Search results for "Matrix"

Unraveling the extracellular matrix-tumor cell interactions to aid better targeted therapies for neuroblastoma

2021

Treatment in children with high-risk neuroblastoma remains largely unsuccessful due to the development of metastases and drug resistance. The biological complexity of these tumors and their microenvironment represent one of the many challenges to face. Matrix glycoproteins such as vitronectin act as bridge elements between extracellular matrix and tumor cells and can promote tumor cell spreading. In this study, we established through a clinical cohort and preclinical models that the interaction of vitronectin and its ligands, such as αv integrins, are related to the stiffness of the extracellular matrix in high-risk neuroblastoma. These marked alterations found in the matrix led us to speci…

Permutation properties and the fibonacci semigroup

1989

Automorphisms of the integral group ring of the hyperoctahedral group

1990

The purpose of this paper is to verify a conjecture of Zassenhaus [3] for hyperoctahedral groups by proving that every normalized automorphism () of ZG can be written in the form () = Tu 0 I where I is an automorphism of ZG obtained by extending an automorphism of G linearly to ZG and u is a unit of (JJG. A similar result was proved for symmetric groups by Peterson in [2]; the reader should consult [3] or the survey [4] for other results of this kind. 1989

Transitive factorizations in the hyperoctahedral group

2008

The classical Hurwitz enumeration problem has a presentation in terms of transitive factor- izationsin the symmetric group. This presentationsuggestsageneralizationfromtypeAto otherfinite reflection groups and, in particular, to type B.W e study this generalization both from ac ombinatorial and a geometric point of view, with the prospect of providing am eans of understanding more of the structure of the moduli spaces of maps with an S2-symmetry. The type A case has been well studied and connects Hurwitz numbers to the moduli space of curves. W ec onjecture an analogous setting for the type B case that is studied here. 1I ntroduction Transitive factorizations of permutations into transposit…

Boolean Functions of Low Polynomial Degree for Quantum Query Complexity Theory

2007

The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. This is why Boolean functions are needed with a high number of essential variables and a low polynomial degree. Unfortunately, it is a well-known problem to construct such functions. The best separation between these two complexity measures of a Boolean function was exhibited by Ambai- nis [5]. He constructed functions with polynomial degree M and number of variables Omega(M2). We improve such a separation to become exponenti…

An algorithm to find all paths between two nodes in a graph

1990

The irregularity strength of circulant graphs

2005

AbstractThe irregularity strength of a simple graph is the smallest integer k for which there exists a weighting of the edges with positive integers at most k such that all the weighted degrees of the vertices are distinct. In this paper we study the irregularity strength of circulant graphs of degree 4. We find the exact value of the strength for a large family of circulant graphs.

On the consequences of the standard polynomial

1998

The purpose of this paper is to shed some light on the polynomial identities of low degree for the n × n matrix algebra over a field of characteristic 0.Our main result is that we have found all the consequences of degree n + 2 of the standard polynomial have calculated the S n+2-character of the T-ideal generated by this polynomial.

Covering and differentiation

1995

New structural parameters of fullerenes for principal component analysis

2003

The Kekule structure count and the permanent of the adjacency matrix of fullerenes are related to structural parameters involving the presence of contiguous pentagons p, q, r, q/p and r/p, where p is the number of edges common to two pentagons, q is the number of vertices common to three pentagons and r is the number of pairs of nonadjacent pentagons adjacent to another common pentagon. The cluster analysis of the structural parameters allows classification these parameters. Principal component analysis (PCA) of the structural parameters and the cluster analyses of the fullerenes permit their classification. PCA clearly distinguishes five classes of fullerenes. The cluster analysis of fulle…