Mathematics Commons^™

Mathematical Modeling Of Nonlinear Blood Glucose-Insulin Dynamics With Beta Cells Effect, Gabriela Urbina, Daniel N. Riahi, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

We consider mathematical modeling of blood glucose-insulin regulatory system with the additional effect of the secreted insulin by the pancreatic beta cells and in the presence of an external energy input to such system. Such modeling system is investigated to determine the time-dependent nonlinear dynamics that take place by the quantities, which represent the glucose and insulin concentrations in the blood, insulin action as well as in the absence or presence of secreted insulin due to the pancreatic beta cells. Using both analytical and numerical procedures, we determine such quantities versus time for both diabetes patients and normal human and …

Phase-Adjusted Estimation Of The Covid-19 Outbreak In South Korea Under Multi-Source Data And Adjustment Measures: A Modelling Study, Xiaomei Feng, Jing Chen, Kai Wang, Lei Wang, Fengqin Zhang, Zhen Jin, Lan Zou, Xia Wang

Mathematics Faculty Articles

Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (C_rI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R₀ of COVID-19 to be 4.79(95% C_rI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to R_c ≈ 0.32(95% C_rI …

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Review Of Major Role Of Vitamin D3 In Human Immune System And Its Possible Use For Novel Corona Virus Treatment, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

the evidences showing major role of Vitamin D3 in human immune system and its potential use for novel corona virus treatment. Our argument is based on research finding that corona virus has viral envelope glycoproteins. In this regard, Vitamin D3 proves to offer various beneficial effects, including immunomodulatory effect, in order to break the glycoproteins envelope of the virus. One of the greatest benefit of vitamin D3 is the fact that it is easy to get 10,000 - 20,000 IU of daily intake requirement, by sunbathing for more or less twenty minutes. Such a method is likely applicable in many …

Novel Inference Methods For Generalized Linear Models Using Shrinkage Priors And Data Augmentation., Arinjita Bhattacharyya

Electronic Theses and Dissertations

Generalized linear models have broad applications in biostatistics and sociology. In a regression setup, the main target is to find a relevant set of predictors out of a large collection of covariates. Sparsity is the assumption that only a few of these covariates in a regression setup have a meaningful correlation with an outcome variate of interest. Sparsity is incorporated by regularizing the irrelevant slopes towards zero without changing the relevant predictors and keeping the resulting inferences intact. Frequentist variable selection and sparsity are addressed by popular techniques like Lasso, Elastic Net. Bayesian penalized regression can tackle the curse of …

Mathematical Modeling Of Nonlinear Dynamics Of Blood Hormones On The Regulatory System, Gabriela Urbina

Theses and Dissertations

We study a mathematical modeling of nonlinear dynamics of blood hormones, which includes glucose and insulin. On Chapter I, II, III and IV, we introduce this work, analyze an effect of the secreted insulin by the pancreatic beta cells and glucagon hormones and state concluding remarks, respectively. This model considers the time evolution of nonlinear dynamics of the equations for glucose, glucagon and insulin concentrations plus insulin and glucagon actions and the secreted insulin as a result of elevation of glucose in the blood plasma. Using both analytical and numerical procedures, we determine such quantities using different parameters for different …

Association Of Visceral Adipose Tissue And Subclinical Atherosclerosis In Us-Born Mexican Americans But Not First Generation Immigrants, Clarence Gill, Miryoung Lee, Kristina Vatcheva, Nahid Rianon, Beverly Smulevitz, David D. Mcpherson, Joseph B. Mccormick, Susan P. Fisher-Hoch, Susan T. Laing

School of Mathematical & Statistical Sciences Faculty Publications

BACKGROUND: Excess visceral adipose tissue (VAT) is a primary driver for the cardiometabolic complications of obesity; VATassociated cardiovascular disease risk varies by race, but most studies have been done on Non-Hispanics. This study aimed to evaluate the clinical and metabolic correlates of VAT, its association with subclinical atherosclerosis, and the factors affecting this association in Mexican Americans.

METHODS AND RESULTS: Participants (n=527) were drawn from the Cameron County Hispanic Cohort (CCHC), on whom a carotid ultrasound to assess carotid intima media thickness and a dual-energy X-ray absorptiometry scan to assess for VAT were obtained. Those in the highest quartiles of …

Estimating Population Immunity Without Serological Testing, Andrew Lesniewski

Publications and Research

We propose an approximate methodology for estimating the overall level of immunity against COVID-19 in a population that has been affected by the recent epidemic. The methodology relies on the currently available mortality data and utilizes the properties of the SIR model. We illustrate the application of the method by estimating the recent levels of immunity in 10 US states with highest case numbers of COVID-19.

Volume 12, Haleigh James, Hannah Meyls, Hope Irvin, Megan E. Hlavaty, Samara L. Gall, Austin J. Funk, Karyn Keane, Sarah Ghali, Antonio Harvey, Andrew Jones, Rachel Hazelwood, Madison Schmitz, Marija Venta, Haley Tebo, Jeremiah Gilmer, Bridget Dunn, Benjamin Sullivan, Mckenzie Johnson

Incite: The Journal of Undergraduate Scholarship

Introduction, Dr. Roger A. Byrne, Dean

From the Editor, Dr. Larissa "Kat" Tracy

From the Designers, Rachel English, Rachel Hanson

Immortality in the Mortal World: Otherworldly Intervention in "Lanval" and "The Wife of Bath's Tale" by Haleigh James

Analysis of Phenolic Compounds in Moroccan Olive Oils by HPLC by Hannah Meyls

Art by Hope Irvin

The Effects of Cell Phone Use on Gameplay Enjoyment and Frustration by Megan E. Hlavaty, Samara L. Gall, and Austin J. Funk

Care, No Matter What: Planned Parenthood's Use of Organizational Rhetoric to Expand its Reputation by Karyn Keane

Analysis of Petroleum Products for …

Insights From The Influx Of Prescription Painkillers In Northeast Florida: A Retrospective Analysis, Joseph Free, Michelle Dedeo

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

The opioid epidemic has had, and will have, long-lasting ramifications in the United States. To better understand its impact in the Northeast Florida, this research seeks to identify relationships between hydro- and oxycodone pill concentration at the county and zip code levels and socio-economic factors such as average adjusted gross income and opioid related mortality. This project utilizes time series, regression, and GIS methods to examine local opioid saturation and has led to the development of an interactive Tableau dashboard which allows users to view opioid saturation at various levels of granularity. This analysis is made possible by longitudinal data …

H-Discrete Fractional Model Of Tumor Growth And Anticancer Effects Of Mono And Combination Therapies, Kamala Dadashova

Masters Theses & Specialist Projects

In this thesis, we focus on h–discrete and h–discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model which describes tumor growth considering time on hNa, where h>0. First, we introduce some definitions, lemmas and theorems on both h–discrete and h–discrete fractional calculus in the preliminary section. In Chapter 3, we work on the PD model with delay by exam ining nabla h–discrete equations and nabla h–discrete fractional equations as well as variation of constants formulas, accordingly. We introduce our model and solve it using theorems we proved in the last section of the indicated chapter. When we do simulation for …

Circada: Shiny Apps For Exploration Of Experimental And Synthetic Circadian Time Series With An Educational Emphasis, Lisa Cenek, Liubou Klindziuk, Cindy Lopez, Eleanor Mccartney, Blanca Martin Burgos, Selma Tir, Mary E. Harrington, Tanya L. Leise

Psychology: Faculty Publications

Circadian rhythms are daily oscillations in physiology and behavior that can be assessed by recording body temperature, locomotor activity, or bioluminescent reporters, among other measures. These different types of data can vary greatly in waveform, noise characteristics, typical sampling rate, and length of recording. We developed 2 Shiny apps for exploration of these data, enabling visualization and analysis of circadian parameters such as period and phase. Methods include the discrete wavelet transform, sine fitting, the Lomb-Scargle periodogram, autocorrelation, and maximum entropy spectral analysis, giving a sense of how well each method works on each type of data. The apps also …

Optimal Control With Manf Treatment Of Photoreceptor Degeneration, Erika T. Camacho, Suzanne Lenhart, Luis A. Melara, Cristina Villalobos, Stephen Wirkus

School of Mathematical & Statistical Sciences Faculty Publications

People afflicted with diseases such as retinitis pigmentosa and age-related macular degeneration experience a decline in vision due to photoreceptor degeneration, which is currently unstoppable and irreversible. Currently there is no cure for diseases linked to photoreceptor degeneration. Recent experimental work showed that mesencephalic astrocyte-derived neurotrophic factor (MANF) can reduce neuron death and, in particular, photoreceptor death by reducing the number of cells that undergo apoptosis. In this work, we build on an existing system of ordinary differential equations that represent photoreceptor interactions and incorporate MANF treatment for three experimental mouse models having undergone varying degrees of photoreceptor degeneration. Using …

Mathematical Modelling Of The Tuberculosis Epidemiology, Ally Yeketi Ayinla

Student Works (2020-2029)

This project analyses the tuberculosis (TB) epidemic mathematically using compartmental modelling approach. Three models are presented to discuss drug susceptible and multi-drug resistant TB. The first model presented has 4 compartments; susceptible, exposed, infectious and recovered. The relevance of the exposed class in managing TB is analysed and found to be useful in delaying the eventual onset of the infection. Compared to previous researches, our results significantly show that when efforts are made such that no infected individual bypasses the exposed class and progresses directly to the infectious, the TB epidemic is successfully combatted. Also, the model is used to …

Use Of Kalman Filtering In State And Parameter Estimation Of Diabetes Models, Cassidy Le

HMC Senior Theses

Diabetes continues to affect many lives every year, putting those affected by it at higher risk of serious health issues. Despite many efforts, there currently is no cure for diabetes. Nevertheless, researchers continue to study diabetes in hopes of understanding the disease and how it affects people, creating mathematical models to simulate the onset and progression of diabetes. Recent research by David J. Albers, Matthew E. Levine, Andrew Stuart, Lena Mamykina, Bruce Gluckman, and George Hripcsak¹ has suggested that these models can be furthered through the use of Data Assimilation, a regression method that synchronizes a model with a …

Comparative Survival Of Asian And White Metastatic Castration-Resistant Prostate Cancer Men Treated With Docetaxel, Susan Halabi, Sandipan Dutta, Catherine M. Tangen, Mark Rosenthal, Daniel P. Petrylak, Ian M. Thompson Jr., Kim N. Chi, Johann S. De Bono, John C. Araujo, Christopher Logothetis, Mario A. Eisenberger, David I. Quinn, Karim Fizazi, Michael J. Morris, Celestia S. Higano, Ian F. Tannock, Eric J. Small, William Kevin Kelly

Mathematics & Statistics Faculty Publications

There are few data regarding disparities in overall survival (OS) between Asian and white men with metastatic castration-resistant prostate cancer (mCRPC). We compared OS of Asian and white mCRPC men treated in phase III clinical trials with docetaxel and prednisone (DP) or a DP-containing regimen. Individual participant data from 8820 men with mCRPC randomly assigned on nine phase III trials to receive DP or a DP-containing regimen were combined. Men enrolled in these trials had a diagnosis of prostate adenocarcinoma. The median overall survival was 18.8 months (95% confidence interval [CI] = 17.4 to 22.1 months) and 21.2 months (95% …

Quantifying The Varying Predictive Value Of Physical Activity Measures Obtained From Wearable Accelerometers On All-Cause Mortality Over Short To Medium Time Horizons In Nhanes 2003-2006, Lucia Tabacu, Mark Ledbetter, Andrew Leroux, Ciprian Crainiceanu, Ekaterina Smirnova

Mathematics & Statistics Faculty Publications

Physical activity measures derived from wearable accelerometers have been shown to be highly predictive of all-cause mortality. Prediction models based on traditional risk factors and accelerometry-derived physical activity measures are developed for five time horizons. The data set contains 2978 study participants between 50 and 85 years old with an average of 13.08 years of follow-up in the NHANES 2003–2004 and 2005–2006. Univariate and multivariate logistic regression models were fit separately for five datasets for one- to five-year all-cause mortality as outcome (number of events 46, 94, 155, 218, and 297, respectively). In univariate models the total activity count (TAC) …

Classification Models Of Idiopathic Pulmonary Fibrosis Patients, Mohammed Alqawba, Luis R. Rodriguez, Norou Diawara, Rebecca T. Beuschel, Maryann Kaler, Amisha V. Barochia, Stewart J. Levine, Steven D. Nathan, Geraldine Grant

Mathematics & Statistics Faculty Publications

Idiopathic pulmonary fibrosis (IPF) is a chronic and fatal interstitial lung disease with no current cure. Progression of IPF is difficult to predict as the clinical course can be highly variable and range from a rapidly deteriorating state to a relatively stable state, or may be characterized by a slow progressive decline. Therefore, the need for an accurate diagnosis and improved tools for monitoring and managing IPF is of paramount importance, all for understanding the mitochondrial structure and the function played in the IPF. Mitochondrial DNA copy number (MtDCN) has been correlated with mortality in IPF patients and is a …

A Short Remark On Multipurpose Laser Therapy “Helios” In Ukraine And Its Potential Application For Treatment Of Neurology Disorders, Florentin Smarandache, Volodymyr Krasnoholovets, Victor Christianto, Rizha Vitania, The Houw Liong

Branch Mathematics and Statistics Faculty and Staff Publications

However, a truly multipurpose laser therapy method is very rarely available. Here we introduce a multipurpose laser therapy device in Ukraine, which is capable to take care a multitude of diseases. It is called “Helios”, by one of us (VK). We also give a case where a patient who suffered from Covid-19 has been treated successfully until he is recovered to healthy condition. In the last section we also discuss potential future application of Helios for other fields; i.e. neurology disorders.

A Short Remark On Bong Han Duct System (Pvs) As A Neutrosophic Bridge Between Eastern And Western Medicine Paradigms, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a previous paper in this journal (IJNS), it is mentioned about a possible approach of “curemony” as a middle way in order to reconcile Eastern and Western’s paradigms of medicine [1]. Although it is known in literature that there are some attempts to reconcile between Eastern and Western medicine paradigms, known as “integrative medicine,” here a new viewpoint is submitted, i.e. Bong Han duct system (PVS), which is a proof of Meridian system, can be a bridge between those two medicine paradigms in neutrosophic sense. This can be considered as a Neutrosophic Logic way to bridge or reconcile the …

Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk

Department of Mathematics: Faculty Publications

One quarter of veterans returning from the 1990–1991 Persian Gulf War have developed Gulf War Illness (GWI) with chronic pain, fatigue, cognitive and gastrointestinal dysfunction. Exertion leads to characteristic, delayed onset exacerbations that are not relieved by sleep. We have modeled exertional exhaustion by comparing magnetic resonance images from before and after submaximal exercise. One third of the 27 GWI participants had brain stem atrophy and developed postural tachycardia after exercise (START: Stress Test Activated Reversible Tachycardia). The remainder activated basal ganglia and anterior insulae during a cognitive task (STOPP: Stress Test Originated Phantom Perception). Here, the role of attention …

Diabetes And Its Effect On Abdominal Aortic Aneurysm Growth Rate In Hispanic Patients, Monica Betancourt-Garcia, Kristina Vatcheva, Amrit Thakur, Prateek Gupta, Eugene Postevka, Ricardo Martinez, R. Armour Forse

School of Mathematical & Statistical Sciences Faculty Publications

Background

The growth rate of abdominal aortic aneurysms (AAA) can vary depending on age, baseline diameter, blood pressure, race, and history of smoking. Paradoxically, previous studies show evidence of a protective effect of diabetes on the rate of AAA expansion despite its well-established role in the morbidity and mortality of cardiovascular disease. This study aims to investigate the impact diabetes plays on AAA growth within a Hispanic population.

Methods

Data were collected from patients who were predominantly Mexican-American at a single hospital site. Baseline and follow-up measures for AAA diameter were obtained from serial imaging studies. Demographics, medical history, the …

Oscillation In Mathematical Epidemiology, Meredith Greer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

9th Annual Postdoctoral Science Symposium, University Of Texas Md Anderson Cancer Center Postdoctoral Association

Annual Postdoctoral Science Symposium Abstracts

The mission of the Annual Postdoctoral Science Symposium (APSS) is to provide a platform for talented postdoctoral fellows throughout the Texas Medical Center to present their work to a wider audience. The MD Anderson Postdoctoral Association convened its inaugural Annual Postdoctoral Science Symposium (APSS) on August 4, 2011.

The APSS provides a professional venue for postdoctoral scientists to develop, clarify, and refine their research as a result of formal reviews and critiques of faculty and other postdoctoral scientists. Additionally, attendees discuss current research on a broad range of subjects while promoting academic interactions and enrichment and developing new collaborations.

Effective Statistical Energy Function Based Protein Un/Structure Prediction, Avdesh Mishra

LSU New Orleans Theses and Dissertations

Proteins are an important component of living organisms, composed of one or more polypeptide chains, each containing hundreds or even thousands of amino acids of 20 standard types. The structure of a protein from the sequence determines crucial functions of proteins such as initiating metabolic reactions, DNA replication, cell signaling, and transporting molecules. In the past, proteins were considered to always have a well-defined stable shape (structured proteins), however, it has recently been shown that there exist intrinsically disordered proteins (IDPs), which lack a fixed or ordered 3D structure, have dynamic characteristics and therefore, exist in multiple states. Based on …

Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds

Department of Math & Statistics Faculty Publications

In an inflammatory setting, macrophages can be polarized to an inflammatory M1 phenotype or to an anti-inflammatory M2 phenotype, as well as existing on a spectrum between these two extremes. Dysfunction of this phenotypic switch can result in a population imbalance that leads to chronic wounds or disease due to unresolved inflammation. Therapeutic interventions that target macrophages have therefore been proposed and implemented in diseases that feature chronic inflammation such as diabetes mellitus and atherosclerosis. We have developed a model for the sequential influx of immune cells in the peritoneal cavity in response to a bacterial stimulus that includes macrophage …

Long-Dose Intensive Therapy Is Necessary For Strong, Clinically Significant, Upper Limb Functional Gains And Retained Gains In Severe/Moderate Chronic Stroke, Janis J. Daly, Jessica P. Mccabe, John P. Holcomb, Michelle Monkiewicz, Jennifer Gansen, Svetlana Pundik

Mathematics and Statistics Faculty Publications

Background. Effective treatment methods are needed for moderate/severely impairment chronic stroke. Objective. The questions were the following: (1) Is there need for long-dose therapy or is there a mid-treatment plateau? (2) Are the observed gains from the prior-studied protocol retained after treatment? Methods. Single-blind, stratified/randomized design, with 3 applied technology treatment groups, combined with motor learning, for long-duration treatment (300 hours of treatment). Measures were Arm Motor Ability Test time and coordination-function (AMAT-T, AMAT-F, respectively), acquired pre-/posttreatment and 3-month follow-up (3moF/U); Fugl-Meyer (FM), acquired similarly with addition of mid-treatment. Findings. There was no group difference in …

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.

Network Analyses Of Glomerular Capillaries, Jason Cory Brunson, Justin Sardi, Mark Terasaki

Biology and Medicine Through Mathematics Conference

No abstract provided.

Bifurcation Analysis Of A Photoreceptor Interaction Model For Retinitis Pigmentosa, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.