Applied Mathematics Commons^™

Applications Of Incomplete Gamma Functions To The Incomplete Normal Distribution, Eric S. Watson

Physics & Astronomy Faculty publications

This paper gives a derivation of a relationship that can be used to estimate the area under a Normal Distribution through the use of Incomplete Gamma Functions.

Spreading Speeds And Traveling Waves In Some Population Models., Quancheng Meng

Electronic Theses and Dissertations

Virtually every ecosystem has been invaded by exotic organisms with potentially drastic consequences for the native fauna or flora. Studying the forms and rates of invading species has been an important topic in spatial ecology. We investigate two two-species competition models with Allee effects in the forms of reaction-diffusion equations and integro-difference equations. We discuss the spatial transitions from a mono-culture equilibrium to a coexistence equilibrium or a different mono-culture equilibrium in these models. We provide formulas for the spreading speeds based on the linear determinacy and show the results on the existence of traveling waves. We also study a …

Nonlinear Partial Differential Equations, Their Solutions, And Properties, Prasanna Bandara

Boise State University Theses and Dissertations

Although valuable understanding of real-world phenomena can be gained experimentally, it is often the case that experimental investigations can be found to be limited by financial, ethical or other constraints making such an approach impractical or, in some cases, even impossible. To nevertheless understand and make predictions of the natural world around us, countless processes encountered in the physical and biological sciences, engineering, economics and medicine can be efficiently described by means of mathematical models written in terms of ordinary or/and partial differential equations or their systems. Fundamental questions that arise in the modeling process need care that relies on …

An Economic Regression Model To Predict Market Movements, Timothy A. Smith, Andrew Hawkins

Publications

In finance, multiple linear regression models are frequently used to determine the value of an asset based on its underlying traits. We built a regression model to predict the value of the S&P 500 based on economic indicators of gross domestic product, money supply, produce price and consumer price indices. Correlation between the error in this regression model and the S&P’s volatility index (VIX) provides an efficient way to predict when large changes in the price of the S&P 500 may occur. As the true value of the S&P 500 deviates from the predicted value, obtained by the regression model, …

On The Relationship Between Two Notions Of Compatibility For Bi-Hamiltonian Systems, Manuele Santoprete

Mathematics Faculty Publications

Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fass`o and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector fields tangent to the leaves of a Lagrangian foliation. …

Stochastic Models For Plant Microtubule Self-Organization And Structure, Ezgi Can Eren, Ram Dixit, Natarajan Gautam

Biology Faculty Research

One of the key enablers of shape and growth in plant cells is the cortical microtubule (CMT) system, which is a polymer array that forms an appropriately-structured scaffolding in each cell. Plant biologists have shown that stochastic dynamics and simple rules of interactions between CMTs can lead to a coaligned CMT array structure. However, the mechanisms and conditions that cause CMT arrays to become organized are not well understood. It is prohibitively time-consuming to use actual plants to study the effect of various genetic mutations and environmental conditions on CMT self-organization. In fact, even computer simulations with multiple replications are …

Existence Of Homoclinic Solutions For Second Order Difference Equations With P-Laplacian, John R. Graef, Lingju Kong, Min Wang

College of Science & Mathematics Departmental Research

Using the variational method and critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation described in the paper.

Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting entails …

From Subcompact To Domain Representable, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

No abstract provided.

Partial Covariance Based Functional Connectivity Computation Using Ledoit-Wolf Covariance Regularization, Matthew R. Brier, Anish Mitra, John E. Mccarthy, Beau M. Ances, Abraham Z. Snyder

Mathematics Faculty Research

Highlights •We use the well characterized matrix regularization technique described by Ledoit and Wolf to calculate high dimensional partial correlations in fMRI data. •Using this approach we demonstrate that partial correlations reveal RSN structure suggesting that RSNs are defined by widely and uniquely shared variance. •Partial correlation functional connectivity is sensitive to changes in brain state indicating that they contain functional information. Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a …

Local And Distributed Pib Accumulation Associated With Development Of Preclinical Alzheimer's Disease, Matthew R. Brier, John E. Mccarthy, Tammie L.S. Benzinger, Ari Stern, Yi Su, Karl A. Friedrichsen, John C. Morris, Beau M. Ances, Andrei G. Vlassenko

Mathematics Faculty Research

Amyloid-beta plaques are a hallmark of Alzheimer's disease (AD) that can be assessed by amyloid imaging (e.g., Pittsburgh B compound [PiB]) and summarized as a scalar value. Summary values may have clinical utility but are an average over many regions of interest, potentially obscuring important topography. This study investigates the longitudinal evolution of amyloid topographies in cognitively normal older adults who had normal (N = 131) or abnormal (N = 26) PiB scans at baseline. At 3 years follow-up, 16 participants with a previously normal PiB scan had conversion to PiB scans consistent with preclinical AD. We investigated the multivariate …

Algebraic Complexity Theory, Jerzy Weyman

Dalrymple Lecture Series

I will discuss the basic notions related to the complexity theory. The classes of P and NP problems will be defined, with examples given. Besides discussing the statements of the problems, I will talk about the effectiveness of algorithms used in linear algebra (multiplying matrices and solving the systems of linear equations). No previous knowledge of complexity theory will be assumed, however some knowledge of linear algebra (matrices and their multiplication) will be needed.

A Nonlinear Splitting Algorithm For Systems Of Partial Differential Equations With Self-Diffusion, Matthew Beauregard, Joshua L. Padgett, Rana D. Parshad

Faculty Publications

Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular, self-diffusion is a nonlinear term that models overcrowding of a particular species. The nonlinearity complicates attempts to construct efficient and accurate numerical approximations of the underlying systems of equations. In this paper, a new nonlinear splitting algorithm is designed for a partial differential equation that incorporates self diffusion. We present a general model that incorporates self-diffusion and develop a numerical approximation. The numerical analysis of the approximation provides criteria for …

Geometric Approach To Convex Subdifferential Calculus, Boris S. Mordukhovich, Nguyen Mau Nam

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic results of convex subdifferential calculus in full generality and also derive new results of convex analysis concerning optimal value/marginal functions, normals to inverse images of sets under set-valued mappings, calculus rules for coderivatives of single-valued and set-valued mappings, and calculating coderivatives of solution maps to parameterized generalized equations governed by set-valued mappings with convex graphs.

Using An Agent-Based Model To Study The Effect Of Reproductive Skew On Mongoose Populations, Stacy Lee Mowry

Theses and Dissertations

Reproductive skew is the name given to the unequal partitioning of breeding

within social groups. Within these groups a mating hierarchy emerges wherein one dominant mating pair holds an unproportional majority of the group's reproductive benefit, while other members mate infrequently, yet allocate energy and resources toward the offspring of the dominant group members. In this paper, we use an agent-based model, which mimics dwarf and banded mongoose populations, to investigate how reproductive skew aftects the speed natural selection, and thus how reproductive skew affects fitness. The results of the model show that due to the geometric structure of skewed …

Congruent Visual Speech Enhances Entrainment To Continuous Auditory Speech In Noise-Free Conditions, Michael Crosse, John S. Butler, Edmumd Lalor

Articles

Congruent audiovisual speech enhances our ability to comprehend a speaker, even in noise-free conditions. When incongruent auditory and visual information is presented concurrently, it can hinder a listener’s perception and even cause him or her to perceive information that was not presented in either modality. Efforts to investigate the neural basis of these effects have often focused on the special case of discrete audiovisual syllables that are spatially and temporally congruent, with less work done on the case of natural, continuous speech. Recent electrophysiological studies have demonstrated that cortical response measures to continuous auditory speech can be easily obtained using …

Local Characterization Of A Class Of Ruled Hypersurfaces In C2, Michael Bolt

University Faculty Publications and Creative Works

Let M3⊂C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-hermitian part of the second fundamental form transforms under fractional linear transformation. The surfaces for which these forms are constant multiples of each other were identified in previous work, but when the constant had unit modulus there was a global requirement. Here we give a local characterization of hypersurfaces for which the constant has unit modulus.

Wright State University Math And Statistics Department History, Joanne Dombrowski, David Miller

Mathematics and Statistics Faculty Publications

No abstract provided.

Comparison Of Fecal Microbiota In Children With Autism Spectrum Disorders And Neurotypical Siblings In The Simons Simplex Collection, Joshua S. Son, Ling J. Zheng, Leahana M. Rowehl, Ellen Li, Xinyu Tian, Yuanhao Zhang, Wei Zhu, Leighann Litcher-Kelly, Kenneth D. Gadow, Grace Gathungu, Charles E. Robertson, Diana Ir, Daniel N. Frank

Department of Applied Mathematics & Statistics Faculty Publications

In order to assess potential associations between autism spectrum disorder (ASD) phenotype, functional GI disorders and fecal microbiota, we recruited simplex families, which had only a single ASD proband and neurotypical (NT) siblings, through the Simons Simplex Community at the Interactive Autism Network (SSC@IAN). Fecal samples and metadata related to functional GI disorders and diet were collected from ASD probands and NT siblings of ASD probands (age 7–14). Functional gastrointestinal disorders (FGID) were assessed using the parent-completed ROME III questionnaire for pediatric FGIDs, and problem behaviors were assessed using the Child Behavior Check List (CBCL). Targeted quantitative polymerase chain reaction …

Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings, A. Berezovski, J. Engelbrecht, Mihhail Berezovski

Publications

Elastic wave propagation through diffraction gratings is studied numerically in the plane strain setting. The interaction of the waves with periodically ordered elastic inclusions leads to a self-imaging Talbot effect for the wavelength equal or close to the grating size. The energy localization is observed at the vicinity of inclusions in the case of elastic gratings. Such a localization is absent in the case of rigid gratings.