Presentation on the consideration of local ancestry of admixed populations, or populations comprised of genetically distinct ancestral populations which can alter their gene flow in unique ways. It was presented at the UNT Transdisciplinary Conference on Ancestral Genomics Research which was held virtually on November 20-21, 2020.

Data management plan for the grant, "Approximation Theory and Complex Dynamics." This project involves the study of approximation theory in the setting of complex functions, with applications to complex dynamics. Approximation theory seeks to understand the extent to which the behavior of a general function can be effectively modeled by that of functions drawn from a more restricted class. Efficient approximation of functions is of relevance for numerical calculation. Since the only calculations that can be carried out numerically are the elementary operations of addition, subtraction, multiplication, and division, in practical terms it is of importance to understand when the values of general functions are well approximated by the values of either polynomial or rational functions. In many situations, the values of the approximant resemble those of the general function only for a sampling of input values. What can be said about values of the approximant for other choices of input? This is the main question studied in this project, with the following application in mind: when a general function is iterated to produce a dynamical system, to what extent does the dynamical behavior of an approximant resemble the dynamical behavior of the original function? The project will also contribute …

Data management plan for the grant, "Collaborative Research: Conference: Texas-Oklahoma Representations and Automorphic forms (TORA)."

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.

Data management plan for the grant, "Conference: Dynamical Systems and Fractal Geometry."

Article verifying a conjecture of Vershik by showing that Hall’s universal countable locally finite group can be embedded as a dense subgroup in the isometry group of the Urysohn space and in the automorphism group of the random graph. It shows the same for all automorphism groups of known infinite ultraextensive spaces.

Article discusses how a Cantor series expansion for a real number x with respect to a basic sequence Q=(q), where qi≥2, is a generalization of the base b expansion to an infinite sequence of bases. The authors show that for any basic sequence the set of distribution normal numbers is Π03-complete, and if Q is 1-divergent then the sets of normal and ratio normal numbers are Π03-complete.

Article describes how the Tirilman spaces were introduced by Casazza and Shura as variations of the spaces constructed by Tzafriri. We prove that all subsymmetric basic sequences in the dual space are equivalent to its canonical subsymmetic but not symmetric basis.

Article describes how the authors plant to deal with orientation preserving homeomorphisms and, more specifically, diffeomorphisms of the unit circle S1. By employing the recurrence method worked out in Pawelec the authors provide effective lower estimates of the proper-dimensional Hausdorff measure of minimal sets of circle homeomorphisms that are not conjugate to any rotation.

Article describes how a set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. The authors show that over some mild large cardinal theory, sealing is equiconsistent with LSA-over-uB.

Article studies radial solutions of ∆u + K(r)f(u) = 0 on the exterior of the ball of radius R > 0 centered at the origin in ℝᶰ where f is odd with f < 0 on (0, β), f > 0 on (β, δ), f ≡ 0 for u > δ, and where the function K(r) is assumed to be positive and K(r) → 0 as r → ∞.

Article proves the existence of an infinite number of radial solutions to ∆u+K(r)f(u) = 0 on ℝᶰ such that limᵣ →∞ u(r) = 0 with prescribed number of zeros on the exterior of the ball of radius R > 0 where f is odd with f < 0 on (0, β), f > 0 on (β, ∞) with f superlinear for large u, and K(r) ∼ r ⁻ᵅ with α > 2(N − 1).

Article proposes a powerful and computationally efficient gene-based association test, called Overall. Using extended Simes procedure, Overall aggregates information from three types of traditional gene-based association tests and also incorporates expression quantitative trait locus (eQTL) information into a gene-based association test using GWAS summary statistics. The results show that this newly developed method can identify more significant genes than other methods.

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.

Article describes how anthracyclines are highly effective in treating cancer, despite increased risk of cardiomyopathy. This study examined gene-level associations with cardiomyopathy among cancer survivors using whole-exome sequencing data.

Article describes the high-quality, 887-Mb genome of jojoba assembled into 26 chromosomes with 23,490 protein-coding genes.

Article describes how anthracycline-related cardiomyopathy is a leading cause of premature death in childhood cancer survivors. The authors interrogated differentially expressed genes (DEGs) to identify genetic variants serving regulatory functions or genetic variants not easily identified when using genomewide array platforms.

Article presents a study where whole transcriptome sequencing (RNA-seq) and differential expression analysis were used to identify early (1–3 hr) transcriptional changes induced by the exogenous treatment of NAE 18:2 and NAE 18:3 in cotyledons, roots, and seedlings.

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.

This article explores the relationship among MYB30, the ROS wave, and systemic acclimation in Arabidopsis by determining the SAA response to HL stress of MYB30 mutants and wild-type plants.

This article proposes a new model to represent a vesicle membrane with internal nematic order whose equilibrium states depend on the competition between the bending, elastic and anchoring energies.

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Article addresses the question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. The authors e answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space.

This article proves an explicit integral representation—involving the pullback of a suitable Siegel Eisenstein series—for the twisted standard L-function associated to a holomorphic vector-valued Siegel cusp form of degree n and arbitrary level.