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Open problems in Euclidean Ramsey theory
 Geocombinatorics
, 2004
"... Ramsey theory is a branch of combinatorics that deals with unavoidable structure in large systems. Euclidean Ramsey theory specifically looks at structure that remains when some geometric object is partitioned, and this note is a survey of some open problems in that field. 1 ..."
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Cited by 2 (1 self)
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Ramsey theory is a branch of combinatorics that deals with unavoidable structure in large systems. Euclidean Ramsey theory specifically looks at structure that remains when some geometric object is partitioned, and this note is a survey of some open problems in that field. 1
Transitive sets in Euclidean Ramsey theory
 J. Comb. Th. (A
"... A finite set X in some Euclidean space R n is called Ramsey if for any k there is a d such that whenever R d is kcoloured it contains a monochromatic set congruent to X. This notion was introduced by ..."
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Cited by 4 (0 self)
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A finite set X in some Euclidean space R n is called Ramsey if for any k there is a d such that whenever R d is kcoloured it contains a monochromatic set congruent to X. This notion was introduced by
Hypergraph list coloring and Euclidean Ramsey Theory
, 2010
"... A hypergraph is simple if it has no two edges sharing more than a single vertex. It is slist colorable (or schoosable) if for any assignment of a list of s colors to each of its vertices, there is a vertex coloring assigning to each vertex a color from its list, so that no edge is monochromatic. W ..."
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Cited by 6 (3 self)
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A hypergraph is simple if it has no two edges sharing more than a single vertex. It is slist colorable (or schoosable) if for any assignment of a list of s colors to each of its vertices, there is a vertex coloring assigning to each vertex a color from its list, so that no edge is monochromatic. We prove that for every positive integer r, there is a function dr(s) such that no runiform simple hypergraph with average degree at least dr(s) is slistcolorable. This extends a similar result for graphs, due to the first author, but does not give as good estimates of dr(s) as are known for d2(s), since our proof only shows that for each fixed r ≥ 2, dr(s) ≤ 2 crsr−1. We use the result to prove that for any finite set of points X in the plane, and for any finite integer s, one can assign a list of s distinct colors to each point of the plane, so that any coloring of the plane that colors each point by a color from its list contains a monochromatic isometric copy of X.
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
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 886 (35 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
A theory of timed automata
, 1999
"... Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of ..."
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Cited by 2651 (32 self)
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and logic, and much progress has been made in developing verification algorithms, heuristics, and tools. This paper provides a survey of the theory of timed automata, and their role in specification and verification of realtime systems.
The large N limit of superconformal field theories and supergravity
, 1998
"... We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and ..."
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Cited by 5673 (21 self)
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We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory
Prospect theory: An analysis of decisions under risk
 Econometrica
, 1979
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 5935 (24 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Antide Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories
 Adv. Theor. Math. Phys
, 1998
"... The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum phenome ..."
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Cited by 1087 (4 self)
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The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum
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