We demonstrate that the answer to the question posed in the title is “yes” and “no”: “no” if the set of permissible operations is restricted to {+,−,×,/,mod,<}; “yes” if we are also allowed a gcd-oracle as a permissible operation. It has been shown (see [Sto76, MST91]) that no strongly polynomial algorithm exists for the problem of finding the greatest common divisor (gcd) of two arbitrary inte...

In 1991, Weidong Fang and Huiling Li proved that there are only finitely many non-trivial linear spaces that admit a line-transitive, point imprimitive group action, for a given value of gcd(k, r), where k is the line size and r is the number of lines on a point. The aim of this paper is to make that result effective. We obtain a classification of all linear spaces with this property having gcd...

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...