Related papers: A numerical algorithm for zero counting II: Random…

In a recent paper (Cucker, Krick, Malajovich and Wschebor, A Numerical Algorithm for Zero Counting. I: Complexity and accuracy, J. Compl.,24:582-605, 2008) we analyzed a numerical algorithm for computing the number of real zeros of a…

We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those…

We propose the construction of entire functions with a given random collection of zeros. There are considered two particular cases. In the first one we are dealing with simple zeros. And the second corresponds to random zeros with random…

This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).

This paper has been withdrawn by the authors, since it has been merged with Part I (ID 0802.3570)

Some of my previous publications were incomplete in the sense that non trivial zeros belonging to a particular type of fundamental domain have been inadvertently ignored. Due to this fact, I was brought to believe that computations done by…

I provide the algorithm that solves the challenge proposed by Wm. G. Hoover and Carol G. Hoover in their recent paper "Time-Reversible Random Number Generators", arXiv:1305.0961, with an explanation on how to derive it analytically.

We propose a numerical analysis of a simplified version of the previous paper "Multiplicity hunting and approximating multiple roots of polynomial systems" written by the two authors.

This paper was withdrawn by the authors.

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

This paper improves algorithms given in math.CO/0012036. Although the graph (digraph) becomes non-random as the algorithm proceeds, the probability for success stays the same. We also give examples.

Randomness is an invaluable resource in today's life with a broad use reaching from numerical simulations through randomized algorithms to cryptography. However, on the classical level no true randomness is available and even the use of…

The results of this paper have been subsumed by those of our new paper arXiv:0910.1858

Work in progress concerning alternative formalizations of arithmetic.

We give an implementation of a statistical model, which can be successfully applied for compressing of a sequence of binary digits with behavior close to random.

This article gives an elementary introduction to quantum computing. It is a draft for a book chapter of the "Handbook of Nature-Inspired and Innovative Computing", Eds. A. Zomaya, G.J. Milburn, J. Dongarra, D. Bader, R. Brent, M.…

We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(n D kappa(f)) iterations where n is the number of polynomials (as well as the dimension of the ambient space), D…

In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distribution of the crossing numbers of such random knots. We also…

Revisions are almost entirely in the introduction and conclusion. Results are unchanged, however the comments and recommendations on different generators were changed, and more references were added.

We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…