Mathematics Commons^™

Comparative Analysis Of All-Terrain Vehicles, Motorcycle And Automobile-Related Trauma In A Rural Border Community Of The Usa, Haissam S. Elzaim, Kristina Vatcheva, Annelyn Torres-Reveron, Gregery Pequeno, Monica Michelle Betancourt-Garcia

School of Mathematical & Statistical Sciences Faculty Publications

Introduction: There is widespread use of all-terrain vehicles (ATVs) in the USA for both work-related and recreational activities. In this study, we aimed to determine the difference in injury severity, Glasgow Coma scales and length of stay between ATV-related injuries and injuries sustained from motorcycles (MOTOs) and automobiles (AUTOs).

Methods: We retrospectively analysed ATV, MOTO and AUTO injuries from a Level 2 Trauma Center between 01 January 2015 and 31 August 2020. Proportional odds regression analyses, as well as multivariable regression models, were used to analyse the data.

Results: There were significantly more male and paediatric patients that suffered ATV-related …

Optimal Quantization For Some Triadic Uniform Cantor Distributions With Exact Bounds, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Let {Sj:1≤j≤3} be a set of three contractive similarity mappings such that Sj(x)=rx+j−12(1−r) for all x∈R, and 1≤j≤3, where 0

Let {Sj:1≤j≤3}">{Sj:1≤j≤3}{Sj:1≤j≤3} be a set of three contractive similarity mappings such that Sj(x)=rx+j−12(1−r)">Sj(x)=rx+j−12(1−r)Sj(x)=rx+j−12(1−r) for all x∈R">x∈Rx∈R, and 1≤j≤3">1≤j≤31≤j≤3, where 0Phas support the Cantor set generated by the similarity mappings Sj">SjSj for 1≤j≤3">1≤j≤31≤j≤3. Let r0=0.1622776602">r0=0.1622776602r0=0.1622776602, and r1=0.2317626315">r1=0.2317626315r1=0.2317626315 (which are ten digit rational approximations of two real numbers). In this paper, for 00n-means and the nth quantization errors for the triadic uniform Cantor distribution P for all positive integers n≥2">n≥2n≥2. Previously, Roychowdhury …

On Equivariant Flag F-Vectors For Balanced Relative Simplicial Complexes, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We study the equivariant flag f-vector and equivariant flag h-vector of a balanced relative simplicial complex with respect to a group action. When the complex satisfies Serre's condition (Sℓ), we show that the equivariant flag h-vector, the equivariant h-vector, and the equivariant f-vector satisfy several inequalities.
We apply these results to the study of P-partitions of double posets, and weak colorings of mixed graphs.

A Mesh-Free Method Using Piecewise Deep Neural Network For Elliptic Interface Problems, Cuiyu He, Xiaozhe Hu, Lin Mu

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the interface, we employ different neural networks for each sub-domain. By reformulating the interface problem as a least-squares problem, we discretize the objective function using mean squared error via sampling and solve the proposed deep least-squares method by standard training algorithms such as stochastic gradient descent. The discretized objective function utilizes only the point-wise information on the sampling points and thus no underlying mesh …

Eigen’S Paradox And The Quasispecies Model In A Non-Archimedean Framework, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

In this article we present a new p -adic generalization of the Eigen–Schuster model where the genomes (sequences) are represented by words written in the alphabet { 0 , 1 , … , p − 1 } , where p is a prime number, with a time variable length. The time evolution of the concentration of a given sequence is controlled by a p -adic evolution equation. The long term behavior of the concentration of a sequence depends on a fitness function f , a mutation measure Q , and an initial concentration distribution. The new model provides essentially two …

Norm And Numerical Radius Of Single Operators Through Tools And Techniques From Multivariable Operator Theory, Raul E. Curto, Sang Hoon Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We employ tools and techniques from multivariable operator theory to obtain new proofs and extensions of well known inequalities regarding the norm and the numerical radius of elementary operators defined on the C⁎" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">C⁎C⁎–algebra of all bounded operators on Hilbert space, or on the ⁎–ideal of Hilbert-Schmidt operators. In the process, we provide new insights on the study of Heinz-type inequalities related to the arithmetic-geometric mean inequality, and generalize results of several authors, including R. Bhatia, G. Corach, C. Davis, F. Kittaneh, and M.S. Moslehian. To estimate the norm, our approach …

Darboux Transformation And Solitonic Solution To The Coupled Complex Short Pulse Equation, Bao-Feng Feng, Liming Ling

School of Mathematical & Statistical Sciences Faculty Publications

The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact solutions including bright soliton, dark-soliton, breather and rogue wave solutions to the CCSP equation. In case of vanishing boundary condition (VBC), we perform the inverse scattering analysis to understand the soliton solution better. Breather and rogue wave solutions are constructed in case of non-vanishing boundary condition (NVBC). Moreover, we conduct a modulational instability (MI) analysis based on the method of squared eigenfunctions, whose result confirms the condition for the existence of rogue …

Definite Condition Of The Evolutionary (P)Over-Right-Arrow(X)-Laplacian Equation, Huashui Zhan, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

For the nonlinear degenerate parabolic equations, how to find an appropriate boundary value condition to ensure the well-posedness of weak solution has been an interesting and challenging problem. In this paper, we develop the general characteristic function method to study the stability of weak solutions based on a partial boundary value condition.

Statistical Analysis Methods Applied To Early Outpatient Covid-19 Treatment Case Series Data, Eleftherios Gkioulekas, Peter A. Mccullough, Vladimir Zelenko

School of Mathematical & Statistical Sciences Faculty Publications

When confronted with a public health emergency, significant innovative treatment protocols can sometimes be discovered by medical doctors at the front lines based on repurposed medications. We propose a statistical framework for analyzing the case series of patients treated with such new protocols, that enables a comparison with our prior knowledge of expected outcomes, in the absence of treatment. The goal of the proposed methodology is not to provide a precise measurement of treatment efficacy, but to establish the existence of treatment efficacy, in order to facilitate the binary decision of whether the treatment protocol should be adopted on an …

Towards Fast Weak Adversarial Training To Solve High Dimensional Parabolic Partial Differential Equations Using Xnode-Wan, Paul Valsecchi Oliva, Yue Wu, Cuiyu He, Hao Ni

School of Mathematical & Statistical Sciences Faculty Publications

Due to the curse of dimensionality, solving high dimensional parabolic partial differential equations (PDEs) has been a challenging problem for decades. Recently, a weak adversarial network (WAN) proposed in Zang et al. (2020)[17] offered a flexible and computationally efficient approach to tackle this problem defined on arbitrary domains by leveraging the weak solution. WAN reformulates the PDE problem as a generative adversarial network, where the weak solution (primal network) and the test function (adversarial network) are parameterized by the multi-layer deep neural networks (DNNs). However, it is not yet clear whether DNNs are the most effective model for the parabolic …

A Comparison Of Statistical Methods For Modeling Count Data With An Application To Hospital Length Of Stay, Gustavo Fernandez, Kristina Vatcheva

School of Mathematical & Statistical Sciences Faculty Publications

Background

Hospital length of stay (LOS) is a key indicator of hospital care management efficiency, cost of care, and hospital planning. Hospital LOS is often used as a measure of a post-medical procedure outcome, as a guide to the benefit of a treatment of interest, or as an important risk factor for adverse events. Therefore, understanding hospital LOS variability is always an important healthcare focus. Hospital LOS data can be treated as count data, with discrete and non-negative values, typically right skewed, and often exhibiting excessive zeros. In this study, we compared the performance of the Poisson, negative binomial (NB), …

Quantization For A Nonuniform Triadic Cantor Distribution, Asha Barua

Theses and Dissertations

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. Let P be a Borel probability measure on R such that P := 1/4 P◦ S1−1 + 1\2 P◦ S2−1 + 1/4 P◦ S3−1, where S1, S2 and S3 are three contractive similarity mappings such that Sj(x) = 1/5x+2(j−1)/5, for all x ∈ R. For this probability measure, in this thesis, we determine the optimal sets of n-means and the nth quantization errors for …

Mathematics Teachers’ Working With Cooperative Learning, Jaime Gomez

Theses and Dissertations

Teaching styles vary greatly amongst educators. One being extensively researched and highly discussed is the method of cooperative learning. Although many studies have shown the benefits of incorporating cooperative learning into classrooms, it has not been a widely used method of teaching in high school mathematics classrooms. This study explores some of the efforts that teachers, who utilize cooperative learning in their classrooms, make to implement cooperative learning lessons successfully. Furthermore, this study also explores the challenges these teachers have encountered when using cooperative learning. Data was collected qualitatively by interviews and surveys from six in-service high …

Thermal Convection In A Cylindrical Annulus Filled With Porous Material, Anirban Ray

Theses and Dissertations

Here a study on thermal convection in a porous vertical cylindrical annulus which is heated from below is carried out. The walls are considered to be impermeable that is the velocity is 0 at the boundary walls. The cylindrical annulus is radially insulated. The governing system consists of the continuity equation, Darcy-Boussinesq equation, heat equation and the equation of state. Employing weakly non-linear approach, the basic state system and the perturbed system are derived. After obtaining the solutions to the basic state system, the pressure term in perturbed system is eliminated by taking double curl, and then eliminating the velocity, …

Traveling Wave Solutions For The Negative Order Hierarchy Of The D-Akns Equations, Brayton Isaac Wario

Theses and Dissertations

In the thesis work, based on the D-AKNS spectral problem, we study the negative-order D-AKNS (ND-AKNS) hierarchy. In particular, the first ND-AKNS equation is derived from the negative-order D-AKNS hierarchy, which is proved integrable in the sense of Lax pair. Furthermore, we discuss the traveling wave solutions to the ND-AKNS Equation, including possible soliton solutions.

A Gpu Accelerated Genetic Algorithm For The Construction Of Hadamard Matrices, Andras Balogh, Raven Ruiz

School of Mathematical & Statistical Sciences Faculty Publications

We use a genetic algorithm to construct Hadamard Matrices. The initial population of random matrices is generated to have a balanced number of +1 and −1 entries in each column except the first column with all +1. Several fitness functions are implemented in order to find the most effective one. The crossover process creates offspring matrix population by exchanging columns of the parent matrix population. The mutation process flips +1 and −1 entry pairs in random columns. The use of CuPylibrary in Python on graphics processing units enables us to handle populations of thousands of matrices and matrix operations in …

Quantization For A Probability Distribution Generated By An Infinite Iterated Function System, Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

The Cartesian Analytical Solutions For The N-Dimensional Compressible Navier-Stokes Equations With Density-Dependent Viscosity, Engui Fan, Zhijun Qiao, Manwai Yuen

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the N-dimensional compressible Navier-Stokes equations with density-dependent viscosity, based on the matrix and curve integration theory. Two exact solutions are obtained by solving the reduced systems.

Adjacency And Connectivity Matrices To Airline Connections Among Airports, Alejandra Munoz

Theses and Dissertations

We study how powers of adjacency and connectivity matrices can be used to investigate airline connections among airports. For this study, only matrices with all diagonal elements of “0” are considered (i.e., an airport is not connected to itself) and each matrix must contain at least one entry of “1” in each row and column (i.e., each airport contains at least one inbound and one outbound route). Sets of 3, 4, and 5 airports are discussed in this study, comparing cases with up to 3, 4, and 5 round routes, respectively, in an effort to find the amount of paths …

Navigating Mathematics Teacher Preparation During A Time Of Crisis, Zareen G. Rahman, Rani Satyam, Younggon Bae

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we highlight the experience of a mathematics teacher educator (MTE) and their preservice teachers (PTs) in a middle school mathematics methods course during the 2020 shift to online instruction due to the COVID-19 pandemic. We believe it is valuable to report how the MTE reflected on their instructional decision-making in response to this massive transition to remote instruction. We also report that PTs needed support and guidance to employ new teaching practices they had learned in the methods course instead of reverting to familiar teaching methods.

Ultrametric Diffusion, Rugged Energy Landscapes And Transition Networks, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

In this article we introduce the ultrametric networks which are p-adic continuous analogues of the standard Markov state models constructed using master equations. A p-adic transition network (or an ultrametric network) is a model of a complex system consisting of a hierarchical energy landscape, a Markov process on the energy landscape, and a master equation. We focus on networks where the transition rates between two different basins are constant functions, and the jumping process inside of each basin is controlled by a p-adic radial function. We solve explicitly the Cauchy problem for the master equation attached to this type of …

Monotonicity Properties Of Functionals Under Ricci Flow On Manifolds Without And With Boundary, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, the idea of the Ricci flow is introduced and its significance and importance to related problems in mathematics had been discussed. Several functionals are defined and their behavior is studied under Ricci flow. A unique minimizer is shown to exist for one of the functionals. This functional evaluated at the minimizer is strictly increasing. The results for the first functional considered are extended to manifold with boundary. Finally, two physically motivated examples are presented.

General Rogue Wave Solutions To The Sasa-Satsuma Equation, Chengfa Wu, Guangxiong Zhang, Changyan Shi, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

General rogue wave solutions to the Sasa-Satsuma equation are constructed by the Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions are presented in three different forms. The first form is expressed in terms of recursively defined differential operators while the second form shares a similar solution structure except that the differential operators are no longer recursively defined. Instead of using differential operators, the third form is expressed by Schur polynomials.

Solution Of The Reconstruction-Of-The-Measure Problem For Canonical Invariant Subspaces, Raul E. Curto, Sang H. Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We study the Reconstruction-of-the-Measure Problem (ROMP) for commuting 2-variable weighted shifts W(α,β), when the initial data are given as the Berger measure of the restriction of W(α,β) to a canonical invariant subspace, together with the marginal measures for the 0–th row and 0–th column in the weight diagram for W(α,β). We prove that the natural necessary conditions are indeed sufficient. When the initial data correspond to a soluble problem, we give a concrete formula for the Berger measure of W(α,β). Our strategy is to build on previous results for back-step extensions and onestep extensions. A key new theorem allows us …

On Three-Dimensional Rotating Viscoelastic Jets In The Giesekus Model, Daniel N. Riahi, Saulo Orizaga

School of Mathematical & Statistical Sciences Faculty Publications

We investigate three-dimensional nonlinear rotating viscoelastic curved jets in the presence of gravity force. Applying the Giesekus model for the viscoelastic stress parts of the jet flow system and using perturbation methods with a consistent scaling, a relatively simple system of equations with realistic three-dimensional centerlines is developed. We determine numerically the relevant solution quantities of the model in terms of the radius, speed, tensile force, stretching rate, strain rate and the jet centerline versus arc length and for different parameter values associated with gravity, viscosity, rotation, surface tension and viscoelasticity. Considering the jet flow system in full 3-dimensions and …

Justice And The Mathematics Classroom: Realizing The Goals Of The Amte Standards For Preparing Teachers Of Mathematics, Shandy Hauk, Marilyn Strutchens, Dorothy Y. White, Jennifer Bay-Williams, Jenq Jong Tsay, Billy Jackson

School of Mathematical & Statistical Sciences Faculty Publications

This chapter is an introduction to justice in the post-secondary context of mathematics courses for prospective teachers. The chapter is a research-to-practice report (i.e., it describes an aspect of instruction and discusses how it is informed by, connects to, or is illustrative of findings from research). While the reader might be any type of mathematics teacher educator, the focus here is supporting those who teach mathematics content courses for elementary school teacher candidates. In addition to having an effect on discipline-specific knowledge, college mathematics classes contribute to the ways candidates communicate in/with/through mathematics in working with children. The chapter includes …

Non-Archimedean Statistical Field Theory, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The advantage of the approach presented here is that all the perturbation calculations can be carried out in the standard way using functional derivatives, but in a mathematically rigorous way.

Canonical Sequences Of Optimal Quantization For Condensation Measures, Doğan Çömez, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

We consider condensation measures of the form P:=13P∘S−11+13P∘S−12+13ν associated with the system (S,(13,13,13),ν), where S={Si}2i=1 are contractions and ν is a Borel probability measure on R with compact support. Let D(μ) denote the quantization dimension of a measure μ if it exists. In this paper, we study self-similar measures ν satisfying D(ν)>κ, D(ν)κ, the D(P)-dimensional lower and upper quantization coefficients are finite, positive and unequal; and for D(ν)≤κ, the D(P)-dimensional lower quantization coefficient is infinity.

We consider condensation measures of the form P:=13P∘S−11+13P∘S−12+13ν associated with the system (S,(13,13,13),ν), where S={Si}2i=1 are contractions and ν is a Borel probability measure …

Quantization For A Probability Distribution Generated By An Infinite Iterated Function System, Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on R. For such a probability measure P , an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ …

Networks Of Necessity: Simulating Covid-19 Mitigation Strategies For Disabled People And Their Caregivers, Thomas E. Valles, Hannah Shoenhard, Joseph Zinski, Sarah Trick, Mason A. Porter, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Abstract

A major strategy to prevent the spread of COVID-19 is the limiting of in-person contacts. However, limiting contacts is impractical or impossible for the many disabled people who do not live in care facilities but still require caregivers to assist them with activities of daily living. We seek to determine which interventions can best prevent infections of disabled people and their caregivers. To accomplish this, we simulate COVID-19 transmission with a compartmental model that includes susceptible, exposed, asymptomatic, symptomatically ill, hospitalized, and removed/recovered individuals. The networks on which we simulate disease spread incorporate heterogeneity in the risk levels of …