The task of determining the approximate greatest common divisor (GCD) of univariate polynomials with inexact coefficients can be formulated as computing for a given Sylvester matrix a new Sylvester matrix of lower rank whose entries are near the corresponding entries of that input matrix. We solve the approximate GCD problem by a new method based on structured total least norm (STLN) algorithms...

Granule cell dispersion (GCD) is observed in approximately 40% of cases of hippocampal sclerosis (HS) in patients with epilepsy. Studies in animal models suggest that GCD may be a consequence of enhanced proliferation of granule cell precursors as a result of seizures. We quantified the number of cells in cycle in subfields of the hippocampus with immunohistochemistry for Mcm2 in 14 HS cases wi...

In this paper we examine the applicability of the previously proposed Greatest Common Divisor GCD method to blind image deconvolution In this method the desired image is approximated as the GCD of the two dimensional polynomials corresponding to the z transforms of two or more distorted and noisy versions of the same scene assuming that the distortion lters are FIR and relatively co prime We ju...

Let S = {x1, x2, . . . , xn} be a set of distinct positive integers such that gcd(xi, xj) ∈ S for 1 ≤ i, j ≤ n. Such a set is called GCD-closed. In 1875/1876, H.J.S. Smith showed that, if the set S is “factor-closed”, then the determinant of the matrix eij = gcd(xi, xj) is det(E) = ∏n m=1 φ(xm), where φ denotes Euler’s Phi-function. Since the early 1990’s there has been a rebirth of interest in...

Purpose. The purpose of this study was to elucidate the pathophysiological process in primary cultured corneal fibroblasts (PCFs) from normal subjects and granular corneal dystrophy (GCD) II patients, by using cDNA microarrays. Methods. PCFs were isolated from the corneas of normal subjects and GCD II patients who were heterozygous and homozygous for the TGFBI R124H mutation. RNA was isolated f...

As a consequence of Algorithm 1 below, there always exist integers x, y ∈ Z such that ax+by = gcd(a, b). We say that a and b are co-prime (or relatively prime) if gcd(a, b) = 1, i.e., ax = 1 mod b. From this, x is the multiplicative inverse of a modulo b, and likewise y is the multiplicative inverse of b modulo a. The following deterministic algorithm shows that gcd(a, b) (and additionally, the...

The computation of the Greatest Common Divisor (GCD) of a set of polynomials is an important issue in computational mathematics and it is linked to Control Theory very strong. In this paper we present different matrix-based methods, which are developed for the efficient computation of the GCD of several polynomials. Some of these methods are naturally developed for dealing with numerical inaccu...