Applied Mathematics Commons^™

Reconstructing 3d Reentrant Cardiac Electrical Wave Dynamics Using Data Assimilation, Elizabeth Cherry

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Analysis And Simulations Involving Chemotherapy And Surgery On Large Human Tumours Under A Suitable Cell-Kill Functional Response, Diego S. Rodrigues

Biology and Medicine Through Mathematics Conference

No abstract provided.

General Models For Ecological Drivers Of Poverty, Calistus Ngeh Ngonghala

Biology and Medicine Through Mathematics Conference

No abstract provided.

Force Generation And Contraction Of Random Actomyosin Bundles., Dietmar B. Oelz

Biology and Medicine Through Mathematics Conference

No abstract provided.

Influence Of Concurrency, Partner Choice, And Viral Suppression On Racial Disparity In The Prevalence Of Hiv Infected Women, Katharine Gurski, Kathleen Hoffman

Biology and Medicine Through Mathematics Conference

No abstract provided.

Movement And Dynamics Of Norway Rats In An Urban Landscape, Rosalyn Rael, Caz Taylor

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Lubricated Immersed Boundary Method In Two Dimensions, Thomas G. Fai

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Theoretical Model Of The Increase In Venous Oxygen Saturation Levels In Advanced Glaucoma Patients, Julia C. Arciero

Biology and Medicine Through Mathematics Conference

No abstract provided.

Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev

Biology and Medicine Through Mathematics Conference

No abstract provided.

Maximally Informative Next Experiments For Nonlinear Models, Reginald Mcgee

Biology and Medicine Through Mathematics Conference

No abstract provided.

Accuracy Of Wave Speeds Computed From The Dpg And Hdg Methods For Electromagnetic And Acoustic Waves, Nicole Michelle Olivares

Dissertations and Theses

We study two finite element methods for solving time-harmonic electromagnetic and acoustic problems: the discontinuous Petrov-Galerkin (DPG) method and the hybrid discontinuous Galerkin (HDG) method.

The DPG method for the Helmholtz equation is studied using a test space normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. We find that, as the parameter approaches zero, better results are obtained, under some circumstances. A dispersion analysis on the multiple interacting stencils that form the DPG method shows that the discrete wavenumbers of the method are complex, explaining …

Statistics In League Of Legends: Analyzing Runes For Last-Hitting, Brian M. Hook

Mathematics: Student Scholarship & Creative Works

While other sports have statisticians to evaluate players and their stats, in electronic sports there is a need for statisticians to evaluate different parts of the game. League of Legends is the most popular of ESports and is the focus of this discussion. The mechanic of focus here is runes which give boosts to the players stats in-game like being able to do extra damage. We will be finding the effectiveness of these runes by looking at gold efficiency, help with last hitting, and extra damage dealt through the use of Python.

A General Framework Of Large-Scale Convex Optimization Using Jensen Surrogates And Acceleration Techniques, Soysal Degirmenci

McKelvey School of Engineering Graduate Student Theses & Dissertations

In a world where data rates are growing faster than computing power, algorithmic acceleration based on developments in mathematical optimization plays a crucial role in narrowing the gap between the two. As the scale of optimization problems in many fields is getting larger, we need faster optimization methods that not only work well in theory, but also work well in practice by exploiting underlying state-of-the-art computing technology.

In this document, we introduce a unified framework of large-scale convex optimization using Jensen surrogates, an iterative optimization method that has been used in different fields since the 1970s. After this general treatment, …

Introducing Complex Systems Analysis In High School Mathematics Using System Dynamics Modeling: A Potential Game-Changer For Mathematics Instruction, Diana Marie Fisher

Dissertations and Theses

Complex systems abound on this planet, in the composition of the human body, in ecosystems, in social interaction, in political decision-making, and more. Analytical methods allowing us to better understand how these systems operate and, consequently, to have a chance to intervene and change the undesirable behavior of some of the more pernicious systems have developed and continue to be enhanced via quickly changing technology. Some of these analytical methods are accessible by pre-college students, but have not been widely used at that level of education. Jay Forrester, the founder of one of the methodologies, System Dynamics (SD), used to …

Investigating How Calcium Diffusion Affects Metabolic Oscillations And Synchronization Of Pancreatic Beta Cells, George Eskandar, Jennifer Houser, Ellen Prochaska, Jessica Wojtkiewicz, Teresa Lebair, Bradford E. Peercy, Margaret Watts, Arthur Sherman

Spora: A Journal of Biomathematics

Diabetes is a disease characterized by improper concentrations of blood glucose due to irregular insulin production or sensitivity. Coupled in islets of Langerhans within the pancreas, β-cells are responsible for the production and regulation of insulin based on changes in glucose levels. Using the Dual Oscillator Model (DOM), we will examine how calcium handling between individual pancreatic β-cells affects the synchronization of metabolic oscillations within electrically coupled islets. Calcium permeability was implemented into the DOM, and numerical solutions of the system were obtained via MATLAB using a modified ordinary differential equation solver for stiff systems and the Automatic Differentiation for …

Tau And Aβ Imaging, Csf Measures, And Cognition In Alzheimer's Disease, Matthew R. Brier, Brian Gordon, Karl Friedrichsen, John E. Mccarthy, Ari Stern, Jon Christensen, Christopher Owen, Patricia Aldea, Yi Su, Jason Hassenstab, Nigel J. Cairns, David M. Holtzman, Anne M. Fagan, John C. Morris, Tammie L.S. Benzinger, Beau M. Ances

Mathematics Faculty Research

Alzheimer’s disease (AD) is characterized by two molecular pathologies: cerebral β-amyloidosis in the form of β-amyloid (Aβ) plaques and tauopathy in the form of neurofibrillary tangles, neuritic plaques, and neuropil threads. Until recently, only Aβ could be studied in humans using positron emission tomography (PET) imaging owing to a lack of tau PET imaging agents. Clinical pathological studies have linked tau pathology closely to the onset and progression of cognitive symptoms in patients with AD. We report PET imaging of tau and Aβ in a cohort of cognitively normal older adults and those with mild AD. Multivariate analyses identified unique …

Discrete Stability Of Dpg Methods, Ammar Harb

Dissertations and Theses

This dissertation presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, for triangular meshes, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree. Finally, for rectangular meshes, the test space is …

Nonlinear Dynamics Of Filaments In Free Space And Fluids, Victoria Kelley

Senior Honors Projects, 2010-2019

The purpose of this paper is to study a straight rod, held at both ends, with a known twist and tension or compression. We study the stability of this steady state when the system is dominated either by inertia or drag. In order to do this, we first replicate the work of Goriely and Tabor to look at the case with inertia, without drag. After conducting the analysis for that case, we then apply their framework to perform a linear stability analysis of a model that is without inertia, but with hydrodynamic drag. Our motivation is the study of locomotion …

A Computational Investigation Of Large Gaps In Contingency Tables, Noah J. Watson

Senior Honors Projects, 2010-2019

Integer programming can be used to find upper and lower bounds on the cells of a multi-dimensional contingency table using the information from the released margins. The linear relaxation of these programs also provides bounds and the discrepancy between these bounds, the integer programming gap, can be large. While the more notable examples of large gaps have been shown to be rare, here we provide some results on the rarity of large gaps on small tables.