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EdgeUnfolding Nested Polyhedral Bands
, 2006
"... A band is the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. The intersection of the planes and the polyhedron produces two convex polygons. If one of these polygons contains the ot ..."
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Cited by 4 (3 self)
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the other in the projection orthogonal to the parallel planes, then the band is nested. We prove that all nested bands can be unfolded, by cutting along exactly one edge and folding continuously to place all faces of the band into a plane, without intersection.
Edgeunfolding Medial Axis Polyhedra
"... It is shown that a convex medial axis polyhedron has two distinct edge unfoldings: cuttings along edges that unfold the surface to a simple planar polygon. One of these unfoldings is a generalization of the point source unfolding, and is easily established to avoid overlap. The other is a novel unfo ..."
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Cited by 1 (0 self)
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It is shown that a convex medial axis polyhedron has two distinct edge unfoldings: cuttings along edges that unfold the surface to a simple planar polygon. One of these unfoldings is a generalization of the point source unfolding, and is easily established to avoid overlap. The other is a novel
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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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 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 was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
EdgeUnfolding AlmostFlat Convex Polyhedral Terrains
, 2013
"... In this thesis we consider the centuriesold question of edgeunfolding convex polyhedra, focusing specifically on edgeunfoldability of convex polyhedral terrain which are “almost flat ” in that they have very small height. We demonstrate how to determine whether cuttrees of such almostflat terra ..."
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In this thesis we consider the centuriesold question of edgeunfolding convex polyhedra, focusing specifically on edgeunfoldability of convex polyhedral terrain which are “almost flat ” in that they have very small height. We demonstrate how to determine whether cuttrees of such almostflat
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
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.
Symmetry and Related Properties via the Maximum Principle
, 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
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Cited by 539 (4 self)
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We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plane. We treat solutions in bounded domains and in the entire space.
Mean shift, mode seeking, and clustering
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... AbstractMean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some kmeans like clustering algorithms its special cases. It is shown that mean shift is a modeseeki ..."
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Cited by 620 (0 self)
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AbstractMean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some kmeans like clustering algorithms its special cases. It is shown that mean shift is a modeseeking process on a surface constructed with a “shadow ” kernel. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis is treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications in clustering and Hough transform are demonstrated. Mean shift is also considered as an evolutionary strategy that performs multistart global optimization. Index TermsMean shift, gradient descent, global optimization, Hough transform, cluster analysis, kmeans clustering. I.
Cognitive Radio: BrainEmpowered Wireless Communications
, 2005
"... Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a softwaredefined radio, is defined as an intelligent wireless communication system that is aware of its environment and use ..."
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Cited by 1479 (4 self)
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Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a softwaredefined radio, is defined as an intelligent wireless communication system that is aware of its environment and uses the methodology of understandingbybuilding to learn from the environment and adapt to statistical variations in the input stimuli, with two primary objectives in mind: • highly reliable communication whenever and wherever needed; • efficient utilization of the radio spectrum. Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks. 1) Radioscene analysis. 2) Channelstate estimation and predictive modeling. 3) Transmitpower control and dynamic spectrum management. This paper also discusses the emergent behavior of cognitive radio.
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