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Computational Geometry Column 31
, 1993
"... Several topics related to packing on a sphere are discussed: packing points, packing lines through the center, and packing kflats in dimension d. Two frequently asked questions in the graphics community (e.g., on the Usenet newsgroup comp.graphics.algorithms) are: How can points be randomly placed ..."
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Several topics related to packing on a sphere are discussed: packing points, packing lines through the center, and packing kflats in dimension d. Two frequently asked questions in the graphics community (e.g., on the Usenet newsgroup comp.graphics.algorithms) are: How can points be randomly placed on a sphere?, and, How can points be regularly arranged on a sphere? I will start with these two questions and move to generalizations: packing lines in space and packing affine subspaces in higherdimensional spaces. 1 Random Points on a Sphere Define a zone on a sphere to be the portion between two parallel planes that both intersect the sphere. For a sphere S of radius r, the area of a zone of width h is 2ßrh. This area is independent of where S is sliced, a fact that may seem countertuitive. The implication is that the zcoordinates (say) of random points on a sphere are uniformly distributed. Thus random points (x; y; z) on a sphere of radius 1 can be generated as follows: 1. Choose z ...
String theory and noncommutative geometry
 JHEP
, 1999
"... We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from ..."
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Cited by 801 (8 self)
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We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 484 (3 self)
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
A survey of generalpurpose computation on graphics hardware
, 2007
"... The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the l ..."
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Cited by 545 (18 self)
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The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings of graphs in twodimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.
Formalising trust as a computational concept
, 1994
"... Trust is a judgement of unquestionable utility — as humans we use it every day of our lives. However, trust has suffered from an imperfect understanding, a plethora of definitions, and informal use in the literature and in everyday life. It is common to say “I trust you, ” but what does that mean? T ..."
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Cited by 518 (5 self)
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Trust is a judgement of unquestionable utility — as humans we use it every day of our lives. However, trust has suffered from an imperfect understanding, a plethora of definitions, and informal use in the literature and in everyday life. It is common to say “I trust you, ” but what does that mean? This thesis provides a clarification of trust. We present a formalism for trust which provides us with a tool for precise discussion. The formalism is implementable: it can be embedded in an artificial agent, enabling the agent to make trustbased decisions. Its applicability in the domain of Distributed Artificial Intelligence (DAI) is raised. The thesis presents a testbed populated by simple trusting agents which substantiates the utility of the formalism. The formalism provides a step in the direction of a proper understanding and definition of human trust. A contribution of the thesis is its detailed exploration of the possibilities of future work in the area. Summary 1. Overview This thesis presents an overview of trust as a social phenomenon and discusses it formally. It argues that trust is: • A means for understanding and adapting to the complexity of the environment. • A means of providing added robustness to independent agents. • A useful judgement in the light of experience of the behaviour of others. • Applicable to inanimate others. The thesis argues these points from the point of view of artificial agents. Trust in an artificial agent is a means of providing an additional tool for the consideration of other agents and the environment in which it exists. Moreover, a formalisation of trust enables the embedding of the concept into an artificial agent. This has been done, and is documented in the thesis. 2. Exposition There are places in the thesis where it is necessary to give a broad outline before going deeper. In consequence it may seem that the subject is not receiving a thorough treatment, or that too much is being discussed at one time! (This is particularly apparent in the first and second chapters.) To present a thorough understanding of trust, we have proceeded breadth first in the introductory chapters. Chapter 3 expands, depth first, presenting critical views of established researchers.
A Survey of Computer VisionBased Human Motion Capture
 Computer Vision and Image Understanding
, 2001
"... A comprehensive survey of computer visionbased human motion capture literature from the past two decades is presented. The focus is on a general overview based on a taxonomy of system functionalities, broken down into four processes: initialization, tracking, pose estimation, and recognition. Each ..."
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Cited by 508 (14 self)
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A comprehensive survey of computer visionbased human motion capture literature from the past two decades is presented. The focus is on a general overview based on a taxonomy of system functionalities, broken down into four processes: initialization, tracking, pose estimation, and recognition. Each
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consi ..."
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Cited by 1103 (7 self)
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A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken
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