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...connection between lower bounds on the size of non-commutative arithmetic circuits and a problem about commutative degree four polynomials, the classical...an exponential lower bound on the size of arithmetic circuits computing the non-commutative permanent. more generally, we consider such sum-of-squares identities for any m polynomial...
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...we consider optimization problems with polynomial inequality constraints in non-commuting variables. these non-commuting variables are viewed as bounded...at a given relaxation step and show how to extract a global optimizer from the solution of the corresponding semidefinite programming problem....
Published in 2009.
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...a symmetric non-commutative polynomial p when evalu- ated at a tuple of operators on a flnite dimensional...takes positive semideflnite values on the variety z of spherical isometries is represented as a sum of squares of polynomials plus a residual part...
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...we study the quantization of two examples of classically chaotic dynamics, the anosov dynamics of “cat maps” on a two...a quantized torus. we compute the non-commutative generalization of the kolmogorov–sinai entropy, namely the connes–størmer entropy, of the generator of this group, and find that its value is...
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...we extend the complete mellin (cm) representation of feynman amplitudes to the non-commutative quantum field theories. this
representation...complete
mellin representation also allows the study of asymptotic behavior under rescaling of arbitrary subsets of external invariants
of any feynman amplitude....
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the sum of square roots problem over integers is the task of deciding the sign of a non-zero sum, s = pn=1 i p...be used to settle (positively) the sum of square roots problem for a special class of integers: suppose each integer ai is of the form, ai = x d i...
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...lyapunov functions which are generalisations of those used for the derivation of the multivariable circle and popov criteria. these conditions can be given in terms of polynomial inequalities and so sum of squares techniques can be used to...
Published in 2011.
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...alternative to numerical optimization, namely the exact validation via symbolic methods of the global minimality
of our deformations. semidefinite programming and newton refinement are used to...we demonstrate our approach on the approximate gcd, approximate
factorization, and rump’s model problems. the talk covers joint work with bin li, zhengfeng yang and lihong zhi.
...
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...is a natural bijection between the set of pure states of m and the cartesian product of s with the real projective (t-1)-space...also discuss what happens for non-symmetric matrix polynomials or in the absence of the archimedean assumption, and review some of the related classical results. the methods employed are both algebraic...
Published in 2009.
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...show that a wide variety of non-linear cellular automata (cas) can be decomposed into a quasidirect product of linear ones. these cas can be predicted by parallel circuits of depth o(log^2 t...