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161,065
Semidefinite Programming Relaxations for Semialgebraic Problems
, 2001
"... A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility. The mai ..."
Abstract

Cited by 365 (23 self)
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. The main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials, and some results from real algebraic geometry. The techniques provide a constructive approach for finding bounded degree solutions to the Positivstellensatz
Polynomial time algorithms for multicast network code construction
 IEEE TRANS. ON INFO. THY
, 2005
"... The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediat ..."
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Cited by 316 (29 self)
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that the intermediate nodes are allowed to reencode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized
A support vector method for multivariate performance measures
 Proceedings of the 22nd International Conference on Machine Learning
, 2005
"... This paper presents a Support Vector Method for optimizing multivariate nonlinear performance measures like the F1score. Taking a multivariate prediction approach, we give an algorithm with which such multivariate SVMs can be trained in polynomial time for large classes of potentially nonlinear per ..."
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Cited by 305 (6 self)
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This paper presents a Support Vector Method for optimizing multivariate nonlinear performance measures like the F1score. Taking a multivariate prediction approach, we give an algorithm with which such multivariate SVMs can be trained in polynomial time for large classes of potentially non
Common Persistence in Conditional Variances
 ECONOMETRIC REVIEWS
, 1993
"... Since the introduction of the autoregressive conditional heteroskedastic (ARCH) model in Engle (1982), numerous applications of this modeling strategy have already appeared. A common finding in many of these studies with high frequency financial or monetary data concerns the presence of an approxima ..."
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Cited by 343 (20 self)
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of an approximate unit root in the autoregressive polynomial in the univariate time series representation for the conditional second order moments of the process, as in the socalled integrated generalized ARCH (IGARCH) class of models proposed in Engle and Bollerslev (1986). In the IGARCH models shocks
Unifying SATbased and Graphbased Planning
 In IJCAI
, 1999
"... The Blackbox planning system unifies the planning as satisfiability framework (Kautz and Selman 1992, 1996) with the plan graph approach to STRIPS planning (Blum and Furst 1995). We show that STRIPS problems can be directly translated into SAT and efficiently solved using new randomized systemati ..."
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Cited by 293 (15 self)
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systematic solvers. For certain computationally challenging benchmark problems this unified approach outperforms both SATPLAN and Graphplan alone. We also demonstrate that polynomialtime SAT simplification algorithms applied to the encoded problem instances are a powerful complement to the “mutex
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
 IN ADVANCES IN CRYPTOLOGY, EUROCRYPT’2000, LNCS 1807
, 2000
"... The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaus ..."
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Cited by 183 (20 self)
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The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms
Faulttolerant quantum computation
 In Proc. 37th FOCS
, 1996
"... It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information i ..."
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Cited by 264 (5 self)
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as originally believed. For any quantum computation with t gates, we show how to build a polynomial size quantum circuit that tolerates O(1 / log c t) amounts of inaccuracy and decoherence per gate, for some constant c; the previous bound was O(1 /t). We do this by showing that operations can be performed
Multivariate Quadratic Polynomials
, 2005
"... Proefschrift voorgedragen tot het behalen van het doctoraat in de ingenieurswetenschappen door ..."
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Proefschrift voorgedragen tot het behalen van het doctoraat in de ingenieurswetenschappen door
Results 1  10
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161,065