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Automatic Discovery of Linear Restraints Among Variables of a Program
, 1978
"... The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs. ..."
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Cited by 733 (47 self)
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The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs.
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
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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, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme
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.
The role of deliberate practice in the acquisition of expert performance
 Psychological Review
, 1993
"... The theoretical framework presented in this article explains expert performance as the end result of individuals ' prolonged efforts to improve performance while negotiating motivational and external constraints. In most domains of expertise, individuals begin in their childhood a regimen of ef ..."
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Cited by 633 (13 self)
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The theoretical framework presented in this article explains expert performance as the end result of individuals ' prolonged efforts to improve performance while negotiating motivational and external constraints. In most domains of expertise, individuals begin in their childhood a regimen of effortful activities (deliberate practice) designed to optimize improvement. Individual differences, even among elite performers, are closely related to assessed amounts of deliberate practice. Many characteristics once believed to reflect innate talent are actually the result of intense practice extended for a minimum of 10 years. Analysis of expert performance provides unique evidence on the potential and limits of extreme environmental adaptation and learning. Our civilization has always recognized exceptional individuals, whose performance in sports, the arts, and science is vastly superior to that of the rest of the population. Speculations on the causes of these individuals ' extraordinary abilities and performance are as old as the first records of their achievements. Early accounts commonly attribute these individuals' outstanding performance to divine intervention, such as the
Impulses and Physiological States in Theoretical Models of Nerve Membrane
 Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 496 (0 self)
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the 4dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.
Hypercube Embeddings of Wythoffians
 ARS MATHEMATICA CONTEMPORANEA 1 (2008) 99–111
, 2008
"... The Wythoff construction takes a ddimensional polytope P, a subset S of {0,..., d} and returns another ddimensional polytope P (S). If P is a regular polytope, then P (S) is vertextransitive. This construction builds a large part of the Archimedean polytopes and tilings in dimension 3 and 4. We w ..."
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Cited by 1 (0 self)
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want to determine, which of those Wythoffians P (S) with regular P have their skeleton or dual skeleton isometrically embeddable into the hypercubes Hm and halfcubes 1 2 Hm. We find six infinite series, which, we conjecture, cover all cases for dimension d> 5 and some sporadic cases in dimension 3
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