Applied Mathematics Commons^™

Characterization Of Biological Particles Using An Integrated Hyperspectral Imaging And Machine Learning, Kaeul Lim, Arezoo Ardekani

Graduate Industrial Research Symposium

Hyperspectral imaging (HSI) is a promising modality in medicine with many potential applications. This study focuses on developing a label-free lipid nanoparticle characterization method using a convolutional neural network (CNN) analysis of HSI images. The HSI data, hypercube, consists of a series of images acquired at different wavelengths for the same field of view, providing continuous spectra information for each pixel. Three distinct liposome samples were collected for analysis. Advanced image preprocessing and classification methods for HSI data were developed to differentiate liposomes based on their material compositions. Our machine learning-based classification method was able to distinguish different liposome types …

Characterizing Linearizable Qaps By The Level-1 Reformulation-Linearization Technique, Lucas Waddell, Warren Adams

Faculty Journal Articles

The quadratic assignment problem (QAP) is an extremely challenging NP-hard combinatorial optimization program. Due to its difficulty, a research emphasis has been to identify special cases that are polynomially solvable. Included within this emphasis are instances which are linearizable; that is, which can be rewritten as a linear assignment problem having the property that the objective function value is preserved at all feasible solutions. Various known sufficient conditions for identifying linearizable instances have been explained in terms of the continuous relaxation of a weakened version of the level-1 reformulation-linearization-technique (RLT) form that does not enforce nonnegativity on a subset …

Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

The Journal of Purdue Undergraduate Research

No abstract provided.

Compartmental Modeling For The Neophyte: An Application Of Berkeley Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans

Spora: A Journal of Biomathematics

Compartmental modeling serves as a necessary framework in many fields, especially biomathematics and ecology. This article introduces readers to a user-friendly approach to constructing compartmental models and solving the resulting systems of differential equations to simulate real-world applications. The platform used is Berkeley Madonna, a software package that has an intuitive graphical interface which empowers users—even those with limited mathematical and programming backgrounds—to focus on modeling concepts rather than mathematical or programming intricacies. This makes Berkeley Madonna an ideal platform for students, educators, and researchers.

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

Mansoura Engineering Journal

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

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 …

Adaptation Reshapes The Distribution Of Fitness Effects, Diego Tenoch Morales Lopez

Electronic Thesis and Dissertation Repository

The process of adaptation has been of interest since the XIX century, when Darwin first proposed the idea of natural selection. Since then, there has been a myriad of theoretical and empirical works that have expanded the field. From the many evolutionary insights these works have produced, a foundational idea is that spontaneous mutations in the genome of organisms can produce changes to their reproductive success that might confer an advantage for the mutant organisms with respect to their peers. Therefore, mutations drive adaptive evolution by virtue of their heritable effects on fitness. Empirical measures of the distribution of these …

Nonsmooth Epidemic Models With Evolutionary Game Theory, Cameron Morin

Electronic Theses and Dissertations

This thesis explores the utilization of game theory and nonsmooth functions to enhance the accuracy of epidemiological simulations. Traditional sensitivity analysis encounters difficulties when dealing with nondifferentiable points in nonsmooth functions. However, by incorporating recent advancements in nonsmooth analysis, sensitivity analysis techniques have been adapted to accommodate these complex functions. In pursuit of more accurate simulations, evolutionary game theory, primarily the replicator equation, is introduced, modeling individuals’ decision making processes when observing others’ choices. The SEIR model is explored in depth, and additional complexities are incorporated, leading to the creation of an expanded SEIR model, the Be-SEIMR model.

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

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 …

Statistical Analysis Of Health Habits For Incoming College Students, Wendy Isamara Lizarraga Noriega

Electronic Theses, Projects, and Dissertations

Health habits among college students are commonly overseen, especially for students transitioning from high school right into college. These students are becoming independent young adults, and learning how to adapt to a different scenery when it comes to their learning environment. As these young adults transition into college, this is the perfect time for the students to become more vulnerable and comfortable with their independence, and their weight begins to fluctuate. Many variables come into consideration when increasing weight as an incoming first-year student. Students are more likely to live alone, get a job, and rely on fast food and …

Long-Acting Cabotegravir And The Emergence Of Drug-Resistant Hiv, Katharine Gurski

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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.

Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Exploring Disease Spread Patterns In A Heterogeneous Environment: The Impact Of Travel Restrictions, Seoyun Choe

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.

A Game-Theoretic Analysis Of Covid-19 Dynamics With Self-Isolation And Vaccination Behavior In Heterogeneous Populations, Igor V. Erovenko

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Kondrashov: Teaching Computer Programming To Mathematics Students, Glenn Ledder

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Game-Theoretic Analysis Of Covid-19 Dynamics With Self-Isolation And Vaccination Behavior, Liam Gilmore-Greiss, Gleb Gribovskii

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.

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.

Lnksc Method On Pde-Constrained Optimization For Mcf-7 Breast Cancer Cell Growth Predictions And Treatment Response With Gold Nanoparticles, Widodo Samyono, Shakhawat Bhuiyan

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Mathematical Model Of The Disruption Of Glucose Homeostasis In Cancer Patients, Peter Hinow

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Ledder: Automated Data Analysis In Netlogo, Glenn Ledder

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Overwash Processes On Barrier Islands, Beth Thomas

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Mathematical Model For Wound Healing In The Reef-Building Coral Pocillopora Damicornis, Quintessa Hay, Luke Gardner, Eunice Pak, Liza M. Roger, Rebecca A. Segal, Nastassja A. Lewinski, Angela M. Reynolds, Anna Shaw

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Model Of Competing Nest Founding Strategies By Queen Harvester Ant Pogonomyremex Californicus, Tamantha Pizarro, Yun Kang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling Of The Impact Of Lobbying On Climate Policy, Andrew Jacoby, Claire Hannah, James Hutchinson, Jasmine Narehood, Aditi Ghosh, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Compartmental Modeling For The Neophyte: An Application Of Berkeley-Madonna, Olcay Akman, Siddharth Bhumpelli, Cody Cline, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Study Of Behaviour Change And Impact On Infectious Disease Dynamics By Mathematical Models, Tianyu Cheng

Electronic Thesis and Dissertation Repository

This thesis uses mathematical models to study human behaviour changes' effects on infectious disease transmission dynamics. It centers on two main topics. The first concerns how behaviour response evolves during epidemics and the effects of adaptive precaution behaviour on epidemics. The second topic is how to build general framework models incorporating human behaviour response in epidemiological modelling.

In the first project, based on the fact that a fraction of the epidemiologically susceptible population is actually susceptible due to precautions, we present a novel perspective on understanding the infection force, incorporating human protection behaviours. This view explains many existing infection force …