Applied Mathematics Commons^™

Tools For Biomolecular Modeling And Simulation, Xin Yang

Mathematics Theses and Dissertations

Electrostatic interactions play a pivotal role in understanding biomolecular systems, influencing their structural stability and functional dynamics. The Poisson-Boltzmann (PB) equation, a prevalent implicit solvent model that treats the solvent as a continuum while describes the mobile ions using the Boltzmann distribution, has become a standard tool for detailed investigations into biomolecular electrostatics. There are two primary methodologies: grid-based finite difference or finite element methods and body-fitted boundary element methods. This dissertation focuses on developing fast and accurate PB solvers, leveraging both methodologies, to meet diverse scientific needs and overcome various obstacles in the field.

Mathematically Modeling How Trapping Regimes That Target Specific Crayfish Life Stages Impact Removal Efficacy, Rini Pattison

Seaver College Research And Scholarly Achievement Symposium

The red swamp crayfish, Procambarus clarkii, is an invasive species introduced into several streams within the Santa Monica Mountains (SMM) in Southern California. Crayfish predation decimates native aquatic species. Thus, the Mountains Restoration Trust (MRT) and Environmental Restoration Group have worked to remove crayfish through regular trapping in Malibu Creek.

To aid conservation efforts, former SURB students William Milligan and Dev Patel developed mathematical models of crayfish removal efficacy. Milligan created a differential equation model of how crayfish removal affects local newt populations. Patel expanded Milligan’s crayfish model by creating a discrete model of the crayfish life cycle that newly …

A Coupled Model Of Population, Poaching, And Economic Dynamics To Assess Rhino Conservation Through Legal Trade, Henry Doyle, Kylie Champagne, Ditto Rajpal, Grace Seebeck, David J. Gerberry

Spora: A Journal of Biomathematics

Rhinoceros populations in Africa are in peril largely due to the high value of their horns and the poaching that ensues. The strategy of legalizing the international trade of rhino horn is receiving increased support among both the people and government officials in Africa. Many in the international conservation community remain opposed to the idea. The legalization strategy is straightforward in theory: legalizing the trade of rhino horn will introduce a large quantity of horn to the market, the increased supply will lead to lower prices for rhino horn, and lower prices will reduce the overall poaching pressure these animals …

Human System Composite Performance Measures: General Systems Performance Theory Insights, Lawrence Disalvi

Bioengineering Dissertations - Archive

Composite Performance Measures (CPMs) of human performance are widely employed in applications that range from mundane to life-changing, yet they are frequently presented without explanation or reference to theoretical underpinnings. The conceptual soundness of a widely used CPM approach, based on additive combination of constituent components, has been called into question by Kondraske. He argues the relevance of General Systems Performance Theory (GSPT) and performance capacity envelope concepts when applied to multidimensional CPM measures.

To obtain evidence-based answers to assertions regarding CPM types and rationale employed in medical and non-medical contexts, a Systematic Descriptive Review was conducted. Separately, the GSPT-based …

Mathematical Modeling Of Microscale Biology In Polyelectrolyte Brushes, William J. Ceely

CGU Theses & Dissertations

Biological macromolecules including nucleic acids, proteins, and glycosaminoglycans are typically anionic and can span domains of up to hundreds of nanometers and even micron length scales. The structures exist in crowded environments that are dominated by multivalent electrostatic interactions that can be modeled using mean-field continuum approaches that represent underlying molecular nanoscale biophysics. In this thesis, we develop such models for polyelectrolyte brushes using both steady state modified Poisson-Boltzmann models and transient modified Poisson-Nernst-Planck models that incorporate important ion-specific (Hofmeister) effects. The transient model enables observation of the relative physical effects as an initial non-equilibrium state relaxes to the steady …

Batch Culture Models Of The Murine Gut Microbiome & The Impact Of Simple Dormancy On Dormancy-Capable Microorganisms Models, Ana C. Mendez

Mathematics Dissertations - Archive

The proposed mathematical biology research utilizes mathematical models to gain insight into biological systems. These systems of ordinary differential equations model diverse topics, ranging from gut microbiomes to harmful algal blooms. A complete stability analysis, supporting phase plane portraits, bifurcation diagrams, and numerical simulations will accompany the models presented. In Chapter 2, the murine gut microbiome is modeled to match laboratory experiments in the literature. In these experiments, mice eat plasmid-carrying “donor” bacteria and naturally carry plasmid-free “resident” bacteria in their gut. The models aim to capture the behavior of plasmids, donor bacteria, and resident bacteria. Chapter 3 explores dormancy …

A Few Lessons From Venezuela: Introducing A New Path Of Appropriate Farming And Appropriate Renewable Energy, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In development economics literatures, there is a known term for developing countries which tend to mismanage natural resources, that term is called natural resources curse. And two examples which have been discussed quite often is Venezuela and Norway. Here we also discuss other countries as well, including Argentina and a few lessons for Indonesia in choosing the next course of development path, especially with appropriate farming and appropriate renewable energy.

Determination Of Spore Viability In Concrete Across Several Factors Using Most Probable Number, Samuel Boyer

Williams Honors College, Honors Research Projects

To determine the lowest concentration of spore added to polyurethane-cement composite (PUCCO) particles that can still germinate after curing in concrete. This research project is a small addition to the larger research project being undertaken by Mirza Mohammed Rashiduzzaman for his Masters. The larger project involves the use of fungal spores added in concrete to act as a self-healing component when cracks form in the concrete structure over time. These spores are suspended in a protective oil and loaded into small, hardened sponge-like PUCCO cubes to act as growth points when water and air can reach the PUCCO in the …

Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, Felipe Xavier Costa

Electronic Theses & Dissertations (2024 - present)

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, …

Mathematical Modeling And Analysis Of Inflammation And Tissue Repair: Lung Inflammation And Wound Healing In Corals Under Stress, Quintessa Hay

Theses and Dissertations

A variety of insults, including tissue injury and/or exposure to pathogen, elicit an immune response in many organisms. An improperly regulated immune response can result in deleterious effects to the organism. Here we present models for lung injury in young and old mice and models for wound healing in coral reefs.

It is well known that the immune response becomes less effective in older individuals. This is of particular interest in pulmonary insults such as ventilator induced lung injury (VILI) or lung infection. We extended a mathematical model for the inflammatory response to VILI and used experimental data to select …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

Department of Mathematics: Dissertations, Theses, and Student Research

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …

(R2059) Modeling The Spread Of Coronavirus With Self-Protection And Quarantine Effect, Dileep Sharma, Agraj Tripathi, Ram Naresh Tripathi

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear mathematical model to study the effect of transmission dynamics of COVID-19 virus in a population with variable size structure is proposed and analyzed. The model divides the total human population into five subclasses: susceptibles, self-protected susceptibles, infectives, quarantined infectives, and recovered population including a class representing cumulative density of coronavirus in the environmental reservoir. The model exhibits two equilibria, namely, the diseasefree and the endemic equilibrium. Model analysis reveals the global dynamics of the spread of COVID-19 is completely determined by the basic reproduction number. If basic reproduction number is greater than one, the endemic equilibrium is locally …

Effects Of A Protection Zone In A Reaction-Diffusion Model With Strong Allee Effect., Isaac Johnson

Electronic Theses and Dissertations

A protection zone model represents a patchy environment with positive growth over the protection zone and strong Allee effect growth outside the protection zone. Generally, these models are considered through the corresponding eigenvalue problem, but that has certain limitations. In this thesis, a general protection zone model is considered. This model makes no assumption on the direction of the traveling wave solution over the Strong Allee effect patch. We use phase portrait analysis of this protection zone model to draw conclusions about the existence of equilibrium solutions. We establish the existence of three types of equilibrium solutions and the necessary …

Incorporating Adaptive Human Behavior Into Epidemiological Models Using Equation Learning, Austin Barton, Jordan Klein, Jonathan Greer, Kevin Flores, Patrick Haughey

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Baa-Ttling Sore Mouth In Sheep With Mathematical Modeling, David C. Elzinga, W. Christopher Strickland

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Multi-Model Approach To Understanding Growth, Reproduction, And Life History Strategies In Bromeliads, Erin N. Bodine

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using A Coupled Integral Projection Model To Investigate Interspecific Competition During An Invasion: An Application To Silver Carp (Hypophthalmichthys Molitrix) And Gizzard Shad (Dorosoma Cepedianum), James Peirce

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Distinguishing Community Assembly Through Functional Redundancy Models., Sandra A. Tsiorintsoa, Sharon Bewick, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Thoracoabdominal Asynchrony In A Virtual Preterm Infant: Computational Modeling And Analysis, Richard R. Foster, Bradford Smith, Laura Ellwein Fix

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Nutrient Driven Dynamics Of Ecosystem Diseases, Rebecca Everett

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Impacts On Malaria Transmission Of Altered Biogenic Amine Levels In {\It Anopheles} Mosquitoes: Insights From A Mathematical Model, Michael Robert

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Minimization Of Diet For Optimum Consumption Using Linear Programming, Nita Ngozi Ezekwem, Aditi Ghosh

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Single And Multiple Pacemaker Interaction In Jellyfish Locomotion, Alexander Hoover

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Gaff-Msis-Ledder: Agent-Based Modeling Of Tick Population Genetics, Holly Gaff

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Intracellular Transport And Filament Organization In Neurons, Maria-Veronica Ciocanel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Long-Distance Effects Of Predation, Henry Ogu

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Glenn: Natural Selection In Wolves Leads To Domesticated Dogs Predicted By Agent-Based Model Simulations, Alex Capaldi, David C. Elzinga

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Kadelka: Modularizing The Control Search For Biological Systems, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Ledder: Empowering Future Physicians: Modeling Disease Transmission With Netlogo To Encourage Mathematical Reasoning, Anne E. Yust

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.