Applied Mathematics Commons^™

Zero-Inflated Longitudinal Mixture Model For Stochastic Radiographic Lung Compositional Change Following Radiotherapy Of Lung Cancer, Viviana A. Rodríguez Romero

Theses and Dissertations

Compositional data (CD) is mostly analyzed as relative data, using ratios of components, and log-ratio transformations to be able to use known multivariable statistical methods. Therefore, CD where some components equal zero represent a problem. Furthermore, when the data is measured longitudinally, observations are spatially related and appear to come from a mixture population, the analysis becomes highly complex. For this matter, a two-part model was proposed to deal with structural zeros in longitudinal CD using a mixed-effects model. Furthermore, the model has been extended to the case where the non-zero components of the vector might a two component mixture …

L1-Norm Regularized L1-Norm Best-Fit Line Problem, Xiao Ling, Paul Brooks

Graduate Research Posters

Background

Conventional Principal Component Analysis (PCA) is a widely used technique to reduce data dimension. PCA finds linear combinations of the original features capturing maximal variance of data via Singular Value Decomposition (SVD). However, SVD is sensitive to outliers, and often leads to high dimensional results. To address the issues, we propose a new method to estimate best-fit one-dimensional subspace, called l1-norm Regularized l1-norm.

Methods

In this article, we describe a method to fit a lower-dimensional subspace by approximate a non-linear, non-convex, non-smooth optimization problem called l1 regularized l1-norm Best- Fit Line problem; minimize a combination of the l1 error …

Modeling The Evolution Of Barrier Islands, Greg Robson

Theses and Dissertations

Barrier islands form off the shore of many coastal areas and serve as the first line of defense, protecting littoral communities against storms. To study the effects that climate change has on barrier islands, we use a cellular model of wind erosion, surface dynamics, beach dynamics, marsh dynamics, and vegetation development. We will show the inhibition of movement when vegetation is present.

Estimating Response Status In Sequential Multiple Assignment (Smar)-Like Trials, Keighly Bradbrook

Theses and Dissertations

Sequential, multiple assignment, randomized trials (SMARTs) allow investigators to develop and compare experimental treatment regimens in which individuals are successively randomized to different treatments based on some set of predetermined rules. The rules used to make decisions on when and how to switch treatments are based on a chosen set of tailoring variables. Although not always true, intermediate response is commonly used as the primary tailoring variable as it is often predictive of future treatment success. As such, successful implementation depends on identifying patients who respond to treatment, though in some situations such mechanisms may not exist. Further, patient-level covariates …

The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling

Theses and Dissertations

Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach.

Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network …

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

Biology and Medicine Through Mathematics Conference

No abstract provided.

Seasonal Variation Of Nutrient Loading In A Stoichiometric Producer-Consumer System, Lale Asik, Jackson Kulik, Kevin R. Long, Angela Peace

Biology and Medicine Through Mathematics Conference

No abstract provided.

Effects Of Predator Diversity On Optimal Communities For Prey Suppression, Amanda N. Laubmeier

Biology and Medicine Through Mathematics Conference

No abstract provided.

Investigating Drivers Of Dengue Emergence In Cordoba, Argentina, Michael Andrew Robert, Rachel Sippy, Anna M. Stewart-Ibarra, Rebecca C. Christofferson, Helen J. Wearing, Elizabet L. Estallo

Biology and Medicine Through Mathematics Conference

No abstract provided.

Analyzing The Structural Properties Of Pulmonary Arterial Networks, Megan J. Chambers

Biology and Medicine Through Mathematics Conference

No abstract provided.

Understanding The Role Of Macrophages In Lung Inflammation Through Mathematical Modeling, Sarah B. Minucci

Biology and Medicine Through Mathematics Conference

No abstract provided.

Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, Olusegun M. Otunuga, Anna Mummert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Stochastic Modeling Of Neuronal Transport In Various Cellular Geometries, Abhishek Choudhary Mr., Peter Kramer

Biology and Medicine Through Mathematics Conference

No abstract provided.

Quantifying The Contribution Of Environmental Pathways To The Transmission Of Clostridium Difficile, Lindsey R. Fox, Cara Sulyok, Judy Day, Cristina Lanzas, Suzanne Lenhart

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Pbpk Model Of Low-Concentration Vitamin D Supplementation In The Absence Of Sunlight, Colton Sawyer

Biology and Medicine Through Mathematics Conference

No abstract provided.

Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Spraying Strategies For Controlling Re-Infestation By Chagas Disease Vectors, Bismark Oduro, Winfried Just, Mario Grijalva

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Study Of Pair Formation Disease Models With A Two Phase Infection, Berlinda Rosa Batista

Biology and Medicine Through Mathematics Conference

No abstract provided.

Β Cell Network Dysfunction In Pancreatic Islets By Silencing Hub Cells, Janita Patwardhan, Bradford E. Peercy

Biology and Medicine Through Mathematics Conference

No abstract provided.

Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Pharmacokinetic Model Of Lead Absorption And Calcium Competitive Dynamics, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Immunofluorescence Image Feature Analysis And Clustering Pipeline For Distinguishing Epithelial-Mesenchymal Transition, Shreyas Hirway, Nadiah Hassan, Dr. Christopher Lemmon, Dr. Seth Weinberg

Biology and Medicine Through Mathematics Conference

No abstract provided.

Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

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

Mathematics and Applied Mathematics 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 …

Classification Of Symmetry Lie Algebras Of The Canonical Geodesic Equations Of Five-Dimensional Solvable Lie Algebras, Hassan Almusawa, Ryad Ghanam, Gerard Thompson

Mathematics and Applied Mathematics Publications

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A_{5,7}^{abc} to A_{18}^a. For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

Determination Of Optimal Parameter Estimates For Medical Interventions In Human Metabolism And Inflammation, Marcella Torres

Theses and Dissertations

In this work we have developed three ordinary differential equation models of biological systems: body mass change in response to exercise, immune system response to a general inflammatory stimulus, and the immune system response in atherosclerosis. The purpose of developing such computational tools is to test hypotheses about the underlying biological processes that drive system outcomes as well as possible real medical interventions. Therefore, we focus our analysis on understanding key interactions between model parameters and outcomes to deepen our understanding of these complex processes as a means to developing effective treatments in obesity, sarcopenia, and inflammatory diseases.

We develop …

Kings In The Direct Product Of Digraphs, Morgan Norge

Theses and Dissertations

A k-king in a digraph D is a vertex that can reach every other vertex in D by a directed path of length at most k. A king is a vertex that is a k-king for some k. We will look at kings in the direct product of digraphs and characterize a relationship between kings in the product and kings in the factors. This is a continuation of a project in which a similar characterization is found for the cartesian product of digraphs, the strong product of digraphs, and the lexicographic product of digraphs.

Transport Phenomena In Field Effect Transistors, Ryan M. Evans, Arvind Balijepalli, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Quantitative Electroencephalography For Detecting Concussions, Sara Krehbiel, Kathy Hoke, Joanna Wares

Biology and Medicine Through Mathematics Conference

No abstract provided.

Applications Of Multidimensional Time Model For Pdf To Model Permeability Of Plasma Membrane And Transcription Of Cytoplasmic Dna For Different Vaccination Trails., Michael Fundator

Biology and Medicine Through Mathematics Conference

No abstract provided.