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Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 523 (3 self)
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CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves
The SLAM project: debugging system software via static analysis
 SIGPLAN Not
"... Abstract. The goal of the SLAM project is to check whether or not a program obeys "API usage rules " that specif[y what it means to be a good client of an API. The SLAM toolkit statically analyzes a C program to determine whether or not it violates given usage rules. The toolkit has two un ..."
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Cited by 472 (17 self)
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and automated deduction.}V ~ have successfully applied the SLAM toolkit to Windows XP device drivers, to both validate behavior and find defects in their usage of kernel APIs. Context. Today, many programmers are realizing the benefits of using languages with static type systems. By providing
Conditions For Unique Graph Realizations
 SIAM J. Comput
, 1992
"... . The graph realization problem is that of computing the relative locations of a set of vertices placed in Euclidean space, relying only upon some set of intervertex distance measurements. This paper is concerned with the closely related problem of determining whether or not a graph has a unique re ..."
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Cited by 155 (1 self)
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theoretic conditions for a graph to have a unique realization in any dimension. Efficient sequential and NC algorithms are presented for each condition, although these algorithms have very different flavors in different dimensions. 1. Introduction. Consider a graph G = (V; E) consisting of a set of n
On Supersymmetry Breaking in String Theory and its Realization in Brane Worlds
 Nucl. Phys. B
, 2001
"... We use string duality to describe instanton induced spontaneous supersymmetry breaking in string compactifications with additional background fields. Dynamical supersymmetry breaking by spacetime instantons in the heterotic string theory is mapped to a tree level breaking in the type II string whic ..."
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Cited by 109 (8 self)
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is determined by Mstr, which can be in the TeV range, and the geometry transverse to the gauge theory. March 2000 1. Introduction and
VAlgebras and Their Free Field Realizations
, 1997
"... The Valgebras are the nonlocal matrix generalization of the wellknown Walgebras. Their classical realizations are given by the second Poisson brackets associated with the matrix pseudodifferential operators. In this paper, by using the general Miura transformation, we give the decomposition theo ..."
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The Valgebras are the nonlocal matrix generalization of the wellknown Walgebras. Their classical realizations are given by the second Poisson brackets associated with the matrix pseudodifferential operators. In this paper, by using the general Miura transformation, we give the decomposition
On Bus Graph Realizability
 CCCG ABS/CS/0609127
, 2007
"... We consider the following graph embedding problem: Given a bipartite graphG = (V1, V2;E), where the maximum degree of vertices in V2 is 4, can G be embedded on a two dimensional grid such that each vertex in V1 is drawn as a line segment along a grid line, each vertex in V2 is drawn as a point at a ..."
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Cited by 2 (0 self)
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We consider the following graph embedding problem: Given a bipartite graphG = (V1, V2;E), where the maximum degree of vertices in V2 is 4, can G be embedded on a two dimensional grid such that each vertex in V1 is drawn as a line segment along a grid line, each vertex in V2 is drawn as a point at a
Behavioral theories and the neurophysiology of reward,
 Annu. Rev. Psychol.
, 2006
"... ■ Abstract The functions of rewards are based primarily on their effects on behavior and are less directly governed by the physics and chemistry of input events as in sensory systems. Therefore, the investigation of neural mechanisms underlying reward functions requires behavioral theories that can ..."
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Cited by 187 (0 self)
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(see Glimcher 2003 for details). He soon realized that humans make decisions by weighing the potential outcomes by their associated probabilities and then go for the largest result. Or, mathematically speaking, they sum the products of magnitude and probability of all potential outcomes of each option
1.2 Fermionic realization
, 2010
"... iEii = (iδij), i∈Z v (k) m = q −km/2 Λ m q k ∆ (k, m ∈ Z, q  < 1) [v (k) m, v (l) n] = (q (lm−kn)/2 − q (kn−lm)/2)v (k+l) m+n Remark: Classical torus Lie algebra (Poisson algebra on 2D torus) {v (k) m, v (l) m} = (lm − kn)v (k+l) m+n 2 1. Quantum torus Lie algebra ..."
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iEii = (iδij), i∈Z v (k) m = q −km/2 Λ m q k ∆ (k, m ∈ Z, q  < 1) [v (k) m, v (l) n] = (q (lm−kn)/2 − q (kn−lm)/2)v (k+l) m+n Remark: Classical torus Lie algebra (Poisson algebra on 2D torus) {v (k) m, v (l) m} = (lm − kn)v (k+l) m+n 2 1. Quantum torus Lie algebra
Results 1  10
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3,635