Mathematics Commons^™

Depression, Obesity, And Metabolic Syndrome: Prevalence And Risks Of Comorbidity In A Population-Based Study Of Mexican Americans, Rene L. Olvera, Douglas E. Williamson, Susan P. Fisher-Hoch, Kristina Vatcheva, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Introduction: We examined the prevalence of depression, obesity, and metabolic syndrome and associations between them in a population-based representative cohort of Mexican Americans living on the United States-Mexico border.

Method: The sample in this cross-sectional analysis consisted of 1,768 Mexican American adults (≥ 18 years of age) assessed between the years 2004 and 2010, with whom we tested our central hypothesis of a significant relationship between obesity and depression. Depression was measured using the Center for Epidemiologic Studies-Depression scale (CES-D) with a cutoff score of ≥ 16 for depression and a cutoff score of ≥ 27 for severe depression. We …

Completion Of Hankel Partial Contractions Of Non-Extremal Type, In Hyoun Kim, Seonguk Yoo, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose …

Barriers To Disaster Preparedness Among Medical Special Needs Populations, Leslie Meyer, Kristina Vatcheva, Stephanie Castellanos, Belinda M. Reininger

School of Mathematical & Statistical Sciences Faculty Publications

A medical special needs (MSN) assessment was conducted among 3088 respondents in a hurricane prone area. The sample was female (51.7%), Hispanic (92.9%), aged >45 years (51%), not insured for health (59.2%), and with an MSN (33.2%). Barriers to preparedness were characterized for all households, including those with inhabitants reporting MSN ranging from level 0 (mild) to level 4 (most severe). Multivariable logistic regression tested associations between hurricane preparedness and barriers to evacuation by level of MSN. A significant interaction effect between number of evacuation barriers and MSN was found. Among households that reported individuals with level 0 MSN, the …

Association Of Total And Differential White Blood Cell Counts To Development Of Type 2 Diabetes In Mexican Americans In Cameron County Hispanic Cohort, Kristina Vatcheva, Susan P. Fisher-Hoch, Mohammad H. Rahbar, Minjae Lee, Rene L. Olvera, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Objective: To evaluate the relationship between total and differential White Blood Cell (WBC) counts with time to transition to type 2 diabetes in Mexican Americans using prospective data from the Cameron County Hispanic Cohort (CCHC).

Results: Multivariable Cox proportional hazards regression models revealed that obese Mexican-American cohort participants whose total WBC or granulocyte count increased over time had 1.39 and 1.35 times higher risk respectively of transition to type 2 diabetes when compared to overweight participants. The granulocyte or total WBC count in participants with BMI≥35 were significant risk factors for transition to type 2 diabetes.

Conclusions: Increased total WBC …

Undiagnosed Diabetes And Pre-Diabetes In Health Disparities, Susan P. Fisher-Hoch, Kristina Vatcheva, Mohammad H. Rahbar, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Globally half of all diabetes mellitus is undiagnosed. We sought to determine the extent and characteristics of undiagnosed type 2 diabetes mellitus and pre-diabetes in Mexican Americans residing in the United States. This disadvantaged population with 50% lifetime risk of diabetes is a microcosm of the current pandemic. We accessed baseline data between 2004 and 2014 from 2,838 adults recruited to our Cameron County Hispanic Cohort (CCHC); a two-stage randomly selected 'Framingham-like' cohort of Mexican Americans on the US Mexico border with severe health disparities. We examined prevalence, risk factors and metabolic health in diagnosed and undiagnosed diabetes and pre-diabetes. …

Non-Communicable Diseases And Preventive Health Behaviors: A Comparison Of Hispanics Nationally And Those Living Along The Us-Mexico Border, Belinda M. Reininger, Jing Wang, Susan P. Fisher-Hoch, Alycia Boutte, Kristina Vatcheva, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Background: Non-communicable diseases (NCDs) are rising among US Hispanics, but few studies have examined the preventive health behaviors for these NCDs among Hispanics. This study compared the preventive health behaviors of smoke-free living, physical activity, fruit and vegetable consumption, and avoidance of heavy alcohol use in Hispanics in the United States and Hispanics living along the US-Mexico border.

Methods: Two weighted data sets with information on Hispanic populations were analyzed: 1) the national Behavioral Risk Factor Surveillance Survey (n = 29,942) from 2009; and 2) the Cameron County Hispanic Cohort (n = 1,439) recruited from the US-Mexico border between 2008–2011. …

Bounded Rationality Alters The Dynamics Of Paediatric Immunization Acceptance, Tamer Oraby, Chris T. Bauch

School of Mathematical & Statistical Sciences Faculty Publications

Interactions between disease dynamics and vaccinating behavior have been explored in many coupled behavior-disease models. Cognitive effects such as risk perception, framing, and subjective probabilities of adverse events can be important determinants of the vaccinating behaviour, and represent departures from the pure “rational” decision model that are often described as “bounded rationality”. However, the impact of such cognitive effects in the context of paediatric infectious disease vaccines has received relatively little attention. Here, we develop a disease-behavior model that accounts for bounded rationality through prospect theory. We analyze the model and compare its predictions to a reduced model that lacks …

Subclinical Atherosclerosis And Obesity Phenotypes Among Mexican Americans, Susan T. Laing, Beverly Smulevitz, Kristina Vatcheva, Mohammad H. Rahbar, Belinda M. Reininger, David D. Mcpherson, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

Background

Data on the influence of obesity on atherosclerosis in Hispanics are inconsistent, possibly related to varying cardiometabolic risk among obese individuals. We aimed to determine the association of obesity and cardiometabolic risk with subclinical atherosclerosis in Mexican‐Americans.

Methods and Results

Participants (n=503) were drawn from the Cameron County Hispanic Cohort. Metabolic health was defined as <2 of the following: blood pressure ≥130/85; triglyceride ≥150 mg/dL; high‐density lipoprotein cholesterol <40 mg/dL (men) or <50 mg/dL (women); fasting glucose ≥100 mg/dL; homeostasis model assessment of insulin resistance value >5.13; or high‐sensitivity C‐reactive protein >3 mg/L. Carotid intima media thickness (cIMT) was measured. A high proportion of participants (77.8%) were metabolically unhealthy; they were more likely to be male, older, with fewer years of education, and less likely to meet daily recommendations regarding …

Asymptotic Analysis Of A Magnetized Target Fusion Reactor, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Nonlinear conservation laws with moving boundaries often arise in applications such as gas dynamics and more recently in the context of nuclear fusion reactors. Gaining insight into the nature of solutions to such models and their dependence upon design parameters is often done numerically. We use formal asymptotics to study a model of a magnetized target fusion reactor for producing energy. We will asymptotically solve the compressible Euler equations with two free moving boundaries, with an algebraic coupling of fluid pressure at one of the free boundaries. The model consists of an intense pressure being imparted on the boundary of …

Some Results For The Hodge Decomposition Theorem In Euclidean Three-Space, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The Hodge Decomposition Theorem plays a significant role in the study of partial differential equations. Several interrelated propositions which are required for the proof of the Hodge theorem in Euclidean three-space are introduced and proved in a novel way.

Connections Of Zero Curvature And Bäcklund Transformations, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Zero curvature connections in a principal bundle are introduced. It is shown that such connections are very useful in formulating the Bäcklund problem and in constructing transformations. A general technique can be proposed for producing such transformations by defining the relevant connection coefficients appropriately. Finally, several applications of this work to various types of nonlinear partial differential equations will be presented.

Customizing Course Redesign And Flipped Classroom Models To Improve Learning Environment, Taeil Yi, Jerzy Mogilski

School of Mathematical & Statistical Sciences Faculty Publications

This article is about a successful adoption of course redesign model of mathematics courses at the Department of Mathematics in the University of Texas at Brownsville (UTB), a Hispanic serve university in the south Texas. Around 2007 National Center for Academic Transformation (NCAT) recommended six models for using of information technology to redesign courses in mathematics: the supplemental model, the replacement model, the emporium model, the fully online model, the buffet model, and the linked workshop model. Because of the local educational environment and resources none of the six models could be implemented exactly like it was described by NCAT. …

Critical Controlled Branching Processes And Their Relatives, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and emigration is reviewed in detail. Critical controlled branching processes with continuous state space are also discussed.

Symmetries Of Monocoronal Tilings, Dirk Frettlöh, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal. We provide a classification of monocoronal tilings in the Euclidean plane and derive a list of all possible symmetry groups of monocoronal tilings. In particular, any monocoronal tiling with respect to direct congruence is crystallographic, whereas any monocoronal tiling with respect to congruence (reflections allowed) is either crystallographic or it has a one-dimensional translation group. Furthermore, bounds on the number of the dimensions of the translation group of monocoronal tilings in higher …

Gradient-Based Compressive Sensing For Noise Image And Video Reconstruction, Huihuang Zhao, Yaonan Wang, Xiaojiang Peng, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this study, a fast gradient-based compressive sensing (FGB-CS) for noise image and video is proposed. Given a noise image or video, the authors first make it sparse by orthogonal transformation, and then reconstruct it by solving a convex optimisation problem with a novel gradient-based method. The main contribution is twofold. Firstly, they deal with the noise signal reconstruction as a convex minimisation problem, and propose a new compressive sensing based on gradient-based method for noise image and video. Secondly, to improve the computational efficiency of gradient-based compressive sensing, they formulate the convex optimisation of noise signal reconstruction under Lipschitz …

Connections Of Zero Curvature And Applications To Nonlinear Partial Differential Equations, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as well. It is also shown that the connection coefficients can be defined so that the partial differential equation to be studied appears as the curvature term in the structure equations. It is discussed how Lax pairs and Bäcklund tranformations can be formulated for such equations that occur as zero curvature terms.

Limit Distributions Of Random Walks On Stochastic Matrices, Santanu Chakraborty, Arunava Mukherjea

School of Mathematical & Statistical Sciences Faculty Publications

Problems similar to Ann. Prob. 22 (1994) 424–430 and J. Appl. Prob. 23 (1986) 1019–1024 are considered here. The limit distribution of the sequence XnXn−1 ··· X1, where (Xn)n≥1 is a sequence of i.i.d. 2 × 2 stochastic matrices with each Xn distributed as μ, is identified here in a number of discrete situations. A general method is presented and it covers the cases when the random components Cn and Dn (not necessarily independent), (Cn, Dn) being the first column of Xn, have the same (or different) Bernoulli distributions. Thus (Cn, Dn) is valued in {0, r}2, where r is …

Energy And Potential Enstrophy Flux Constraints In Quasi-Geostrophic Models, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We investigate an inequality constraining the energy and potential enstrophy flux spectra in two-layer and multi-layer quasi-geostrophic models. Its physical significance is that it can diagnose whether any given multi-layer model that allows co-existing downscale cascades of energy and potential enstrophy can allow the downscale energy flux to become large enough to yield a mixed energy spectrum where the dominant k−3 scaling is overtaken by a subdominant k−5/3 contribution beyond a transition wavenumber kt situated in the inertial range. The validity of the flux inequality implies that this scaling transition cannot occur within the inertial range, whereas a violation of …

Anxiety, Depression And Smoking Status Among Adults Of Mexican Heritage On The Texas-Mexico Border, Anna V. Wilkinson, Kristina Vatcheva, Adriana Pérez, Belinda M. Reininger, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical & Statistical Sciences Faculty Publications

The goal of the current analysis is to examine relationships between smoking status and anxiety and depression among adults of Mexican heritage to inform the development of culturally relevant smoking cessations efforts. Mexican heritage residents (N=1,791) of the city of Brownsville, TX, aged 18 years or older, enrolled in the Cameron County Hispanic Cohort, were selected through two stage cluster sampling of randomly selected census tracts from the first and third quartile of SES using Census 2000. Among current smokers, anxiety and depression scores were highest among women who had not completed high school (p<0.05). Former smoking women, but not men, with at least a high school education and former smoking women born in the United States reported higher levels of anxiety and depression than never smoking women. Negative affective states may represent a greater barrier to smoking cessation among women than men.

Reconstruction Of Structured Quadratic Pencils From Eigenvalues On Ellipses And Parabolas, R. Ibragimov, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper we study the reconstruction of a structured quadratic pencil from eigenvalues distributed on ellipses or parabolas. A quadratic pencil is a square matrix polynomial

QP(λ) = M λ²+Cλ +K,

where M, C, and K are real square matrices. The approach developed in the paper is based on the theory of orthogonal polynomials on the real line. The results can be applied to more general distribution of eigenvalues. The problem with added single eigenvector is also briefly discussed. As an illustration of the reconstruction method, the eigenvalue problem …

Illustrations And Supporting Texts For Sound Standing Waves Of Air Columns In Pipes In Introductory Physics Textbooks, Liang Zeng, Chris Smith, G. Herold Poelzer, Jennifer Rodriguez, Edgar Corpuz, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

In our pilot studies, we found that many introductory physics textbook illustrations with supporting text for sound standing waves of air columns in open-open, open-closed, and closed-closed pipes inhibit student understanding of sound standing wave phenomena due to student misunderstanding of how air molecules move within these pipes. Based on the construct of meaningful learning from cognitive psychology and semiotics, a quasiexperimental study was conducted to investigate the comparative effectiveness of two alternative approaches to student understanding: a traditional textbook illustration approach versus a newly designed air molecule motion illustration approach. Thirty volunteer students from introductory physics classes were randomly …

Quantization Dimension For Gibbs-Like Measures On Cookie-Cutter Sets, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper using the Banach limit we have determined a Gibbs-like measure μ h supported by a cookie-cutter set E which is generated by a single cookie-cutter mapping f . For such a measure μ h and r ∈ ( 0 , + ∞ ) we have shown that there exists a unique κ r ∈ ( 0 , + ∞ ) such that κ r is the quantization dimension function of the probability measure μ h , and we established its functional relationship with the temperature function of the thermodynamic formalism. The temperature function is commonly used to …

Solution Of Fractional Harmonic Oscillator In A Fractional B-Poly Basis, Muhammad I. Bhatti

School of Mathematical & Statistical Sciences Faculty Publications

An algorithm for approximating solutions to fractional-order differential equations in fractional polynomial basis is presented. A finite generalized fractional-order basis set is obtained from the modified Bernstein Polynomials, where α is the fractional-order of the modified Bernstein type polynomials (B-polys). The algorithm determines the desired solution in terms of continuous finite number of generalized fractional polynomials in a closed interval and makes use of Galerkin method to calculate the unknown expansion coefficients for constructing the approximate solution to the fractional differential equations. The Caputo’s definition for a fractional derivative is used to evaluate derivatives of the polynomials. Each term in …

Optimal Control In The Treatment Of Retinitis Pigmentosa, Erika T. Camacho, Luis A. Melara, Cristina Villalobos, Stephen Wirkus

School of Mathematical & Statistical Sciences Faculty Publications

Numerous therapies have been implemented in an effort to minimize the debilitating effects of the degenerative eye disease Retinitis Pigmentosa (RP), yet none have provided satisfactory long-term solution. To date there is no treatment that can halt the degeneration of photoreceptors. The recent discovery of the RdCVF protein has provided researchers with a potential therapy that could slow the secondary wave of cone death. In this work, we build on an existing mathematical model of photoreceptor interactions in the presence of RP and incorporate various treatment regiments via RdCVF. Our results show that an optimal control exists for the administration …

On Cubic Multisections Of Eisenstein Series, Andrew Alaniz, Timothy Huber

School of Mathematical & Statistical Sciences Faculty Publications

A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. We prove that the resulting series are rational functions of η(τ) and η(3τ), where η is the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations. These operators exhibit properties that mirror those of similarly defined quintic operators.

Assessing The Optimal Virulence Of Malaria‐Targeting Mosquito Pathogens: A Mathematical Study Of Engineered Metarhizium Anisopliae, Bernhard Konrad, Michael R. Lindstrom, Anja Gumpinger, Jielin Zhu, Daniel Coombs

School of Mathematical & Statistical Sciences Faculty Publications

Background

Metarhizium anisopliae is a naturally occurring fungal pathogen of mosquitoes. Recently, Metarhizium has been engineered to act against malaria by directly killing the disease agent within mosquito vectors and also effectively blocking onward transmission. It has been proposed that efforts should be made to minimize the virulence of the fungal pathogen, in order to slow the development of resistant mosquitoes following an actual deployment.

Results

Two mathematical models were developed and analysed to examine the efficacy of the fungal pathogen. It was found that, in many plausible scenarios, the best effects are achieved with a reduced or minimal pathogen …

Ill-Posedness Of The Two-Dimensional Keller-Segel Model In Triebel-Lizorkin Spaces, Chao Deng, John Villavert

School of Mathematical & Statistical Sciences Faculty Publications

This article proves the ill-posedness of the Cauchy problem for the two-dimensional Keller–Segel model in Triebel–Lizorkin spaces, for . In particular, it is shown that solutions can develop norm inflation under certain settings in that the solution can become arbitrarily large after an arbitrarily short time even for small initial data.

Lessons Learned In Establishing Stem Student Cohorts At A Border University And The Effect On Student Retention And Success, Mikhail M. Bouniaev, Immanuel Edinbarough, Bill W. Elliott

School of Mathematical & Statistical Sciences Faculty Publications

The University of Texas at Brownsville (UTB) serves more than 8,000 students in the Lower Rio Grande Valley area and broader Mexico region. UTB is a Hispanic-serving institution that attracts students from the surrounding areas, including the Mexico border region. The College of Science, Mathematics and Technology (CSMT) established a Science, Technology, Engineering, and Mathematics (STEM) cohort program to help the majority of students to earn a degree in a STEM field in the shortest possible time. The challenges and obstacles encountered during the planning and implementation phase of the STEM cohort program are discussed in this paper, as are …

Peakon, Pseudo-Peakon, And Cuspon Solutions For Two Generalized Camassa- Holm Equations, Jibin Li, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study peakon, cuspon, and pseudo-peakon solutions for two generalized Camassa-Holm equations. Based on the method of dynamical systems, the two generalized Camassa-Holm equations are shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, pseudo-peakons, and periodic cusp solutions. In particular, the pseudo-peakon solution is for the first time proposed in our paper. Moreover, when a traveling system has a singular straight line and a heteroclinic loop, under some parameter conditions, there must be peaked solitary wave solutions appearing.

Mexican-American Children's Perspectives: Neighborhood Characteristics And Physical Activity In Texas-Mexico Border Colonias, Nelda Mier, Chanam Lee, Matthew Lee Smith, Xiaohui Wang, Elias H. Avila-Rodriguez, Laura Trevino, Marcia G. Ory

School of Mathematical & Statistical Sciences Faculty Publications

The qualitative study described in this article investigated perceptions about environmental factors influencing physical activity (PA) among children from underserved neighborhoods known as colonias in the U.S.-Mexico border. Ten focus groups were conducted with 67 Mexican-American colonia children ages 8 to 13 living in one of the poorest border counties in the U.S. Analyses indicated that PA among children was influenced by neighborhood characteristics, including litter, speeding cars, unleashed dogs, and dark streets. The children also underlined intrapersonal and social environmental factors. Findings may inform policy makers and public health professionals about ways to promote PA among underserved children through …