The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

“WHAT can men do, what do they do, and what do they want to do ?”—these are the uestions that Prof. Thorndike seeks to answer in a very comprehensive and elaborate treatise. His undertaking is inspired by the belief that man has the possibility of almost complete control of his fate if only he will be guided by science, and that his failures are attributable to ignorance or folly. The main approach is through biological psychology, but all the social sciences are appealed to and utilized in an effort to deal with the human problem as a whole. The relative immaturity of the sciences dealing with man is continually stressed, but it is claimed that they provide a body of facts and principles which are “far above zero knowledge”, and that even now they are capable of affording valuable guidance in the shaping of public policy. Human Nature and the Social Order By E. L. Thorndike. Pp. xx + 1020. (New York: The Macmillan Company, 1940.) 18s. net.

Human Nature and the Social Order

Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficulties in practical situations where true DOAs are not on the discretized sampling grid. To deal with such an off-grid DOA estimation problem, this paper studies an off-grid model that takes into account effects of the off-grid DOAs and has a smaller modeling error. An iterative algorithm is developed based on the off-grid model from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming a Laplace prior for signals at all snapshots. The new approach applies to both single snapshot and multi-snapshot cases. Numerical simulations show that the proposed algorithm has improved accuracy in terms of mean squared estimation error. The algorithm can maintain high estimation accuracy even under a very coarse sampling grid.

Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference

A tutorial on modeling and analysis of dynamic social networks. Part I

We study nonconvex distributed optimization in multiagent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and nonseparable) function—the agents’ sum-utility—plus a convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually employed to enforce some structure in the solution, typically sparsity. The proposed method hinges on successive convex approximation techniques while leveraging dynamic consensus as a mechanism to distribute the computation among the agents: each agent first solves (possibly inexactly) a local convex approximation of the nonconvex original problem, and then performs local averaging operations. Asymptotic convergence to (stationary) solutions of the nonconvex problem is established. Our algorithmic framework is then customized to a variety of convex and nonconvex problems in several fields, including signal processing, communications, networking, and machine learning. Numerical results show that the new method compares favorably to existing distributed algorithms on both convex and nonconvex problems.

NEXT: In-Network Nonconvex Optimization

This chapter first introduces CS in the conventional setting where one device acquires one signal and sends it to a receiver, and then extends it to the distributed framework in which multiple devices acquire multiple signals. In particular, we focus on two key problems related to the distributed setting. The former is the definition of sparsity models for an ensemble of signals, as opposed to just one signal. The second is the structure of the corresponding recovery algorithm, which can be centralized or distributed; each solution entails specific advantages and drawbacks that are preliminarily discussed in this chapter, whereas a detailed description of the corresponding recovery algorithms is given in Chaps. 4 and 5.

Distributed Compressed Sensing

Algorithms and dynamics over networks often involve randomization and randomization can induce oscillating dynamics that fail to converge in a deterministic sense. Under assumptions of independence across time and linearity of the updates, we show that the oscillations are ergodic if the expected dynamics is stable. We apply this result to three problems of network systems, namely, the estimation from relative measurements, the PageRank computation, and the dynamics of opinions in social networks. In these applications, the randomized dynamics is the asynchronous counterpart of a deterministic (stable) synchronous one. By ergodicity, the deterministic limit can be recovered via a time-averaging operation, which can be performed locally by each node of the network.

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Ergodic Randomized Algorithms and Dynamics Over Networks

Gossips and prejudices: ergodic randomized dynamics in social networks

Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications, in which the dynamics is the randomized asynchronous counterpart of a well-behaved synchronous one. These three applications are network localization, PageRank computation, and opinion dynamics. Motivated by their formal similarity, we show the following general fact, under the assumptions of independence across time and linearities of the updates: if the expected dynamics is stable and converges to the same limit of the original synchronous dynamics, then the oscillations are ergodic and the desired limit can be locally recovered via time-averaging.

Chiara Ravazzi

Papers

Distributed Compressed Sensing

Ergodic Randomized Algorithms and Dynamics Over Networks

Gossips and prejudices: ergodic randomized dynamics in social networks

Ergodic Randomized Algorithms and Dynamics over Networks

Distributed randomized algorithms for opinion formation, centrality computation and power systems estimation: A tutorial overview☆