Using the DNA microarray technology, biologists have thousands of array data available. Discovering the function relations between genes and their involvements in biological processes depends on the ability to efficiently process and quantitatively analyze large amounts of array data. Clustering algorithms are among the popular tools that can be used to help biologists achieve their goals. Alth...

We present new Furi-Pera theorems for acyclic maps between topological spaces. 1. Introduction. In this paper, we present new Furi-Pera theorems [6, 7] for acyclic maps between Hausdorff topological spaces. The main result in our paper is based on a new Leray-Schauder alternative [1] for such maps which in turn is based on the notion of compactly null-homotopic. We first recall some results and...

A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappinngs and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balanc...

In this paper, we describe our Brand Association MapTM (BAM) tool which maps and visualizes the way consumers naturally think and talk about brands across billions of unaided conversations online. BAM is a semi-supervised tool that leverages text-mining algorithms to identify key correlated phrases, terms and issues out of millions of candidate terms which were derived from billions of online c...

We will study the lattice dynamical system of a nonlinear Boussinesq equation. Our objective is to explore the existence of the global attractor for the solution semiflow of the introduced lattice system and to investigate its upper semicontinuity with respect to a sequence of finite-dimensional approximate systems. As far as we are aware, our result here is the first concerning the lattice dyn...

In the last several years, remote sensing technology has opened up the possibility of performing large scale building detection from satellite imagery. Our work is some of the first to create population density maps from building detection on a large scale. The scale of our work on population density estimation via high resolution satellite images raises many issues, that we will address in thi...

Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli space of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 with determinant equal to a theta characteristic whose Frobenius pull-back is not sta...

We compute the domain of existence of two-dimensional invariant tori with fixed frequency vectors for a fourdimensional, complex, symplectic map. The map is a generalization of the semi-standard map studied by Greene and Percival; it has three parameters, a, and a, representing the strength of the kicks in each degree of freedom, and E, the coupling. The domain of existence of a torus in (a,, a...

In [1] we defined semi-monotone sets, as open bounded sets, de-finable in an o-minimal structure over the reals, and having connected intersections with all translated coordinate cones in R n. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equivalent conditions for a bounded continuous d...