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On Projection Algorithms for Solving Convex Feasibility Problems

by Heinz H. Bauschke, Jonathan M. Borwein , 1996
"... Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of the ..."
Abstract - Cited by 331 (43 self) - Add to MetaCart
09, 49M45, 65-02, 65J05, 90C25; Secondary 26B25, 41A65, 46C99, 46N10, 47N10, 52A05, 52A41, 65F10, 65K05, 90C90, 92C55. Key words and phrases. Angle between two subspaces, averaged mapping, Cimmino's method, computerized tomography, convex feasibility problem, convex function, convex

Generalized secret sharing and monotone functions

by Josh Benaloh, Jerry Leichter - in Proceedings on Advances in cryptology. Springer-Verlag , 1990
"... Secret Sharing from the perspective of threshold schemes has been well-studied over the past decade. Threshold schemes, however, can only handle a small fraction of the secret sharing functions which we may wish to form. For example, if it is desirable to divide a secret among four participants A, ..."
Abstract - Cited by 184 (0 self) - Add to MetaCart
secret sharing function. There is a natural correspon-dence between the set of “generitlized ” secret sharing functions and the set of monotone functions, and tools developed for simplifying the latter set can be applied equally well t o the former set. 1

Renormalization group flows from holography -- Supersymmetry and a c-theorem

by D. Z. Freedman, S. S. Gubser, K. Pilch, N. P. Warner - ADV THEOR. MATH. PHYS , 1999
"... We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. ..."
Abstract - Cited by 294 (25 self) - Add to MetaCart
sector of N = 2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For even-dimensional boundaries, the c-function coincides with the trace anomaly

Maximizing non-monotone submodular functions

by Uriel Feige, Vahab S. Mirrokni, Jan Vondrák - IN PROCEEDINGS OF 48TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS , 2007
"... Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular fu ..."
Abstract - Cited by 146 (18 self) - Add to MetaCart
Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular

The monotone circuit complexity of Boolean functions

by N. Alon, R. B. Boppana - COMBINATORICA , 1987
"... Recently, Razborov obtained superpolynomial lower bounds for monotone circuits that lect cliques in graphs. In particular, Razborov showed that detecting cliques of size s in a graph dh m vertices requires monotone circuits of size.Q(m-'/(log m) ~') for fixed s, and size rn ao°~') for ..."
Abstract - Cited by 144 (2 self) - Add to MetaCart
cliques of size s requires 'm'/(log m)') AND gates. We show that even a very rough approximation of the maximum clique e of a graph requires superpolynomial size monotone circuits, and give lower bounds for some net Boolean functions. Our best lower bound fi~r an NP function of n variables

Recursive identification for Wiener model with discontinuous piece-wise linear function

by Han-fu Chen - IEEE Transactions Automatic Control
"... Abstract—This paper deals with identification of Wiener systems with nonlinearity being a discontinuous piece-wise linear function. Recursive estimation algorithms are proposed to estimate six un-known parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem by u ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
Abstract—This paper deals with identification of Wiener systems with nonlinearity being a discontinuous piece-wise linear function. Recursive estimation algorithms are proposed to estimate six un-known parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem

VLSI Complexity Reduction by Piece-Wise Approximation of the Sigmoid Function

by Valeriu Beiu Jan, Jan A. Peperstraete, Joos Vandewalle, Rudy Lauwereins , 1994
"... . The paper is devoted to show that there are simple and accurate ways to compute a sigmoid nonlinearity in digital hardware by piece-wise linearization. This is done as the computations involved are complex, but even more interesting, for the data compression performed by the sigmoid, which can ..."
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. The paper is devoted to show that there are simple and accurate ways to compute a sigmoid nonlinearity in digital hardware by piece-wise linearization. This is done as the computations involved are complex, but even more interesting, for the data compression performed by the sigmoid, which

Kernels and Regularization on Graphs

by Alexander J. Smola, Risi Kondor , 2003
"... We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that di#usion kernels can be found as a special cas ..."
Abstract - Cited by 244 (11 self) - Add to MetaCart
case of our reasoning. We show that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators.

3 VECTOR TRANSFORM OPERATORS FOR PIECE-WISE HARMONIC FUNCTIONS

by O. Yaremko Y. Parfenova
"... ar ..."
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Abstract not found

Real-time logics: complexity and expressiveness

by Rajeev Alur, Thomas A. Henzinger - INFORMATION AND COMPUTATION , 1993
"... The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about real-time systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via ..."
Abstract - Cited by 252 (16 self) - Add to MetaCart
a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by! -regular sets. Several more expressive variants are proved to be highly undecidable. This framework
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