<![CDATA[ IEEE Transactions on Network Science and Engineering - new TOC ]]>
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TOC Alert for Publication# 6488902 2017December 14<![CDATA[How Complex Contagions Spread Quickly in Preferential Attachment Models and Other Time-Evolving Networks]]>$k$-complex contagion model is a social contagion model which describes the diffusion of behaviors in networks where the successful adoption of a behavior requires influence from multiple contacts. It has been argued that complex contagions better model behavioral changes such as adoption of new beliefs, fashion trends or expensive technology innovations. A contagion in this model starts from a set of initially infected seeds and progresses in rounds. In any round any node with at least $k>1$ infected neighbors becomes infected. Previous work on $k$-complex contagions was focused on networks with uniform degree distributions. However, many real-world network topologies have non-uniform degree distribution and evolve over time. We analyze the spreading rate of a $k$-complex contagion in a general family of time-evolving networks which includes the preferential attachment (PA) model. We prove that if the initial seeds are chosen as the $k$ earliest nodes in a network of this family, a $k$-complex contagion covers the entire network of $n$ nodes in $O(log n)$ rounds with high probability (w.h.p). We prove that the choice of the seeds is crucial: in the PA model, even if a much larger number of seeds are chosen uniformly randomly, the contagion stops prematurely w.h.p. Although the earliest nodes in a PA model are likely to have high degrees, it is actually the evolutionary graph structure of such models that facilitates fast spreading of complex contagions. The general family of time-evolving graphs with this property even contains networks without a power law degree distribution. Finally, we prove that when a $k$-complex contagion starts from an arbitrary set of initial seeds on a general graph, determining if the number of infected vertices is above a given threshold is ${mathbf {P}}$-complete. Thus, one cannot hope to categorize all the settings in which $k$-complex contagions percolate in a graph.]]>44201214350<![CDATA[Moment-Based Spectral Analysis of Random Graphs with Given Expected Degrees]]>expected degrees, denoted by $overline{w}_n = (w^{(n)}_1,ldots, w^{(n)}_n)$, is prescribed on the $n$ nodes of a random graph. We focus on the eigenvalues of the normalized (random) adjacency matrix of the graph ensemble, defined as $mathbf {A}_n$$=$$sqrt{nrho _n}[mathbf {a}^{(n)}_{i,j}]_{i,j=1}^{n}$, where $rho _n = 1/sum _{i=1}^{n} w^{(n)}_i$ and $mathbf {a}^{(n)}_{i,j} =1$ if there is an edge between the nodes $lbrace i,jrbrace$, 0 otherwise. The empirical spectral distribution of $mathbf {A}_n$, denoted by $mathbf {F}_n(mathord {cdot})$, is the empirical measure putting a mass $1/n$ at each of the $n$ real eigenvalues of the symmetric matrix $mathbf {A}_n$. Under some technical conditions on the expected degree sequence, we show that with probability one $mathbf {F}_n(mathord {cdot})$ converges weakly to a deterministic distribution $F(mathord {cdot})$ as $nrightarrow infty$. Furthermore, we fully characterize this deterministic distribution by providing explicit closed-form expressions for the moments of $F(mathord {cdot})$. We illustrate our results with two well-known degree distributions, namely, the powe]]>44215228505<![CDATA[Network Maximal Correlation]]>442292471310<![CDATA[Stochastic Subgradient Algorithms for Strongly Convex Optimization Over Distributed Networks]]>$Oleft(frac{Nsqrt{N}}{(1-sigma)T}right)$ after $T$ gradient updates for each node on a network of $N$ nodes, where $0leq sigma <1$ denotes the second largest singular value of the communication matrix. This rate of convergence matches the performance lower bound up to constant terms. Similar to the SSD algorithm, the computational complexity of the proposed algorithm also scales linearly with the dimensionality of the data. Furthermore, the communication load of the proposed method is the same as the communication load of the SSD algorithm. Thus, the proposed algorithm is highly efficient in terms of complexity and communication load. We illustrate the merits of the algorithm with respect to the state-of-art methods over benchmark real life data sets.]]>442482601373