Least Cost Influence Maximization Across Multiple Social Networks

Recently in Online Social Networks (OSNs), the Least Cost Influence (LCI) problem has become one of the central research topics. It aims at identifying a minimum number of seed users who can trigger a wide cascade of information propagation. Most of existing literature investigated the LCI problem only based on an individual network. However, nowadays users often join several OSNs such that information could be spread across different networks simultaneously. Therefore, in order to obtain the best set of seed users, it is crucial to consider the role of overlapping users under this circumstances. In this article, we propose a unified framework to represent and analyze the influence diffusion in multiplex networks. More specifically, we tackle the LCI problem by mapping a set of networks into a single one via lossless and lossy coupling schemes. The lossless coupling scheme preserves all properties of original networks to achieve high quality solutions, while the lossy coupling scheme offers an attractive alternative when the running time and memory consumption are of primary concern. Various experiments conducted on both real and synthesized datasets have validated the effectiveness of the coupling schemes, which also provide some interesting insights into the process of influence propagation in multiplex networks.Comment: 21 pages, published in IEEE/ACM Transactions on Networkin

Comment on "Potential Energy Landscape for Hot Electrons in Periodically Nanostructured Graphene"

In a recent letter [Phys. Rev. Lett. 105 (2010) 036804] the unoccupied electronic states of single layers of graphene on ruthenium are investigated. Here we comment on the interpretation, which deviates in four points from [J. Phys.: Condens. Matter 22 (2010) 302001] and outline the corresponding consequences

Rotational constants of multi-phonon bands in an effective theory for deformed nuclei

We consider deformed nuclei within an effective theory that exploits the small ratio between rotational and vibrational excitations. For even-even nuclei, the effective theory predicts small changes in the rotational constants of bands built on multi-phonon excitations that are linear in the number of excited phonons. In 166Er and 168Er, this explains the main variations of the rotational constants of the two-phonon gamma vibrational bands. In 232Th, the effective theory correctly explains the trend that the rotational constants decrease with increasing spin of the band head. We also study the effective theory for deformed odd nuclei. Here, time-odd terms enter the Lagrangian and generate effective magnetic forces that yield the high level densities observed in such nuclei.Comment: 9 page

Sharp RIP Bound for Sparse Signal and Low-Rank Matrix Recovery

This paper establishes a sharp condition on the restricted isometry property (RIP) for both the sparse signal recovery and low-rank matrix recovery. It is shown that if the measurement matrix $A$ satisfies the RIP condition $\delta_k^A<1/3$, then all $k$-sparse signals $\beta$ can be recovered exactly via the constrained $\ell_1$ minimization based on $y=A\beta$. Similarly, if the linear map $\cal M$ satisfies the RIP condition $\delta_r^{\cal M}<1/3$, then all matrices $X$ of rank at most $r$ can be recovered exactly via the constrained nuclear norm minimization based on $b={\cal M}(X)$. Furthermore, in both cases it is not possible to do so in general when the condition does not hold. In addition, noisy cases are considered and oracle inequalities are given under the sharp RIP condition.Comment: to appear in Applied and Computational Harmonic Analysis (2012

Inference for High-dimensional Differential Correlation Matrices

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.Comment: Accepted for publication in Journal of Multivariate Analysi