Results 1  10
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384
Information flow and cooperative control of vehicle formations.
 In Proceeings of 15th IFAC Conference,
, 2002
"... Abstract We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. We apply tools from graph theory to relate the topology of the communication network to formation stability. We prove a Nyquist crite ..."
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Cited by 551 (11 self)
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Abstract We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. We apply tools from graph theory to relate the topology of the communication network to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the graph on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that states that formation stability is achieved if the information flow is stable for the given graph and if the local controller stabilizes the vehicle. The information flow can be rendered highly robust to changes in the graph, thus enabling tight formation control despite limitations in intervehicle communication capability.
Deeper Inside PageRank
 INTERNET MATHEMATICS
, 2004
"... This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniq ..."
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Cited by 208 (4 self)
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This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, suggested alternatives to the traditional solution methods, sensitivity and conditioning, and finally the updating problem. We introduce a few new results, provide an extensive reference list, and speculate about exciting areas of future research.
Dooren, “Measure of similarity between graph vertices: Applications to synonym extraction and web searching
 SIAM Review, Society for Industrial and Applied Mathematics
, 2004
"... Abstract. We introduce a concept of similarity between vertices of directed graphs. Let G A and G B be two directed graphs with respectively n A and n B vertices. We define a n A × n B similarity matrix S whose real entry s ij expresses how similar vertex i (in G A ) is to vertex j (in G B ) : we s ..."
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Cited by 109 (4 self)
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Abstract. We introduce a concept of similarity between vertices of directed graphs. Let G A and G B be two directed graphs with respectively n A and n B vertices. We define a n A × n B similarity matrix S whose real entry s ij expresses how similar vertex i (in G A ) is to vertex j (in G B ) : we say that s ij is their similarity score. In the special case where G A = G B = G, the score s ij is the similarity score between the vertices i and j of G and the square similarity matrix S is the selfsimilarity matrix of the graph G. We point out that Kleinberg's "hub and authority" method to identify webpages relevant to a given query can be viewed as a special case of our definition in the case where one of the graphs has two vertices and a unique directed edge between them. In analogy to Kleinberg, we show that our similarity scores are given by the components of a dominant vector of a nonnegative matrix and we propose a simple iterative method to compute them. Potential applications of our similarity concept are manifold and we illustrate one application for the automatic extraction of synonyms in a monolingual dictionary.
Methods and Applications of (max,+) Linear Algebra
 STACS'97, NUMBER 1200 IN LNCS, LUBECK
, 1997
"... Exotic semirings such as the "(max, +) semiring" (R # {#},max,+), or the "tropical semiring" (N #{+#},min,+), have been invented and reinvented many times since the late fifties, in relation with various fields: performance evaluation of manufacturing systems and discrete ev ..."
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Cited by 93 (30 self)
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Exotic semirings such as the "(max, +) semiring" (R # {#},max,+), or the "tropical semiring" (N #{+#},min,+), have been invented and reinvented many times since the late fifties, in relation with various fields: performance evaluation of manufacturing systems and discrete event system theory; graph theory (path algebra) and Markov decision processes, HamiltonJacobi theory; asymptotic analysis (low temperature asymptotics in statistical physics, large deviations, WKB method); language theory (automata with multiplicities) . Despite this apparent profusion, there is a small set of common, nonnaive, basic results and problems, in general not known outside the (max, +) community, which seem to be useful in most applications. The aim of this short survey paper is to present what we believe to be the minimal core of (max, +) results, and to illustrate these results by typical applications, at the frontier of language theory, control, and operations research (performance evaluation of...
Human sperm competition
 In: Smith , R.L. (Ed.), Sperm Competition and the Evolution of Animal Mating Systems
, 1984
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Positive and Negative Circuits in Dynamical Systems
 J. B,iol. SVs
, 1998
"... We state precisely and demonstrate two conjectures of R. Thomas following which a) the existence of a positive circuit in the oriented interaction graph of a dioeerential system is a necessary condition for the existence of several steady states, and b) the existence of a negative nonoriented circu ..."
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Cited by 91 (2 self)
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We state precisely and demonstrate two conjectures of R. Thomas following which a) the existence of a positive circuit in the oriented interaction graph of a dioeerential system is a necessary condition for the existence of several steady states, and b) the existence of a negative nonoriented circuit of length at least two is a necessary condition for the existence of a stable periodic orbit.
HTCP: TCP for highspeed and longdistance networks
, 2004
"... In this paper we present a congestion control protocol that is suitable for deployment in highspeed and longdistance networks. The new protocol, HTCP, is shown to fair when deployed in homogeneous networks, to be friendly when competing with conventional TCP sources, to rapidly respond to bandwidt ..."
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Cited by 87 (2 self)
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In this paper we present a congestion control protocol that is suitable for deployment in highspeed and longdistance networks. The new protocol, HTCP, is shown to fair when deployed in homogeneous networks, to be friendly when competing with conventional TCP sources, to rapidly respond to bandwidth as it becomes available, and to utilise link bandwidth in an e#cient manner.
An ISS SmallGain Theorem for General Networks
, 2007
"... We provide a generalized version of the nonlinear small gain theorem for the case of more than two coupled inputtostate stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small gain condition requires bounds on the image of this gain ma ..."
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Cited by 84 (45 self)
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We provide a generalized version of the nonlinear small gain theorem for the case of more than two coupled inputtostate stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated lowerdimensional discrete time dynamical system.
On Asynchronous Iterations
, 2000
"... Asynchronous iterations arise naturally parallel computers wants minimize times. This paper reviews certain models asynchronous iterations, using a common theoretical framework. The corresponding convergence theory and various domains applications presented. These include nonsingular linear systems, ..."
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Cited by 73 (10 self)
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Asynchronous iterations arise naturally parallel computers wants minimize times. This paper reviews certain models asynchronous iterations, using a common theoretical framework. The corresponding convergence theory and various domains applications presented. These include nonsingular linear systems, nonlinear systems, initial value problems.
A positive systems model of TCPlike congestion control: Asymptotic results
 IEEE/ACM Transactions on Networking
, 2004
"... In this paper we study communication networks that employ droptail queueing and AdditiveIncrease MultiplicativeDecrease (AIMD) congestion control algorithms. We show that the theory of nonnegative matrices may be employed to model such networks. In particular, we show that important network p ..."
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Cited by 64 (10 self)
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In this paper we study communication networks that employ droptail queueing and AdditiveIncrease MultiplicativeDecrease (AIMD) congestion control algorithms. We show that the theory of nonnegative matrices may be employed to model such networks. In particular, we show that important network properties such as: (i) fairness; (ii) rate of convergence; and (iii) throughput; can be characterised by certain nonnegative matrices that arise in the study of AIMD networks. We demonstrate that these results can be used to develop tools for analysing the behaviour of AIMD communication networks. The accuracy of the models is demonstrated by means of several NSstudies.