Physical Sciences and Mathematics Commons^™

Linear Operators That Preserve Graphical Properties Of Matrices: Isolation Numbers, Leroy B. Beasley, Seok-Zun Song, Young Bae Jun

Mathematics and Statistics Faculty Publications

Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A. A linear operator on the set of m × n Boolean matrices is a mapping which is additive and maps the zero matrix, O, to itself. A mapping strongly preserves a set, S, if it …

Stability Of Traveling-Wave Solutions For A Schrodinger System With Power-Type Nonlinearities, Nghiem Nguyen, Rushun Tian, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

In this article, we consider the Schrodinger system with powertype nonlinearities, (Formula presented) where j = 1,...,m, u_j are complex-valued functions of (x, t) 2 R^N+1, a, b are real numbers. It is shown that when b > 0, and a + (m - 1)b > 0, for a certain range of p, traveling-wave solutions of this system exist, and are orbitally stable.

A Shortcut For Multiple Testing On The Directed Acyclic Graph Of Gene Ontology, Garrett Saunders, John R. Stevens, S. Clay Isom

Mathematics and Statistics Faculty Publications

Background: Gene set testing has become an important analysis technique in high throughput microarray and next generation sequencing studies for uncovering patterns of differential expression of various biological processes. Often, the large number of gene sets that are tested simultaneously require some sort of multiplicity correction to account for the multiplicity effect. This work provides a substantial computational improvement to an existing familywise error rate controlling multiplicity approach (the Focus Level method) for gene set testing in high throughput microarray and next generation sequencing studies using Gene Ontology graphs, which we call the Short Focus Level.

Results: The Short Focus …