Search Results - "Koiran, Pascal"

Absolute reconstruction for sums of powers of linear forms: degree 3 and beyond by Koiran, Pascal, Saha, Subhayan

“…We study the decomposition of multivariate polynomials as sums of powers of linear forms. We give a randomised algorithm for the following problem: If a…”
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On the uniqueness and computation of commuting extensions by Koiran, Pascal

“…A tuple (Z1,…,Zp) of matrices of size r×r is said to be a commuting extension of a tuple (A1,…,Ap) of matrices of size n×n if the Zi pairwise commute and each…”
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Arithmetic circuits: The chasm at depth four gets wider by Koiran, Pascal

“…In their paper on the “chasm at depth four”, Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of…”
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Orthogonal tensor decomposition and orbit closures from a linear algebraic perspective by Koiran, Pascal

“…We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of…”
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Derandomization and absolute reconstruction for sums of powers of linear forms by Koiran, Pascal, Skomra, Mateusz

“…We study the decomposition of multivariate polynomials as sums of powers of linear forms. As one of our main results, we give a randomized algorithm for the…”
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Hidden Cliques and the Certification of the Restricted Isometry Property by Koiran, Pascal, Zouzias, Anastasios

“…Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix…”
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The topological entropy of iterated piecewise affine maps is uncomputable by Koiran, Pascal

“…We show that it is impossible to compute (or even to approximate) the topological entropy of a continuous piecewise affine function in dimension four. The same…”
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PT-symmetry in one-way wormholes by Koiran, Pascal, Zejli, Hicham, Levy, J.-P., Margnat, Florent, Duval, M.-F., Zejli, Hasnae

“…In a recent paper, we studied a modified version of the Einstein–Rosen bridge. This modified bridge is traversable and works as a one-way membrane: a particle…”
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Computing the multilinear factors of lacunary polynomials without heights by Chattopadhyay, Arkadev, Grenet, Bruno, Koiran, Pascal, Portier, Natacha, Strozecki, Yann

“…We present a deterministic algorithm which computes the multilinear factors of multivariate lacunary polynomials over number fields. Its complexity is…”
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An efficient uniqueness theorem for overcomplete tensor decomposition by Koiran, Pascal

“…We give a new, constructive uniqueness theorem for tensor decomposition. It applies to order 3 tensors of format $n \times n \times p$ and can prove uniqueness…”
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A Wronskian approach to the real τ-conjecture by Koiran, Pascal, Portier, Natacha, Tavenas, Sébastien

“…According to the real τ-conjecture, the number of real roots of a sum of products of sparse univariate polynomials should be polynomially bounded in the size…”
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On the uniqueness and computation of commuting extensions by Koiran, Pascal

“…A tuple (Z_1,...,Z_p) of matrices of size r is said to be a commuting extension of a tuple (A_1,...,A_p) of matrices of size n <r if the Z_i pairwise commute…”
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Interpolation in Valiant’s Theory by Koiran, Pascal, Perifel, Sylvain

“…We investigate the following question: if a polynomial can be evaluated at rational points by a polynomial-time boolean algorithm, does it have a…”
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Lower bounds by Birkhoff interpolation by García-Marco, Ignacio, Koiran, Pascal

“…In this paper we give lower bounds for the representation of real univariate polynomials as sums of powers of degree 1 polynomials. We present two families of…”
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The complexity of two problems on arithmetic circuits by Koiran, Pascal, Perifel, Sylvain

“…By using arithmetic circuits, encoding multivariate polynomials may be drastically more efficient than writing down the list of monomials. Via the study of two…”
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On the Intersection of a Sparse Curve and a Low-Degree Curve: A Polynomial Version of the Lost Theorem by Koiran, Pascal, Portier, Natacha, Tavenas, Sébastien

“…Consider a system of two polynomial equations in two variables: F ( X , Y ) = G ( X , Y ) = 0 , where F ∈ R [ X , Y ] has degree d ≥ 1 and G ∈ R [ X , Y ] has…”
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On the complexity of the multivariate resultant by Grenet, Bruno, Koiran, Pascal, Portier, Natacha

“…The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous…”
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Infall time in the Eddington-Finkelstein metric, with application to Einstein-Rosen bridges by Koiran, Pascal

“…The Eddington-Finkelstein metric is obtained from the Schwarzschild metric by a change of the time variable. It is well known that a test mass falling into a…”
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Undercomplete Decomposition of Symmetric Tensors in Linear Time, and Smoothed Analysis of the Condition Number by Koiran, Pascal, Saha, Subhayan

“…We study symmetric tensor decompositions, i.e., decompositions of the form $T = \sum_{i=1}^r u_i^{\otimes 3}$ where $T$ is a symmetric tensor of order 3 and…”
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A ...-Conjecture for Newton Polygons by Koiran, Pascal, Portier, Natacha, Tavenas, Sebastien, Thomasse, Stephan

“…(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).One can associate to any bivariate polynomial ... its Newton polygon. This is the…”
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