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Many people would agree that without our health we have nothing. Unfortunately, the burden of chronic, degenerative diseases in the United States and around the world continues to climb. More than 39 million people in the United States alone have osteoporosis or pre-osteoporosis (osteopenia). As the population ages that number is increasing. Fractures are the most dangerous aspect of osteoporosis. People with ostepororosis who fracture a hip have a 20% chance of dying within one year. There are many things people can do, however, to reduce their risk of chronic diseases, whether it's osteoporosis, cardiovascular disease, or many of the other chronic diseases afflicting millions of people.
Many studies have shown that diet and lifestyle changes reduce the risk of chronic diseases. It's been estimated that two-thirds of cancers alone could be prevented by dietary and lifestyle changes. And in Japan the natural ingredient, MK4 in Osteo-K and Osteo-K Minis has been shown in clinical trials to reduce the risk of fractures by 87% in people with osteoporosis, and help people with acute myeloid leukemia (AML), myelodysplastic syndrome, liver cancer and acute promyelocytic leukemia. For AML and MDS, the the blood work was significantly improved in one clinical trial in 30% of the volunteers. And the added benefit of helping yourself with diet, lifestyle changes and natural products is that they are considered safe and nontoxic. And clinical trials support their benefits as well.
Here are some basic ideas that can help you improve your health throughout your life:


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Exposed 2Favorites [+]
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Running Time: 109 minutes
Released: 12/2006
Studio Name: Hustler
Director: Richard Hamilton
Description: Hustler's favorite girls strip down go down and get down and dirty! These hungry little nymphs are hot and horny and ready for some big dick action. Anal squirting girl-girl and much more!
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Sweats are an vital for courses! Whether you're paying long hrs in the freezing library or took place to press the snooze button 1 also many instances, you'll undoubtedly want a pair of comfy sweat pants! But you don't have to sacrifice design for comfort. There are numerous lines out there that make matching tops and bottoms which are even now cute. This way, you'll fit in with the "I don't care how I seem" crowd, but nevertheless look wonderful!discount longchamp
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The Russian February Revolution of 1917 was one of two revolutions which happened in Russia in the year 1917. It forced the Tsar Nicholas II to abdicate the throne in March of the same year.
- On 22nd February, the Putilov Steel Works Factory in Petrograd (as St Petersburg was then called) went on strike, protesting the conditions they had to work and live in.
- The following day happened to be International Women's Day, which meant women joined the fun of protesting!
- The protesters were joined over the next few days by more and more workers to the extent that Petrograd effectively came to a standstill.
- The city continues to descend into chaos over the next week.
- Tsar Nicholas II abdicates the throne on 2nd March, ending the 300 year old Romanov dynasty.
The first Revolution of 1917 was interesting in that it wasn't an organised demonstration against the Tsarist regime, but more of a culmination of discontent which had been growing over the past decade in Russia. Since 1914, Russia had been fighting in World War One on the side of the Great Powers (Britain, America, France, etc), and following the Russian Revolution of 1905, the country had still not properly recovered from the economic hardships. War, significantly contributing to the deterioration of Russian society, was a primary factor in causing the Revolution.
Following, the abdication of the Tsar, a centre wing Provisional Government was set up with the idea of following Westernised democracy. However, the Government was very fragile, went through two different leaders in 8 months, and was overthrown by the Bolsheviks in the October Revolution of the same year, which led to the creation of the Soviet Union in 1924.
See AlsoEdit
Russian October Revolution of 1917


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A new video game that features Michigan State University mascot Sparty taking on up-to-no-good snowmen is the latest creation by students and faculty at MSU's Games for Entertainment and Learning Laboratory.
In the game, titled "Grumpy Snowmen," rival Big Ten schools have set up snow forts on the MSU campus which are populated by, what else, grumpy snowmen. It is up to Sparty to rid the campus of these menaces.
GEL Lab co-director Brian Winn, who supervised and produced the game, said the team developed the game to showcase the students' skills while creating a fun experience for Spartan fans around the world.
"We knew the concept of an 'Angry Birds' parody would be fun to develop and play," Winn said. "At the same time, this game showcases the level of design, animation, programming and project management skills that our students are developing at MSU."
The game, he said, was initially launched with four levels of increasing difficulty.
"We are now launching a deluxe version of the game that adds sixteen additional levels for a total of twenty," Winn said. "The new levels were developed in response to player requests for additional campus locations and challenges."
The game is available for free online through a website and also as an application on the Apple iTunes store.Share via these networks:


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If I hear the word "multifunctional" one more time I will rip my ears off. In last night's episode of The Apprentice (BBC One), the girls designed a chair that multifunctioned as a tray and a box and a desk. The boys designed a chair that multifunctioned as a table and, well that was about it. Candidate Uzma Yakoob multifunctioned as a design guru, commercial genius, Thunderbirds puppet and general pain in the backside. By the end, there was so much multifunctionality it was hard to tell whether I was watching TV or a piece of Japanese puppet theatre. And they call this a reality show.
Of course, The Apprentice these days is anything but real. Never mind, last night's task to design a new piece of flatpack furniture, these candidates appear to have been hastily assembled from someone's production notes. Posh one. Wide boy. Villain. Bitch. Clearly someone has been watching "constructed reality" shows, such as The Only Way Is Essex, where events are set up and partially scripted to appear spontaneous. So, last night, we saw the very ITV2-looking girls painting male candidate Jordan Poulton's toenails black in a sitting room that looked like the lobby of Laboratoires Garnier.
The other unreal thing was the gullibility of those working in the retail industry. Both flatpack designs were horrible primary school approximations of what furniture should look like, but in several meeting rooms, a buyer with a beard was ready to nod enthusiastically and make a purchase. The boys' piece, Foldo (really), looked like a replica electric chair for ghoulish suburbanites. The girls' multifunctional (arghhh!) TideySidey looked like something the Stasi might store secrets in. "We've given it an industrial feel" said Francesca MacDuff-Varley with desperation. "Cool," said the trendy urban type she was pitching to.
For the third week in a row, the girls lost. Which wouldn't be so humiliating if the boys weren't so rubbish. You've got Wales's answer to David Gest, a dwarf who spouts management speak and a fop (played by Jack Davenport) who, last night, assembled the Foldo with cries of "Here we go, clickety boo…" What hope is there for the future of British business?
In the end, it was quiet, dignified Sophie Lau who was fired, presumably because she was less of a cartoon than perma-tanned harpies Yakoob and Natalie Panayi who shrieked at each other as if they were in an episode of EastEnders. The girls' product was the worst, though. "TideySidey, wishy-washy, poxy boxy," growled Lord Sugar. And yet, strangely, amid the over-wrought madness, the girls' box/tray/seat/desk/mug tree felt more realistic than anything else in The Apprentice.


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Charles van Sandwyk: Illustrator, Writer, Wanderer
You are invited to peek into the whimsical, magical world of Charles van Sandwyk, sitting down by the fire to be inspired by his love of storytelling!
We visited this beloved artist and author to discover how illustration, etching, watercolour, and book-binding by hand play into his work. See his process come alive as Charles transports you to his magical home studio in North Vancouver, where elves, fairies, and woodland creatures are conjured up to impart ancient lessons from the tales of old.
Watch our short documentary with Charles above or on the Opus YouTube Channel to see how this Canadian artist truly embodies the title of Charles van Sandwyk: Illustrator, Writer, Wanderer.
Interested in some of the products Charles uses?
Winsor & Newton Professional Water Colours
Winsor & Newton Series 7 Brushes
Arches Watercolour Paper
Arches Watercolour Blocks
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Somerset Etching Paper - try Canson Infinity Edition Etching Rag
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donald127 Review
One word - Awesome! Auto starts everyday, vacuums under furniture, along base boards, bathrooms, carpet, hardwood and tile - 4300 sq ft ... then back to the docking station every time! Shocking part is having to empty the container everyday from dog hair and dust ... never thought the house was so bad. PLUS ... great entertainment!
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The day came, they opened the house, and behold there was enough ice for exactly one julep!
Stephen drank that julep with reverence, and then the Colonel gave him a cigar.
Your room's all ready, sir, and Burwell shall bring you a julep.
"No, he had some words, I had a julep," and the colonel smiled grimly.
Mint is one of the few productions not common out there, and we are learning to make the julep with sage instead.
I know what you mean, but you've made this julep too strong.
On that morning during the big meeting General Price must make his own julep.
I tell you, my boy, the only thing on earth to do is to take a julep.
Sulphate of copper, 10 gr.; camphor mixture (julep), 1⁄2 pint; dissolve.
When they stop you, tell them you come from Donnegan and that you have to get me some mint for a julep.
late 14c., a syrupy drink in which medicine was given, from Old French julep (14c.), from Medieval Latin julapium, from Arabic julab, from Persian gulab "rose water," from gul "rose" (related to Greek rhodon, Latin rosa) + ab "water," from PIE root *ap- (see water (n.1)). Sense of "alcoholic drink flavored with mint" is first recorded 1787, American English.


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– Shawn Michaels announced on tonight's RAW from Washington, DC that he will be in Triple H's corner for his match against Brock Lesnar at WrestleMania 29.
– The official Twitter account of Vince McMahon posted the following tonight:
"Hello @WWEUniverse! The Chairman is now on @Twitter. Get ready for #BigReveal on Friday night. In the meantime…#RAW"
Big Backstage Update on The Shield, Why WWE Is Turning Cena Heel and More


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Oxi-Leech from Martian Dreams manual
|Only appearance:
|Martian Dreams
The Oxi-Leech of Mars feeds on the material Oxium. The leech itself -- despite being proably one of the most disgusting sights on the planet -- isn't a threat in combat. It does next to no damage and is easily killed. Its true danger lies in that it snatches and devours the needed Oxium at an alarming rate, leaving the adventurer with bare hands, since Oxium is needed to breathe without too much trouble in the atmosphere of Mars.
Therefore, oxi-leeches should be killed from a distance with maximum prejudice.
Lore Edit
This slug-like underground life form feeds on oxium. Unfortunately, these primitive creatures make no distinction between veins of oxium ore and travelling adventurers with oxium in their packs. The oxy-leech has a hideous, toothy mouth opening, but does very little physical damage, preferring to steal oxium and flee before victims can react. Generally found near cave entrances and in ravines, the oxy-leech is a disgusting creature. but more a nuisance than a genuine threat.


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A new age combo guard, Jalen Carey is someone with the requisite size, athleticism, and shooting ability to really make an impact at the college level. He should be comfortable playing with the Playaz Basketball Club in the spring and summer, and his upside makes him someone who could really see his stock soar.
Carey will be playing on the ball a lot as a point guard, so his development will be easy to track in terms of decision making and making others better. If Carey takes the steps that seem very possible given his physical abilities, he is someone who could shoot up the rankings
Recruiting: Rutgers, Seton Hall, Connecticut, Notre Dame, Pittsburgh, Temple
A big guard with positional versatility, Will Richardson has a chance to really explode on the scene during spring and summer. Already a top 100 recruit, Richardson has the natural ability to be better than that.
He has very good size, can play on the ball or off the ball, and is also a good athlete. Richardson has an ability to shoot the ball as well, and likely will find himself in a starring role for his AAU team. Richardson was a high school teammate of Davion Mitchell, so now it is his time to be a breakout player
Recruiting: Georgia, Auburn, Wake Forest, Georgia Tech, UAB
Playing for Mike Rice during the high school season, Valdir Manuel made good strides. He improved quite a bit the second half of the season, and shows solid hands, to go with good athleticism, and a big frame.
Manuel is just gaining experience on the court, so his learning curve is greater than most. He has to continue to gain strength and confidence in his post moves, but it is very possible he emerges in a big way with a solid spring.
Recruiting: Temple, Seton Hall, Rutgers
Big, with good hands, and solid athleticism, J'Raan Brooks has a chance to really be one of the most coveted players on the West Coast and make a jump in the spring when he gets out and is the focus of an offense on the AAU ciruit.
Brooks played for a guard dominated high school team, but still flashed the raw ability to be very good. He runs the floor well, and also is a good passer, so he should find ways to impact the game beyond just scoring.
Recruiting: Baylor, Oklahoma, Stanford, USC, Washington, Washington State
There has never been any question surrounding the ability to score of Damezi Anderson. Anderson has big time size for a wing and good athleticism, but it is his ability to put the ball in the basket from all over the court that is most impressive.
Anderson has good range well beyond the three point line, but is also capable of driving and creating off the bounce. He has to show that he can be consistent with his effort and improve his shot selection, but the talent is there for Anderson to make a big jump in the rankings with a solid spring.


text: Dimeline Sportsbook slow-pays By SBR Tuesday, February 26, 2013 Share with: Sportsbook Review.com provides an SBR Industry News video update for Tuesday, February 26th, 2013. Covered in today's video is the recent downgrading of Dimeline Sportsbook (SBR rating D+) for their handling of players with payout requests. A third Dimeline complaint has since been filed after the latest SBR report. Dimeline Sportsbook slow-pays SBR reported last week that Dimeline Sportsbook was slow-paying two players. Their rating has since been lowered to D+. One player has had six $2,000 payout requests pending since late November. He received one payment in January, and now the sportsbook is stating that since he filed a complaint through SBR, his being paid is no longer a priority. The second player, owed just $900, was offered a $500 settlement to close his balance. Dimeline later claimed that the manager who made this offer did so in error. A third Dimeline player filed a complaint yesterday indicating a $1,000 payout request been pending since mid-January. Follow SportsbookReview.com on twitter. SBR has been the leading online sportsbook industry watchdog since 1999. Players in need of assistance should submit a sportsbook complaint form. Players with general questions may also contact by writing to email@example.com.


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Dynamic garments decorated through vivid pattern, showcasing avant garde silhouettes and erupting in ruffles which unfold a subjective narrative are the result of Fashion Graduate, Rebecca Carrington's latest collection. Studying at Manchester Metropolitan University, Carrington specialised in print and womenswear, in turn developing her unique aesthetic tearing away from the mainstream and embedding a wearable art feel in every aspect of her designs.
The theme of childhood inspires Carringtons latest collection, thus the diminishing of the stereotype regarding the transition into adulthood and the ideology that we should conform to a certain type of expectation is ever apparent, through Carrington's chosen aesthetic, for example, the illustrative expression referencing that of a child's drawings detailed through abstract colouring and further juxtaposed by the harsh black which outlines the garments, also the scaling of prints to appear as giant toys.
Looking deeper than face value, the inspiration is embedded within the multi-layered silhouettes, spilling from the frills that withhold the narrative Carrington intelligently embeds. The collection entails a narrative of a girl named Ruby Ribbon who is transported to a new world entitled Childhood City where she meets her inner child, who teaches her the ways of her youth. The joyous collection beautifully uses contemporary fashion to transport us back to our youth, evoking both whimsical and nostalgic elements which awake the child inside us.
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Situated in a prime location with downtown Limassol on one side, the tourist zone on the other, and the beach only 50 metres away, both the business and leisure travellers will enjoy easy access to all that Limassol has to offer, including the recently redeveloped Olympus promenade with charming walkways, wooden decks, cycling paths and gardens.
Dining options available to customers include "Diana Restaurant", a spacious restaurant overlooking the swimming pool and the hotel gardens serving international and local specialties accompanied with a rich list of superior local and imported wines. Dining options include à la carte, table d'hote, magnificent hot and cold buffets, with live entertainment. The "Lido Tavern", a cozy Lido Tavern serving à la carte dishes as well as hot and cold lunch buffets in an irresistible traditional Cypriot setting. The "O'Brien's Pub and Restaurant", open for lunch, dinner or just a drink, offering the warm and rustic atmosphere that goes with an inviting Irish bar. A great variety of food and drinks, a full bar and good music make it one of the most popular pubs in the area. "Apollo Pool Bar & Terrace" serving drinks and juices, snacks, light meals and barbecues around the pool. The "Piano Lobby & Terrace", a place to relax and enjoy a drink or cocktail in a beautiful setting extending onto a cozy and romantic terrace with casual bamboo furniture overlooking the hotel gardens.All 159 rooms have been designed and decorated to offer maximum comfort for business and leisure guests featuring air conditioning/heating according to season, en suite bathroom with hairdryer, satellite TV with pay movies, telephone, radio and balcony or terrace. Subject to availability and at a local charge mini bar, tea and coffee making facilities and wireless internet access are also available. For additional space and total privacy there are also superior rooms with large terrace and sunbathing facilities.
* Children's pool
* Fitness room / Gym
* Lounge
* Massage
* Outdoor pool
* Pool table
* Reception - 24 hrs
* Sauna
* Sunbeds
* Table tennis


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Faculty: Terry Peterson
|Professor of Adventuresports
Office: #CAOS-1003
Phone: 301-387-3327
|Current Courses
ASI 160 01 (Docs)
ASI 131 01 (Docs)
ASI 130 01 (Docs)
ASI 230 01 (Docs)
ASI 231 01 (Docs)
ASI 201 01 (Docs)
2014 ICF Canoe Slalom World Championships Water Safety Officer
|Education and Awards
|James Madison University, B.S. Sports Management
West Virginia University, M.S. Recreation Resource Management; Educational Psychology
|Personal Background / Teaching Philosophy / Biography
|Professional Memberships
|American Canoe Association
Professional Ski Instructors of America


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Cesaria Evora
December 18, 2011 by staff
Cesaria Evora, The legendary Cape Verdean singer Cesaria Evora, who won international acclaim with her sultry voice and ballads of lost love, died on Saturday in a hospital on her native island of Sao Vicente at the age of 70, three months after retiring due to ill health, reported Agence France-Presse.
In September, her record label Lusafrica said Evora had decided to end her career due to health problems.
"I have no strength, no energy. I want to say to my fans: forgive me, but now I need to rest," Evora told French newspaper Le Monde three months ago.
Evora has sung the blues-influenced "saudade" of her native Cape Verde since a young age, but came to world fame late in life in 1992 after three decades spent performing in the bars of Mindello, Sao Vicente. In all, she has produced 10 studio albums and an anthology of historic radio recordings while touring far from her Atlantic island home.
Her voice was compared to that of US great Billie Holiday. In 2004, her album Voz d'Amor won a Grammy Award for Best World Music Album and stars such as Madonna, David Byrne and Brandford Marsalis descended on her New York concert.
Cape Verde immediately announced a two-day national mourning period and heaped tributes on the singer for putting the tiny Atlantic archipelago nation on the world map. President Jorge Carlos Fonseca said Evora was "one of the major cultural references of Cape Verde", while the prime minister Jose Maria Neves hailed her "invaluable contribution to the greatness of our nation and our pride".
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Eigenvalues of graphs are useful for controlling many graph
- Claude Gaines
- 2 years ago
- Views:
1 Spectra of radom graphs with give expected degrees Fa Chug, Liyua Lu, ad Va Vu Departmet of Mathematics, Uiversity of Califoria at Sa Diego, La Jolla, CA Edited by Richard V. Kadiso, Uiversity of Pesylvaia, Philadelphia, PA, ad approved February 20, 2003 (received for review December 9, 2002) I the study of the spectra of power-law graphs, there are basically two competig approaches. Oe is to prove aalogues of Wiger s semicircle law, whereas the other predicts that the eigevalues follow a power-law distributio. Although the semicircle law ad the power law have othig i commo, we will show that both approaches are essetially correct if oe cosiders the appropriate matrices. We will prove that (uder certai mild coditios) the eigevalues of the (ormalized) Laplacia of a radom power-law graph follow the semicircle law, whereas the spectrum of the adjacecy matrix of a power-law graph obeys the power law. Our results are based o the aalysis of radom graphs with give expected degrees ad their relatios to several ey ivariats. Of iterest are a umber of (ew) values for the expoet, where phase trasitios for eigevalue distributios occur. The spectrum distributios have direct implicatios to umerous graph algorithms such as, for example, radomized algorithms that ivolve rapidly mixig Marov chais. Eigevalues of graphs are useful for cotrollig may graph properties ad cosequetly have umerous algorithmic applicatios icludig low ra approximatios, iformatio retrieval (), ad computer visio. Of particular iterest is the study of eigevalues for graphs with power-law degree distributios (i.e., the umber of vertices of degree j is proportioal to j for some expoet ). It has bee observed by may research groups (2 8, ) that may realistic massive graphs icludig Iteret graphs, telephoe-call graphs, ad various social ad biological etwors have power-law degree distributios. For the classical radom graphs based o the Erdös Réyi model, it has bee proved by Füredi ad Komlós that the spectrum of the adjacecy matrix follows the Wiger semicircle law (9). Wiger s theorem (0) ad its extesios have log bee used for the stochastic treatmet of complex quatum systems that lie beyod the reach of exact methods. The semicircle law has extesive applicatios i statistical ad solid-state physics (2, 22). I the 999 article by Faloutsos et al. (6) o Iteret topology, several power-law examples of Iteret topology are give, ad the eigevalues of the adjacecy matrices are plotted, which do ot follow the semicircle law. It is cojectured that the eigevalues of the adjacecy matrices have a power-law distributio with its ow expoet differet from the expoet of the graph. Faras et al. () looed beyod the semicircle law ad described a triagular-lie shape distributio (see ref. 2). Recetly, M. Mihail ad C. H. Papadimitriou (upublished wor) showed that the eigevalues of the adjacecy matrix of power-law graphs with expoet are distributed accordig to a power law for 3. Here we ited to recocile these two schools of thought o eigevalue distributios. To begi with, there are i fact several ways to associate a matrix to a graph. The usual adjacecy matrix A associated with a (simple) graph has eigevalues quite sesitive to the maximum degree (which is a local property). The combiatorial Laplacia D A, with D deotig the diagoal degree matrix, is a major tool for eumeratig spaig trees ad has umerous applicatios (3, 4). Aother matrix associated with a graph is the (ormalized) Laplacia L I D /2 AD /2, which cotrols the expasioisoperimetrical properties (which are global) ad essetially determies the mixig rate of a radom wal o the graph. The traditioal radom matrices ad radom graphs are regular or almost regular, thus the spectra of all the above three matrices are basically the same (with possibly a scalig factor or a liear shift). However, for graphs with ueve degrees, the above three matrices ca have very differet distributios. I this article, we will cosider radom graphs with a geeral give expected degree distributio, ad we examie the spectra for both the adjacecy matrix ad the Laplacia. We first will establish bouds for eigevalues for graphs with a geeral degree distributio from which the results o radom power-law graphs the follow. The followig is a summary of our results.. The largest eigevalue of the adjacecy matrix of a radom graph with a give expected degree sequece is determied by m, the maximum degree, ad d, the weighted average of the squares of the expected degrees. We show that the largest eigevalue of the adjacecy matrix is almost surely ( o())max{d, m} provided some mior coditios are satisfied. I additio, suppose that the th largest expected degree m is sigificatly d 2. The the th largest eigevalue of the adjacecy matrix is almost surely ( o())m. 2. For a radom power-law graph with expoet 2.5, the largest eigevalue of a radom power-law graph is almost surely [ o()]m, where m is the maximum degree. Moreover, the largest eigevalues of a radom power-law graph with expoet have a power-law distributio with expoet 2 if the maximum degree is sufficietly large ad is bouded above by a fuctio depedig o, m, ad d, the average degree. Whe 2 2.5, the largest eigevalue is heavily cocetrated at cm 3 for some costat c depedig o ad the average degree. 3. We will show that the eigevalues of the Laplacia satisfy the semicircle law uder the coditio that the miimum expected degree is relatively large ( the square root of the expected average degree). This coditio cotais the basic case whe all degrees are equal (the Erdös Réyi model). If we weae the coditio o the miimum expected degree, we ca still have the followig strog boud for the eigevalues of the Laplacia, which implies strog expasio rates for rapidly mixig, 4 max i o i 0 w glog2, This paper was submitted directly (Trac II) to the PNAS office. To whom correspodece should be addressed. Achlioptas, D. & McSherry, F., Thirty-Third Aual ACM Symposium o Theory of Computig, July 6 8, 200, Crete, Greece. Fowles, C., Belogie, S., Chug, F. & Mali, J., Europea Coferece o Computer Visio, May 27 Jue 2, 2002, Copehage. Lu, L., Twelfth Aual ACM-SIAM Symposium o Discrete Algorithms, Jauary 7 9, 200, Washigto, DC. MATHEMATICS PNAS May 27, 2003 vol. 00 o
2 where w is the expected average degree, is the miimum expected degree, ad g() is ay slow-growig fuctio of. I applicatios, it usually suffices to have the i values (i 0) bouded away from 0. Our result shows that (uder some mild coditios) these eigevalues are actually very close to. The rest of the article has two parts. I the first part we preset our model ad the results cocerig the spectrum of the adjacecy matrix. The last part deals with the Laplacia. The Radom Graph Model The primary model for classical radom graphs is the Erdos Réyi model G p, i which each edge is idepedetly chose with the probability P for some give P 0 (see ref. 5). I such radom graphs the degrees (the umber of eighbors) of vertices all have the same expected value. Here we cosider the followig exteded radom-graph model for a geeral degree distributio (also see refs. 6 ad 7). For a sequece w (w, w 2,...,w ), we cosider radom graphs G(w) i which edges are idepedetly assiged to each pair of vertices (i, j) with probability w i w j, where w i. i Notice that we allow loops i our model (for computatioal coveiece), but their presece does ot play ay essetial role. It is easy to verify that the expected degree of i is w i. To this ed, we assume that max i w 2 i w such that p ij for all i ad j. This assumptio isures that the sequece w i is graphical [i the sese that it satisfies the ecessary ad sufficiet coditio for a sequece to be realized by a graph (8) except that we do ot require the w i values to be itegers]. We will use d i to deote the actual degree of v i i a radom graph G i G(w), where the weight w i deotes the expected degree. For a subset S of vertices, the volume Vol(S) is defied as the sum of weights i S ad vol(s) is the sum of the (actual) degrees of vertices i S. That is, Vol(S) is w i ad vol(s) is d i. I particular, we have Vol(G) i w i, ad we deote Vol(G). The iduced subgraph o S is a radom graph G(w), where the weight sequece is give by w i w i Vol(S) for all i S. The expected average degree is w i w i (). The secod-order average degree of G(w) is d ( is w 2 i i w i ) is w 2 i. The maximum expected degree is deoted by m. The classical radom graph G(, p) ca be viewed as a special case of G(w) by taig w to be (p, p,...,p). I this special case, we have d w m p. It is well ow that the largest eigevalue of the adjacecy matrix of G(, p) is almost surely [ o()]p provided that p log. The asymptotic otatio is used uder the assumptio that, the umber of vertices, teds to ifiity. All logarithms have the atural base. Spectra of the Adjacecy Matrix of Radom Graphs with Give Degree Distributio For radom graphs with give expected degrees (w, w 2,..., w ), there are two easy lower bouds for the largest eigevalue A of the adjacecy matrix A, amely, [ o()]d ad [ o()]m. It has bee prove that the maximum of the above two lower bouds is essetially a upper boud (also see ref. 9). Chug, F., Lu, L. & Vu, V., Worshop o Algorithms ad Models for the Web-Graph, November 6, 2002, Vacouver, BC, Caada. Theorem. If d m log, the the largest eigevalue of a radom graph i G(w) is almost surely [ o()]d. Theorem 2. If m d log 2, the almost surely the largest eigevalue of a radom graph i G(w) is [ o()]m. If the th largest expected degree m satisfies m d log 2, the almost surely the largest eigevalues of a radom graph i G(w) is [ o()]m. Theorem 3. The largest eigevalue of a radom graph i G(w) is almost surely at most 7log maxm, d. We remar that the largest eigevalue A of the adjacecy matrix of a radom graph is almost surely [ o()]m if m is d by a factor of log 2, ad A is almost surely [ o()]d if m is d by a factor of log. I other words, A is (asymptotically) the maximum of m ad d if the two values of m ad d are far apart (by a power of log ). Oe might be tempted to cojecture that A omaxm, d. This, however, is ot true as show by a couterexample give previously (0). We also ote that with a more careful aalysis the factor of log i Theorem 3 ca be replaced by (log()) /2 ad the factor of log 2 ca be replaced by (log()) 3/2 for ay positive provided that is sufficietly large. We remar that the costat 7 i Theorem 3 ca be improved. We made o effort to get the best costat coefficiet here. Eigevalues of the Adjacecy Matrix of Power-Law Graphs I this sectio we cosider radom graphs with power-law degree distributio with expoet. We wat to show that the largest eigevalue of the adjacecy matrix of a radom powerlaw graph is almost surely approximately the square root of the maximum degree m if 2.5 ad is almost surely approximately cm 3 if A phase trasitio occurs at 2.5. This result for power-law graphs is a immediate cosequece of a geeral result for eigevalues of radom graphs with arbitrary degree sequeces. We choose the degree sequece w (w, w 2,..., w ) satisfyig w i ci /() for i 0 i i 0. Here c is determied by the average degree, ad i 0 depeds o the maximum degree m, amely, c 2 d/(), d 2 i 0. m It is easy to verify that the umber of vertices of degree is proportioal to. The secod-order average degree d ca be computed as follows. 2 2 o if 3. 3 d d 2 d l2m o if 3. d m d o if 2 3. d Chug et al.
3 We remar that for 3, the secod-order average degree is idepedet of the maximum degree. Cosequetly, the power-law graphs with 3 are much easier to deal with. However, may massive graphs are power-law graphs with 2 3, i particular, Iteret graphs (9) have expoets betwee 2. ad 2.4, whereas the Hollywood graph (6) has expoet 2.3. I these cases, it is d that determies the first eigevalue. Theorem 4 is a cosequece of Theorems ad 2. Whe 2.5, the ith largest eigevalue i is i m i i i 0 /[(2)], for i sufficietly large. These large eigevalues follow the power-law distributio with expoet 2. (The expoet is differet from oe i Mihail ad Papadimitriou s upublished wor, because they use a differet defiitio for power law.) Theorem 4.. For 3 ad m d 2 log 3, almost surely the largest eigevalue of the radom power-law graph G is [ o()]m. 2. For ad m d (2)/(2.5) log 3/(2.5), almost surely the largest eigevalue of the radom power-law graph G is [ o()]m. 3. For ad m log 3/2.5, almost surely the largest eigevalue is [ o()]d. 4. For (dm log ) ad 2.5, almost surely the largest eigevalues of the radom power-law graph G with expoet have power-law distributios with expoet 2, provided that m is large eough (satisfyig the iequalities i ad 2). Spectrum of the Laplacia Suppose G is a graph that does ot cotai ay isolated vertices. The Laplacia L is defied to be the matrix L I D /2 AD /2, where I is the idetity matrix, A is the adjacecy matrix of G, ad D deotes the diagoal degree matrix. The eigevalues of L are all oegative betwee 0 ad 2 (see ref. 20). We deote the eigevalues of L by For each i, let i deote a orthoormal eigevector associated with i. We ca write L as L i i P i, where P i deotes the i projectio ito the eigespace associated with eigevalue i. We cosider M I L P 0 ( i )P i. i0 For ay positive iteger, we have TraceM 2 ( i ) 2. i0 Lemma. For ay positive iteger, we have max i M TraceM 2 /2. i 0 The matrix M ca be writte as M D /2 AD /2 P 0 D /2 AD /2 * 0 0 D /2 AD /2 volg D/2 KD /2, where 0 is regarded as a row vector (d vol(g),..., d vol(g)), * 0 is the traspose of 0, ad K is the all s matrix. Let W deote the diagoal matrix with the (i, i) etry havig value w i, the expected degree of the ith vertex. We will approximate M by C W /2 AW /2 VolG W/2 KW /2 W /2 AW /2 *, where is a row vector (w,...,w ). We ote that * * is strogly cocetrated at 0 for radom graphs with give expected degree w i. C ca be see as the expectatio of M, ad we shall cosider the spectrum of C carefully. A Sharp Boud for Radom Graphs with Relatively Large Miimum Expected Degree I this sectio we cosider the case whe the miimum of the expected degrees is ot too small compared to the mea. I this case, we are able to prove a sharp boud o the largest eigevalue of C. Theorem 5. For a radom graph with give expected degrees w,..., w where w log 3, we have almost surely C o 2 w. Proof: We rely o the Wiger high-momet method. For ay positive iteger ad ay symmetric matrix C which implies TraceC 2 C 2 C 2, E C 2 ETraceC 2, where is the eigevalue with maximum absolute value: C. If we ca boud E(Trace(C 2 )) from above, the we have a upper boud for E( (C) 2 ). The latter would imply a upper boud (almost surely) o (C) via Marov s iequality provided that is sufficietly large. Let us ow tae a closer loo at Trace(C 2 ). This is a sum where a typical term is c i i 2 c i2 i 3,...,c i2 i 2 c i2 i. I other words, each term correspods to a closed wal of legth 2 (cotaiig 2, ot ecessarily differet, edges) of the complete graph K o {,..., } (K has a loop at every vertex). O the other had, the etries c ij of C are idepedet radom variables with mea zero. Thus, the expectatio of a term is ozero if ad oly if each edge of K appears i the wal at least twice. To this ed, we call such a wal a good wal. Cosider a closed good wal that uses l differet edges e,...,e l with correspodig multiplicities m,..., m l (the m h values are positive itegers at least 2 summig up to 2). The (expected) cotributio of the term defied by this wal i E(Trace(C 2 )) is l m Ec h eh. [] h I order to compute E(c ij m ), let us first describe the distributio of c ij : c ij w i w j w i wj q ij w i w j with probability p ij w i w j ad c ij w i w j p ij w i w j with probability q ij p ij. This implies that for ay m 2, MATHEMATICS Chug et al. PNAS May 27, 2003 vol. 00 o. 635
4 Ec m ij q ij m p ij p ij m q ij w i w j m/2 p ij w i w j m/2 w i w j m/2 m2. [2] Here we used the fact that q m ij p ij (p ij ) m q ij p ij i the first iequality (the reader ca cosider this fact a easy exercise) ad the defiitio p ij w i w j i the secod equality. Let W l, deote the set of closed good wals o K of legth 2 usig exactly l differet vertices. Notice that each wal i W l, must have at least l differet edges. By Eqs. ad 2, the cotributio of a term correspodig to such a wal toward E(Trace(C 2 )) is at most l w 22l mi. It follows that ETraceC 2 W l, l0 22l. [3] I order to boud the last sum, we eed the followig result of Füredi ad Komlós (9). Lemma 2. For all l, W l,... l 2l 2 2l l l l 4l. I order to prove Theorem 5, it is more coveiet to use the followig cleaer boud, which is a direct corollary of Eq W l, l 4l 2ll 4l [5] Substitutig Eq. 5 ito 3 yields l 2 22l l 4l ETraceC 2 l0 2ll 4l l0 s l,. [4] [6] Now fix g()log, where g() teds to ifiity (with ) arbitrarily slowly. With this ad the assumptio about the degree sequece, the last sum i Eq. 6 is domiated by its highest term. To see this, let us cosider the ratio s, s l, for some l : s, 4 s l, 2 2ll 4l 2 l 4w 2 mi l 2 2l 4l 2 4w 2 mi 6 where i the first iequality we used the simple fact that 2l 2 22l 2 l! 22l. l, ETraceC 2 s l, os, l 0 o 4 o4. Because E( (C) 2 ) E(Trace(C 2 )) ad w, we have E C 2 o w 2 2. [7] By Eq. 7 ad Marov s equality P C w 2 2 P C 2 w 2 2 E C 2 2 w 2 2 o w w 2 2 o 2. Because (log ), we ca fid a () tedig to 0 with such that ( ) 2 o(), which implies that almost surely (C) [ o()](2w ) as desired. The lower boud o (C) follows from the semicircle law proved i the ext sectio. The Semicircle Law We show that if the miimum expected degree is relatively large, the the eigevalues of C satisfy the semicircle law with respect to the circle of radius r 2w cetered at 0. Let W be a absolute cotiuous distributio fuctio with (semicircle) desity w(x) (2) x 2 for x ad w(x) 0 for x. For the purpose of ormalizatio, cosider C or (2w ) C. Let N(x) be the umber of eigevalues of C or x ad W (x) N(x). Theorem 6. For radom graphs with a degree sequece satisfyig w, W (x) teds to W(x) i probability as teds to ifiity. Remar: The assumptio here is weaer tha that of Theorem 5 due to the fact that we oly eed to cosider momets of costat order. Proof: Because covergece i probability is etailed by the covergece of momets, to prove this Theorem 6 we eed to show that for ay fixed s, the sth momet of W (x) (with tedig to ifiity) is asymptotically the sth momet of s W(x). The sth momet of W (x) equals ()E(Trace(C or )). For s eve, s 2, the sth momet of W x is (2)!2 2!( )! (see ref. 0). For s odd, the sth momet of W x is 0 by symmetry. I order to verify Theorem 6, we eed to show that for ay fixed ETraceC or 2 o 2! 2 2!! [8] With a proper choice of g(), the assumptio (log 3 2 )w guaratees that (4 6 ) (), where () teds to ifiity with, which implies s, s l, [()] l. Cosequetly, ad ETraceC or 2 )) o. [9] 636 Chug et al.
5 Fig.. The large eigevalues of the adjacecy matrix follow the power law. Fig. 2. The Laplacia spectrum follows the semicircle law. We first cosider Eq. 8. Let us go bac to Eq. 3. Now we eed to use the more accurate estimate of W l, give by Eq. 4 istead of the weaer but cleaer oe i Eq. 5. Defie s l, l 22l... l 2 2l l 2l l l 4l. Oe ca chec, with a more tedious computatio, that the sum s l, l0 is still domiated by the last term, amely s l, os,. l0 It follows that E(Trace(C 2 )) [ o()]s,. O the other had, E(Trace(C 2 )) W,. Now comes the importat poit, for l, W l, is ot oly upper-bouded by but i fact equals the right-had side of Eq. 4. Therefore, It follows that ETraceC 2 os,. ETraceC 2 or ow2 2 s, 2! o 2 2!!, which implies Eq. 8. Now we tur to Eq. 9. Cosider a term i Trace(C 2 ). If the closed wal correspodig to this term has at least differet edges, the there should be a edge with multiplicity oe, ad the expectatio of the term is 0. Therefore, we oly have to loo at terms with wals that have at most differet edges (ad at most differet vertices). It is easy to see that the umber of closed good wals of legth 2 with exactly l differet vertices is at most O( l ). The costat i O depeds o ad l (recall that ow is a costat), but for the curret tas we do ot eed to estimate this costat. The cotributio of a term correspodig to a wal with at most l differet edges is bouded by l w 22l mi. Thus E(Trace(C 2 )) is upper-bouded by l0 c l 22l l [0] for some costat c. To compute the (2 )th momet of W (x), we eed to multiply E(Trace(C 2 )) by the ormalizig factor 2 2. It follows from Eq. 4 that the absolute value of the (2 )th momet of W (x) is upper-bouded by l 22l l. 2 2 l0 l0 22l 2 [] Uder the assumptio of the theorem (2 ) o(). Thus, the last sum i Eq. is o(), completig the proof. Summary I this article we prove that the Laplacia spectrum of radom graphs with give expected degrees follows the semicircle law, provided some mild coditios are satisfied. We also show that the spectrum of the adjacecy matrix is essetially determied by its degree distributio. I particular, the largest eigevalues of the adjacecy matrix of a radom power-law graph follow a power-law distributio, provided that the largest degrees are large i terms of the secod-order average degree. Here we compute the spectra of a subgraph G of a simulated radom power-law graph with expoet 2.2. The graph G has 588 vertices with the average degree w ad the secod average degree d The largest eigevalue of its adjacecy matrix is 6.78, which is very close to the secod-order average degree d, as asserted by Theorem (see Fig. ). All the otrivial eigevalues of the Laplacia are withi 0.3 (2w ) from, as predicted by Theorems 5 ad 6 (see Fig. 2). This research was supported i part by Natioal Sciece Foudatio Grats DMS ad ITR (to F.C. ad L.L.) ad DMS (to V.V.) ad a A. Sloa fellowship (to V.V.). MATHEMATICS Chug et al. PNAS May 27, 2003 vol. 00 o. 637
6 . Kleiberg, J. (999) J. Assoc. Comput. Mach. 46, Aiello, W., Chug, F. & Lu, L. (200) Exp. Math. 0, Aiello, W., Chug, F. & Lu, L. (2002) i Hadboo of Massive Data Sets, eds. Abello, J., Pardalos, P. M. & Resede, M. G. C. (Kluwer, Dordrecht, The Netherlads), pp Albert, R., Jeog, H. & Barabási, A.-L. (999) Nature 40, Barabási, A.-L. & Albert, R. (999) Sciece 286, Faloutsos, M., Faloutsos, P. & Faloutsos, C. (999) ACM SIG-COMM 99 29, Jeog, H., Tomber, B., Albert, R., Oltvai, Z. & Barábasi, A.-L. (2000) Nature, 407, Kleiberg, J., Kumar, R., Raghava, P., Rajagopala, S. & Tomis, A. (999) i Computig ad Combiatorics, Proceedigs of the 5th Aual Iteratioal Coferece, COCOON 99, eds. Asao, T., Imai, H., Lee, D. T., Naao, S.-I. & Tooyama, T. (Spriger, Berli), pp Füredi, Z. & Komlós, J. (98) Combiatorica, Wiger, E.-P. (958) A. Math. 67, Faras, I. J., Deréyi, I., Barabási, A.-L. & Vicse, T. (200) Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Iterdiscip. Top. 64, , cod-mat Goh, K.-I., Kahg, B. & Kim, D. (200) Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Iterdiscip. Top. 64, 05903, cod-mat Biggs, N. (993) Algebraic Graph Theory (Cambridge Uiv. Press, Cambridge, U.K.). 4. Kirchhoff, F. (847) A. Phys. Chem. 72, Erdos, P. & Réyi, A. (959) Publ. Math. 6, Chug, F. & Lu, L. (2003) A. Comb. 6, Chug, F. & Lu, L. (2002) Proc. Natl. Acad. Sci. USA 99, Erdos, P. & Gallai, T. (96) Mat. Lapo, Chug, F., Lu, L. & Vu, V. (2003) A. Comb. 7, Chug, F. (997) Spectral Graph Theory (Am. Math. Soc., Providece, RI). 2. Crisati, A., Paladi, G. & Vulpiai, A. (993) Products of Radom Matrices i Statistical Physics, Spriger Series i Solid-State Scieces (Spriger, Berli), Vol Guhr, T., Müller-Groelig, A. & Weidemüller, H. A. (998) Phys. Rep. 299, Chug et al.
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Description: n these new essays, a group of experienced ethnographers, a literary critic, and a historian of anthropology, all known for advanced analytic work on ethnographic writing, place ethnography at the center of a new intersection of social history, interpretive anthropology, travel writing, discourse theory, and textual criticism. The authors analyze classic examples of cultural description, from Goethe and Catlin to Malinowski, Evans-Pritchard, and Le Roy Ladurie, showing the persistence of allegorial patterns and rhetorical tropes. They assess recent experimental trends and explore the functions of orality, ethnicity, and power in ethnographic composition. Writing Cultureargues that ethnography is in the midst of a political and epistemological crisis: Western writers no longer portray non-Western peoples with unchallenged authority; the process of cultural representation is now inescapably contingent, historical, and contestable. The essays in this volume help us imagine a fully dialectical ethnography acting powerfully in the postmodern world system. They challenge all writers in the humanities and social sciences to rethink the poetics and politics of cultural invention.
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List price: $27.95Copyright year: 1986Publisher: University of California PressPublication date: 4/11/1986Binding: PaperbackPages: 345Size: 6.00" wide x 9.00" long x 0.75" tall Weight: 0.946Language: English
James Clifford is Professor, History of Consciousness Department at the University of California, Santa Cruz. George E. Marcus is Chancellor's Professor, Department of Anthropology at the University of California, Irvine.
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Scott Thatcher Hvac, heating contractor, listed under "Heating Contractors" category, is located at 3895 Rosemary St Salt Lake City UT, 84120 and can be reached by 8012315111 phone number. Scott Thatcher Hvac has currently 0 reviews.This business profile is not yet claimed, and if you are the owner, claim your business profile for free. If you are not the owner you can invite this business to join by email or by phone.Browse all Heating Contractors in Salt Lake City UT. Discover census data for Salt Lake City, UT.
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Eye colour:
Hair Colour/Style:
brown, medium length, wavy
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Client Orientation:
Men & Women
Evenings, Weekends
Cities you are willing to travel to:
My greatest passions are having adventures and telling stories. I am an avid reader and also love writing, film, performance, and music. Sitting down over a meal or a glass of wine and connecting over escapades, whether those which we might have had in common or those which we might surprise one another with, is something which really excites me. I love taking chances and making unexpected discoveries. I love to laugh and make others feel happy and comfortable.
I am Canadian. I grew up in Toronto and then enjoyed two years on the west coast of Canada in Vancouver before moving to London. I find mountains, trees, ocean, sky, travel, and animals magical and beautiful. I enjoy running, dance, yoga, cycling and swimming, so I'm quite physically active! I also love cooking, learning: about cuisine, nature, the human body, and the people I meet!
I believe that any two people can connect through collective experience and sharing, and if we meet I'm sure we will enjoy our own special adventure!
My Interests Include:
- Theatre, Film, Ballet, Opera
- Dancing
- Live music
- Nature walks
- Karaoke
- Great food and conversation
- Fashion
- Books
Book me this evening and we can share any of the following experiences:
- Work functions
- Dinner dates
- Theatre
- Live music, shows, gigs
- Jazz jams
- Swing dancing
- Any kind of class (movement, cooking, etc)
I am open to ideas! I have a variety of interests and love to learn. If you are interested in experiencing something with me that is not shown here I would be very happy to hear your ideas
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Congratulations to Kanni Huang (Media & Information Studies Ph.D., '13) who won the oral presentation award at the MSU interdisciplinary conference for her presentation: "Knowledge about Climate Change among Regional Journalists and Climate Scientists."
Huang presented a paper at the Graduate Academic Conference (GAC) on her work with a National Science Foundation project that identifies major climate science initiatives and facilitates collaboration between climate science and education practitioners in the Great Lakes region.
"In order to invite the audience to engage in my presentation at the conference, I tried to make connections between my research and the audience's everyday life and demonstrated how the research findings could contribute to the training of environmental journalists in the 'real world.'"
Huang's interests focus on environmental journalism and climate change information, environmental communication with the adoption of new media technologies, online social relations and the exchange of environmental information.
"When the GAC announced the winners, I was surprised at first and then felt honored to be awarded. The great experience boosted my confidence in sharing research findings to more diverse audiences," Huang said.
"I appreciate the opportunity provided by graduate school and the precious experience working for the School of Journalism and the Knight Center for Environmental Journalism."
Great job, Kanni!Share via these networks:


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Products References/ Testimonials
Was auch immer da so erscheinen soll


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- 5 unpeeled garlic cloves
- 2 pounds broccoli—cut into 1-inch florets, stems reserved for another use
- 2 tablespoons extra-virgin olive oil
- 2 tablespoons unsalted butter, melted
- Salt
- Freshly ground pepper
- 4 ounces cream cheese
- 3 cups low-sodium chicken broth
- Croutons, for serving
Preheat the oven to 400°. Wrap the garlic in a foil packet and roast for 50 minutes, until softened. Meanwhile, in a small roasting pan, toss the broccoli with the olive oil and butter and season with salt and pepper. Roast for 20 minutes, or until tender.
Squeeze the garlic cloves from their skins into a blender. Add the roasted broccoli, cream cheese and broth and puree until smooth. Transfer the soup to a saucepan and bring to a simmer. Season with salt and pepper and serve with croutons.


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Regarding the story "Neighbors' spat highlights Long Hill meeting," (Echoes-Sentinel, Nov. 23): Mayor Suzanne Dapkins was not aware the primary grievance of resident John Cilli was the recent clearing of a property behind his home. My family's property, located two roads away from his neighbor, has been under renovation for nearly two years. Our lot had been legally approved and the trees have been cleared for eight months. The right of way issue mentioned involving stockpiled soils was remediated by us three months ago. I am at a loss as to why this public forum was allowed. Our Board of Adjustment meeting was more than a year ago and all surrounding residents were informed via certified mail as required by the township. Unfortunately, this Township Committee meeting became a circus with our name as the main attraction.
Meyersville Road


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Kawa Bowl
Kawa Bowl
Slip cast with a leather mold, each one of these bowls from Souda take on a slightly different shape with every cast. The exterior of the bowl retains the leather-like finish, while the interior features a gold glaze. A truly striking centerpiece for any table.
After spending the last two decades in New York, boutique owners Ivy and Josh Elrod relocated to Nashville to open up Wilder. As artists, performers, parents and dreamers, they bring a unique vision to creating provocative spaces. Their experiences living in New York and performing around the globe have cultivated an appreciation for eclecticism which is expressed in every facet of their shop. The curated selection of products includes abstract lighting, unique artwork, the perfect his and hers gifts, and more, reflecting Ivy and Josh's love for nature and the unexpected. Wilder is much more than just a lifestyle boutique, it's a design shop and art space for your home and life.
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In the last 90 days, 3 listings have been made available, which means new availabilities might be leasing quickly. You'll want to be prepared to make an offer immediately. About 100% of the office spaces in the White Oak are subleases, so you might be able to find a shorter term or below market rent. There aren't many listings below 2,000 square feet on the market, so finding a space for a small business might be tough.
Even though the median size is 9,000 sqft, there are still 0 spaces below 2,000 sqft. Most buildings in this region are close to 2 floors. Most buildings in this area were built in 2004 and are Class C.
Trends and status of the commercial real estate market in White Oak.
Market Report
Real time and historical data on commercial real estate listings in White Oak.