Applied Mathematics Commons^™

The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling

Theses and Dissertations

Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach.

Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network …

Personalized Detection Of Anxiety Provoking News Events Using Semantic Network Analysis, Jacquelyn Cheun Phd, Luay Dajani, Quentin B. Thomas

SMU Data Science Review

In the age of hyper-connectivity, 24/7 news cycles, and instant news alerts via social media, mental health researchers don't have a way to automatically detect news content which is associated with triggering anxiety or depression in mental health patients. Using the Associated Press news wire, a semantic network was built with 1,056 news articles containing over 500,000 connections across multiple topics to provide a personalized algorithm which detects problematic news content for a given reader. We make use of Semantic Network Analysis to surface the relationship between news article text and anxiety in readers who struggle with mental health disorders. …

On Improving Performance Of The Binary Logistic Regression Classifier, Michael Chang

UNLV Theses, Dissertations, Professional Papers, and Capstones

Logistic Regression, being both a predictive and an explanatory method, is one of the most commonly used statistical and machine learning method in almost all disciplines. There are many situations, however, when the accuracies of the fitted model are low for predicting either the success event or the failure event. Several statistical and machine learning approaches exist in the literature to handle these situations. This thesis presents several new approaches to improve the performance of the fitted model, and the proposed methods have been applied to real datasets.

Transformations of predictors is a common approach in fitting multiple linear and …

A Pedagogic Analysis Of Linear Algebra Courses, Andrew Taylor

Mathematics & Statistics ETDs

This project is concerned with investigating the question, "Do our applied linear algebra courses (at the University of New Mexico) adequately prepare STEM students for future work in their respective fields?" In order to explore this, surveys were issued to three groups (sections) of students (among two different instructors) at the conclusion of their applied linear algebra course, as well as STEM professors/instructors from a variety of STEM fields. Students were surveyed regarding their perceived mastery of given topics/ideas from the course and professors/instructors were surveyed about the level of mastery they felt was necessary (referred to as ``desired mastery") …

Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker

Publications and Research

We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.

An (S - 1; S) Inventory System With Negative Arrivals And Multiple Vacations, Kathiresan Jothivel, Anbazhagan Neelamegam

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a continuous review one-to-one ordering policy inventory system with multiple vacations and negative customers. The maximum storage capacity is S. The customers arrive according to a Poisson process with finite waiting hall. There are two types of customers: ordinary and negative. An ordinary customer, on arrival, joins the queue and the negative customer does not join the queue and takes away any one of the waiting customers. When the waiting hall is full, the arriving primary customer is considered to be lost. The service time and lead time are assumed to have independent exponential distribution. …

Analysis Of Batch Arrival Single And Bulk Service Queue With Multiple Vacation Closedown And Repair, T. Deepa, A. Azhagappan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyze batch arrival single and bulk service queueing model with multiple vacation, closedown and repair. The single server provides single service if the queue size is ‘< a’ and bulk service if the queue size is ‘ ≥ a’. After completing the service (single or bulk), the server may breakdown with probability ξ and then it will be sent for repair. When the system becomes empty or the server is ready to serve after the repair but no one is waiting, the server resumes closedown and then goes for a multiple vacation of random length. Using supplementary variable technique, the steady-state probability generating function (PGF) of …

Analysis Of Two Stage M[X1],M[X2]/G1,G2/1 Retrial G-Queue With Discretionary Priority Services, Working Breakdown, Bernoulli Vacation, Preferred And Impatient Units, G. Ayyappan, B. Somasundaram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study M^[X₁] , M^[X2] /G₁ ,G₂ /1 retrial queueing system with discretionary priority services. There are two stages of service for the ordinary units. During the first stage of service of the ordinary unit, arriving priority units can have an option to interrupt the service, but, in the second stage of service it cannot interrupt. When ordinary units enter the system, they may get the service even if the server is busy with the first stage of service of an ordinary unit or may enter into the orbit or leave …

Function Space Tensor Decomposition And Its Application In Sports Analytics, Justin Reising

Electronic Theses and Dissertations

Recent advancements in sports information and technology systems have ushered in a new age of applications of both supervised and unsupervised analytical techniques in the sports domain. These automated systems capture large volumes of data points about competitors during live competition. As a result, multi-relational analyses are gaining popularity in the field of Sports Analytics. We review two case studies of dimensionality reduction with Principal Component Analysis and latent factor analysis with Non-Negative Matrix Factorization applied in sports. Also, we provide a review of a framework for extending these techniques for higher order data structures. The primary scope of this …

The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the list of minor-minimal graphs that have no Γ-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.

Diabetes And Its Effect On Abdominal Aortic Aneurysm Growth Rate In Hispanic Patients, Monica Betancourt-Garcia, Kristina Vatcheva, Amrit Thakur, Prateek Gupta, Eugene Postevka, Ricardo Martinez, R. Armour Forse

School of Mathematical & Statistical Sciences Faculty Publications

Background

The growth rate of abdominal aortic aneurysms (AAA) can vary depending on age, baseline diameter, blood pressure, race, and history of smoking. Paradoxically, previous studies show evidence of a protective effect of diabetes on the rate of AAA expansion despite its well-established role in the morbidity and mortality of cardiovascular disease. This study aims to investigate the impact diabetes plays on AAA growth within a Hispanic population.

Methods

Data were collected from patients who were predominantly Mexican-American at a single hospital site. Baseline and follow-up measures for AAA diameter were obtained from serial imaging studies. Demographics, medical history, the …

An Agent-Based Modeling Approach For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Joey Gaudy, Craig Garzella

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Distribution In Carbon Uptake Across A Global Measurement Network Of Terrestrial Ecosystems, John Zobitz, Madeline Oswood

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Integrating Mathematics And Biology In The Classroom: A Compendium Of Case Studies And Labs, Becky Sanft, Anne Walter

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Pollen Traits To Build A Mathematical Model Of Pollen Competition - A Biologist's Perspective, Rob Swanson, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Adaptive Feature Engineering Modeling For Ultrasound Image Classification For Decision Support, Hatwib Mugasa

Doctoral Dissertations

Ultrasonography is considered a relatively safe option for the diagnosis of benign and malignant cancer lesions due to the low-energy sound waves used. However, the visual interpretation of the ultrasound images is time-consuming and usually has high false alerts due to speckle noise. Improved methods of collection image-based data have been proposed to reduce noise in the images; however, this has proved not to solve the problem due to the complex nature of images and the exponential growth of biomedical datasets. Secondly, the target class in real-world biomedical datasets, that is the focus of interest of a biopsy, is usually …

Quasilinearization And Boundary Value Problems At Resonance, Kareem Alanazi, Meshal Alshammari, Paul W. Eloe

Mathematics Faculty Publications

A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

Practical Modelling Of The Vanilla Option Volatility Smile, Jacob E. Shanley

Mathematics & Statistics ETDs

Many discussions on how best to model the standard American Option derivative focus solely upon the volatility smile modelling itself from a mathematical perspective. This thesis instead closely examines both the practical and mathematical implications of processing market data, modelling the volatility smile, and making real-world trading decisions from the results. In particular, it contains an analysis of market data processing algorithms, new volatility smile models, multiple empirically-driven weighting schemes, Gauss-Newton and Levenberg-Marquardt optimization algorithms, and various trading strategies. The top performing combinations found were those that involved the Smile and Twist volatility smile models, Volatility Width Vega Multiplier weighting …

A Deep Learning Approach To Uncertainty Quantification, Mst Afroja Akter

Mathematics & Statistics ETDs

In this thesis we consider ordinary differential equations (ODEs) with random parameters. We focus on Monte Carlo (MC) sampling for computing the statistics of some quantities of interest (QoIs) given by the solution of the ODE problems. We use the 4th order accurate Runge-Kutta (RK4) method as the deterministic ODE solver. We then develop a hybrid MC sampling method that combines RK4 with neural network models to efficiently compute the statistics of QoIs within a desired accuracy. We present several numerical examples to verify the accuracy and efficiency of the proposed hybrid method compared to classical MC sampling. The hybrid …

Graphicacy For Numeracy: Review Of Fundamentals Of Data Visualization: A Primer On Making Informative And Compelling Figures By Claus O. Wilke (2019), Christy M. Bebeau

Numeracy

Wilke, Claus O. 2019. Fundamentals of Data Visualization: A Primer on Making Informative and Compelling Figures. (Sebastopol, CA: O’Reilly Media, Inc.). 390 pp. ISBN 978-1-492-03108-6. First edition. First release: 03-15-2019.

Claus O. Wilke has authored an excellent reference about producing and understanding static figures, figures used online, in print, and for presentations. His book is neither a statistics nor programming text, but familiarity with basic statistical concepts is helpful. Written in three parts, the book presents both the math and artistic design aspects of telling a story through figures. Wilke makes extensive use of examples, labels them good, bad, …

Extending Statistical Learning For Aneurysm Rupture Assessment To Finnish And Japanese Populations Using Morphology, Hemodynamics, And Patient Characteristics, Felicitas J. Detmer, Sara Hadad, Bong Jae Chung, Fernando Mut, Martin Slawski, Norman Juchler, Vartan Kurtcuoglu, Sven Hirsch, Philippe Bijlenga, Yuya Uchiyama, Soichiro Fujimura, Makoto Yamamoto, Yuichi Murayama, Hiroyuki Takao, Timo Koivisto, Juhana Frösen, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

OBJECTIVE: Incidental aneurysms pose a challenge for physicians, who need to weigh the rupture risk against the risks associated with treatment and its complications. A statistical model could potentially support such treatment decisions. A recently developed aneurysm rupture probability model performed well in the US data used for model training and in data from two European cohorts for external validation. Because Japanese and Finnish patients are known to have a higher aneurysm rupture risk, the authors' goals in the present study were to evaluate this model using data from Japanese and Finnish patients and to compare it with new models …

Mittag–Leffler Stability Of Systems Of Fractional Nabla Difference Equations, Paul W. Eloe, Jaganmohan Jonnalagadda

Mathematics Faculty Publications

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

Image-Based Modeling Of Blood Flow In Cerebral Aneurysms Treated With Intrasaccular Flow Diverting Devices, Fernando Mut, Bong Jae Chung, Jorge Chudyk, Pedro Lylyk, Ramanathan Kadirvel, David F. Kallmes, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Modeling the flow dynamics in cerebral aneurysms after the implantation of intrasaccular devices is important for understanding the relationship between flow conditions created immediately posttreatment and the subsequent outcomes. This information, ideally available a priori based on computational modeling prior to implantation, is valuable to identify which aneurysms will occlude immediately and which aneurysms will likely remain patent and would benefit from a different procedure or device. In this report, a methodology for modeling the hemodynamics in intracranial aneurysms treated with intrasaccular flow diverting devices is described. This approach combines an image-guided, virtual device deployment within patient-specific vascular models with …

Performance And Economic Evaluation Of Differentiated Multiple Vacation Queueing System With Feedback And Balked Customers, Amina A. Bouchentouf, Latifa Medjahri

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with a single server feedback queueing system under two differentiated multiple vacations and balked customers. It is assumed that the service times of the two vacation types are exponentially distributed with different means. The steady-state probabilities of the model are obtained. Some important performance measures of the system are derived. Then, a cost model is developed. Further, a numerical study is presented.

Exact Reliability For Consecutive K-Out-Of-R-From-N: F System With Equal And Unequal Components Probabilities, Yaser Amirian, Ahmad Khodadadi, Omid Chatrabgoun

Applications and Applied Mathematics: An International Journal (AAM)

A consecutive k-out-of-r-from-n: F system consists of n linear ordered components such that the system fails if and only if there exist a set of r consecutive linear component that contains at least k failed components. Consecutive k-out-of-r-from-n: F system has been considered in many fields such as reliability analysis. All recent efforts in this area have been focused on acquiring band or approximation for their reliability such that less attention has been paid to their closed form and exact reliability in the literature. In the present paper, with designing an innovative algorithm the exact reliability for extensive class of …

Transient Analysis Of A Markovian Single Vacation Feedback Queue With An Interrupted Closedown Time And Control Of Admission During Vacation, A. Azhagappan, T. Deepa

Applications and Applied Mathematics: An International Journal (AAM)

This paper analyzes the transient behavior of an M/M/1 queueing model with single vacation, feedback, interrupted closedown time and control of admission during vacation. The time-dependent system size probabilities for the proposed model are obtained using generating function in the closed form. Further, the system performance measures like mean and variance of system size are also obtained for the time-dependent case. Finally, numerical illustrations are presented to understand the effect for various system parameters.

Analysis Of M[X1],M[X2]/G1,G2/1 Retrial Queueing System With Priority Services, Working Breakdown, Collision, Bernoulli Vacation, Immediate Feedback, Starting Failure And Repair, G. Ayyappan, P. Thamizhselvi, B. Somasundaram

Applications and Applied Mathematics: An International Journal (AAM)

This paper considers an M^[X₁] , M^[X₂] /G1,G2/1 general retrial queueing system with priority services. Two types of customers from different classes arrive at the system in different independent compound Poisson processes. The server follows the non-pre-emptive priority rule subject to working breakdown, Bernoulli vacation, starting failure, immediate feedback, collision and repair. After completing each service, the server may go for a vacation or remain idle in the system. The priority customers who find the server busy are queued in the system. If a low-priority customer finds the server busy, he is routed to …

Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium, Dilip K. Jaiswal, Gulrana _

Applications and Applied Mathematics: An International Journal (AAM)

One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.

The Martingale Approach To Financial Mathematics, Jordan M. Rowley

Master's Theses

In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …