Distributed Community Detection in Dynamic Graphs

Inspired by the increasing interest in self-organizing social opportunistic networks, we investigate the problem of distributed detection of unknown communities in dynamic random graphs. As a formal framework, we consider the dynamic version of the well-studied \emph{Planted Bisection Model} \sdG(n,p,q) where the node set $[n]$ of the network is partitioned into two unknown communities and, at every time step, each possible edge $(u,v)$ is active with probability $p$ if both nodes belong to the same community, while it is active with probability $q$ (with $q<<p$) otherwise. We also consider a time-Markovian generalization of this model. We propose a distributed protocol based on the popular \emph{Label Propagation Algorithm} and prove that, when the ratio $p/q$ is larger than $n^{b}$ (for an arbitrarily small constant $b>0$), the protocol finds the right "planted" partition in $O(\log n)$ time even when the snapshots of the dynamic graph are sparse and disconnected (i.e. in the case $p=\Theta(1/n)$).Comment: Version I

Phylogenetic Analysis of Kindlins Suggests Subfunctionalization of an Ancestral Unduplicated Kindlin into Three Paralogs in Vertebrates

Kindlin proteins represent a newly discovered family of evolutionarily conserved FERM domain-containing proteins. This family includes three highly conserved proteins: Kindlin-1, Kindlin-2 and Kindlin-3. All three Kindlin proteins are associated with focal adhesions and are involved in integrin activation. The FERM domain of each Kindlin is bipartite and plays a key role in integrin activation. We herein explore for the first time the evolutionary history of these proteins. The phylogeny of the Kindlins suggests a single ancestral Kindlin protein present in even the earliest metazoan ie, hydra. This protein then underwent duplication events in insects and also experienced genome duplication in vertebrates, leading to the Kindlin family. A comparative study of the Kindlin paralogs showed that Kindlin-2 is the slowest evolving protein among the three family members. The analysis of synonymous and non-synonymous substitutions in orthologous Kindlin sequences in different species showed that all three Kindlins have been evolving under the influence of purifying selection. The expression pattern of Kindlins along with phylogenetic studies supports the subfunctionalization model of gene duplication

Differential item functioning due to gender between depression and anxiety items among Chilean adolescents

Although much is known about the higher prevalence of anxiety and depressive disorders among adolescent females, less is known about the differential item endorsement due to gender in items of commonly scales used to measure anxiety and depression. We conducted a study to examine if adolescent males and females from Chile differed on how they endorsed the items of the Youth Self-Report (YSR) anxious/depressed problem scale. We used data from a cross-sectional sample consisting of 925 participants (Mean age = 14, SD=1.3, 49% females) of low to lower-middle socioeconomic status. A two-parameter logistic (2PL) IRT DIF model was fit. Results revealed differential item endorsement (DIF) by gender for six of the 13 items with adolescent females being more likely to endorse a depression item while males were found more likely to endorse anxiety items. Findings suggest that items found in commonly utilized measures of anxiety and depression symptoms may not equally capture true levels of these behavioral problems among adolescent males and females. Given the high levels of mental disorders in Chile and surrounding countries, further attention should be focused on increasing the number of empirical studies examining potential gender differences in the assessment of mental health problems among Latin American populations to better aid our understanding of the phenomenology and determinants of these problems in the region.R01 HD033487 - NICHD NIH HHS; R01 DA021181-05 - NIDA NIH HHS; R01 DA021181 - NIDA NIH HH

Network Transitivity and Matrix Models

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix model, where matrices are random, but their elements take values 0 and 1 only. Confusion present in some papers where earlier attempts to incorporate transitivity in a similar framework have been made is hopefully dissipated. Inspired by more conventional matrix models, new analytic techniques to develop a static model with non-trivial clustering are introduced. Computer simulations complete the analytic discussion.Comment: 11 pages, 7 eps figures, 2-column revtex format, print bug correcte

Percolation in the classical blockmodel

Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation transition in the classical blockmodel has not been examined so far, although the phenomenon has been studied in a variety of much more complicated models of interconnected and multiplex networks. In this paper we derive the self-consistent equation for the size the global percolation cluster in the classical blockmodel. We also find the condition for percolation threshold which characterizes the emergence of the giant component. We show that the discussed percolation phenomenon may cause unexpected problems in a simple optimization process of the multilevel network construction. Numerical simulations confirm the correctness of our theoretical derivations.Comment: 7 pages, 6 figure

Effect of disorder on superconductivity in the boson-fermion model

We study how a randomness of either boson or fermion site energies affects the superconducting phase of the boson fermion model. We find that, contrary to what is expected for s-wave superconductors, the non-magnetic disorder is detrimental to the s-wave superconductivity. However, depending in which subsystem the disorder is located, we can observe different channels being affected. Weak disorder of the fermion subsystem is responsible mainly for renormalization of the single particle density of states while disorder in the boson subsystem directly leads to fluctuation of the strength of the effective pairing between fermions.Comment: 7 pages, 6 figures. Physical Review B (accepted for publication

Laser-induced collective excitations in a two-component Fermi gas

We consider the linear density response of a two-component (superfluid) Fermi gas of atoms when the perturbation is caused by laser light. We show that various types of laser excitation schemes can be transformed into linear density perturbations, however, a Bragg spectroscopy scheme is needed for transferring energy and momentum into a collective mode. This makes other types of laser probing schemes insensitive for collective excitations and therefore well suited for the detection of the superfluid order parameter. We show that for the special case when laser light is coupled between the two components of the Fermi gas, density response is always absent in a homogeneous system.Comment: 6 pages, no figure

Social Cohesion, Structural Holes, and a Tale of Two Measures

EMBARGOED - author can archive pre-print or post-print on any open access repository after 12 months from publication. Publication date is May 2013 so embargoed until May 2014.This is an author’s accepted manuscript (deposited at arXiv arXiv:1211.0719v2 [physics.soc-ph] ), which was subsequently published in Journal of Statistical Physics May 2013, Volume 151, Issue 3-4, pp 745-764. The final publication is available at link.springer.com http://link.springer.com/article/10.1007/s10955-013-0722-

Subgraphs in random networks

Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g edges scales with network size as \mean{G} ~ N^{n-g}. However, many natural networks have a non-Poissonian degree distribution. Here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks, characterized by an arbitrary degree sequence. We find new scaling rules for the commonly occurring case of directed scale-free networks, in which the outgoing degree distribution scales as P(k) ~ k^{-\gamma}. Considering the power exponent of the degree distribution, \gamma, as a control parameter, we show that random networks exhibit transitions between three regimes. In each regime the subgraph number of appearances follows a different scaling law, \mean{G} ~ N^{\alpha}, where \alpha=n-g+s-1 for \gamma<2, \alpha=n-g+s+1-\gamma for 2<\gamma<\gamma_c, and \alpha=n-g for \gamma>\gamma_c, s is the maximal outdegree in the subgraph, and \gamma_c=s+1. We find that certain subgraphs appear much more frequently than in Erdos networks. These results are in very good agreement with numerical simulations. This has implications for detecting network motifs, subgraphs that occur in natural networks significantly more than in their randomized counterparts.Comment: 8 pages, 5 figure