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3,197
Families of Commuting Integrals of Motion with Certain Symmetries
, 2004
"... Some results for commuting local integrals of motion for free bosonic theories are presented, which can be applied in construction of integrable boundary states. Usable program code for calculation of these integrals of motion is also introduced. 1 ..."
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Cited by 2 (0 self)
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Some results for commuting local integrals of motion for free bosonic theories are presented, which can be applied in construction of integrable boundary states. Usable program code for calculation of these integrals of motion is also introduced. 1
Design of capacityapproaching irregular lowdensity paritycheck codes
 IEEE TRANS. INFORM. THEORY
, 2001
"... We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the unde ..."
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Cited by 588 (6 self)
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that the underlying communication channel is symmetric, we prove that the probability densities at the message nodes of the graph possess a certain symmetry. Using this symmetry property we then show that, under the assumption of no cycles, the message densities always converge as the number of iterations tends
Features of similarity.
 Psychological Review
, 1977
"... Similarity plays a fundamental role in theories of knowledge and behavior. It serves as an organizing principle by which individuals classify objects, form concepts, and make generalizations. Indeed, the concept of similarity is ubiquitous in psychological theory. It underlies the accounts of stimu ..."
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Cited by 1455 (2 self)
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and metric assumptions are open to question. It has been argued by many authors that dimensional representations are appropriate for certain stimuli (e.g., colors, tones) but not for others. It seems more appropriate to represent faces, countries, or personalities in terms of many qualitative features than
Mirror symmetry, D–branes and counting holomorphic discs
, 2000
"... We consider a class of special Lagrangian subspaces of CalabiYau manifolds and identify their mirrors, using the recent derivation of mirror symmetry, as certain holomorphic varieties of the mirror geometry. This transforms the counting of holomorphic disc instantons ending on the Lagrangian subman ..."
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Cited by 202 (25 self)
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We consider a class of special Lagrangian subspaces of CalabiYau manifolds and identify their mirrors, using the recent derivation of mirror symmetry, as certain holomorphic varieties of the mirror geometry. This transforms the counting of holomorphic disc instantons ending on the Lagrangian
Braid group actions on derived categories of coherent sheaves
 DUKE MATH. J
, 2001
"... This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety X. The motivation for this is M. Kontsevich’s homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results is ..."
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Cited by 255 (8 self)
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This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety X. The motivation for this is M. Kontsevich’s homological mirror conjecture, together with the occurrence of certain braid group actions in symplectic geometry. One of the main results
Mirror Symmetry for Lattice Polarized K3 Surfaces
 J. Math. Sci
, 1996
"... Introduction. There has been a recent explosion in the number of mathematical publications due to the discovery of a certain duality between some families of CalabiYau threefolds made by a group of theoretical physicists (see [11,26] for references). Roughly speaking this duality, called mirror sym ..."
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Cited by 139 (4 self)
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Introduction. There has been a recent explosion in the number of mathematical publications due to the discovery of a certain duality between some families of CalabiYau threefolds made by a group of theoretical physicists (see [11,26] for references). Roughly speaking this duality, called mirror
Disk instantons, mirror symmetry and the duality web
, 2001
"... We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of Dbranes wrapped over Lagrangian cycles of noncompact CalabiYau 3folds. Along the way we clarify the notion of “flat coordinates” for the boundary theory. We also discover ..."
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Cited by 136 (26 self)
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We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of Dbranes wrapped over Lagrangian cycles of noncompact CalabiYau 3folds. Along the way we clarify the notion of “flat coordinates” for the boundary theory. We also
SYMMETRY AND STABILITY IN DIFFERENTIAL EQUATIONS
"... Many mathematical models for physical, biological or sociological phenomena exhibit various kinds of symmetry, such as symmetry with respect to reflection, rotation, translation, dilation, gauge transformation, and so on. Given an equation with certain symmetry, a natural question that arises is whe ..."
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Many mathematical models for physical, biological or sociological phenomena exhibit various kinds of symmetry, such as symmetry with respect to reflection, rotation, translation, dilation, gauge transformation, and so on. Given an equation with certain symmetry, a natural question that arises
Symmetry Theorems and Uniform Rectifiability
, 2007
"... We study overdetermined boundary conditions for positive solutions to some elliptic partial differential equations of pLaplacian type in a bounded domain D. We show that these conditions imply uniform rectifiability of ∂D and also that they yield the solution to certain symmetry problems. ..."
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We study overdetermined boundary conditions for positive solutions to some elliptic partial differential equations of pLaplacian type in a bounded domain D. We show that these conditions imply uniform rectifiability of ∂D and also that they yield the solution to certain symmetry problems.
Results 1  10
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