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3,991
Capacity of Fading Channels with Channel Side Information
, 1997
"... We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "waterpouring" in time, analogous to waterpouring in frequency for timeinvariant frequencysele ..."
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Cited by 579 (23 self)
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We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "waterpouring" in time, analogous to waterpouring in frequency for timeinvariant frequencyselective fading channels. Inverting the channel results in a large capacity penalty in severe fading.
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Matroids
, 2009
"... One of the primary goals of pure mathematics is to identify common patterns that occur in disparate circumstances, and to create unifying abstractions which identify commonalities and provide a useful framework for further theorems. For example the pattern of an associative operation with inverses a ..."
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One of the primary goals of pure mathematics is to identify common patterns that occur in disparate circumstances, and to create unifying abstractions which identify commonalities and provide a useful framework for further theorems. For example the pattern of an associative operation with inverses and an identity occurs frequently, and gives rise to the notion of an abstract group. On top of the basic axioms of a group, a vast
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 423 (37 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena; in particular, the existence of easilyverifiable conditions under which optimallysparse solutions can be found by concrete, effective computational methods. Such theoretical results inspire a bold perspective on some important practical problems in signal and image processing. Several wellknown signal and image processing problems can be cast as demanding solutions of undetermined systems of equations. Such problems have previously seemed, to many, intractable. There is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to underdetermined systems energizes research on such signal and image processing problems – to striking effect. In this paper we review the theoretical results on sparse solutions of linear systems, empirical
Lectures on matroids and oriented matroids
, 2005
"... These lecture notes were prepared for the Algebraic Combinatorics; in Europe (ACE) Summer School in Vienna, July 2005. ..."
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Cited by 1 (0 self)
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These lecture notes were prepared for the Algebraic Combinatorics; in Europe (ACE) Summer School in Vienna, July 2005.
Espousable societies and infinite matroids
"... Abstract. Given a society Γ = (M, W, K), where M, W are disjoint sets and K ⊆ M ×W, and a matroid T on M, a Tespousal of Γ is an injective partial function E: M → W such that E ⊆ K and dom E is spanning in T. The problem of characterizing Tespousable societies is a generalization of characterizing ..."
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systems of matroids with disjoint bases. Wojciechowski [15] formulated a criterion for a society Γ = (M, W, K) to be P(M)espousable, where P(M) is the matroid on M consisting of all subsets of M. In this paper, we generalize this criterion to the case when T is an arbitrary matroid on M, and we prove
Rayleigh matroids
 COMBIN. PROB. COMPUT
, 2003
"... Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. These form a subclass of the balanced matroids defined by Feder and Mihail [10] in 1992. We prove a variety of results relating Rayleigh matroids to other well–known classes – in particular ..."
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Cited by 8 (1 self)
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Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. These form a subclass of the balanced matroids defined by Feder and Mihail [10] in 1992. We prove a variety of results relating Rayleigh matroids to other well–known classes
Results 1  10
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3,991