Related papers: On computing the fixpoint of a set of boolean equa…
A representation of an arbitrary system of strict linear inequalities in R^n as a system of points is proposed. The representation is obtained by using a so-called polarity. Based on this representation an algorithm for constructing a…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…
Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem of counting the number of integer points inside $P$, assuming that $P$ is $\Delta$-modular, where the polytope $P$ is called $\Delta$-modular if all the rank…
This paper presents a simplified method of expressing the solution to cubic equations in terms of function evaluation only. The method eliminates the need to manipulate the original coefficients of the cubic polynomial and makes the…
Using logic gates is the traditional way of designing logic circuits. However, most of the minimization algorithms concern a limited set of gates (complete sets), like sum of products, exclusive-or sum of products, NAND gates, NOR gates…
The aim of this paper is to show the use of the coupled quasisolutions method as a useful technique when treating with ordinary differential equations with functional arguments of bounded variation. We will do this by looking for solutions…
In this work, we prove the existence of solutions for a tripled system of integral equations using some new results of fixed point theory associated with measure of noncompactness. These results extend some previous works in the literature,…
We formalize notions of robustness for composite estimators via the notion of a breakdown point. A composite estimator successively applies two (or more) estimators: on data decomposed into disjoint parts, it applies the first estimator on…
In this paper we give a new aggregation framework for linear Diophantine equations. In particular, we prove that an aggregated system of minimum size can be built in polynomial time. We also derive an analytic formula that gives the number…
In this document, we prove the convergence of the model proposed in [1], which aims at estimating the LoRaWAN network performance in a single-gateway scenario. First, we provide an analytical proof of the existence of a fixed point solution…
We present in this article a general approach (in the form of recommendations and guidelines) for tackling Diophantine equation problems (whether single equations or systems of simultaneous equations). The article should be useful in…
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…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time--space complexity is roughly quadratic in the logarithm of the…
We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogo- nal functions defined on…
Current critical systems commonly use a lot of floating-point computations, and thus the testing or static analysis of programs containing floating-point operators has become a priority. However, correctly defining the semantics of common…
In this paper we consider change-points in multiple sequences with the objective of minimizing the estimation error of a sequence by making use of information from other sequences. This is in contrast to recent interest on change-points in…
This paper deals with the resolutions of fuzzy relation equations with addition-min composition. When the fuzzy relation equations have a solution, we first propose an algorithm to find all minimal solutions of the fuzzy relation equations…