Applied Mathematics Commons^™

Code For "Noise-Enhanced Coding In Phasic Neuron Spike Trains", Cheng Ly, Brent D. Doiron

Statistical Sciences and Operations Research Data

This zip file contains Matlab scripts and ode (XPP) files to calculate the statistics of the models in "Noise-Enhanced Coding in Phasic Neuron Spike Trains". This article is published in PLoS ONE.

A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson

Mathematics and Applied Mathematics Publications

We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …

A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly

Mathematics and Applied Mathematics Publications

Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique …

Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

Theses and Dissertations--Mathematics

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

On Some Impulse Control Problems With Constraint, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The impulse control of a Markov–Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified.

Approximate Statistical Solutions To The Forensic Identification Of Source Problem, Danica M. Ommen

Electronic Theses and Dissertations

Currently in forensic science, the statistical methods for solving the identification of source problems are inherently subjective and generally ad-hoc. The formal Bayesian decision framework provides the most statistically rigorous foundation for these problems to date. However, computing a solution under this framework, which relies on a Bayes Factor, tends to be computationally intensive and highly sensitive to the subjective choice of prior distributions for the parameters. Therefore, this dissertation aims to develop statistical solutions to the forensic identification of source problems which are less subjective, but which retain the statistical rigor of the Bayesian solution. First, this dissertation focuses …

C.V. - Wojciech Budzianowski, Wojciech M. Budzianowski

Wojciech Budzianowski

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Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Solitary Wave Solution Of Flat Surface Internal Geophysical Waves With Vorticity, Alan Compelli

Conference papers

A fluid system bounded by a flat bottom and a flat surface with an internal wave and depth-dependent current is con-sidered. The Hamiltonian of the system is presented and the dynamics of the system are discussed. A long-wave regime is then considered and extended to produce a KdV approximation. Finally, a solitary wave solution is obtained.

A Mathematical System For Human Implantable Wound Model Studies, Salomonsky Paul-Michael, Rebecca Segal

Mathematics and Applied Mathematics Publications

In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between …

Management Of Invasive Allee Species, David Chan, C. M. Kent, D. M. Johnson

Mathematics and Applied Mathematics Publications

In this study, we use a discrete, two-patch population model of an Allee species to examine different methods in managing invasions. We first analytically examine the model to show the presence of the strong Allee effect, and then we numerically explore the model to test the effectiveness of different management strategies. As expected invasion is facilitated by lower Allee thresholds, greater carrying capacities and greater proportions of dispersers. These effects are interacting, however, and moderated by population growth rate. Using the gypsy moth as an example species, we demonstrate that the effectiveness of different invasion management strategies is context-dependent, combining …

Eigenvector Centrality: Illustrations Supporting The Utility Of Extracting More Than One Eigenvector To Obtain Additional Insights Into Networks And Interdependent Structures, Dawn Iacobucci, Rebecca Mcbride, Deidre L. Popovich

University Faculty Publications and Creative Works

Among the many centrality indices used to detect structures of actors’ positions in networks is the use of the first eigenvector of an adjacency matrix that captures the connections among the actors. This research considers the seeming pervasive current practice of using only the first eigenvector. It is shows that, as in other statistical applications of eigenvectors, subsequent vectors can also contain illuminating information. Several small examples, and Freeman’s EIES network, are used to illustrate that while the first eigenvector is certainly informative, the second (and subsequent) eigenvector(s) can also be equally tractable and informative.

Weihrauch Reducibility And Finite-Dimensional Subspaces, Sean Sovine

Theses, Dissertations and Capstones

In this thesis we study several principles involving subspaces and decompositions of vector spaces, matroids, and graphs from the perspective of Weihrauch reducibility. We study the problem of decomposing a countable vector space or countable matroid into 1-dimensional subspaces. We also study the problem of producing a finite-dimensional or 1-dimensional subspace of a countable vector space, and related problems for producing finite-dimensional subspaces of a countable matroid. This extends work in the reverse mathematics setting by Downey, Hirschfeldt, Kach, Lempp, Mileti, and Montalb´an (2007) and recent work of Hirst and Mummert (2017). Finally, we study the problem of producing a …

High Performance Techniques Applied In Partial Differential Equations Library, Shilei Lin

All College Thesis Program, 2016-2019

This thesis explores various Trilinos packages to determine a method for updating the deal.ii library, which specializes in solving partial differential equations by finite element methods. It begins with introducing related concepts and general goals, followed by exploring computational and mathematical methods which are analytical solutions of one-dimensional Boussinesq equations and developing newer prototypes for solvers in deal.ii based on Trilinos packages. After demonstrating the methods, it indicates the reducing solving time in newer prototypes. Based on results from the prototype, similar methods are applied to update the deal.ii library. In the end, a testing program is exploited to demonstrate …

A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

Theses and Dissertations--Mechanical Engineering

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model is …

2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics, Otterbein Office Of Graduate Programs

Graduate School

Graduate Handbook on the MAEM Program at Otterbein University.

Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2

Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of (G, B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph without a (2Ct , ∅)-minor is at most n(Γ, t). Other results pertaining to contrabalanced biased graphs are presented as well as an analogue …

The Effects Of Disturbance And Species Specific Interactions On Diversity In An Agent Based Forest Simulation, Matthew E. Mills

Theses and Dissertations

In ecology literature, there is much data which suggests that conspecific negative density dependence (CNDD) and abiotic disturbances increase biodiversity in forests. This thesis elucidates the notion that not only do these two forces increase diversity, but they may also interact with one another in order to achieve higher levels of biodiversity. Abiotic disturbances, like fires and hurricanes, can indirectly impact conspecific effects because when these forces remove individuals from the landscape, the role of the conspecific effects will change. The interaction of these two factors in biodiversity are explored in an agent based forest simulation through a resource surface. …

Mathematical Models Of The Inflammatory Response In The Lungs, Sarah B. Minucci

Theses and Dissertations

Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, proteins, and cytokines, recommendations for treatment with antibiotics, and a foundation for more …