Applied Mathematics Commons^™

A New Hybrid Method For Solving Nonlinear Fractional Differential Equations, R. Delpasand, M. M. Hosseini, F. M. Maalek Ghaini

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, numerical solution of initial and boundary value problems for nonlinear fractional differential equations is considered by pseudospectral method. In order to avoid solving systems of nonlinear equations resulting from the method, the residual function of the problem is constructed, as well as a suggested unconstrained optimization model solved by PSOGSA algorithm. Furthermore, the research inspects and discusses the spectral accuracy of Chebyshev polynomials in the approximation theory. The following scheme is tested for a number of prominent examples, and the obtained results demonstrate the accuracy and efficiency of the proposed method.

Fractional Order Thermoelastic Deflection In A Thin Circular Plate, J. J. Tripathi, S. D. Warbhe, K. C. Deshmukh, J. Verma

Applications and Applied Mathematics: An International Journal (AAM)

In this work, a quasi-static uncoupled theory of thermoelasticity based on time fractional heat conduction equation is used to model a thin circular plate, whose lower surface is maintained at zero temperature whereas the upper surface is insulated. The edge of the circular plate is fixed and clamped. Integral transform technique is used to derive the analytical solutions in the physi-cal domain. The numerical results for temperature distributions and thermal deflection are com-puted and represented graphically for Copper material.

Radial Basis Function Differential Quadrature Method For The Numerical Solution Of Partial Differential Equations, Daniel Watson

Dissertations

In the numerical solution of partial differential equations (PDEs), there is a need for solving large scale problems. The Radial Basis Function Differential Quadrature (RBFDQ) method and local RBF-DQ method are applied for the solutions of boundary value problems in annular domains governed by the Poisson equation, inhomogeneous biharmonic equation, and the inhomogeneous Cauchy-Navier equations of elasticity. By choosing the collocation points properly, linear systems can be obtained so that the coefficient matrices have block circulant structures. The resulting systems can be efficiently solved using matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs). For the local RBFDQ method, the …

Graph Analytics Methods In Feature Engineering, Theophilus Siameh

Electronic Theses and Dissertations

High-dimensional data sets can be difficult to visualize and analyze, while data in low-dimensional space tend to be more accessible. In order to aid visualization of the underlying structure of a dataset, the dimension of the dataset is reduced. The simplest approach to accomplish this task of dimensionality reduction is by a random projection of the data. Even though this approach allows some degree of visualization of the underlying structure, it is possible to lose more interesting underlying structure within the data. In order to address this concern, various supervised and unsupervised linear dimensionality reduction algorithms have been designed, such …

Making Models With Bayes, Pilar Olid

Electronic Theses, Projects, and Dissertations

Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects …

Neutrosophic Hough Transform, Florentin Smarandache, Umit Budak, Yanhui Guo, Abdulkadir Sengur

Branch Mathematics and Statistics Faculty and Staff Publications

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its …

On The Existence Of Bogdanov-Takens Bifurcations, Zachary Deskin

Graduate Theses/Dissertations

In bifurcation theory, there is a theorem (called Sotomayor's Theorem) which proves the existence of one of three possible bifurcations of a given system, provided that certain conditions of the system are satisfied. It turns out that there is a "similar" theorem for proving the existence of what is referred to as a Bogdanov-Takens bifurcation. The author is only aware of one reference that has the proof of this theorem. However, most of the details were left out of the proof. The contribution of this thesis is to provide the details of the proof on the existence of Bogdanov-Takens bifurcations.

Stochastic Analysis Of A Mammalian Circadian Clock Model: Small Protein Number Effects, David W. Morgens, Blerta Shtylla

Spora: A Journal of Biomathematics

The circadian clock, responsible for coordinating organism function with daily and seasonal changes in the day-night cycle, is controlled by a complex protein network that constitutes a robust biochemical oscillator. Deterministic ordinary differential equation models have been used extensively to model the behavior of these central clocks. However, due to the small number of proteins involved in the circadian oscillations, mathematical models that track stochastic variations in the numbers of clock proteins may reveal more complex and biologically relevant behaviors. In this paper, we compare the response of a robust yet detailed deterministic model for the mammalian circadian clock with …

Infinite-Dimensional Measure Spaces And Frame Analysis, Palle Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ℋ, we study three cases of measures. We first show that, for ℋ infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ℋ. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.

Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly

Spora: A Journal of Biomathematics

As the leading cause of death in the United States, heart disease has become a principal concern in modern society. Cardiac arrhythmias can be caused by a dysregulation of calcium dynamics in cardiomyocytes. Calcium dysregulation, however, is not yet fully understood and is not easily predicted; this provides motivation for the subsequent research. Excitation-contraction coupling (ECC) is the process through which cardiomyocytes undergo contraction from an action potential. Calcium induced calcium release (CICR) is the mechanism through which electrical excitation is coupled with mechanical contraction through calcium signaling. The study of the interplay between electrical excitation, calcium signaling, and mechanical …

Age-Structured And Vaccination Models Of Devil Facial Tumor Disease, Christopher D. Bruno, Timothy Comar, Megan O. Powell, Adjo Tameklo

Spora: A Journal of Biomathematics

Tasmanian devil populations have been devastated by devil facial tumor disease (DFTD) since its first appearance in 1996. The average lifespan of a devil has decreased from six years to three years. We present an age-structured model to represent how the disease has affected the age and breeding structures of the population. We show that with the recent increase in the breeding of juvenile devils, the overall devil population will increase but not nearly to pre-DFTD levels. The basic reproductive number may be increased with the influx of young breeding devils. In addition, our model shows that the release of …

Linking Taxonomic Diversity And Trophic Function: A Graph-Based Theoretical Approach, Marcella M. Jurotich, Kaitlyn Dougherty, Barbara Hayford, Sally Clark

Transactions of the Nebraska Academy of Sciences and Affiliated Societies

The purpose of this study is to develop a novel, visual method in analyzing complex functional trait data in freshwater ecology. We focus on macroinvertebrates in stream ecosystems under a gradient of habitat degradation and employ a combination of taxonomic and functional trait diversity analyses. Then we use graph theory to link changes in functional trait diversity to taxonomic richness and habitat degradation. We test the hypotheses that: 1) taxonomic diversity and trophic functional trait diversity both decrease with increased habitat degradation; 2) loss of taxa leads to a decrease in trophic function as visualized using a bipartite graph; and …

Differential Equations Of Dynamical Order, Andrei Ludu, Harihar Khanal

Publications

No abstract provided.

Which Factors Influence Student Success In Intermediate Algebra, Math 101-102-103?, Linh T. Ward

Mathematics & Statistics ETDs

At The University of New Mexico (UNM), Intermediate Algebra (MATH 120 and MATH 101-102-103) has historically been a so-called “killer course”, with very low pass rates: approximately 40% in Fall 2009 to Spring 2011 and about 50% from Fall 2011 to Spring 2013. Furthermore, many students failed the class multiple times. Since 2013, a computer system called ALEKS has been used to teach the course and, along with some additional interventions, on Albuquerque/Main campus success rates for MATH 101 have increased to roughly 80% and MATH 102 to about 70%. This thesis provides a strategy to identify those 20-30% as-risk …

Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry

LSU Doctoral Dissertations

In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical …

Modeling Aggregation Of Proliferating Microglia In Response To Amyloid-Beta In Dementia, Adrienne C. Kinney, Ellen R. Swanson

Spora: A Journal of Biomathematics

Amyloid-beta plaques are prominent biological markers in dementia brains. In response to plaque formation, the brain's immune cells, microglia, become reactive. Microglia are measurable cells that surround amyloid-beta plaques, indicating their location. A system of partial differential equations describes the concentration of microglia in dementia brains by incorporating chemotactic signaling. However, this system fails to incorporate increasing numbers of reactive microglia cells in response to amyloid-beta aggregation. A system of ordinary differential equations describing the number of significant cells and proteins in the brain suggests the amount of reactive microglia increases significantly during the progression of dementia. We couple these …

Angioarchitectures And Hemodynamic Characteristics Of Posterior Communicating Artery Aneurysms And Their Association With Rupture Status, Bong Jae Chung, Ravi Doddasomayajula, Fernando Mut, Felicitas Detmer, Michael Pritz, Farid Hamzei-Sichani, Waleed Brinjikji, David F. Kallmes, Carlos M. Jimenez, Christopher Putman, Juan Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Intracranial aneurysms originating at the posterior communicating artery are known to have high rupture risk compared with other locations. We tested the hypothesis that different angioarchitectures (ie, branch point configuration) of posterior communicating artery aneurysms are associated with aneurysm hemodynamics, which in turn predisposes aneurysms to rupture.

MATERIALS AND METHODS: A total of 313 posterior communicating artery aneurysms (145 ruptured, 168 unruptured) were studied with image-based computational fluid dynamics. Aneurysms were classified into different angioarchitecture types depending on the location of the aneurysm with respect to parent artery bifurcation. Hemodynamic characteristics were compared between ruptured and unruptured …

Reproducible Research For Computing In Science & Engineering, Lorena A. Barba, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

The editors of the new track for reproducible research outline the parameters for future peer review, submission, and access, highlighting the magazine’s previous work in this field and some of the challenges still to come.

Environmental Effects On Drosophila Brain Development And Learning, Xia Wang, Amei Amei, J. Steven De Belle, Stephen P. Roberts

Mathematical Sciences Faculty Research

Brain development and behavior are sensitive to a variety of environmental influences including social interactions and physicochemical stressors. Sensory input in situ is a mosaic of both enrichment and stress, yet little is known about how multiple environmental factors interact to affect brain anatomical structures, circuits and cognitive function. In this study, we addressed these issues by testing the individual and combined effects of sub-adult thermal stress, larval density and early-adult living spatial enrichment on brain anatomy and olfactory associative learning in adult Drosophila melanogaster. In response to heat stress, the mushroom bodies (MBs) were the most volumetrically impaired among …

Perfect Matchings Of Trimmed Aztec Rectangles, Tri Lai

Department of Mathematics: Faculty Publications

We consider several new families of subgraphs of the square grid whose matchings are enumerated by powers of several small prime numbers: 2, 3, 5, and 11. Our graphs are obtained by trimming two opposite corners of an Aztec rectangle. The result yields a proof of a conjecture posed by Ciucu. In addition, we reveal a hidden connection between our graphs and the hexagonal dungeons introduced by Blum.