Article discusses the determination of the spectrum of two interesting stochastic matrices appearing in an engineering paper.

This article discusses the first Vafa-Witten bound for two-dimensional tori.

This article reports that local application of light stress to one rosette leaf of bolting Arabidopsis (Arabidopsis thaliana) plants resulted in a metabolic response that encompassed local, systemic and transport tissues, demonstrating a high degree of physical and metabolic continuity between different tissues throughout the plant.

In this paper, the authors discuss a novel statistical method for rare-variant association studies in general pedigrees for quantitative traits. This method uses a retrospective view that treats the traits as fixed and the genotypes as random, which accounts for complex and undefined ascertainment of families.

This article proposes a new and general goodness-of-fit (GOF) test, called TEDE (TEsting Direct Effects), applicable to both correlated and independent SNPs/IVs as commonly used in transcriptome-wide association studies (TWAS) and Mendelian randomization (MR) respectively.

Article describes study in which novel approaches to test the effects of gene-environment (GE) interactions of rare and/or common risk, and/or protective variants in sequencing association studies were developed.

Article reveals that plants can integrate different local and systemic signals generated during conditions of stress combination. Furthermore, results show that the specific part at which plants sense the two co-occurring stresses makes a significant difference in how fast and efficient they acclimate.

Article describes how gene-based association tests provide a useful alternative and complement to the usual single marker association tests, especially in genome-wide association studies (GWAS). The authors propose a test named OWC based on summary statistics from GWAS data.

This article reports on promising statistical approaches and findings of the members of the Genome-wide Association Study group applied on real and simulated data which encompass the current topics of epigenetic and pharmacogenomics.

This article discusses the development of two statistical methods to test the gene environment interaction effect of rare variants.

Article presents an overview of the data sets and the contributions analyzing data related to human lipid-related phenotypes, DNA methylation, and single-nucleotide markers in a study involving a pharmaceutical intervention.

This article demonstrates that whole genome sequencing is an efficient approach for identification of causative genes underlying symbiotic nitrogen fixation defective phenotypes in Medicago truncatula Tnt1 insertion mutants obtained via forward genetic screens.

This article identifies that an rRNA released in hemolysis activates clotting in human and zebrafish plasma. Furthermore, it shows that fish Hgfac plays a role in rRNA-mediated activation of coagulation.

Article proposing a new direct proof of the fact that L^1 verifies the strong maximum principle, i.e., any analytic map from the complex unit disk into L^1, constant in norm, must be constant.

This article outlines the proof that over some mild large cardinal theory, Sealing is equiconsistent with Largest Suslin Axiom (LSA)-over-uB. Let LSA-over-uB be the statement that in all (set) generic extensions there is a model of LSA whose Suslin, co-Suslin sets are the universally Baire sets.

Article discussing projecting on polynomial solutions of second order partial differential operators.

Presentation for the 2011 University Scholars Day at the University of North Texas discussing research on continued fractions as an alternative to decimal expansions.

Presentation for the 2011 University Scholars Day at the University of North Texas discussing a mathematical game using the tiling of a plane.

Presentation for the 2011 University Scholars Day at the University of North Texas discussing research on predictable patterns in continued fractions and decimal expansions.

Presentation for the 2011 University Scholars Day at the University of North Texas discussing descriptive set theory and why we should study it.

Poster presentation for the 2012 University Scholars Day at the University of North Texas discussing research on correlations between parent's education and children's test scores.

Presentation for the 2006 University Scholars Day at the University of North Texas discussing research on the effects of technology on achievement in mathematics in middle school.

Presentation for the 2008 University Scholars Day at the University of North Texas discussing an analysis of math anxiety.

Data management plan for the research grant, "Collaborative Research: Using Uncertainty Quantification and Validated Computational Models to Analyze Pumping Performance of Valveless, Tubular Hearts." This project will develop a computational model of the essential features of the circulatory system: the electrical activity of the heart, muscle contractions of the tube walls, and the fluid-structure interactions of the heart walls and blood within. This computational framework aims to be faithful to that of a real, model animal (tunicate, or sea squirt). The model will then be analyzed with mathematical tools to determine the physical limits of the pumping system. Results of this project will improve the understanding of human heart development at the earliest stages. Also, it will point to how the large, multi-chambered hearts of vertebrates could have evolved from smaller structures.