Applied Mathematics Commons^™

Cancer Quasispecies And Stem-Like Adaptive Aneuploidy, Domenico Napoletani, M. Signore, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we develop a theoretical frame to understand self-regulation of aneuploidy rate in cancer and stem cells. This is accomplished building upon quasispecies theory, by leaving its formal mathematical structure intact, but by drastically changing the meaning of its objects. In particular, we propose a novel definition of chromosomal master sequence, as a sequence of physically distinct whole or fragmented chromosomes, whose length is taken to be the sum of the copy numbers of each whole or fragmented chromosome. This fundamental change in the functional objects of quasispecies theory allows us to show that previously measured aneuploidy rates …

Automatic Elucidation Of Gpi Molecular Structures With Grid Computing Technology, Juan Clemente Aguilar Bonavides

Open Access Theses & Dissertations

Glycosylphosphatidylinositol (GPI)-anchored proteins are involved in many biological processes and are of medical importance. The identification and analysis of the entire collection of free and protein-linked GPIs within an organism (i.e., GPIomics) requires highly sensitive instruments. At present, liquid chromatography-tandem mass spectrometry (LC-MS/MS or -MSⁿ) is the most efficient laboratory technique for these tasks. As a typical MSⁿ experiment produces hundreds of thousands of spectra, the data analysis creates a major bottleneck in high-throughput GPIomic projects. Yet, no computational tool for characterizing the chemical structures of GPI is available to date. We propose a library-search algorithm to …

Modeling The Human Gait Phases Using Granular Computing, Melaku Ayenew Bogale

Open Access Theses & Dissertations

Gait analysis is applied for the provision of diagnosis, evaluation, and for the design of therapeutic intervention for subjects suffering from neurological disorders. The benefits accruing from gait analysis are well established. People with neurological disorders like mild traumatic brain injury, Cerebral Palsy and Multiple Sclerosis, suffer associated functional gait problems. The symptoms and sign of these gait deficits are different from subject to subject and even for the same subject at different stage of the disease. Identifying these gait related abnormalities helps in the treatment planning and rehabilitation process.

The dynamic behavior of gait parameters is cyclic and the …

Global Attracting Equilibria For Coupled Systems With Ceiling Density Dependence, Eric A. Eager, Mary Hebert, Elise Hellwig, Francisco Hernandez, Richard Rebarber, Brigitte Tenhumberg, Bryan Wigianto

School of Biological Sciences: Faculty Publications

In this paper, we present a system of two difference equations modeling the dynamics of a coupled population with two patches. Each patch can house only a limited number of individuals (called a carrying capacity) because resources like food and breeding sites are limited in each patch. We assume that the population in each patch is governed by a linear model until reaching a carrying capacity in each patch, resulting in map which is nonlinear and not sublinear. We analyze the global attractors of this model.

Population Models, Jessica Hauer

EWU Masters Thesis Collection

This thesis will examine mathematical interpretations of biological situations through the study of differential equations. It will first explore the interactions of the lynx and hare populations in Canada based on data retrieved by the Hudson Bay Company. The purpose of this study is to find a suitable mathematical model, namely that of a three-variable Lotka-Volterra system. Also, the paper will explore short-term infectious disease models as they relate to particular epidemics throughout history, including the Iowa Mumps outbreak of 1966 and the Bubonic Plaque. The thesis will then work to make sense of the rise and fall patterns in …

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Department of Mathematics: Dissertations, Theses, and Student Research

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to …

Robust Analysis Of Metabolic Pathways, Emily Gruber, Amy Ko, Michael Macgillvray, Miranda Sawyer

Mathematical Sciences Technical Reports (MSTR)

Flux Balance Analysis (FBA) is a widely used computational model for studying the metabolic pathways of cells and the role individual metabolites and reactions play in maintaining cell function. However, the successes of FBA have been limited by faulty biological assumptions and computational imperfections. We introduce Robust Analysis of Metabolic Pathways (RAMP) to provide a more theoretically sound and computationally accurate model of cellular metabolism. RAMP overcomes the faulty assumptions of traditional FBA by allowing deviation from steady-state and accounting for variability across a cellular culture. Computationally, RAMP more successfully predicts the lethality of gene knockouts and reduces degeneracy in …

Quantitative Reasoning And Sustainability, Corrine H. Taylor

Numeracy

Quantitative Reasoning and Sustainability have much in common. Both are complex, nuanced concepts with rather long definitions that have evolved over time. Both subjects are “everybody’s business” on college campuses, and must be approached in courses across the curriculum, not merely in one course on QR or in one course on Sustainability. The growing, wider presence of both QR and Sustainability on college campuses is due to their applicability in individuals’ personal, professional, and public lives. Moreover, QR and Sustainability support and enhance each other in and out of the classroom. Sustainability is an important, authentic, relevant context for lessons …

A Mathematical Study On The Dynamics Of An Eco-Epidemiological Model In The Presence Of Delay, T. K. Kar, Prasanta K. Mondal

Applications and Applied Mathematics: An International Journal (AAM)

In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical …

Derivation Of Hill's Equation From Scale Invariance, Andres Ortiz^, Vladik Kreinovich*

COURI Symposium Abstracts, Spring 2012

No abstract provided.

On The Global Stability Of A Generalized Cholera Epidemiological Model, Yuanji Cheng, Jin Wang, Xiuxiang Yang

Mathematics & Statistics Faculty Publications

In this paper, we conduct a careful global stability analysis for a generalized cholera epidemiological model originally proposed in [J. Wang and S. Liao, A generalized cholera model and epidemic/endemic analysis, J. Biol. Dyn. 6 (2012), pp. 568-589]. Cholera is a water-and food-borne infectious disease whose dynamics are complicated by the multiple interactions between the human host, the pathogen, and the environment. Using the geometric approach, we rigorously prove the endemic global stability for the cholera model in three-dimensional (when the pathogen component is a scalar) and four-dimensional (when the pathogen component is a vector) systems. This work unifies the …

The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The principle of linearized stability for size-structured population dynamics models is proved giving validity to previous stability results reported in, for example, El-Doma (2008-1). In particular, we show that if all the roots of the characteristic equation lie to the left of the imaginary axis then the steady state is locally exponentially stable, and on the other hand, if there is at least one root that lies to the right of the imaginary axis then the steady state is unstable. We also point out cases when there is resonance

Modelling Β2ar Regulation, Sharat J. Vayttaden

Dissertations and Theses (Open Access)

The β2 adrenergic receptor (β2AR) regulates smooth muscle relaxation in the vasculature and airways. Long- and Short-acting β-agonists (LABAs/SABAs) are widely used in treatment of chronic obstructive pulmonary disorder (COPD) and asthma. Despite their widespread clinical use we do not understand well the dominant β2AR regulatory pathways that are stimulated during therapy and bring about tachyphylaxis, which is the loss of drug effects. Thus, an understanding of how the β2AR responds to various β-agonists is crucial to their rational use. Towards that end we have developed deterministic models that explore the mechanism of drug- induced β2AR regulation. These mathematical models …

Use Of Optimal Control Models To Predict Treatment Time For Managing Tick-Borne Disease, Holly D. Gaff, Elsa Schaefer, Suzanne Lenhart

Biological Sciences Faculty Publications

Tick-borne diseases have been on the rise recently, and correspondingly, there is an increased interest in implementing control measures to decrease the risk. Optimal control provides an ideal tool to identify the best method for reducing risk while accounting for the associated costs. Using a previously published model, a variety of frameworks are assessed to identify the key factors influencing mitigation strategies. The level and duration of tick-reducing efforts are key metrics for understanding the successful reduction in tick-borne disease incidence. The results show that the punctuated nature of the tick's life history plays a critical role in reducing risk …

A Study On Facility Planning Using Discrete Event Simulation: Case Study Of A Grain Delivery Terminal, Sarah M. Asio

Department of Industrial and Management Systems Engineering: Dissertations, Theses, and Student Research

The application of traditional approaches to the design of efficient facilities can be tedious and time consuming when uncertainty and a number of constraints exist. Queuing models and mathematical programming techniques are not able to capture the complex interaction between resources, the environment and space constraints for dynamic stochastic processes. In the following study discrete event simulation is applied to the facility planning process for a grain delivery terminal. The discrete event simulation approach has been applied to studies such as capacity planning and facility layout for a gasoline station and evaluating the resource requirements for a manufacturing facility. To …

Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang

Mathematics & Statistics Faculty Publications

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

Shooting Neural Networks Algorithm For Solving Boundary Value Problems In Odes, Kais I. Ibraheem, Bashir M. Khalaf

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to use Neural Networks for solving boundary value problems (BVPs) in Ordinary Differential Equations (ODEs). The Neural networks use the principle of Back propagation. Five examples are considered to show effectiveness of using the shooting techniques and neural network for solving the BVPs in ODEs. The convergence properties of the technique, which depend on the convergence of the integration technique and accuracy of the interpolation technique are considered.

Modeling Human Immune Response To The Lyme Disease-Causing Bacteria, Yevhen Rutovytskyy

Honors Scholar Theses

The purpose of this project is to develop and analyze a mathematical model

for the pathogen-host interaction that occurs during early Lyme disease.

Based on the known biophysics of motility of Borrelia burgdorferi and a

simple model for the immune response, a PDE model was created which tracks

the time evolution of the concentrations of bacteria and activated immune

cells in the dermis. We assume that a tick bite inoculates a highly

localized population of bacteria into the dermis. These bacteria can

multiply and migrate. The diffusive nature of the migration is assumed and

modeled using the heat equation. Bacteria …

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan

HMC Senior Theses

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.

Preliminary Analysis Of An Agent-Based Model For A Tick-Borne Disease, Holly Gaff

Biological Sciences Faculty Publications

Ticks have a unique life history including a distinct set of life stages and a single blood meal per life stage. This makes tick-host interactions more complex from a mathematical perspective. In addition, any model of these interactions must involve a significant degree of stochasticity on the individual tick level. In an attempt to quantify these relationships, I have developed an individual-based model of the interactions between ticks and their hosts as well as the transmission of tick-borne disease between the two populations. The results from this model are compared with those from previously published differential equation based population models. …

Inter-Colony Comparison Of Diving Behavior Of An Arctic Top Predator: Implications For Warming In The Greenland Sea, Nina J. Karnovsky, Zachary W. Brown '07, Jorg Welcker, Ann M.A. Harding, Wojciech Walkusz, André Cavalcanti, Johanna S. Hardin, Alexander Kitaysky, Geir Gabrielsen, David Grémillet

Pomona Faculty Publications and Research

The goal of this study was to assess how diverse oceanographic conditions and prey communities affect the foraging behavior of little auks Alle alle. The Greenland Sea is characterized by 3 distinct water masses: (1) the East Greenland Current (EGC), which carries Arctic waters southward; (2) the Sørkapp Current (SC), which originates in the Arctic Ocean but flows north along the west coast of Spitsbergen; and (3) the West Spitsbergen Current (WSC), which carries warm Atlantic-derived water north. Each of these 3 water masses is characterized by a distinct mesozooplankton community. Little auks breeding adjacent to the EGC have …

Neural Spike Renormalization. Part I — Universal Number 1, Bo Deng

Department of Mathematics: Faculty Publications

For a class of circuit models for neurons, it has been shown that the transmembrane electrical potentials in spike bursts have an inverse correlation with the intra-cellular energy conversion: the fewer spikes per burst the more energetic each spike is. Here we demonstrate that as the per-spike energy goes down to zero, a universal constant to the bifurcation of spike-bursts emerges in a similar way as Feigenbaum’s constant does to the period-doubling bifurcation to chaos generation, and the new universal constant is the first natural number 1.

Cooper’S Hawk Nest Site Characteristics In The Pineywoods Region, Richard R. Schaefer, D. Craig Rudolph, Josh B. Pierce, Jesse F. Fagan

Faculty Publications

Early accounts describe the Cooper’s Hawk (Accipiter cooperi) as a species in decline in much of North America during the early twentieth century (Bent 1937), particularly when in close proximity to humans (Eaton 1914). This decreasing population trend continued to be recognized later in the century in both Texas (Oberholser 1974) and Louisiana (Lowery 1974). Shooting and trapping during the first half of the 1900s, and pesticide use (especially DDT) after World War II are suggested as primary causes of the decline (Henny and Wight 1972, Bednarz et al. 1990). The Migratory Bird Treaty Act of 1972 and the ban …

Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng

Department of Mathematics: Faculty Publications

Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

A Comprehensive Uncertainty Analysis And Method Of Geometric Calibration For A Circular Scanning Airborne Lidar, Michael Oliver Gonsalves

Dissertations

This dissertation describes an automated technique for ascertaining the values of the geometric calibration parameters of an airborne lidar. A least squares approach is employed that adjusts the point cloud to a single planar surface which could be either a narrow airport runway or a dynamic sea surface. Going beyond the customary three boresight angles, the proposed adjustment can determine up to eleven calibration parameters to a precision that renders a negligible contribution to the point cloud’s positional uncertainty.

Presently under development is the Coastal Zone Mapping and Imaging Lidar (CZMIL), which, unlike most contemporary systems that use oscillating mirrors …

Global Stability Of Worms In Computer Network, Bimal Kumar Mishra, Aditya Kumar Singh

Applications and Applied Mathematics: An International Journal (AAM)

An attempt has been made to show the impact of non-linearity of the worms through SIRS (susceptible – infectious – recovered - susceptible) and SEIRS (susceptible – exposed – infectious – recovered - susceptible) e-epidemic models in computer network. A very general form of non-linear incidence rate has been considered satisfying the worm propagating behavior in computer network. The concavity conditions with a non-linear incidence rate and under the constant population size assumption are shown to be stable. Such systems have either a unique and stable endemic equilibrium state or no endemic equilibrium state at all; in the latter case, …

Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely efficient to solve this complicated biological model.

Computational Biology, Harvey Greenberg, Allen Holder

Mathematical Sciences Technical Reports (MSTR)

Computational biology is an interdisciplinary field that applies the techniques of computer science, applied mathematics, and statistics to address biological questions. OR is also interdisciplinary and applies the same mathematical and computational sciences, but to decision-making problems. Both focus on developing mathematical models and designing algorithms to solve them. Models in computational biology vary in their biological domain and can range from the interactions of genes and proteins to the relationships among organisms and species.

G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg

Mathematical Sciences Technical Reports (MSTR)

We look at the Pure Parsimony problem and the Perfect Phylogeny Haplotyping problem. From the Pure Parsimony problem we consider structures of genotypes called g-lattices. These structures either provide solutions or give bounds to the pure parsimony problem. In particular, we investigate which of these structures supports an unrooted perfect phylogeny, a condition that adds biological interpretation. By understanding which g-lattices support an unrooted perfect phylogeny, we connect two of the standard biological inference rules used to recreate how genetic diversity propagates across generations.

A Spectral Approach To Protein Structure Alignment, Yosi Shibberu, Allen Holder

Mathematical Sciences Technical Reports (MSTR)

We present two algorithms that use spectral methods to align protein folds. One of the algorithms is suitable for database searches, the other for difficult alignments. We present computational results for 780 pairwise alignments used to classify 40 proteins as well as results for a separate set of 36 protein alignments used for comparison to four other alignment algorithms. We also provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach.