Results 11  20
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910
Aggregation, Blowup, And Collapse: The Abc's Of Taxis In Reinforced Random Walks
 SIAM J. APPL. MATH
, 1997
"... In many biological systems, movement of an organism occurs in response to a diffusible or otherwise transported signal, and in its simplest form this can be modeled by diffusion equations with advection terms of the form first derived by Patlak [Bull. of Math. Biophys.,15 (1953), pp. 311338]. How ..."
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Cited by 104 (9 self)
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. We first derive several general classes of partial differential equations that depend on how the movement rules are affected by the local modulator concentration. We then show that a variety of dynamics is possible, which we classify as aggregation, blowup, or collapse, depending on whether
Collapsed Riemannian Manifolds with Bounded Sectional Curvature
 ICM 2002 VOL. III 13
, 2002
"... In the last two decades, one of the most important developments in Riemannian geometry is the collapsing theory of CheegerFukayaGromov. A Riemannian manifold is called (sufficiently) collapsed if its dimension looks smaller than its actual dimension while its sectional curvature remains bounded (s ..."
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Cited by 3 (0 self)
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In the last two decades, one of the most important developments in Riemannian geometry is the collapsing theory of CheegerFukayaGromov. A Riemannian manifold is called (sufficiently) collapsed if its dimension looks smaller than its actual dimension while its sectional curvature remains bounded
Collapsing with a lower bound on the curvature operator
, 2012
"... Cheeger and Gromov showed that Fstructures are related to collapse with a doublesided curvature bound. We define fibered Fstructures and extend some of the CheegerGromov results to the setting of collapse with a lower bound on the curvature operator. ..."
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Cited by 1 (0 self)
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Cheeger and Gromov showed that Fstructures are related to collapse with a doublesided curvature bound. We define fibered Fstructures and extend some of the CheegerGromov results to the setting of collapse with a lower bound on the curvature operator.
Collapsed Riemannian manifolds with bounded diameter and bounded covering geometry
 GAFA (Geometrical And Functional Analysis)
, 1995
"... We study the class of nRiemannian manifolds in the title such that the torsion elements in the fundamental group have a definite bound on their orders. Our main result asserts the existence of a kind of generalized Seifert fiber structure on M", for which the fundamental group of fibers in ..."
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Cited by 8 (2 self)
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We study the class of nRiemannian manifolds in the title such that the torsion elements in the fundamental group have a definite bound on their orders. Our main result asserts the existence of a kind of generalized Seifert fiber structure on M", for which the fundamental group of fibers
Graph Nonisomorphism Has Subexponential Size Proofs Unless The PolynomialTime Hierarchy Collapses
 SIAM Journal on Computing
, 1998
"... We establish hardness versus randomness tradeoffs for a broad class of randomized procedures. In particular, we create efficient nondeterministic simulations of bounded round ArthurMerlin games using a language in exponential time that cannot be decided by polynomial size oracle circuits with acce ..."
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Cited by 110 (4 self)
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We establish hardness versus randomness tradeoffs for a broad class of randomized procedures. In particular, we create efficient nondeterministic simulations of bounded round ArthurMerlin games using a language in exponential time that cannot be decided by polynomial size oracle circuits
Collapsing threemanifolds under a lower curvature bound
 J. Differential Geom
"... Abstract The purpose of this paper is to completely characterize the topology of threedimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension. Introduction We study the topology of threedimensional Riemannian manifolds ..."
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Cited by 30 (3 self)
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diameter bound D (see Remark 4.6). Observe that ∂X × D 2 ⊂ M i collapses to ∂X. We have the following corollary of Theorem 0.3. Corollary 0.4. Let M i , X, and Seif i (X) be as in Theorem 0.3, and let g and k denote the genus of X and the number of components of ∂X respectively. Then we have the following
Notes on Polynomially Bounded Arithmetic
"... We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general modeltheoretical investigations on fragments of bounded arithmetic. Contents 0 Introduction and motivation. 1 1 Preliminaries. 3 1.1 The p ..."
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Cited by 58 (1 self)
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We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general modeltheoretical investigations on fragments of bounded arithmetic. Contents 0 Introduction and motivation. 1 1 Preliminaries. 3 1
ÂGENUS AND COLLAPSING
, 1997
"... Abstract. If M is a compact spin manifold, we give relationships between the vanishing of Â(M) and the possibility that M can collapse with curvature bounded below. 1. ..."
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Cited by 5 (0 self)
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Abstract. If M is a compact spin manifold, we give relationships between the vanishing of Â(M) and the possibility that M can collapse with curvature bounded below. 1.
Outer Bounds for User Cooperation
"... Abstract—We obtain a dependence balance based outer bound on the capacity region of the twouser multiple access channel with generalized feedback (MACGF). We investigate a Gaussian MAC with usercooperation (MACUC), where each transmitter receives an additive white Gaussian noise corrupted versio ..."
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version of the channel input of the other transmitter. For all nonzero values of cooperation noise variances, our outer bound strictly improves upon the cutset outer bound. Moreover, as the variances of the cooperation noises become large, our outer bound collapses to the capacity region of the Gaussian
Results 11  20
of
910