Mathematics Commons^™

Application Of Mixture Models For Doubly Inflated Count Data, Monika Arora, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

In health and social science and other fields where count data analysis is important, zero-inflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k > 0 occurs with high frequency. The zero- and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation–maximization (EM) algorithm to obtain the parameter …

Hart, Robert W., Papers, 1924-1966, Special Collections, Leonard H. Axe Library

Finding Aids

Personal documents, correspondence, and financial records of Robert W. Hart, former professor at Pittsburg State University.

Robert William Hart was born in 1896 to William and Sarah Hart and grew up in Crawford County, Kansas. In 1916 he graduated from the State Manual Training Normal School (now Pittsburg State University), and found early work as an engineer. Robert served as an ensign in the navy during World War I. He taught in the public schools in Fort Scott and Pittsburg from 1916-1918; 1921-1923. In 1920 he married Retta Statler and they had two children. In 1923 he was hired as …

Medical Diagnosis Via Refined Neutrosophic Fuzzy Logic: Detection Of Illness Using Neutrosophic Sets, K. Hemabala, B. Srinivasa Kumar, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets.

Remark On Regenerative Medicine And Potential Utilization Of Low-Intensity Laser Photobiomodulation To Activate Human Stem Cells, Victor Christianto, Florentin Smarandache, Robert N. Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

Recently, a friend of one of these writers told her story of using one of a healthcare product to activate her stem cells as part of regenerative medicine. Regenerative medicine is a field of medicine that seeks to repair or replace damaged or diseased tissues and organs. This can be done through a variety of methods, including stem cell therapy, tissue engineering, and gene therapy. This is a short review article on this rapid field called regenerative medicine, in particular via a new method called photobiomodulation, especially by virtue of low-intensity laser pen treatment. Hopefully it will attract more research …

[Research Note] The Random Somatic Mutation Is Not Quite Random, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This research note challenges the idea that Random Somatic Mutations are entirely random, highlighting their non-equiprobable nature and their influence on evolution, involution, or indeterminacy. It recalls the Neutrosophic Theory of Evolution, extending Darwin’s theory, and emphasizes the importance of distinguishing between different senses of “random mutation” in evolutionary theory.

Predicting The Outcomes Of Internet-Based Cognitive Behavioral Therapy For Tinnitus: Applications Of Artificial Neural Network And Support Vector Machine, Hansapani Rodrigo, Eldré W. Beukes, Gerhard Andersson, Vinaya Manchaiah

School of Mathematical & Statistical Sciences Faculty Publications

Purpose:

Internet-based cognitive behavioral therapy (ICBT) has been found to be effective for tinnitus management, although there is limited understanding about who will benefit the most from ICBT. Traditional statistical models have largely failed to identify the nonlinear associations and hence find strong predictors of success with ICBT. This study aimed at examining the use of an artificial neural network (ANN) and support vector machine (SVM) to identify variables associated with treatment success in ICBT for tinnitus.

Method:

The study involved a secondary analysis of data from 228 individuals who had completed ICBT in previous intervention studies. A 13-point reduction …

Stochastic Models Of Zoonotic Avian Influenza With Multiple Hosts, Environmental Transmission, And Migration In The Natural Reservoir, Kaia Smith

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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 …

Accelerating Multiparametric Mri For Adaptive Radiotherapy, Shraddha Pandey

USF Tampa Graduate Theses and Dissertations

MR guided Radiotherapy (MRgRT) marks an important paradigm shift in the field of radiotherapy. Superior tissue contrast of MRI offers better visualization of the abnormal lesions, as a result precise radiation dose delivery is possible. In case of online treatment planning, MRgRT offers better control of intratumoral motion and quick adaptation to changes in the gross tumor volume. Nonetheless, the MRgRT process flow does suffer from some challenges that limit its clinical usability. The primary aspects of MRgRT workflow are MRI acquisition, tumor delineation, dose map prediction and administering treatment. It is estimated that the acquisition of MRI takes around …

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 …

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), …

Development Of Graphical Models And Statistical Physics Motivated Approaches To Genomic Investigations, Yashwanth Lagisetty

Dissertations and Theses (Open Access)

Identifying genes involved in disease pathology has been a goal of genomic research since the early days of the field. However, as technology improves and the body of research grows, we are faced with more questions than answers. Among these is the pressing matter of our incomplete understanding of the genetic underpinnings of complex diseases. Many hypotheses offer explanations as to why direct and independent analyses of variants, as done in genome-wide association studies (GWAS), may not fully elucidate disease genetics. These range from pointing out flaws in statistical testing to invoking the complex dynamics of epigenetic processes. In the …

Social Justice And Exponential Functions: Using Pandemic Data To Increase Student Understanding, Jane Friedman

Journal of Humanistic Mathematics

This paper describes a class activity based on real data about COVID-19 death rates in California. The activity helps students learn about exponential functions while providing an opportunity to integrate social justice concerns into the mathematics classroom.

Rainbow Perfect And Near-Perfect Matchings In Complete Graphs With Edges Colored By Circular Distance, Shuhei Saitoh, Naoki Matsumoto, Wei Wu

Theory & Applications of Graphs

Given an edge-colored complete graph K_n on n vertices, a perfect (respectively, near-perfect) matching M in K_n with an even (respectively, odd) number of vertices is rainbow if all edges have distinct colors. In this paper, we consider an edge coloring of K_n by circular distance, and we denote the resulting complete graph by K^●_n. We show that when K^●_n has an even number of vertices, it contains a rainbow perfect matching if and only if n=8k or n=8k+2, where k is a nonnegative integer. In the case of an odd …

Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

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 …

Will Reducing Drug Prices Slow Innovation?, Gregory Vaughan, Fred Ledley

Mathematical Sciences Faculty Publications

The pharmaceutical industry has long argued that high drug prices reflect the high cost of innovation and that reducing drug prices would necessarily slow the pipeline of new drugs. These arguments have been bolstered by studies of large pharmaceutical companies showing statistical associations between the projected market size or revenue for pharmaceutical products and research & development (R&D) activity. Our analysis recognizes the increasingly important role of small biopharmaceuticals in drug development , companies that typically have little revenue and negative earnings, but are now responsible for more than 40% of new drug approvals. We examine the relationship between changes …

An Application Of Matrices To The Spread Of The Covid 19, Selena Suarez

Theses and Dissertations

We represented a restaurant seating arrangement using matrices by using 0 entry for someone without covid and 1 entry for someone with covid. Using the matrices we found the best seating arrangements to lessen the spread of covid. We also investigated if there was a factor needed to create a formula that could calculate the matrix that shows who would be affected with covid with each seating arrangement. However, there did not seem to be a clear pattern within the factors. Aside from covid applications, we also investigated the symmetries in seating arrangements and the possible combinations with these arrangements …

Volume 13, Payton Davenport, Audrey Lemons, Jacob Shope, Haley Smith, Cassandra Poole, Rachel Cannon, Rachel Boch, Suzanne Stetson

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

The Effect of Compliment Type on the Estimated Value of the Compliment by Payton Davenport, Audrey Lemons, and Jacob Shope

The Imperial Japanese Military: A New Identity in the Twentieth Century, 1853–1922 by Haley Smith

Longwood University’s campus: Human-cultivated Soil has Higher Microbial Diversity than Soil Collected from Wild Sites by Cassandra Poole

Reminiscent Modernism: Poetry Magazine’s Modernist Nostalgia for the Past by Rachel Cannon

Challenges Faced by Healthcare Workers During the COVID-19 Pandemic: A Preliminary Study of Age and …

Economic Losses From Covid-19 Cases In The Philippines: A Dynamic Model Of Health And Economic Policy Trade-Offs, Elvira P. De Lara-Tuprio, Ma. Regina Justina E. Estuar, Joselito T. Sescon, Cymon Kayle Lubangco, Rolly Czar Joseph T. Castillo, Timothy Robin Y. Teng, Lenard Paulo V. Tamayo, Jay Michael R. Macalalag, Gerome M. Vedeja

Mathematics Faculty Publications

The COVID-19 pandemic forced governments globally to impose lockdown measures and mobility restrictions to curb the transmission of the virus. As economies slowly reopen, governments face a trade-off between implementing economic recovery and health policy measures to control the spread of the virus and to ensure it will not overwhelm the health system. We developed a mathematical model that measures the economic losses due to the spread of the disease and due to different lockdown policies. This is done by extending the subnational SEIR model to include two differential equations that capture economic losses due to COVID-19 infection and due …

Poster Session, Emma Beeler, Maddison Caldwell, Mackenzie Paul, Shirli Salihaj, Sara Lynn Sligh, Stephen Trest

Mississippi Undergraduate Honors Conference

Video provided is of MacKenzie Paul's presentation.

Abstracts

Humanities

Emma Beeler, Mississippi University for Women

Adultery and Fidelity in the Lais of Marie de France

Using both literary and historical analysis, I will examine contrasting depictions of adultery and fidelity within the lais written by 12th-century poet Marie de France. A lai is a type of narrative poem, ranging in length from 118 to 1184 lines. Many of Marie de France’s lais follow the literary trope known as courtly love; however, the reader is encouraged to sympathize with different characters depending on the lai. In some lais, the reader …

A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang

Faculty Publications

Immunotherapy is an innovative treatment that enlists the patient's immune system to battle tumors. The optimal dose for treating patients with an immunotherapeutic agent may differ according to their biomarker status. In this article, we propose a biomarker-based phase I/II dose-finding design for identifying subgroup-specific optimal dose for immunotherapy (BSOI) that jointly models the immune response, toxicity, and efficacy outcomes. We propose parsimonious yet flexible models to borrow information across different types of outcomes and subgroups. We quantify the desirability of the dose using a utility function and adopt a two-stage dose-finding algorithm to find the optimal dose for each …

Mathematics For The Masses: Door-To-Door Missionaries Of Math And Twelve-Step Recovery Programs, Daniel S. Helman

Journal of Humanistic Mathematics

Conversion of strangers, or proselytizing, is a feature of a range of groups for religious, organizational and other aims. In twelve-step recovery programs, such as Alcoholics Anonymous, belief in a higher power is a requirement for working the steps to recovery. People are encouraged to find a higher power of their own understanding. This paper presents a model for using mathematics as a higher power, and shows how recovery works with mathematics in that role instead of a more traditional higher power such as God. A contemplative definition of math is given along with a description of a three-categoried epistemology: …

Perspectives Of Orthodontists Of The Diagnosis, Prevention, And Management Of White Spot Lesions: A Qualitative Study, Salwa Taibah, Neamat Hassan Abubakr Hassan, Hassan Ziada

Dental Medicine Faculty Research

Aims: Several factors influence the development of white spot lesions (WSLs), and one of these is fixed orthodontic appliances. This study aims to evaluate the awareness, preventive strategies, and management of WSLs among a group of Orthodontists. Materials and Methods: A qualitative methodology was applied; four focus groups made up a purposive sample from Orthodontists with various training backgrounds while working within the same healthcare services. Results: Three main themes emerged: awareness and ability to diagnose WSLs, perceived influences on the development of WSLs, and prevention and management strategies and barriers to care delivery. All focus groups agreed that there …

Using A Stochastic Continuous-Time Markov Chain Model To Examine Alternative Timing And Duration Of The Covid-19 Lockdown In Kuwait: What Can Be Done Now?, Mustafa Al-Zoughool, Tamer Oraby, Harri Vainio, Janvier Gasana, Joseph C. Longenecker, Walid Al Ali, Mohammad Alseaidan, Susie Elsaadany, Michael G. Tyshenko

School of Mathematical & Statistical Sciences Faculty Publications

Background

Kuwait had its first COVID-19 in late February, and until October 6, 2020 it recorded 108,268 cases and 632 deaths. Despite implementing one of the strictest control measures-including a three-week complete lockdown, there was no sign of a declining epidemic curve. The objective of the current analyses is to determine, hypothetically, the optimal timing and duration of a full lockdown in Kuwait that would result in controlling new infections and lead to a substantial reduction in case hospitalizations.

Methods

The analysis was conducted using a stochastic Continuous-Time Markov Chain (CTMC), eight state model that depicts the disease transmission and …

Cholera Transmission Dynamic Model With Environmental Impacts Of Plankton Reservoirs, Sweety Sarker

Electronic Theses and Dissertations, 2020-2023

Cholera is an acute disease that is a global threat to the world and can kill people within a few hours if left untreated. In the last 200 years, seven pandemics occurred, and, in some countries, it remains endemic. The World Health Organization (WHO) declared a global initiative to prevent cholera by 2030. Cholera dynamics are contributed by several environmental factors such as salinity level of water, water temperature, presence of plankton especially zooplankton such as cladocerans, rotifers, copepods, etc. Vibrio cholerae (V. cholerae) bacterium is the main reason behind the cholera disease and the growth of V. cholerae depends …

Robust Testing Of Paired Outcomes Incorporating Covariate Effects In Clustered Data With Informative Cluster Size, Sandipan Dutta

Mathematics & Statistics Faculty Publications

Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on …

Collected Papers (On Neutrosophics Theory And Applications), Volume Xii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This twelfth volume of Collected Papers includes 86 papers comprising 976 pages on Neutrosophic Theory and Applications, published between 2013-2021 in the international journal and book series NSS by the author alone or in collaboration with the following 112 co-authors (alphabetically ordered) from 21 countries.

Realtime Event Detection In Sports Sensor Data With Machine Learning, Mallory Cashman

Honors Theses and Capstones

Machine learning models can be trained to classify time series based sports motion data, without reliance on assumptions about the capabilities of the users or sensors. This can be applied to predict the count of occurrences of an event in a time period. The experiment for this research uses lacrosse data, collected in partnership with SPAITR - a UNH undergraduate startup developing motion tracking devices for lacrosse. Decision Tree and Support Vector Machine (SVM) models are trained and perform with high success rates. These models improve upon previous work in human motion event detection and can be used a reference …

Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth

Publications

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of …