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Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
Neural network approaches have been applied to computational morphology with great success, improving the performance of most tasks by a large margin and providing new perspectives for modeling. This paper starts with a brief introduction…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
This thesis details a Python-based software designed to calculate the Jones polynomial, a vital mathematical tool from Knot Theory used for characterizing the topological and geometrical complexity of curves in \( \mathbb{R}^3 \), which is…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
We review the field of Optical Quantum Computation, considering the various implementations that have been proposed and the experimental progress that has been made toward realizing them. We examine both linear and nonlinear approaches and…
We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for…
We report recent research on computing with biology-based neural network models by means of physics-based opto-electronic hardware. New technology provides opportunities for very-high-speed computation and uncovers problems obstructing the…
Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes…
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on…
Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on the world's largest computers are spent simulating problems…
Computational models pervade all branches of the exact sciences and have in recent times also started to prove to be of immense utility in some of the traditionally 'soft' sciences like ecology, sociology and politics. This volume is a…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
In the 6th Int. Symposium on OPSFA there were several communications dealing with concrete applications of orthogonal polynomials to experimental and theoretical physics, chemistry, biology and statistics. Here I make suggestions concerning…
We show that the amoeba of a complex algebraic variety defined as the solutions to a generic system of $n$ polynomials in $n$ variables has a finite basis. In other words, it is the intersection of finitely many hypersurface amoebas.…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…