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"Olshevsky"
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Consensus with Ternary Messages
We provide a protocol for real-valued average consensus by networks of agents which exchange only a single message from the ternary alphabet $\\{-1,0,1\\}$ between neighbors at each step. Our protocol works on time-varying undirected graphs subject to a connectivity condition, has a worst-case convergence time which is polynomial in the number of agents and the initial values, and requires no global knowledge about the graph topologies on the part of each node to implement except for knowing an upper bound on the degrees of its neighbors. [PUBLICATION ABSTRACT]
Journal Article
CONVERGENCE SPEED IN DISTRIBUTED CONSENSUS AND AVERAGING
We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worst-case convergence time for various classes of linear, time-invariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a time-varying topology, and provide a polynomial-time averaging algorithm. [PUBLICATION ABSTRACT]
Journal Article
Dynamics of High-Energy Proton Fluxes in the South Atlantic Anomaly Region According to ARINA and VSPLESK Satellite Experiment Data
This paper studies the dynamics of proton flux in the South Atlantic Anomaly (SAA) region according to ARINA (was operated on the Resurs-DK1 satellite from 2006 to 2015) and VSPLESK (which was mounted on the ISS from 2008 to 2013) satellite experiment data. Both spectrometers have the same scheme. The SAA drift is determined by the position of the maximum flux of high-energy protons with energies in the range from 30 to 100 MeV at the altitude of the Resurs-DK1 satellite (about 580 km) and the ISS (380–420 km). Part of the time the instruments operated simultaneously.
Journal Article
Convergence Speed in Distributed Consensus and Averaging
We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worst-case convergence time for various classes of linear, time-invariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a time-varying topology, and provide a polynomial-time averaging algorithm.
Journal Article
NP-hardness of deciding convexity of quartic polynomials and related problems
We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, strong convexity, quasiconvexity, and pseudoconvexity of polynomials of even degree four or higher is strongly NP-hard. By contrast, we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time.
Journal Article
Graph-Theoretic Analysis of Belief System Dynamics under Logic Constraints
Opinion formation cannot be modeled solely as an ideological deduction from a set of principles; rather, repeated social interactions and logic constraints among statements are consequential in the construct of belief systems. We address three basic questions in the analysis of social opinion dynamics: (i) Will a belief system converge? (ii) How long does it take to converge? (iii) Where does it converge? We provide graph-theoretic answers to these questions for a model of opinion dynamics of a belief system with logic constraints. Our results make plain the implicit dependence of the convergence properties of a belief system on the underlying social network and on the set of logic constraints that relate beliefs on different statements. Moreover, we provide an explicit analysis of a variety of commonly used large-scale network models.
Journal Article
The contribution of solar radiation to the heat balance of a high-rise building in the summer period using the Lakhta Center as an example
The object of research is the thermal regime of a high-rise building (the Lakhta Center) equipped with modular double-skin facade structures with buffer zones. Method. A comprehensive approach was used, which included the development of a numerical model of the buffer zone and conducting field observations with the use of an actinometric station for accurate measurement of solar radiation parameters. Results. It was shown that solar radiation has a substantial impact on the building's thermal regime in the summer. The maximum recorded temperature in the buffer zone reached +54°C. The obtained results confirm the significant contribution of solar radiation to the heat and mass transfer processes within the buffer zone of a skyscraper with a transparent facade.
Journal Article
Fast Algorithms for Structured Matrices: Theory and Applications
One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged. This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc. The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices.
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