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THE TOTAL sENERGY OF A MULTIAGENT SYSTEM
 SIAM J. CONTROL OPTIM, VOL. 49, NO. 4, PP. 1680–1706
, 2011
"... We introduce the total senergy of a multiagent system with timedependent links. This provides a new analytical perspective on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology ..."
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Cited by 5 (4 self)
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We introduce the total senergy of a multiagent system with timedependent links. This provides a new analytical perspective on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology.
Survival in a quasideath process
, 2007
"... Abstract. We consider a Markov chain in continuous time with one absorbing state and a finite set S of transient states. When S is irreducible the limiting distribution of the chain as t → ∞, conditional on survival up to time t, is known to equal the (unique) quasistationary distribution of the ch ..."
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Cited by 2 (1 self)
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Abstract. We consider a Markov chain in continuous time with one absorbing state and a finite set S of transient states. When S is irreducible the limiting distribution of the chain as t → ∞, conditional on survival up to time t, is known to equal the (unique) quasistationary distribution of the chain. We address the problem of generalizing this result to a setting in which S may be reducible, and obtain a complete solution if the eigenvalue with maximal real part of the generator of the (sub)Markov chain on S has geometric (but not, necessarily, algebraic) multiplicity one. The result is applied to pure death processes and, more generally, to quasideath processes.
Performance and Implementation of Adaptive Partial Response Maximum Likelihood Detection
, 1998
"... Motivated by previous comparison work, a configuration for partial response maximum likelihood detection using the Viterbi algorithm (PRML/VA) detectors with adaptive target polynomials is examined. In this configuration, a meanquared error decision feedback equalization (MSEDFE) is used to adapt ..."
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Cited by 1 (0 self)
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Motivated by previous comparison work, a configuration for partial response maximum likelihood detection using the Viterbi algorithm (PRML/VA) detectors with adaptive target polynomials is examined. In this configuration, a meanquared error decision feedback equalization (MSEDFE) is used to adapt both the forward equalizer and the target channel for the Viterbi detector. The performance of this adaptive PRML/VA is analyzed and compared with other detection techniques. The issue of convergence speed is also studied. Index TermsAdaptive target polynomials, analytical performance comparison, partial response maximum likelihood detection. I. INTRODUCTION P ARTIAL response maximum likelihood detection using the Viterbi algorithm (PRML/VA) [9], decision feedback equalization (DFE) [10], [13], and fixeddelay tree search with decision feedback (FDTS/DF) [2] are the three sampling detection techniques most often considered for digital magnetic recording. In a previous paper, detailed p...
VariableSample Methods and Simulated Annealing for Discrete Stochastic Optimization
, 1999
"... In this paper we discuss the application of a certain class of Monte Carlo methods to stochastic optimization problems. Particularly, we study variablesample techniques, in which the objective function is replaced, at each iteration, by a sample average approximation. We first provide general resul ..."
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In this paper we discuss the application of a certain class of Monte Carlo methods to stochastic optimization problems. Particularly, we study variablesample techniques, in which the objective function is replaced, at each iteration, by a sample average approximation. We first provide general results on the schedule of sample sizes, under which variablesample methods yield consistent estimators as well as bounds on the estimation error. Because the convergence analysis is performed samplepath wise, we are able to obtain our results in a flexible setting, which includes the possibility of using different sampling distributions along the algorithm, without making strong assumptions on the underlying distributions. In particular, we allow the distributions to depend on the decision variables x. We illustrate these ideas by studying a modification of the wellknown simulated annealing method, adapting it to the variablesample scheme, and show conditions for convergence of the algorithm.
Programmatic Table of Contents
, 2004
"... Alle rechten voorbehouden. Niets uit deze uitgave mag worden vermenigvuldigd en/of openbaar gemaakt worden door middel van druk, fotocopie, microfilm, electronisch of op welke andere wijze ook zonder voorafgaande schriftelijke toestemming van de uitgever. All rights reserved. No part of the publicat ..."
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Alle rechten voorbehouden. Niets uit deze uitgave mag worden vermenigvuldigd en/of openbaar gemaakt worden door middel van druk, fotocopie, microfilm, electronisch of op welke andere wijze ook zonder voorafgaande schriftelijke toestemming van de uitgever. All rights reserved. No part of the publication may be reproduced in any form by print, photo print, microfilm or by any other means without written permission of the publisher. ISBN 9038629559 23rd Benelux Meeting on Systems and Control Book of Abstracts
SMOOTHNESS OF UNORDERED CURVES IN TWODIMENSIONAL STRONGLY COMPETITIVE SYSTEMS
"... Abstract. It is known that in twodimensional systems of ODEs of the form ˙x i = x i f i (x) with ∂f i /∂x j < 0 (strongly competitive systems), boundaries of the basins of repulsion of equilibria consist of invariant Lipschitz curves, unordered with respect to the coordinatewise (partial) order. We ..."
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Abstract. It is known that in twodimensional systems of ODEs of the form ˙x i = x i f i (x) with ∂f i /∂x j < 0 (strongly competitive systems), boundaries of the basins of repulsion of equilibria consist of invariant Lipschitz curves, unordered with respect to the coordinatewise (partial) order. We prove that such curves are in fact of class C 1. (S) A twodimensional system of C 1 ordinary differential equations (ODEs) ˙x i = x i f i (x), where f = (f 1, f 2) : K → R 2, K: = {x = (x 1, x 2) ∈ R 2: x i ≥ 0 for i = 1, 2} is called strongly competitive if ∂f i (x) < 0 ∂xj for all x ∈ K, i, j = 1, 2, i ̸ = j (see M. W. Hirsch’s papers [4] and [5]). Systems of the form (S) describe communities of two interacting biological species: the function f i represents the per capita growth rate of the ith species. Strong competitiveness means that the growth of each species inhibits the growth of the other. An important subclass of strongly competitive systems consists of strongly competitive Lotka–Volterra systems of the form ˙x i = x i( 2∑ bi + aijx j) j=1
ON THE SPECTRUM OF MARKOV SEMIGROUPS VIA SAMPLE PATH LARGE DEVIATIONS.
, 2004
"... Abstract. The essential spectral radius of a subMarkovian process is defined as the infimum of the spectral radiuses of all local perturbations of the process. When the family of rescaled processes satisfies sample path large deviation principle, the spectral radius and the essential spectral radiu ..."
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Abstract. The essential spectral radius of a subMarkovian process is defined as the infimum of the spectral radiuses of all local perturbations of the process. When the family of rescaled processes satisfies sample path large deviation principle, the spectral radius and the essential spectral radius are expressed in terms of the rate function. The paper is motivated by applications to reflected diffusions and jump Markov processes describing stochastic networks for which the sample path large deviation principle has been established and the rate function has been identified while essential spectral radius has not been calculated. 1.
1 A Necessary and Sufficient Condition for Consensus Over Random Networks
"... Abstract — We consider the consensus problem for stochastic discretetime linear dynamical systems. The underlying graph of such systems at a given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient co ..."
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Abstract — We consider the consensus problem for stochastic discretetime linear dynamical systems. The underlying graph of such systems at a given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. This easily verifiable condition uses the spectrum of the average weight matrix. Finally, we investigate a special case for which the linear dynamical system converges to a fixed vector with probability one. Index Terms — Consensus problem, random graphs, weak ergodicity, tail events. I.