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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.
Noncommutative geometry and stochastic calculus
 Applications in mathematical finance
"... The present report contains an introduction to some elementary concepts in noncommutative differential geometry. The material extends upon ideas first presented by Dimakis and MüllerHoissen. In particular, stochastic calculus and the Ito formula are shown to arise naturally from introducing noncomm ..."
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Cited by 1 (1 self)
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The present report contains an introduction to some elementary concepts in noncommutative differential geometry. The material extends upon ideas first presented by Dimakis and MüllerHoissen. In particular, stochastic calculus and the Ito formula are shown to arise naturally from introducing
Combinatorial stochastic processes
"... This is a collection of expository articles about various topics at the interface between enumerative combinatorics and stochastic processes. These articles expand on a course of lectures given at the École d’Été de Probabilités de St. Flour in July 2002. The articles are called ’chapters ’ and numb ..."
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Cited by 219 (15 self)
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This is a collection of expository articles about various topics at the interface between enumerative combinatorics and stochastic processes. These articles expand on a course of lectures given at the École d’Été de Probabilités de St. Flour in July 2002. The articles are called ’chapters
Probability and Geometry on some Noncommutative Manifolds by
, 2001
"... Abstract: In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also fo ..."
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Cited by 11 (2 self)
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Abstract: In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also
Noncommutative Geometry and Some Issues
, 2003
"... Recent observations of Ultra High Energy Cosmic rays suggest a small violation of Lorentz symmetry. Such a violation is expected in schemes with discrete/quantized spacetime. We examine this situation and suggest tests which could be carried out, for example by NASA’s GLAST Satellite. The considerat ..."
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Recent observations of Ultra High Energy Cosmic rays suggest a small violation of Lorentz symmetry. Such a violation is expected in schemes with discrete/quantized spacetime. We examine this situation and suggest tests which could be carried out, for example by NASA’s GLAST Satellite. The considerations are extrapolated to the large scale cosmos. 1
Noncommutative geometry and irreversibility
, 2008
"... A kinetics built upon qcalculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the “quasiposition ” whose eigenvalues are the levels of the hierarchy, corresponding to the volume of phase space avail ..."
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A kinetics built upon qcalculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the “quasiposition ” whose eigenvalues are the levels of the hierarchy, corresponding to the volume of phase space available to the system at any given time. Motion along the lattice of quasipositions is irreversible.
The Convex Geometry of Linear Inverse Problems
, 2010
"... In applications throughout science and engineering one is often faced with the challenge of solving an illposed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constr ..."
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Cited by 181 (18 self)
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. The class of simple models considered are those formed as the sum of a few atoms from some (possibly infinite) elementary atomic set; examples include wellstudied cases such as sparse vectors (e.g., signal processing, statistics) and lowrank matrices (e.g., control, statistics), as well as several others
NONCOMMUTATIVE GEOMETRY AND ITS RELATION TO STOCHASTIC CALCULUS AND SYMPLECTIC MECHANICS
, 1996
"... This paper rests on three, a priori quite distinct domains, namely, noncommutative geometry, stochastic calculus (StC) and symplectic mechanics (SyM). Hence we give below a very brief outline of some basic facts concerning StC and SyM. StC is motivated by the desire to put in a firm mathematical bas ..."
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Cited by 1 (1 self)
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This paper rests on three, a priori quite distinct domains, namely, noncommutative geometry, stochastic calculus (StC) and symplectic mechanics (SyM). Hence we give below a very brief outline of some basic facts concerning StC and SyM. StC is motivated by the desire to put in a firm mathematical
Modeling and estimation of multiresolution stochastic processes
 IEEE TRANS. ON INFORMATION THEORY
, 1992
"... An overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing. As described, a natural framework for developing such a theory ..."
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Cited by 109 (18 self)
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An overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing. As described, a natural framework for developing such a
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