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88
MONOTONE MAPS AND EMAPS
"... In this paper, a compactum is a compact metric space; a continuum is a connected compactum, and a map is a con tinuous function. A map f: X + Y is an £map, for £> 0, if and only if diam(fl(y » < £ for each y E Y. If X is a continuum, and ~ is a class of continua, then X is ~like if and only ..."
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In this paper, a compactum is a compact metric space; a continuum is a connected compactum, and a map is a con tinuous function. A map f: X + Y is an £map, for £> 0, if and only if diam(fl(y » < £ for each y E Y. If X is a continuum, and ~ is a class of continua, then X is ~like
Monotone graph limits and quasimonotone graphs
, 2011
"... The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences (Gn) of graphs in terms of a limiting object which may be represented by a symmetric function W on [0, 1], i.e., a kernel or graphon. In this context it is natural to wi ..."
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Cited by 4 (2 self)
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prove an inequality relating the cut and L 1 norms of kernels of the form W1 − W2 with W1 and W2 monotone that may be of interest in its own right; no such inequality holds for general kernels.
Converse KAM Theory for monotone positive symplectomorphisms
 Nonlinearity
, 1998
"... . We apply variational methods to Converse KAM theory. These are useful for symplectomorphisms in the annulus that satisfy weaker hypotheses than those usually required. For instance, we do not need the existence of a global Lagrangian generating function. We obtain the variational principles from t ..."
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Cited by 7 (2 self)
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the primitive function of our symplectomorphism. They are introduced not only for the orbits of a symplectomorphism, but also for the socalled invariant Lagrangian graphs. Among the nondegenerate i.L.g. we focus on the minimizing ones. Applications are also described for a broad class of examples. AMS
Whom You Know Matters: Venture Capital Networks and Investment Performance,
 Journal of Finance
, 2007
"... Abstract Many financial markets are characterized by strong relationships and networks, rather than arm'slength, spotmarket transactions. We examine the performance consequences of this organizational choice in the context of relationships established when VCs syndicate portfolio company inv ..."
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Cited by 138 (8 self)
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Capital, Networks, Syndication, Investment Performance JEL classification: G24, L14. Networks are widespread in many financial markets. Bulgebracket investment banks, for instance, have strong relationships with institutional investors which they make use of when pricing and distributing corporate
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
, 2006
"... This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps ..."
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Cited by 94 (9 self)
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the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution
A Lower Bound for Noncommutative Monotone Arithmetic Circuits (Extended Abstract)
, 1993
"... ) Rimli Sengupta College of Computing Georgia Institute of Technology Atlanta, GA 303320280 email : rimli@cc.gatech.edu GITICS94/05 November, 1993 College of Computing Georgia Institute of Technology Atlanta, Georgia 303320280 Abstract We consider arithmetic circuits over the semiring (\S ..."
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(\Sigma ; min; concat) and show that such circuits require superpolynomial size to compute the lexicographically minimum perfect matching of a bipartite graph. By defining monotone analogues of optimization classes such as OptP, OptL and OptSAC 1 using the monotone analogues of their arithmetic
On the subdijferentiability of convex functions
 Bull. Amer. Math. Soc
, 1965
"... Each lower semicontinuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E * called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones whose graphs are maximal "cyclically monotone " relatio ..."
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Cited by 84 (2 self)
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Each lower semicontinuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E * called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones whose graphs are maximal "cyclically monotone "
Hierarchical Motion Planning Using a Spatial Index
, 1996
"... We investigate the problem of constructing a shortest path of a pointlike robot between two configurations in the euclidean plane cluttered with (intersecting) convex polygonal obstacles. One common approach is to construct the visibility graph and search within this graph in a total time of O(n ..."
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Cited by 16 (0 self)
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(n 2 ). We show that in general it is not necessary to construct the entire visibility graph. In contrast, we develop two hierarchical motionplanning techniques based on the monotonous bisector tree and the visibility graph, which are shown to be more efficient in scenes of low object density. We
The Neumann problem for nonlocal nonlinear diffusion equations
 J. Evol. Equations
"... Abstract. We study nonlocal diffusion models of the form (γ(u))t(t, x) = Ω J(x − y)(u(t, y) − u(t, x)) dy. Here Ω is a bounded smooth domain and γ is a maximal monotone graph in R2. This is a nonlocal diffusion problem analogous with the usual Laplacian with Neumann boundary conditions. We prove ex ..."
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Cited by 29 (7 self)
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Abstract. We study nonlocal diffusion models of the form (γ(u))t(t, x) = Ω J(x − y)(u(t, y) − u(t, x)) dy. Here Ω is a bounded smooth domain and γ is a maximal monotone graph in R2. This is a nonlocal diffusion problem analogous with the usual Laplacian with Neumann boundary conditions. We prove
Level Planar Embedding in Linear Time
, 1999
"... A level graph G  (V, E, q) is a directed acyclic graph with a mapping q: V  {1, 2,...,k), k _ 1, that partitions the vertex set V as V V10V20 ...V k, vj = ql(j), Vi [ vj = for i j, such that q(v) _ q(u) + 1 for each edge (u, v) E. The level planarity testing problem is to decide if G can be ..."
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Cited by 21 (0 self)
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A level graph G  (V, E, q) is a directed acyclic graph with a mapping q: V  {1, 2,...,k), k _ 1, that partitions the vertex set V as V V10V20 ...V k, vj = ql(j), Vi [ vj = for i j, such that q(v) _ q(u) + 1 for each edge (u, v) E. The level planarity testing problem is to decide if G can
Results 1  10
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88