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Nevanlinna Prize Winner

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it's a great pleasure for me to introduce the speaker of the after the winner of the role of money that price for a job that be said you would say about the work performed by birth and is careers 4 you start that received his Ph.D. things from MIT in 1996 and is now a professor of computer science at the computer science department at that Congo the scientific work of drunk drivers given the age of the review is aggressively Brault and Spain's diverse topics including think of others is and what laying off the World Wide Web and related information networks discrete optimization and network rooms high-growth approaches clustering indexing and they die so in his work you always talked problems with great
impact practical application in the process of slowing he derives deed its structural another matter inside and develops officially and applies them Girolamo experiments although his work has outstanding practical application is is this admirer of contributions are clearly is theoretical In the sense that good curious Best fructose drive her work has been acknowledged already not only in the public by several procedures prizes with went up prices it is certainly the highest recognition so far as to highlight freed important topics which correct lies at least in my opinion the scientific work of John 1st Chunga creates new concepts and definitions by introducing mathematics to areas which had eluded mathematics on that point leaving efficient alone for example if his work is most Rob breaking and influential work paper at of rotate sources in the hyperlink the environment from the he introduced eigenvectors related toe incident prisoners Rao I had to use this to determine certain actually grown between authorities and hops which had he realized played an important role in the significance of Volvo's link furthermore 2nd you develop sufficient by using mathematics from different areas your talk topics where only productivity results so far have existed for example in his work all war world for a moment that he introduced the clustering exponent of and he proved among existing by showing that only the exponent of our um had the property that there exists FI tool had a property exists an efficient fiber them that defined the sergeant and putting normal number of steps were over In his work all word and Pembroke among users the interviews the formalism of Markov chain then asian Markov models and Markoff sources all these has important impact of the fuel off network promos Serb the practical impact I think form joined birds impact on on a houses is the development of the World Wide Web can hardly be overestimated it's not easy to find a comparable story of success and the recent studios offer immediately educational methods for solving practical problems however as I said the concept shortly originality and depth we used beside the practical impact perhaps the most impressive a tribute of client end he has not only want outstanding results even fewer every free he comes out With you a spectacular results in different directions with ongoing U.S. insightful ideas I think we can expect maybe more than original contribution was the only thing which I think is hard to predict is rich doing this will happen this is all and I should make it a further announcement before planned starts for namely that a store probe the talk on Tuesday they said will be councils that is you will be used for missile sober look will how a OK looks like them because of the running you're very well so thanks very much they arrests introduction thanks very
much for the honor both of those there prize committee and the organizing committee of the congress if best a series for me altered to attend Ali socks and I certainly learned a lot so what
I want to talk about today has some some issues at the intersection of mathematical models and the structure of information networks and in order to other citrus besotted aboard the provide some context and the context begins with begins sense the following dichotomy which is that With science the field Eldoret rich mathematical framework for opposing research questions and that it has sort of a possible fight the following general namely a computer like this 1 here receives
inputs a computer for a while it produces about and obviously when faced with Brussels like that naturally gravitate toward is issues like How up but be computer or for certain problems we truth there there there there is no fast there's now if we think about it it is about how you use your computers are
everyday public uses computers every day yes deep down inside they're doing calculations they get in for example it a lot his output but tho also world experiences computer use is as as a form of mediators namely the computers mediating their access to information and 2 other people are so everything about media access information on the weather the people browse the Web users and so forth when expect other people's to things like e-mail the messaging interact with other people electronic markets and the start of in between ground which you could say simultaneously by connecting with information people things like warriorlike my discussion like file-sharing so it does have also the world experiences Jury namely that the all rhythms are somehow immune Charles what they're doing is address of information and and other people the natural Trust computer scientist no as a result is how should 1 combined this the tremor with these these kinds of developments and at the end at the assumed that frames the talk how we can take the styled after years of research questions and apply of of domains now what ingredients emitters of course is not as the information but the Reds structures the crop around information and we started often take the form of complex networks so by networks era sizable drafts either directly or under 2 graphs and I'm thinking of networks here really all levels of the computer Reser a ranging from about communication networks the actual physical networks that summer packets communicator surface mission to the kind of more virtually the information networks like the World Wide Web where the nodes are Web pages in length and theaters are directed hyperlinks to even more virtual kinds of networks like human social networks where the nodes of people and the believes represent either friendship acquaintanceship collaboration or simply exchange of messages and of course want thing about modern computer systems is that all these networks assertive into intertwine inhabit the same faces all it wants and what see examples like this is for example in pictures of of the sword frontier exacted from lot Dumbarton a time Doris study of electronic mail network the year corporate research lab for Hewlett-Packard so was about 400 people working at a corporate research lab what's frontier is these management hierarchy of the layout but that the lines are all the links 30 people who exchanged as the number of electronic mail messages about direction rights we have a social network superimposed on organizational see other communications sort of follows official hierarchy but also sought traverses the emperor's we have not as The social network riding on top of this we have a communication network that carries a mail information exchanging all somehow all entangled 1 analysts as I say on on tangling what's going on pictures like for the challenges that we face in asking his 1st resounding else going on we think about information networks and social networks and the following that a what were really about his networks as Obama namely unlike the great words of the past century telecommunication network the power grid of the highway and rail systems over fundamentally engineered artifacts although there was lots of local variations and lots of pervasive fundamentally those were mapped out designed engineered by a small group of people who have a global plan of sister honoring and something like the World Wide Web site the social network of all Of all a case of the world is not something that's designed originators of capital directly as it as it as of Obama exploiting growth over the past 10 years really do to be completely asynchronous on coordinated actions of hundreds of millions of people as is all that's how we get about these networks not of things that were designed by them phenomena have to be study on their own terms and as a result of the the kinds of models the real thing about art rooted not just in graph theory and Greg Kraft novels which fiercely side but also in discrete probability truth things like remove draft models which through a randomized meetings are designed to capture the uncoordinated gross Of these kinds of its kind words at the same time is that the 1st lady inevitably prison a contact with social science series like economics sociology and 1 other Fred running through the research areas the way which don't really models have begun to emerge with notions in in the social sciences strike provide an elderly foundation for some other social processes that we see and finally although it networks that a revolver number on we treated us phenomena the models that we developed very rapidly become principles were analyzed data we see any then a circular stairway become vessels for designing new because obviously although they systems were a growing Vermont participation are also being shaped by the kinds of tools that we develop tools like like search engines or social systems so we have Ford progression of information networks have bridge data mathematical models that eventually design principles and water out the stock is that 1 particular
strand of research that bodies all these themes and tried it so you its progressive less from from beginning Jan necessarily omitting all sorts of about parts of it simply do through the bound amount of time I have Wichita there are another example might actually used the phrase strong progressive I want start pirated duties examples does does to convey 1 what what's what but discovers her so the 1st trolley most while 1 example is the use of we can also see the context of Web search as depicted here are so it so I don't see what the Christel's sound a serious and understand information on the Web and the way which people access that information and the power of mathematical models for the Web is is apparent in the insects like the fighting the spread the properties of the of the hyperlink draft if in fact are very effective way regret it isn't that form the the basis for a lot of much monasteries and at the same time if the if you want it was the the network were deeply to try exposing some of the sadly communities of pages and his of people that exist on the Web on its again out that analysis of being alone when drafted a mail and because of the novelty of natives accusations as reverse effect also and finally old bundled into the evolution of the web of recent system we see Senior fossils in economics in game theory suffer example the fact that search engines tests years become as profitable effects on the table called the search economy was nice that you could actually bid for an on specific search keywords Lee said kind counterparts the sign because North designed new kinds of games etiquette also and this intersection of Al Rosen game there would not be the focus of my my fight here is a overseer which I say stem rough the recovery has talk on Tuesday afternoon so it this request that we get it if 1 looks at the network structural Web pages a lengthy trial understanding the structure Richard can't if we look up at a higher level of being dynamics taking place on these networks then we see a different set of questions of of structured to died dynamics of and we got the aggregate behavior people as they actually excesses of the wretched from the structural level but of map the scale of billions of people issued before it spreads on a big surge and the like ruble receives several hundred his for for civilian and as a result we didn't start transceivers an area the river micro level so these examples where John here if data on Google worries some time access number of worries for certain term sexist so that a case of time as far as I know even if you just arrived from Morrison nothing about human beings or language you could refer this as the strain of letters Christmas seems very important at certain times of the forever during last December and you know that criteria repudiated rated the price of example of set each but reasonable could Katrina the name of the heart strip struck the southern U.S. in August 2005 and again very little a treatment separates people if that is the name of until the and and soleus fight again you would know something it happened there regardless of the fact they might not know anything about it the domain now they're also presents of is not of the structure level now global Gregory behavior for example it is their basic vocabulary of usage patterns that we couldn't vote here today to try to decompose inside the things listing behavior that's on the line and that I said I visitors more complicated than simply try defined by regular stables is easiest every goes up but note for example some more subtle features are I don't have time limits of 1 of which is that a sort of strange way but the shape of a spy for Christmas is a staples like Katrina time running back and wires that is because Christmas is expected of them you know from white advance was coming worries ramp up and effort was a kind of good data says rooms on other things forgets all about it on Katrina knowing it was coming a few meteorologists tracking it out the Atlantic Ocean and so when it 1st revenues in the loop 4 is likely nearly vertically and fell off slowly if people for a time red on in the sense expected advance look like unexpected events McCrory logs of time running the other direction and reserve phenomena we liked or understand it and it did at a deeper level separately examples and the kind of analysis of this coupled with the need for operate on massive streams of the state right cutting look for patterns like this with apparent over every turned on me a source of data that's getting several hundred million cars a day on visit the area of stream out of which has post-election with a number of different roles in models with periods of proper testing communication complexity actually in some ways literally now being explored some some some nice west of the intersection comets works of art from article houses accessing not a solicitor for some is that the terrorists have brought up in his talk Wednesday morning at 10 it is good that they're going to
carbon talks also for Goebel somebody issues here although quite different forms what did not With the number Rheingold starts there and the summit as strictly users is also a new focus of ready revealed Wednesday but it was ridiculous as I want to interpolate between 2 things the structure of the web of mission or someone and on the other hand is area properties that we see the like understand better behavior human population and in order interplay between is among needs a build a bridge between the underlying structure and the macro level the number we see red the sort of like a macro step and so we need models of How you individual people have little algorithms have agents interactive information how they interact Network and SX agreed the focus of the the bulk of the namely how individual algorithms are aids observed or people explore information networks using only the information that's available Reds were as this would not have global knowledge of what's our social network of of of the entire Web what has all confirmation when users that's a search for information and somehow with the combined efforts of old people doing that is what we desire that exists and is the particular threat of research but I wanted to try freezing out some of its early origins to some of the recent developments Friday Highway 1 away some of the questions the come up so the odds of this issue of coarser Olden retracted into many areas but the the the particular area which I IYY want to chase it specifically was the margins in social psychology via Morgan Stanley over among the so-called small roles which talk about next life from there like to move on some models of this this this notion of small properties in particular searching for permission some sort of privilege work of what Mister gets much some work on a mail room 2000 from these model for Germany intensely very stylized specific residents sensibly scaled down Route tribes strategy general pattern that we cannot funds for him Real network data the kinds of pictures of a joint figures slides and what is seen as having Web hyperlinks if an enemy With Enemy at least the best data we can find on friendship someone if I Tamil briefly also talk about the circularity whereby whereby the models turned back said the design principles of inform the structure of things like decentralized peer-to-peer file psoriasis on any day any sort of woven brothers is good news left point that a lot is models or probabilistic summer theater section of the Republic graph theory vertical or resisting questions for the topic of what we want 1 read percolation graphs all the time of is life of a solid start still start trajectory would small world sperm standard this is a known some of your costs but I wanted to go through the specifics of it because of the important talks so well Was it promised radio is validate this at the time anecdotal notion that we're all connected by a small number of French warm what we now think of all the we did as the Six Degrees of Separation so puppet tests experiment anecdotal we ought to have friends people but if you want assessed experimentally services is in 1967 stealing from operating without computers with an operating budget of 200 on depicts a few hundred people at random out of our the phone book of Townsend of Nebraska because from his position at Harvard Nebraska to him he said seemed far enough out there that was a good challenge he sent a letter tho was ever conducted experiments with like to the 4th this letter falling designated target a friend of his with the a suburb also in any he gave starting 1st and the targets name their address the reputation and a few other details about the and role for that always have their address had sent a letter directly to them instead you have the males letter some you on a first-name basis a friend of yours with these instructions with the goal of reaching its orders quickly as possible and is wary tried a fine whether they really are these sorts of the friendship that you get from essentially random people To do this sets arbitrary target and the changes the chance to get on board and actually as opposed to what would would would be it has been the case now in experiment 67 people were actually quite willing to participate on a row around 70 fibrous took their 1st upon and about a 3rd of the risk their destination and the drop precisely ran over the same but completed a number of steps a set number that was utterly into popular culture as the 60 separation that on average at 6 steps to get from random people but so this actually caused us some amount of surprise even on the vessel social scientist at the time of the Tamil revolt was colleagues as that if will take some thoughts about a hundred some thought would work at all so it so that the into which we have now got this is what were but at Russian of mathematical models for this was an interesting challenge partly because sort housing grasses not Graf theoretically surprising property almost any random graph Molly make already aggressors would have soared and so the question is why there is a small world surprising to and so on a proposal that what's surrogates made an birds little paper 1988 was the reason is a surprise to us is that Real social network somehow superposition a structured network and ran the rights of the reason why it surprising that were all 6 degrees apart is because we want around us we have lots of friends often know it's ready to have that sort of exponential branching but you would want for 2 have have the world small 8 but of course think about it a bit further and what what surrogates were getting most of our friends know each other but there are those few chances long-range connection was a unexplainable stance friendships and a few of those 4th enough to give us that X before branching Baker's almost anywhere the network and so what they both extract was again intensively stylized says it will fight model which would ever talk later more complexity onto announced following so I'm that I wrote a variation on the exact mold proposed were restorative structured grid network stated 2 minutes of here on and there again metaphorically this this might model effectively all live in the service of Europe we all know our neighbors but recent takers 2 with the point and I will add a very small number of randomly together supposedly say 1 really directed at the Smalls our 1 chance Oregon Puerto Rican measure jars of all more lengths of diverted it is as simple as possible to observe of the point is that sexier factor was known from the theory of random graphs as the random here but I have a job very very quickly while local neighborhoods remained fairly close like as a fundamental thing woes was what derivatives model with diameter small world works as a superposition of the predictable structure we know and the random ones that we don't understand the pixels she but this is it actually was not so much the structural question but In a sense striking Alberta punch line of modems experiments namely if not actually wanted to find the source for most people Nebraska this target Boston benefiting about it in a sense he is the right out we should have said 2 starters take this letter said it's all of your friends tell of the Senate to all of their friends and Everett account steps of the shortest chain Reuschel forms that for now if you reflected this for while obvious things involving U.S. Postal Law and other things that preventative doing this experiment I was forced to
abort the much more interesting experiments that Dr. Rick Connolly is way work force people to target is in fact is that succeed right namely complete strangers without any global multiple sources or somehow you implausibly that if they started pouring message in this direction Samples experiment aggressive make its way to Boston BOSTON into the summer Boston share Massachusetts with target of 1 around their 1st ever to reach the target what was it was causing real navigator was on social Welf so obviously at a very high level we sort of know was that no 1 had a map of social work but went to some for of its or geographic coordinates is also social occupational a sort of aid in the direct rhetoric figuring out what to got to Boston will be able they need more accurately and that's exactly what happened that however is not something that remove graph models recapitulate so well and so that's all they were reacting to define what is a model where not overtake short but unlike like most graph models local information suffices To find a they have formalized and of course actually down precisely what might be set myself with weird take a few minutes With that I have right now so what can they be very quickly we want be set myself out the muscles suffice start a decent that Rome has 1 intuitively which started from starting point going somebody knows the grit was on a grid goes before the target but only knows the red edges of seen so far away the have seen so far orally randomly generated 1 just so specifically essential when the Wendy's letter and a lot of experiments is that no date was the half knows these red those things and would have to produce for us from this information is a choice of which neighbors and trying its target should be centered on worries neighbor next door neighbors were should you follow the ready and you're presumably if he really say human being on experiment you're Jewish said all the ready getting awfully close to the targets so that they set up seized part of the network was sort of known structure or an hour figure of merit wearing gun volatility was on his lawyer collards delivery time we would expect never steps over generous graph renewed further red edges and a real choice started target but expect number steps it takes to reach the doesn't end in thinking about what makes for good was out of work Daddy settlers over the article stand amid all the network is an inviting critic no residents were we want our as expeditiously as this would like some of the pommel function of lard and not a greater quantity of called holy water about it for asking this question although what's surrogates tonight designer mobile especially is as is the perfect minimal model posing question is if you want to make this an interesting question we made a few ingredients you do network but forcibly known for sale on reporters because it's really band but really is the problem fighting a short wrote your for permission it is the unknown again not adjusting because if well random note ideas I have no idea how have so far sold dollars for knowledge glittered don't parts in Ivory high-tech Jackson wanted get Nebraska the Boston always by has passage to next neighbors take over at 1 time so they don't part is useful for war it yourself but not useful for doing much message us but the full Graf has has both died diameter borrowed Catholic between all of it and so did the mastery of model was perfect said press the question for subversive aggression is so duties and was out of work well Austria's model and the forces or their city negative that effect although the diameter of last model some of the most positive water Maxson was later nodes is actually expeditiously size no dissent was I find suffering a centralized name with Freddie rule visible Commission if he could give the expectation we some fast times and the two-thirds Obama was elected as so effect August although not showing what succeeded as something else surprised that there really is a slip between the exist nearly all as of Commissioner we can't find OK so obviously this is not and result we want since Reese about water capture works were like experiment like it actually sort virtually confined so what might be a hopefully mild Charles what sort of small designed or succeed and fears over a proposal organ and 1 extra parameters so Ricky bargain buying agreed with random but every everywhere else better control in a sense the distribution of what differences look like suffer each amid a continued at directly to to but it is doubly was the other end point not uniformly random anymore except in extreme cases but probably causal to their lattice distanced the minus L. now it's important era before it wanted a further that ever freeze is the 30 kinds of dozens going on right physical this summer how for argue organ miles and the graft as was the source of the top-seeded together want another right in the case of breast of Boston was large was thousands of miles of 1 6 but so here the fight this agree so when DVW myself a Elf was like a one-dimensional law-abiding would have 0 have uniform distribution as it should have 0 larger numbers I go from very random was more kind of short-range radio points are less likely that is exact type of long-range percolation model and a lot of talk about the connections later on all although the point that results of persuasively was discretion or not directly likable sums although for about structurally systems questions for short of connectivity wears arrest don't really sorry 1 mental model Idaho 0 and assess workers to ram I can't find him but outsider health club extremely hot there are no more editors and Erinna short of define so prisoners is some kind of ideal operating point of such networks a summary in the middle some were there links controllable but still long enough and cancer is fact in this very stylized model is a single that works and efforts to solemnly surgery from an inverse distribution then there actually is a decent rather than the messages in time for proportional logs and Freddie other exploded as you move away from 2 things get worse there Laura Brown surrender some power think as imagined Forrest that this trade-off very sharp looking asymptotically they served very large when you simulated before and abrupt models good Fred much more forgiving ready yet have begs the the Tremont and say the some but I want 0 1 slight about the sketch of approval which is not very difficult even written on full 1st of us or possibly so scarce in in a case that works say sorry history figures that aware that works in officals 2 is a simple out river that affect subjects were employed which is the gritty when you have the message as always it was also the target as possible if you're read it gets a lot closer take it if it leads the wrong direction and your next what they can do something better with a degree of always decrease us the source was edited out really well psoriatic how the progress of the faults wasn't as it is currently a defeat here at this diva target and let's look at what the chances are good but it now this was the target right now the steps so we
can show that would probably about 1 log and the message lightly injured was ball of radio half a distance in the very next day an air force the same In the expected number of steps about and we'll succeed in having assisted noise have heard what in time and had sees you get a little time about what's that so what you can show that there's a flawed probably Messier you're also as a point of crucial but I wanted to therefore is that the ball of half the every Estee over 2 halves large probably regardless of what right onto a somehow greater independence day where the wearer provided by officals cancels the square provided by the area of the ball in a sense that's really at a much higher were faulty level White wanted to use the red expert because should think about is not be riddle what's forget picture of uniformly distributed random if there was a think about how distributor well call scales of just right all people it doesn't want to do to for 48 between every 2 hours until there is a lot and the scales and when now think most sue in Madrid interventions that's what beautiful uniform over these experts increasing in a white around as I see it mentions the rest Wood said that's what uniform and that quite early on a the site I threw it right from the party pictures of us replaced it with Saul Steinberg's some your recover because in a sense he's had right on head mainly workers view of the world might Avenue devotes the same amount paid real estate to street corner at might Avenue as it does that neighborhood of Manhattan as it does the whole city as it does the eastern U.S. the whole U.S. there China Japan Russia spots on horizon it's exactly as lawyer different scales that's the correct distribution right as the son of correct decision friends that you need in order to find targets officially in the network of so that's what I meant by obstructing general have great independent up particularly wanted for Glaser modeled the glass bonus is apparently cannot go and look for In other words uniformly Eurydice so it before embarking on that I want to talk about some of the big nexus a range for Glaser and more country level so it there is a loss of 1 for Glaser which remote motivated request physics on it was a slightly different models of the graph of infinite we we Eddie dimensional with dimensional and integer Lattice easy for every pair of nodes EW included an effort Freeman and a panel probability let us just throw VW myself the gravity of directed and also the no degrees in a wonder fixed older have fix number friends world but my degree is a random variable controlled by the of now Thorpe said the main differences not be small syntactic differences models but that these the price death were structural model was not certain words effect it beautiful quest you sure justices aggressive Brussels were some some some very hard deep problems about the exists of infinite in Ithaca detector components in graphs in which most of us have work and bridges work the of motor there but small world all these particular kinds of questions there's been some recent work on 1 refer which is mostly consider the graph diameter family hops you need to get 1 point to another as a function of a particular let us go back and ask the question when increases for their rates so it officals to you confined but rather was also there there simply invisible so it distant once light here's here's what's known as result of some suburban fears isomers results our back a finite right so they say and white written indeed the case of alpha below Diaz special because here on in it would make sense even if I guess you get bribery boards degrees is when fast the answer diameter is pressed on but the results were actually different question service that l think calls data 1st transition happens a searchable Expo remember on the every for login over what all the between did indeed Obama's what effect retired non-Jews were aggressive and beyond city about the diameter jumps up again attacked restored minutes it's a so effect officals to is a big open question and assesses the point of transition between Michael Small World and the Lord's world between Paul what really went down and when your life is I no from Morgan 80 someone percolation that officals cities progress on analyzing the connectivity us that's what's known about about business is ice imagined that these models ended request from some other existing LW request with all time to really get briefly but it not backed by socialist search wealthy equals did we say islamic replacing on so again as slightly different rates of small the model because no degrees a random and agrees expectation a lot constant and so the greedy will now finds out force Morgan not wants that's not a major differences of consequence of having a bigger degrees but diameter with lawgiver Lord wanted so effectively album was not finding out there with the optimal 1 and a half of wrestlers is there'll be such lawyers that does and this is not the result of Michael Howard we're deals for 7 effective actually match the diameter that it it up missile suffices be local but with slightly so suppose that the people of Burma and Nollie neurons friends but it every knew all the friends of different than I case you could consider all the neighbors of neighbors and rods of 1 of the closest the target and what so that actually gets you with a cost factor of diameter itself so this is a sense of power out of what it wanted to stuffed into mass diameter and of course were looking at what help you asymptotically because you're already without a and then there's the mothers work which I want times about but it's as a sensitive area of distributed systems on trial Friday information were rapidly through a network by telling telegram nodes His information it is out there offer resistance based on scalability president these difference I'm not at all but 1 percolation BX it turns out says feel the best for for them is exactly the heart of Elf equals twice the image as a fact lack of understanding at that exact points is an obstacle to some of the and force with times sense where I want to get worse think about actual human social networks readily Walterboro suggest certain diameter properties that long range friendships a function of distance is always suggest what real social networks might would like it even makes a sort of startlingly specific prediction about what BXY not if the world a searchable and so I see a very compelling question is whether the world actually looks like that does look like a wiry percolation doesn't look like it has the right now 1 addresses question but we have start movie with Marbury stylized of Britain's restructured primitive we sort of match the messiness of real data and so a number of other related laws for both recently rather hang on on a grid it reserve a real scuffle animators walls hanging around images on other kinds of scuffle suffer example you could assume the notorious hierarchically right the where top priority because my work knows all the leaders of the street and the random edges of forms were now you're more likely linked to a close a closed as measured by how high the Treaty of 2 gotta find it's another direct siblings were likely only knows that deal with the group that's what
kind of model there I had the balls for you to this the note for example a magic space that has low comedy 4th Dimension various reasons cultural work on and again showing how long rieslings defended workers of isometric as I was I 1 of these models of the designed to generalize enough a few of earlier 1 the grids trees that's model based on sex as a result instead of metal those residing at 1st base but instead suppose that the roads residing license so I have my nose and they're sets final our ends with matter again as a metaphor for social networks so you and I might know each other for brighter my because with the same country or we have the same religion or because were fans of the same obscure science-fiction novel right and yard fears that a you're more likely know someone where you and they both want the same small group so the real reason were the most likely know each other is perhaps we both share the same very obscure interest around the back of the same country so it is duty double the size of a small step my collection that contains BMW and only In the size of this fears of Pfizer my Russian just now now the market for any possible sets if they for 2nd I would somehow be hopeless so work a census of the property is amid fears that the city grounds me to property franchise by number Linda was the 1 member category so it the 1st is a nasty property which was as if a node people want to set out that also belongs to a proper subset that's not much smaller only smaller by a factor of of the nesting sets and secondly it is a somehow set system analog of low dimensionality need the wanted sets Archer but said that have not entered a section the size their union is not much bigger than the size of largest for like a bunch of bowls a low dimensional space but a budget balls of what little space altogether point them the the ball and closes them not much bigger than what that His exit poll that you need to get our start working again with searchable network some amicable written graph model based on assesses and later we did for the grid is a summer of telling him and we have an expert gamma which is that the sale phone final over the differently because it'll be it's a circuit of value a snow generates Feierman choosing WC and pointedly I independently rests fraud or salty GVW miners rights scaling the law with the size of that and there now is that it equals 1 for any set systems of property it without agreed on what you have a searchable that work and ready at less than 1 any such as represent any Pollard category you don't research and what is the right value here because think about if another dozens did in place in the immigrated to the size of a small set containing government has size about D squares so we won over the size of a small centers 1 these birds there's a translation of the pierced by a factor of Damocles one-year generalizes the chemicals from from the grip of others and offer question that Is it not summer we after property builds Islamic emigrated there's a pathological found examples of the slow mortality and it would be nice to have all that also the better OK now we can finally asked celebrity because once we have results like this where we could allow an arbitrary sets us then we can actually from start align recesses Israel that as does the sexpot really work so what about the picture like a 2 Doris social network 4 3 6 research is if you will at warehouse and rebuild the network was they observe them over three-month period may join Paris exchange we succeed Healthy Choice belted official there was a subsystem obvious life and but they found actually when the group for defined by some for preparatory was Appling scale size the minors before May wait want increasing size a bit too random said to be searchable but always surprising closed the searchable network as bus is advising given course a few levels is designed to do research to further the Goals of Hewlett-Packard Co. not to perform rods the experiment is now it carries a wider said all the a surge voiced agrees that allows a 1st my Water Seal measurement and rebel firstly with some conclusions so the he adopted or was breezy just might be going on but it was a the scale of 405 people meant it was good as I fee structure think that may be a factor was hopeless directly actual riddle setting the modem experiments on and exit at How does friendship the scales with real physical list but in fact these advent of all the reasons online are still such as social networking online data also leader justice but says doesn't there is the work of the now Novak right on time To date for this thing called life journal which is very small version of myspace social norms service the what teenagers and college students hang out on and exactly the data you want wanted because it has about him at the time but half a million members with user profile containing U.S. the housing bill that look at them and links to other friends were so it exactly where to measure how sensitive because of the effect on their 1st what the founders overcome in adapting to base model was 1 of my journal and also give also is suffering in sense that conceptually while Celtic which is a highly nonuniform population density mainly of the Dead Sea of electoral users and we 1st look at it so I thought that's funny it's all in eastern U.S. for this in his life but that actually it's that this is roughly population density of U.S. self wider Wellesley well samples it is simply part with the U.S not uniform so we have to get over them and so they proposed so I want to do that with the group is model and buying groups my In the plane they sells 1 that work better for their also was a single rank French so it's no good say beat ranks all the other simply in order of justice from the rank of W was with a number of other nodes closer but it's a W is 1 2 3 4 5 6 7 and again this translates bonds down by a factor of 2 so you I want to be the surge was them and ask your favorite for essentially any population density of a plane if the link pop probably for 1 or the rank and you you you get searchable says jails it and how they don't actually matters and the in Europe that that large French very closely approximate 1 over the right the empirical data it is blind you see 1 rank as we 1 almost hourly civil war rights of 1 . 0 5 very very closely tracking a rank episodic what's opponents in this article along with other so this is my next less liable for it to conclusions and as wanton maintenance a few ways with I found Saudi startling results 1st did as a small without officals you made again a sort of very specific predictions about what we need research ability as out its some surprising a sense that we knew the bulk parents exceeded 40 years ago it's number was surprised to see that borne out in actual data on secondly it's simply not obviously be driving the networks toward that distribution rights wife drill users use the system to chat with their friends share their interests of write blogs and so forth they don't it's a search through social contact the try find short fails to random people it's not clear what the selective pressure it the cause of retrieval 42nd surge yet Theriot right there is but like the we don't really know what links media what their forms of and all the more so when final stop all the more so online you might imagine that life journal possibly want him again on the system and sure giving spite it doesn't 0 because high school wanted to talk to the Rutherford High School the with the same say by a lot of principally said is roughly 0 but despite the rest the way these sort of uniform after all the online world knows no geographic boundaries it oughta be just as easy to make friends a summit halfway around the world was local where that is not what happened right the prejudice respect always attributes us scales of surely as respects very close as a sort of an interesting contrast of the vessel the bat in the online world propping up geographic barriers missile sealed very very strong and predictable evidence of and as a mail so would be great to understand what so some glitter wrap up with some reflected as there is a sense it is sort of this very rapid fashion try to sell you a progressive research Preston's ranging from early source our research through online data mathematical models to some very recent surprise that figure really need a much better theoretical X X exclamation and on the way it really was restated that not let us study questions that they're really really got the asked whether that would be impossible formally 20 years ago request 1 makes sense once a large fraction world population is this 0 online systems are different missions communicating with slightly more powerful frameworks for thing about this 1 obviously as out like a probable signals that I talked about a 2nd thread of various degrees of this Is the use of quest now techniques sex Novell rebounds in game theory to model these interactions on some recent survey references and again probably talk on Tuesday of forests on my worry seeing that set learn August by observing millions of people who had no intention of ever being observed true they may all the public on the Internet so all we're doing is looking at it but there is a sense of between privacy and messages of human activity attention has been similar attention recently and it is a very pressing issue and is in itself an important research area in the mathematical aspects of pure science get more topics that they could be happy to us talk about but at this time I'd like to stop era but thank you again this vesting virus again thank you grew up in this
Nachbarschaft <Mathematik>
Ungerichteter Graph
Gesetz <Physik>
Gerichteter Graph
Dynamisches System
Negative Zahl
Vorzeichen <Mathematik>
Translation <Mathematik>
Kategorie <Mathematik>
Güte der Anpassung
Dichte <Physik>
Rechter Winkel
Sortierte Logik
Ordnung <Mathematik>
Explosion <Stochastik>
Stabilitätstheorie <Logik>
Abgeschlossene Menge
Spannweite <Stochastik>
Algebraische Struktur
Arithmetische Folge
Fächer <Mathematik>
Reelle Zahl
Hierarchie <Mathematik>
Thermodynamisches System
Stochastische Abhängigkeit
Chirurgie <Mathematik>
Äquivariante Abbildung
Eigentliche Abbildung
Abstimmung <Frequenz>
Prozess <Physik>
Natürliche Zahl
Formale Potenzreihe
Familie <Mathematik>
Kartesische Koordinaten
Superposition <Mathematik>
Komplex <Algebra>
Exakter Test
Uniforme Struktur
Kontrast <Statistik>
Figurierte Zahl
Funktion <Mathematik>
Lineares Funktional
Nichtlinearer Operator
Zentrische Streckung
Physikalischer Effekt
Ideal <Mathematik>
Ganze Zahl
Strategisches Spiel
Körper <Physik>
Toter Winkel
Derivation <Algebra>
Trajektorie <Mathematik>
Physikalische Theorie
Inverser Limes
Zusammenhängender Graph
Diskrete Optimierung
Leistung <Physik>
Einfach zusammenhängender Raum
Fundamentalsatz der Algebra
Wald <Graphentheorie>
Matching <Graphentheorie>
Physikalisches System
Kette <Mathematik>
Numerisches Modell


Formale Metadaten

Titel Nevanlinna Prize Winner
Serientitel International Congress of Mathematicians, Madrid 2006
Anzahl der Teile 33
Autor Kleinberg, Jon
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/15970
Herausgeber Instituto de Ciencias Matemáticas (ICMAT)
Erscheinungsjahr 2006
Sprache Englisch

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