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We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing…
The main aim of the paper is to present a general version of the Fourier Tauberian theorem for monotone functions. This result, together with Berezin's inequality, allows us to obtain a refined version the Li-Yau estimate for the counting…
This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…
In this paper we give a different proof of Kuz'min's result on the number of irreducible polynomials with the first two coefficients fixed. Our technique is to relate the question to the number of points on a curve, and to calculate the…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…
In the modeling of biological systems by Boolean networks a key problem is finding the set of fixed points of a given network. Some constructed algorithms consider certain structural properties of the interaction graph like those proposed…
Compounding submodular monotone (i.e. 2-alternating) set functions on a finite set preserves this property, as shown in 2010. A natural generalization to k-alternating functions was presented in 2018, however hardly readable because of page…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider $f(x_1, \dots, x_N)$, where $x_i \in \mathbb{R}^d$, and $f$ is invariant under permutations of its $N$…
We show the existence of an FPTAS for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed.
An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain…
Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$; these functions are…
We present new bounds for the numerical radius of bounded linear operators and $2\times 2$ operator matrices. We apply upper bounds for the numerical radius to the Frobenius companion matrix of a complex monic polynomial to obtain new…
A notion of combinatorial game over a partially ordered set of atomic outcomes was recently introduced by Selinger. These games are appropriate for describing the value of positions in Hex and other monotone set coloring games. It is…
It is shown that the maximum number of patterns that can occur in a permutation of length $n$ is asymptotically $2^n$. This significantly improves a previous result of Coleman.
We provide an approach to counting roots of polynomial systems, where each polynomial is a general linear combination of prescribed, fixed polynomials. Our tools rely on the theory of Khovanskii bases, combined with toric geometry, the…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…