Physical Sciences and Mathematics Commons^™

Use Of Cubic B-Spline In Approximating Solutions Of Boundary Value Problems, Maria Mungia, Dambaru Bhatta

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Here we investigate the use of cubic B-spline functions in solving boundary value problems. First, we derive the linear, quadratic, and cubic B-spline functions. Then we use the cubic B-spline functions to solve second order linear boundary value problems. We consider constant coefficient and variable coefficient cases with non-homogeneous boundary conditions for ordinary differential equations. We also use this numerical method for the space variable to obtain solutions for second order linear partial differential equations. Numerical results for various cases are presented and compared with exact solutions.

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 and Statistical Sciences Faculty Publications and Presentations

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 …

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 and Statistical Sciences Faculty Publications and Presentations

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 …

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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. …

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

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 and Statistical Sciences Faculty Publications and Presentations

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. …

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 and Statistical Sciences Faculty Publications and Presentations

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 …

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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.

Symmetries Of Monocoronal Tilings, Dirk Frettlöh, Alexey Garber

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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 …

Connections Of Zero Curvature And Bäcklund Transformations, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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.

Critical Controlled Branching Processes And Their Relatives, George Yanev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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.