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592
Active zones in CSG for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms
 ACM Transactions on Graphics
, 1989
"... Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSGbased algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of setmembership classification by traversing the t ..."
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Cited by 29 (9 self)
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Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSGbased algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of setmembership classification by traversing the tree associated with the solid. These algorithms usually generate intermediate results that do not contribute to the final result, and hence may be regarded as redundant and a source of inefficiency. To reduce such inefficiencies, we associate with each primitive A in a tree S an active zone 2 that represents the region of space where changes to A affect the solid represented by S, and we use a representation of 2 instead of S for setmembership classification. In the paper we develop a mathematical theory of active zones, prove that they correspond to the intersection of certain nodes of the original trees, and show how they lead to efficient new algorithms for boundary evaluation, for detecting and eliminating redundant nodes in CSG trees, for interference (nullset) detection, and for graphic shading.
Average number of facets per cell in treestructured vector quantizer partitions
 IEEE Trans. Inform. Theory
, 1993
"... AbstiactUpper and lower bounds are derived for the average number of facets per cell in the encoder partition of binary treestructured vector quantizers. The achievability of the bounds is described as well. It is shown in particular that the average number of facets per cell for unbalanced trees ..."
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Cited by 2 (0 self)
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AbstiactUpper and lower bounds are derived for the average number of facets per cell in the encoder partition of binary treestructured vector quantizers. The achievability of the bounds is described as well. It is shown in particular that the average number of facets per cell for unbalanced trees
Finding duplicates in a data stream
 in Proc. 20th Annual Symposium on Discrete Algorithms (SODA), 2009
"... Given a data stream of length n over an alphabet [m] where n> m, we consider the problem of finding a duplicate in a single pass. We give a randomized algorithm for this problem that uses O((log m) 3) space. This answers a question of Muthukrishnan [Mut05] and Tarui [Tar07], who asked if this pro ..."
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Cited by 3 (2 self)
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this problem to the task of detecting and identifying a Dictatorial variable in a Boolean halfspace. We present various relaxations of the condition n> m, under which one can find duplicates efficiently. 1
The Strong Perfect Graph Conjecture: 40 years of Attempts, and its Resolution
, 2010
"... The Strong Perfect Graph Conjecture (SPGC) was certainly one of the most challenging conjectures in graph theory. During more than four decades, numerous attempts were made to solve it, by combinatorial methods, by linear algebraic methods, or by polyhedral methods. The rst of these three approaches ..."
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Cited by 1 (0 self)
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approaches yielded the rst (and to date only) proof of the SPGC; the other two remain promising to consider in attempting an alternative proof. This paper is an unbalanced survey of the attempts to solve the SPGC; unbalanced, because (1) we devote a signi cant part of it to the `primitive graphs
Energy dispersed large data wave maps in 2 + 1 dimensions
, 2009
"... Abstract. In this article we consider large data WaveMaps from R 2+1 into a compact Riemannian manifold (M, g), and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (nondispersive) concentration is absent. This is a companion to our concurrent article [21], ..."
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Cited by 26 (2 self)
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Abstract. In this article we consider large data WaveMaps from R 2+1 into a compact Riemannian manifold (M, g), and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (nondispersive) concentration is absent. This is a companion to our concurrent article [21], which together with the present work establishes a full regularity theory for large data WaveMaps.
Smith and Sandwell Page 1 1/21/03 Coulomb Stress Accumulation along the San Andreas Fault System
, 2002
"... Stress accumulation rates along the primary segments of the San Andreas Fault system are computed using a threedimensional (3D) elastic halfspace model with realistic fault geometry. The model is developed in the Fourier domain by solving for the response of an elastic halfspace due to a point v ..."
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Stress accumulation rates along the primary segments of the San Andreas Fault system are computed using a threedimensional (3D) elastic halfspace model with realistic fault geometry. The model is developed in the Fourier domain by solving for the response of an elastic halfspace due to a point
Hybrid Classifiers for Object Classification with a Rich Background
"... Abstract. The majority of current methods in object classification use the oneagainstrest training scheme. We argue that when applied to a large number of classes, this strategy is problematic: as the number of classes increases, the negative class becomes a very large and complicated collection o ..."
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Cited by 3 (1 self)
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of images. The resulting classification problem then becomes extremely unbalanced, and kernel SVM classifiers trained on such sets require long training time and are slow in prediction. To address these problems, we propose to consider the negative class as a background and characterize it by a prior
Micromechanical Studies of Cyclic Creep Fracture Under StressControlled Loading
"... Abstract. This paper deals with a study of intergranular failure by creep cavitation under stresscontrolled cyclic loading conditions. Loading is assumed to be slow enough that diffusion and creep mechanisms (including grain boundary sliding) dominate, leading to intergranular creep fracture. This ..."
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limiting case with a facetsize microcrack yields important insight for damage accumulation under balanced loading. Under unbalanced loading, the timeaverage accumulation of creep cavitation gives rise to macroscopic ratchetting, while its rate is demonstrated to depend subtly on material and loading
Micromechanical Studies of Cyclic Creep Fracture Under StressControlled Loading
"... Abstract. This paper deals with a study of intergranular failure by creep cavitation under stresscontrolled cyclic loading conditions. Loading is assumed to be slow enough that diffusion and creep mechanisms (including grain boundary sliding) dominate, leading to intergranular creep fracture. This ..."
Abstract
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limiting case with a facetsize microcrack yields important insight for damage accumulation under balanced loading. Under unbalanced loading, the timeaverage accumulation of creep cavitation gives rise to macroscopic ratchetting, while its rate is demonstrated to depend subtly on material and loading
Machine Learning and Data Mining Via Mathematical Programing Based Support Vector Machines
, 2003
"... Several issues that arise in machine learning and data mining are addressed using mathematical programming based support vector machines (SVMs). We address the following important problems. Instead of a standard SVM that classifies points by assigning them to one of two disjoint halfspaces, points a ..."
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Cited by 1 (0 self)
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Several issues that arise in machine learning and data mining are addressed using mathematical programming based support vector machines (SVMs). We address the following important problems. Instead of a standard SVM that classifies points by assigning them to one of two disjoint halfspaces, points
Results 11  20
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592