Physical Sciences and Mathematics Commons^™

Variable Moving Average Transform Stitching Waves, Vesselin Vatchev

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A moving average transform in the plane with a variable size and shape window depending on the position and the ’time’ is studied. The main objective is to select the window parameters in such a way that the new transform converges smoothly to the identity transform at the boundary of a prescribed bounded plane region. A new approximation of solitary waves arising from Korteweg-de Vries equation is obtained based on results in the paper. Numerical implementation and examples are included.

Multilocality And Fusion Rules On The Generalized Structure Functions In Two-Dimensional And Three-Dimensional Navier-Stokes Turbulence, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator “multilocality.” The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of …

Quantum Dynamics, Entropy And Quantum Versions Of Maxwell’S Demon, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Several subjects which reside in the overlap area of quantum mechanics, statistical physics and thermodynamics are investigated in depth. This collection of subjects shares a common domain which is referred to as Maxwell’s demon. The classical version of this idea is introduced, and then, the contribution made by Szilard to the subject is presented. Several demons are considered, and it is shown that to best understand this area, quantum mechanics and the role information plays in it must be appreciated deeply.

Expert Elicitation On The Uncertainties Associated With Chronic Wasting Disease, Michael G. Tyshenko, Tamer Oraby, Shalu Darshan, Margit Westphal, Maxine C. Croteau, Willy Aspinall, Susie Elsaadany, Daniel Krewski, Neil Cashman

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A high degree of uncertainty exists for chronic wasting disease (CWD) transmission factors in farmed and wild cervids. Evaluating the factors is important as it helps to inform future risk management strategies. Expert opinion is often used to assist decision making in a number of health, science, and technology domains where data may be sparse or missing. Using the "Classical Model" of elicitation, a group of experts was asked to estimate the most likely values for several risk factors affecting CWD transmission. The formalized expert elicitation helped structure the issues and hence provide a rational basis for estimating some transmission …

Existence And Behavior Of Positive Solutions To Elliptic System With Hardy Potential, Lei Wei, Xiyou Cheng, Zhaosheng Feng

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this article, we study a class of elliptic systems with Hardy potentials. We analyze the possible behavior of radial solutions to the system when p; t > 1, q; s > 0 and λ; μ > (N - 2)2=4, and obtain the existence of positive solutions to the system with the Dirichlet boundary condition under certain conditions. When λ; μ > 0, p; t > 1 and q; s > 0, we show that any radial positive solution is decreasing in r.

The Precarious Health Of Young Mexican American Men In South Texas, Cameron County Hispanic Cohort, 2004–2015, Gordon P. Watt, Kristina Vatcheva, Derek M. Griffith, Belinda M. Reininger, Laura Beretta, Michael Fallon, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Introduction

Hispanic men have higher rates of illness and death from various chronic conditions than do non-Hispanic men. We aimed to characterize the health of Mexican American men living on the US–Mexico border in South Texas and elucidate indications of chronic disease in young men.

Methods

We sampled all male participants from the Cameron County Hispanic Cohort, an ongoing population-based cohort of Mexican Americans in Brownsville, Texas. We calculated descriptive statistics and stratified the sample into 3 age groups to estimate the prevalence of sociodemographic, behavioral, and clinical factors by age group and evaluated differences between age groups.

Results

Obesity …

Riemann-Hilbert Approach For The Fqxl Model: A Generalized Camassa-Holm Equation With Cubic And Quadratic Nonlinearity, Zhen Wang, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, the inverse scattering transform associated with a Riemann-Hilbert problem is formulated for the FQXL model: a generalized Camassa-Holm equation mt = 12 k1[m(u2 − u2 x )]x + 1 2 k2(2mux + mxu), m = u − ux x, which was originally included in the work of Fokas [Physica D 87, 145 (1995)] and was recently shown to be integrable in the sense of Lax pair, bi-Hamilton structure, and conservation laws by Qiao, Xia, and Li [e-print arXiv:1205.2028v2 (2012)]. We have discussed the following properties: direct scattering problems and Jost solutions, asymptotical and analytical behavior of Jost …

From Exam To Education: The Math Exam/Education Resources, Carmen Bruni, Christina Koch, Bernhard Konrad, Michael R. Lindstrom, Iain Moyles, Will Thompson

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The Math Exam/Education Resources (MER) is an open online learning resource hosted at The University of British Columbia (UBC), aimed at providing mathematics education resources for students and instructors at UBC. In this paper, there will be a discussion of the motivation for creating this resource on the MediaWiki platform, key features of the implementation that support student learning (including the evolution of the MER wiki from an exam database to a more-general learning resource), data on student use and response, potential for future development, and a brief description of how the project was implemented. Preliminary correlation data between wiki …

Existence Of Positive Solutions To Semilinear Elliptic Systems With Supercritical Growth, Congming Li, John Villavert

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We establish the existence of positive entire solutions to cooperative systems of semilinear elliptic equations involving nonlinearities with critical and supercritical growth. Consequently, we obtain existence results to several well-known model examples such as systems of the Hénon, Lane–Emden, and stationary Schrödinger types. The main technique for generating our results relies on a topological approach for the shooting method combined with nonexistence results to closely related boundary value problems.

Generalized Reciprocal Identities, Timothy Huber, Daniel Schultz

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Included in Ramanujan’s Notebooks are two reciprocal identities. The first identity connects the Rogers-Ramanujan continued fraction with an eta quotient. The second identity is a level thirteen analogue. These are special cases of a more general class of relations between eta quotients and modular functions defined by product generalizations of the Rogers-Ramanujan continued fraction. Each identity is shown to be a relation between generators for a certain congruence subgroup. The degree, form, and symmetry of the identities is determined from behavior at cusps of the congruence subgroup whose field of functions the parameters generate. The reciprocal identities encode information about …

Harmonic Maps Surfaces And Relativistic Strings, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The harmonic map is introduced and several physical applications are presented. The classical nonlinear σ model can be looked at as the embedding of a two-dimensional surface in a threedimensional sphere, which is itself embedded in a four-dimensional space. A system of nonlinear evolution equations are obtained by working out the zero curvature condition for the Gauss equations relevant to this geometric formulation.

Multicollinearity In Regression Analyses Conducted In Epidemiologic Studies, Kristina Vatcheva, Minjae Lee, Joseph B. Mccormick, Mohammad H. Rahbar

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The adverse impact of ignoring multicollinearity on findings and data interpretation in regression analysis is very well documented in the statistical literature. The failure to identify and report multicollinearity could result in misleading interpretations of the results. A review of epidemiological literature in PubMed from January 2004 to December 2013, illustrated the need for a greater attention to identifying and minimizing the effect of multicollinearity in analysis of data from epidemiologic studies. We used simulated datasets and real life data from the Cameron County Hispanic Cohort to demonstrate the adverse effects of multicollinearity in the regression analysis and encourage researchers …

Cirrhosis And Advanced Fibrosis In Hispanics In Texas: The Dominant Contribution Of Central Obesity, Jingjing Jiao, Gordon P. Watt, Minjae Lee, Mohammad H. Rahbar, Kristina Vatcheva, Jen-Jung Pan, Joseph B. Mccormick, Susan P. Fisher-Hoch, Michael Fallon, Laura Beretta

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Liver cirrhosis is a leading cause of death in Hispanics and Hispanics who live in South Texas have the highest incidence of liver cancer in the United States. We aimed at determining the prevalence and associated risk factors of cirrhosis in this population. Clinical and demographic variables were extracted for 2466 participants in the community-based Cameron County Hispanic Cohort in South Texas. Aspartate transaminase to Platelet Ratio Index (APRI) was used to predict cirrhosis in Cameron County Hispanic Cohort. The prevalence of cirrhosis using APRI≥2 was 0.94%, which is nearly 4-fold higher than the national prevalence. Using APRI≥1, the overall …

Liver And Other Gastrointestinal Cancers Are Frequent In Mexican Americans, Ariana L. Garza, Kristina Vatcheva, Jen-Jung Pan, Mohammad H. Rahbar, Michael Fallon, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Background

Disease patterns in Mexican-American health-disparity populations differ from larger United States populations.

Aims

Determine frequency of gastrointestinal cancers in Mexican Americans.

Methods

We analyzed self-reported data from the Cameron County Hispanic Cohort where we find high rates of risk factors for cancer: obesity (48.5%), diabetes (30.7%). Participants provided cancer histories about themselves and first and second degree relatives. Logistic regression models assessed risk factors. Frequencies of cancer sites were ranked and validated using concurrent age local cancer registry data.

Results

Among 9,249 individuals (participants and their relatives) there were 1,184 individuals with reports of cancer. Among cohort participants under …

Depression In Mexican Americans With Diagnosed And Undiagnosed Diabetes, Rene L. Olvera, Susan P. Fisher-Hoch, Douglas E. Williamson, Kristina Vatcheva, Joseph B. Mccormick

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Background: Depression and diabetes commonly co-occur; however, the strength of the physiological effects of diabetes as mediating factors towards depression is uncertain.

Method: We analyzed extensive clinical, epidemiological and laboratory data from n = 2081 Mexican Americans aged 35-64 years, recruited from the community as part of the Cameron County Hispanic Cohort (CCHC) divided into three groups: Diagnosed (self-reported) diabetes (DD, n = 335), Undiagnosed diabetes (UD, n = 227) and No diabetes (ND, n = 1519). UD participants denied being diagnosed with diabetes, but on testing met the 2010 American Diabetes Association and World Health Organization definitions of diabetes. …

Hepatitis C Virus In Mexican Americans: A Population-Based Study Reveals Relatively High Prevalence And Negative Association With Diabetes, Gordon P. Watt, Kristina Vatcheva, Laura Beretta, Jen-Jung Pan, Michael Fallon, Joseph B. Mccormick, Susan P. Fisher-Hoch

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This study aimed to estimate the prevalence and risk factors for hepatitis C virus (HCV) infection in Mexican Americans living in South Texas. We tested plasma for the presence of HCV antibody from the Cameron County Hispanic Cohort (CCHC), a randomized, population-based cohort in an economically disadvantaged Mexican American community on the United States/Mexico border with high rates of chronic disease. A weighted prevalence of HCV antibody of 2·3% [n = 1131, 95% confidence interval (CI) 1·2-3·4] was found. Participants with diabetes had low rates of HCV antibody (0·4%, 95% CI 0·0-0·9) and logistic regression revealed a statistically significant negative …

A Polyhedral Model Of Partitions With Bounded Differences And A Bijective Proof Of A Theorem Of Andrews, Beck, And Robbins, Felix Breuer, Brandt Kronholm

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The smallest part is a rational function. This result is similar to the closely related case of partitions with fixed differences between largest and smallest parts which has recently been studied through analytic methods by Andrews, Beck, and Robbins. Our approach is geometric: We model partitions with bounded differences as lattice points in an infinite union of polyhedral cones. Surprisingly, this infinite union tiles a single simplicial cone. This construction then leads to a bijection that can be interpreted on a purely combinatorial level.

Metabolic Health Has Greater Impact On Diabetes Than Simple Overweight/Obesity In Mexican Americans, Shenghui Wu, Susan P. Fisher-Hoch, Belinda M. Reininger, Kristina Vatcheva, Joseph B. Mccormick

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

To compare the risk for diabetes in each of 4 categories of metabolic health and BMI. Methods. Participants were drawn from the Cameron County Hispanic Cohort, a randomly selected Mexican American cohort in Texas on the US-Mexico border. Subjects were divided into 4 phenotypes according to metabolic health and BMI: metabolically healthy normal weight, metabolically healthy overweight/obese, metabolically unhealthy normal weight, and metabolically unhealthy overweight/obese. Metabolic health was defined as having less than 2 metabolic abnormalities. Overweight/obese status was assessed by BMI higher than 25 kg/m2. Diabetes was defined by the 2010 ADA definition or by being on a diabetic …

Asymptotic And Optimal Liouville Properties For Wolff Type Integral Systems, John Villavert

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This article examines the properties of positive solutions to fully nonlinear systems of integral equations involving Hardy and Wolff potentials. The first part of the paper establishes an optimal existence result and a Liouville type theorem for the integral systems. Then, the second part examines the decay rates of positive bound states at infinity. In particular, a complete characterization of the asymptotic properties of bounded and decaying solutions is given by showing that such solutions vanish at infinity with two principle rates: the slow decay rates and the fast decay rates. In fact, the two rates can be fully distinguished …

An Application Of The Spectral Theorem To The Laplacian On A Riemannian Manifold, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

There continues to be great interest in the study of the heat equation on Riemannian manifolds. This may be due to the remarkable more recent work of Patodi [1]. It may also be due in part to the asymptotic expansion of Minakshisundaram and Pleijel. The heat equation involves a parabolic partial differential equation that describes the distribution of heat in a given region over time. This equation has also appears in probability theory to describe random walks. The heat equation is also of importance in Riemannian geometry, topology and applied mathematics.

Stability Analysis And Hopf Bifurcation Of Density-Dependent Predator-Prey Systems With Beddington-Deangelis Functional Response, Xin Jiang, Zhikun She, Zhaosheng Feng

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this article, we study a density-dependent predator-prey system with the Beddington-DeAngelis functional response for stability and Hopf bifurcation under certain parametric conditions. We start with the condition of the existence of the unique positive equilibrium, and provide two sufficient conditions for its local stability by the Lyapunov function method and the Routh-Hurwitz criterion, respectively. Then, we establish sufficient conditions for the global stability of the positive equilibrium by proving the non-existence of closed orbits in the first quadrant R²+. Afterwards, we analyze the Hopf bifurcation geometrically by exploring the monotonic property of the trace of the Jacobean matrix with …

The Effect Of Ignoring Statistical Interactions In Regression Analyses Conducted In Epidemiologic Studies: An Example With Survival Analysis Using Cox Proportional Hazards Regression Model, Kristina Vatcheva, Joseph B. Mccormick, Mohammad H. Rahbar

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Objective: To demonstrate the adverse impact of ignoring statistical interactions in regression models used in epidemiologic studies.

Study design and setting: Based on different scenarios that involved known values for coefficient of the interaction term in Cox regression models we generated 1000 samples of size 600 each. The simulated samples and a real life data set from the Cameron County Hispanic Cohort were used to evaluate the effect of ignoring statistical interactions in these models.

Results: Compared to correctly specified Cox regression models with interaction terms, misspecified models without interaction terms resulted in up to 8.95 fold bias in estimated …

The Complete Classification Of Five-Dimensional Dirichlet–Voronoi Polyhedra Of Translational Lattices, Mathieu Dutour Sikiric, Alexey Garber, Achill Schürmann, Clara Waldmann

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper reports on the full classification of Dirichlet–Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types (L-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet–Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181 394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check.