-developed”, really just pointing to the natural talent part of the [ natural talent + work = skill ] equation. At least in Haikyuu, it doesn’t feel overly cheap–more just an acknowledgement of the reality of competition. I’m late of two years but I love this analysis! I don’t totally agreed with the last part though: Hinata himself admitted that Oikawa was ready to defend his spike and that He was lucky ’cause he touched the wall! I love how Oikawa sees himself as “Not a Genius” while Ushijima and Kageyama think He is! (Ushijima wanted him as his setter and for Kageyama is a Model, he doesn’t feel at his level.) Oikawa grow up: at the beginning he hated Kageyama, he said “i can’t give you toss as perfect as Kageyama’s” At the end of season two he says “he’s not at my level, but he’s strong however.” He has new self confidence, he comforted Iwaizumi when the team lost, not the contrary. Oikawa was not the main character, but i don’t think he’s weaker than “the genius”. I agreed with Ushijima, he wasn’t in the strong team so he couldn’t shine as much as he could! And agreed with Oikawa too, He’s a great player and his career isn’t ended yet! | Mid | [
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The mountain village of Alájar Nestling underneath the Pena de Arias Montano, and set amidst forests of cork oak and chestnut trees in the Sierra de Aracena, the tranquil mountain village of Alájar is a place to leave the world behind. The village has an idyllic rural setting and must be one of the prettiest in the region. Home to around eight hundred people, there are plenty of bars and restaurants in which to sample the locally produced specialities of this glorious region of Andalusia. Alájar, Andalusia, Spain One of Alájar’s main attractions, other than eating and drinking, are the numerous lovely walks on old tracks between the hamlets of the area. One of the most popular walks takes you up the hill to the pilgrimage site of Pena de Arias Montano. Not only does this offer spectacular views over the village, you can see for miles across the undulating forested hills of the Huelva countryside stretching to the south. The hill is home to a small but historic church, the Ermita de Nuestra Señora de los Angeles, which attracts pilgrims from all over Spain. It’s perhaps most famous for being the place where Spanish theologian, Benito Arias Montano, came to live as a hermit. Montano was royal chaplain to King Philip II and responsible for producing a famed version of the bible, the Antwerp Polyglot. This remarkable book contained the bible translated into Hebrew, Greek, Latin and Aramaic. Peña de Arias Montano, Alájar, Andalusia, Spain Alájar, Andalusia, Spain Alájar, Andalusia, Spain Alájar, Andalusia, Spain Alájar, Andalusia, Spain Alájar, Andalusia, Spain When you arrive at the top of the hill, it’s easy to see why Montano chose this as a place of contemplation. Coming back down towards the village, I followed dirt tracks between the trees and came across fields of inquisitive goats. The scenery was beautiful, and although it was a warm day the trees offered plenty of shade. The only noise I could hear was bird song and the breeze in the trees. Back in the village, time seemed to have decided to stand still. I wandered around the deserted streets, popped into the empty Iglesia de San Marcos, and headed into the main square to see if any of the tapas bars had any life. Not much was the answer. After a light lunch we decided to explore the villages of the area a little more, including Jabugo, legendary home to what many consider to be the very finest jamon in Spain. Alájar, Andalusia, Spain Alájar, Andalusia, Spain Alájar, Andalusia, Spain Alájar, Andalusia, Spain Jabugo may be the epicentre of jamon iberico de bellota, but the town didn’t seem to have the same charm as others we passed through. There were a few to many industrial units – presumably filled with legs of ham – and we decided not to spend too much time here. Driving south again, we came to the arresting sight of the village of Cortegana. It might be possible to overdose on medieval churches and castles in this part of Spain, but we decided to visit anyway. The impressive Castillo de Cortegana was built in 1253, while this area was still under Moorish control, as part of a defensive line of fortifications intended to prevent attack by Christian forces from Portugal. The border is only a short distance form here. Cortegana, Andalusia, Spain Cortegana, Andalusia, Spain Cortegana, Andalusia, Spain Cortegana, Andalusia, Spain Cortegana, Andalusia, Spain Cortegana is a bit bigger than most of the villages in this area, but still felt very sleepy. We walked through quiet streets up to the castle, which has been faithfully restored to its former glory. The views from the keep were magnificent. Deciding we’d had enough history for one day, we headed back to Alájar to sample more delicious local cooking. I guess it depends, there are some short hikes between villages, but it’s mountainous and seems geared more towards long distance walking. It’s a beautiful part of the country though, and I’d go back just to spend some time in the villages. Why camelids? After more than a decade in London it seemed like time to do something completely different, and with the support of our friends in Bolivia we hatched a plan to move to this high altitude Andean nation for a year (maybe more)... COPYRIGHT Please get in touch if you would like to use any of the images or blog posts. DISCLAIMER This is my blog. The thoughts on these pages are my personal views and opinions. They’re not representative of anyone else’s opinion, nor should they be ascribed to any organizations with which I’m associated. Except when intentional, nothing written here is intended to offend. I consider the things I’ve written to be accurate, but making mistakes is part of the human condition and I’m human. It is not my intention to do harm. Nor is it my intention to libel, defame or malign any religion, ethnic group, club, organization, company or individual, especially those that have the resources and desire to pursue a grievance. I accept no responsibility for any harm or good that comes from following any suggestions made in these pages. | Low | [
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Three weeks from the start of a World Cup England have spent four years planning for, there are still a couple of questions left to address. Trevor Bayliss says he is hoping it will all be settled over the course of five one-day games against Pakistan. The first is a day-night game at the Oval on Wednesday and by the time it is over it looks like England will be that much closer to one of the answers. We will likely learn something about whether or not Joe Denly is a good enough bowler to fill in as the second spinner. Joe Root sees value in Jofra Archer’s ‘extra bit of zip’ for England Read more A slight rib injury means Moeen Ali is being rested as a precaution. “He’s fine,” Bayliss said. “Once upon a time you wouldn’t have even got it x-rayed, because it’s only a bruise.” But this is exactly the reason England want Denly in the World Cup squad. During the tournament they can replace an injured player but once they have done it they cannot bring them back into the squad if they recover later on. They need someone around who could conceivably fill in those overs for a stretch of matches until the first choice is ready again. It is asking a lot of Denly’s part-time leg-spin. He has taken only 47 List A wickets in his 15 years in the game but he also offers cover as a top-order batsman, so England want to give him every chance to prove he can do it. Bayliss admitted the selectors still have not quite decided between Denly and Liam Dawson for that position. “Someone like Dawson will certainly be in discussions,” the coach said. “He’s done well this year and he’s done well for us in the past when he’s been given an opportunity at this level. I’m sure he’ll be discussed as well.” Dawson is not part of the squad now but Bayliss said the selectors may still call him up before the series is over. “We’ve decided to give Denly a go this time. But yes we have spoken about it. There will be a little bit of flexibility and I am sure there will be discussions throughout this series.” In the meantime, he said, they would be keeping a close eye on how Dawson goes for Hampshire in the Royal London Cup. “He got a game yesterday and they’ve got a semi-final coming up so there is some game time for him.” Then, of course, there is what Bayliss called “the big one”, which is whether or not to pick Jofra Archer. If they do, he explained, it will certainly be instead of one of the other fast bowlers. Otherwise “you might ask the question if we’re overstocked with fast bowlers and the answer would probably be yes”. So one of the quicks is bound to miss out. Of course, even after all the hype, it may yet be Archer. Bayliss certainly did not get carried away with Archer’s two performances so far. “He looked fairly nervous to me [in last Friday’s ODI] in Ireland and I think that showed in his bowling,” he said. “There have been plenty of big statements made about young guys in the last few years, young guys coming into the team and before you know it they are out of it again, either with injury or loss of form. But he is very skilful, he has a bit of extra pace and he’s fitted into the team in a short space of time very well. He’s a fairly quiet sort of guy, which is always good first time into the team.” The Spin: sign up and get our weekly cricket email. Jason Roy is also going to miss the first match, while he recovers from a back spasm. But again, Bayliss is not worried. “We’ve been fairly laidback about it, it’s just the game. We can keep them in cotton wool but then they don’t play or get to improve or be in form. “If you get injured, well, someone else has just got to take up the slack. But it does give us the chance to give the guys a bit of a rest during this series, which allows us to do what we want to do and give some of the other guys some game time.” | Mid | [
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[Uvulopalatopharyngoplasty and tongue base coblation treat the 112 cases of severe obstructive sleep apnea -hypopnea syndrome]. To study the effect of the combination of UPPP and tongue base Coblation in treatment of the severe OSAHS. One hundred and twelve cases who were diagnosed as severe OSAHS by polysomnography (PSG) were treated surgically by UPPP and tongue base Coblation. The follow up period was twelve months. Twenty-four cases were cured, 52 cases have notable effects, 16 cases had effects, 20 cases had no effects. The total ratio of validity was 82.1%. The combination of UPPP and tongue base Coblation is a effective method for severe multi-level OSAHS treatment. | High | [
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Q: is it grammatical "from as the most perspectives as possible" He tries to consider things from as the most perspectives as possible. I would like to ask whether this sentence is grammatically OK? I try to express that the concerned guy does not jump to conclusions and considers all pros and cons of things. I want to apply the pattern of this type: come as fast as possible. But not sure if my sentence is appropriate. A: Not quite. The "as X Y as possible" pattern does not take a superlative for X. What I think you mean is: from as many perspectives as possible You can also say (though it's a bit more awkward) from the most perspectives possible This is awkard mainly because "the most" nearly always introduces an adjective, as in "the most exciting adventure", so the reader is likely to get momentarily confused by it. But with a different superlative, such as the latest time possible it's fine. | Mid | [
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1. Field of the Invention The present invention relates to a method of and an apparatus for, and a recording medium with a recorded computer program for, searching for an unknown specimen, i.e., identifying an unknown polymer such as a plastic or synthetic resin. 2. Description of the Prior Art It has heretofore been known to identify an unknown polymer by producing data of the unknown polymer according to a process (Py-GC/MS) which is a combination of pyrolysis gas chromatography (Py-GC) and mass spectrometry (MS), and comparing the produced data with a library. Specifically, the data of the unknown polymer are compared with data of known polymers stored in the library to search for the data of the known polymer which agree with the data of the unknown polymer. According to the Py-GC/MS process, a pyrolytic product of the unknown polymer is separated by a capillary column and analyzed by a mass spectrometer, which detects the intensities of molecular ions and fragment ions that are generated when an electron beam is applied to separated molecules. In the mass spectrometer, each time an electron beam is applied to the separated molecules for a predetermined period of time, e.g., 0.008 minute, one set of ion intensities is obtained as detected data. The detected ion intensities of each set are added to calculate a total ion intensity, and the total ion intensities of the sets are plotted successively at detected times, producing a pyrolysis gas chromatogram (pyrogram) as shown in FIG. 5 of the accompanying drawings. The pyrogram itself may be compared with the pyrogram of a known polymer specimen to identify the unknown polymer. According to the Py-GC/MS process, however, it is customary to generate mass spectra of peaks of the pyrogram and search a library of mass spectra of known polymers based on the generated mass spectra. For example, when the ion intensities of total ion intensities that make up portions corresponding to the maximum points of the peaks, as representative values of the total ion intensities, are arranged in the order of masses of the molecular ions and the fragment ions, there is obtained a mass spectrum having a pattern inherent in compounds corresponding to the peaks. The mass spectrum is compared with a library of mass spectra produced with respect to standard specimens to search for a mass spectrum in the library that agrees with the mass spectrum for thereby identifying the unknown polymer. The above conventional library searching process will be described below with respect to an example in which a pyrogram shown in FIG. 5 of the accompanying drawings is plotted as the pyrogram of an unknown polymer. According to the conventional library searching process, the total ion intensity that makes up a portion corresponding to the maximum point of a peak D is divided into individual ion intensities. Then, when the individual ion intensities are arranged in the order of masses of molecular ions and fragment ions, a mass spectrum shown in FIG. 6 of the accompanying drawings is obtained. The mass spectrum shown in FIG. 6 is then compared with a library of mass spectra produced with respect to standard specimens to search for the mass spectrum of a known polymer in the library that agrees with a high probability percentage with the mass spectrum for thereby identifying the unknown polymer. When a commercial library (WILEY) is searched for the mass spectrum shown in FIG. 6, a result is obtained as shown in FIGS. 10(a) through 10(d). FIGS. 10(a) and 10(b) show mass spectra of 4,4xe2x80x2-(1-methylethylidene) bisphenol. FIG. 10(c) shows a mass spectrum of p-phenyl-carbanilic acid, and FIG. 10(d) shows a mass spectrum of [1,1xe2x80x2-biphenyl]-3-yl-carbamic acid. The probability that a pyrolytic product corresponding to the mass spectrum shown in FIG. 6 is the same as the compounds shown in FIGS. 10(a) through 10(d) is 97%, 83%, 46%, and 43%, respectively. According to the conventional library searching process, each of the peaks of the pyrogram shown in FIG. 5 is processed in the same manner as with the peak D to identify compounds corresponding to the peaks. However, the conventional library searching process is time-consuming because the library needs to be searched for each one of the pyrolytic products corresponding to the peaks. Even if each one of the compounds corresponding to the peaks is identified, it requires a high level of expert knowledge, experience, and skill to determine the original polymer from the compounds thus identified. Another process of searching for an unknown polymer uses a mass spectrum measured by directly pyrolyzing the polymer in a mass spectrometer. According to this process, one mass spectrum is obtained with respect to one polymer. Therefore, it is not necessary to search a library for individual mass spectra corresponding to peaks, and it is possible to determine an original polymer immediately from the search result. The above process requires that a specimen introduced into the mass spectrometer be in a minute quantity of several xcexcg or less. However, it is practically difficult to weigh such a minute quantity of specimen. Polymers that are dissolvable into solvents can be weighed in minute quantities of several xcexcg by adjusting the concentration of the solution. However, such a weighing scheme is not applicable to crosslinked polymers that are not dissolvable into solvents. Another problem is that when a specimen of several hundred xcexcg that can be weighed is pyrolyzed, the ionization chamber in the mass spectrometer is contaminated and becomes useless in a short period of time. It is therefore an object of the present invention to provide a method and apparatus, along with a recording medium with a recorded computer program, for easily identifying an unknown polymer such as a plastic or synthetic resin. To achieve the above object, there is provided in accordance with the present invention a method of searching for an unknown polymer, comprising the steps of separating a mixture of pyrolytic products obtained by pyrolyzing an unknown polymer into the pyrolytic products, detecting ion intensities of molecule ions and fragment ions produced by ionizing the separated pyrolytic products in cycles each for a predetermined period of time, adding sets of the ion intensities of the molecule ions and the fragment ions detected in the cycles into total ion intensities, interconnecting maximum levels of the total ion intensities in a histogram composed of the total ion intensities arranged in the order of detection times thereof for thereby plotting a chromatogram, combining, for each ion of the same mass, the ion intensities contained in all the total ion intensities making up peaks in the chromatogram into combined data of the ion intensities of the molecular ions and the fragment ions, generating a combined mass spectrum of the unknown polymer which is composed of the combined data arranged in the order of masses of the molecular ions and the fragment ions, and comparing the generated combined mass spectrum of the unknown polymer with a library of combined mass spectra of a plurality of known polymers which are generated in the same manner as with the combined mass spectrum of the unknown polymer, for thereby searching for the combined mass spectrum of one of the known polymers which agrees with a high probability percentage with the combined mass spectrum of the unknown polymer. In the above searching method, a mixture of pyrolytic products obtained by pyrolyzing an unknown polymer is separated into the pyrolytic products. The pyrolytic products are ionized, and ion intensities of generated molecule ions and fragment ions are detected. Then, total ion intensities as totals of the ion intensities detected in cycles each for a predetermined period of time are calculated, and arranged in the order of detection times thereof thereby to generate a chromatogram of the unknown polymer. The peaks in the chromatogram which correspond to the pyrolytic products and which are formed at respective times required to separate them (retention times) represent clusters of the total ion intensities. Each of the total ion intensities may contain molecule ions or fragment ions of the same mass. Therefore, the ion intensities included in all the total ion intensities making up the peaks are combined, for each ion of the same mass, to produce combined data. The combined data are arranged in the order of the masses of the molecule ions and the fragment ions thereby to obtain a combined mass spectrum of the unknown polymer. The combined mass spectrum corresponds to a mass spectrum which is produced by directly analyzing the mixture of pyrolytic products of the unknown polymer with a mass spectrometer, rather than separating the mixture, and arranging the ion intensities of detected molecule ions and fragment ions in the order of their masses. Consequently, the combined mass spectrum constitutes a single mass spectrum capable of representing data relative to the unknown polymer. The combined mass spectrum of the unknown polymer is then compared with the library. The library is composed of the combined mass spectra of a plurality of known polymers which are generated in the same manner as with the combined mass spectrum of the unknown polymer. The library contains combined mass spectra generated with respect to peaks in certain ranges in the chromatograms of the known polymers, as data libraries. The peaks in the certain ranges in the chromatograms may be all or some of the peaks contained in the chromatograms. The comparison between the combined mass spectrum of the unknown polymer with the library searches for the combined mass spectrum of one of the known polymers which agrees with a high probability percentage with the combined mass spectrum of the unknown polymer. The unknown polymer is thus identified as the known polymer whose combined mass spectrum agrees with a high probability percentage with the combined mass spectrum of the unknown polymer. An apparatus for searching for an unknown polymer according to an aspect of the present invention comprises pyrolyzing means for pyrolyzing a specimen to generate a mixture of pyrolytic products, a separating column for separating said mixture into the pyrolytic products, a mass spectrometer for detecting ion intensities of molecule ions and fragment ions of the separated pyrolytic products, chromatogram generating means for generating a chromatogram from the ion intensities of the molecule ions and the fragment ions, combining means for generating a combined mass spectrum of the unknown polymer, library memory means for generating and storing a library of combined mass spectra of a plurality of known polymers, searching means for searching the library and outputting a search result. The method for searching for an unknown polymer according the present invention can effectively be carried out by the above apparatus. An apparatus for searching for an unknown polymer according to another aspect of the present invention comprises library memory means for storing a library of combined mass spectra of a plurality of known polymers, detected data memory means for storing ion intensities of molecule ions and fragment ions of an unknown polymer as detected data, chromatogram generating means for generating a chromatogram based on total ion intensities obtained from the detected data, combining means for generating a combined mass spectrum of the unknown polymer, and searching means for comparing the library with the combined mass spectrum of the unknown polymer to search for the combined mass spectrum of the unknown polymer. The above apparatus may comprise a personal computer. If the apparatus for searching for an unknown polymer comprises a personal computer, then a recording medium storing an application program executable by the personal computer may be employed. The recording medium records therein a process comprising the steps of storing ion intensities of molecule ions and fragment ions of an unknown polymer as detected data, generating a chromatogram based on total ion intensities obtained from the detected data, generating a combined mass spectrum of the unknown polymer, and comparing the library with the combined mass spectrum of the unknown polymer to search for the combined mass spectrum of a known polymer which agrees with a high probability percentage with the combined mass spectrum of the unknown polymer. A recording medium which stores the library described above may also be employed. Each of these recording mediums may comprise a magnetic recording medium such as a floppy disk or the like, or an optical disk such as a CD-ROM or the like. The above and other objects, features, and advantages of the present invention will become apparent from the following description when taken in conjunction with the accompanying drawings which illustrate a preferred embodiment of the present invention by way of example. | Mid | [
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4 Cal.App.3d 443 (1970) 84 Cal. Rptr. 349 THE PEOPLE, Plaintiff and Respondent, v. FRANK ANSON STEVENSON, Defendant and Appellant. Docket No. 3768. Court of Appeals of California, Fourth District, Division One. February 16, 1970. *444 COUNSEL Edward G. Baker for Defendant and Appellant. Thomas C. Lynch, Attorney General, William E. James, Assistant Attorney General, and Jeffrey T. Miller, Deputy Attorney General, for Plaintiff and Respondent. OPINION THE COURT. Defendant was convicted on jury verdict of first degree burglary and assault by means of force likely to produce great bodily injury. He moved for a new trial on the ground the verdict had been decided by means other than a fair expression of opinion on the part of all jurors, and in support of his motion filed affidavits of two trial jurors. (1) The motion for new trial was denied, and defendant appeals from the judgment of conviction, contending it should be reversed because the affidavits of the jurors supply admissible evidence establishing they improperly reached their verdict by compromise, whereby some jurors surrendered their convictions upon a material issue in return for a like surrender by other jurors. The contention has no merit. In one affidavit a juror alleges, "We had been on jury duty for over a week and deliberation had been going on for two days. I did not feel that by returning to deliberations the next day, we could convince the others to vote not guilty. Therefore, although not convinced of Mr. Stevenson's guilt, or innocence, I decided to vote guilty to the lesser charge." In the other affidavit a second juror alleges, "It was my understanding that we had to come back with a unanimous verdict one way or the other. Since I was one of the few who were for acquittal, I felt that it was useless to persist in my convictions and, therefore, voted for a guilty verdict. Had I known that my continuing to persist in my convictions for Mr. Stevenson's innocence would have resulted in a hung-jury and therefore no guilty verdict, I would not have voted for a guilty verdict." Evidence Code section 1150, subdivision (a) provides: "Upon an inquiry as to the validity of a verdict, any otherwise admissible evidence may be received as to statements made, or conduct, conditions, or events occurring, either within or without the jury room of such a character as is likely to have influenced the verdict improperly. No evidence is admissible to show the effect of such statement, conduct, condition, or event upon a juror either *445 in influencing him to assent to or dissent from the verdict or concerning the mental processes by which it was determined." In the case at bench, the evidence supplied by the jurors' affidavits was inadmissible because it showed only the mental processes of the respective jurors, and the subjective considerations which influenced their verdicts. (People v. Hutchinson, 71 Cal.2d 342, 349-351 [78 Cal. Rptr. 196, 455 P.2d 132].) There was no admissible evidence showing the jurors surrendered their conscientious convictions on a material point, or reached their verdict by compromise. The motion for new trial was properly denied. Judgment affirmed. | Mid | [
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include ../Makefile.tests_common USEMODULE += base64 USEMODULE += fmt USEMODULE += xtimer include $(RIOTBASE)/Makefile.include | Low | [
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Q: Criar listview com dados do banco e colocar um EditText na frente de cada informação preciso criar uma listview dentro de um dialog, usando os dados do banco SQLite, mas em cada um dos dados que vai carregar tem que ter um EditText na frente, por exemplo. Produto Quantidade Adubo EditText A: Após criar sua listagem normalmente (dados e adapter), basta inserí-los no dialog. Algo como: public class MyDialog extends DialogFragment { @Override public Dialog onCreateDialog(Bundle savedInstanceState) { AlertDialog.Builder alertDialogBuilder = new AlertDialog.Builder(getActivity()); View view = LayoutInflater.from(getActivity()).inflate(R.layout.my_list, null, false); // Listagem normal: recuperar ListView, dados do banco, criar adapter que terá seu próprio layout (com o EditText e os TextViews) para os dados alertDialogBuilder.setTitle("Título") .setMessage("Mensagem") .setView(view); .setPositiveButton("Ok", new DialogInterface.OnClickListener() { @Override public void onClick(DialogInterface dialog, int which) { //TODO } }) .setNegativeButton("Cancelar", null); return alertDialogBuilder.create(); } } | High | [
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The tournament will consist of three doubleheaders at Providence Park. Portland and Chicago will square off Sunday, March 26; kickoff is set for 5 p.m. (Pacific). Houston and the U.S. U-23s will face each other in the opening match at 2:30 p.m. (Pacific). On Wednesday, March 29, Chicago takes on Houston at 5 p.m. (Pacific), while Thorns FC play host to the U.S. U-23s at 7:30 p.m. (Pacific). Portland closes out the preseason tournament against Houston on Saturday, April 1, at 7:30 p.m. (Pacific), while Chicago and the U.S. U-23s square off at 5 p.m. (Pacific). Tickets for the tournament are included in Thorns FC Annual Memberships. Individual tickets, which allow entry to both matches each day, start at $8 and go on sale to the general public starting Tuesday, Feb. 21, at 10 a.m. (Pacific) online atwww.thornsfc.com. Full tournament ticket packages, starting at $15, also will be available for purchase online. Fans interested in purchasing Thorns FC Annual Memberships for the 2017 season are encouraged to call the ticket office at (503) 553-5555 or email [email protected]. Single-game ticket information will be released at a later date. | Mid | [
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Quick Start KevScript Registry Execute script in component Directly trigger adaptations This component will send each received messages to the core ModelService as KevScript. This will have the effect of modifying the abstraction layer and so the running system. 1 2 3 4 5 6 7 8 9 10 11 12 @ComponentType(version=1,description="Update the current system using input messages as KevScript")publicclassKevScriptServiceComp{@KevoreeInjectprivateModelServicemodelService;@Inputpublicvoidin(Stringscript){// this will update the abstraction layerthis.modelService.submitScript(script);}} Local execution This component will execute each received messages as KevScript using an empty model as context. Once executed, it will serialize the new model and send it to its output port named json 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 @ComponentType(version=1,description="Transform incoming KevScript messages to JSON model")publicclassKevScript2ModelComp{@KevoreeInjectprivateKevScriptServicekevs;@OutputprivatePortjson;privateKevoreeFactoryfactory=newDefaultKevoreeFactory();privateJSONSerializerserializer=factory.createJSONSerializer();@Inputpublicvoidkevs(Stringscript){// create an empty modelfinalContainerRootmodel=factory.createContainerRoot();factory.root(model);// execute the incoming script to update the empty modelthis.kevs.execute(script,model);// serialize the model to JSON and send it through the output portthis.json.send(this.serializer.serialize(model));}} Directly trigger adaptations This component will send each received messages to the core ModelService as KevScript. This will have the effect of modifying the abstraction layer and so the running system. 1 2 3 4 5 6 7 8 9 10 11 constAbstractComponent=require('kevoree-entities/lib/AbstractComponent');module.exports=AbstractComponent.extend({toString:'KevScriptServiceComp',tdef_version:1,in_in(script){// this will update the abstraction layerthis.kCore.submitScript(script);}}); Local execution This component will execute each received messages as KevScript using an empty model as context. Once executed, it will serialize the new model and send it to its output port named json 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 constAbstractComponent=require('kevoree-entities/lib/AbstractComponent');constkevoree=require('kevoree-library');module.exports=AbstractComponent.extend({toString:'KevScript2ModelComp',tdef_version:1,construct(){constfactory=newkevoree.factory.DefaultKevoreeFactory();this.serializer=factory.createJSONSerializer();},in_kevs(script){// execute the incoming script on an empty model (default behavior in js)this.kCore.kevs.parse(script,(err,model)=>{if(err){console.error('Something went wrong',err.message);}else{// serialize the model to JSON and send it through the output portthis.out_json(this.serializer.serialize(model));}});},out_json(){/* noop as this function will be modified by the runtime */}}); | Mid | [
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{ "activation": { "namespace": "default", "action_name": "nodejs-helloworld-with-params-from-env", "api_host": "", "api_key": "", "activation_id": "", "deadline": "4102498800000" }, "value": { "name" : "Jess", "place" : "OK" } } | Low | [
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Republican Rep. Devin Nunes will say anything to cover for Trump, even if it's obviously not true. House Intelligence Committee chairman Devin Nunes (R-CA) has been covering up for Donald Trump since his committee's investigation began, but now he's telling lies that are stunning even by his low standards. Nunes appeared on "Fox & Friends" Monday to echo the White House's new line of attack: accusing Democrats on his committee of "over a hundred" leaks of classified information. But his lies about the Russia investigation stood out even more boldly. Co-host Brian Kilmeade asked Nunes about the central premise of his debunked intelligence memo, asking him to respond to critics who say, "What about Papadopoulos, they were looking at him earlier? Why don't you look at that?" Kilmeade was referring to Trump campaign adviser George Papadopoulos, who pleaded guilty and is now a cooperating witness in the Mueller probe. Nunes tried to toe the Trump line that Papadopoulos was not a major figure in the campaign. "As far as we can tell," Nunes said, "Papadopoulos never even knew who Trump was you know, never even had met with the president." He then characterized Papadoupolos' boasts about the Russian government having "dirt" on Hillary Clinton as nothing more than "getting drunk in London and talking to diplomats, saying that you don't like Hillary Clinton." Nunes is already famous for never having read the intelligence that went into his own memo, but he would have needed to avoid the entire internet to have missed the photo of Papadopoulos meeting with Trump as part of his "national security team," which was posted on Trump's instagram complete with campaign graphics. Nunes' lack of concern over political opinions stands in stark contrast to his party's crusade against FBI agents who expressed a variety of opinions in text messages, but his description of Papadopulos' encounter in London is also a lie. The then-Trump adviser boasted to an Australian diplomat that Russian dictator Vladimir Putin had "dirt" on Clinton, which that diplomat then relayed to U.S. intelligence authorities. Nunes has proven himself untrustworthy on countless occasions, yet despite a feint at recusing himself, remains entangled in the House investigation into Russia. These blatant lies should be the last straw for any reasonable person, Republican or Democrat. Last week, Democratic leaders Nancy Pelosi and Chuck Schumer publicly called on Speaker Paul Ryan to remove Nunes from his role in the intelligence committee. As Pelosi wrote, "The integrity of the House is at stake." It's time for Ryan to do his job and remove Nunes before he does any more damage. | Mid | [
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Q: Ordering of elements in Pandas stacked bar chart I'm trying to graph information about the portion of a household's income earned in a specific industry across 5 districts in a region. I used groupby to sort the information in my data frame by district: df = df_orig.groupby('District')['Portion of income'].value_counts(dropna=False) df = df.groupby('District').transform(lambda x: 100*x/sum(x)) df = df.drop(labels=math.nan, level=1) ax = df.unstack().plot.bar(stacked=True, rot=0) ax.set_ylim(ymax=100) display(df.head()) District Portion of income A <25% 12.121212 25 - 50% 9.090909 50 - 75% 7.070707 75 - 100% 2.020202 Since this income falls into categories, I would like to order the elements in the stacked bar in a logical way. The graph Pandas produced is below. Right now, the ordering (starting from the bottom of each bar) is: 25 - 50% 50 - 75% 75 - 100% <25% Unsure I realize that these are sorted in alphabetical order and was curious if there was a way to set a custom ordering. To be intuitive, I would like the order to be (again, starting from the bottom of the bar): Unsure <25% 25 - 50% 50 - 75% 75 - 100% Then, I would like to flip the legend to display the reverse of this order (ie, I would like the legend to have 75 - 100 at the top, as that is what will be at the top of the bars). A: To impose a custom sort order on the income categories, one way is to convert them to a CategoricalIndex. To reverse the order of matplotlib legend entries, use the get_legend_handles_labels method from this SO question: Reverse legend order pandas plot import pandas as pd import numpy as np import math np.random.seed(2019) # Hard-code the custom ordering of categories categories = ['unsure', '<25%', '25 - 50%', '50 - 75%', '75 - 100%'] # Generate some example data # I'm not sure if this matches your input exactly df_orig = pd.DataFrame({'District': pd.np.random.choice(list('ABCDE'), size=100), 'Portion of income': np.random.choice(categories + [np.nan], size=100)}) # Unchanged from your code. Note that value_counts() returns a # Series, but you name it df df = df_orig.groupby('District')['Portion of income'].value_counts(dropna=False) df = df.groupby('District').transform(lambda x: 100*x/sum(x)) # In my example data, np.nan was cast to the string 'nan', so # I have to drop it like this df = df.drop(labels='nan', level=1) # Instead of plotting right away, unstack the MultiIndex # into columns, then convert those columns to a CategoricalIndex # with custom sort order df = df.unstack() df.columns = pd.CategoricalIndex(df.columns.values, ordered=True, categories=categories) # Sort the columns (axis=1) by the new categorical ordering df = df.sort_index(axis=1) # Plot ax = df.plot.bar(stacked=True, rot=0) ax.set_ylim(ymax=100) # Matplotlib idiom to reverse legend entries handles, labels = ax.get_legend_handles_labels() ax.legend(reversed(handles), reversed(labels)) | Mid | [
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Q: onLongClick for plain text inside of a WebView I am building an app that contains a WebView which will be used to show the user some links and some plain text. I want to make it so that the user can LongClick on a link, or a body of text and get the option to delete that thing from the html thats being shown in the WebView. This question got me half way there. LongClicking on the links works by using the wv.getHitTestResult() method. But now my problem is when I long click on plain text the onLongClick() method of the listener doesn't get called, and even if it did getHitTestResult() would not return the text that the user is touching(I tried setting an onTouchListener to see if getHitTestResult().getExtra() had a value when I touched plain text) So my questions is does anyone know how I can get LongClick events inside of a WebView that are on text that is not Linkified?(I assume this is possible some how because that is how I can select text in the default browser). and once I get the LongClick event how can I get access to which body of text was clicked? A: I have got an answer here , https://stackoverflow.com/a/5908125/1503130 Also if you have any other fix to the problem then do share it. | Mid | [
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Russian River Zendo links About Me Michelle Wing is a poet and a writer, and Zen practitioner. She is a member of the Healdsburg Sangha, affiliated with Russian River Zendo of Guerneville in California, studying with Tony Patchell of the Suzuki-roshi lineage. Friday, January 29, 2010 When I was living in Japan, I volunteered at a soup kitchen for homeless day laborers in a neighborhood in Osaka. The men who came to the soup kitchen for hot meals each day were the invisible of Japan. Most of them were Korean Japanese, burakumin(the "untouchable" class of Japan) or Ainu (the indigenous people of Japan); all three groups are heavily discriminated against, and because of that, they tend to be underemployed. Much like our immigrant workers in the United States, the men stand in groups on the street in the morning, hoping that a truck will stop and take them to a construction site or other location for a day of work. When they do get work, they take their cash from the day and come back to this ghetto neighborhood, spending the money on alcohol and pachinko (a Korean gambling game), and a night's stay in a boarding house. When they don't work, they sleep on the streets, and spend the few dollars they have buying hot sake out of vending machines. Those who are aging or sick are the most vulnerable, because not working means not having food and shelter. The soup kitchen was a project provided by a group of Japanese Catholic nuns and priests, affiliated with an order from France. I learned of their existence when I met a young Japanese woman who was Catholic. In my own Osaka neighborhood, only four train stops away, no one had ever heard of this ghetto, and all assured me that there were no poor in Japan, and also that there was no discrimination. On weekends in the winter, I sometimes went out on night patrol, driving through the streets in a van. We stopped whenever we found a group of huddled forms in the darkness. We offered rice balls and hot miso soup, and handed out extra blankets. On the coldest nights, it was not uncommon to find a corpse among the living, someone whose poor health could not sustain them through the extreme chill on the concrete. There was one particular older man who I grew to know well. He was aging, and sick, and rarely able to work, and he sought comfort in sake and the friendships he had with other men in the area. He was always good humored and friendly. Once I accompanied him to a medical clinic as an advocate. He was having circulation problems, and one of his legs was turning black. His rough, rambling speech was incomprehensible to most. I found myself in the ironic position of serving as a translator, a white American woman rendering his slurred expostulations into meaningful Japanese for the attending physician and nurses. As the weeks wore on, his condition worsened. He began to be incontinent, showing up in soiled clothing. Finally, the priests decided he needed to be taken to a hospital to be treated, and cared for long-term. When he had been gone for several weeks, I asked if I could visit him. One of the priests took me to see him, at a hospital clear on the other side of the city. They had taken him there, instead of to a nearby hospital, because he kept trying to escape and return "home." Now he was so far away, that if he had wandered into the streets, he would have had no idea how to make his way back to his friends at the soup kitchen. He was in bed in a dorm-style room that could house a dozen men. He was clean, shaven, and in a hospital gown. But his wrist was tied with a length of sheet, secured to the side of the bed. They were trying to prevent him from running away. He was distant and mostly unresponsive. I had brought him a small radio as a gift, because I knew he liked to listen to the baseball games. He barely acknowledged it. I was shocked when I saw him. He looked nothing like the smiling, happy man that I had become friends with at the soup kitchen. I left the hospital in tears. And I never saw him again. I know that those who put him there thought they were doing the right thing. He received needed medical care, a warm place to sleep, and regular food. He was safe. But he was also absolutely miserable. They had saved his body, but killed his spirit. I often think of that old man. Good people want so much to help. And yet sometimes helping can be so complicated. What was the right thing to do? In the best of worlds, we would have been able to provide local care for him, and housing in his own neighborhood. And then, it seems, that allowing him to stay outside all day and drink sake with his buddies, even though it was ruining his health, would have been his decision. Those of us with more money get to make choices like that - but too frequently, poor people and mentally ill people are stripped of their right to decide how to live out their lives, in the name of charity. There are no easy answers. But seeing his vacant eyes in that hospital bed, with all of the joy gone - that was no solution. Thursday, January 28, 2010 My younger sister Ali gave me a piece of artwork two years ago, with a drawing of a dragonfly, and a quote by e.e. cummings: It takes courage to grow up and become who you really are. When I re-painted my home office shortly after, I used the small message as my centerpiece. I chose paint that matched the green, and pumped up the yellow to a brilliant lemon for the opposite walls. My entire room is filled with art, most of it by or from friends. But this little green and yellow missive now hangs directly in front of me when I sit down at my desk to write. I think of it as a Purple Heart, a badge of honor. For many, many years I struggled and fought, questioned and doubted, stubbornly resisted. I said, over and over again, "I am not that!" I wasn't sure exactly who I was, or where I was headed, let alone how to get there. But I knew that someone else's answer wouldn't work. I was convinced that even my family's best wishes for me, though much appreciated for their intent, were off the mark. Stumbling through many dark years, becoming a friend with despair, making mistakes again and again...still, I pushed on. Some small voice in my head said, "You are enough." But I felt so flawed, and so out of step, and so lost. And then my Zen teachers told me: "The goal of practice is not to become a better person; it is to become more fully yourself." To become who you really are. When I received that little painting from my sister, I knew I had finally been seen. And being seen by someone else helped me to see myself. Monday, January 25, 2010 Ghandi - just saying the name conjures up an awesome energy, a reverence, a worshipful adoration. When people are asked, "What if you could have dinner with five people, living or dead, who would you choose?" the name "Ghandi" frequently makes that top five list. And yet - I read something today about the saint-like Ghandi that taught me a lesson not of what to do, but of what to avoid. I am reading the book The Elephant and the Dragon: The Rise of India and China by Forbes magazine Asia editor Robyn Meredith. In it, she chronicles Ghandi's legacy in India. Much of that inheritance, we know, was a great gift. He embodied the idea of nonviolent protest, setting an example that would transform human and civil rights movements in the coming years. And he gave India a sense of identity separate from British colonial rule. But did you know that he also was completely against modern medicine, because of its ties to the Western world? When his own wife lay dying from bronchitis, doctors flew in penicillin to save her life. Ghandi believed that even the use of a needle contradicted his philosophy of nonviolence. So he turned the medicine away, and sat at his wife's bedside, holding her hand until she died, of a completely curable disease. Meredith also states that Ghandi professed the only acceptable form of birth control was abstinence. He remained sexually abstinent for the last 42 years of his life. Wanting to follow his example, his fellow country men and women shunned all methods of contraception. But, being less saintly than their guru, they failed to live up to complete abstinence, of course, leading eventually to the population explosion in India. There is absolutely nothing wrong with Ghandi's belief systems. They are admirable, and praiseworthy. But to these lengths? To the detriment of the lives of others? He failed to see the value of the middle way. Make a vow not simply to make a vow. Hold steadfast to resolution only when it is the right thing to do, not when it is the only thing you know how to do. As much as we admire the saints, it is actually more difficult to live in the world of gray than it is to practice in the realm of black and white. That is our Zen challenge: the middle way. Sunday, January 24, 2010 It was a big moment in sewing class today. Debi Papazian finished her rakusu! She is the first in our group to successfully complete the face, straps and envelope, and is now an official sewing graduate. There are nine of us, seven from the Healdsburg sangha, who have been meeting weekly on Sundays since October to work on our rakusu in preparation for jukai, or Zen lay ordination, which is scheduled for August. When our sewing teacher Connie Ayers first said we would probably be meeting through February, I thought, geez, it won't take that long! This flippancy, however, was born of naivete. It arose from a place of ignorance, before I was properly introduced to the myriad intricacies, convoluted patterns and layers upon layers of stitches that comprise a Zen rakusu. As you can see by my rakusu, pictured above, I am not quite ready to graduate. Now, February seems alarmingly close at hand. I have been assured (repeatedly) that this is not a race. What do you mean, not a race? It's a class, right? Classes are contests! That's what I did throughout my academic life - enroll, study hard, excel, revel in the high grades. Well, with a couple of exceptions, of course. There was that disastrous home economics course my mother forced me to take in ninth grade. I somehow skated through the cooking portion, because we were assigned to teams. On my team, the other two girls cooked, and I ate what they cooked. It worked beautifully. Unfortunately, when it was time to sew, I didn't get to share my A-line skirt with someone else. I had to make my own. Let's just say "horrid," and leave it at that. I haven't been near a needle since. That is, until October. And here I am, spending my Sunday afternoons sewing. (The only person more incredulous than me about this whole state of affairs is my mother. Every time I see her lately, she says, "And you're sewing!" Then she shakes her head, clearly wondering what other surprises the universe has in store for her.) What I am truly beginning to appreciate through this experience is the nature of the student/teacher relationship. Connie has been so patient, and so gentle in her tutelage, moving from person to person around the room. Barely a moment goes by without one of us raising our hand in the air and whimpering, "Connie, can I be next?" When one is confidently stitching away, her neighbor has just knotted her thread in the wrong spot. As another masters the art of pinning, his neighbor finds he has mistakenly sewn through three layers of cloth instead of the aimed-for two. None of us are ever at exactly the same place at exactly the same time. And yet, somehow, Connie manages to keep us all occupied, soothed, supported, challenged, and committed. Now, that's a teacher. So I'm not at the head of the class. I'm learning it feels pretty darn good simply to be showing up. Saturday, January 23, 2010 If you haven't already read Thomas Friedman's Hot, Flat & Crowded: Why We Need a Green Revolution, put it on your list. I'm heading into the last chapter now - and it's one of those books that makes me want to run out and buy a dozen copies, to distribute to all my friends. The title refers to three impending crises: hot (global warming), flat (the burgeoning middle class around the world, leading to greater use of resources and energy), and crowded (the population explosion). Friedman, a New York Times columnist, argues that the dovetailing of these three trends is pushing us into a new age, the Energy Climate Era, in which the world as we know it must either change - or we will all perish. Sounds dire, I know. And the first few chapters are a bit of a downer. The problems seem almost insurmountable. But what makes the book good is that here are not just problems, but also solutions. Friedman talks to experts all over the country, and the world, and shows us how we can change in time to evade disaster. One part that particularly struck me was the chapter called "205 Easy Ways to Save the Earth." Friedman points out that "green" is so hip now, that every magazine, every group, is coming up with lists of ways to make a difference. But they're always presented as "simple" or "easy" - it's painless being green. Sure, all of those little things add up. Using CFLs instead of conventional light bulbs, recycling your aluminum cans, bringing cloth bags to the grocery store - that matters. But Friedman argues that this can hardly be seen as a revolution. It's more like a fashion statement. Revolutions are about turning the world upside down, shaking things up from top to bottom, radically reconfiguring the way we look at everything. We're talking casualties, bloodshed. I don't mean that literally, that people will have to die. But institutions and ideas should definitely be on the chopping block. Friedman gives dozens of real-life examples of people and companies and even government agencies who are re-thinking every product made, every watt used, every structure built, and coming up with the innovation that is critical to save us from Mother Earth's Judgment Day. The good news is that he remains convinced that the most effective ways to change our world originate with grass-roots movements. Nations and politicians need to be on board; but each one of us has the power to steer those governments (and mega-corporations) in the right direction. Keep bringing your own bag to the grocery store. Don't stop composting. Maintain your vigilance when sorting garbage from recyclables. But don't stop there. Take the next step. Think of it as an extension of the bodhisattva vow: "Beings are numberless. I vow to save them." Friday, January 22, 2010 The Fifth Precept is: Avoiding the deliberate loss of awareness. It is sometimes defined as "no intoxication" and also as "to cultivate clarity for self and others." The most literal interpretation is to avoid alcohol and other drugs. That, for me, is easy. I am ten years clean and sober, after earlier escape finally proved too problematic to continue. So when I first read this precept, I thought, "No big deal. I've got this one licked already." But as our discussion in last week's precept class unfolded, it became clear to me that there was still much work ahead. In Ngakpa Chogyam Rinpoche's explanation of the Five Precepts, on the fifth he says, "I commit myself to the avoidance of mindless and unskillful consumption of anything." Now that opens up a whole new dimension. I know this is true, because when I try to quit one of them, just as when I first quit alcohol and drugs, the discomfort and dis-ease of each moment is nearly intolerable. The last time I tried to quit smoking, about six months ago, on the second day I thought to myself in total despair, "I'm never going to enjoy anything ever again!" Talk about drama! And for the last two days, I have been unable to sleep through the night. Normally, sleep is a refuge for me. Lately, it has been filled with bad dreams, and fitful awakenings. Instead of getting up and sitting zazen, or writing in my journal, or doing anything that might be a way of being present with myself, I go into a total tailspin of anxiety and fretting, worried that I will never be able to sleep again. Ngakpa Chogyam Rinpoche does offer an alternative to the "checking out" mode. He says, "I commit myself to inebriation from the hot blood of compassion, and to the experience of kindness, merriment, and freedom for all beings." "The hot blood of compassion" - sounds racy and enticing, yes? And who can argue with experiencing "kindness, merriment, and freedom for all beings"? Makes the sugar and the nicotine look paltry by comparison. Wednesday, January 20, 2010 Be patient toward all that is unsolved in your heart and try to love the questions themselves, like locked rooms and like books that are written in a very foreign tongue. Do not now seek the answers, which cannot be given you because you would not be able to live them. And the point is to live everything. Live the questions now. Perhaps you will then gradually, without noticing it, live along some distant day into the answer. —Rainer Maria Rilke, Letters to a Young Poet, Letter Four Rain and solitude...a good combination for reflection, quiet thought, stillness of emotion. I am in that space of seeking. I seek relief from pain. I seek answers to questions. I seek light in the darkness. I seek a barely visible deer trail on the forest floor, leading out of the wilderness. I seek myself. It is easy to fall prey to the false belief that one answer will come, an answer simple and direct, which will change everything. It is tempting to look for a pre-packaged, bottled, instructions-included solution. And yet I know that what is made to order is not made for me. Rilke says: Try to love the questions themselves. There is no sense expecting that my seeking will lead me anywhere, not any time soon. What I must do, to follow the advice of the great poet, is to love the seeking, enjoy the quest. Live the questions now. What better way to say it? Be there then. Live here now. In the pain, in the emptiness, in the suffering, in the middle of nowhere. When I had my first dokusan, and tearfully exclaimed, "I have been seeking a Zen path for so long," Darlene Cohen said to me, "You are already there." Monday, January 18, 2010 I make lists; I double-check my Outlook calendar and make sure it's in line with the calendar on the wall in the kitchen. I synch my Blackberry. I go through the stacks of unread magazines and put them in order of title and date. I sift through the basket of "mail to take care of" and toss the stuff that is now so long overdue that it is no longer relevant. I look at my bulletin board, and do the same thing - pull off all the items that happened months ago, so a reminder is no longer necessary. I pick up the books perched precariously at the edge of shelves, and file them in the appropriate section on my bookcases, alphabetical by author. I file paperwork from the DMV and other old bills in the color-coded, labeled folders in my file cabinet. When even that is not enough, I go to Office Depot and wander slowly through the office organization aisles. I end up coming home with a new cabinet, or a three-tiered letter holder, or magazine rack. Then I go home and tackle things fresh. Now is one of those times. My energy level has been so low that it would make a three-toed sloth look positively peppy. I have barely been able to drag myself out of bed to do the tasks that are absolutely required, like showing up for work, or keeping commitments to go to my precepts class or doctor's appointments. I seem to be moving through a dense, impenetrable fog. Each step requires vast reserves of energy, and yet I have nothing in that reserve tank. Given that scenario, it makes perfect sense that today I would choose to use my unexpected two or so hours of relative vigor to do the one thing that makes me feel secure. I put things in order. I tried out every pen in the house that I could find and threw out all the ones that don't work, or were so cheap that they'll invariably fail right when you're trying to write down an important phone number. I straightened every picture on the walls. I even moved several of them to new locations, because I saw that the balance wasn't right. I carried things from the left side of my office to the right side of my office. I picked things up from one shelf, and transferred them to another. I went into my Outlook calendar, and changed the due date on everything that was supposed to be done last week, so it wouldn't look like I was so far behind. In other words, I didn't really do a damn thing. I wonder who I think I'm fooling, when I act busy this way? I'm in the privacy of my own home; no one else is watching. So what exactly am I trying to prove to myself? That maybe if the external appearance shifts, it is evidence of real change underneath? That I really am in control of my emotional state and my life, if my mail is properly filed in color-coded folders? Thursday, January 14, 2010 There is a Zen book for everything, it seems. A rapid perusal of the first few hits that come up on Amazon.com reveals the following titles: Zen & the Art of HappinessZen GolfZen to Done: The Ultimate Simple Productivity SystemZen & the Art of KnittingZen Zombie: Better Living from the UndeadThe Zen of CSS Design: Visual Enlightenment for the Weband, of course: Zen Sex: The Way of Making Love So I should not have been surprised when I stumbled upon The Zen Path through Depression by Philip Martin. Since it seemed a natural fit for me, I bought a copy. The trouble is, when I'm not depressed, I find no reason to pick it up. And when I am depressed, I don't have the concentration or the energy to read. There it has sat, on my bookshelf, for at least 10 years. But for some reason, tonight I glanced over in that direction and spotted it. I had enough inclination to at least pick it up and flip through the pages, even though the thought of sitting down to read the whole thing is a little daunting. I just happened to open to this passage: Return to the place you have imagined as your depression. If you have been here a number of times, you know this place well. You may even feel comfortable here. You have found it is no longer a terrifying place, and that there can be much of value in this place.As you return, envision that in this place there is now a path to be found. Perhaps it is a trail that has been worn through the dark forest you were in, or a star to follow to guide yourself out of a deep desert night - or a lifeline you can follow from deep beneath the sea.Look closely at this path, this trail, until it becomes clear to you. Realize that there is a way out of this place you once thought you would be lost in forever. Are you ready to leave? Are you perhaps surprised to find you are sad at the prospect of leaving? Are you ready to begin the journey?So much resonates for me in these words. Yes, I know there is much value to be found in depression. I have lived deeper and more intensely because of these battles, and I believe they have made me more compassionate, more honest, and more courageous. I love the image of the star leading me out of "a deep desert night." There have been many, many nights with no stars. But now, as I think on this, it is exactly like nature's sky: on the night's without stars, they are not actually absent; they are hidden from view. The stars do always come out again. And while I am waiting for the star to appear - it is a long night's journey into day. Tuesday, January 12, 2010 It's the "again" part that is hard. For much of my adult life, I have battled with depression. There are many contributing factors: repeated trauma, biochemical imbalance, personality, philosophical bent. But knowing the cause doesn't help to deal with the numbing heaviness when it once again descends upon me. I have been blessed with relief for much of the past six years. Some of that is due to extensive work on tough issues. Some of that has been thanks to appropriate medication. And some, a huge part, has been because six years ago I met the woman that I would marry, someone who has given me the safe haven and unconditional love that I had been seeking my entire life. As a bonus, my wife also reconnected me with animals. I had strong relationships with a childhood dog and cat, but had not included animals in my adult world, partially because of my itinerant proclivities. Now, when I come home at the end of the day, I am greeted by the faithful lab Ripley who holds a special place in my heart, the adorable kitten Kenji who can always make me smile, and dogs Houla and Teo, parrot Barney, and cats Bailey, Dozer, Gordy and Idgie, each one of whom loves me in that unrelenting and uncomplicated way that only animals are capable of. Also, I have found in the past years, for the first time in my life, a spiritual home. Sangha and zazen and teachers...all have been an incredible comfort and source of strength and growth. And yet - here I am. Barely making it through the days. It is so familiar. The weight, the dreariness, the fatigue. The inability to concentrate, the trouble getting motivated to do anything, even the things that I enjoy. But it is also different. Before, I didn't have all those "good" things from the paragraphs above. Now, I do. Before, I couldn't think of one reason to keep on going. Now, I can make a long list. Before, I truly believed that it was never, ever going to change. Now, I know that the depression did finally lift in the past, and that it will lift again. Monday, January 11, 2010 More thoughts from "Zen Is Right Here," stories of Shunryu Suzuki Roshi - a selection that represents some of the things I'm struggling with at the moment. * * * * *A student of Suzuki Roshi's, a publisher of Beat poetry, saw his teacher of a year and a half in a private interview. He said that he couldn't continue, that every time he sat zazen he started to cry. "I can't take it," he said. "I'm leaving. I can't be here anymore."Suzuki didn't tell him to stay. He merely said, "You try and you try and you fail, and then you go deeper."* * * * *Once in a lecture Suzuki Roshi said, "Hell is not punishment, it's training."* * * * *On the fourth day of sesshin as we sat with our painful legs, aching backs, hopes, and doubts about whether it was worth it, Suzuki Roshi began his talk by saying slowly, "The problems you are now experiencing...""Will go away," we were sure he was going to say."...will continue for the rest of your life," he concluded.The way he said it, we all laughed.* * * * *A student, filled with emotion and crying, implored, "Why is there so much suffering?"Suzuki Roshi replied, "No reason." Sunday, January 10, 2010 For three years, I lived in Kyoto and Osaka, studying, teaching, and becoming part of a community. I was lucky to share my life there with several Japanese families, and with the Nakamuras and the Masumotos, among others, I was able to experience the best of all the holidays. New Year’s is the longest celebration of the year. For the last week of December, women are busy preparing food, every imaginable kind of delicacy. They make enough to last through the first three days of January, so that throughout the days off everyone has plenty to eat, but no one has to spend the holiday in the kitchen. For three days, all the businesses close down, from giant corporations and banks, to the mom and pop stores on the way to the train station. Everything closes. And people focus in on family, on neighbors, on community. On New Year’s Eve, at midnight, everyone goes to their neighborhood Shinto shrine. They bring with them the amulets from the past year, wooden and paper placards, animals, arrows with blessings tied to them. At the shrine, each person takes turns approaching the huge bell, and tugging at the thick rope to ring in the new year. Then the old amulets are brought over to the bonfire, and thrown in. Crowds of people stand around and watch the old year burn away. And each person leaves the shrine with new amulets, for the new animal year, starting off fresh. On New Year’s Day, we usually woke up late and moved slowly. Food was available all day; there was no set meal time. People just ate, and drank, and visited. It is the time of year when you pay respect to relatives, local community leaders, bosses and teachers. When I spent one New Year’s with a high school principal, people came to the door for days bringing small gifts of food, bowing to this teacher, asking for his continued favors for themselves and their families. And it is also a time to visit the large temples, to make religious pilgrimages a little further away. First we spent hours preparing, all the women together, with the older women in the family dressing the younger women up in kimonos. I remember one year standing still for nearly two hours while five elderly aunts and grandmothers labored over my holiday outfit, putting on layer after layer of clothing, tugging and tucking and fussing. By the time the obi had been tied, I had been transformed; I felt like a living doll. Then we all took the train together to the temple, walking through the snow in our zoris, carrying our parasols. And then there were the afternoon karaoke parties, with everyone in the group taking their turn at the microphone, while the others cheered them on. I spent hours rehearsing a Japanese pop song so that I would be able to hold my own. Every year, when our New Year’s Eve parties are being planned, I am flooded with memories of Shinto shrines, kimonos, big snowflakes, bonfires, and friendship. And I find myself checking out airfares to Tokyo in the newspaper. Thursday, January 7, 2010 The night was foggy, and still. I was sitting out on my deck in my pajamas, having a smoke before sitting down at the computer to blog. I had just arrived home from work about 20 minutes earlier; I glanced at the clock - it was 2:15 a.m. Then the quiet was pierced by a squeal of tires, and a huge, thudding crash. The dogs, out on the deck with me, broke out in three-part alarm barking. I jumped up, grabbed the flashlight, put the dogs in the house and snatched up my phone, and ran as fast as I could in my slippers out to our road. I had seen headlights, but now the night was dark again. At the base of Cedar Lane, as I turned onto River Road, I called out: "Anybody there?" I heard the crack of stumbling footsteps, and swung my flashlight beam over to the side, just in time to catch a body falling forward out of the dense undergrowth and trees. A young man staggered towards me. He said, "I had an accident." I turned my light towards the car, which I could now see buried deep in the culvert, air bags deployed, front windshield cracked. His name was Jordan. He was confused and disoriented. I checked him over quickly: bloodied lips, abrasions on his arms, and a discolored dent on his forehead, but no other signs of injury. My primary concern was concussion. I tried to get him to sit down, and pulled out my phone to call local police. The dispatcher said an ambulance was on its way. We waited. Jordan moaned periodically, and started to cry. He kept repeating that his head hurt. I could smell alcohol on his breath, but said nothing - I was afraid he might be aware enough to realize he was soon going to be in a lot of trouble, decide to take off on foot into the night, and end up unconscious somewhere in the vineyards with a head injury. He pulled an iPhone out of his pocket and punched in a number. I said, "Jordan, you know it's really late, don't you?" He said he was calling his parents; he lived with them in Santa Rosa. I listened as Jordan work his mom and dad up, telling them the bad news. A minute into the conversation, he began crying and handed me the phone, saying, "Can you talk to him?" I told his dad that an ambulance was on the way, that he wasn't injured badly, and that I would call again once emergency personnel arrived. He thanked me, the worry evident in his voice. Jordan reached into his pocket and withdrew a pack of cigarettes. He lit a Marlboro, and took a few puffs, seated on the side of the road. I was standing above him, holding the flashlight. He suddenly fell backwards, arm extended above his head, lit cigarette ember-first in the grass. I grabbed the cigarette and stomped it out. Jordan sat up, saying, "It's okay; I'm okay. Oh, my head hurts!" A door opened. The dogs were still barking - they could obviously hear my voice. I knew Sabrina must have woken up, and realized something was amiss when she saw my abandoned coffee cup outside. She appeared a few minutes later, also in her pajamas and slippers. I introduced her to Jordan: "This is my partner. She's a trained EMT. She's going to look you over." Finally, after Sabrina had determined that Jordan's biggest issue was that he was drunk, the fire truck and ambulance arrived. We were surrounded by men and women in crisis mode; they put Jordan's neck into a brace, placed him on the stretcher, and loaded him into the ambulance. Our night was done. Jordan was 20 years old, not even of legal age to drink. Thankfully, no one else was in the car, and no other vehicle was involved in the crash. It was chilling to realize that not 20 minutes before his wreck, I was on that foggy road, coming home. I'm glad we didn't meet. Tuesday, January 5, 2010 We held a special New Year's ceremony at the Healdsburg sangha tonight, to bless and give thanks for our meeting space. The ceremony was fairly simple, moving to each room of the building and lighting a cande, then giving three bows. At the end, we all returned to the main altar, and in between chants, we took turns stepping in front of the altar to announce our practice intentions for the year. Intentions, though coming at the same time of the year in this case, are not the same as resolutions. As Darlene Cohen explained, resolutions are a matter of applying one's will to something: losing weight, quitting smoking, being on time. But intentions are commitments to mindfulness, a form of vow. The intentions voiced by members of the sangha ranged from following the Precepts to the best of one's ability to recommitting to daily zazen, from giving oneself a break to bringing practice from the zendo out into everyday life. Darlene stressed the importance of vow, and of taking the time to state intention, as part of practice. She said since Zen is "nowhere standing," with nothing to hold onto except the fact that there's nothing to hold onto, knowing one's own intentions is critical. She also spoke of daily intentions, making a statement to oneself each day when sitting down to zazen. This reminded me of my friend Clare, who said that her New Year's resolution for 2010 was to take a moment each day to reflect on what she is grateful for. Here, slightly reframed, is a similar thought: once a day, ask yourself why you are doing this Zen practice. Darlene points out that finding an answer is not important; what matters is asking the question and remaining open to whatever comes in - and continuing to sit, regardless. Monday, January 4, 2010 I have a confession to make. I am a complete, unapologetic, wildly out of control book addict. I can't seem to stop buying them. I have five bookshelves in my office/work space at home, and they are almost full. I'm spilling out into the rest of the house: bedside table, bookcase in the bedroom, a row of hard-bound classics on top of the piano. (The picture above shows what it looked like last summer, when I had to clear it all out to paint the room, and then somehow put it all back in order again.) It's not as bad as it could be, because about ten years ago, after slowly accumulating books for the first 35 years of my life, and carting them all around with me, I went through a major purge, and sold or gave away almost all of them. After that, I was lean and mean for a while. I started using the library almost exclusively. When I did have to buy a book, I would read it and then give it to a friend. But somewhere in the nesting that has happened in the past six years, the book habit has crept back into my life. I had kept some volumes, the best of the best, ones that I couldn't bear to part with. And now, I am adding new books all the time. I've been in a book group for the past seven years, so that's one new book a month. Then I hear recommendations, or read one book that references another, or read a review, or stumble across a find on Powells.com, and off I go. I am constantly interested in new things, and that interest always leads me to more books. So I have a shelf of books on Zen and other Buddhist writings, a shelf of books on Japanese language, a collection of Spanish books, an assortment of books on writing, a bookcase full of poetry. Then I veer off into all kinds of topics, from vegan eating to gay culture to classical music and music theory to the history of World War II to contemporary philosophy. There is so much amazing literature out there, so much to learn, so many pages to examine! The problem is that my thirst/appetite outweighs my capacity for consumption, i.e., I have several dozen books that I haven't read yet, and I'm still purchasing new ones. That's where the "addict" label comes into play. I suppose it's better than a lot of addictions. It's not really hurting anyone else. And it doesn't damage my health, or ruin my relationships, or threaten my job. Sometimes it does put a crimp in the paycheck, though. So the big resolution this year is to read, read, read! I read "The Taming of the Shrew" by William Shakespeare tonight. I've discovered books on CD, and that has upped my ability to get in more "reading" time. There are fabulous editions of Shakespearean plays on CD, acted out with full casts. I'm listening to each play in my car during my commute, then reading it from my "Collected Works" at home, then listening to it a second time, to really get in touch with the language. Very enjoyable, and a less daunting way to tackle Shakespeare than trying to read all 1,000-plus pages of the "Collected Works" straight through. Within the next couple of days, I plan to start on the Buddhist reading plan I've laid out for myself - I have lots to choose from. And lots to learn. Maybe I can control myself, and not buy any more Zen texts until I've read the ones I already have. Maybe not.... Sunday, January 3, 2010 I mentioned briefly that Russian River Zendo held its first-ever Full Moon Ceremony on New Year's Eve. What I failed to note was that I hobbled around like an old lady for two days after that. The Full Moon Ceremony lasts about 20 minutes. It has all the fun Zen stuff - big bells, small bells, clappers, the inkan (another bell), and a kokyo script (for the chant leader) that would test Pavarotti. I showed up early for rehearsal, to "shadow" the doan (master of all the bells) and kokyo, with the idea that at some point in the future, I may be able to take on one of those roles. Also, since our sangha had never done the ceremony, Joan Amaral (our ino, person in charge of the ceremony for the night) thought it would be helpful to have one other person (me) who knew what was coming next, to help model for everyone else. For the ceremony, you set aside your zafu, and use only the zabuton. The entire time, you are either standing, bowing, or sitting in chokei, which means knees bent, resting your weight on your knees and shins, with the rest of your body upright, in gassho (hands in prayer position). I have done some exuberant full prostrations at Tassajara, and also at our recent Rohatsu Sesshin, so I know that those bows can work up some body heat. But I had never sat in chokei before. It looked deceptively simple. But, whoa! It turns out that this posture requires some major quadriceps action! Between the bowing and the kneeling, I was warm, winded, and sore by the end of rehearsal. And that was only the rehearsal. I had to do the whole thing all over again about an hour later, the real deal. Don't get me wrong; it was absolutely fabulous. The ceremony, the sounds, the music of it all, combined with the physical movements: It was like being part of a dance. I loved it so much, that I can't wait to do it again. And I really want to learn the kokyo role. But when I woke up the next morning, I groaned. My thighs felt like I had just gone through circuit training at the gym with a gung-ho 20-year-old fitness pro, after spending a year of sloth on the couch eating bon-bons and watching daytime soaps. It was that bad. My partner was in hysterics listening to me vocalize every time I had to either stand up from a chair, or sit back down again - equally painful. I asked around via email, and it turns out I'm not the only one who got a workout. My buddy Malcolm Yuill-Thornton said he had just been saying to someone in his life that he was still "feeling the 'burn' from our prostrations." When I mentioned it to Joan, she sent this reply: "I call the full moon ceremony the 'quad and pec total workout.' Not for sissies!!" So, coming as it did at this auspicious time of year when we're all setting goals for ourselves and turning over the proverbial new leaves...How about introducing the idea of a Zen Monk's Workout? I can already see the ad campaign on late-night TV: "So busy you need to multi-task? Find spirituality and get fit at the same time! Just call this toll-free number. We'll send you a Full Moon Ceremony workout DVD and a zabuton for only $29.99! Call within the next 15 minutes, and we'll include a complete set of oryoki bowls, with detailed instructions on how to lose weight through the clumsy use of chopsticks. But wait! There's more! Tonight only, we'll also throw in a five-inch-high glow-in-the-dark statue of Buddha. Act now, and don't miss this amazing offer!" Saturday, January 2, 2010 When I was in highschool, watching the movie "2001: A Space Odyssey" for the first time, that date seemed so far off in the future. I was sure we'd all be travelling around in Jetson-family-like hovercrafts, and taking one small pill every day to supply all of our dietary needs. It never even occurred to me then that in 2010, I would still feel young. New Year's is a good time to reflect on the past, what has worked, what has not worked, and plan for the future. I tend to get a little carried away with self-improvement plans, though, and set unrealistic goals. So this year, I'm thinking maybe I'll space things out a bit, tackle things one at a time. First on the list: I'm embarrassed to say this, because it's such a cliche. But I've got to get a handle on my food intake, weight and fitness. This is a huge stumbling block for me, one that I have wrestled with for many, many years. I'm trying to figure out how to frame it so I can really make a positive change that sticks. Something about healthy choices: food as fuel, exercise as daily maintenance. And throw in there some Zen awareness about each mouthful, so that I know I eat in the full presence of every bite, hoping that will eliminate all of the unnecessary calories. Second: Continue on the path I am on towards jukai, and expand my knowledge of the Zen community. I feel firmly placed within my sangha, so this should not be hard. I would like to return to Tassajara again this year, and also, if possible, make time for some short stays or even day visits to City Center and Green Gulch, since I have never been to those places. I hope to expand my reading on Zen in particular and Buddhism in general, so that I can begin to get a grasp of the wonderfully rich heritage of this tradition. I also want to re-commit to daily sitting at home, since I've been somewhat lax about that lately. Third: As a writer, I have made good progress in the past year. After attending a writing retreat in August, I was much more productive than I have been in ages. I have finally started writing short fiction (in addition to poetry and essays), something I had wanted to try for years, and I am enjoying it immensely. I have two strong writing partners who I can share my work with, and look forward to continuing to build those relationships. A focus this coming year will be on moving towards a more regular writing practice, and being brave enough to submit to journals and magazines. Fourth: Read more! Of everything! And that's probably enough to work on, at least for now. There are a couple other big ticket items (like quitting smoking) that I hope to get to soon, but I want to try to get a handle on these first. At least get the momentum going, anyway. I'll have to quit smoking eventually, if I even dream of being able to be the kokyo for the Full Moon Ceremony. No way I'll have the lung capacity otherwise! Anybody out there have some goals for the year? Care to share? We could form an online support group! Friday, January 1, 2010 Last night at Russian River Zendo, we finished off 2009 with three hours of sitting, our first full moon ceremony, ringing the densho (bell) 108 times up to the stroke of midnight, and then hearing a neighbor play "Auld Lang Syne" on his trombone. The new decade started upstairs at Tony and Darlene's house, with champagne, hot sake, a varied potluck spread that contained everything from cabbage rolls to sushi to mini-quiches, and lots and lots of chocolate. It has been quite a year for me as a Zen practitioner. 2009 is the year that I decided to plunge in completely, to give myself to this practice and open my heart to my sangha. After two years of rather erratic attendance, last January I made the commitment to attend my Tuesday night sangha every week - a commitment that, with a few rare exceptions, I was able to keep. Regular attendance meant that I began to feel part of the group, and gradually took on responsibilities, and now I miss it terribly when a scheduling conflict keeps me away. I also began attending a study class at Russian River Zendo one Saturday a month, and in April, started participating in the monthly Precepts class as well. That led to fairly regular attendance at Saturday morning sits and service at RRZ, allowing me to expand still further my Zen family contacts, as I grew close to people in that context. Before this year, I had only done one all-day sit. This year, I participated in two all-day sits at RRZ, one at Berkeley Zen Center, plus a three-day sit and a five-day sit with RRZ at Black Mountain Center. The one day sits were fairly tortuous, and I thought I would never survive a longer sit. The three-day one was difficult - but the most recent, the Rohatsu Sesshin, although the longest at five days, was the easiest so far. I fell so completely into the rhythm of the experience, that I believe I could have continued for a couple of weeks. What a surprise! It has made me eager for more sesshin days. This past summer, I made the decision to pursue jukai (lay ordination). With a group of my other sangha members, I have been studying the Precepts, and since October, we have been sewing our rakusu together. The sewing has been challenging but also unexpectedly pleasant, considering the fact that I had very little faith at the outset that I was going to be able to do it. I also broadened my Zen world byvisiting other places. I went to services at the Berkeley Zen Center and the Santa Cruz Zen Center this year, as well as a small zendo in Las Cruces, New Mexico. The trip to Tassajara made me become enchanted with the forms and rituals of Zen, and so I was thrilled to be able to be part of two classes with Joan Amaral on the forms, and have brought that knowledge into my role as kokyo (chant leader) at the Tuesday night group. I have become so enamored of chanting, that I have added it to my home sitting routine as well. I just can't get enough. Along with others, I made a ceramic jizo for the new temple grounds at RRZ, which was so much fun that I went back to artist Susan Spencer's house to make a second for my own garden. At the urgings of Tony, Darlene and Joan, I started a blog for Russian River Zendo during the last days in September, and have now posted over 90 entries in the past three months. This "practice" has proven to be both challenging and rewarding, and has led me to many new insights and richer understandings of everything else I am learning. And, as a culmination of all of these things, I asked Tony to be my teacher, and am in the process of beginning what I hope will be a long relationship of guidance and tutelage. So, all in all, it has been one amazing year of deepening practice and Zen discovery. Thank you to all of you for being part of it. | Mid | [
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Q: Serenity BDD : How to loop on Steps with Soft Assertions I need to run tests on an array of datas, and I can't find a way to do a soft assert in my step AND show the error at the correct step in the Serenity Report. Example code @Then("All my datas are correct") public void verifyMyDatas(){ int[] myDataArray = new int[] {1,2,3,4}; for(int i = 0; i < myDataArray.length; i++){ mySteps.myAwesomeValidator(myDataArray[i]); } } And an example step : @Step("Checking the value {0}") public void myAwesomeValidator(int value){ //I need a soft assertion here } My attempt : I tried using the assertj framework. But my problem with it is that the "All my datas are correct" step is correctly flagged as a FAILURE, but all the substeps "Checking the value X" are marked as SUCCESSes on Serenity's report. my test code : @Then("All my datas are correct") public void verifyMyDatas(){ SoftAssertions softAssertion = new SoftAssertions(); int[] myDataArray = new int[] {1,2,3,4}; for(int i = 0; i < myDataArray.length; i++){ my mySteps.myAwesomeValidator(myDataArray[i], softAssertion); } softAssertion.assertAll(); } And the step : @Step("Checking the value {0}") public void myAwesomeValidator(int value, SoftAssertions softAssertion){ softAssertion.assertThat(value < 3).isTrue(); } Edit : tried to clarify the problem with my attempt A: I would try as() to describe the assertion and not introduce a Step to see if it works (I believe it should): @Then("All my datas are correct") public void verifyMyDatas(){ SoftAssertions softAssertion = new SoftAssertions(); int[] myDataArray = new int[] {1,2,3,4}; for(int i = 0; i < myDataArray.length; i++) { myAwesomeValidator(myDataArray[i], softAssertion); } softAssertion.assertAll(); } public void myAwesomeValidator(int value, SoftAssertions softAssertion){ // use as() to describe the assertion softAssertion.assertThat(value) .as("awesomely validate value %d", value); .isLessThan(3); } | Mid | [
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On Media On veep selection, look to Wikipedia Tech President's Micah Sifry dismisses the speculation and hearsay and identifies what might just be the most surefire way to anticipate Mitt Romney's running mate selection: Sarah Palin's Wikipedia page was updated at least 68 times the day before John McCain announced her selection, with another 54 changes made in the five previous days previous. Tim Pawlenty, another leading contender for McCain's favor, had 54 edits on Aug. 28, with just 12 in the five previous days. By contrast, the other likely picks — Romney, Kay Bailey Hutchison — saw far fewer changes. The same burst of last-minute editing appeared on Joe Biden's Wikipedia page, Terry Gudaitis of Cyveillance, told The Washington Post. None of Wikipedia entries for the current candidates being bandied about by Romney-watchers — Rob Portman, Marco Rubio, Paul Ryan, Bobby Jindal, Chris Christie, Kelly Ayotte or Pawlenty — are currently showing anything like the spike in edits that Cyveillance spotted on Palin and Biden's pages in 2008. But most of those came in the 24 hours prior to the official announcement. That said, if Wikipedia changes offer any hint of what's coming, then today might be a good day to bet on Ryan. In the Internet age, vetting includes not only a rigorous look at a candidate's past, but rigorous editing of his or her public record. It's a simple but oft overlooked point. Kudos to Sifry for keeping it in mind. | High | [
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Election officials in Pennsylvania have found several hundred ballots cast illegally by people who reside in the state but aren't U.S. citizens, dating back to 2000, after previously acknowledging a software glitch that improperly allowed them to register to vote. The Associated Press reported Wednesday that the Pennsylvania Department of State's Jonathan Marks reported to a state House committee that his office found 544 ballots cast illegally out of 93 million during the past 18 years. Marks also reportedly cautioned that the number could rise. ADVERTISEMENT The news comes just weeks after Pennsylvania's top election official, Secretary of the Commonwealth Pedro Cortés (D), resigned without explanation. Cortés said during a 2016 hearing that the glitch in the state's driver licensing software "may inadvertently register" noncitizen immigrants to vote without their knowledge. A Republican member of the state's election commission in September called the glitch a serious issue, explaining that the improper voter registrations could result in denial of citizenship for the immigrants through no fault of their own. "This is a real concern," Al Schmidt told The AP. "It is harmful to election integrity, and it is harmful to members of the immigrant community who are applying for citizenship. If you've registered to vote in the U.S., and you're not a citizen, it's potential grounds for the denial of your citizenship application." About 6.1 million people voted in Pennsylvania during the 2016 presidential election. President Trump won the state with 48.6 percent of the vote, topping former Secretary of State Hillary Clinton Hillary Diane Rodham ClintonJoe Biden looks to expand election battleground into Trump country Biden leads Trump by 12 points among Catholic voters: poll The Hill's Campaign Report: Biden goes on offense MORE by less than 100,000 votes. A month after taking office, Trump established a White House commission to investigate his unproven claim that millions of undocumented immigrants voted for Clinton during the election. | Mid | [
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A Little More on the Graph Isomorphism Algorithm - urish https://rjlipton.wordpress.com/2015/11/21/a-little-more-on-the-graph-isomorphism-algorithm/ ====== colanderman NC;DR (no context, didn't read) super-dumbed-down summary, found in this [1] linked page, is that there is now a quasipolynomial algorithm to solve graph isomorphism ("are these two graphs identical?"). This is important because: "[…] it could be that GI will become the first ever problem which is NP- intermediate (assuming P is not NP), but from historical patterns it seems more likely that it will fall into P. So people are excited because it’s tantalizing: everyone believes it should be in P, but nobody can prove it. It’s right at the edge of the current state of knowledge about the theoretical capabilities and limits of computation." NP-intermediate being that space between P and NP-complete where quasipolynomial algorithms sit. [1] [http://jeremykun.com/2015/11/12/a-quasipolynomial-time- algor...](http://jeremykun.com/2015/11/12/a-quasipolynomial-time-algorithm- for-graph-isomorphism-the-details/) ------ discardorama Anyone else getting "latex path not specified" in that blog? ~~~ mdonahoe Yup | Low | [
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Lakes Are Frozen, But On-Ice Activities Should Wait Madison Fire Department Warns Of Unsafe Conditions As a deep freeze sinks into Madison after a mild December, many are itching to enjoy winter activities on the city’s lakes. “Not so fast!” says the Madison Fire Department. Although the State Climatology Office declared Madison’s lakes officially “frozen” as of January 11, it will be a little while before the ice is thick enough for people or vehicles to occupy. At least three inches of ice must accumulate before it is safe for people and light activities. At least five inches must accumulate before snowmobiles and ATVs can safely drive on it. Vehicles should not be on the ice unless there is at least one foot of ice. The Madison Fire Department’s Lake Rescue Team typically sees an increase in calls for people in distress on the ice around this time. Anyone who plans to enjoy Madison’s frozen lakes should wait until the ice reaches sufficient depth. The Madison Fire Department Lake Rescue Team is comprised over 50 trained SCUBA divers certified by the Professional Association of Diving Instructors. On-duty divers respond year-round to topside, underwater, and ice rescues, as well as recoveries, vehicle recoveries, and assistance calls from the City of Madison Police Department and Dane County Sheriff’s Office. | Mid | [
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Q: Get next and previous 3 posts in a term in single post page I have a the following Custom post type: episode Custom taxonomy: series sub terms real deal -> season 1, season 2, season 3, etc. The terms are hierarchical, and the entire thing is intended to be structured like a TV series (each "series" has "seasons"). On the single-episode.php page, I want to display the current episode, AS WELL AS links to the next 3 episodes and previous 3 episodes in that season. As an example, if on the "Season 1 - Episode 5" page, I need to get content for Season 1, Episodes 4,3,2 + Season 1 Episodes 6,7,8. I'm having trouble figuring out how to do this inside the loop on a single episode page. Here's what I currently have, however it does not work -- it just repeats the current page episode title over and over with a trying to get property of non-object error. <?php $args = array( 'post-type' => 'episode', 'post-status' => 'publish', 'posts_per_page' => 6, 'tax_query' => array( 'relation' => 'AND', array( 'taxonomy' => 'series', 'field' => 'slug', /* Name of the "series" (in slug format) */ 'terms' => array( 'season-1' ), ), array( 'taxonomy' => 'series', 'field' => 'slug', /* Name of the "seasons" (in slug format) DYNAMIC */ 'terms' => array( $term->slug ), ) ) ); $episodes = new WP_Query( $args ); foreach( $episodes as $episode ) { echo get_the_title($episode->id); } ?> EDIT: Here's my updated query, still a work in progress. It does not seem to be getting anything at the moment. I want to get a total of 6 results, 3 posted BEFORE to the current post, 3 posted AFTER the current post. I'm trying to use the post_date for both the before and after properties of date_query but not sure if I'm doing it right. $args = [ 'tax_query' => [ 'relation' => 'AND', [ 'taxonomy' => 'series', 'field' => 'slug', /* Name of the "series" (in slug format) */ 'terms' => ['season-1'], ] ], 'posts_per_page' => 6, /* make query more efficient */ 'no_found_rows' => true, /* dont let filters/pre_get_posts modify query */ 'suppress_filters' => true, 'date_query' => [ [ 'before' => $post_object->post_date, 'after' => $post_object->post_date, ], 'inclusive' => false ] ]; $q = new WP_Query( $args ); return $q->posts; EDIT 2: I've gotten my desired effect working using a very inefficient method -- it works, but I'd LOVE to hear some tips to optimize it! seems very expensive in terms of queries right now. $orig_post = $post; $orig_terms = wp_get_post_terms($orig_post->ID, 'series'); $current_post = $post; $adjPost = [ 'prev' => [], 'next' => [] ]; for($i = 1; $i <= 3; $i++){ $post = get_previous_post(true, '', 'series'); // this uses $post->ID if ( $post ) { $these_terms = wp_get_post_terms($post->ID, 'series'); if ( $these_terms[1]->slug === $orig_terms[1]->slug) { array_push( $adjPost['prev'], $post ); } } } $post = $current_post; for($i = 1; $i <= 3; $i++){ $post = get_next_post(true, '', 'series'); // this uses $post->ID if ( $post ) { $these_terms = wp_get_post_terms($post->ID, 'series'); if ( $these_terms[1]->slug === $orig_terms[1]->slug) { array_push( $adjPost['next'], $post ); } } } $post = $current_post; echo "<h1>Prev:</h1>"; foreach ( $adjPost['prev'] as $prev ) { echo '<br>'; echo $prev->post_title; } echo "<h1>Next:</h1>"; foreach ( $adjPost['next'] as $next ) { echo '<br>'; echo $next->post_title; } A: You second approach (EDIT 2) is quite buggy and inefficient unfortunately. Also, you are not going to do this in one query. As I already stated, you need to look at the approach in this answer I have recently done. You were almost there in your first edit, the only problem is, you cannot do this in one query, you will have to do two, one to get the previous set of posts, the other to get the next set of posts. I have optimized the code to do only get the necessary info and nothing more. WP_Query results is also cached, so you really don't have to to worry that much about efficiency. I'm not going to rerun through all the detail again in this answer, you should go through the linked post in detail, but you can try something like this (CAVEAT: Untested. Please see the notes in linked answer) $post_object = get_queried_object(); $terms = wp_get_post_terms( $post_object->ID, 'series', array( 'fields' => 'ids' ) ); // Set fields to get only term ID's to make this more effient $args = [ 'post_type' => $post_object->post_type, 'tax_query' => [ [ 'taxonomy' => 'series', 'terms' => $terms, ] ], 'posts_per_page' => 3, 'order' => 'ASC' // CHANDE TO DESC IF NOT CORRECT /* make query more efficient */ 'no_found_rows' => true, /* dont let filters modify query */ 'suppress_filters' => true, 'date_query' => [ [ 'before' => $post_object->post_date, 'inclusive' => false ], ] ]; $q1 = new WP_Query( $args ); var_dump( $q1->posts ); $args1 = [ 'post_type' => $post_object->post_type, 'tax_query' => [ [ 'taxonomy' => 'series', 'terms' => $terms, ] ], 'posts_per_page' => 3, 'order' => 'DESC' // CHANDE TO ASC IF NOT CORRECT /* make query more efficient */ 'no_found_rows' => true, /* dont let filters modify query */ 'suppress_filters' => true, 'date_query' => [ [ 'after' => $post_object->post_date, 'inclusive' => false ], ] ]; $q2 = new WP_Query( $args1 ); var_dump( $q2->posts ); | Low | [
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INTRODUCTION ============ Motor proteins convert chemical energy into structural changes and produce mechanical work necessary for various cellular processes including vesicle transport ([@R1]), cell division ([@R2]), muscle contraction ([@R3]), and beating of flagella and cilia ([@R4]). In vivo, motor proteins do not work alone but as a team ([@R5]--[@R7]). In intracellular transport, approximately 10 motors coordinate to transport a cargo ([@R8]--[@R10]) and cooperate to produce a higher speed or larger force than that by a single motor. The velocity of cargo with several kinesin motors increases by three- to fourfold compared to a single kinesin motor in vitro ([@R11], [@R12]). Similarly, the force exerted by kinesin-14 motors increases with their number ([@R13], [@R14]). In cell divisions, 20 to 100 motors are involved in assembling the spindle to segregate chromosomes ([@R15]). Approximately 10^4^ axonemal dynein molecules, assembled with a defined spacing of 24 or 96 nm, collectively produce the beating motion of a cilium or a flagellum ([@R16], [@R17]). Evidently, to understand the physiological functions of motor proteins, it is necessary to know how the number and spacing of motor proteins influence their motility. The effect of the number of motors on microtubule behavior has been investigated using a microtubule gliding assay because the number of motors interacting with gliding microtubules can be estimated from the length of the microtubule and motor density on the surface (i.e., the number of motor molecules per unit area). Bieling *et al.* ([@R18]) found that the microtubule velocity decreased with an increase in motor density when a truncated kinesin-1 was used. Roostalu *et al.* ([@R19]) reported that the directionality of gliding microtubules could be switched by increasing the number of kinesin-5 proteins and argued that directionality was determined by the total number of kinesin-5 proteins interacting with the microtubule. These studies suggest that the number of motors is an important factor in the collective dynamics of motors. The spacing between motors has also been shown to affect the collective dynamics of motors. Axonemal dynein molecules are arranged along the microtubule of cilia and flagella at equally spaced intervals ([@R16], [@R17]). Using extract from cilia, Seetharam and Satir ([@R20]) reconstituted that the gliding of microtubules on axonemal dynein molecules is periodically arranged in vitro and found that the microtubules could slide at a high velocity (average of 196 μm/s). As this measured velocity is an order of magnitude greater than the typical gliding velocity on a dynein-coated glass surface, where the spacing of axonemal dynein molecules is variable ([@R21]), it is thought that equal spacing between dynein molecules may be necessary to realize a higher velocity. One disadvantage of a conventional gliding assay is that it cannot distinguish the effects of direct and indirect interactions between motors on their collective dynamics. Direct interactions caused by steric hindrance between adjacent motors lead to detachment or pausing of motors, decreasing the velocity of microtubules ([@R22]). An indirect interaction occurs when one motor's activity influences other more distant motors transporting the same microtubule ([@R6]). When a microtubule is transported by multiple kinesins, some of them generate a force that acts in a direction that is opposite to the moving direction of the microtubule because not all kinesins are synchronized. Direct interactions could be eliminated by increasing the space between the motors. Therefore, to investigate the individual effects of direct and indirect interactions, the spacing between motors could be controlled. The mechanisms explaining how the number and spacing of motors affect their collective dynamics remain poorly understood, primarily because of the experimental difficulties in controlling these parameters in vitro. Using flat surfaces, the number and spacing of motors can be controlled by varying their concentration and the length of the microtubules. However, the estimated number of motors interacting with a microtubule is less deterministic, because motors are stochastically distributed on the surface. Although DNA origami scaffolding allowed us to precisely define the number and spacing of motors ([@R13], [@R23]--[@R25]), only up to 10 motors can be controlled, which is much lower than the number in vivo. It is necessary to develop a method to modulate the number and spacing of motors in vitro. Several studies have addressed the difficulty of controlling the number of motors using micro/nanopillars. Lard *et al.* ([@R26], [@R27]) demonstrated that the number of myosin interacting with an actin filament can be controlled by immobilizing myosin molecules on a nanowire array. However, because myosin molecules were immobilized not only on the top of nanowires but also on the substrate and sides of the nanowires, actin filaments frequently glided along the sides of the nanowires down to the substrate, resulting in short observation times. In addition, their method is less deterministic because multiple motor molecules were attached on the tops of the large-diameter (150 to 170 nm) nanowires. Roos *et al.* ([@R28]) took an approach similar to Lard *et al.*, selectively immobilizing kinesin molecules on the tip of micropillars made of polydimethylsiloxane. However, many kinesin molecules were attached to a single micropillar owing to its large diameter (1 to 5 μm). Here, we propose the nanopatterning method of kinesins to accurately determine the number (10 to 100 motors per microtubule) and spacing (200 to 1000 nm) of kinesin motors. Because we used smaller nanopillars (50 nm in diameter) to immobilize only a single kinesin molecule per pillar, we can precisely define the number of motors and the spacing of the motors interacting with a microtubule. Moreover, this method enables us to perform the microtubule gliding assay at a much lower motor density (\<10 molecules/μm^2^) than that required for the conventional gliding assay with flat surfaces (20 to 10,000 molecules/μm^2^) ([@R18]). This makes it possible to study the relationship between the number and velocity of motors in the range of 3 to 100 motors, similar to the number of motors working together in vivo ([@R29]). In addition, our method enables us to isolate the effects of indirect interactions between motors because the distance between them is greater than twice the length of a kinesin molecule. We found that the number and spacing of kinesin molecules separately affect the microtubule velocity in the case of nonprocessive kinesin-14, whereas the velocity is independent of both the number and spacing for processive kinesin-1. The proposed patterning method facilitates a new assay that can be used to investigate how the number and spacing of motors affect the collective dynamics of multiple motors. In addition to enabling the study of the relationship between velocity and the number and/or spacing of motors, our method has the potential to guide microtubules along nanopillars and motivate practical usage of motor-driven bio-nano/microdevices ([@R30]). The microtubule-kinesin system can be combined with microfluidics and used as a molecular transporter, sorter, concentrator, and detector. The directional control of gliding microtubule shuttles has been a challenge that has hampered practical usage of microtubule-kinesin, as microtubules glide in random directions owing to Brownian motion of the free leading tip ([@R31]). Although a fabricated track can control the gliding direction of microtubules, the precision is still limited up to a few micrometers, and the efficiency of microtubule transport is deteriorated by frequent sidetrack of microtubules. In this study, we demonstrate that the gliding direction is defined with high precision by defining the position of each kinesin with nanometer-scale precision. Therefore, our method can also be used to control the direction of gliding microtubules and drive the practical usage of microtubule-kinesin systems. RESULTS AND DISCUSSION ====================== Nanofabrication of gold nanopillars and selective immobilization of kinesin molecules on self-assembled monolayer--modified surfaces ------------------------------------------------------------------------------------------------------------------------------------ Kinesin molecules were selectively immobilized on gold nanopillars as illustrated in [Fig. 1A](#F1){ref-type="fig"}. Gold nanopillar arrays were fabricated on a silicon dioxide substrate by electron beam lithography and lift-off processes, followed by the passivation of a silicon dioxide surface with a silane--poly(ethylene glycol) (PEG) self-assembled monolayer (SAM) ([Fig. 1B](#F1){ref-type="fig"} and fig. S1A). To attach only one kinesin molecule to a nanopillar, we designed the diameter of the nanopillars to measure 50 nm. By optimizing the smallest spacing in the nanofabrication processes, nanopillar arrays with spacing ranging from 200 to 1000 nm were fabricated (fig. S1B). SEM observations confirmed that the diameters of the nanopillars were close to the designed value (55.7 ± 4.17 nm, mean ± SD, *n* = 30) (fig. S1C). {#F1} Before performing a gliding assay on the pillars, we confirmed that both kinesin-1 and kinesin-14 could be selectively immobilized only on a planar gold surface and not on the passivated silicon dioxide surface. On the gold surface, where biotinylated kinesin-1 was immobilized via nonspecifically absorbed streptavidin, the microtubule velocity was recorded as 0.75 ± 0.02 μm/s (mean ± SD, *n* = 5). No microtubule was found on the silicon dioxide surface because of the silane-PEG SAM ([@R32]). In a control experiment using a glass substrate, where kinesin-1 was immobilized via streptavidin and biotinylated bovine serum albumin, the microtubule velocity was recorded as 0.42 ± 0.02 μm/s (mean ± SD, *n* = 5). When the same measurement was conducted using kinesin-14, recorded velocities were 0.123 ± 0.015 μm/s (mean ± SD, *n* = 5) on a gold surface and 0.091 ± 0.003 μm/s (mean ± SD, *n* = 5) on a glass surface. The silane-PEG SAM--modified surface also suppressed microtubule absorption in the kinesin-14 assay. It is known that the velocity strongly depends on temperature ([@R33]), the construct (length) of kinesin ([@R18]), and the surface density of the motors ([@R18]). Therefore, measured velocities are compared to previous studies conducted under conditions similar to ours. Our recorded velocity on a kinesin-1--coated glass surface (0.42 ± 0.02 μm/s) is in agreement with the ≈0.43 μm/s obtained in a previous study ([@R18]). Experimental conditions for our study were similar to theirs: a surface density of ≈1000 molecules/μm^2^ using a truncated kinesin-1 (Kin401, amino acids 1 to 401; 1 to 465 in this study) at 26°C (23° to 25°C in this study). Velocity on a kinesin-14--coated glass surface (0.091 ± 0.003 μm/s) is slightly lower than a previously reported value (0.135 ± 0.006 μm/s) ([@R34]). We used the same truncated kinesin-14 (amino acid 195 to 700) as Furuta *et al.*, so the difference in velocity may have come from their use of green fluorescent protein tag or a difference in the surface density of motors, since theirs was not controlled. Our results show that the velocities on kinesin-1-- or kinesin-14--coated gold surfaces are higher than those on glass surfaces. A possible explanation is the elevation of temperature near the gold surface owing to the absorption of excitation light. According to our previous study ([@R35]), the temperature on a gold surface is elevated from 23°C to 28°C when the surface is illuminated by excitation light with an irradiance of 7.2 W/cm^2^ (equivalent to the intensity we used in this study), resulting in an increased velocity compared to that on a glass surface. Motility functions of kinesin molecules were retained after the selective patterning on a gold surface. Therefore, we decided to immobilize kinesin molecules on gold nanopillars via nonspecifically absorbed streptavidin. Microtubule gliding assay on kinesin-1-- or kinesin-14--immobilized nanopillars ------------------------------------------------------------------------------- A microtubule gliding assay was performed to verify the selective immobilization of kinesin molecules on gold nanopillars. It was found that, in the gold nanopillar region where kinesin-1 motors were immobilized, many microtubules attached to the surface and glided smoothly ([Fig. 1C](#F1){ref-type="fig"} and movie S1). On the other hand, we found no microtubule attachment within the silicon dioxide region. When the microtubules crossed the boundary from the nanopillar region and entered the silicon dioxide region, they detached from the surface ([Fig. 1D](#F1){ref-type="fig"} and movie S2). The same behavior was observed on the kinesin-14--patterned surface (fig. S2 and movies S3 and S4). These results support the idea that kinesin molecules exist only within the gold nanopillar region. To evaluate the number of kinesin molecules attached to the nanopillars, we observed the behavior of short microtubules on patterned kinesin-1. We used kinesin-1 because it is a highly processive motor, and a single molecule has the ability to move a microtubule. Short microtubules (1 to 5 μm) were introduced into a flow chamber where kinesin-1 was patterned by 5-μm spacing nanopillars. We observed that several microtubules exhibited pivoting motions on an anchored point (fig. S3B), which is known to be observed when a microtubule is driven by a single kinesin-1 molecule (fig. S3A) ([@R36]). In addition, the microtubules showed a gliding motion at the anchored point (fig. S3D). These results indicated that a single kinesin-1 molecule was attached to a pillar and drove the microtubules. As kinesin-14 is not a processive motor, it frequently detaches from microtubules in the presence of adenosine triphosphate (ATP). For this reason, we evaluated the number of kinesin-14 on a pillar by the same method for kinesin-1 but in the absence of ATP (see Materials and Methods for detail). We observed pivoting motions of microtubules at an anchored point (fig. S3C), indicating that a single kinesin-14 molecule was attached to a pillar. As the hydrodynamic radius of kinesin is approximately 10 nm ([@R37]), six kinesin molecules can be immobilized on a pillar with a diameter of 50 nm. However, this assumption is inconsistent with our finding that only a single kinesin was attached to each pillar. Here, casein may have a significant role in decreasing the number of kinesin molecules on a pillar, because it forms micelles with a hydrodynamic radius of \~12 nm and attaches to pillars ([@R38]). Our result also indicates that there are very few, if any, pillars with more than one motor. If pillars had more than one motor, then we would have observed a smooth gliding of short microtubules. However, we did not observe this behavior; we observed only instances of pivoting motions. To statistically examine whether all nanopillars capture a single kinesin molecule, the average spacing between kinesin motors immobilized on nanopillars can be discussed. When a short microtubule glides on a kinesin-1--coated surface, it frequently binds to a single kinesin-1 molecule and displays a pivoting motion around the motor ([@R39]). The average distance travelled by the microtubule between successive rotations depends on the length of the microtubule and the average spacing between kinesin-1 motors. Hence, the average distance between motors \<*d*~k~\> was derived using the following equation ([@R40])$$< S > = \frac{L + 2 < d_{k} >}{L + 3d_{k}}\frac{{< d_{k} >}^{2}}{L}\left( e^{\frac{L}{d_{k}}} - 1 - \frac{L}{< d_{k} >} \right)$$ Here, \<*S*\> is the average distance travelled between pivots, and *L* is the length of the microtubule. If the measured average spacing between motors is equivalent to the spacing of nanopillars (*d*~p~), then we can assume that each nanopillar has a kinesin molecule. Previously, we demonstrated a selective immobilization of kinesin-1 on a nanopillar array via thiol-PEG-biotin SAM and measured the average spacing between motors ([@R41]). When the diameter of the pillars was 50 nm, the measured spacing was 99.2 ± 4.2 nm for pillars designed with 100-nm spacings. However, the difference between the measured and designed spacings increased when the diameter of the pillars was 100 nm (267 ± 10 nm for 300-nm spacing; 452 ± 21 nm for 500-nm spacing). These results indicate that pillars with diameters of 50 nm have only a single kinesin molecule, whereas multiple kinesin molecules can be immobilized on pillars with diameters of \>100 nm. Although we immobilized kinesin molecules via a different method (nonspecific absorption of streptavidin), we are able to assume that almost all the nanopillars have a single kinesin molecule in the current study. Our method enables us to conduct microtubule gliding assays at an extremely low motor density (1 to 10 molecules/μm^2^), which cannot be done in a conventional gliding assay on a flat glass surface (20 to 10,000 molecules/μm^2^) ([@R18]). This can be explained by the difference in the number of motors interacting with a microtubule. On a flat surface, motors are stochastically immobilized and attach to a microtubule only when the distance between the longitudinal axis of the microtubule and a motor is less than 45 nm ([@R42]). Therefore, the number of motors attached to the microtubules can be calculated as (2 × 0.045 μm) × ρ = 0.09ρ (molecules/1-μm microtubule). Here, ρ is the surface density of the motors (molecules/μm^2^). On a nanopillar array, a microtubule glides on aligned pillars as discussed in the following sections. When focusing on a microtubule gliding in the direction of highest pillar density ([Fig. 2B](#F2){ref-type="fig"}, line A), the number of motors attached to the microtubule can be calculated as 1/*d*~p~ = $0.66\sqrt{\rho}$ (molecules/1-μm microtubule). Here, we used the relationship between the spacing of nanopillars and the surface density of nanopillars (motors): $d_{p} = \sqrt{2/\rho\text{sin}60{^\circ}} = 1.52/\sqrt{\rho}$. Therefore, when the density is set to ρ = 1.0 molecule/μm^2^, a 10-μm microtubule can bind to only ≈1 motor on a flat surface, which easily leads to detachment of the microtubules from the surface. However, ≈7 motors can support microtubule gliding on a nanopillar array, resulting in stable gliding of microtubules. One advantage of our method is that the gliding assay can be conducted at such a low motor density (3 to 100 motors per microtubule), similar to the number of motors working together in vivo ([@R29]). {#F2} Compared to previous studies using a micro/nanopillar array ([@R26]--[@R28]), our method allows us to more accurately count the motors and define their spacing. Even in studies with a pillar array, motors coated all surfaces, including the substrate and sidewall of the pillars ([@R26], [@R27]). This resulted in actin filaments gliding unpredictably across surfaces. However, in our study, the SAM coating and SiO~2~ substrate prevented nonspecific binding and limited microtubule gliding to the tops of pillars. In addition, we used smaller nanopillars (50 nm in diameter) than previous studies (\> 150 nm in diameter) to immobilize only a single kinesin molecule on each nanopillar. Therefore, our assay continued for enough time to study the relationship between the velocity and the number or spacing of motors. The method can be applied to kinesin-microtubules, actin-myosin, and other motors. Alignment of microtubules on patterned kinesin molecules -------------------------------------------------------- We measured the orientation angle of microtubules with two kinds of kinesins (kinesin-1 or kinesin-14), two buffers with different ionic strengths (BRB12 or BRB80), and eight kinds of pillar spacings (300 to 1000 nm). [Figure 2A](#F2){ref-type="fig"} shows the fluorescence image and the schematic illustration of microtubules on patterned kinesin molecules. The angles of the microtubules are defined with respect to the solid red lines ([Fig. 2B](#F2){ref-type="fig"}, line A) connecting two adjacent pillars with the designed spacing, *p*, which ranges from −30° to +30°. We found that there are two populations of microtubules indicated by the two peaks in the probability graph in [Fig. 2 (C to F)](#F2){ref-type="fig"}: one glides in the direction of 0° and the other glides in the direction of ±30°. The former peak corresponds to the main population of the microtubules that glide along line A. The latter corresponds to the subpopulation of the microtubules moving along line B, as shown in [Fig. 2B](#F2){ref-type="fig"}. These two populations of microtubules are independent of the type of motors, the ionic strength of the buffer, and the spacing of the pillars ([Fig. 2, C to F](#F2){ref-type="fig"}, and fig. S4, A to D). Fluorescence images of aligned microtubules under each condition are summarized in fig. S4 (A to D). As the persistence length of 4 to 8 mm is much larger than the pillar spacings, it is evident that most microtubules keep gliding straight once they start gliding on aligned pillars ([@R43], [@R44]). In addition, the microtubules are more likely to land in the directions of lines A and B, as the microtubules can bind to larger number of kinesin molecules in this region than in other directions (fig. S5, A and B). This is the reason why microtubules are settled in these two directions, and two peaks can be observed in [Fig. 2 (C to F)](#F2){ref-type="fig"}. The degree of microtubule alignment becomes higher with an increase in the spacing of the pillars, reaching a maximum at a spacing of 700 nm in any condition ([Fig. 2, C to F](#F2){ref-type="fig"}, and fig. S4, A to D). When the spacing between pillars is small, microtubules land not only in the direction of the two lines A and B but also in other directions because they can bind to enough kinesins to remain on the surface. For example, a microtubule with a length of 10 μm lands in other than the two directions and binds only to \~2 kinesin molecules in the case of a 700-nm pillar spacing, whereas it can bind to \~12 kinesin molecules in the case of a 300-nm spacing (fig. S5B). This is why the height of the peaks increases when the spacing of the pillars increases. In the case where spacing between pillars is equal to or more than 700 nm, we found that many microtubules changed their gliding directions by touching pillars or the silicon dioxide surface owing to tip fluctuation. Numerical simulation (see the next section for details) reveals that the tip thermally fluctuates by 37.9 nm (3× SD) at a 700-nm spacing. Therefore, when microtubules fluctuate in the *z* direction, their tip can easily touch the substrate as the pillar height (the chromium and gold thickness) is only 23 nm. When the leading tip touches the substrate, the tip would be pinned on the surface, while the microtubule rear end continues to move forward, resulting in rotation of the microtubule around the pinned point and a change in the gliding direction. The ionic strength of the motility buffer also influences the degree of microtubule alignment. The population of microtubules that moves along line A or line B is larger in BRB80 buffer than in BRB12 buffer on both the kinesin-1--patterned surface ([Fig. 2, C and D](#F2){ref-type="fig"}, and fig. S4, A and B) and the kinesin-14--patterned surface ([Fig. 2, E and F](#F2){ref-type="fig"}, and fig. S4, C and D). This can be explained by the difference in the off-rate of kinesins from microtubules. As a run length of kinesins decreases with increasing ionic strength ([@R34], [@R45]), it is suggested that the off-rate increases with increasing ionic strength. In addition, the off-rate is known to increase when neck linkers of kinesin molecules are extended ([@R42], [@R46]). Thus, the microtubules detached more frequently from the surface in BRB80 than in BRB12 if they landed in other than the two directions. Therefore, in BRB80, it is observed that most of microtubules continue to attach to kinesin molecules in the directions of lines A and B rather than in other directions, and the degree of microtubule alignment increases. We also found that the degree of the microtubule alignment is higher on the kinesin-14-- than on kinesin-1--patterned surface: The height of peaks at 0° and ±30° are higher on kinesin-14 ([Fig. 2, E and F](#F2){ref-type="fig"}) than kinesin-1 ([Fig. 2, C and D](#F2){ref-type="fig"}) in both BRB80 and BRB12. This is because kinesin-14 has a smaller detachment force (i.e., stall force) than kinesin-1: \<1 pN for kinesin-14 ([@R13]) and \~6 pN for kinesin-1 ([@R47]). As the load applied to kinesin heads increases with the extension of neck linkers, microtubules are detached more frequently from the kinesin-14--patterned surface than from the kinesin-1--patterned surface when the microtubules land in other than the two directions. A run length of motors also plays a role in aligning microtubules along pillars. Kinesin-14 has a shorter run length (≈−400 nm) than kinesin-1 (≈1600 nm) ([@R34]). The shorter run length causes rapid detachment of microtubules from the surface when a microtubules lands in other than the two directions. In summary, the microtubules were highly aligned on patterned kinesins according to the pillar arrangement. The degree of microtubule alignment increases with (i) an increase in spacing and reached a maximum at a spacing of 700 nm; (ii) an increase in the ionic strength of the buffer solution; (iii) a decrease in the stall force of the motors; and (iv) a decrease in the run length of motors. Simulating thermal fluctuation of the free tip of a microtubule on patterned kinesins ------------------------------------------------------------------------------------- Next, we simulated the fluctuation of the leading tips of microtubules and investigated how the microtubules aligned along the pillars ([Fig. 3A](#F3){ref-type="fig"}). Here, the microtubule is assumed to move along line A ([Fig. 2B](#F2){ref-type="fig"}), and the free tip is considered as a cantilever beam tethered at one end ([@R31]). The length of a free tip, *L*, is equal to the spacing of the pillars, *d*~p~. {#F3} [Figure 3B](#F3){ref-type="fig"} shows the probability density functions of displacement of the tip in the *y* direction for the 300- and 1000-nm pillar spacings. It is obvious that microtubules glide toward pillar A because the probability is maximum at *y* = 0 nm, resulting in the peaks at 0° as shown in [Fig. 2 (C to F)](#F2){ref-type="fig"}. Next, we evaluated the amplitude of thermal fluctuation by comparing the SD of the displacement of the tip: SD is calculated as 3.54 nm for *d*~p~ = 300 nm and 21.2 nm for *d*~p~ = 1000 nm. The distance between pillar B and the microtubule is 0.865 *d*~p~ as shown in [Fig. 3B](#F3){ref-type="fig"} and is calculated as \~260 nm for *d*~p~ = 300 nm and \~870 nm for *d*~p~ = 1000 nm. This indicates that the distance between pillar B and the microtubule is more than 40 times larger than the amplitude of the free tip. Therefore, the possibility that the end of a free tip moved to the position of pillar B is zero. The amplitude of thermal fluctuation can also be analytically calculated by the effective elastic constant of the tip as *K* = 3κ~MT~/*d*~p~^3^ and the fluctuation amplitude as $\sigma~ = ~\sqrt{k_{B}T/K}$, where *k*~B~ is the Boltzmann constant, and *T* is the temperature in the experiments (298 K). With this calculation, σ = 3.51 nm for *p* = 300 nm and σ = 21.4 nm for *p* = 1000 nm, which is consistent with our simulation results and confirms the adequacy of our simulation model. Together, the numerical simulation indicates that the microtubules move along the straight lines ([Fig. 2B](#F2){ref-type="fig"}, line A) corresponding to the pillars when kinesin molecules are immobilized only on pillars. However, we observed that some microtubules changed their direction of gliding. To find an explanation for this contradiction, we investigated how the microtubules changed their gliding directions on patterned kinesin molecules. Behavior of microtubules that changed their direction of gliding on patterned kinesin molecules ----------------------------------------------------------------------------------------------- We carefully observed the behavior of microtubules on patterned kinesin molecules and investigated how the microtubules changed their direction of gliding. We found that events related to changes in the gliding direction can be classified into four types: (I) collision and unchanged, (II) collision and changed, (III) spontaneous, and (IV) pinning. [Figure 4 (A to D)](#F4){ref-type="fig"} shows the sequential images of microtubules that represent the events (I) to (IV). (I) "Collision and unchanged" is the event where the leading tip of a microtubule collides with other microtubules but does not change its gliding direction ([Fig. 4A](#F4){ref-type="fig"}). (II) "Collision and changed" represents the event where the tip collides with other microtubules, and the microtubule changes its direction of gliding ([Fig. 4B](#F4){ref-type="fig"}). In detail, the tip detached from the surface, glided over the other microtubules, and then exhibited Brownian motion. Last, the tip reattached to a kinesin in a different direction from the initial one and kept gliding ([Fig. 4B](#F4){ref-type="fig"}, 16 to 20 s). (III) "Spontaneous" represents the event where the leading tip spontaneously changes its gliding direction by Brownian motion without colliding with other microtubules ([Fig. 4C](#F4){ref-type="fig"}). (IV) "Pinning" indicates the event where the leading tip is temporally pinned on the surface, and the microtubule starts rotating around the pinned point and changes its gliding direction ([Fig. 4D](#F4){ref-type="fig"}). {#F4} [Figure 4E](#F4){ref-type="fig"} shows the frequency of each event, i.e., the number of observations for each event per second, on patterned kinesin-1 and kinesin-14. The sum of the frequency of (II) to (IV) indicates how many times the microtubules changed their gliding directions per second: 0.023 s^−1^ on kinesin-1 and 0.003 s^−1^ on kinesin-14. Microtubules changed their gliding directions on kinesin-1 at a frequency that was seven times higher than that on kinesin-14. On kinesin-1, the change was mainly caused by Collision and changed (0.017 s^−1^) and the effects of Spontaneous (0.006 s^−1^), and Pinning were negligible (0.0005 s^−1^). On kinesin-14, the frequencies of Collision and changed (0.001 s^−1^) and Spontaneous (0.002 s^−1^) were almost the same and that of Pinning was also negligible. According to these results, the collision of the leading tip (II. Collision and changed; [Fig. 4B](#F4){ref-type="fig"}) is the main reason for the change in direction observed in the experiments but not in the numerical simulation. Although the frequency of the Spontaneous event was not zero in the experiments, the low frequency can reasonably explain why no microtubule could bind to a kinesin on pillar B in the simulation. One possible reason why we observed Spontaneous events in the experiment, but not in the numerical simulation, is the underestimation of the amplitude of the free tip of a microtubule in the simulation. We assumed that the microtubule was tightly clamped to pillars, and the tip could be considered as a cantilever rigidly fixed at the frontmost motor. However, the stalk domain of a kinesin molecule is flexible in the experiment ([@R42]), and thus, the tip of microtubule is rather loosely clamped to the pillar, causing a larger fluctuation than that seen in the simulation. To estimate the amplitude of fluctuating tip more accurately, it will be necessary to construct a simulation that considers the elasticity of kinesin molecules. Investigating the relationship between microtubule velocity and the number or spacing of motors ----------------------------------------------------------------------------------------------- [Figures 5](#F5){ref-type="fig"} and [6 (A and B)](#F6){ref-type="fig"} show the dependence of the microtubule velocity on the number and spacing of kinesin-1 and kinesin-14 motors in the BRB80 buffer. We assumed that only a single kinesin molecule is attached to a nanopillar for both the kinesin-1 and kinesin-14 cases, according to the observed pivoting motion of short microtubules on nanopillars. The velocity was found to be independent of the number of kinesin-1 motors in the range of 3 to 30 motors and spacing of the kinesin-1 motors ([Fig. 5](#F5){ref-type="fig"} and fig. S6). In contrast, the velocity decreased within the range of 3 to 10 kinesin-14 motors and reached a plateau of over 10 motors ([Fig. 6A](#F6){ref-type="fig"}). On the other hand, the velocity is independent of the spacing for kinesin-14 motors ([Fig. 6B](#F6){ref-type="fig"}). {#F5} {#F6} [Figure 6 (C and D)](#F6){ref-type="fig"} shows the dependence of the microtubule velocity on the number and spacing of kinesin-14 motors in BRB12 buffer. Unlike in the BRB80 buffer, in the BRB12 buffer, both the number and spacing of kinesin-14 motors affect the microtubule velocity. In BRB12 buffer, such as in the BRB80 buffer ([Fig. 6A](#F6){ref-type="fig"}), the velocity decreased with an increase in the number of kinesin-14 motors ([Fig. 6C](#F6){ref-type="fig"}).On the other hand, the velocity increased with an increase in the spacing until the spacing reached 0.6 μm and decreased with an increase in the spacing of over 0.6 μm ([Fig. 6D](#F6){ref-type="fig"}). The relationship between the microtubule velocity and the number of kinesin-1 motors has been examined in previous studies. Bieling *et al.* ([@R18]) reported that, when a truncated kinesin-1 (amino acid residues 1 to 401) was used, the microtubule velocity sharply decreased with an increase in motor density in the case of high motor density (\>500 molecules/μm^2^) and slightly decreased with an increase in motor density in the case of low motor density (\<500 molecules/μm^2^). In our experiments, a truncated kinesin (amino acid residues 1 to 465) was used at a very low-density range owing to the patterning (2 to 58 molecules/μm^2^) and could not be investigated with a glass substrate. Therefore, our experiment indicates that velocity is independent of the number and spacing of motors at such a low motor density. The relationship between the microtubule velocity and the number of kinesin-14 motors was also evaluated in a previous study. Furuta *et al.* ([@R13]) revealed that the velocity of kinesin-14 motors was independent of the number of motors in the range of 1 to 4 motors. Lüdecke *et al.* ([@R14]) examined the relationship between the velocity at which a microtubule glides on a kinesin-14--coated surface and the length of the microtubule. They found that the velocity was independent of microtubule length and thus motor number. When Lüdecke *et al.* performed the assay using \>1-μm microtubules on a surface coated with a saturated kinesin-14 motor (i.e., the density of the motor was ≈4000 molecules/μm^2^) ([@R48]), their results indicated that the velocity is independent of motor number for \>50 motors. Our results revealed that the velocity decreased from 3 motors to 10 motors and was constant in the range of 10 to 30 motors ([Fig. 6, A and C](#F6){ref-type="fig"}), which fills the gap of motor number between two studies ([@R13], [@R14]). Together, our studies reveal that velocity is independent of motor number in the range of 1 to 3 motors, decreases in the range of 3 to 10 motors, and is again independent at \>10 motors. The dependency of velocity on the number and spacing of kinesin-14 motors also agrees with a previous study ([@R49]), which reported that the velocity decreased with increasing kinesin-14 density. Braun *et al.* attributed the decrease in velocity to the direct interaction (steric hindrance) between motors but not to the indirect interaction between motors bridged by a solid microtubule structure. However, in our system, motors cannot directly interact on the nanopillar array because they are separated by a distance of more than 200 nm, which is more than twice as long as the roughly 60-nm kinesin stalk ([@R50]). Therefore, the decrease in velocity with an increasing number and spacing of motors is explained by the indirect interaction between motors through microtubules. The velocity decreased with an increase in the number of kinesin-14 motors in the range of 3 to 10 motors ([Fig. 6, A and C](#F6){ref-type="fig"}). This can be explained by the greater diffusive motion of kinesin-14 motor domains along a microtubule ([@R34]); unlike kinesin-14, kinesin-1 is known as a processive motor. The construct of kinesin-14 that was used in this study has two microtubule binding domains (MTBDs): The first MTBD, which is referred to as the motor domain, is at the C terminus, and the second MTBD is at the N terminus. However, the kinesin-14 motors on the nanopillars could interact with a microtubule only via the first MTBD, because the N terminus was immobilized via streptavidin-biotin binding. Furuta and Toyoshima ([@R34]) generated a kinesin-14 construct without the second MTBD by truncating the N terminus and calculated the diffusion coefficient (*D* = 7.1 × 10^4^ nm^2^/s) and the mean velocity (*v* = −20 nm/s) in the BRB12 buffer by the quadratic fit \[*msd*(*t*) = 2 *Dt* + *v*^2^*t*^2^ + *C*\], where *t* is the time and *v* is the mean velocity. This calculation indicates that the first MTBD of the kinesin-14 motor, compared to kinesin-1 (*D* = 0.48 × 10^4^ nm^2^/s, *v* = 690 nm/s), shows significant diffusive motion along a microtubule ([@R34]). The diffusive motion of kinesin-14 motors implies that the motors hinder each other's movement during collective transport. When multiple kinesin-14 motors transport a microtubule, a fraction of motors move toward the plus end of the microtubule owing to their diffusive motion, while most of the motors move toward the minus end. According to a previous study, kinesin-14 motors generate a drag force when they are pulled backward ([@R13]). This indicates that kinesin-14 motors that move to the plus end hinder the movement of the microtubule by transmitting the drag force through the microtubule. Such an indirect interaction via a microtubule causes the decrease in velocity observed on the nanopillar array. We also obtained the unexpected dependence of velocity on spacing. The velocity increased with an increase in the spacing of the kinesin-14 motors and reached a maximum at a 600-nm spacing, when the ionic strength was low ([Fig. 6D](#F6){ref-type="fig"}). This result indicates that, although kinesin-14 motors indirectly interfere with each other, the interaction was weakened with increasing spacing of kinesin-14 motors. At a spacing over 600 nm, the velocity decreased with an increase in the spacing of kinesin-14 motors ([Fig. 6D](#F6){ref-type="fig"}). We observed that microtubules sometimes showed stop-and-go motions with the large spacings, causing lower average velocities. The thermal fluctuation of the tip increased with spacing, and the tip frequently touched the substrate. Unlike in low ionic strength buffers, we did not find any dependence of velocity on spacing in high ionic strength buffers ([Fig. 6B](#F6){ref-type="fig"}). This was possibly because the affinity between the kinesin-14 motor heads and microtubules was weak; therefore, kinesin-14 motors did not interact via a microtubule ([@R34]). CONCLUSION ========== In this study, we proposed a nanopatterning method of kinesin molecules that enables us to control the number and spacing of motors transporting a single microtubule filament. Using the patterned motor, we revealed that both the number and spacing of motors affect the velocity of the microtubule transported by multiple motors in the case of kinesin-14 but not in the case of kinesin-1. As the proposed method is applicable for various motor species such as kinesin-5 (Eg5) and kinesin-7 (CENP-E), it can be a powerful assay platform to study the coordination of motors. MATERIALS AND METHODS ===================== Proteins -------- The kinesin-1 sequence from *Homo sapiens* (amino acid 1 to 465) was ligated into the pET30b (Novagen) plasmid containing an N-terminal His~6~ tag and a C-terminal AviTag (Avidity). The AviTag peptide is covalently linked to biotin by *Escherichia coli* biotin ligase (BirA) ([@R51]). The plasmid was transformed into an *E. coli* Rosetta (DE3) pLysS (Novagen). This construct was a gift from Y. Hiratsuka of the School of Materials Science, Japan Advanced Institute of Science and Technology. The His~6~-tagged kinesin-1 was purified by nickel-nitrilotriacetic acid (Ni-NTA) affinity as previously described ([@R52]). The kinesin-14 was constructed from *Drosophila melanogaster* (amino acids 195 to 700) and cloned into the pBirAcm (Avidity) plasmid containing an N-terminal histidine tag and AviTag. The construct was expressed in BL21 (DE3) Star (Novagen) and purified by Ni-NTA affinity as previously described ([@R34]). Phosphocellulose (PC) tubulin was purified from porcine brains after 2 cycles of assembly-disassembly and PC chromatography ([@R53]) and stored in liquid nitrogen. Fluorophore-tagged tubulin was prepared by adding a 10-fold molar excess of carboxytetramethylrhodamine (TAMRA, C-1171, Invitrogen, Carlsbad, CA, USA) to tubulin for a labeling stoichiometry of 0.40 to 0.70 ([@R54]). Buffers ------- The experiments were conducted in two types of PIPES-based buffer solutions: (i) BRB80 consisting of 80 mM PIPES, which was adjusted to pH 6.8 by using KOH, 1 mM EGTA, and 1 mM MgCl~2~; and (ii) BRB12, which is identical to BRB80 except for its PIPES concentration, which was 12 mM, and MgCl~2~ concentration, which was 2 mM. To adjust the kinesin concentration, we used a casein-containing solution (casein buffer) composed of BRB80, 1 mM dithiothreitol (DTT), 100 μM ATP, and casein (0.1 to 0.7 mg/ml). To optimize kinesin-driven microtubule motility, we used a motility buffer with a different composition for the experiments using kinesin-1 and kinesin-14. For kinesin-1, we used the motility buffer consisting of BRB80 or BRB12 supplemented with 3 mM MgCl~2~ (4 mM final concentration), 20 mM DTT, 1% 2-mercaptoethanol, casein (0.3 mg/ml), and 1 mM ATP. For kinesin-14, the motility buffer was composed of BRB80 or BRB12, 25 mM potassium acetate, casein (0.7 mg/ml), and 3 mM ATP. Nanofabrication --------------- Arrays of 50-nm-diameter nanopillars, including variations in the spacing (from 0.2 to 5.0 μm) were fabricated on a silicon wafer with a 1-μm-thick thermal oxide film. The wafers were cleaned in piranha solution (H~2~SO~4~: H~2~O~2~ = 7:3) at 80°C for 10 min. Caution: Piranha solution reacts violently with most organic materials and must be handled with extreme care. The positive photoresist (ZEP520A, ZEON) was diluted with an equal volume of anisole and spin-coated onto wafers at 1800 rpm for 60 s, followed by baking at 180°C for 2 min. An organic antistatic compound (Espacer 300Z, Showa Denko) was spin-coated at 1500 rpm for 60 s and baked at 100°C for 60 s. The pattern of the nanopillar arrays was written using an electron beam writer (F7000s-KYT01, Advantest). The Espacer was removed by rinsing the wafer with deionized water. The resist was developed by placing the wafer in the ZED-N50 developer (ZEON) for 140 s. A 3-nm-thick chromium adhesion layer and a 20-nm-thick gold layer were evaporated onto the patterned resist using a thermal deposition machine (VPC-260FI, ULVAC). The resist was removed by soaking the wafer in the ZDMAC remover (ZEON) at 65°C for 10 min, followed by a 10-min sonication in acetone. To protect the nanopillars, the photoresist (S1813, Shipley) was spin-coated onto the wafers at 1500 rpm for 40 s and was baked at 90°C for 2 min. The wafer was diced into flow cell--sized (15 mm × 10 mm) substrates (DAD322, Disco). The resist was removed by soaking substrates in acetone for 10 min, followed by rinsing with isopropyl alcohol and the deionized water. The pillars were visualized by a field-emission scanning electron microscope (SU8020, Hitachi High Technologies). The diameter and spacing of the fabricated nanopillar array were measured with ImageJ software (National Institutes of Health). Microtubule gliding assay on kinesin-1-- or kinesin-14--immobilized gold nanopillars ------------------------------------------------------------------------------------ The substrates with arrays of nanopillars were cleaned in the piranha solution (H~2~SO~4~: H~2~O~2~ = 7:3) at 80°C for 10 min, followed by extensive rinsing with deionized water and drying under N~2~ flow. Within 1 hour after the cleaning, the substrates were incubated in the SAM solution for \~16 hours with nitrogen gas providing the inert atmosphere. The SAM solution is a mixture of 3 mM 2-\[methoxy(polyethyleneoxy)9-12propyl\]trimethoxysilane (S25236, Fluorochem) and hydrochloric acid (0.8 ml/liter) in toluene. After SAM treatment, the substrates were rinsed in toluene, ethanol, and deionized water, followed by a 2-min sonication in deionized water and drying in the N~2~ flow. The substrates were baked at 120°C for an hour for annealing. The substrates were stored under a nitrogen atmosphere and used within a day. A flow chamber (15 mm by 5 mm, 3.75-μl volume) was constructed with a coverslip (C030401, Matsunami micro cover glass, Matsunami), and a substrate with SAM-modified gold nanopillars was separated by two stripes of 50-μm-thick double-stick tape (400P50, Kyodo Giken Chemical Co.). First, a solution of streptavidin (0.2 mg/ml; 434301, Thermo Fisher Scientific) diluted in BRB80 buffer was flushed three times into a chamber and was incubated for 5 min, followed by washing with BRB80 buffer three times. The flow chamber was then incubated with biotin-conjugated kinesin (0.1 mg/ml; ≈0.85 μM) in casein buffer for 5 min, followed by washing with casein buffer. Last, microtubules in the motility buffer supplemented with 20 μM paclitaxel and O~2~ scavenging system \[catalase (36 μg/ml), glucose oxidase (216 μg/ml), and 25 mM [d]{.smallcaps}-glucose\] were sequentially introduced to observe microtubule gliding. The experiments were performed at room temperature (23° to 25°C). Evaluation of the number of kinesin molecules attached to the nanopillars ------------------------------------------------------------------------- To evaluate the number of kinesin-1 molecules attached to the nanopillars, kinesin-1 molecules were immobilized on pillars with 5.0-μm spacing. Short microtubules (*L* = 3.55 ± 1.46 μm, *n* = 9) were prepared by shearing through a 30-gauge syringe needle (90030; Osaka Chemical). A gliding assay was performed in an assay buffer containing 10 μM ATP. For evaluation of the number of kinesin-14 molecules, a gliding assay was conducted in the same manner, except that the assay buffer did not contain ATP. Microtubule gliding assay on a plane surface -------------------------------------------- The experiments were performed at room temperature (23° to 25°C). A flow cell was constructed using a plane gold substrate. The flow cell was filled with BRB80 and incubated in streptavidin (1.0 mg/ml) for 3 min. After rinsing the flow cell with BRB80, biotin-conjugated kinesin-1 or kinesin-14 (4.5 μg/ml, ≈36 nM) was introduced and incubated for 3 min before rinsing again. Last, microtubules in the motility buffer supplemented with 20 μM paclitaxel and O~2~ scavenging system (see above) were sequentially introduced to observe microtubule gliding. As a control experiment, the microtubule gliding assay on a glass substrate was conducted in the same manner except that the flow cell was incubated with biotinylated bovine serum albumin (1.0 mg/ml; A8549, Sigma) for 3 min before introducing the streptavidin solution. To evaluate the protein-repellent ability of silane-PEG SAM, the microtubule gliding assay was conducted on a SAM-modified silicon dioxide surface. A flow cell was constructed using a silane-PEG SAM--modified silicon dioxide substrate, and the gliding assay was performed as described in the "Microtubule gliding assay on kinesin-1-- or kinesin-14--immobilized gold nanopillars" section. Imaging ------- Images were obtained using an Olympus IX73 inverted epifluorescence microscope equipped with an Hg lamp (U-HGLGPA, Olympus), a 100× oil-immersion objective lens (UPlanSApo, numerical aperture of 1.40, Olympus), and a scientific complementary metal--oxide semiconductor camera (ORCA-Flash4.0, Hamamatsu) in conjunction with HCImage (Hamamatsu) software. Rhodamine-labeled microtubules were imaged with a U-FGW filter set (excitation, 530/50; dichroic, 570; absorption 575/infinity; Olympus). The images (1024 pixels × 1024 pixels) were acquired at 0.5-s intervals for 180 to 360 s with a 200-ms exposure time for each image. To evaluate the number of kinesins on the nanopillars, we used an electron multiplying charge-coupled device camera (iXon Ultra, Andor) in conjunction with iQ3 (Andor) software. Images (512 pixels × 512 pixels) were acquired at 0.1-s intervals for 360 s with a 10-ms exposure time for each image. Analysis -------- To measure microtubule velocities, the ends of the microtubules were tracked with the Mark2 image analysis software at 2-s intervals (four frames) for kinesin-1 and 30-s intervals (60 frames) for kinesin-14. To evaluate the number of kinesin molecules on the nanopillars, the distances between the rotation center and the end of the microtubule were measured with ImageJ. To quantify the alignment of microtubules, we measured the orientation angle of the microtubule using the OrientationJ plugin, an ImageJ plugin. OrientationJ characterizes the orientation angle of a region of interest in an image based on an evaluation of the structure tensor in a local neighborhood ([@R55]). The angle of the microtubule with respect to line A is defined as shown in [Fig. 2B](#F2){ref-type="fig"}. Using OrientationJ, the angles were calculated for each pixel of the fluorescence images of the microtubules. The fluorescence images of the microtubules were converted into binary images via Otsu's thresholding algorithm using ImageJ. Using this binary image of microtubules, we acquired the orientation angle of only a region of microtubules with a custom-written MATLAB algorithm (MathWorks). The distributions of the orientation angle of the microtubules were normalized by the total area of the microtubules, which was measured from binary images of microtubules. Simulation ---------- The thermal fluctuation of the free tip of the microtubules was simulated using the same method used in our previous work ([@R31]). Briefly, we modeled the free tip of a microtubule as a cantilever beam tethered at one end. The flexural rigidity (κ~MT~) was set to 0.3 × 10^−23^ N m^2^, which is the typical flexural rigidity of paclitaxel-stabilized microtubules ([@R56]). The length of the free tip (*L*) was assumed to be equal to the spacing between pillars and set to 0.3 and 1.0 μm. We set the *x* and *y* axes as shown in [Fig. 3A](#F3){ref-type="fig"}. The origin of the coordinates was set at the point where the microtubule segment attached to the first pillar. The shape of the microtubule-free segment *y*(*s*) was expressed by the following equation$$y(s) = \sum\limits_{n = 1}^{\infty}\sqrt{\frac{1}{L}}a_{n}W_{n}\left( \frac{s}{L} \right)$$ Here, *s* is the path length from the tethered end along the microtubule. *W~n~*(*s*/*L*) is expressed as$$\begin{array}{cl} {W_{n}\left( \frac{s}{L} \right) =} & {\frac{- \text{cosh}(q_{n}) - \text{cos}(q_{n})}{\text{sin}(q_{n}) + \text{sinh}(q_{n})}\left( \text{sin}\left( \frac{q_{n}s}{L} \right) - \text{sinh}\left( \frac{q_{n}s}{L} \right) \right) +} \\ & {\text{cos}\left( \frac{q_{n}s}{L} \right) - \text{cosh}\left( \frac{q_{n}s}{L} \right)} \\ \end{array}$$where *q~n~* is 1.875 (*n* = 1), 4.695 (*n* = 2), 7.855 (*n* = 3), and (*n* − 0.5)π (*n* ≥ 4). The SD of the amplitude *a~n~* was calculated using the following equation$$\text{var}(a_{n}) = \frac{k_{B}T}{\kappa_{\text{MT}}}\left( \frac{L}{q_{n}} \right)^{4}$$where *k~B~* is the Boltzmann constant, and *T* is the temperature in the experiments (298 K). We numerically solved [Eq. 2](#E2){ref-type="disp-formula"} using a custom-made algorithm in MATLAB and calculated the probability density function of displacement of the end of the tip (*s* = *L*) from the calculation results of simulation that was run 1000 times. In this study, we set *n* in the range of 1 ≤ *n* ≤ 12. The result of the numerical analysis is expressed as "Numerical" in [Fig. 3](#F3){ref-type="fig"}. Separately, we derived an analytical solution of the probability density function of displacement of the end of tip, R(*y*), from [Eq. 2](#E2){ref-type="disp-formula"}$$R(y) = \frac{1}{\sqrt{2\pi\sum_{k}^{12}\sigma_{k}^{2}}}\text{exp}\left( - \frac{y^{2}}{2\sum_{k}^{12}\sigma_{k}^{2}} \right)$$ σ*~k~* is defined by the following equation$$\sigma_{k}^{2} = \frac{1}{L}W_{k}\left( \frac{s}{L} \right)\frac{k_{B}T}{\kappa_{\text{MT}}}\left( \frac{L}{q_{k}} \right)^{4}$$ The result of this analysis is given in "Analytical" in [Fig. 3](#F3){ref-type="fig"}. Supplementary Material ====================== ###### http://advances.sciencemag.org/cgi/content/full/6/4/eaax7413/DC1 ###### Download PDF ###### Movie S1 ###### Movie S2 ###### Movie S3 ###### Movie S4 ###### Different motilities of microtubules driven by kinesin-1 and kinesin-14 motors patterned on nanopillars We thank S. Erickson for language editing of the manuscript. **Funding:** This study was partially supported by JSPS KAKENHI (grant number JP17H03206), the Tateishi Science and Technology Foundation, Japan, and JKA and its promotion funds from KEIRIN RACE, Japan. A part of this work was conducted at Kyoto University, Nanotechnology Hub, supported by Nanotechnology Platform Program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, Grant Number JPMXP09F19KT0107. **Author contributions:** T.K. and R.Y. designed the experiments. T.K. performed the experiments and analyzed the data. T.K., K.F., K.O., H.S., H.K., and R.Y. discussed and interpreted the results. T.K. and R.Y. wrote the paper. All authors approved the final version of the manuscript. **Competing interests:** The authors declare that they have no competing interests. **Data and materials availability:** All data needed to evaluate the conclusions in this paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. Supplementary material for this article is available at <http://advances.sciencemag.org/cgi/content/full/6/4/eaax7413/DC1> Fig. S1. Fabrication of the gold nanopillars. Fig. S2. Fluorescence images of microtubules gliding in the kinesin-14--patterned region on gold nanopillars. Fig. S3. Pivoting motion of a microtubule driven by a single kinesin motor on a nanopillar. Fig. S4. Fluorescence images of microtubules on patterned kinesin-1 or kinesin-14. Fig. S5. Relationship between microtubule angle and the number of kinesin molecules attached to the microtubules. Fig. S6. Dependence of microtubule velocity on the spacing of kinesin-1 in BRB80. Movie S1. Microtubules gliding in the kinesin-1--patterned region on the gold nanopillars. Movie S2. Microtubule at the boundary between the kinesin-1--patterned region on the gold nanopillars and passivated silicon dioxide region. Movie S3. Microtubules gliding in the kinesin-14--patterned region on the gold nanopillars. Movie S4. Microtubule at the boundary between the kinesin-14--patterned region on the gold nanopillars and passivated silicon dioxide region. Reference ([@R42]) [View/request a protocol for this paper from *Bio-protocol*](https://en.bio-protocol.org/rap.aspx?eid=10.1126/sciadv.aax7413). | Mid | [
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New prognostic biomarkers in multiple myeloma. Multiple myeloma is a malignant neoplastic disease, characterized by uncontrolled proliferation and accumulation of plasma cells in the bone marrow, which is usually connected with production of a monoclonal protein. It is the second most common hematologic malignancy. It constitutes approximately 1% of all cancers and 10% of hematological malignancies. Despite the huge progress that has been made in the treatment of multiple myeloma in the past 30 years including the introduction of new immunomodulatory drugs and proteasome inhibitors, it is still an incurable disease. According to current data, the five-year survival rate is 45%. Multiple myeloma is a very heterogeneous disease with a very diverse clinical course, which is expressed by differences in effectiveness of therapeutic strategies and ability to develop chemoresistance. This diversity implies the need to define risk stratification factors that would help to create personalized and optimized therapy and thereby improve treatment outcomes. Prognostic markers that aim to objectively evaluate the risk of a poor outcome, relapse and the patient's overall outcome are useful for this purpose. The existing, widely used prognostic classifications, such as the Salmon-Durie classification or ISS, do not allow for individualization of treatment. As a result of the development of diagnostic techniques, especially cytogenetics and molecular biology, we were able to discover a lot of new, more sensitive and specific prognostic factors. The paper presents recent reports on the role of molecular, cytogenetic and biochemical alterations in pathogenesis and prognosis of the disease. | High | [
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China’s ZTE Reports $1.1 Billion Loss The telecom company’s first-half results cover the period of U.S. penalties HONG KONG—China’s ZTE Corp. disclosed a loss of 7.8 billion yuan—about $1.1 billion—during the first half of the year, after a ban on purchasing American supplies forced a life-threatening shutdown of the telecommunications giant. The loss covers most of the period during which ZTE was shuttered, and marks its first official accounting of the period. The Commerce Department banned U.S. companies from selling to ZTE in April after it found the firm broke the terms of its settlement resolving earlier violations of U.S. sanctions... RELATED VIDEO Why Trump’s ZTE U-Turn Has Sparked Backlash President Trump’s mixed messages about a plan to help controversial Chinese telecom giant ZTE has baffled Washington. WSJ's Shelby Holliday breaks down three reasons why lawmakers see the company as a threat. Illustration: Adam Falk (Originally published May 31, 2018) | Mid | [
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AS141/05 power supply problems when using multiplug adapter Hello I received the Android dock AS141 for Christmas 2012 and I've noticed some very odd behaviour which is now preventing me from using it. The unit was bought in the UK and if I plug it into a wall socket directly, it works fine. However, as many people have, I use a multi-plug connector to increase the number of devices (laptop chargers, phone chargers, etc) that I can plug into a wall socket. When I plug the AS141 into one of these multi socket adapters, it simply doesn't work. If I then leave it off for a few hours, and then plug it back into the wall socket, it works again, but it needs to be powered off for quite some time. My worry then came because I live in Belgium most of the time, I would then use a simple UK to European plug adapter to be able to use devices on the continent (ie. in Belgium). I came back to Belgium yesterday and plugged the device into a wall socket, using a UK adapter, as I do with many UK devices, and again it doesn't work. It eventually powers up after some minutes and shows -- -- for the time, and will eventually connect to my phone bluetooth, but it will not play through the speaker of the dock and will not sync the time, as it did do well in the UK. I am really really surprised by the sensitive power requirements of this Philips device and that it is so difficult to get it to work properly. Why doesn't think work in various situations, like 99.99% of other devices on the market? Why doesn't it come with a simple adapter where I can then plug in a two pronged connector like a standard radio etc, since then I can use either a UK plug or a continental one? Even with an Apple Mac laptop connector I can do this. It isn't the first time I have come across very strange behaviour of Philips products (I have a tv that randomly switches digital channels after a period of time - but this only happened after a year or so of useage). Are these products not tested properly? Or is it that my device is faulty? I don't want to waste my time changing it in the shop only to find it does the same with a replacement model. I do hope you can help me, because I am losing faith in Philips products and a simple "that's the way that device works" would be very disappointing. I have forgotten my password Don't worry, it happens. We'll send you a link to create a new password. {* #forgotPasswordForm *} {* forgotPassword_emailAddress *} {* forgotPassword_sendButton *} {* /forgotPasswordForm *} Email sent We have sent you an email with a link to change your password. Log in with your Philips account We see that this email address, {* data_emailAddress *}, is already connected to a Philips account. However, this email address has not been verified yet. We have sent a verification email to this address. Please click the link in that email to log in to My Philips. Please provide a valid email address. To login with your account, Provide an email address Create a new Philips account We see that this email, , is already connected to a Philips account. You can create a new Philips account by providing another email address. {* #socialRegistrationNoEmailForm *} {* socialRegistrationNoEmail_emailAddress *} {* socialRegistration_signInButton *} {* /socialRegistrationNoEmailForm *} Almost done You are almost done, please provide or verify the following information. Philips values and respects your privacy.Please read the privacy policy for more information. {* /socialRegistrationForm *} {* #resendVerificationForm *} Verify your email address We see that this email address, {* data_emailAddress *}, is already connected to a Philips account. However, this email address has not been verified yet. We have sent a verification email to this address. Please click the link in that email to log in to My Philips. {* resendVerification_emailAddress *} {* submitButton *} {* /resendVerificationForm *} Email sent An activation email has been sent to {* data_emailAddress *}. Please click on the link in this email to activate your Philips account and to verify your email address. New Posts My SHB7150 connects with Dell Inspiron (seen in Bluetooth device control), but the sound comes from laptop speakers. I can't help with your solution, because in playback devices menu I have 3... | Low | [
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Featured Stories Vittorio Pozzo is Italy’s most successful International manager but he failed to defeat one team in his trophy laded career – England. Vittorio Pozzo’s reign in 1930s ushered a golden era which would see Italy win consecutive world cups & an Olympic gold medal. Pozzo’s Italy defeated each of the three teams of the Danubian school of short passing football – Czechoslovakia, Austria and Hungary to stamp their manager’s own “Metodo” system on continental football. Yet, for all his success Pozzo would never be able to outmaneuver the team which believed itself to be best in the world – England. This was an intriguing pre war rivalry, which climaxed in the infamous “Battle of Highbury” of 1934. The first meeting between two countries came on 13th May 1933 in Rome, ending in a 1-1 draw. This match would pit two of the great pre-war minds of football against each other with Vittorio Pozzo facing off against Herbert Chapman. Italy, largely comprised of players who would win World Cup a year later, took the lead through Giovanni Ferrari, only to be pegged by Cliff Bastin’s first goal for the national team. Over a year later Italy travelled to Highbury, as world champions. England had not participated in world cup but for the English press, they were the best team in the world & this was the “real” world cup final. Seven players from First Division champions Arsenal started for England in front of 56,000 spectators. There was great pre-match hype and Il Duce Mussolini had reportedly offered each player money and an Alfa Romeo car if they managed to defeat England. The world champions were in complete disarray from the start. Center half Luis Monti, only man to play for two countries in a world cup final, went off injured as Italy had to play with 10 men, with no subs allowed. Italian keeper Carlo Ceresoli, described by an English paper as “Spring-heel Jack with a splendid sense of anticipation”, saved an early penalty but was powerless to stop Eric Brook who scored a brace within 10 minutes. Ted Drake added a third on 12th minute as England seemed to be staying true to their pre match billing of being best in the world. In second half Italy rallied brilliantly, with Giuseppe Meazza scoring twice. The legendary Italian striker also struck the post once and forced off a series of good saves from the English custodian. But by this time the match has descended into chaos and a number of players would get injured in off the ball skirmishes. English captain Eddie Hapgood suffered from a broken nose, five other English players suffered serious injuries. England held out the 3-2 scoreline but Italian players were hailed in their homeland for their fight back. Even the English press while universally criticizing the “unsportsmanship” of Italian players, praised their second half comeback. “England’s prestige was bruised badly by the things that happened in that second half”, noted a prominent journalist grimly. Pozzo’s Italy went on to win more silverware but defeating England remained a distant dream. In 1939, Italy was just 13 minutes away from a historic win but an equalizer from Willie Hall resulted in a 2-2 draw. Both countries had to wait for 9 years to play again. Pozzo had been one of the most powerful men in Italian football for over three decades but by this time his legacy had begun to lose its sheen. In the post fascism Italy Pozzo’s ties with the Mussolini regime was seen with suspicion. Pozzo’s post war record was still solid and Italy had defeated the likes of Austria, Hungary, France and Switzerland when football restarted. But their run would shatter when they came up against Walter Winterbottom’s England in 1948. Italy was not a weak team by any means and was largely made up with players from Il Grande Torino, captained by the legendary Valentino Mazzola. Tactically though, the only coach to win back to back World Cups may have got it wrong even before the ball was kicked. Pozzo tried to apply his favourite “Metodo” formation to a team the crux of which came from a club used to playing the “WM” formation. Italy began as the stronger of two teams but soon found themselves trailing thanks to a brilliant strike from Stan Mortensen. Italians continued to pour forward but were thwarted by English ‘keeper Swift, who was having the game of his life. The English front five continued to pick out gaps in their opponents’ defence while the Italians had a goal ruled out controversially. Tommy Lawton doubled England’s lead in first half while a brace from Tom Finney in second half ended this match as a contest. In the end, what was supposed to be a chance for Pozzo to finally outwit England became a body blow to his national team career. England’s 4-0 thrashing remains the worst defeat La Nazionale has suffered at home, ever. Pozzo lasted just two more matches before being dismissed after a loss to Denmark in 1948 Olympics. The man who had learnt English in Manchester as a young man and picked up football from the Isles won a lot in his career but in his four meetings with England he was never able to defeat them. | High | [
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Whats that Skip, you want a double mocha decaf half caf soy latte with a twist of lemon? Well you can’t because Urban Rustic is closed today. But you can have this original Bessemer melamine mug from the 70’s. The one on top is mine, it’s quite fuzzy and faded from years of Milo addiction [not for sale] the bottom one’s in great shape. Considering. Want? $25 + post. Hop to it. And if you are wondering what the flaming heck I am talking about Ailsa? The story you are about to witness is true. It actually happened. Only the names have been changed to make it funny… Sitting at home last Sunday morning, me mate boomerang Said he was having a few people around for a barbie, said he might kookaburra or two I said, “Sounds great, will Wallaby there?” He said, “Yeah and Vegemite come too” So I said to the wife, “Do you wanna goanna?” She said, “I’ll go if dingos” So I said, “Wattle we do about Nulla?” He said, “Nullabors me to tears, leave him at home” We got to the party about two and walked straight out the kitchen to put some booze in the fridge And you wouldn’t believe it, there’s Boomer’s wife Warra sitting there trying to platypus! Now, I don’t like to speak Illawarra, but I was shocked; I mean how much can a koala bear? So I grabbed a beer, flashed me Wangaratta and went out and joined the party Pretty soon Ayers Rocks in and things really started jumping This Indian girl Marsu turns up, dying to go to the toilet, but she couldn’t find it I said to me mate Al, “Hey, where can marsupial?” He said “She can go outback with the fellas, she’s probably seen a cockatoo” Well just then Warra comes out of the kitchen with a few drinks for everybody Fair dinkum, you’ve never seen a Coolabah maid I grabbed a beer and said, “Thanks Warra – tah” A couple of Queensland at the party, one smelling pretty strongly of aftershave One of them sat down next to me and I turned to him and I said, “Ya know mate, Eureka Stockade!” It was a really hot day; Oscar felt like a swim He said to Ina, “Do you want a have a dip in the Riverina?” She said, “I haven’t got my Kosciusko” Well Bo says, “Come in starkers, Wattle Lake Eyre!” Ina says, “What, without so much as a Thredbo?” “Ah, Perisher thought! Has Eucumbene in yet?” Well a few of the blokes decided to play some cricket Boomer says “Why doesn’t wombat?” “Yeah, and let Tenterfield” He said I should have a bowl, but I was too out of it to play cricket so I suggested a game of cards I said to Lyptus, “Wanna game of eucalyptus?” He said, “There’s no point mate, Darwins every time” Well Bill said he’d like a smoke Nobody knew where the dope was stashed I said, “I think Merinos” But I was just spinning a bit of a yarn Barry pulls a joint out of his pocket Bill says “Great, Barrier Reefer, what is it mate?” “Noosa Heads of course. Me mate Adelaide ’em on me” And it was a great joint too, Blue Mountains away and his Three Sisters Well I thought I’d roll one meself, I said, “Chuck us the Tally Hobart” He said “They’re out on the Laun, Ceston, can you get ’em for us?” Burnie says, “It’s okay mate, she’s apples, I’ll get em for ya” Just then Alice Springs into action, starts to pack billabong And you wouldn’t believe it, the bong’s broken I said “Lord Howe!” “Hayman,” somebody says, “will a didgeridoo?” I said “Hummmmm, mummmm, mummmmm, mummmmm, maybe it’ll have to” I look in the corner and there’s Bass sitting there, not getting into it, not getting out of it I said, “What, is Bass Strait or something?” Boomer says, “As a matter a fact mate, he’s a cop” I said, “You’re joking mate, a cop? I’m getting outta here, let’s goanna” She said, “No way, I’m hangin round till Gum leaves. Besides, I don’t wanna leave Jacaranda party on his own Have you seen him? I think he’s trying to crack on Toowoomba; he’s already tried to Mount Isa And he’ll definitely try to lead you Australiana!” Apparently. According to Holly Hobbie, uber earnest maxi-bonnet wearing writer/character from the 1970s. My oldest sister had a rag doll. I wished I did. There were others but I only collect the blue girl. Yeah they are quite twee but sometimes in the battle of nostalgia versus design, innocent memories win. As they should. Who wants to live in a meaningless catalogue of objects? Like this: It’s Thursday, it’s also my Birthday tomorrow. So I am recycling again, any excuse to take a shortcut…Here’s my Throwback. This was my 7th Birthday present from my mum and as I recall The Best Gift Ever! And a total surprise. I remember coming home from school one day and finding Albert on the kitchen table and not thinking much of it. Obviously he had just had a sitting. He was my best friend and the reason I am not so fond of cats. [Tragically, devastatingly killed some years later by our neighbour’s semi-feral feline.] I haven’t had this on display for years as I a] grew up and b] became unhappy with the mock ornate frame but now I love the irony of it’s fancy-ness. It’s kind of the Mona Lisa of pet portraits. Like this: So maybe I am crazy. Defiinitely nostalgic. I certainly don’t need to take on any further collections in this jumbled headspace but when I stumbled upon a few anodised pieces all at once, it seemed like the thrifting universe was talking to me. Mixed up? Yes. Delusional even. It does remind me of my childhood. Those stacking tumblers. Remember them? In a cute little vinyl case with a zipper. I passed up a set not so long ago for $10 because the cups inside where in a terrible, corroded state, then I was filled with that annoying state of mind I always seem to experience. Regret. Not for the things I buy, but for the times I put the WRONG thing down. Not so much time later I found a reasonably priced decent condition set of cups, with no case. Arrh! The irony. [Aluminium actually] So anyway, moving on…. The red Prestige [UK] ice bucket is sold already. The wine cooler reminds me of my father for some reason. Not that he was into wine at all, [my parents were teetotallers, whatever that means] but there must have been something years ago anodised with this gorgeous shiny blue stripeyness. It says Alf to me. That’s my Dad. Flaming Heck, can you get a funnier name than that? I think not. There was, of course, in my mid-century decorated family bungalow a set of twin anodised bedside lights clamped onto the veneered parental bedhead. In bronze. There was also a chenille bedspread. And as you may, or may not recall, a fat baby Elvis girl. But thats another story… So here it is. All out there for all to see. The extent of my psycho-anodising. Am I cured? Who knows? I’m letting it go, so that’s a good sign, isn’t it? | Low | [
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Q: Extract Data from Soap XML with Namespaces I am trying to extract the data contained the in the a SOAP Response XML that I have that contains multiple and variable namespaces in an SSIS Script component using C#. My XML looks like this: <?xml version="1.0" encoding="UTF-8"?> <soap:Envelope xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/"> <soap:Body> <ns3:getCacheEntryResponse xmlns:ns3="http://com.vedaadvantage/dp3/Enterprise/StandardTradeCreditCommercial/SilverChef/IndividualCommercialService" xmlns:ns2="http://com.vedaadvantage/dp3/Enterprise/StandardTradeCreditCommercial/SilverChef" xmlns:ns4="http://com.vedaadvantage/dp3/Enterprise/StandardTradeCreditCommercial/SilverChef/IndividualCommercialDecision" xmlns:ns5="http://vedaadvantage.com/dp3/service/fault" xmlns:ns6="http://com/vedaadvantage/dp3/businessDecisionResultOverride" xmlns:ns7="http://com.vedaadvantage/dp3/connectors" xmlns:ns8="http://com.vedaadvantage/dp3/connectors/vedaxml/vedascore" xmlns:ns9="http://com.vedaadvantage/dp3/connectors/vedaxml/individualalerts"> <ns3:CacheEntry> <cacheEntryData>&lt;Response xmlns="http://com.vedaadvantage/dp3/connectors/vedaxml/vedascore" xmlns:b="http://com.vedaadvantage/dp3/connectors"&gt;&lt;enquiryReport&gt;&lt;primaryMatch&gt;&lt;bureauReference&gt;805917662&lt;/bureauReference&gt;&lt;individual&gt;&lt;individualName&gt;&lt;familyName&gt;MOHAMMADINEJAD&lt;/familyName&gt;&lt;firstGivenName&gt;ALI&lt;/firstGivenName&gt;&lt;createDate&gt;2014-07-15&lt;/createDate&gt;&lt;/individualName&gt;&lt;gender&gt;male&lt;/gender&gt;&lt;dateOfBirth&gt;1982-01-06&lt;/dateOfBirth&gt;&lt;driversLicenceNumber&gt;&lt;countryCodes&gt;AU&lt;/countryCodes&gt;&lt;value/&gt;&lt;/driversLicenceNumber&gt;&lt;b:address&gt;&lt;b:unitNumber/&gt;&lt;b:streetNumber&gt;43&lt;/b:streetNumber&gt;&lt;b:property&gt;43&lt;/b:property&gt;&lt;b:streetName&gt;KING EDWARD&lt;/b:streetName&gt;&lt;b:streetType&gt;AVE&lt;/b:streetType&gt;&lt;b:suburb&gt;ALBION&lt;/b:suburb&gt;&lt;b:city/&gt;&lt;b:state&gt;VIC&lt;/b:state&gt;&lt;b:postcode&gt;3020&lt;/b:postcode&gt;&lt;b:countryCode&gt;AU&lt;/b:countryCode&gt;&lt;b:addressType&gt;residentialCurrent&lt;/b:addressType&gt;&lt;b:createDate&gt;2015-09-04&lt;/b:createDate&gt;&lt;/b:address&gt;&lt;/individual&gt;&lt;individualConsumerCreditFile&gt;&lt;creditEnquiry&gt;&lt;accountType&gt;&lt;accountType&gt;UA&lt;/accountType&gt;&lt;value&gt;Utilities&lt;/value&gt;&lt;/accountType&gt;&lt;role&gt;&lt;consumerRoleTypeCodesResponse&gt;principal&lt;/consumerRoleTypeCodesResponse&gt;&lt;/role&gt;&lt;enquiryAmount&gt;&lt;currencyCodeType/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/enquiryAmount&gt;&lt;coBorrower/&gt;&lt;creditEnquirer&gt;AGL ENGY SALES &amp; MKTG LTD&lt;/creditEnquirer&gt;&lt;clientReference/&gt;&lt;consumerCreditEnquiryTypeResponse&gt;creditApplication&lt;/consumerCreditEnquiryTypeResponse&gt;&lt;enquiryDate&gt;2015-09-04&lt;/enquiryDate&gt;&lt;/creditEnquiry&gt;&lt;creditEnquiry&gt;&lt;accountType&gt;&lt;accountType&gt;TC&lt;/accountType&gt;&lt;value&gt;Telecommunication Service&lt;/value&gt;&lt;/accountType&gt;&lt;role&gt;&lt;consumerRoleTypeCodesResponse&gt;principal&lt;/consumerRoleTypeCodesResponse&gt;&lt;/role&gt;&lt;enquiryAmount&gt;&lt;currencyCodeType/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/enquiryAmount&gt;&lt;coBorrower/&gt;&lt;creditEnquirer&gt;VODAFONE DECISION POINT&lt;/creditEnquirer&gt;&lt;clientReference&gt;1-DCQJWZG&lt;/clientReference&gt;&lt;consumerCreditEnquiryTypeResponse&gt;creditApplication&lt;/consumerCreditEnquiryTypeResponse&gt;&lt;enquiryDate&gt;2014-07-15&lt;/enquiryDate&gt;&lt;/creditEnquiry&gt;&lt;/individualConsumerCreditFile&gt;&lt;individualCommercialCreditFile&gt;&lt;creditEnquiry&gt;&lt;accountType&gt;&lt;commercialAccountTypeCodesResponse&gt;CR&lt;/commercialAccountTypeCodesResponse&gt;&lt;value&gt;Commercial Rental&lt;/value&gt;&lt;/accountType&gt;&lt;enquiryAmount&gt;&lt;currencyCodeType/&gt;&lt;value&gt;25000&lt;/value&gt;&lt;/enquiryAmount&gt;&lt;role&gt;&lt;commercialRoleTypeCodesResponse&gt;principal&lt;/commercialRoleTypeCodesResponse&gt;&lt;/role&gt;&lt;coBorrower/&gt;&lt;creditEnquirer&gt;GOGETTA EQUIPMENT FUNDING&lt;/creditEnquirer&gt;&lt;clientReference/&gt;&lt;commercialCreditEnquiryTypeResponse&gt;creditEnquiry&lt;/commercialCreditEnquiryTypeResponse&gt;&lt;enquiryDate&gt;2016-04-04&lt;/enquiryDate&gt;&lt;/creditEnquiry&gt;&lt;/individualCommercialCreditFile&gt;&lt;matchType&gt;strong&lt;/matchType&gt;&lt;/primaryMatch&gt;&lt;summaryData&gt;&lt;summary&gt;&lt;name&gt;enquiry-amount&lt;/name&gt;&lt;summaryType&gt;amount&lt;/summaryType&gt;&lt;currencyCode&gt;AUD&lt;/currencyCode&gt;&lt;value&gt;25000&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;age-of-file&lt;/name&gt;&lt;summaryType&gt;months&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;20&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;age-of-subject&lt;/name&gt;&lt;summaryType&gt;years&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;34&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;time-at-address&lt;/name&gt;&lt;summaryType&gt;months&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;7&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;time-at-employer&lt;/name&gt;&lt;summaryType&gt;months&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value/&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;total-value-of-outstanding-defaults&lt;/name&gt;&lt;summaryType&gt;amount&lt;/summaryType&gt;&lt;currencyCode&gt;AUD&lt;/currencyCode&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults-paid&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults-12&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults-12-paid&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults-12-unpaid&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults-24-paid&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults-24-unpaid&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults-36-paid&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;defaults-36-unpaid&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;time-since-last-default&lt;/name&gt;&lt;summaryType&gt;months&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value/&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;total-credit-enquiries&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;3&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;credit-enquiries-1&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;1&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;credit-enquiries-3&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;1&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;credit-enquiries-6&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;1&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;credit-enquiries-12&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;2&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;credit-enquiries-60&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;3&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;time-since-last-enquiry&lt;/name&gt;&lt;summaryType&gt;months&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;7&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;telco-and-utility-defaults&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;telco-and-utility-defaults-12&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;telco-and-utility-enquiries&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;2&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;telco-and-utility-enquiries-6&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;telco-and-utility-enquiries-12&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;1&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;authorised-agents-enquiries-12&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;authorised-agents-enquiries-60&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;directorships-current&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;directorships-previous&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;judgements&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;proprietorships&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;adverse-on-file&lt;/name&gt;&lt;summaryType/&gt;&lt;currencyCode/&gt;&lt;value&gt;No&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;file-notes&lt;/name&gt;&lt;summaryType/&gt;&lt;currencyCode/&gt;&lt;value&gt;No&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;known-identities&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;1&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;bankruptcies&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;writs-and-summons&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;summary&gt;&lt;name&gt;external-administration-director&lt;/name&gt;&lt;summaryType&gt;count&lt;/summaryType&gt;&lt;currencyCode/&gt;&lt;value&gt;0&lt;/value&gt;&lt;/summary&gt;&lt;/summaryData&gt;&lt;scoreData&gt;&lt;score&gt;&lt;scorecardModel&gt;0303&lt;/scorecardModel&gt;&lt;relativeRisk&gt;2.3&lt;/relativeRisk&gt;&lt;vedascore1_1Index&gt;4.0863&lt;/vedascore1_1Index&gt;&lt;applicantOdds&gt;26.9&lt;/applicantOdds&gt;&lt;contributingFactor&gt;&lt;impact&gt;Greatly Decreases Risk&lt;/impact&gt;&lt;value&gt;Lack of Consumer Adverse Information&lt;/value&gt;&lt;/contributingFactor&gt;&lt;contributingFactor&gt;&lt;impact&gt;Moderately Decreases Risk&lt;/impact&gt;&lt;value&gt;Number of Consumer Credit Applications&lt;/value&gt;&lt;/contributingFactor&gt;&lt;contributingFactor&gt;&lt;impact&gt;Marginally Decreases Risk&lt;/impact&gt;&lt;value&gt;Individual Shopping Pattern&lt;/value&gt;&lt;/contributingFactor&gt;&lt;contributingFactor&gt;&lt;impact&gt;Marginally Decreases Risk&lt;/impact&gt;&lt;value&gt;Current and Historic Credit Type Sought&lt;/value&gt;&lt;/contributingFactor&gt;&lt;population&gt;&lt;populationOdds&gt;11.9&lt;/populationOdds&gt;&lt;/population&gt;&lt;vedaScore&gt;675&lt;/vedaScore&gt;&lt;percentile&gt;30&lt;/percentile&gt;&lt;scoreType&gt;VS 1.1 COMMERCIAL + CONSUMER&lt;/scoreType&gt;&lt;/score&gt;&lt;/scoreData&gt;&lt;/enquiryReport&gt;&lt;/Response&gt;</cacheEntryData> <connectorGroup>vedaxml</connectorGroup> <connectorId>vedascore</connectorId> <connectorVersion>2014-08-28</connectorVersion> <request>&lt;Request xmlns:ns2="http://com.vedaadvantage/dp3/connectors" xmlns="http://com.vedaadvantage/dp3/connectors/vedaxml/vedascore"&gt;&lt;product&gt;&lt;name&gt;vedascoreFinancialCommercialPlusConsumer1_1&lt;/name&gt;&lt;summary&gt;true&lt;/summary&gt;&lt;/product&gt;&lt;individual&gt;&lt;individualName&gt;&lt;familyName&gt;Mohammadinejad&lt;/familyName&gt;&lt;firstGivenName&gt;Ali&lt;/firstGivenName&gt;&lt;otherGivenName&gt;&lt;/otherGivenName&gt;&lt;/individualName&gt;&lt;gender&gt;unknown&lt;/gender&gt;&lt;dateOfBirth&gt;1982-01-06Z&lt;/dateOfBirth&gt;&lt;driversLicenceNumber&gt;&lt;countryCodes&gt;AU&lt;/countryCodes&gt;&lt;value&gt;06011982&lt;/value&gt;&lt;/driversLicenceNumber&gt;&lt;ns2:address&gt;&lt;ns2:addressType&gt;residentialCurrent&lt;/ns2:addressType&gt;&lt;ns2:unitNumber&gt;3 U&lt;/ns2:unitNumber&gt;&lt;ns2:streetNumber&gt;43&lt;/ns2:streetNumber&gt;&lt;ns2:property&gt;43&lt;/ns2:property&gt;&lt;ns2:streetName&gt;KING EDWARD&lt;/ns2:streetName&gt;&lt;ns2:streetType&gt;AVE&lt;/ns2:streetType&gt;&lt;ns2:suburb&gt;ALBION&lt;/ns2:suburb&gt;&lt;ns2:state&gt;VIC&lt;/ns2:state&gt;&lt;ns2:postcode&gt;3020&lt;/ns2:postcode&gt;&lt;ns2:countryCode&gt;AU&lt;/ns2:countryCode&gt;&lt;/ns2:address&gt;&lt;role&gt;principal&lt;/role&gt;&lt;/individual&gt;&lt;enquiry&gt;&lt;accountType&gt;&lt;accountType&gt;CR&lt;/accountType&gt;&lt;/accountType&gt;&lt;enquiryAmount&gt;&lt;currencyCodeType&gt;AUD&lt;/currencyCodeType&gt;&lt;value&gt;25000&lt;/value&gt;&lt;/enquiryAmount&gt;&lt;enquiryType&gt;creditEnquiry&lt;/enquiryType&gt;&lt;/enquiry&gt;&lt;customerReference&gt;GoGetta&lt;/customerReference&gt;&lt;/Request&gt;</request> </ns3:CacheEntry> </ns3:getCacheEntryResponse> </soap:Body> </soap:Envelope> I have used http://xmltocsharp.azurewebsites.net/ to generate my C# classes which look like this: [XmlRoot(ElementName = "CacheEntry", Namespace = "http://com.vedaadvantage/dp3/Enterprise/StandardTradeCreditCommercial/SilverChef/IndividualCommercialService")] public class CacheEntry { [XmlElement(ElementName = "cacheEntryData")] public string CacheEntryData { get; set; } [XmlElement(ElementName = "connectorGroup")] public string ConnectorGroup { get; set; } [XmlElement(ElementName = "connectorId")] public string ConnectorId { get; set; } [XmlElement(ElementName = "connectorVersion")] public string ConnectorVersion { get; set; } [XmlElement(ElementName = "request")] public string Request { get; set; } } [XmlRoot(ElementName = "getCacheEntryResponse", Namespace = "http://com.vedaadvantage/dp3/Enterprise/StandardTradeCreditCommercial/SilverChef/IndividualCommercialService")] public class GetCacheEntryResponse { [XmlElement(ElementName = "CacheEntry", Namespace = "http://com.vedaadvantage/dp3/Enterprise/StandardTradeCreditCommercial/SilverChef/IndividualCommercialService")] public CacheEntry CacheEntry { get; set; } [XmlAttribute(AttributeName = "ns3", Namespace = "http://www.w3.org/2000/xmlns/")] public string Ns3 { get; set; } [XmlAttribute(AttributeName = "ns2", Namespace = "http://www.w3.org/2000/xmlns/")] public string Ns2 { get; set; } [XmlAttribute(AttributeName = "ns4", Namespace = "http://www.w3.org/2000/xmlns/")] public string Ns4 { get; set; } [XmlAttribute(AttributeName = "ns5", Namespace = "http://www.w3.org/2000/xmlns/")] public string Ns5 { get; set; } [XmlAttribute(AttributeName = "ns6", Namespace = "http://www.w3.org/2000/xmlns/")] public string Ns6 { get; set; } [XmlAttribute(AttributeName = "ns7", Namespace = "http://www.w3.org/2000/xmlns/")] public string Ns7 { get; set; } [XmlAttribute(AttributeName = "ns8", Namespace = "http://www.w3.org/2000/xmlns/")] public string Ns8 { get; set; } [XmlAttribute(AttributeName = "ns9", Namespace = "http://www.w3.org/2000/xmlns/")] public string Ns9 { get; set; } } [XmlRoot(ElementName = "Body", Namespace = "http://schemas.xmlsoap.org/soap/envelope/")] public class Body { [XmlElement(ElementName = "getCacheEntryResponse", Namespace = "http://com.vedaadvantage/dp3/Enterprise/StandardTradeCreditCommercial/SilverChef/IndividualCommercialService")] public GetCacheEntryResponse GetCacheEntryResponse { get; set; } } [XmlRoot(ElementName = "Envelope", Namespace = "http://schemas.xmlsoap.org/soap/envelope/")] public class Envelope { [XmlElement(ElementName = "Body", Namespace = "http://schemas.xmlsoap.org/soap/envelope/")] public Body Body { get; set; } [XmlAttribute(AttributeName = "soap", Namespace = "http://www.w3.org/2000/xmlns/")] public string Soap { get; set; } } Here is how I am trying to extract the cacheEntryData field but it is not retrieving the node list (xnList) and it is not returning anything in my foreach statement. public override void CreateNewOutputRows() { string soap_resp = Variables.getCacheEntryRspXML.ToString(); soap_resp = soap_resp.Replace("\"\"", "\""); System.Windows.Forms.MessageBox.Show(soap_resp); XmlDocument agv = new XmlDocument(); agv.LoadXml(soap_resp); XmlNamespaceManager nsmgr = new XmlNamespaceManager(agv.NameTable); nsmgr.AddNamespace("soap", "http://schemas.xmlsoap.org/soap/envelope/"); nsmgr.AddNamespace("ns3", "http://com.vedaadvantage/dp3/Enterprise/StandardTradeCreditCommercial/SilverChef/IndividualCommercialService"); XmlNodeList xnList = agv.SelectNodes("//ns3:CacheEntry", nsmgr); foreach (XmlNode xn in xnList) { var cacheEntryData = xn["ns3:CacheEntry"].InnerText; System.Windows.Forms.MessageBox.Show(Convert.ToString(cacheEntryData)); } } A: This is very unusual. The code looks like in was html encoded so I had to html decode. using System.Linq; using System.Text; using System.Xml; using System.Xml.Linq; using System.IO; using System.Net; namespace ConsoleApplication73 { class Program { const string FILENAME = @"c:\temp\test.xml"; static void Main(string[] args) { string xml = File.ReadAllText(FILENAME); CreateNewOutputRows(xml); } static public void CreateNewOutputRows(string xml) { XDocument doc = XDocument.Parse(xml); XElement cacheEntryData = doc.Descendants().Where(x => x.Name.LocalName == "cacheEntryData").FirstOrDefault(); string cacheEntryDataXml = WebUtility.HtmlDecode(cacheEntryData.ToString()); XElement cacheEntryData2 = XElement.Parse(cacheEntryDataXml); } } } | Mid | [
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Google Street View in Colombia In June 2012 Google Colombia announced to the media that the Google Street View cars would be circulating throughout Colombia collecting images. In September 2013 Google Street View became available. It covers a major part of the Colombian territory including 21 cities and many smaller towns. Among the major cities covered by Street view are Bogotá, Cartagena, Manizales, Barranquilla, Bucaramanga, Santa Marta and Neiva. The initial collecting of images begun in Bogota. Google explained to the Colombian media that the well known privacy concerns would be addressed with the blurring of faces and car plates. They also explained that a contact form would be available for users if they believed that there was data that they deemed private. By the time of the first release some locations were not still covered, but Google assured that within the next months they would cover those areas still missing; namely Medellin and Cali. According to Semana magazine, the first stage of image collection included a coverage of more than 30.000 km of streets and roads. In addition to the cars, Google also used trikes since they were convenient for many narrow streets and colonial areas where cars might not be allowed. Google introduced Street View officially to the Colombian people and the Colombian media at a press conference at the Interactive Center Maloka, a center for the diffusion of knowledge in science and technology located in the city of Bogota. Google executive for Colombia explained that Maloka had been chosen because it was known as a place that inspired exploration and innovation. During a press conference general manager for Google in Colombia Laura Camacho explained that Colombia was the 4th country in Latin America to have a major Street View coverage after Mexico, Brazil and Chile (which was started almost at the same time). She also expressed that after a year of operations in Colombia, the releasing of Street View in this country, implied an acknowledgment by Google that Colombia is an important market in Latin America. Timeline of introductions Municipalities with Google Street View Coverage See also Google Street View in Latin America Google Street View in Canada References External links Google Colombia Category:Maps of Colombia Category:Google Street View Category:Internet in Colombia | High | [
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SUPREME COURT OF THE STATE OF NEW YORK Appellate Division, Fourth Judicial Department 94 KA 12-01643 PRESENT: SCUDDER, P.J., FAHEY, LINDLEY, VALENTINO, AND MARTOCHE, JJ. THE PEOPLE OF THE STATE OF NEW YORK, APPELLANT, V MEMORANDUM AND ORDER FRANK VANALST, ALSO KNOWN AS SHAUN JOHNSON, DEFENDANT-RESPONDENT. R. MICHAEL TANTILLO, DISTRICT ATTORNEY, CANANDAIGUA (BRIAN D. DENNIS OF COUNSEL), FOR APPELLANT. LEANNE LAPP, PUBLIC DEFENDER, CANANDAIGUA (DAVID M. ABBATOY, JR., OF COUNSEL), FOR DEFENDANT-RESPONDENT. Appeal from an order of the Ontario County Court (Frederick G. Reed, A.J.), entered April 9, 2012. The order granted the motion of defendant to dismiss the indictment. It is hereby ORDERED that the case is held, the decision is reserved and the matter is remitted to Ontario County Court for further proceedings in accordance with the following Memorandum: The People appeal from an order dismissing the sole count of the indictment, which charged defendant with criminal possession of a controlled substance in the third degree (Penal Law § 220.16 [1]), based on the alleged legal insufficiency of the evidence before the grand jury. The People contend that County Court applied an incorrect legal standard in reviewing that evidence. We agree. “The grand jury ‘must have before it evidence legally sufficient to establish a prima facie case, including all the elements of the crime, and reasonable cause to believe that the accused committed the offense to be charged’ ” (People v Wyant, 98 AD3d 1277, 1277, quoting People v Jensen, 86 NY2d 248, 251-252). Legally sufficient evidence is “competent evidence which, if accepted as true, would establish every element of an offense charged and the defendant’s commission thereof” (CPL 70.10 [1]; see People v Swamp, 84 NY2d 725, 730). On a motion to dismiss an indictment for legal insufficiency (see CPL 210.20 [1] [b]), the court “must consider whether the evidence, viewed most favorably to the People, if unexplained and uncontradicted . . . would warrant conviction” (Swamp, 84 NY2d at 730; see Jensen, 86 NY2d at 251; People v Jennings, 69 NY2d 103, 114). Thus, the foregoing standard limits the reviewing court to determining whether the evidence before the grand jury, together with the inferences that logically flow therefrom, supplies proof of every element of the charged crimes “and whether ‘the [g]rand [j]ury could rationally have -2- 94 KA 12-01643 drawn the guilty inference’ ” (People v Bello, 92 NY2d 523, 526, quoting People v Deegan, 69 NY2d 976, 979). Here, in dismissing the indictment, the court concluded that the police were not justified in pursuing defendant when he fled and thereafter allegedly dropped the narcotics that he was charged with possessing. That was error. The court did not decide the motion under the well-established standards set forth above; rather, the court decided the motion based on its improper determination of a suppression issue in the context of a motion to dismiss pursuant to CPL 210.20 (1) (b) (see generally Jensen, 86 NY2d at 251-252). In any event, it is further well established that, even “[i]f competent prima facie evidence underlying an indictment is subsequently rendered inadmissible [after a suppression hearing,] the legal sufficiency of the indictment is not undermined” (People v Gordon, 88 NY2d 92, 96; cf. CPL 210.20 [1] [h]). We therefore hold the case, reserve decision, and remit the matter to County Court to determine whether the evidence before the grand jury is legally sufficient to support the indictment without regard to the alleged violations of defendant’s rights under the Fourth Amendment or article I, § 12 of the New York Constitution, and to determine any remaining issues in connection with defendant’s request for dismissal of the indictment. Entered: February 8, 2013 Frances E. Cafarell Clerk of the Court | Mid | [
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Q: How do I index this postgres table to allow for efficient MIN(time) group by `id` query? I want to get the earliest time for a given id. So for this table: table | id | time | |----|------| | a1 | t1 | | a1 | t2 | | a1 | t3 | | a2 | t4 | | a3 | t5 | | a3 | t6 | where for each id, time is in ascending order, I want: | id | time | |----|------| | a1 | t1 | | a2 | t4 | | a3 | t5 | I want to eventually run this query: SELECT MIN(time) as earliestTime, table."id" FROM table WHERE table."id" IN %s GROUP BY table."id"; where %s is a large array of ids. However table can be very large. To speed things up, I tried to create indexes for this column: create index stream_time on table using btree ("id" ASC, "time" ASC); but I am not sure if this would be the most efficient way for my purpose. Could someone please advise me? A: There is no index that will speed up this query, it always requires a sequential scan. If there are not too many groups, there are tricks to get the result faster using a recursive query. | Mid | [
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Solution structure of BSTI: a new trypsin inhibitor from skin secretions of Bombina bombina. The three-dimensional solution structure of BSTI, a trypsin inhibitor from the European frog Bombina bombina, has been solved using (1)H NMR spectroscopy. The 60 amino acid protein contains five disulfide bonds, which were unambiguously determined to be Cys (4--38), Cys (13--34), Cys (17--30), Cys (21--60), and Cys (40--54) by experimental restraints and subsequent structure calculations. The main elements of secondary structure are four beta-strands, arranged as two small antiparallel beta-sheets. The overall fold of BSTI is disk shaped and is characterized by the lack of a hydrophobic core. The presumed active site is located on a loop comprising residues 21--34, which is a relatively disordered region similar to that seen in many other protease inhibitors. However, the overall fold is different to other known protease inhibitors with the exception of a small family of inhibitors isolated from nematodes of the family Ascaris and recently also from the haemolymph of Apis mellifera. BSTI may thus be classified as a new member of this recently discovered family of protease inhibitors. | Mid | [
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]
|
t c(s) be the second derivative of s**7/147 + s**6/21 + 4*s**5/35 + 2*s**4/21 + 2*s. Find f such that c(f) = 0. -2, -1, 0 Let r = 27 - 17. Let f = -6 + r. What is g in 2*g**5 + g**3 - 2*g + 4*g**2 - g**3 - 4*g**f = 0? -1, 0, 1 Let r(c) be the first derivative of 2/3*c**3 + 3 + 0*c + 0*c**2 - 1/2*c**4. Factor r(k). -2*k**2*(k - 1) Let u(q) = q**2 - 12*q + 30. Let k be u(3). Find t, given that -8/7*t**k + 2/7*t + 0 + 6/7*t**2 = 0. -1/4, 0, 1 Suppose -9*r = -0*r. Solve 0*h**3 + 4/7*h**2 + 2/7*h**5 - 2/7*h - 4/7*h**4 + r = 0 for h. -1, 0, 1 Let b(v) be the first derivative of -v**5/50 + v**4/30 + 3*v + 1. Let q(l) be the first derivative of b(l). Let q(x) = 0. What is x? 0, 1 Let j(l) be the third derivative of -l**6/180 - l**5/45 - l**4/36 - 8*l**2. Factor j(n). -2*n*(n + 1)**2/3 Solve 5*h**4 + 59*h**2 - 24*h**3 - 4*h + 5*h**4 - 41*h**2 = 0. 0, 2/5, 1 Let i(n) = 23*n**3 + 10*n**2 - 37*n + 30. Let j(u) = -11*u**3 - 5*u**2 + 19*u - 15. Let a(c) = -6*i(c) - 13*j(c). Factor a(l). 5*(l - 1)**2*(l + 3) Factor 2/5*x**2 + 0 - 3/5*x + 1/5*x**3. x*(x - 1)*(x + 3)/5 Let i(a) = -2*a**3 - 4*a**2 + 2*a + 4. Suppose 3*w + s = 0, 4*w + s = -0*s + 1. Let x(n) = n**4 - n**2. Let u(k) = w*i(k) + 6*x(k). Factor u(j). 2*(j - 1)**2*(j + 1)*(3*j + 2) Let t(k) be the third derivative of k**8/288 - k**7/252 - k**6/80 + k**5/72 + k**4/72 - 10*k**2. Suppose t(g) = 0. What is g? -1, -2/7, 0, 1 Let i(w) = -12*w - 72. Let g be i(-6). Suppose -3*h - 3 = -4*f + 1, 3*h - 3*f = -3. Find s, given that 1/2*s**3 + g*s + h + 1/2*s**2 = 0. -1, 0 Let b(f) be the second derivative of -f**4/12 + 5*f**3/6 + 2*f**2 + 2*f. Let x be b(5). Factor -2*v**3 + 6*v**x + v**3 - 7*v**2 - v**3 + 3*v**2. 2*v**2*(v - 1)*(3*v + 2) Let r = 24 + -22. Suppose 18 + 2*d**3 + 3*d + 27*d - 6*d**2 + 18*d**r + 2*d**2 = 0. What is d? -3, -1 Let j(v) = 2*v - 1. Let a be j(2). Suppose 4*h = a*h. Factor 2/5*i**5 + 0*i - 2/5*i**4 + 0*i**2 + h + 0*i**3. 2*i**4*(i - 1)/5 Let x(a) = -2*a - 7. Let b be x(-7). Let n = b - 2. Factor -n + 5 - p**2 - p. -p*(p + 1) Let n(t) be the second derivative of -t**5/60 - 7*t**4/36 - 4*t**3/9 + 8*t**2/3 + 2*t. What is x in n(x) = 0? -4, 1 Let s = 89 + -89. Let y(t) be the second derivative of -1/10*t**3 + 3/20*t**4 + s - t - 3/5*t**2. Suppose y(h) = 0. What is h? -2/3, 1 Let u = 18 + -20. Let v(p) = -p. Let r(w) = -2*w**2 - w. Let k(h) = u*v(h) + 2*r(h). Factor k(m). -4*m**2 Suppose -24*b + 19*b = -10. Factor 0*f - 1/2*f**b + 0. -f**2/2 Suppose -20*z = -22*z. Let q(t) be the third derivative of 0*t + z - 1/60*t**6 - 1/30*t**5 + 1/6*t**4 + 0*t**3 - 2*t**2. Let q(w) = 0. Calculate w. -2, 0, 1 Let v(i) be the second derivative of -i**4/42 - 5*i**3/21 - 4*i**2/7 - 14*i. Let v(x) = 0. Calculate x. -4, -1 Suppose -3*l = -58 + 13. Suppose 3*p + 3 - l = 0. Suppose -z**p - 16*z + z**2 + 2 + 5*z**3 + 14*z - 2 - 3*z**5 = 0. What is z? -1, 0, 2/3, 1 Let n be (9/(-24))/(18/4). Let c = 35/132 + n. Find v such that 0 + 0*v**2 + 0*v**4 - c*v - 2/11*v**5 + 4/11*v**3 = 0. -1, 0, 1 Suppose w**2 - w - 2*w - 3*w**2 + 3*w**2 = 0. What is w? 0, 3 Suppose -78*o = -67*o. Solve 0*q + 3/5*q**3 - 6/5*q**4 + o + 0*q**2 + 3/5*q**5 = 0 for q. 0, 1 Solve 8*m**2 + m**2 - 7*m**2 - 8 = 0 for m. -2, 2 Let j(a) be the second derivative of -a**4/72 + a**3/36 + a**2/6 - 9*a. Let j(k) = 0. What is k? -1, 2 Determine j so that 93*j**2 + 94*j**2 - 4*j - 191*j**2 = 0. -1, 0 Factor 28/5*r + 2/5 + 98/5*r**2. 2*(7*r + 1)**2/5 Let p(v) = -5*v**3 + 5*v - 6. Let c(t) = -t**3 + t. Let l(w) = 17*w**3 - 17*w + 13. Let f(x) = -6*c(x) - l(x). Let o(y) = 6*f(y) - 13*p(y). Factor o(z). -z*(z - 1)*(z + 1) Let 2/3*b**3 + 7/6*b**5 - 8/3*b**4 - 11/6*b + 7/3*b**2 + 1/3 = 0. What is b? -1, 2/7, 1 Factor -i**2 + 1/5*i**4 + 0 - 1/5*i**5 + 2/5*i + 3/5*i**3. -i*(i - 1)**3*(i + 2)/5 Let x(l) be the first derivative of 1/18*l**3 + 1/8*l**4 + 0*l + 1 + 1/36*l**6 + 1/10*l**5 + 0*l**2. Let x(n) = 0. Calculate n. -1, 0 Suppose 15*k = 53 + 22. Suppose 0 + 2/5*a**3 + 2/5*a**k + 6/5*a**4 - 6/5*a**2 - 4/5*a = 0. What is a? -2, -1, 0, 1 Let l(v) be the third derivative of 0 - 1/180*v**5 + 4*v**2 + 0*v**3 - 1/72*v**4 + 0*v. Solve l(d) = 0 for d. -1, 0 Factor 8/5 + 2/5*w**2 + 8/5*w. 2*(w + 2)**2/5 Solve 7*d**3 + 0*d**3 - 5*d**3 = 0. 0 Factor 0*b**2 + 2/3*b**3 + 0*b + 0 - 2/3*b**4. -2*b**3*(b - 1)/3 Let c(z) be the first derivative of z**6/120 + z**3 + 4. Let r(k) be the third derivative of c(k). Factor r(w). 3*w**2 Suppose -1/2*l**2 + 0*l + 1/6*l**3 + 2/3 = 0. What is l? -1, 2 Let d(j) be the third derivative of -j**6/60 - 7*j**2. Determine r, given that d(r) = 0. 0 Determine v, given that 0*v - 6*v**4 + 8*v**3 + 14*v**2 + 0*v**3 - 8*v - 8 = 0. -1, -2/3, 1, 2 Let w(c) = -c**3 + 3*c**2 + 2*c - 2. Let f be w(3). Suppose -j - 9 = -f*j. Factor k**j + k**3 - 4*k**3 + 2*k. -2*k*(k - 1)*(k + 1) Let p be (-2)/9 - (-116)/36. Suppose -2*s - p*j + 2 = 0, 5*s - j - 22 = -0*j. Factor -1/2*n**s - 2*n - 3*n**2 - 2*n**3 - 1/2. -(n + 1)**4/2 Let -57/7*z**3 + 0 + 99/7*z**2 - 27/7*z + 9/7*z**4 = 0. Calculate z. 0, 1/3, 3 Let u be -8*-2*(-3)/(-12). Factor 0*f**u + f**3 + f**4 + f**4 + 2*f**3 - f. f*(f + 1)**2*(2*f - 1) Let k(u) = -u**4 - u**3 + u + 1. Let l(w) = -w**4 - 12*w**3 - 4*w**2 + 12*w + 5. Let d(q) = -6*k(q) + l(q). Factor d(i). (i - 1)**2*(i + 1)*(5*i - 1) Let d(j) be the second derivative of j**5/30 - j**4/9 + j**3/9 - j. Factor d(k). 2*k*(k - 1)**2/3 Suppose 121*t = 116*t. Factor -2/3*o**3 + t*o**2 + 1/3*o**4 + 0 + 0*o. o**3*(o - 2)/3 Let o(j) be the third derivative of -j**8/40320 - j**7/5040 - j**6/1440 - j**5/30 - 3*j**2. Let a(b) be the third derivative of o(b). Factor a(t). -(t + 1)**2/2 Determine u, given that -5*u**2 + 2*u**2 - 11*u + 2*u**2 + 12*u = 0. 0, 1 Let o = 24 - 47/2. Suppose -1/2*w**2 + 1 - o*w = 0. Calculate w. -2, 1 Let m(p) = -35*p**5 + 20*p**4 + 50*p**3 - 20*p**2 - 10*p + 5. Let d(w) = w**4 - w**3 - w**2 - 1. Let i(z) = 5*d(z) + m(z). Let i(g) = 0. What is g? -1, -2/7, 0, 1 Let f = 5627/63 - 800/9. Let -f*w**2 + 4/7 - 1/7*w**3 + 0*w = 0. What is w? -2, 1 Let w(l) be the third derivative of l**7/2100 - l**6/1800 - l**4/24 + 3*l**2. Let q(a) be the second derivative of w(a). Find j such that q(j) = 0. 0, 1/3 Factor -2/7*z - 3/7*z**2 + 9/7*z**3 + 0. z*(3*z - 2)*(3*z + 1)/7 Let q = -2522 + 17686/7. Factor 8/7 + 34/7*y**2 - q*y - 10/7*y**3. -2*(y - 2)*(y - 1)*(5*y - 2)/7 Let 2*z**4 - 71*z**3 + 138*z**3 - 70*z**3 - 3*z**4 = 0. What is z? -3, 0 Let g be ((-15)/(-6))/(4 - (-44)/(-16)). Find c, given that 0 - 2/3*c**3 + 0*c**g - 8/3*c**4 + 0*c = 0. -1/4, 0 Let x = 2/67 + 191/335. Let h(m) be the first derivative of m**3 + 3/4*m**4 + 0*m - 3/2*m**2 - 1 - x*m**5. Factor h(c). -3*c*(c - 1)**2*(c + 1) Let o(q) be the second derivative of -q**6/55 + q**5/22 - q**4/33 + 6*q. Determine c, given that o(c) = 0. 0, 2/3, 1 Let q(v) be the first derivative of -4*v**5/5 - 2*v**4 + 4*v**2 + 4*v - 14. Find f such that q(f) = 0. -1, 1 Suppose n + n + 5*f = 25, 4*f = 5*n + 20. Find q, given that q**3 - q**2 + n*q**2 + q**2 = 0. 0 Let f(l) = 2*l**2 - 2*l - 1. Let w be f(-1). Suppose y - 3*y + 10 = -o, 5*y - 25 = -w*o. Factor 4*q**3 + 0*q - 2*q + 0*q**3 - 2*q**y. -2*q*(q - 1)**2*(q + 1)**2 Let u be (4 - 55/15)/(2/8). Factor 0 - u*n**3 + 2/3*n**4 + 2/3*n**2 + 0*n. 2*n**2*(n - 1)**2/3 Let c(h) be the third derivative of -h**6/30 + h**4/6 - 2*h**2. Factor c(f). -4*f*(f - 1)*(f + 1) Let v = 8074/5 - 1589. Let g = 26 - v. Solve 1/5*d**4 - 2/5*d**2 - g*d - 1/5*d**5 + 2/5*d**3 + 1/5 = 0. -1, 1 Let d = -611/2 - -306. Factor 0 + 1/2*g**3 - 1/4*g**2 - d*g + 1/4*g**4. g*(g - 1)*(g + 1)*(g + 2)/4 Let n be 693/(-18) + (-2)/(-4). Let r = -35 - n. Factor -1/3*a**4 - 2/3 + a**2 + 1/3*a - 1/3*a**r. -(a - 1)**2*(a + 1)*(a + 2)/3 Let a(c) be the second derivative of -c**4/3 + 2*c**3/3 + 4*c**2 - 20*c. Let a(q) = 0. Calculate q. -1, 2 Suppose -c - 4*d - 7 = -31, 0 = -3*c - 5*d + 37. Let i be (8/14)/(c/14). Factor 2/7 + 4/7*f**i - 6/7*f. 2*(f - 1)*(2*f - 1)/7 Let k(a) be the second derivative of 0 + 1/5*a**4 - 2/15*a**3 + 0*a**2 - a - 9/100*a**5. Factor k(m). -m*(3*m - 2)**2/5 Let y(k) be the first derivative of 14*k**3/33 + k**2/11 + 3. Solve y(s) = 0. -1/7, 0 Let z(f) be the third derivative of 1/105*f**7 + 1/90*f**5 - 1/504*f**8 + 0*f**4 + 0 + 0*f**3 - 3*f**2 - 1/60*f**6 + 0*f. Factor z(w). | Low | [
0.498721227621483,
24.375,
24.5
]
|
Originally published on June 1, 2019. New science is emerging that suggests the moral panic about video games is misguided, and that many games can be benign or even beneficial by helping with social and intellectual development. In fact, researchers are exploring the use of games as pedagogical tools in education and even as therapeutic tools for anxiety and depression. A huge number of adults and kids enjoy playing video games: 61 per cent of Canadians define themselves as a gamer, and more than 90 per cent of teens play video games, according to a 2018 survey conducted by the Entertainment Software Association of Canada. But there's been a long-standing concern about the impact of video games on players, largely driven by outrage at some of the violent, sexist and anti-social behaviour that games like the Grand Theft Auto series seem to model. Concerns about video games unfounded: researcher According to Canadian researcher Isabela Granic , chair and professor in the developmental psychopathology department at Radboud University in the Netherlands, the research suggests that there's little good evidence to support the notion that video games are harmful to children or adults. "There have been a couple of meta-analyses conducted on whether video games incite violence, and the largest two meta-analyses have shown that there's almost no impact of video games on violence and aggression," Granic told Quirks & Quarks host Bob McDonald. The immensely popular video game Fortnite has nearly 250 million registered players. The huge appeal of the game reflects the wider appeal of video games in general (BARTOSZ SIEDLIK/AFP/Getty Images) Addiction is another concern often cited. In June, the World Health Organization classified video game addiction as a mental health disorder. Granic prefers to use the term "compulsive use" instead and says there's no real evidence that indicate that video games are much different from other hobbies. "About one to two per cent of kids who play video games daily are at a point where we should be concerned. They're playing eight to 10 hours a day," Granic said. On the other hand, she said the vast majority of kids are only playing one to three hours per day, and they're often playing games socially, with friends from school either in the same room or online. She suggests this digital playground is not too different from the analog one that older generations played on. "They're talking to one another, and it's a space that they're sharing that's outside of the eyes of parents where they can get a little bit of autonomy, a little bit of control and have that little corner of the playground where they can have some privacy," said Granic. "And they're just fun — joyful, fun games." Granic doesn't dismiss the idea that video games can contribute to problems with childhood development. But she suggests that they're less significant than things like socio-economic status. "It depends on the child and the context. It depends on the diet of digital games and other media that they're consuming, and it hugely depends on parenting." Minecraft for education One popular game that's well on its way to becoming not just an entertaining pastime, but a valuable tool in education, is Minecraft. The virtual building game has been one of the most popular games in the world for nearly a decade. Schools in many countries, including U.S. and Sweden, have actually integrated Minecraft into their standard curricula. Three years ago, Thierry Karsenti saw the potential of the game for education and brought Minecraft to 118 elementary school students in Montreal. Karsenti is a Canada Research Chair in technologies in education and professor in the faculty of education at the University of Montreal. A reproduction of the Titanic created by students in the Minecraft program. (Thierry Karsenti) Unbeknownst to the students, he incorporated elements of the schools' history and math curricula into the customized version of Minecraft. He ran the program for 15 weeks, and the results he got were decisive. "The kids who participated in the after school Minecraft project had significantly higher results in math at the end of the year than those who didn't participate in the project," said Karsenti. In addition to that, he said, students also developed problem-solving skills and people skills, and the program had a positive effect on their self-esteem and motivation. Elementary school students playing Minecraft together. (Thierry Karsenti) The most exciting result, according to Karsenti, were the social benefits derived from the game. "[Kids] were helping each other, not just within the team, but also other teams that were stuck after they completed their task," he said. Karsenti says the results suggest that Minecraft could keep students engaged in an activity that they enjoy while also learning along the way. But he warns that the program must be focused on education and be supervised. Therapeutic games for anxiety and depression Beyond social and educational development, there's growing evidence that custom designed games could also be used in therapy for a variety of mental illnesses — anxiety, autism and even schizophrenia. In her work as a developmental psychologist, Granic has developed and tested several games to help children struggling with anxiety and depression. A child playing Mindlight, a video game designed to help children with anxiety. (GEMH Lab) One example is Mindlight, a neurofeedback game that incorporates clinical techniques to reduce anxiety in at-risk children. Kids playing the game have to navigate a haunted house and they control the brightness of the game with their mind. A headset monitors electrical activity in the brain, and particularly the kind of activity associated with anxiety. The calmer they are, the brighter their surroundings become and vice versa. This teaches players to overcome their fears by changing their state of mind. Granic has tested the game in four studies looking at more than 500 children. Playing the game was shown to decrease children's anxiety levels by about half, and the effects remained even six months after kids stopped playing. What she found most encouraging was the way the children applied the calming techniques that worked in the game in anxiety-inducing situations in real life. "Mindlight was shown to be as effective in reducing anxiety as cognitive behaviour therapy, the gold standard of psychotherapy. But it did it in half the time and one tenth the cost." said Granic. Going forward, Granic hopes to introduce these therapeutic games to the wider population beyond individuals with clinical conditions. "We all struggle with anxiety, and we all struggle with sad days," Granic said. "Learning how to regulate those emotions in a context that's playful and that allows us to be delighted at the time as we're learning these skills, I think there's immense potential to reach people that otherwise would be stigmatized." | Mid | [
0.6540284360189571,
34.5,
18.25
]
|
Effects of different 3-year cropping systems on soil microbial communities and rhizoctonia diseases of potato. ABSTRACT Eight different 3-year cropping systems, consisting of soybean-canola, soybean-barley, sweet corn-canola, sweet corn-soybean, green bean-sweet corn, canola-sweet corn, barley-clover, and continuous potato (non-rotation control) followed by potato as the third crop in all systems, were established in replicated field plots with two rotation entry points in Presque Isle, ME, in 1998. Cropping system effects on soil microbial community characteristics based on culturable soil microbial populations, single carbon source substrate utilization (SU) profiles, and whole-soil fatty acid methyl ester (FAME) profiles were evaluated in association with the development of soilborne diseases of potato in the 2000 and 2001 field seasons. Soil populations of culturable bacteria and overall microbial activity were highest following barley, canola, and sweet corn crops, and lowest following continuous potato. The SU profiles derived from BIOLOG ECO plates indicated higher substrate richness and diversity and greater utilization of certain carbohydrates, carboxylic acids, and amino acids associated with barley, canola, and some sweet corn rotations, indicating distinct differences in functional attributes of microbial communities among cropping systems. Soil FAME profiles also demonstrated distinct differences among cropping systems in their relative composition of fatty acid types and classes, representing structural attributes of microbial communities. Fatty acids most responsible for differentiation among cropping systems included 12:0, 16:1 omega5c, 16:1 omega7c, 18:1 omega9c, and 18:2omega6c. Based on FAME biomarkers, barley rotations resulted in higher fungi-to-bacteria ratios, sweet corn resulted in greater mycorrhizae populations, and continuous potato produced the lowest amounts of these and other biomarker traits. Incidence and severity of stem and stolon canker and black scurf of potato, caused by Rhizoctonia solani, were reduced for most rotations relative to the continuous potato control. Potato crops following canola, barley, or sweet corn provided the lowest levels of Rhizoctonia disease and best tuber quality, whereas potato crops following clover or soybean resulted in disease problems in some years. Both rotation crop and cropping sequence were important in shaping the microbial characteristics, soilborne disease, and tuber qualities. Several microbial parameters, including microbial populations and SU and FAME profile characteristics, were correlated with potato disease or yield measurements in one or both harvest years. In this study, we have demonstrated distinctive effects of specific rotation crops and cropping sequences on microbial communities and have begun to relate the implications of these changes to crop health and productivity. | High | [
0.690763052208835,
32.25,
14.4375
]
|
/*
* Copyright Andrey Semashev 2016.
* Distributed under the Boost Software License, Version 1.0.
* (See accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*/
/*!
* \file keywords/capacity.hpp
* \author Andrey Semashev
* \date 23.02.2016
*
* The header contains the \c capacity keyword declaration.
*/
#ifndef BOOST_LOG_KEYWORDS_CAPACITY_HPP_INCLUDED_
#define BOOST_LOG_KEYWORDS_CAPACITY_HPP_INCLUDED_
#include <boost/parameter/keyword.hpp>
#include <boost/log/detail/config.hpp>
#ifdef BOOST_HAS_PRAGMA_ONCE
#pragma once
#endif
namespace boost {
BOOST_LOG_OPEN_NAMESPACE
namespace keywords {
//! The keyword allows to pass interprocess queue capacity to the queue constructor
BOOST_PARAMETER_KEYWORD(tag, capacity)
} // namespace keywords
BOOST_LOG_CLOSE_NAMESPACE // namespace log
} // namespace boost
#endif // BOOST_LOG_KEYWORDS_CAPACITY_HPP_INCLUDED_
| Mid | [
0.632241813602015,
31.375,
18.25
]
|
Q: `pthread_mutex_trylock` and `pthread_mutex_lock` behaviour This is a follow up to this question. In that code, when I was not using fflush(stdout) output was not flushed to the screen when I kept sleep(1). #define S sleep(0) void* xThread_fn(void* arg) { while(1) { S; pthread_mutex_lock(&read_c_mutex); if(!read_c) { pthread_mutex_unlock(&read_c_mutex); printf(" X"); } else { pthread_mutex_unlock(&read_c_mutex); pthread_exit(NULL); } fflush(stdout); <---THIS ONE HERE } } But when I keep sleep(0) there is no need for fflush(stdout), the output is properly updated on stdout. Why is this so? Q1. Why should the presence of sleep(0) cause any change in the way output is flushed? If i modify the code as follows (to track execution), #define S sleep(1) int read_c = 0; pthread_mutex_t read_c_mutex = PTHREAD_MUTEX_INITIALIZER; void* inputThread_fn(void* arg) { printf("%p is Input\n",pthread_self()); char inputChar; int i = 0; while(1) { S; printf("\nChecking input"); scanf("%c",&inputChar); if(inputChar=='C' || inputChar == 'c') { pthread_mutex_trylock(&read_c_mutex); printf("%p has lock %d\n",pthread_self(),i); read_c = 1; pthread_mutex_unlock(&read_c_mutex); printf("%p has UNlockED %d\n",pthread_self(),i++); printf("%p is Gone!\n",pthread_self()); fflush(stdout); pthread_exit(NULL); } } } void* xThread_fn(void* arg) { int i = 0; printf("%p is X\n",pthread_self()); while(1) { S; printf("X trying for a lock\n"); pthread_mutex_trylock(&read_c_mutex); printf("%p has lock %d\n",pthread_self(),i); if(!read_c) { pthread_mutex_unlock(&read_c_mutex); printf("%p has UNlockED %d\n",pthread_self(),i++); printf("X\n"); fflush(stdout); } else { printf("%p is Gone!\n",pthread_self()); pthread_mutex_unlock(&read_c_mutex); fflush(stdout); pthread_exit(NULL); } } } void* yThread_fn(void* arg) { printf("%p is Y\n",pthread_self()); int i = 0; while(1) { S; printf("Y trying for a lock\n"); pthread_mutex_trylock(&read_c_mutex); printf("%p has lock %d\n",pthread_self(),i); if(!read_c) { pthread_mutex_unlock(&read_c_mutex); printf("%p has UNlockED %d\n",pthread_self(),i++); printf("Z\n"); fflush(stdout); } else { printf("%p is Gone!\n",pthread_self()); pthread_mutex_unlock(&read_c_mutex); fflush(stdout); pthread_exit(NULL); } } } a sample output is 0xb6700b70 is Input 0xb6f01b70 is Y 0xb7702b70 is X Checking inputY trying for a lock 0xb6f01b70 has lock 0 0xb6f01b70 has UNlockED 0 Z X trying for a lock 0xb7702b70 has lock 0 0xb7702b70 has UNlockED 0 X Y trying for a lock 0xb6f01b70 has lock 1 0xb6f01b70 has UNlockED 1 Z X trying for a lock 0xb7702b70 has lock 1 0xb7702b70 has UNlockED 1 X Y trying for a lock 0xb6f01b70 has lock 2 0xb6f01b70 has UNlockED 2 Z X trying for a lock 0xb7702b70 has lock 2 0xb7702b70 has UNlockED 2 X Y trying for a lock 0xb6f01b70 has lock 3 0xb6f01b70 has UNlockED 3 Z X trying for a lock 0xb7702b70 has lock 3 0xb7702b70 has UNlockED 3 X Y trying for a lock 0xb6f01b70 has lock 4 0xb6f01b70 has UNlockED 4 Z X trying for a lock 0xb7702b70 has lock 4 0xb7702b70 has UNlockED 4 X c Y trying for a lock 0xb6f01b70 has lock 5 0xb6f01b70 has UNlockED 5 Z X trying for a lock 0xb7702b70 has lock 5 0xb7702b70 has UNlockED 5 X 0xb6700b70 has lock 0 0xb6700b70 has UNlockED 0 0xb6700b70 is Gone! Y trying for a lock 0xb6f01b70 has lock 6 0xb6f01b70 is Gone! X trying for a lock 0xb7702b70 has lock 6 0xb7702b70 is Gone! Q2. I have made use of pthread_mutex_trylock() because I wanted the code to proceed in the while loop till it acquires a lock to check the value of read_c. The same appears to be achieved with pthread_mutex_lock();. That confuses me more. With pthread_mutex_trylock(); too, the output always be like this? One X followed by one Z. Won't there be a situation where it might be like X X Z X (Provided the thread is switched by the OS and ythread tried for a lock and failed)? A: Answering the "trylock" question. pthread_mutex_trylock only attempts to lock the mutex. If someone else has the mutex locked, it will just return an error and keep running. Since you're not checking the return value you might touch the data that is protected by the mutex without holding the mutex. Your code is equivalent to not having any mutexes at all. pthread_mutex_trylock should only be used in situations where you for some very special reason can't wait for a lock and will fall back to a different behavior when acquiring the mutex has failed. Calling it without checking the return value is always a bug. To be perfectly correct, you should check the return value of pthread_mutex_lock too. But you can most often get away with not doing that. You can never get away with not checking the return value of trylock. | Mid | [
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Welcome Welcome to the POZ Community Forums, a round-the-clock discussion area for people with HIV/AIDS, their friends/family/caregivers, and others concerned about HIV/AIDS. Click on the links below to browse our various forums; scroll down for a glance at the most recent posts; or join in the conversation yourself by registering on the left side of this page. Privacy Warning: Please realize that these forums are open to all, and are fully searchable via Google and other search engines. If you are HIV positive and disclose this in our forums, then it is almost the same thing as telling the whole world (or at least the World Wide Web). If this concerns you, then do not use a username or avatar that are self-identifying in any way. We do not allow the deletion of anything you post in these forums, so think before you post. The information shared in these forums, by moderators and members, is designed to complement, not replace, the relationship between an individual and his/her own physician. All members of these forums are, by default, not considered to be licensed medical providers. If otherwise, users must clearly define themselves as such. Forums members must behave at all times with respect and honesty. Posting guidelines, including time-out and banning policies, have been established by the moderators of these forums. Click here for “Am I Infected?” posting guidelines. Click here for posting guidelines pertaining to all other POZ community forums. We ask all forums members to provide references for health/medical/scientific information they provide, when it is not a personal experience being discussed. Please provide hyperlinks with full URLs or full citations of published works not available via the Internet. Additionally, all forums members must post information which are true and correct to their knowledge. Author Topic: I finally found her! (Read 7008 times) Those of you who have known me for some years will know that I lost contact with my sister back in 1997. I was up late last night and took a spur of the moment decision to finally join Facebook with my full name and see if I couldn't find my sister. For some reason I kept thinking about her last night, but I haven't thought of her in a while, really. I've searched for her on the internet many times, but with a last name like Smith, it's like looking for a needle in a haystack. I sent a message asking if she was indeed the right person I was looking for (I've found others who turned out to not be her) and she messaged me back within about 20 minutes. Yes! I'd finally found her after all these years! We ended up talking on Skype for a couple hours, but she finally had to go to bed. We were still talking when my daughter got up for work though, and my daughter was just as delighted as I was. She hasn't seen her aunt since she was three years old. Funny thing is, my sister said she'd been thinking of me on her way home from work - and she also hadn't really thought of me recently. Spooky or what? She's gone back to college and is now an RN who works in ICU and ER medicine. I was absolutely gobsmacked - she always had a "thing" about blood. (as in "ew") She's in a very happy ten-year relationship with a woman (and her two children). She's very close to her lover's family and that makes me well up - we come from a pretty shit family and it's so good to know she's now got a family around her who really cares and loves her. That's fantastic. I disclosed my status and that went fine, probably because I was laughing and joking about it, like I do. But wow, I can't believe it. Those of you who are aware of the previous situation with my sister will probably understand just how happy I am today. She's the only person in my family (on that side of the pond) who I really care to have anything to do with and it always cut me to pieces that we lost touch. "...health will finally be seen not as a blessing to be wished for, but as a human right to be fought for." Kofi Annan Nymphomaniac: a woman as obsessed with sex as an average man. Mignon McLaughlin HIV is certainly character-building. It's made me see all of the shallow things we cling to, like ego and vanity. Of course, I'd rather have a few more T-cells and a little less character. Randy Shilts Turns out she's been scouring the internet from time to time for me too, but I'm pretty crafty at hiding my tracks. Guess she is too. There was some time a few years ago when I had the feeling she was no longer in the area where we grew up, and I was right, she was in CA and CO working as a nurse. She's back in Ohio now, not far at all from where we grew up. I'm so excited I still haven't been to bed. I'd go have a nap but I've got a GP appointment this afternoon and I just know I wouldn't wake up. I still can't believe it. I fully expected another brick wall last night. Yippee! "...health will finally be seen not as a blessing to be wished for, but as a human right to be fought for." Kofi Annan Nymphomaniac: a woman as obsessed with sex as an average man. Mignon McLaughlin HIV is certainly character-building. It's made me see all of the shallow things we cling to, like ego and vanity. Of course, I'd rather have a few more T-cells and a little less character. Randy Shilts Back in early 1997, my sister and I had a bit of a spat over the fact that I left to go live on a Rock in the middle of the Irish Sea and she was stuck alone dealing with our behaviourally challenged mother (euphemism for vindictive, manipulative bitch) as mom had long ago disowned our brother. She was feeling resentful towards me and I get that. Don't blame her, but hey, I had the smarts to hit the road first. Anyway, before we made up, she made some life-changing decisions. She sold her house and moved, then went to nursing school, and I moved not long after, so we ended up not having each other's details. The spat has been long forgotten and we've both been looking for each other online - me since 2001, her since around 2005 (I think). And thanks to the magic of the internet and the new search filtering features on Facebook, I finally found her last night. I really didn't expect to - I've been disappointed so many times before I'd given up any real hope. Technically, I'm a Hoosier (Ft Wayne IN), but my family are all Buckeyes. Mother from Columbus, father, brother and sister from Cleveland. My father had been on a temporary transfer, I think we were there for less than three years, including during my incubation. (you guys do know I was hatched, right?) Thanks again for all the well-wishes - it really means a lot to me. I know I don't often share many personal details (ok, aside from poking fun at my sex life) but this one was too exciting and wonderful to not share with you guys. You're all like family in a way, so it seemed appropriate. I've been walking around with a big dopey grin on my face all day! And now I'm going to go have a quiet celebration with a few friends. They're all really happy for us too - they know how much this has bothered me over the years. When my sister was missing, it was like half my family was gone and it was just me and my daughter (as far as blood relations go). "...health will finally be seen not as a blessing to be wished for, but as a human right to be fought for." Kofi Annan Nymphomaniac: a woman as obsessed with sex as an average man. Mignon McLaughlin HIV is certainly character-building. It's made me see all of the shallow things we cling to, like ego and vanity. Of course, I'd rather have a few more T-cells and a little less character. Randy Shilts Ann, I am very happy for you. I too have a facebook account and have had one for a few yrs. I hardly ever went to it but one day i got an email saying someone on facebook was wanting to be my friend, so i went and checked and it was one of the friends i went to school with, well she let others know and now i have a lot of friends i went to school with on facebook. Funny i was in Indiana for 14 yrs. and tried to find my old friends but it took someone that doesn't live in In. to find me. Now i am in Fl. and can still talk with old friends. I love the internet.Congrats. on finding your sister. Ann, that's fantastic news! We've talked about your family before, and I know how you feel about the rest of 'em. It must be wonderful to find out how well she's doing. So, maybe this will warrant a trip to the States sometime? Logged I've never killed anyone, but I frequently get satisfaction reading the obituary notices.-Clarence Darrow it must be amazing to connect again with the people you love. i hope you've put fail safes in place to never let this happen again. oh, the wonderful conversations and stories you two smiths will tell. hmm, now that i think about it, i'd LOVE to be a fly on the wall in the room of the after dinner conversation now that you found her, you can close your facebook and resume your searches on adam4adam to lure hot men to the rock...wait, those are sirens. Considering she's a nurse I wonder how much she might actually know about HIV. I have a neighbor who is a nurse and whenever HIV has come up in conversation I can't help thinking that she's not really all that knowledgeable about it (apart from the basics of course). I have to say that my joy in finding my sister is very much tempered today through the loss of Tim, a forum family member. As I said in another thread, life can be so cruel. I've gone from the heights of happiness to the depths of despair in less than 24 hours. I know Tim would want me to be happy, so I'm doing my best. But right now, it's so very hard. I have to believe he's in a better place now. I have to believe that. My sister said she will come and visit us, but we're going to have to work out the timing. My daughter Alice will be going to the University of East Anglia in Norwich in September to study for her teaching certificate. This means my sister will have to visit before September, or over Christmas, or after Alice's course is finished next spring. I'll have to start saving my pennies to be able to visit Ohio. My sister is three and a half years older. She's a 1959 Taurus, I'm a 1962 Scorpio. We mainly fought like cat and dog as kids - and a lot of that was orchestrated by our mother - but after I reached the age of fourteen or so, we got along very well and became quite close. Part of that was because I told her I knew she was gay and that was just fine by me. She was amazed that I never used it against her where our mother was concerned and believe me, it would have been a very effective weapon in that regard. She came to realise that the persona my mother tried to make me fit into just wasn't me at all. I'm not sure quite how knowledgeable my sister is where hiv is concerned. I asked her what sort of experience she had with poz patients and she doesn't have much, other than poz people who came through one of the ERs she worked in - and she said that it was rare for one to come in with a problem directly related to their hiv. She does seem to know the basics and that's something I'll have to pick her brains about in the coming weeks. She was concerned over whether or not I knew much myself and whether or not I was being routinely monitored. I told her about my numbers over the years, about not needing meds yet, and about flying over to Liverpool for my hiv care. I also told her about my work here and all that combined to put her mind at rest that I really am ok and will be for the foreseeable future. Provided I look both way before I cross the street, of course. Oh, and I also told her about my hep C and its successful treatment. She's just about to ring me on Skype now, so maybe I'll know more later. "...health will finally be seen not as a blessing to be wished for, but as a human right to be fought for." Kofi Annan Nymphomaniac: a woman as obsessed with sex as an average man. Mignon McLaughlin HIV is certainly character-building. It's made me see all of the shallow things we cling to, like ego and vanity. Of course, I'd rather have a few more T-cells and a little less character. Randy Shilts That's very cool! As for her having you on her mind too... it was just time for you two to connect. It wasn't that long ago you seemed a bit anti-Facebook. See, it's not all bad! I hope you sisters (and her family and your daughter) all have a chance to get to know each other. See, Facebook can be a good thing. I'm so happy for you and your sister. My brother and I had been distant lately, but got together just tonight for his birthday. I hope you guys can see each other in person soon. My sister is three and a half years older. She's a 1959 Taurus, I'm a 1962 Scorpio. We mainly fought like cat and dog as kids - and a lot of that was orchestrated by our mother - but after I reached the age of fourteen or so, we got along very well and became quite close. Part of that was because I told her I knew she was gay and that was just fine by me. She was amazed that I never used it against her where our mother was concerned and believe me, it would have been a very effective weapon in that regard. She came to realise that the persona my mother tried to make me fit into just wasn't me at all. Cheers... There is a little crazy in every family, or that's what I think or else I'm the one that's crazy. Perfect family I have seen on the tele but not in life. There is still tension between me and my family, I have no problem with that, but I am glad that you and your sister have found solace with each other. My your reunion be a delightfully full of joy and happy tears. Wowser, that's where I go. If it's good enough for the infamous Ann, I'll stop playing holy hell everytime I'm there!! That's put a smile on my face (although will be a bigger one when they've rebuilt the bloody place). Ann...I'm so glad I didn't miss this thread. As folks who go back a ways here indeed, you're like an online sister to me here. It's great that bygones are bygones with your sister and now you can not just be sisters again but friends as well...And an aunt has come into your daughters life as David said. So good for you for reaching out, it showed class and confidence...And why not considering the source. Jody Logged "Wake up to find out that you are the eyes of the world". "Try to discover that you are the song that the morning brings." | Mid | [
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Switching regulators and linear regulators are well known types of voltage regulators for converting an unregulated voltage, such as a battery voltage, to a regulated DC output voltage of a desired value. Linear regulators, also referred to as low dropout (LDO) regulators, include a control circuit and a linear switch (transistor) that is connected between the unregulated power supply and an output terminal. The control circuit monitors the regulated DC output voltage at the output terminal by way of a feedback signal, and controls the gate voltage of the linear switch such that the switch's conductance is adjusted to produce the desired DC output voltage level. Switching regulators include a switch (transistor) and an inductor connected in series between the unregulated voltage and the output terminal, a filter capacitor, and an oscillator-based control circuit. The oscillator-based control circuit provides a time-varying control signal to the gate terminal of the switch, whereby the switch is turned on to pass the unregulated voltage to the inductor in short pulses. These pulses cause the inductor to store energy in its magnetic field, which produces the regulated DC output voltage. The filter capacitor serves to smooth and maintain the regulated DC output voltage between pulses. The regulated DC output voltage is fed back to an oscillator-based control circuit, which compares the feedback voltage with a reference voltage, and controls the oscillator output such that the switch duty cycle produces the desired regulated DC output voltage. Switching regulators can generally be classified by the type of oscillator control as either pulse-width-modulated (PWM) or pulse-frequency-modulated (PFM) regulators. PWM regulators include an oscillator control circuit that produces a pulse train having a fixed frequency and a variable pulse width. PFM regulators, on the other hand, use oscillator control circuits that produce a fixed pulse width and a variable pulse frequency. In either case, the duty cycle of the transistor is controlled by the feedback voltage such that the regulated output voltage maintains the desired voltage level. Switching regulators are also characterized by whether they convert the unregulated voltage upward (boost or step-up configuration), convert the unregulated voltage downward (buck or step-down configuration), or invert the unregulated voltage (buck-boost or inverting configuration). Switching regulators are generally considered to be more efficient than linear regulators, but are generally much noisier during operation. A linear regulator provides a very smooth output voltage because the linear switch is always partially on (conducting), but wastes power due to the large voltage differential across the linear switch. In contrast, the switching regulator transistor is either fully on or fully off. When a switching regulator transistor is fully on, such as in saturation or near the edge of saturation, the transistor is a highly efficient switch, and there is a minimum of wasted power through the switch. However, when load conditions suddenly increase, unlike linear voltage regulators that instantaneously adjust to the increased current demand, switching-type regulators can experience delays because the current through the inductor cannot change instantaneously with time. In addition, the control system around the switching regulator requires a longer time than a linear system to adjust the duty cycle to current-load the inductor properly. What is needed is a voltage regulator circuit that combines the smooth, quickly responding output voltage of a linear voltage regulator and the high efficiency of a switching-type voltage regulator. | Mid | [
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Atracurium infusion in liver transplantation. A continuous infusion of atracurium was used to provide neuromuscular blockade in 25 adult patients undergoing liver transplantation following atracurium, suxamethonium or vecuronium for intubation. Blockade was monitored by recording evoked electromyographic response and maintained with a mean infusion rate of 0.38 +/- 0.14 mg kg-1 h-1 during 306 +/- 80 min of operation. Atracurium requirements appeared to be less during the anhepatic period and greater after removal of the vascular clamps on the new liver. No instances of arterial hypotension or anaphylactoid reactions attributable to atracurium were reported. It can be concluded that a continuous infusion of atracurium is a safe, effective and convenient technique of ensuring neuromuscular blockade during liver transplantation, at a rate of infusion no different from that needed in patients with normal hepatic function. | Mid | [
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34 P.3d 37 (2001) 136 Idaho 376 STATE of Idaho, Plaintiff-Respondent, v. Edward Jessie WARFIELD, Defendant-Appellant. No. 26570. Court of Appeals of Idaho. October 16, 2001. *38 Ronaldo A. Coulter, State Appellate Public Defender; Paul S. Sonenberg, Deputy Appellate Public Defender, Boise, for appellant. Hon. Alan G. Lance, Attorney General; Kenneth K. Jorgensen, Deputy Attorney General, Boise, for respondent. LANSING, Judge. Appellant Edward Jessie Warfield was a resident of the Aryan Nations compound near Hayden, Idaho. He was convicted of aggravated assault for his involvement in an attack upon two white motorists who drove past the compound. The principal issue presented by this appeal is whether the district court violated Warfield's First Amendment rights when the court took Warfield's racist beliefs into consideration in denying Warfield's motion for a reduction of his sentence. BACKGROUND Warfield was a member of the Aryan Nations, a white supremacist organization, and was a security guard at the Aryan Nations compound. On the evening of July 1, 1998, Victoria Keenan and her son, Jason Keenan, drove past the compound on their way home from a wedding. While they were passing the compound, Jason accidentally threw his wallet out the window of the moving car. When Victoria turned the car around to go back and search for the wallet, the car backfired. Once the wallet was found, the Keenans drove away. Persons at the compound apparently mistook the sound of the backfire for a gunshot and concluded that the compound was being fired upon. This led Warfield and two other occupants of the compound to give chase in their pickup truck. Warfield drove while his two confederates sat in the pickup bed. One of the Aryans yelled at the Keenans to stop. When they did not comply, those in the bed of the pickup fired shots at the Keenans' car, hitting it five times. The Keenans' car left the highway and came to a stop in the ditch. Warfield pulled his pickup behind the disabled Keenan vehicle, and all of the Aryans approached the Keenans. The Aryans yelled and demanded to know whether the Keenans had fired shots at the compound. The Keenans denied shooting and said that the gun-like noise that the men heard was likely the backfiring of the Keenans' car. At that point, Warfield reached through the driver's side window of the car and grabbed Victoria Keenan by her hair. While thus grasping Victoria, Warfield struck her arm with the butt of his gun, called her a "white bitch," and said, "Because you're white we're gonna let you live today." Warfield and the other Aryans then returned to the pickup truck and drove away. Warfield was charged with two counts of aggravated assault and exhibition of a deadly weapon during the commission of a crime. He and the prosecution ultimately reached a plea agreement whereby Warfield pleaded guilty to one count of aggravated assault and the remaining charges were dismissed. The district court imposed a unified five-year sentence with a two-year determinate term. Warfield thereafter filed a motion for reduction of the sentence pursuant to Idaho Criminal Rule 35. In the order denying this motion, the district court stated: After considering the matters presented at the motion and reassessing the original sentencing, the Court is not persuaded that defendant has abandoned his interracial philosophy and, as such, still presents a significant need to maintain the sentence as imposed for the protection of society. (Emphasis added). On appeal, Warfield submits that his racist beliefs were irrelevant to his sentencing for *39 an offense against white victims and that the district court's consideration of Warfield's racial philosophy in denying the Rule 35 motion therefore violated his rights to freedom of speech and freedom of association under the First Amendment to the United States Constitution and Article I, § 9 of the Idaho Constitution. Warfield requests a new Rule 35 hearing in which evidence of his racial beliefs will not be taken into consideration. Alternatively, Warfield argues that his sentence is excessive and that the district court therefore abused its discretion in declining to reduce the sentence on Warfield's motion. ANALYSIS A. Constitutional Issues The First Amendment to the United States Constitution, as applied to the states by the Fourteenth Amendment, prohibits government from abridging freedom of speech or the right to peaceably assemble. It has been interpreted to protect an individual's right to join groups and to associate with others holding similar beliefs. Dawson v. Delaware, 503 U.S. 159, 163, 112 S.Ct. 1093, 117 L.Ed.2d 309 (1992); Aptheker v. Secretary of State, 378 U.S. 500, 84 S.Ct. 1659, 12 L.Ed.2d 992 (1964); Holloway v. E.C. Palmer, 105 Idaho 220, 227, 668 P.2d 96, 103 (1983). These constitutional protections prohibit imposition of a criminal sentence on the basis of a defendant's abstract beliefs. Dawson, 503 U.S. at 167, 112 S.Ct. 1093; State v. Pratt, 125 Idaho 546, 562-63, 873 P.2d 800, 816-17 (1993).[1] On the other hand, "the Constitution does not erect a per se barrier to the admission of evidence concerning one's beliefs and associations at sentencing simply because those beliefs and associations are protected by the First Amendment." Dawson, 503 U.S. at 165, 112 S.Ct. 1093. The United States Supreme Court has addressed this subject in a trilogy of cases, Wisconsin v. Mitchell, 508 U.S. 476, 113 S.Ct. 2194, 124 L.Ed.2d 436 (1993); Dawson; and Barclay v. Florida, 463 U.S. 939, 103 S.Ct. 3418, 77 L.Ed.2d 1134 (1983). In Barclay, the defendant was a member of the Black Liberation Army, an organization whose apparent sole purpose was to indiscriminately kill white persons and start a race war. Barclay, in concert with others, killed a white man in furtherance of the BLA's objectives, and was consequently sentenced to death. On appeal, he contended that his sentence should be vacated because the trial judge, in explaining his sentencing decision, discussed the racial motive for the murder. The Supreme Court rejected Barclay's argument, holding that the Constitution does not prohibit consideration of elements of racial hatred in a sentencing and that the judge had not erred in finding that Barclay's desire to start a race war was relevant to several aggravating factors. Barclay, 463 U.S. at 949-50, 103 S.Ct. 3418. In Dawson, the defendant, who was white and a member of the Aryan Brotherhood, was found guilty of the murder of a white woman. In advance of the penalty hearing before the jury, the prosecution gave notice that it intended to introduce expert testimony about the origin and nature of the Aryan Brotherhood as well as evidence that Dawson had the words "Aryan Brotherhood" and a swastika tattooed on his body. Dawson argued that such evidence was inflammatory and irrelevant and would violate his First Amendment rights. Before the penalty phase began, the parties agreed that, in lieu of presentation of the proffered testimony, the jury would be read a stipulation that stated: The Aryan Brotherhood refers to a white racist prison gang that began in the 1960's in California in response to other gangs of racial minorities. Separate gangs calling themselves the Aryan Brotherhood now exist in many state prisons including Delaware. Dawson, 503 U.S. at 162, 112 S.Ct. 1093. Although Dawson agreed to the stipulation in order to avoid presentation of the expert testimony, he continued to assert that admission *40 of the stipulated facts violated the Constitution. Before the United States Supreme Court, Dawson argued that because his right to associate with the Aryan Brotherhood is constitutionally protected, admission of the evidence related to that association violated his constitutional rights. The Supreme Court found Dawson's argument to be too broad, noting that the Court had previously upheld the consideration of evidence of racial intolerance and subversive advocacy where such evidence was relevant to issues involved. Id. at 164, 112 S.Ct. 1093. Nevertheless, the Court held that admission of the stipulation in Dawson's case was error, not because it violated his constitutional rights but because "the narrowness of the stipulation left the Aryan Brotherhood evidence totally without relevance to Dawson's sentencing proceeding." Id. at 165, 112 S.Ct. 1093. The Court noted that even if the Delaware group to which Dawson belonged was racist, those beliefs had no relevance to his sentencing proceeding because the murder victim was white, like Dawson, and therefore elements of racial hatred were not involved in the killing. The Court noted that although the narrow stipulation presented no relevant evidence in Dawson's case, in many cases associational evidence would serve a legitimate purpose in showing that the defendant represents a future danger to society. As an example, the Court said that membership in an organization which endorses the killing of any identifiable group might be relevant to the question whether the defendant would be dangerous in the future, and other evidence concerning associations might be relevant in demonstrating other aggravating circumstances. Id. at 166, 112 S.Ct. 1093. Thus, although the evidence of association with a racist group was deemed improperly admitted in Dawson, the Court clearly rejected the notion that use of such evidence is unconstitutional per se. Finally, in Mitchell, the Supreme Court held that where a sentence for aggravated battery was enhanced because the defendant selected the victim on account of the victim's race, the penalty enhancement was not prohibited by the First and Fourteenth Amendments. The defendant's argument that the penalty-enhancement statute was invalid because it punished the defendant's discriminatory motive or racist beliefs was rejected. The Court held that it is permissible for governments to enhance penalties for bias-inspired conduct because such conduct is thought to inflict greater individual and societal harm. Mitchell, 508 U.S. at 487-88, 113 S.Ct. 2194. From the foregoing decisions we glean a rule that, while the First Amendment protects an individual's right to speak and to associate with others of like beliefs, it does not prohibit consideration of a defendant's racial animus in structuring a sentence if the evidence is relevant to legitimate sentencing issues. Applying this rule in Warfield's case, we conclude that no constitutional violation occurred. Warfield was a member of the Aryan Nations and was serving as a security guard at the organization's compound when this offense occurred. The white supremacist beliefs espoused by that organization have been highly publicized and are well known in the area where this offense occurred. Although the victims in this case are white, and therefore racial bias was apparently not a motive in the assault,[2] Warfield's statement to Victoria Keenan that she would be allowed to live "because you're white" conveys a chilling implication that if the Keenans had been members of a racial minority, they might have been killed. Thus, Warfield's racist belief system was relevant in assessing the danger he presents to society, a factor that is unquestionably legitimate for consideration by a sentencing court. At the hearing on his Rule 35 motion, in an effort to persuade the court to reduce his sentence, Warfield presented evidence that he had severed his ties with the Aryan Nations and had become racially tolerant. The district court's expression of doubt that Warfield had "abandoned his interracial philosophy," indicated that the court was not persuaded by such evidence and that the court believed Warfield still harbored racist beliefs which could cause him to pose a threat to *41 society. This was a permissible consideration and did not violate Warfield's constitutional rights of free speech or free association. B. Reasonableness of Sentence Warfield also contends that his sentence is excessive and that the district court therefore abused its discretion in denying his Rule 35 motion for reduction of the sentence. A motion under Rule 35 is essentially a request for leniency and is committed to the discretion of the sentencing court. State v. Lopez, 106 Idaho 447, 450, 680 P.2d 869, 872 (Ct.App.1984). On appeal, our criteria for review of rulings on Rule 35 motions are the same as those applied in determining whether the original sentence was reasonable. Id. Where a sentence is not illegal, the defendant bears the burden of showing that it is unreasonably harsh in light of the primary objective of protecting society and the related goals of deterrence, rehabilitation and retribution. State v. Broadhead, 120 Idaho 141, 145, 814 P.2d 401, 405 (1991), overruled on other grounds by State v. Brown, 121 Idaho 385, 825 P.2d 482 (1992); State v. Toohill, 103 Idaho 565, 568, 650 P.2d 707, 710 (Ct.App.1982). Our focus on review is upon the nature of the offense and the character of the offender. State v. Reinke, 103 Idaho 771, 772, 653 P.2d 1183, 1184 (Ct. App.1982). For purposes of appellate review, we consider the minimum period of confinement to be the probable duration of incarceration. Broadhead, 120 Idaho at 146, 814 P.2d at 405; State v. Sanchez, 115 Idaho 776, 777, 769 P.2d 1148, 1149 (Ct.App.1989). The record here does not demonstrate that Warfield's sentence is excessive. His crime was extremely serious; Warfield drove a vehicle in pursuit of the Keenans while his confederates shot at the Keenans. The gunfire could have led to the death of one or both of the Keenans. In light of the violent nature of this offense, we perceive no abuse of discretion in the denial of Warfield's motion for reduction of his sentences. The district court's order denying Warfield's motion for reduction of his sentence is affirmed. Chief Judge SCHWARTZMAN and Judge PERRY concur. NOTES [1] Because Warfield has not argued that Article I, § 9 of the Idaho Constitution affords greater protections than the First Amendment, we will not separately address the state constitutional claim. See State v. Ross, 129 Idaho 380, 381, 924 P.2d 1224, 1225 (1996); State v. Jordan, 122 Idaho 771, 772 n. 2, 839 P.2d 38, 39 n. 2 (Ct. App.1992). [2] It is not apparent from the record whether Warfield and his confederates could discern that the Keenans were white while the Aryans were pursuing and shooting at the Keenans' vehicle. | Low | [
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Filed 3/25/19 CERTIFIED FOR PUBLICATION IN THE COURT OF APPEAL OF THE STATE OF CALIFORNIA SECOND APPELLATE DISTRICT DIVISION FOUR GEORGE ZAKK, B284432 Plaintiff and Appellant, (Los Angeles County Super. Ct. No. BC619933) v. VIN DIESEL et al., Defendants and Respondents. APPEAL from a judgment of the Superior Court for Los Angeles County, John P. Doyle, Judge. Affirmed in part and reversed in part. Hamrick & Evans, Martin J. Barab, Jonathan D. Dutton and A. Raymond Hamrick, III, for Plaintiff and Appellant. Freedman + Taitelman, Sean M. Hardy and Bryan J. Freedman for Defendants and Respondents Vin Diesel and One Race Films, Inc. Manatt, Phelps & Phillips, John M. Gatti, Katrina Dela Cruz and Benjamin G. Shatz for Defendant and Respondent Revolution Studios. This case involves a dispute over whether plaintiff and appellant George Zakk is entitled to be paid and receive an executive producer credit for a film that is a sequel to a film he had worked on and developed. Zakk sued defendants Vin Diesel, One Race Films, Inc., and Revolution Studios1 for breach of an oral contract, breach of an implied- in-fact contract, intentional interference with contractual relations, quantum meruit, promissory estoppel, and declaratory relief. His case was dismissed after the trial court sustained defendants’ demurrers to Zakk’s third amended complaint. The primary bases for the trial court’s ruling were its findings that the third amended complaint was a sham pleading and that the breach of oral contract claim (and its derivative claims) were barred by the statute of frauds. In addition, the court found that Zakk’s quantum meruit claim was barred by the statute of limitations, and it dismissed his claim for promissory estoppel because it was added without leave of court. With regard to oral contracts that fall within the statute of frauds category of contracts not to be performed within a year, we hold that the promisee’s full performance of all of his or her obligations under the contract takes the contract out of the statute of frauds, and no further showing of estoppel is required. We distinguish cases involving other categories of contracts within the statute of frauds, such as contracts to make a will or contracts not to be performed within the promisor’s lifetime, because those categories of contracts historically have been 1 We will refer to Vin Diesel and One Race Films, Inc. collectively as Diesel/One Race, and to all defendants collectively as defendants. 2 treated differently than contracts not to be performed within a year. Therefore, we conclude that to the extent those cases hold that avoidance of the statute of frauds requires the promisee to satisfy the elements of estoppel--showing extraordinary services by the promisee or unjust enrichment by the promisor--they do not apply to the category of contracts not to be performed within a year. Here, Zakk’s allegation that he fully performed his obligations under the alleged oral contract at issue is enough to avoid the statute of frauds. Therefore, in finding that Zakk’s breach of contract and related claims were barred by the statute of frauds absent alleged facts showing defendants were estopped to assert the statute, the trial court erred. We also conclude the trial court erred in finding the third amended complaint was a sham pleading, and that the statute of limitations barred his quantum meruit claim. However, we conclude the trial court did not abuse its discretion in dismissing the promissory estoppel claim. Accordingly, we affirm the judgment to the extent it dismisses Zakk’s promissory estoppel claim and reverse the judgment as to his remaining claims. BACKGROUND Because this appeal raises the question whether the third amended complaint was a sham pleading, we must discuss each version of the complaint, the demurrers, and the rulings on the demurrers in some detail to give some context to our analysis of that issue. In accordance with the standard of review, we treat the facts alleged in the 3 complaints as true for the purposes of this appeal. (Thaler v. Household Finance Corp. (2000) 80 Cal.App.4th 1093, 1098.) A. Original Complaint 1. Allegations Zakk filed the original complaint in this case on May 10, 2016. It asserted four causes of action--breach of contract, breach of implied-in- fact contract, declaratory relief, and intentional interference with contractual relations--based upon his assertion that he was entitled to receive an executive producer credit and a $275,000 executive producing fee for the sequel to a film entitled xXx. The complaint alleged as follows. Vin Diesel is an actor, producer, and director. Diesel founded One Race, a production company, in or about 1995; it was incorporated in March 2001. Zakk ran One Race from its inception, and was responsible for developing projects and managing them to conclusion. Zakk did not receive a salary, reimbursement for expenses, or any other compensation for his daily work. Instead, he “had an oral and/or implied-in-fact agreement with DIESEL and ONE RACE FILMS which provided that for each motion picture in which (a) DIESEL would star in and act in the capacity as producer in and (b) ZAKK helped develop and/or worked on while running the operations of ONE RACE FILMS, including sequels based thereon, ZAKK would, unless otherwise agreed, receive the following: [¶] (a) A fee that ranged from $250,000 to $275,000; and [¶] (b) An Executive Producer or Producer credit on screen and in promotional materials on a Most Favored Nation (MFN) 4 basis with other Executive Producers or Producers (depending on whether ZAKK received an Executive Producer or Producer credit on the motion picture).” The complaint alleged “there is a considerable amount of precedent which evidences ZAKK’s oral and/or implied-in-fact agreement with DIESEL and ONE RACE FILMS,” and listed six original films and one sequel for which he was paid and given executive producer or co-producer credit. The first film, Strays, was produced in 1997; the last original film listed, Find Me Guilty, was produced in 2006. The one sequel listed, Riddick (which was a sequel to the 2004 original film, The Chronicles of Riddick) was produced in 2013; Zakk received an executive producer fee and credit for the sequel even though his relationship with Diesel and One Race had terminated in 2007. With regard to the film xXx, which was produced in 2002, the complaint alleged: “ZAK worked on and helped develop xXx. Accordingly, with respect to xXx and any sequel of xXx which would be starring and produced by DIESEL, Defendants DIESEL, ONE RACE FILMS, and/or REVOLUTION STUDIOS (the production company) agreed to provide ZAKK with an Executive Producer credit and $275,000 executive producing fee in exchange for his services.” The complaint further alleged that defendants were currently in production of a sequel to xXx, entitled xXx: The Return of Xander Cage, starring Diesel, which was directly based upon the original film and was set to be released on January 20, 2017. 5 In the first cause of action for breach of oral contract, the complaint alleged that “[i]n exchange for ZAKK’s work on the original xXx, ZAKK, on the one hand, and DIESEL, ONE RACE FILMS, and/or REVOLUTION STUDIOS, on the other entered into an oral agreement which provided that ZAKK would receive the following as respects the xXx Sequel: [¶] (a) An Executive Producer fee of $275,000; and [¶] (b) An Executive Producer credit on screen and in promotional materials on a Most Favored Nation basis with other Executive Producers (e.g., same size print and card).” It alleged that Zakk had “performed all material conditions, covenants, obligations and promises required on [his] part to be performed in accordance with the oral agreement except for those conditions, covenants, obligations and promises that have been waived, excused, rendered impossible and/or prevented by Defendants,” and that Diesel, One Race, and/or Revolution breached the agreement by refusing to pay Zakk his fee or provide him with an executive producer credit. The second cause of action, for breach of implied-in-fact contract (which was alleged only against Diesel and One Race), alleged that by reason of the practices and conduct as described in the complaint there existed an implied-in-fact agreement between Zakk and Diesel/One Race pursuant to which Zakk was entitled to an executive producer fee of $275,000 and an executive producer credit for the xXx sequel. This cause of action included the same performance and breach allegations as alleged in the breach of oral contract cause of action. The third cause of action, for declaratory relief, alleged there was an actual dispute between Zakk and defendants concerning their rights 6 and duties with respect to the xXx sequel. It sought a declaration that Zakk is entitled to an executive producer fee of $275,000 and executive producer credit for the xXx sequel. The fourth cause of action, for intentional interference with contractual relations (only against Revolution), alleged that, to the extent Revolution is not found to have entered into the oral contract with respect to the xXx sequel, it knew of the oral and/or implied-in-fact contract between Zakk and Diesel/One Race. The complaint alleged that Revolution’s conduct prevented, or made more expensive or difficult, Diesel/One Race’s performance of the contract, that Revolution intended to disrupt the performance of the contract or knew that disruption was certain or substantially certain to occur, and that Revolution’s conduct was a substantial factor in causing Zakk damage. 2. Demurrer Diesel/One Race filed a demurrer to the complaint. They argued that all causes of action were barred by the two-year statute of limitations found in Code of Civil Procedure section 339(1), and that the complaint failed to allege facts sufficient to state any cause of action. With regard to the statute of limitations, Diesel/One Race noted that in all of his causes of action, Zakk was seeking to recover compensation for his personal services. They observed that Zakk’s services related to the original xXx film “were completely performed by 2002” and that he alleged that he stopped providing services to One Race in 2007. Thus, they argued that because the statute of limitations for oral or implied-in-fact contracts for personal services begins to run 7 when those services end, Zakk’s claims expired in 2004 (if based upon the completion of services related to the original xXx film) or 2009 (if based upon the completion of all services to One Race). Diesel/One Race also argued that Zakk failed to alleged facts sufficient to state a breach of oral contract claim because (1) the alleged contract was fatally uncertain and (2) the alleged contract was barred by the statute of frauds. With regard to the first ground, Diesel/One Race asserted that the alleged contract was uncertain because “[i]t is uncertain who the parties are. It is uncertain what the respective obligations of the parties are. It is even uncertain whether [Zakk] has alleged one contract or several and under which contract(s) his claims arise.” With regard to the statute of frauds, Diesel/One Race argued that the alleged oral agreement by its terms was not to be performed within a year from its making and therefore was barred under Civil Code section 1624, subdivision (a)(1). Finally, Diesel/One Race contended that (1) Zakk’s breach of implied-in-fact contract cause of action failed to state a claim because an action based on an implied-in-fact contract cannot lie where there exists an express contract covering the same subject, and Zakk alleged both a valid express contract and an implied-in-fact contract; and (2) Zakk’s cause of action for declaratory relief failed because it did not allege an justiciable controversy, but instead alleged an accrued cause of action for an actual breach. 8 3. Ruling The trial court sustained in part the demurrer, and granted leave to amend. The court rejected Diesel/One Race’s statute of limitations argument. It observed that the statute begins to run on a breach of contract cause of action when the contract is repudiated, and the complaint did not allege when that repudiation took place. The court agreed in part with Diesel/One Race’s uncertainty argument. It found the complaint was unclear about whether the alleged agreement provided that Zakk was to be paid and credited for sequels even if he did not develop or work on the sequel. It noted if that were the case, Diesel/One Race’s assertion of the statute of frauds would be proper. Therefore, it sustained the demurrer to the breach of oral contract cause of action on the ground of uncertainty. The court also agreed with Diesel/One Race’s argument that Zakk could not assert breach of both an implied-in-fact contract and an express contract covering the same subject matter, and sustained the demurrer to the breach of implied-in-fact contract claim on that ground. In doing so, however, it acknowledged that Zakk could assert both claims in the alternative. Finally, the court sustained the demurrer to Zakk’s declaratory relief claim because it only concerned an accrued claim and did not seek prospective relief by way of a declaration of rights. 9 B. First Amended Complaint 1. Allegations Zakk filed a first amended complaint with the following changes and additions. First, where Zakk had alleged an “oral and/or implied-in-fact agreement” in the original complaint, the first amended complaint alleged an “oral or implied-in-fact agreement.” The first amended complaint also did not incorporate by reference in his breach of implied- in-fact cause of action the allegations of his breach of oral contract cause of action (those allegation had been incorporated in the original complaint). Second, Zakk added allegations regarding the alleged contract in an attempt to clear up any uncertainty. He alleged that under the contract he “was to be paid and credited for all sequels to motion pictures that (a) DIESEL would star in and (b) ZAKK helped develop and/or worked on the original picture upon which the sequel is based, regardless of whether ZAKK helped develop or work on such sequels.” Zakk also alleged that “[b]y virtue of the services that ZAKK provided in connection with xXx (i.e., working on the picture and helping to develop it), ZAKK fully performed all of his obligations under the oral or implied-in-fact agreement that ZAKK had with DIESEL and ONE RACE FILMS, thereby entitling ZAKK to an Executive Producer credit and $275,000 executive producing fee with respect to any sequel of xXx which DIESEL would star in, regardless of whether ZAKK helped develop or work on such sequels.” In addition, Zakk specifically alleged an oral contract with Revolution with regard to xXx and any 10 sequel starring Diesel, and that he fully performed all of his obligations under that oral agreement.2 Zakk also included some additional language to his allegation regarding the payment and producing credit he received for the sequel to The Chronicles of Riddick. Thus, he alleged: “For example, in 2013, in exchange for the services that ZAKK provided (work and development) in connection with The Chronicles of Riddick (released in 2004), ZAKK received an Executive Producer fee and credit for the sequel to The Chronicles of Riddick--i.e., the motion picture entitled, Riddick (released in 2013).” (Additional language underlined.) In addition, Zakk made a slight addition to his allegation of performance in his breach of oral contract and breach of implied-in-fact contract causes of action, presumably to address the trial court’s comments regarding the statute of frauds. He added the word “fully” to both allegations, so the allegations stated that he “has fully performed” all his obligations except for those “that have been waived, excused, rendered impossible and/or prevented by Defendants.” Finally, Zakk amended his declaratory relief cause of action to allege that a controversy had arisen concerning the rights and duties 2 Those allegations stated: “17. In exchange for the services that ZAKK provided in connection with xXx as alleged herein, REVOLUTION STUDIOS (the production company for xXx) also orally agreed to provide ZAKK with an Executive Producer credit and $275,000 executive producing fee with respect to any sequel of xXx which DIESEL would star in, regardless of whether ZAKK helped develop or work on such sequels. [¶] 18. By virtue of the services that ZAKK provided in connection with xXx as alleged herein, ZAKK fully performed all of his obligations under his oral agreement with REVOLUTION STUDIOS.” 11 with respect to “sequels to motion pictures that (a) DIESEL will star in and (b) ZAKK helped develop and/or worked on the original picture upon which the sequel is based.” He alleged that he contends and seeks a declaration that for each such sequel he is entitled to a fee equal to the fee he received in connection with the film upon which the sequel is based, as well as an executive producer or producer credit (depending upon whether he received an executive producer or producer credit on the original film).3 2. Demurrers Diesel/One Race and Revolution each filed a demurrer to the first amended complaint. In their demurrer, Diesel/One Race asserted that the statute of frauds barred Zakk’s breach of oral contract claim because it could not be performed within one year and Zakk did not plead any facts to support an exception to the statute or estoppel to assert the statute. They also argued that that claim failed on the merits because there was no breach, since the xXx sequel had not yet been completed and released. They contended that the cause of action for breach of implied- in-fact contract failed for the same reasons the breach of oral contract failed, and because no such claim can lie where there is a valid express contract. Finally, they argued the declaratory relief claim failed 3 We note that Zakk did not make any change to the prayer for relief as to the declaratory relief cause of action, so that the prayer still sought a declaration only as to the xXx sequel. 12 because (a) it sought declaratory relief that was duplicative of the breach of oral contract claim; (b) it sought declaratory relief concerning Revolution, which was a party to only one alleged oral contract with Zakk, i.e., with regard to xXx and its sequel; and (c) there was no actual controversy concerning sequels that are wholly speculative. In its demurrer, Revolution also argued that the statute of frauds barred Zakk’s breach of oral contract claim, and that the declaratory relief claim failed because there was no existing actual controversy regarding speculative sequels. It also contended that the breach of oral contract claim failed because the first amended complaint did not include any specific allegations regarding the existence of the contract and thus was uncertain, nor did it include facts regarding the formation of the contract or consideration for the contract. Finally, it challenged the intentional interference with contractual relations claim (which was alleged only against Revolution) on two grounds: (1) the first amended complaint did not plead sufficient facts to show the existence of a valid contract and intentional wrongful acts to interfere with any contract; and (2) the claim was factually inconsistent with Zakk’s allegations that Revolution entered into an oral agreement with him. 3. Ruling The trial court sustained both demurrers with leave to amend. The court found that the alleged agreement--which the court identified as an agreement “for Plaintiff to be paid and credited for sequels merely because Plaintiff had developed or worked on the original films even if Plaintiff did not develop or work on the sequels”--was subject to the 13 statute of frauds because it was not to be performed within a year, since there was no definitive time for the agreement to terminate. (Citing Tostevin v. Douglas (1958) 160 Cal.App.2d 321, 328 (Tostevin).) The court rejected Zakk’s argument that his allegation that he fully performed his obligations under the agreement was sufficient to defeat the statute of frauds bar; the court found that Zakk must also allege facts sufficient to establish an estoppel to assert the statute. Although the court concluded that its finding regarding the statute of frauds applied to all causes of action alleged in the complaint because all of them were derivative of the contract claims, it also addressed defendants’ other arguments. It rejected Diesel/One Race’s and Revolution’s arguments regarding the purported insufficiency of the allegations to support the breach of oral contract, breach of implied-in- fact, and declaratory relief causes of action. The court agreed, however, with Revolution’s argument regarding the inadequacies of the allegations of intentional interference with contractual relations, and sustained Revolution’s demurrer to that cause of action on this ground (as well as on the statute of frauds ground). C. Second Amended Complaint 1. Allegations Zakk filed the second amended complaint on December 7, 2016. The only differences between the first amended complaint and the second amended complaint were found in three paragraphs: one in the background and general allegations section and two in the fourth cause of action for interference with contractual relations. 14 In the background and general allegations section, Zakk updated one paragraph to state that defendants “have recently produced a sequel to the original xXx, which was produced in 2002,”4 and added factual allegations to establish estoppel to assert the statute of frauds. Among the facts alleged were that Zakk “fully performed all of his obligations under the alleged agreement,” that his “performance as respects xXx was directly induced” by defendants’ promise to provide him a producer fee and credit for any sequel starring Diesel, and that he “agreed to accept substantially less than what his services were worth in connection with his creating and developing the xXx film franchise based specifically” on defendants’ promise with regard to any sequel starring Diesel. In the intentional interference cause of action, Zakk added an allegation naming an individual at Revolution who knew about the oral agreement and its terms, and added additional language to another paragraph about Revolution’s conduct that prevented Diesel/One Race’s performance of the oral agreement. 2. Demurrers Once again, Diesel/One Race and Revolution each filed a demurrer to the second amended complaint. In their demurrer, Diesel/One Race argued that the alleged contracts were barred by the statute of frauds, and that Zakk failed to 4 The first amended complaint had alleged that defendants “are now in production of a sequel to xXx.” 15 plead facts to support any exception to the statute of frauds. They contended that estoppel did not apply under the circumstances of this case because the rendition of personal services compensable in quantum meruit is an insufficient basis for estoppel, and because Zakk cannot claim that his personal services in connection with the original xXx film clearly related to the alleged contract regarding a speculative sequel. Finally, Diesel/One Race challenged the declaratory relief claim on the same grounds as previously asserted. Revolution argued in its demurrer that the breach of oral contract claim was barred by the statute of frauds because Zakk did not allege facts sufficient to show that he would suffer an unconscionable injury, or that defendants would be unjustly enriched if the statute of frauds were applied. Revolution also argued that the declaratory relief claim failed because the underlying contract was barred by the statute of frauds, and that the intentional interference claim failed because Zakk did not allege facts sufficient to establish a valid contract or intentional wrongful acts by Revolution. 3. Ruling Once again, the trial court sustained the demurrers with leave to amend. It found that Zakk’s allegations that he was not fully compensated for his work on the original xXx film were insufficient to allege estoppel to assert the statute of frauds because he failed to allege facts showing that he provided services of an extraordinary or exceptional character. The court explained, “[s]tated differently, Plaintiff fails to allege facts why estoppel should be applied to permit 16 enforcement of the alleged contract instead of Plaintiff being required to pursue a quantum meruit claim.” Based upon this finding, the court sustained the demurrers to all causes of action, but granted Zakk leave to amend, including leave to add an alternative quantum meruit claim. Although the court found that all causes of action were barred by the statute of frauds, it also specifically addressed, and rejected, Revolution’s argument that Zakk failed to allege sufficient facts to state a claim for intentional interference with contractual relations. D. Third Amended Complaint 1. Allegations Sometime after Zakk filed his second amended complaint in December 2016, he received documents he had requested in requests for production that he had propounded at the inception of the lawsuit (which was filed in May 2016). One of those documents was a letter that Zakk contended constituted a written agreement or memorandum evidencing the terms of the alleged oral contract at issue, although one of those terms was somewhat different than the term he previously had alleged. He filed a third amended complaint that included several significant, and some less significant, changes from the previous complaints; many of those changes appear to be the result of Zakk’s receipt of this discovery. The changes are as follows. First, the third amended complaint added an introductory paragraph setting forth the nature of the action. It stated that the action arises out of defendants’ “wrongful and unjustified refusal to credit and compensate . . . ZAKK, as agreed,” for his services provided 17 to them “in connection with the xXx film franchise--a film franchise which ZAKK was instrumental in creating, developing, and bringing to fruition.” Second, the description of the nature of Zakk’s relationship with One Race was slightly modified in the third amended complaint. Whereas the previous complaints alleged that Zakk ran and/or managed One Race, the third amended complaint alleged that he “worked for” One Race. Third, the third amended complaint alleged that Zakk and Diesel/One Race entered into several different oral or implied-in-fact agreements--i.e., a different agreement for each film that Diesel starred in and Zakk worked on and/or helped develop. The complaint alleged that those agreements “generally provided” that for each film, Zakk would receive “[a] fee that ranged from approximately $200,000 to $275,000,” and an executive producer or producer credit. With regard to the xXx film, the complaint alleged that Diesel/One Race and Revolution agreed that, in exchange for Zakk’s services on the original xXx film, Zakk would receive compensation of at least $200,000 and no less than 125 percent of his then current quote, and executive producer credit on the xXx sequel starring Diesel. Fourth, the third amended complaint alleged that the agreement with respect to xXx was memorialized in a writing signed by Diesel’s agent and Revolution’s agent. The complaint also included alleged language from that letter. Fifth, the third amended complaint included additional allegations to support Zakk’s position that the alleged agreement was 18 not barred under the statute of frauds. Those allegations included allegations (1) that Zakk “was instrumental in creating, developing, and bringing the xXx film franchise to fruition,” and that the services he performed in connection with that franchise “were extraordinary and of an exceptional character in that, among other things, no one else could have performed [them]”; and (2) that the alleged oral or implied-in-fact agreement was an at-will agreement that could have been terminated at any time before Zakk fully performed his services in connection with the original xXx film. Finally, the third amended complaint added two causes of action, one for quantum meruit and one for promissory estoppel. The quantum meruit cause of action alleged that defendants requested that Zakk perform services for their benefit in connection with the xXx film franchise and promised to pay Zakk the reasonable value of those services (which is alleged to be no less than $2 million), and that Zakk performed those services. The complaint alleged that within the past two years Zakk requested that defendants pay him the reasonable value of the services that he performed in connection with the xXx sequel, but they refused to do so. The promissory estoppel cause of action alleged that defendants promised Zakk that in exchange for the services he provided in connection with the original xXx film, Zakk would receive in connection with the xXx sequel the compensation and credit alleged, that defendants have not performed any part of their promise, and as a result of Zakk’s reasonable reliance upon defendants’ promises he has suffered substantial monetary damages. 19 2. Demurrers Diesel/One Race and Revolution each filed a demurrer to the third amended complaint, as well as a motion to strike the promissory estoppel cause of action and a request for judicial notice of (among other things) the document the complaint alleged memorialized the purported oral agreement.5 In their demurrer, Diesel/One Race argued that the third amended complaint was a sham pleading because (1) it alleged several different oral or implied-in-fact agreements rather than a single agreement; and (2) it contradicted the previously-alleged facts that Zakk generally was to be paid a fee ranging from $250,000 to $275,000, and that he was to be paid $275,000 for the xXx sequel, by now alleging that he generally was to be paid a fee ranging from $200,000 to $275,000, and was to be paid at least $200,000 and no less than 125 percent of his then current quote for the xXx sequel. Diesel/One Race also argued that Zakk’s amendments failed to cure the previously-identified defects with regard to application of the statute of frauds, and that the writing identified in the third amended complaint was insufficient to take the alleged oral agreement out of the statute of frauds. With regard to the writing, Diesel/One Race asserted that it not only directly contradicted the terms of the agreement alleged in the earlier complaints, but that Zakk misrepresented the actual 5 The document at issue, which was produced under a protective order, was filed under seal. 20 language of the letter (of which Diesel/One Race asked the court to take judicial notice). Finally, Diesel/One Race challenged the newly-added causes of action for quantum meruit and promissory estoppel. They contended that the quantum meruit cause of action was barred by the two-year statute of limitations. They argued that the statute begins to run on a quantum meruit claim alleging a promise to pay for personal services when those services are terminated. Thus, because Zakk’s services on the original xXx film terminated in 2002, the statute of limitations expired in 2004. With regard to the promissory estoppel cause of action, Diesel/One Race’s challenge was two-fold. They contended it was improperly added without leave of court (which was the basis of their motion to strike), and they argued that it failed on the merits as a matter of law. Revolution made similar arguments in its demurrer. It argued (in a footnote) that the third amended complaint was a sham pleading because it changed the amount of the fee he was to receive for the xXx sequel under the alleged contract; it did not argue that the change in the number of contracts alleged rendered the complaint a sham pleading. It contended that the complaint failed to allege sufficient facts to support estoppel to assert the statute of frauds. It also asserted that the alleged writing was insufficient to take the oral agreement out of the statute of frauds, and that the complaint mischaracterized the 21 writing.6 And, like Diesel/One Race, it argued the quantum meruit cause of action was barred by the statute of limitations, and challenged the promissory estoppel cause of action on the merits and on the ground that Zakk was not given leave to amend to allege such a claim. 3. Ruling Over Zakk’s objection, and following additional briefing and a separate hearing on the issue, the trial court granted defendants’ requests for judicial notice of the alleged writing. The court then sustained defendants’ demurrers without leave to amend. The court found that the third amended complaint was a sham pleading because it alleged there were multiple oral contracts, as opposed to one contract as previously alleged.7 It observed that 6 As noted, Revolution also asked the trial court to take judicial notice of the document referenced in the complaint. In its request for judicial notice, Revolution submitted two versions of the document; one was identical to the one submitted by Diesel/One Race (except for the Bates number), and the other was that same document with handwritten notations on it. 7 At oral argument, counsel for Revolution asserted that the trial court also found that the third amended complaint was a sham pleading because it changed the allegation regarding the amount of compensation Zakk was to receive for the xXx sequel. That is not correct. In its ruling, the court stated: “Defendants contend that the demurrer should . . . be sustained because the [third amended complaint] is a sham pleading. Specifically, Defendants assert that the [third amended complaint] (1) now alleges the existence of multiple oral contracts . . . and (2) alleges different compensation . . . . [¶] The Court agrees in part. The allegation that [Zakk] entered into several contracts, as opposed to one contract as previously alleged . . . is clearly an attempt by [Zakk] to engineer the [third amended complaint] to escape the reaches of a demurrer.” (Italics added.) The court then discussed only the 22 “Plaintiff consistently alleged the existence of one oral or implied-in-fact contract, but suddenly, and without reference to any reason for the change, asserts the existence of multiple contracts.” The court found that this change was “clearly an attempt by Plaintiff to engineer the [third amended complaint] to escape the reaches of a demurrer,” and concluded that this was a sufficient basis to sustain the demurrer or strike the complaint. In addition, the court found that the writing quoted in the third amended complaint was insufficient to take the alleged oral contract out of the statute of frauds and, for the reasons stated in its rulings on the prior demurrers, that the complaint failed to allege facts sufficient to establish an estoppel to assert the statute. Finally, the court found that the quantum meruit cause of action was barred by the statute of limitations, which began to run in 2002, when Zakk performed the services on the original xXx film, and it sustained the demurrer to the promissory estoppel cause of action on the ground that it was added without leave of the court.8 The court entered a judgment of dismissal, from which Zakk timely filed a notice of appeal. allegation of multiple contracts, thus impliedly rejecting the other ground defendants asserted. 8 On the day of the hearing on the demurrer, Zakk filed fictitious name amendments to the complaint to add One Race Productions, Inc.; Revolution Production Services, LLC; and Revolution Films. The trial court ordered them stricken without prejudice. 23 DISCUSSION Zakk raises several contentions on appeal, only some of which we will need to address. He contends the trial court erred in finding that the third amended complaint was a sham pleading, erred in finding that the breach of oral contract, breach of implied-in-fact contract, intentional interference with contractual relations, and declaratory relief claims (collectively, the contract claims) were barred by the statute of frauds, erred in finding that the quantum meruit claim was barred by the statute of limitations, and abused its discretion in dismissing the promissory estoppel claim. We agree as to all but the dismissal of the promissory estoppel claim. In light of that, we need not address Zakk’s contentions regarding the trial court’s granting defendants’ requests for judicial notice, refusal to consider Zakk’s offer of proof made with respect to those requests, and his request for leave to amend.9 A. Standard of Review Governing Judgment Sustaining Demurrers “On appeal from a judgment sustaining a demurrer to a complaint the allegations of the complaint must be regarded as true. The court must, in every stage of an action, disregard any defect in the pleadings which does not affect the substantial rights of the parties. [Citation.] Pleadings must be reasonably interpreted; they must be read as a whole 9 Zakk also challenges the trial court’s ruling striking his fictitious name amendments, which were filed the day of the hearing on the demurrers to the third amended complaint. We need not address this issue because that ruling was without prejudice, so Zakk is not precluded from filing the amendments when the matter is remanded to the trial court. 24 and each part must be given the meaning that it derives from the context wherein it appears. . . . In determining whether the complaint is sufficient as against the demurrer on the ground that it does not state facts sufficient to constitute a cause of action, the rule is that if on consideration of all the facts stated it appears the plaintiff is entitled to any relief at the hands of the court against the defendants the complaint will be held good although the facts may not be clearly stated, or may be intermingled with a statement of other facts irrelevant to the cause of action shown, or although the plaintiff may demand relief to which he is not entitled under the facts alleged. In passing upon the sufficiency of a pleading, its allegations must be liberally construed with a view to substantial justice between the parties. While orderly procedure demands a reasonable enforcement of the rules of pleading, the basic principle of the code system in this state is that the administration of justice shall not be embarrassed by technicalities, strict rules of construction, or useless forms.” (Gressley v. Williams (1961) 193 Cal.App.2d 636, 638-639.) B. Sham Pleading Under the sham pleading doctrine, “[i]f a party files an amended complaint and attempts to avoid the defects of the original complaint by either omitting facts which made the previous complaint defective or by adding facts inconsistent with those of previous pleadings, the court may take judicial notice of prior pleadings and may disregard any inconsistent allegations.” (Colapinto v. County of Riverside (1991) 230 Cal.App.3d 147, 151.) Where no explanation for an inconsistency is 25 offered, the trial court is entitled to conclude that the pleading party’s cause of action is a sham and sustain a demurrer without leave to amend. (Amid v. Hawthorne Community Medical Group, Inc. (1989) 212 Cal.App.3d 1383, 1390-1391.) As noted, Diesel/One Race argued in their demurrer to the third amended complaint that the complaint was a sham pleading for two reasons: it alleged there were multiple contracts (one for each film) rather than a single contract (applicable to all films), and it changed the range of compensation Zakk was to receive for sequels generally and the compensation for the xXx sequel specifically. (In its demurrer, Revolution argued, in a footnote, only the latter.) The trial court rejected Diesel/One Race’s second (and Revolution’s only) reason, finding that the third amended complaint was a sham pleading solely because it asserted that there were several oral contracts, whereas the prior complaints “consistently alleged the existence of one oral or implied-in-fact contract.”10 On appeal, Zakk contends the trial court’s finding was erroneous because the original, first amended, and second amended complaints 10 The trial court’s rejection of defendants’ argument that the amendment to change the compensation term was proper. As Zakk explained in his oppositions to the demurrers, he amended the compensation term due to his recent receipt of discovery, including the written memorandum that allegedly set forth the compensation he was to receive for any xXx sequel. In light of the many years that had passed from the time he entered into the alleged agreement and the time he filed this lawsuit, the change in the allegation does not “‘carr[y] with it the onus of untruthfulness.’” (Berman v. Bromberg (1997) 56 Cal.App.4th 936, 946.) Rather, it simply reflects a faulty recollection. 26 consistently had alleged multiple oral contracts. We conclude that although the allegations in the prior iterations of the complaint were not as clear as the third amended complaint with regard to alleging multiple oral contracts, we agree that taken in context, the prior versions did allege more than one contract. There is no question that the prior versions of the complaint alleged a single overarching oral or implied-in-fact contract in which Diesel/One Race agreed that “for each” film that Diesel starred in and Zakk helped to develop and/or worked on, Zakk would receive a producer or executive producer fee and credit. Nor is there any question that the third amended complaint no longer alleges that overarching contract, and instead alleges there were separate oral or implied-in-fact contracts for each film. But read in context, the allegations of the overarching contract in the prior complaints implied it was a contract to enter into separate contracts with respect to each film, because it alleged a range of compensation and credits. Thus, it implied that the exact fee and credit Zakk would receive had to be agreed upon for each film. In other words, there would be a separate agreement for each film with the same general terms as alleged in the overarching contract, but with the specific compensation and credit to be given for that film. That this is a plausible interpretation of the allegations of the prior complaints was implicitly acknowledged by Diesel/One Race in their demurrer to the original complaint, when they asserted the complaint was uncertain because, among other things, it was “uncertain whether [Zakk] has alleged one contract or several[,] and under which contract(s) his claims arise.” 27 But even if the prior complaints did not impliedly allege separate contracts for every one of the films that Zakk helped develop and/or worked on, there is no question that each of the previous versions of the complaint expressly alleged an oral or implied-in-fact contract specifically with respect to the xXx film and its sequel. For example, in the original complaint, Zakk alleged in paragraph 15: “That picture [i.e., Strays, produced in 1997] was followed in 2002 with xXx. ZAKK worked on and helped develop xXx. Accordingly, with respect to xXx and any sequel of xXx which would be starring and produced by DIESEL, Defendants DIESEL, ONE RACE FILMS, and/or REVOLUTION STUDIOS (the production company) agreed to provide ZAKK with an Executive Producer credit and $275,000 executive producing fee in exchange for his services.” (Italics added.) In the first and second amended complaints, Zakk alleged two separate agreements with regard to xXx and its sequel, one with Diesel/One Race (in paragraph 16) and one with Revolution (in paragraph 17). Because the focus of Zakk’s complaint has been, from the start and throughout the amended complaints, on the alleged agreement with respect to xXx and its sequel, the omission from the third amended complaint of the allegation of the overarching agreement has no practical effect.11 If anything, the amended pleading merely clarifies 11 The only possible exception is the declaratory relief cause of action, because after the trial court sustained Diesel/One Race’s demurrer to that cause of action in the original complaint on the ground that it only sought a declaration as to the parties’ rights and obligations with respect to the xXx sequel, the cause of action was amended to seek a declaration of rights with regard to any qualifying sequels of films that Zakk helped develop and/or 28 the basis for Zakk’s claims for relief. Therefore the sham pleading doctrine does not apply. (Hahn v. Mirda (2007) 147 Cal.App.4th 740, 751 [“The doctrine is not intended to prevent honest complainants from correcting erroneous allegations or to prevent the correction of ambiguous facts”].) C. Statute of Frauds Zakk contends the trial court erred in finding the contract causes of action were barred by the statute of frauds. He argues the statute does not apply because (1) the third amended complaint alleged the oral contract was terminable at will, and therefore it could be performed within a year; (2) the complaint alleged he had fully performed all of his obligations under the contract; and (3) the complaint alleged a written memorandum that memorialized the oral agreement. Zakk also contends that, even if the statute of frauds applied, the third amended complaint alleged facts sufficient to establish that defendants were estopped to assert the statute of frauds. We agree that the statute of frauds does not apply under the allegations of the third amended complaint. worked on. However, given our conclusion that the allegations of the previous complaints implied that there were separate contracts with respect to each film, the third amended complaint’s omission of the allegation of an overarching contract coupled with the addition of express allegations of separate contracts for each film cannot trigger the sham pleading doctrine. 29 The statute of frauds, as memorialized in Civil Code12 section 1624, sets forth several categories of contracts that “are invalid, unless they, or some note or memorandum thereof, are in writing and subscribed by the party to be charged or by the party’s agent.” (§ 1624, subd. (a).) The defendants contend, and the trial court found, that the contract at issue in this case falls within the category described in subdivision (a)(1), i.e., “[a]n agreement that by its terms is not to be performed within a year from the making thereof.” (§ 1624, subd. (a)(1).) In finding the alleged agreement was one that was not to be performed within a year, the trial court relied upon Tostevin, supra, 160 Cal.App.2d 321. In that case, the court of appeal held that an oral contract with no termination date, in which the defendant agreed to pay the plaintiff a certain sum weekly for services in connection with a television show, was an agreement not to be performed within a year. The appellate court explained, “[s]ince it is clear from the pleadings that payment was to continue so long as the program was broadcast throughout the world, the parties must have contemplated that the continued performance of the contract was to last more than one year from the date of making, as indeed it did.” (Id. at p. 328.) Defendants contend the contract alleged in this case is similar to the contract at issue in Tostevin because it is evident that the parties intended it was to be performed over a period longer than a year, inasmuch as it covers sequels, which could not have been produced within a year. 12 Further undesignated statutory references are to the Civil Code. 30 Zakk contends that Tostevin is distinguishable because the plaintiff in that case alleged in his verified complaint that the contract at issue was to continue for “‘an indefinite period,’” while the third amended complaint in the present case alleged that the contract was an at-will contract that could be terminated at any time. (Citing Tostevin, supra, 160 Cal.App.2d at p. 326.) He argues that under the Supreme Court opinions in White Lighting Co. v. Wolfson (1968) 68 Cal.2d 336 and Foley v. Interactive Data Corp. (1988) 47 Cal.3d 654, when an alleged oral contract may be terminated at will by either party, it is capable of being performed within a year and therefore it is not within the statute of frauds. Defendants respond that those cases are not applicable here because, unlike in this case, they involved straight- forward employment contracts. We need not determine whether the contract alleged in this case was capable of being performed within a year because even if it could not, there is a different ground for concluding that the statute of frauds does not apply. Zakk contends that his allegation that he fully performed all of his obligations under the contract takes the contract out of the statute of frauds. (Citing, among other cases, Secrest v. Security National Mortgage Loan Trust 2002-2 (2008) 167 Cal.App.4th 544, 556 (Secrest) [“‘Where the contract is unilateral, or, though originally bilateral, has been fully performed by one party, the remaining promise is taken out of the statute [of frauds], and the party who performed may enforce it against the other’”], quoting 1 Witkin, Summary of Cal. Law (10th ed. 2005) Contracts, § 370, p. 414.) Defendants argue that full performance 31 by itself is not sufficient to take the contract out of the statute and that Zakk also must allege facts showing such unusual and extraordinary circumstances that the equitable doctrine of estoppel applies to bar the assertion of the statute. They are mistaken. We acknowledge that most of the cases defendants rely upon in support of their argument (and that the trial court cited in its ruling) held that the plaintiffs must show more than full performance in order to avoid the statute of frauds.13 But all but four of those cases involved oral contracts to make a will (or to devise property in a will) or contracts not to be performed during the lifetime of the promisor. (See, e.g., Day v. Greene (1963) 59 Cal.2d 404, 406 [contract to devise property in will]; Di Salvo v. Bank of America (1969) 274 Cal.App.2d 351, 353 [contract to make a will]; Dini v. Dini (1961) 188 Cal.App.2d 506, 513 [contract not to be performed during promisor’s lifetime]; Palmer v. Phillips (1954) 123 Cal.App.2d 291, 292 [contract to make a will]; Jirschik v. Farmers & Merch. Nat. Bank (1951) 107 Cal.App.2d 405 [contract to devise 13 In some of the cases defendants cite, the courts used language of estoppel in finding that the statute of frauds did not apply, but they did not hold that facts sufficient to support estoppel are required when full performance is alleged. (See, e.g., Dougherty v. California Kettleman, etc. (1937) 9 Cal.2d 58, 81 (Dougherty) [“the circumstances of this case, showing as they do complete performance by Dougherty, clearly create an estoppel to plead the statute. Dougherty’s performance was clearly induced by Ochsner’s representation that he would sign the contract. This creates an estoppel”]; Tobola v. Wholey (1946) 75 Cal.App.2d 351, 357 [“In any event, to permit appellant at this late date, when the agreement in question has been performed in its entirety by respondent, to rely on the defense of the statute of frauds would be manifestly unfair to respondent and would allow the appellant to be enriched unjustly at his expense”].) 32 property in a will]; Walker v. Calloway (1950) 99 Cal.App.2d 675, 676 [contract to devise property in will]; Baker v. Bouchard (1932) 122 Cal.App. 708, 709 [contract to devise property in a will].) Those contracts, which fall under different contract categories in the statute of frauds,14 are treated differently than contracts that fall under subdivision (a)(1) of section 1624. The section of the Restatement Second of Contracts describing the applicability of the statute of frauds on contracts not to be performed within a year states: “(1) Where any promise in a contract cannot be fully performed within a year from the time the contract is made, all promises in the contract are within the Statute of Frauds until one party to the contract completes his performance. [¶] (2) When one party to a contract has completed his performance, the one-year provision of the Statute does not prevent enforcement of the promises of other parties.” (Rest.2d, Contracts, § 130.) Comment d to this section further explains: “If either party promises a performance that cannot be completed within a year, the Statute applies to all promises in the contract, including those which can or even must be performed within a year. But unlike other provisions of the Statute, the one-year provision does not apply to a contract . . . which has been fully performed on one 14 A contract that is not to be performed during the lifetime of the promisor falls under section 1624, subdivision (a)(5). A contract to make a will or devise property in a will made before 1985 fell under former section 1624, subdivision (6); such a contract made currently is governed by Probate Code section 21700. (14 Witkin, Summary of Cal. Law (11th ed. 2017) Wills and Probate, § 358, p. 437.) 33 side, whether the performance is completed within a year or not.” (Rest.2d, Contracts, § 130, comment d, italics added.) The California Supreme Court followed this rule in Dougherty, supra, 9 Cal.2d 58 and Dutton v. Interstate Investment Corp. (1941) 19 Cal.2d 65 (Dutton). In Dougherty, the plaintiff sought to enforce against the defendant an oral contract (which was reduced to writing, but the defendant’s predecessor never signed it) in which the defendant’s predecessor agreed to pay the plaintiff, in exchange for the plaintiff’s services in locating lands and obtaining prospecting permits, a royalty in any oil or gas produced from lands embraced within the prospecting permit. (Dougherty, supra, 9 Cal.2d at p. 64.) The plaintiff located the lands and obtained the permits, but the defendant refused to pay the agreed-upon royalty. The Supreme Court rejected the defendant’s contention that enforcement of the contract was barred by the statute of frauds. The Court stated: “The fact that the agreement between Dougherty and [the defendant’s predecessor] rested in parol is of no legal significance in this case. This agreement was fully executed by Dougherty. Assuming the contract could not be performed within a year and therefore fell within the statue of frauds, the circumstances of this case, showing as they do complete performance by Dougherty, clearly create an estoppel to plead the statute. Dougherty’s performance was clearly induced by [the defendant’s predecessor’s] representations that he would sign the contract. This creates an estoppel.” (Id. at p. 81.) Thus, although the Court in Dougherty spoke in terms of estoppel, it did not require the plaintiff to show anything 34 more than his full performance in reliance on the promise of the defendant. In Dutton, the plaintiff (Dutton), and two others entered into an oral agreement in which Dutton and one of the others would obtain, on behalf of a corporation controlled by the third person, a lease and permit for oil development on land Dutton located, and the three parties would share any profits from the development. When the corporation assigned the permit to another company for consideration, it refused to share any portion of the consideration with Dutton. The Supreme Court rejected the corporation’s argument that the statute of frauds barred Dutton from enforcing the oral contract because it was not intended to be performed within a year. The Court stated, “Assuming that the agreement in the present case falls within this provision of the statute of frauds, the finding of the trial court that Dutton had fully performed all of his obligations under the contract operates to remove the bar of the statute.” (Dutton, supra, 19 Cal.2d at p. 70.) The Court cited to, among other authorities, section 198 of the original Restatement of Contracts in support of its statement that full performance removes the statute from the statute of frauds. That section provides: “Where any of the promises in a bilateral contract cannot be fully performed within a year from the time of the formation of the contract, all promises in the contract are within Class V of § 178 [which sets out classes of contracts within the statute of frauds], unless and until one party to such a contract completely performs what he has promised. When there has been such complete performance, none of the promises in the contract is within Class V.” (Rest. Contracts, § 198.) 35 In contrast to oral contracts that are not to be performed within a year, oral contracts to make a will or devise property in a will consistently have been subjected to stricter application of the statute of frauds. The reason for the stricter application was noted by the California Law Revision Commission in its report recommending legislation that resulted in the repeal from section 1624 of the oral contract to devise property in a will provision and enacting a specific statute of frauds for such contracts as part of the Probate Code. The Commission observed: “Where an oral agreement to make or not to revoke a will is alleged after promisor is deceased and unable to testify, there is an opportunity for the fabrication of testimony concerning the existence of the agreement. Sound policy requires some form of written evidence that such an agreement actually exists.” (16 Cal. Law Revision Com. Rep. (1982) pp. 2348-2349, fns. omitted.) This concern about fabrication of testimony is significantly lessened in a case such as this one, where all parties to the alleged contract are able to testify as to its existence or nonexistence. Thus, we conclude that the holdings of cases involving oral contracts to make a will or devise property in a will, which require evidence of unusual and extraordinary circumstances to support application of estoppel regardless whether there was full performance by one party, do not apply here. We also conclude that the holdings of two other cases that defendants rely upon--Secrest, supra, 167 Cal.App.4th 544 and Denio v. Brennecke (1935) 6 Cal.App.2d 678, 680 (Denio)--similarly do not apply here because they both involve provisions of the statute of frauds other 36 than the “not to be performed within a year” provision. The alleged oral contract in Secrest was a forbearance agreement that purportedly modified a promissory note and deed of trust. The alleged oral contract in Denio was an agreement by the defendants to give the plaintiffs an interest in oil rights in the defendants’ land in exchange for the plaintiffs’ legal services. The courts in both cases found that the contracts came within the provision of section 1624 governing agreements for the sale of real property or an interest in real property. (Secrest, supra, 167 Cal.App.4th at pp. 552-553; Denio, supra, 6 Cal.App.2d at pp. 680-681.) Thus, neither court addressed the provision governing contracts not to be performed within a year. Although the remaining two cases defendants rely upon for their argument that full performance is not sufficient by itself to take an oral contract out of the statute of frauds involved contracts under the “not to be performed within a year” category, neither applies here. In Gressley v. Williams, supra, 193 Cal.App.2d 636, the appellate court rejected the plaintiff’s argument that his full performance of an oral contract not to be performed within a year took the contract out of the statute of frauds. The court observed that “[t]he mere rendition of services is not usually such a part performance of an oral contract as will relieve the contract from the operation of the statute.” (Id. at p. 641.) The only support the court gave for this statement, however, was Kobus v. San Diego Trust & Savings Bank (1959) 172 Cal.App.2d 574, which involved an oral contract to make a will. Thus, we find Gressley unpersuasive on this point. 37 The other case involving a contract not to be performed within a year, Ruinello v. Murray (1951) 36 Cal.2d 687 is inapposite because it involved partial, rather than full, performance of the contract at issue. In that case, the alleged oral contract was for five years, but the parties ended the relationship after three years. Thus, the Supreme Court did not address the effect of full performance on the statute of frauds; the only issue raised and discussed was whether the plaintiff had alleged facts sufficient to establish estoppel to assert the statute. We agree with the court of appeal in Nesson v. Moes (1963) 215 Cal.App.2d 655, which found that “Ruinello is peculiarly within the area of the law relating to estoppel,” and therefore is not applicable to a case in which the plaintiff alleges he fully performed all of his obligations under an oral contract that falls under the “not to be performed within a year” provision of the statute of frauds. (Id. at p. 658.) In short, we hold that Zakk’s allegation that he fully performed all of his obligations under the alleged oral or implied-in-fact contract was sufficient to take the contract out of the statute of frauds. In light of our holding, we need not address Zakk’s other arguments related to the statute of frauds, including whether the trial court properly took judicial notice of the letter defendants submitted or whether the court erred in failing to consider the materials Zakk submitted in response to defendants’ submission and in support of his offer of proof. D. Quantum Meruit Defendants’ demurrer to the quantum meruit cause of action alleged in the third amended complaint, and the trial court’s ruling 38 sustaining those demurrers, were based on the ground that the two- year statute of limitations began to run when Zakk’s services with respect to the original xXx film ended in 2002, and therefore the claim, brought in 2017, was time-barred. Zakk contends on appeal that the trial court erred in sustaining the demurrers on this ground because (1) Code of Civil Procedure section 339, subdivision (1), which sets forth the statute of limitations, expressly states that the cause of action shall not be deemed to have accrued until the aggrieved party discovers the loss or damage; and (2) a quantum meruit claim does not accrue until the repudiation or breach of the oral promise upon which it is based, which in the present case did not occur until the xXx sequel was released in 2017. Zakk’s first contention is based upon a misreading of Code of Civil Procedure section 339, subdivision (1). That statute provides, in relevant part, that it applies to “[a]n action upon a contract, obligation or liability not founded upon an instrument of writing . . . ; or an action founded upon a contract, obligation or liability, evidence by a certificate, or abstract or guaranty of title of real property, or by a policy of title insurance; provided, that the cause of action upon a contract, obligation or liability evidenced by a certificate, or abstract or guaranty of title of real property or policy of title insurance shall not be deemed to have accrued until the discovery of the loss or damage suffered by the aggrieved party thereunder.” (Italics added.) As is clear from the italicized language, the discovery of damages provision does not apply to the facts of this case, because the contract at issue is not alleged to have been evidenced “by a certificate, or abstract or guaranty of title of 39 real property or policy of title insurance.” Thus, Zakk’s first contention fails. Zakk’s second contention, however, is well taken. Although the statute of limitations on a cause of action for quantum meruit for personal services usually begins to run when those services or the relationship between the parties terminate (see, e.g., Maglica v. Maglica (1998) 66 Cal.App.4th 442, 452-454), that is not always the case. Where services are provided with the understanding that payment for those services will be made at some time after the termination of those services or upon some contingency, the statute of limitations does not begin to run until that time arrives or contingency occurs. (See, e.g., Fracasse v. Brent (1972) 6 Cal.3d 784, 791-792 [attorney was hired under a contingency fee agreement and discharged by client without cause; “the attorney’s [cause of] action for reasonable compensation accrues only when the contingency stated in the original agreement has occurred”]; Thompson v. Ruiz (1901) 134 Cal. 26, 28 [the plaintiff provided services for the promisor, and parties agreed he would be paid upon the promisor’s sale of certain land; Supreme Court held that “the statute of limitations did not begin to run against plaintiff’s claim until it matured and could be enforced, . . . regardless of whether the time fixed was reasonable or unreasonable”].) In the present case, Zakk alleged that defendants agreed to pay him the reasonable value of the services he performed “when the xXx Sequel was released.” He also alleged that the sequel was released “on or about January 20, 2017.” Therefore, the two-year statute of limitations on his quantum meruit cause of action did not begin to run 40 until January 20, 2017, and the trial court erred in finding that his claim, filed on March 17, 2017, was time-barred.15 E. Promissory Estoppel As noted, the trial court sustained defendants’ demurrers to Zakk’s promissory estoppel cause of action on the ground that he added it without leave of court. Zakk contends the court’s ruling was in error because his “new cause of action for promissory estoppel responds directly to the Court’s reasoning for sustaining the Demurrers to the [second amended complaint].” We conclude the trial court did not abuse its discretion in dismissing the cause of action. “Following an order sustaining a demurrer or a motion for judgment on the pleadings with leave to amend, the plaintiff may amend his or her complaint only as authorized by the court’s order. [Citation.] The plaintiff may not amend the complaint to add a new cause of action without having obtained permission to do so, unless the new cause of action is within the scope of the order granting leave to amend.” (Harris v. Wachovia Mortgage, FSB (2010) 185 Cal.App.4th 1018, 1023.) In this case, when the trial court sustained the demurrers to the second amended complaint on statute of frauds grounds, it granted Zakk leave to amend, and specifically granted him leave to add a quantum meruit cause of action. Zakk argues that even though the 15 Because defendants did not challenge Zakk’s quantum meruit claim on the merits in their demurrers or their respondents’ briefs, we do not address the merits here. 41 court did not directly give him leave to add a promissory estoppel cause of action, he was allowed to do so because that cause of action “directly responds to the Trial Court’s concerns” regarding the statute of frauds because promissory estoppel is not subject to the statute. We disagree. The granting of leave to amend after a demurrer is sustained on one ground does not give the plaintiff a license to add any possible cause of action that might not be subject to dismissal on that ground. Otherwise, there would be virtually no limitation on amendments following the sustaining of a demurrer. Because Zakk did not obtain leave from the trial court to amend his complaint to add a promissory estoppel cause of action, we affirm the judgment of dismissal with respect to that cause of action. DISPOSITION The judgment is affirmed to the extent it dismissed the cause of action for promissory estoppel, and reversed with respect to the remaining causes of action. Zakk shall recover his costs on appeal. CERTIFIED FOR PUBLICATION WILLHITE, Acting P. J. We concur: COLLINS, J. CURREY, J. 42 | Mid | [
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]
|
Oxygen saturation levels in the juxta-papillary retina in eyes with glaucoma. Oxygen saturation (OS) levels in the juxta-papillary retina particularly inferotemporal retina were investigated in open-angle glaucoma (OAG) patients as well as normal subjects. Fifty-six eyes of 56 OAG Japanese patients and 20 eyes of 20 age-matched normal subjects were recruited for the study. OAG eyes (56) were subdivided into two groups: 15 eyes of low-tension (LT) subgroup and 41 eyes of high-tension (HT) subgroup. The average of age of the LT, HT subgroup and normal group were 60.5, 55.9 and 52.6 years, respectively. OS levels in the retina were measured using a Fourier transform-based spectral retinal imaging (SRI) system (Retinal Cube; ASI Co. Migdal Hemak, Israel), with which OS levels in the fundus could be computed at every pixel point of a 35 degrees fundus image. We calculated OS levels at five points in the retina near the optic disc and retinal arteries and veins in all eyes. The OS levels were also compared with the results analyzed using Humphrey visual field Analyzer with the program 30-2 SITA. At the superior and nasal juxta-papillary retinal points, OS level of the LT subgroup showed significant decrease as compared with the HT subgroup and the normal group (p=0.048-0.009). The LT and the HT subgroups were significantly lower than the normal group at the inferotemporal and the average of the retinal points (p=0.047-0.001). There were no statistically significant differences among the three groups in regards to the OS in the retinal artery. There was a statistical significant correlation between the mean of total deviation of the 17 points in the upper arcuate area and OS of the inferotemporal point (p=0.018), and between mean deviation and the average of OS of the inferotemporal and the superotemporal point (p=0.037) in the HT subgroup. However, there was no significant correlation in the LT subgroup. OS levels in the retina were especially decreased in the low-tension glaucoma subtype. There was a correlation between the visual field defect and OS in the HT eyes in the inferotemporal region. OS measurement may be a novel adjunct to study glaucoma patients. | High | [
0.6914285714285711,
30.25,
13.5
]
|
Donor/recipient kidney transplant THE STORY: I have polycystic kidney disease. I had a heart attack leaving work due to my failing kidneys and COPD. I have been out of work for the past year and a sole supporter.I made it on the transplant list in December. My daughter fought and endured a lot of tests to be my donor. It's a hereditary disease and you have to be 30+ to donate. She is now 27. She has missed a lot of work for appointments and will be out of work for 4-6 weeks after surgery. We have to stay in Rochester after the surgery, her a week, I will be over a month. The money amount I am requesting is minimal compared to what out of pocket costs will be, but will help cover her time from work, prescriptions, travel and food. The other portion will go towards our housing which at minimum will be $3500. We will be going through a long healing process and donations would lessen the stress and financial set back from her to give me the gift of life. Donor Comments Fundraise online and raise money for charity and causes you’re passionate about. CrowdRise is an innovative, cost-effective online fundraising website for personal fundraising pages, non-profit fundraising and event fundraising. Raise money online for causes and have the most fun in the world while doing it. | Mid | [
0.55863539445629,
32.75,
25.875
]
|
The prevalence of traumatic events in young Japanese women. In an effort to address important cross-cultural considerations in the study of posttraumatic stress disorder (PTSD), the present study is the first to assess the prevalence of a variety of potentially traumatic events among young Japanese women across life phases. Overall, our results proved similar to those reported in previous Western studies: Traumatic events were quite common among our participants (80.3%; n = 883). This finding is not surprising given that many of them lived through the 1995 Kobe earthquake. Yet our study found that even when "natural disaster" was excluded, the rate remained 53.1%. Comparing four life phases, we found the most consistent differences between preschool and other life phases. The prevalence of potentially traumatic events and the percentage of most distressing events that participants reported were significantly lower in the preschool phase. | High | [
0.658823529411764,
35,
18.125
]
|
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