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1,958
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
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
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
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
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.
Covering matroid
"... Abstract. In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of coveringbased rough sets and some existing special matroids. Firstly, as an extension of partitions, coverings are more natural combinatorial objects and ca ..."
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Abstract. In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of coveringbased rough sets and some existing special matroids. Firstly, as an extension of partitions, coverings are more natural combinatorial objects
Triangulations Of Oriented Matroids
, 1997
"... We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing ..."
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Cited by 26 (10 self)
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between triangulations of an oriented matroid M and extensions of its dual M , via the socalled lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids
Oriented Matroids  From Matroids and Digraphs to Polyhedral Theory
, 2010
"... These notes are intended for participants of the MAA Shortcourse on Matroid Theory January 2011 in New Orleans. Therefore our intention is not to give an introduction into the theory of oriented matroids from scratch (as in [9]), but to recapture how they arise from matroids. Therefore, we assume ba ..."
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These notes are intended for participants of the MAA Shortcourse on Matroid Theory January 2011 in New Orleans. Therefore our intention is not to give an introduction into the theory of oriented matroids from scratch (as in [9]), but to recapture how they arise from matroids. Therefore, we assume
Matchings, Matroids and Unimodular Matrices
, 1995
"... We focus on combinatorial problems arising from symmetric and skewsymmetric matrices. For much of the thesis we consider properties concerning the principal submatrices. In particular, we are interested in the property that every nonsingular principal submatrix is unimodular; matrices having this p ..."
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Cited by 13 (1 self)
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this property are called principally unimodular. Principal unimodularity is a generalization of total unimodularity, and we generalize key polyhedral and matroidal results on total unimodularity. Highlights include a generalization of Hoffman and Kruskal's result on integral polyhedra, a generalization
Results 1  10
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1,958