Results 1  10
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87,840
The selfduality equations on a Riemann surface
 Proc. Lond. Math. Soc., III. Ser
, 1987
"... In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instanton ..."
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Cited by 524 (6 self)
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In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled &apos
Understanding Normal and Impaired Word Reading: Computational Principles in QuasiRegular Domains
 PSYCHOLOGICAL REVIEW
, 1996
"... We develop a connectionist approach to processing in quasiregular domains, as exemplified by English word reading. A consideration of the shortcomings of a previous implementation (Seidenberg & McClelland, 1989, Psych. Rev.) in reading nonwords leads to the development of orthographic and phono ..."
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Cited by 583 (94 self)
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divisionoflabor between semantic and phonological processes. Such a view is consistent with the more general Seidenberg and McClelland framework and has some similarities withbut also important differences fromthe standard dualroute account.
Robust Monte Carlo Localization for Mobile Robots
, 2001
"... Mobile robot localization is the problem of determining a robot's pose from sensor data. This article presents a family of probabilistic localization algorithms known as Monte Carlo Localization (MCL). MCL algorithms represent a robot's belief by a set of weighted hypotheses (samples), whi ..."
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Cited by 826 (88 self)
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Mobile robot localization is the problem of determining a robot's pose from sensor data. This article presents a family of probabilistic localization algorithms known as Monte Carlo Localization (MCL). MCL algorithms represent a robot's belief by a set of weighted hypotheses (samples), which approximate the posterior under a common Bayesian formulation of the localization problem. Building on the basic MCL algorithm, this article develops a more robust algorithm called MixtureMCL, which integrates two complimentary ways of generating samples in the estimation. To apply this algorithm to mobile robots equipped with range finders, a kernel density tree is learned that permits fast sampling. Systematic empirical results illustrate the robustness and computational efficiency of the approach.
The Lumigraph
 In Proceedings of SIGGRAPH 96
, 1996
"... This paper discusses a new method for capturing the complete appearanceof both synthetic and real world objects and scenes, representing this information, and then using this representation to render images of the object from new camera positions. Unlike the shape capture process traditionally used ..."
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Cited by 1034 (43 self)
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This paper discusses a new method for capturing the complete appearanceof both synthetic and real world objects and scenes, representing this information, and then using this representation to render images of the object from new camera positions. Unlike the shape capture process traditionally used in computer vision and the rendering process traditionally used in computer graphics, our approach does not rely on geometric representations. Instead we sample and reconstruct a 4D function, which we call a Lumigraph. The Lumigraph is a subset of the complete plenoptic function that describes the flow of light at all positions in all directions. With the Lumigraph, new images of the object can be generated very quickly, independent of the geometric or illumination complexity of the scene or object. The paper discusses a complete working system including the capture of samples, the construction of the Lumigraph, and the subsequent rendering of images from this new representation. 1
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0. In contrast, heuristic attempts to sparsely solve such systems – greedy algorithms and thresholding – perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almostspherical sections in Banach space theory, and deviation bounds for the eigenvalues of random Wishart matrices.
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.
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
A standardized set of 260 pictures: Norms for name agreement, image agreement, familiarity, and visual complexity
 JOURNAL OF EXPERIMENTAL PSYCHOLOGY: HUMAN LEARNING AND MEMORY
, 1980
"... In this article we present a standardized set of 260 pictures for use in experiments investigating differences and similarities in the processing of pictures and words. The pictures are blackandwhite line drawings executed according to a set of rules that provide consistency of pictorial represent ..."
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Cited by 615 (1 self)
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In this article we present a standardized set of 260 pictures for use in experiments investigating differences and similarities in the processing of pictures and words. The pictures are blackandwhite line drawings executed according to a set of rules that provide consistency of pictorial representation. The pictures have been standardized on four variables of central relevance to memory and cognitive processing: name agreement, image agreement, familiarity, and visual complexity. The intercorrelations among the four measures were low, suggesting that the) ' are indices of different attributes of the pictures. The concepts were selected to provide exemplars from several widely studied semantic categories. Sources of naming variance, and mean familiarity and complexity of the exemplars, differed significantly across the set of categories investigated. The potential significance of each of the normative variables to a number of semantic and episodic memory tasks is discussed.
Face Recognition: A Literature Survey
, 2000
"... ... This paper provides an uptodate critical survey of still and videobased face recognition research. There are two underlying motivations for us to write this survey paper: the first is to provide an uptodate review of the existing literature, and the second is to offer some insights into ..."
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Cited by 1363 (21 self)
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... This paper provides an uptodate critical survey of still and videobased face recognition research. There are two underlying motivations for us to write this survey paper: the first is to provide an uptodate review of the existing literature, and the second is to offer some insights into the studies of machine recognition of faces. To provide a comprehensive survey, we not only categorize existing recognition techniques but also present detailed descriptions of representative methods within each category. In addition,
Alternatingtime Temporal Logic
 Journal of the ACM
, 1997
"... Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general var ..."
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Cited by 615 (55 self)
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Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general variety of temporal logic: alternatingtime temporal logic offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves. While lineartime and branchingtime logics are natural specification languages for closed systems, alternatingtime logics are natural specification languages for open systems. For example, by preceding the temporal operator "eventually" with a selective path quantifier, we can specify that in the game between the system and the environment, the system has a strategy to reach a certain state. Also the problems of receptiveness, realizability, and controllability can be formulated as modelchecking problems for alternatingtime formulas.
Results 1  10
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87,840