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Non-negative Matrices and Markov Chains
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TLDR
Finite Non-Negative Matrices as mentioned in this paper are a generalization of finite stochastic matrices, and finite non-negative matrices have been studied extensively in the literature.Abstract:
Finite Non-Negative Matrices.- Fundamental Concepts and Results in the Theory of Non-negative Matrices.- Some Secondary Theory with Emphasis on Irreducible Matrices, and Applications.- Inhomogeneous Products of Non-negative Matrices.- Markov Chains and Finite Stochastic Matrices.- Countable Non-Negative Matrices.- Countable Stochastic Matrices.- Countable Non-negative Matrices.- Truncations of Infinite Stochastic Matrices.read more
Citations
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Coordination of groups of mobile autonomous agents using nearest neighbor rules
Ali Jadbabaie,Jie Lin,A.S. Morse +2 more
TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Journal ArticleDOI
The Graph Neural Network Model
TL;DR: A new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains, and implements a function tau(G,n) isin IRm that maps a graph G and one of its nodes n into an m-dimensional Euclidean space.
Book
Prediction, learning, and games
Nicolò Cesa-Bianchi,Gábor Lugosi +1 more
TL;DR: In this paper, the authors provide a comprehensive treatment of the problem of predicting individual sequences using expert advice, a general framework within which many related problems can be cast and discussed, such as repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems.
Journal ArticleDOI
Stability of multiagent systems with time-dependent communication links
TL;DR: It is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence, even for the simple models discussed in the present paper.
Book
Markov Chains and Mixing Times
TL;DR: Markov Chains and Mixing Times as mentioned in this paper is an introduction to the modern approach to the theory of Markov chains and its application in the field of probability theory and linear algebra, where the main goal is to determine the rate of convergence of a Markov chain to the stationary distribution.
References
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Book
Matrix Algebra: Theory, Computations, and Applications in Statistics
TL;DR: This book presents the relevant aspects of the theory of matrix algebra for applications in statistics and describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.