Physical Sciences and Mathematics Commons^™

Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We develop some new results for a general class of transfer operators, as they are used in a construction of multi-resolutions. We then proceed to give explicit and concrete applications. We further discuss the need for such a constructive harmonic analysis/dynamical systems approach to fractals.

Creating A Computational Tool To Simulate Vibration Control For Piezoelectric Devices, Ahmet Ozkan Ozer, Emma J. Moore

Posters-at-the-Capitol

Piezoelectric materials have the unique ability to convert electrical energy to mechanical vibrations and vice versa. This project takes a stab to develop a reliable computational tool to simulate the vibration control of a novel “partial differential equation” model for a piezoelectric device, which is designed by integrating electric conducting piezoelectric layers constraining a viscoelastic layer to provide an active and lightweight intelligent structure. Controlling unwanted vibrations on piezoelectric devices (or harvesting energy from ambient vibrations) through piezoelectric layers has been the major focus in cutting-edge engineering applications such as ultrasonic welders and inchworms. The corresponding mathematical models for piezoelectric …

The Compensation For Few Clusters In Clustered Randomized Trials With Binary Outcomes, Lily Stalter

Mathematics & Statistics ETDs

Cluster randomized trials are increasingly popular in epidemiological and medical research. When analyzing the data from such studies it is imperative that the hierarchical structure of the data be taken into account. Multilevel logistic regression is used to analyze clustered data with binary outcomes. Previous literature shows that a greater number of clusters is more important than a large number of subjects per cluster. This paper investigates if it is possible to compensate for the increased bias found for parameter estimates when the number of clusters is decreased. A simulation study was conducted where the absolute percent relative bias for …

Divisibility In The Stone-Cech Compactification Of N, Salahddeen Khalifa

Dissertations

Let S a discrete semigroup. The associative operation on S extends naturally to an associative operation on βS,the Stone Cech compactification of S. This involves both topology and algebra and leads us to think how to extend properties and operations that are defined on S to βS. A good application of this is the extension of relations and divisibility operations that are defined on the discrete semigroup of natural numbers (N,.) with multiplication as operation to relations and divisibility operations that are defined on (βN,?) where (?) is the extension of the operation (.). In this research I studied extending …

Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe

Shared Knowledge Conference

Chemical Reaction Networks (CRNs) are a popular tool in the chemical sciences for providing a means of analyzing and modeling complex reaction systems. In recent years, CRNs have attracted attention in the field of molecular computing for their ability to simulate the components of a digital computer. The reactions within such networks may occur at several different scales relative to one another – at rates often too difficult to directly measure and analyze in a laboratory setting. To facilitate the construction and analysis of such networks, we propose a reduced order model for simulating such networks as a system of …

Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov

Shared Knowledge Conference

Numerical simulations of partial differential equations (PDE) are used to predict the behavior of complex physics phenomena when the real life experiments are expensive. Discretization of a PDE is the representation of the continuous problem as a discrete problem that can be solved on a computer. The discretization always introduces a certain inaccuracy caused by the numerical approximation. By increasing the computational cost of the numerical algorithm the solution can be computed more accurately. In the theory of numerical analysis this fact is called the convergence of the numerical algorithm. The idea behind high order methods is to improve the …

Translation Theorems For The Fourier-Feynman Transform On The Product Function Space C2 A,B, [0,T], Seung Jun Chang, Jae Gil Choi, David Skoug

Department of Mathematics: Faculty Publications

In this article, we establish the Cameron{Martin translation theo- rems for the analytic Fourier{Feynman transform of functionals on the product function space C2 a;b[0; T]. The function space Ca;b[0; T] is induced by the gener- alized Brownian motion process associated with continuous functions a(t) and b(t) on the time interval [0; T]. The process used here is nonstationary in time and is subject to a drift a(t). To study our translation theorem, we introduce a Fresnel-type class Fa;b A1;A2 of functionals on C2 a;b[0; T], which is a generaliza- tion of the Kallianpur and Bromley{Fresnel class FA1;A2 . We then …

Modeling Association In Microbial Communities With Clique Loginear Models, Adrian Dobra, Camilo Valdes, Dragana Ajdic, Bertrand S. Clarke, Jennifer Clarke

Department of Mathematics: Faculty Publications

There is a growing awareness of the important roles that microbial communities play in complex biological processes. Modern investigation of these often uses next generation sequencing of metagenomic samples to determine community composition. We propose a statistical technique based on clique loglinear models and Bayes model averaging to identify microbial components in a metagenomic sample at various taxonomic levels that have significant associations. We describe the model class, a stochastic search technique for model selection, and the calculation of estimates of posterior probabilities of interest. We demonstrate our approach using data from the Human Microbiome Project and from a study …

Development And Internal Validation Of An Aneurysm Rupture Probability Model Based On Patient Characteristics And Aneurysm Location, Morphology, And Hemodynamics, Felicitas J. Detmer, Bong Jae Chung, Fernando Mut, Martin Slawski, Farid Hamzei-Sichani, Christopher Putman, Carlos Jiménez, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Purpose: Unruptured cerebral aneurysms pose a dilemma for physicians who need to weigh the risk of a devastating subarachnoid hemorrhage against the risk of surgery or endovascular treatment and their complications when deciding on a treatment strategy. A prediction model could potentially support such treatment decisions. The aim of this study was to develop and internally validate a model for aneurysm rupture based on hemodynamic and geometric parameters, aneurysm location, and patient gender and age. Methods: Cross-sectional data from 1061 patients were used for image-based computational fluid dynamics and shape characterization of 1631 aneurysms for training an aneurysm rupture probability …

Hemodynamic Characteristics Of Stable And Unstable Vertebrobasilar Dolichoectatic And Fusiform Aneurysms, Waleed Brinjikji, Bong Jae Chung, Ding Yong-Hong, John T. Wald, Fernando Mut, Ramanathan Kadirvel, David F. Kallmes, Aymeric Rouchaud, Giuseppe Lanzino, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background and purpose Vertebrobasilar dolichoectatic and fusiform aneurysms (VBDAs) are known to have a poor natural history, with high rates of growth, rupture, and stroke. The purpose of this study was to identify hemodynamic characteristics that differ between VBDAs associated with growth, rupture, and stroke. Materials and methods VBDAs with CT angiography or MR angiography followed longitudinally without treatment were studied. Unstable aneurysms were defined as those that grew or ruptured during follow-up. Aneurysms associated with stroke were defined as those associated with posterior circulation infarct at follow-up. Baseline data, including demographics, comorbidities, and aneurysm morphology and size were collected. …

A Mathematical Framework On Machine Learning: Theory And Application, Bin Shi

FIU Electronic Theses and Dissertations

The dissertation addresses the research topics of machine learning outlined below. We developed the theory about traditional first-order algorithms from convex opti- mization and provide new insights in nonconvex objective functions from machine learning. Based on the theory analysis, we designed and developed new algorithms to overcome the difficulty of nonconvex objective and to accelerate the speed to obtain the desired result. In this thesis, we answer the two questions: (1) How to design a step size for gradient descent with random initialization? (2) Can we accelerate the current convex optimization algorithms and improve them into nonconvex objective? For application, …

On The Qualitative Theory Of The Nonlinear Parabolic P-Laplacian Type Reaction-Diffusion Equations, Roqia Abdullah Jeli

Theses and Dissertations

This dissertation presents full classification of the evolution of the interfaces and asymptotics of the local solution near the interfaces and at infinity for the nonlinear second order parabolic p-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration ut − ( |ux| p−2 ux ) x +buβ = 0, p > 1, β > 0. (1) Nonlinear partial differential equation (1) is a key model example expressing competition between nonlinear diffusion with gradient dependent diffusivity in either slow (p > 2) or fast (1 < p < 2) regime and nonlinear state dependent reaction (b > 0) or absorption (b < 0) forces. If interface is finite, it may expand, shrink, or remain stationary as a result of the competition of the diffusion and reaction terms near the interface, expressed in terms of the parameters p, β,sign b, and asymptotics of the initial function near its support. In the fast diffusion regime strong domination of the diffusion causes infinite speed of propagation and interfaces are absent. In all cases with finite interfaces we prove the explicit formula for the interface and the local solution with accuracy up to constant coefficients. We prove explicit asymptotics of the local solution at infinity in all cases with infinite speed of propagation. The methods of the proof are generaliii ization of the methods developed in U.G. Abdulla & J. King, SIAM J. Math. Anal., 32, 2(2000), 235-260; U.G. Abdulla, Nonlinear Analysis, 50, 4(2002), 541-560 and based on rescaling laws for the nonlinear PDE and blow-up techniques for the identification of the asymptotics of the solution near the interfaces, construction of barriers using special comparison theorems in irregular domains with characteristic boundary curves.

Signal Flow Graph Approach To Efficient Dst I-Iv Algorithms, Sirani M. Perera

Sirani Mututhanthrige Perera

In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST I-IV. The presented algorithms have low arithmetic cost compared to the known fast DST algorithms. Furthermore, the language of signal flow graph representation of digital structures is used to describe these efficient and recursive DST algorithms having (n􀀀1) points signal flow graph for DST-I and n points signal flow graphs for DST II-IV.

Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang

Electronic Thesis and Dissertation Repository

In this thesis, we apply bifurcation theory to study two biological systems. Main attention is focused on complex dynamical behaviors such as stability and bifurcation of limit cycles. Hopf bifurcation is particularly considered to show bistable or even tristable phenomenon which may occur in biological systems. Recurrence is also investigated to show that such complex behavior is common in biological systems.

First we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. Main attention is focused on the sta- bility and bifurcation of equilibria when the prey has a …

Quantitative Appraisal Of Non-Irrigated Cropland In South Dakota, Shelby Riggs

Honors Theses

This appraisal attempts to remove subjectivity from the appraisal process and replace it with quantitative analysis of known data to generate a fair market value of the subject property. Two methods of appraisal were used, the income approach and the comparable sales approach. For the income approach, I used the average cash rent for the region, the current property taxes for the subject property, and a capitalization rate based on Stokes' (2018) capitalization rate formula to arrive at my income-based valuation. For the comparable sales approach, I utilized Stokes' (2018) research in optimization modeling to estimate a market value for …

Ecology And Evolution Of Dispersal In Metapopulations, Jingjing Xu

Electronic Thesis and Dissertation Repository

Dispersal plays a key role in the persistence of metapopulations, as the balance between local extinction and colonization is affected by dispersal. Herein, I present three pieces of work related to dispersal. The first two are devoted to the ecological aspect of delayed dispersal in metapopulations. The first one focuses on how dispersal may disrupt the social structure on patches from which dispersers depart. Examinations of bifurcation diagrams of the dynamical system show a metapopulation will, in general, be either in the state of global extinction or persistence, and dispersal only has a limited effect on metapopulation persistence. The second …

Quantitative Validation Of Simulated Sea Ice Displacements, Bryan R. Mccormick

Mathematics & Statistics ETDs

Accurate simulations of Arctic sea ice are important for forecasting as well as for understanding the global climate. However, quantitative measures for simulation displacements are underutilized. We present five such measures proposed as being useful in the validation of simulated sea ice displacements. Using drifting buoy and satellite measurements of sea ice motion as observation, we apply the metrics in a comparison of observed displacements and predicted displacements from the Arctic sea ice simulation MPM\_ice. We find the metric scores are useful for comparing simulations and observations. The metrics also brought to light problems in the simulation MPM_ice, demonstrating their …

Cartan Triples, Allan P. Donsig, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

We introduce the class of Cartan triples as a generalization of the notion of a Car- tan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi’s theorem to this setting. This context contains that of Fulman’s generalization of Cartan MASAs and we discuss his generalization in an appendix.

Of Mice And Math: Four Models, Four Collaborations., Ami Radunskaya

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Novel Cell-Based Model Of The Generation And Maintenance Of The Shape And Structure Of The Multi-Layered Shoot Apical Meristem Of Arabidopsis Thaliana, Mikahl Banwarth-Kuhn, Ali Nematbakhsh, Stephen Snipes, Kevin Rodriguez, Carolyn Rasmussen, G. Venugopala Reddy, Mark Alber

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Mathematical Model Of The Inflammatory Response To Pathogen Challenge, Lester Caudill, Fiona Lynch

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analyzing Bigger Networks With Polynomial Algebra, Ian H. Dinwoodie

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Application Of Data Assimilation In Forecasting Of Influenza In The United States, Hannah Biegel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Student Research In Algebraic And Combinatorial Mathematical Biology, Raina Robeva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Calcium Signaling In The Sperm Head, Julie Simons, Lisa Fauci

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.