Social scientists have observed that human behavior in society can often be modeled as corresponding to a threshold type policy. A new behavior would propagate by a procedure in which an individual adopts the new behavior if the fraction of his neighbors or friends having adopted the new behavior exceeds some threshold. In this paper we study the question of whether the emergence of threshold policies may be modeled as a result of some rational process which would describe the behavior of non-cooperative rational members of some social network. We focus on situations in which individuals take the decision whether to access or not some content, based on the number of views that the content has. Our analysis aims at understanding not only the behavior of individuals, but also the way in which information about the quality of a given content can be deduced from view counts when only part of the viewers that access the content are informed about its quality. In this paper we present a game formulation for the behavior of individuals using a meanfield model: the number of individuals is approximated by a continuum of atomless players and for which the Wardrop equilibrium is the solution concept. We derive conditions on the problem's parameters that result indeed in the emergence of threshold equilibria policies. But we also identify some parameters in which other structures are obtained for the equilibrium behavior of individuals.
The paper @cite_3 provides analysis of power law behavior for the rank distribution of contents; the distribution of most watched videos is found heavily skewed towards the most popular ones.
@cite_3
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A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential attachment and copying mechanisms that existing evolving graph processes fail to model due to technical obstacles. The result also serves as a further cautionary note reinforcing the point of view that a power law degree distribution should not be regarded as the only important characteristic of a complex network, as has been previously argued [D. Achlioptas, A. Clauset, D. Kempe, C. Moore, On the bias of traceroute sampling, or power-law degree distribution in regular graphs, in: Proceedings of the 37th ACM Symposium on Theory of Computing, STOC'05, 2005, pp. 694-703; L. Li, D. Alderson, J. Doyle, W. Willinger, Towards a theory of scale-free graphs: Definition, properties, and implications, Internet Mathematics 2 (4) (2005) 431-523; M. Mitzenmacher, The future of power law research, Internet Mathematics, 2 (4) (2005) 525-534]. Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out. We propose a plausible explanation of the power law distributions of degrees observed in the graphs arising in the Internet topology [Faloutsos, Faloutsos, and Faloutsos, SIGCOMM 1999] based on a toy model of Internet growth in which two objectives are optimized simultaneously: "last mile" connection costs, and transmission delays measured in hops. We also point out a similar phenomenon, anticipated in [Carlson and Doyle, Physics Review E 1999], in the distribution of file sizes. Our results seem to suggest that power laws tend to arise as a result of complex, multi-objective optimization. Considerable attention has been focused on the properties of graphs derived from Internet measurements. Router-level topologies collected via traceroute-like methods have led some to conclude that the router graph of the Internet is well modeled as a power-law random graph. In such a graph, the degree distribution of nodes follows a distribution with a power-law tail. We argue that the evidence to date for this conclusion is at best insufficient We show that when graphs are sampled using traceroute-like methods, the resulting degree distribution can differ sharply from that of the underlying graph. For example, given a sparse Erdos-Renyi random graph, the subgraph formed by a collection of shortest paths from a small set of random sources to a larger set of random destinations can exhibit a degree distribution remarkably like a power-law. We explore the reasons for how this effect arises, and show that in such a setting, edges are sampled in a highly biased manner. This insight allows us to formulate tests for determining when sampling bias is present. When we apply these tests to a number of well-known datasets, we find strong evidence for sampling bias. Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have conjectured that preferential connectivity and incremental growth are both required for the power law distribution. In this paper, we propose a different web graph model with power law distribution that does not require incremental growth. We also provide a comparison of our model with several others in their ability to predict web graph clustering behavior. We show that the empirical distribution of the PageRank values in a large set of Web pages does not follow a power-law except for some particular choices of the damping factor. We argue that for a graph with an in-degree distribution following a power-law with exponent between 2.1 and 2.2, choosing a damping factor around 0.85 for PageRank yields a power-law distribution of its values. We suggest that power-law distributions of PageRank in Web graphs have been observed because the typical damping factor used in practice is between 0.85 and 0.90. Video is the main driver for the inexorable increase in wireless data traffic. In this paper we analyze a new architecture in which device-to-device (D2D) communications is used to drastically increase the capacity of cellular networks for video transmission. Users cache popular video files and - after receiving requests from other users - serve these requests via D2D localized transmissions; the short range of the D2D transmission enables frequency reuse within the cell. We analyze the scaling behavior of the throughput with the number of devices per cell. The user content request statistics, as well as the caching distribution, are modeled by a Zipf distribution with parameters γ r and γ c , respectively. For the practically important case γ r c > 1, we derive a closed form expression for the scaling behavior of the number of D2D links that coexist without interference. Our analysis relies on a novel Poisson approximation result for wireless networks obtained through the Chen-Stein Method. This paper develops a framework for studying the popularity dynamics of user-generated videos, presents a characterization of the popularity dynamics, and proposes a model that captures the key properties of these dynamics. We illustrate the biases that may be introduced in the analysis for some choices of the sampling technique used for collecting data; however, sampling from recently-uploaded videos provides a dataset that is seemingly unbiased. Using a dataset that tracks the views to a sample of recently-uploaded YouTube videos over the first eight months of their lifetime, we study the popularity dynamics. We find that the relative popularities of the videos within our dataset are highly non-stationary, owing primarily to large differences in the required time since upload until peak popularity is finally achieved, and secondly to popularity oscillation. We propose a model that can accurately capture the popularity dynamics of collections of recently-uploaded videos as they age, including key measures such as hot set churn statistics, and the evolution of the viewing rate and total views distributions over time. We present a dynamical model for rewiring and attachment in bipartite networks. Edges are placed between nodes that belong to catalogs that can either be fixed in size or growing in size. The model is motivated by an empirical study of data from the video rental service Netflix, which invites its users to give ratings to the videos available in its catalog. We find that the distribution of the number of ratings given by users and that of the number of ratings received by videos both follow a power law with an exponential cutoff. We also examine the activity patterns of Netflix users and find bursts of intense video-rating activity followed by long periods of inactivity. We derive ordinary differential equations to model the acquisition of edges by the nodes over time and obtain the corresponding time-dependent degree distributions. We then compare our results with the Netflix data and find good agreement. We conclude with a discussion of how catalog models can be used to study systems in which agents are ... Making recommendations by learning to rank is becoming an increasingly studied area. Approaches that use stochastic gradient descent scale well to large collaborative filtering datasets, and it has been shown how to approximately optimize the mean rank, or more recently the top of the ranked list. In this work we present a family of loss functions, the k-order statistic loss, that includes these previous approaches as special cases, and also derives new ones that we show to be useful. In particular, we present (i) a new variant that more accurately optimizes precision at k, and (ii) a novel procedure of optimizing the mean maximum rank, which we hypothesize is useful to more accurately cover all of the user's tastes. The general approach works by sampling N positive items, ordering them by the score assigned by the model, and then weighting the example as a function of this ordered set. Our approach is studied in two real-world systems, Google Music and YouTube video recommendations, where we obtain improvements for computable metrics, and in the YouTube case, increased user click through and watch duration when deployed live on www.youtube.com. We present a detailed statistical analysis of a 2-hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accurately described using “heavy-tailed” distributions (e.g., Pareto); (2) the autocorrelation of the VBR video sequence decays hyperbolically (equivalent to long-range dependence ) and can be modeled using self-similar processes. We combine our findings in a new (non-Markovian) source model for VBR video and present an algorithm for generating synthetic traffic. Trace-driven simulations show that statistical multiplexing results in significant bandwidth efficiency even when long-range dependence is present. Simulations of our source model show long-range dependence and heavy-tailed marginals to be important components which are not accounted for in currently used VBR video traffic models. This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnov test for goodness-of-fit tailored to power-law distributions in which the power-law exponent is estimated using MLE. The techniques presented here will advance the application of complex network theory by allowing reliable estimation of power-law models from data and further allowing quantitative assessment of goodness-of-fit of proposed power-law models to empirical data. In the study of the spectra of power-law graphs, there are basically two competing approaches. One is to prove analogues of Wigner's semicircle law, whereas the other predicts that the eigenvalues follow a power-law distribution. Although the semicircle law and the power law have nothing in common, we will show that both approaches are essentially correct if one considers the appropriate matrices. We will prove that (under certain mild conditions) the eigenvalues of the (normalized) Laplacian of a random power-law graph follow the semicircle law, whereas the spectrum of the adjacency matrix of a power-law graph obeys the power law. Our results are based on the analysis of random graphs with given expected degrees and their relations to several key invariants. Of interest are a number of (new) values for the exponent β, where phase transitions for eigenvalue distributions occur. The spectrum distributions have direct implications to numerous graph algorithms such as, for example, randomized algorithms that involve rapidly mixing Markov chains. The analysis of the leading social video sharing platform YouTube reveals a high amount of redundancy, in the form of videos with overlapping or duplicated content. In this paper, we show that this redundancy can provide useful information about connections between videos. We reveal these links using robust content-based video analysis techniques and exploit them for generating new tag assignments. To this end, we propose different tag propagation methods for automatically obtaining richer video annotations. Our techniques provide the user with additional information about videos, and lead to enhanced feature representations for applications such as automatic data organization and search. Experiments on video clustering and classification as well as a user evaluation demonstrate the viability of our approach. Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and circular substructures, and the sizes of molecular similarity clusters all show linear trends on log-log rank frequency plots, suggesting underlying power-law distributions. The number of unique features also follow Heaps'-like laws. The characteristic exponents of the power-laws lie in the 1.5-3 range, consistently with the exponents observed in other power-law phenomena. The power-law nature of these distributions leads to several applications including the prediction of the growth of available data through Heaps' law and the optimal allocation of experimental or computational resources via the 80 20 rule. More importantly, we also show how the power-laws can be leveraged to efficiently compress chemical fingerprints in a lossless manner, useful for the improved storage and retrieval of molecules in large chemical databases. In this paper, we examine mobile users' behavior and their corresponding video viewing patterns from logs extracted from the servers of a large scale VoD system. We focus on the analysis of the main discrepancies that might exist when users access the VoD system catalog from WiFi or 3G connections. We also study factors that might impact mobile users' interests and video popularity. The users' behavior exhibits strong daily and weekly patterns, with mobile users' interests being surprisingly spread across almost all categories and video lengths, independently of the connection type. However, by examining the activity of users individually, we observed a concentration of interests and peculiar access patterns, which allows to classify the users and thus better predict their behavior. We also find a skewed video popularity distribution and then demonstrate that the popularity of a video can be predicted using its very early popularity level. We further analyzed the sources of video viewing and found that even if search engines are the dominant sources for a majority of videos, they represent less than 10 (resp. 20 ) of the sources for the highly popular videos in 3G (resp. WiFi) network. We report that both the type of connections and mobile devices in use have an impact on the viewing time and the source of viewing. Based on our findings, we provide insights and recommendations that can be used to design intelligent mobile VoD systems and help improving personalized services on these platforms. This paper presents an efficient approach for copies detection in a large videos archive consisting of several hundred of hours. The video content indexing method consists of extracting the dynamic behavior on the local description of interest points and further on the estimation of their trajectories along the video sequence. Analyzing the low-level description obtained allows to highlight trends of behaviors and then to assign a label of behavior to each local descriptor. Such an indexing approach has several interesting properties: it provides a rich, compact and generic description, while labels of behavior provide a high-level description of the video content. Here, we focus on video Content Based Copy Detection (CBCD). Copy detection is problematic as similarity search problem but with prominent differences. To be efficient, it requires a dedicated on-line retrieval method based on a specific voting function. This voting function must be robust to signal transformations and discriminating versus high similarities which are not copies. The method we propose in this paper is a dedicated on-line retrieval method based on a combination of the different dynamic contexts computed during the off-line indexing. A spatio-temporal registration based on the relevant combination of detected labels is then applied. This approach is evaluated using a huge video database of 300 hours with different video tests. The method is compared to a state-of-the art technique in the same conditions. We illustrate that taking labels into account in the specific voting process reduces false alarms significantly and drastically improves the precision. We examine the fundamental properties that determine the basic performance metrics for opportunistic communications. We first consider the distribution of intercontact times between mobile devices. Using a diverse set of measured mobility traces, we find as an invariant property that there is a characteristic time, order of half a day, beyond which the distribution decays exponentially. Up to this value, the distribution in many cases follows a power law, as shown in recent work. This power law finding was previously used to support the hypothesis that intercontact time has a power law tail, and that common mobility models are not adequate. However, we observe that the timescale of interest for opportunistic forwarding may be of the same order as the characteristic time, and thus, the exponential tail is important. We further show that already simple models such as random walk and random waypoint can exhibit the same dichotomy in the distribution of intercontact time as in empirical traces. Finally, we perform an extensive analysis of several properties of human mobility patterns across several dimensions, and we present empirical evidence that the return time of a mobile device to its favorite location site may already explain the observed dichotomy. Our findings suggest that existing results on the performance of forwarding schemes based on power law tails might be overly pessimistic. Online social networks (OSNs) have become popular destinations for connecting friends and sharing information. Recent statistics suggest that OSN users regularly share contents from video sites, and a significant amount of requests of the video sites are indeed from them nowadays. These behaviors have substantially changed the workload of online video services. To better understand this paradigm shift, we conduct a long-term and extensive measurement of video sharing in RenRen, the largest Facebook-like OSN in China. In this paper, we focus on the video popularity distribution and evolution. In particular, we find that the video popularity distribution exhibits perfect power-law feature (while videos in YouTube exhibit a power-law waist with a long truncated tail). Moreover, we observe that the requests for the new published videos generally experience two or three days latency to reach the peak value, and then change dynamically with a series of unpredictable bursts (while in YouTube, videos reach the global peak immediately after introduction to the system, and then the accesses generally decrease overtime, except possibly on some special days). These differences can raise new challenges to content providers. For example, the video popularity is now hard to predict based on their historical requests. We further develop a simple yet effective model to simulate user requests process across videos in OSNs. Trace-based simulation shows that it can well capture the observed features. The rapid growth of social networking and gaming sites is associated with an increase of online bullying activities which, in the worst scenario, result in suicidal attempts by the victims. In this paper, we propose an effective technique to detect and rank the most influential persons (predators and victims). It simplifies the network communication problem through a proposed detection graph model. The experimental results indicate that this technique is highly accurate.