Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols

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Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calcul ...

We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterm ...

We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. Our approach is based on a simultaneous law of the ...

The value of a life settlement investment, manifested through a traded life insurance policy, is highly dependent on the insured's life expectancy (LE). LE estimation in life settlements relies heavily on medical underwriting. Employing different evaluatio ...

Two subsets A,B of an n-element ground set X are said to be crossing, if none of the four sets AB, A\B, B\A and X(AB) are empty. It was conjectured by Karzanov and Lomonosov forty years ago that if a family F of subsets of X does not contain k pairwise cr ...

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...

Consider the problem of constructing a polar code of block length N for a given transmission channel W. Previous approaches require one to compute the reliability of the N synthetic channels and then use only those that are sufficiently reliable. However, ...

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...

Haxell's condition [14] is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the existence of a perf ...

Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scal ...

The research work reported in this dissertation is aimed to develop efficient and stable numerical schemes in order to obtain accurate numerical solution for viscoelastic fluid flows within the spectral element context. The present research consists in the ...

We address the problem of blind audio source separation in the under-determined and convolutive case. The contribution of each source to the mixture channels in the time-frequency domain is modeled by a zero-mean Gaussian random vector with a full rank cov ...

Let X = {X(t); t ∈ RN} be a (N,d) fractional Brownian motion in Rd of index H ∈ (0,1). We study the local time of X for all temporal dimensions N and spatial dimensions d for which local time exist. We obtain two main results : R1. If we denote by Lx(I) th ...

Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols

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On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions

Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields

Propagation of singularities for the stochastic wave equation

Dating Death: An Empirical Comparison of Medical Underwriters in the U.S. Life Settlements Market

On the Size of K-Cross-Free Families

New Graph Algorithms via Polyhedral Techniques

Construction of Polar Codes With Sublinear Complexity

Arithmetic and geometric structures in cryptography

On some problems related to 2-level polytopes

Finding Perfect Matchings in Bipartite Hypergraphs

Evaluating functions of positive-definite matrices using colored-noise thermostats

Simulation of Time-Dependent Viscoelastic Fluid Flows by Spectral Elements

Nonnegative Matrix Factorization and Spatial Covariance Model for Under-Determined Reverberant Audio Source Separation

Propriétés fines des trajectoires du mouvement brownien fractionnaire