Learning Cooperative Games

This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given $m$ random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the values of unseen coalitions? We study the PAC learnability of several well-known classes of cooperative games, such as network flow games, threshold task games, and induced subgraph games. We also establish a novel connection between PAC learnability and core stability: for games that are efficiently learnable, it is possible to find payoff divisions that are likely to be stable using a polynomial number of samples.Comment: accepted to IJCAI 201

Robustness of Transcriptional Regulation in Yeast-like Model Boolean Networks

We investigate the dynamical properties of the transcriptional regulation of gene expression in the yeast Saccharomyces Cerevisiae within the framework of a synchronously and deterministically updated Boolean network model. By means of a dynamically determinant subnetwork, we explore the robustness of transcriptional regulation as a function of the type of Boolean functions used in the model that mimic the influence of regulating agents on the transcription level of a gene. We compare the results obtained for the actual yeast network with those from two different model networks, one with similar in-degree distribution as the yeast and random otherwise, and another due to Balcan et al., where the global topology of the yeast network is reproduced faithfully. We, surprisingly, find that the first set of model networks better reproduce the results found with the actual yeast network, even though the Balcan et al. model networks are structurally more similar to that of yeast.Comment: 7 pages, 4 figures, To appear in Int. J. Bifurcation and Chaos, typos were corrected and 2 references were adde

Video Pandemics: Worldwide Viral Spreading of Psy's Gangnam Style Video

Viral videos can reach global penetration traveling through international channels of communication similarly to real diseases starting from a well-localized source. In past centuries, disease fronts propagated in a concentric spatial fashion from the the source of the outbreak via the short range human contact network. The emergence of long-distance air-travel changed these ancient patterns. However, recently, Brockmann and Helbing have shown that concentric propagation waves can be reinstated if propagation time and distance is measured in the flight-time and travel volume weighted underlying air-travel network. Here, we adopt this method for the analysis of viral meme propagation in Twitter messages, and define a similar weighted network distance in the communication network connecting countries and states of the World. We recover a wave-like behavior on average and assess the randomizing effect of non-locality of spreading. We show that similar result can be recovered from Google Trends data as well.Comment: 10 page

Learning with a Drifting Target Concept

We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target concept that can change on each round. One of our main contributions is a refinement of the best previous results for polynomial-time algorithms for the space of linear separators under a uniform distribution. We also provide general results for an algorithm capable of adapting to a variable rate of drift of the target concept. Some of the results also describe an active learning variant of this setting, and provide bounds on the number of queries for the labels of points in the sequence sufficient to obtain the stated bounds on the error rates

Multiscale mobility networks and the large scale spreading of infectious diseases

Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. In order to study the interplay between small-scale commuting flows and long-range airline traffic in shaping the spatio-temporal pattern of a global epidemic we i) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms; ii) integrate in a worldwide structured metapopulation epidemic model a time-scale separation technique for evaluating the force of infection due to multiscale mobility processes in the disease dynamics. Commuting flows are found, on average, to be one order of magnitude larger than airline flows. However, their introduction into the worldwide model shows that the large scale pattern of the simulated epidemic exhibits only small variations with respect to the baseline case where only airline traffic is considered. The presence of short range mobility increases however the synchronization of subpopulations in close proximity and affects the epidemic behavior at the periphery of the airline transportation infrastructure. The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multi-scale framework.Comment: 10 pages, 4 figures, 1 tabl

Phase transitions in contagion processes mediated by recurrent mobility patterns

Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modeled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyze contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected. This transition cannot be uncovered by continuous deterministic models due to the stochastic features of the contagion process and defines an invasion threshold that depends on mobility parameters, providing guidance for controlling contagion spread by constraining mobility processes. We recover the threshold behavior by analyzing diffusion processes mediated by real human commuting data.Comment: 20 pages of Main Text including 4 figures, 7 pages of Supplementary Information; Nature Physics (2011

Analytical Solution of a Stochastic Content Based Network Model

We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches, for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behavior to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show scaling behavior. The results might be of interest for understanding the emergence of genomic interaction networks, which rely, to a large extent, on mechanisms based on sequence matching, and exhibit similar global features to those found here.Comment: 13 pages, 5 figures. Rewrote conclusions regarding the relevance to gene regulation networks, fixed minor errors and replaced fig. 4. Main body of paper (model and calculations) remains unchanged. Submitted for publicatio

Dynamical real-space renormalization group calculations with a new clustering scheme on random networks

We have defined a new type of clustering scheme preserving the connectivity of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving process. Our new clustering scheme performs much better for correlation length and dynamical critical exponents in high dimensions, where the conventional Migdal-Kadanoff bond moving scheme breaks down. In two and three dimensions we find the dynamical critical exponents for the kinetic Ising Model to be z=2.13 and z=2.09, respectively at pure Ising fixed point. These values are in very good agreement with recent Monte Carlo results. We investigate the phase diagram and the critical behaviour for randomly bond diluted lattices in d=2 and 3, in the light of this new transformation. We also provide exact correlation exponent and dynamical critical exponent values on hierarchical lattices with power-law degree distributions, both in the pure and random cases.Comment: 8 figure