Physical Sciences and Mathematics Commons^™

Geometric Characterization Of Continuously Defective Elastic Crystals, Marek Z. Elźanowski

Mathematics and Statistics Faculty Publications and Presentations

We show how some differential geometric structures associated with a concept of a homogeneous space appear naturally in a kinematic model of continuously distributed defects in an elastic crystal solid and discuss how one can use them to describe the defectiveness of such a continuum.

Effects Of Progesterone Concentrations And Follicular Wave During Growth Of The Ovulatory Follicle On Conceptus And Endometrial Transcriptome In Dairy Cows, R S. Bisinotto, E S. Ribeiro, L F. Greco, Daniel Taylor-Rodríguez, A D. Ealy, H Ayres, F S. Lima, N Martinez, W W. Thatcher, J E P Santos

Mathematics and Statistics Faculty Publications and Presentations

Objectives were to evaluate the effects of follicular wave and progesterone concentration on growth of the ovulatory follicle, conceptus elongation, uterine IFN-τ concentration, and transcriptome of conceptus and endometrium of pregnant cows on d 17 of gestation. Nonlactating nonpregnant Holstein cows were assigned randomly to one of 3 treatments: ovulation of a first-wave follicle (FW, n = 15); ovulation of a first-wave follicle and progesterone supplementation (FWP4, n = 12); and ovulation of a second-wave follicle (SW, n = 19). Ovulation of a first- or second-wave follicle was achieved by initiating the Ovsynch protocol (d -9 GnRH, d -2 and …

Convergence Analysis Of Some Tent-Based Schemes For Linear Hyperbolic Systems, Dow Drake, Jay Gopalakrishnan, Joachim Schöberl, Christoph Wintersteiger

Mathematics and Statistics Faculty Publications and Presentations

Finite element methods for symmetric linear hyperbolic systems using unstructured advancing fronts (satisfying a causality condition) are considered in this work. Convergence results and error bounds are obtained for mapped tent pitching schemes made with standard discontinuous Galerkin discretizations for spatial approximation on mapped tents. Techniques to study semidiscretization on mapped tents, design fully discrete schemes, prove local error bounds, prove stability on spacetime fronts, and bound error propagated through unstructured layers are developed.

Linear Nearest Neighbor Flocks With All Distinct Agents, R. G. Lyons, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

This paper analyzes the global dynamics of one-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second-order linear ODE’s with constant coefficients. The novel part of this research is that the couplings are different for each distinct agent. We allow the forces to depend on the positions and velocity (damping terms) but the magnitudes of both the position and velocity couplings are different for each agent. We, also, do not assume that the forces are “Newtonian” (i.e. the force due to A on B equals the minus the force of B on A) as this assumption …

Application Of Topological Data Analysis To Multi-Resolution Matching Of Aerosol Optical Depth Maps, Dorcas Ofori-Boateng, Huikyo Lee, Krzysztof M. Gorski, Michael J. Garay, Yulia R. Gel

Mathematics and Statistics Faculty Publications and Presentations

Topological data analysis (TDA) combines concepts from algebraic topology, machine learning, statistics, and data science which allow us to study data in terms of their latent shape properties. Despite the use of TDA in a broad range of applications, from neuroscience to power systems to finance, the utility of TDA in Earth science applications is yet untapped. The current study aims to offer a new approach for analyzing multi-resolution Earth science datasets using the concept of data shape and associated intrinsic topological data characteristics. In particular, we develop a new topological approach to quantitatively compare two maps of geophysical variables …

Multilevel Hierarchical Decomposition Of Finite Element White Noise With Application To Multilevel Markov Chain Monte Carlo, Hillary R. Fairbanks, Umberto E. Villa, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications and Presentations

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable …

Networking Frameworks: A Method For Analyzing The Complexities Of Classroom Cultures Focusing On Justifying, Eva Thanheiser, Kathleen Melhuish, Amanda Sugimoto, Brenda Rosencrans, Ruth Heaton

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we network five frameworks (cognitive demand, lesson cohesion, cognitive engagement, collective argumentation, and student contribution) for an analytic approach that allows us to present a more holistic picture of classrooms which engage students in justifying. We network these frameworks around the edges of the instructional triangle as a means to coordinate them to illustrate the observable relationships among teacher, students(s), and content. We illustrate the potential of integrating these frameworks via analysis of two lessons that, while sharing surface level similarities, are profoundly different when considering the complexities of a classroom focused on justifying. We found that …

One-Sided Derivative Of Distance To A Compact Set, Logan S. Fox, Peter Oberly, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We give a complete and self-contained proof of a folklore theorem which says that in an Alexandrov space the distance between a point γ(t) on a geodesic γ and a compact set K is a right-differentiable function of t. Moreover, the value of this right-derivative is given by the negative cosine of the minimal angle between the geodesic and any shortest path to the compact set (Theorem 4.3). Our treatment serves as a general introduction to metric geometry and relies only on the basic elements, such as comparison triangles and upper angles.

Stability Conditions For Coupled Autonomous Vehicles Formations, Pablo Baldivieso, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give necessary conditions for stability of coupled autonomous vehicles in R. We focus on linear arrays with decentralized vehicles, where each vehicle interacts with only a few of its neighbors. We obtain explicit expressions for necessary conditions for stability in the cases that a system consists of a periodic arrangement of two or three different types of vehicles, i.e. configurations as follows: 2-1-2-1 or 3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single vehicle type (1-1-1) held that the first moment of certain coefficients of the interactions between vehicles …

Probability Axioms And Set Theory Paradoxes, Ari Herman, John Caughman

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we show that Zermelo–Fraenkel set theory with Choice (ZFC) conflicts with basic intuitions about randomness. Our background assumptions are the Zermelo–Fraenekel axioms without Choice (ZF) together with a fragment of Kolmogorov’s probability theory. Using these minimal assumptions, we prove that a weak form of Choice contradicts two common sense assumptions about probability—both based on simple notions of symmetry and independence.

Boolean Network Control With Ideals, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

A method is given for finding controls to transition an initial state x0 to a target set in deterministic or stochastic Boolean network control models. The algorithms use multivariate polynomial algebra. Examples illustrate the application.

Torsion And Curvature In Continuously Defective Solid Crystals, Marek Z. Elźanowski

Mathematics and Statistics Faculty Publications and Presentations

I show how one can utilize the concept of a canonical connection on a homogeneous space to describe defectiveness of a continuous elastic crystal solid.

Simulations Of Single- And Two-Tone Tm-Doped Optical Fiber Laser Amplifiers, Tathagata Goswami, J. Grosek, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

This work uses numerical simulations of a thulium-doped optical fiber amplifier to predict various performance characteristics such as peak temperatures, expected output powers and efficiencies, presence of amplified spontaneous emission (ASE), and transverse mode instability (TMI) onset power thresholds. Single- and two-tone configurations are studied. In the latter case, the two laser sources are separated in frequency by the amount that corresponds to the peak Raman gain, and a few seed ratios at various total seed powers are examined. The goal is to provide the field with pertinent information on what is feasible for this type of amplifier.

Five Ps (Policies, Practices, Power Structures, Places; And People): A Framework To Analyze Systemic Inequalities, Eva Thanheiser, Lisa Weasel, Idowu Ajibade, Larry Martinez, Gina Greco

Mathematics and Statistics Faculty Publications and Presentations

This chart is part of a framework to establish institutional equity and is part of the following National Science Foundation grant project:

The Spaces of Empowerment for Equity and Diversity: Advancement Through Access (SEE-DATA) project at Portland State University (PSU) aims to identify, understand, and improve the workplace experiences and retention of faculty in STEM fields who have been traditionally minoritized and marginalized based on gender, race/ethnicity, and other intersectional identities (e.g., sexual orientation, disability, socioeconomic status, national origin, immigrant status). The project will collect, analyze, and map data about faculty’s experiences at PSU to inform programs and policies that …