Other Applied Mathematics Commons^™

Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, Mahbubur Rahman 6203748

Showcase of Faculty Scholarly & Creative Activity

Approximation of stochastic differential equations (SDEs) with parametric noise plays an important role in a range of application areas, including engineering, mechanics, epidemiology, and neuroscience. A complete understanding of SDE theory with perturbed noise requires familiarity with advanced probability and stochastic processes. In this paper, we derive an asymptotic estimate of variance, and it is shown that numerical method gives a useful step toward solving SDEs with perturbed noise. Our goal is to diffuse the results to an audience not entirely familiar with functional notations or semi-group theory, but who might nonetheless be interested in the practical simulation of dynamical …

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …

Ns-Cross Entropy-Based Magdm Under Single-Valued Neutrosophic Set Environment, Florentin Smarandache, Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

Branch Mathematics and Statistics Faculty and Staff Publications

A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties. Also we define weighted NS-cross entropy measure and investigate its basic properties. We develop a novel multi-attribute group decision-making (MAGDM) strategy that is free from the drawback of asymmetrical behavior and undefined phenomena. It is …

Progenitors Involving Simple Groups, Nicholas R. Andujo

Electronic Theses, Projects, and Dissertations

I will be going over writing representations of both permutation and monomial progenitors, which include 2^{*4} : D_4, 2^(*7) :L_2 (7) as permutation progenitors, and monomial progenitors 7^(*2) :_m S_3 \times 2, 11^{*2} :_m (5:2)^{*}5, 11^{*3} :_m (25:3), 11^{*4} :_m (4 : 5)^{*}5. Also, the images of these different progenitors at both lower and higher fields and orders. \\ We will also do the double coset enumeration of S5 over D6, S6 over 5 : 4, A_5 x A_5 over (5:2)^{*}5, and go on to also do the double coset enumeration over maximal subgroups for larger constructions. We will also …

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Publications and Research

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

Sequential Probing With A Random Start, Joshua Miller

HMC Senior Theses

Processing user requests quickly requires not only fast servers, but also demands methods to quickly locate idle servers to process those requests. Methods of finding idle servers are analogous to open addressing in hash tables, but with the key difference that servers may return to an idle state after having been busy rather than staying busy. Probing sequences for open addressing are well-studied, but algorithms for locating idle servers are less understood. We investigate sequential probing with a random start as a method for finding idle servers, especially in cases of heavy traffic. We present a procedure for finding the …

Climate Modeling, Outgoing Longwave Radiation, And Tropical Cyclone Forecasting, Thomas Rechtman

Honors Undergraduate Theses

Climate modeling and tropical cyclone forecasting are two significant is- sues that are continuously being improved upon for more accurate weather forecasting and preparedness. In this thesis, we have studied three climate models and formulated a new model with a view to determine the outgoing longwave radiation (OLR) budget at the top of the atmosphere (TOA) as ob- served by the National Oceanic and Atmospheric Administration’s (NOAA) satellite based Advanced Very High Resolution Radiometer (AVHRR). In 2006, Karnauskas proposed the African meridional OLR as an Atlantic hur- ricane predictor, the relation was further proven in 2016 by Karnauskas and Li …

Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher

College of Graduate Studies: Theses & Dissertations

Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always …

Investigation Of Toppling Ball Flight In American Football With A Mechanical Field-Goal Kicker, Chase M Pfeifer, Timothy J. Gay, Jeff A. Hawks, Shane Farritor, Judith M. Burnfield

Department of Mechanical and Materials Engineering: Faculty Publications

A mechanical field-goal kicking machine was used to investigate toppling ball flight in American football place-kicking, eliminating a number of uncontrollable impact variables present with a human kicker. Ball flight trajectories were recorded using a triangulation-based projectile tracking system to account for the football’s 3-dimensional position during flight as well as initial launch conditions. The football flights were described using kinematic equations relating to projectile motion including stagnant air drag and were compared to measured trajectories as well as projectile motion equations that exclude stagnant air drag. Measured football flight range deviations from the non-drag equations of projectile motion corresponded …

Material Thermal Property Estimation Of Fibrous Insulation: Heat Transfer Modeling And The Continuous Genetic Algorithm, Elora Frye

Theses and Dissertations

Material thermal properties are highly sought after to better understand the performance of a material under particular conditions. As new materials are created, their physical properties will determine their performance for various applications. These properties have been estimated using many techniques including experimental testing, numerical modeling, and a combination of both. Existing methods can be time consuming, thus, a time-efficient and precise method to estimate these thermal properties was desired. A one-dimensional finite difference numerical model was developed to replicate the heat transfer through an experimental apparatus. A combination of this numerical model and the Continuous Genetic Algorithm optimization technique …

Boundization, Closure And Convergence For The Ultra Extended Complex Banach And Hilbert Spaces With Applications, Salah Hamad

Graduate Theses, Dissertations, and Problem Reports (ETD)

We study Boundization, Closure and Convergence of Complex Banach and Hilbert spaces. We augment a Banach space with elements “infinity” and turn the augmented set into a metric space by appropriate distance functions. This new metric space is called the Ultra Extended Banach Space. A new family of bijections, motivated by nonlinear projections, take an Ultra Extended Banach Space into bounded subsets of a “larger” Banach space. We compare the family of new metrics induced and show which ones are equivalent and which ones are unexpectedly not equivalent. Some applications are provided.

Generating Species Assemblages For Restoration And Experimentation: A New Method That Can Simultaneously Converge On Average Trait Values And Maximize Functional Diversity, David C. Laughlin, Loïc Chalmandrier, Chaitanya Joshi, Michael Renton, John M. Dwyer, Jennifer L. Funk

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

1.Restoring resilient ecosystems in an era of rapid environmental change requires a flexible framework for selecting assemblages of species based on functional traits. However, current trait‐based models have been limited to algorithms that select species assemblages that only converge on specified average trait values, and could not accommodate the common desire among restoration ecologists to generate functionally diverse assemblages.

2.We have solved this problem by applying a nonlinear optimization algorithm to solve for the species relative abundances that maximize Rao's quadratic entropy (Q) subject to other linear constraints. Rao's Q is a closed‐form algebraic expression of functional diversity …

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

Evaporation Of A Sessile Droplet On A Slope, Mitch Timm

Dissertations, Master's Theses and Master's Reports

We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from a purely diffusive transport of the liquid vapor and that the contact line is a pinned circle. For the purposes of our analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the …

A Mathematical Model Of A Corrosion System Containing Inhibitors, Abigael Frey

Williams Honors College, Honors Research Projects

A two dimensional model is developed to describe how organic and inorganic inhibitors slows down the corrosion damage of a coated metal plate that contains a defect. The model contains a metal covered on one side by a coating that contains organic and inorganic inhibitors, electrolytes that are on the outside of the coating, and a small defect in the coating. The defect is an area where the coating is more porous and allows the electrolytes to leak in faster. In this model the organic inhibitor is presumed to be dissolved into the coating and the inorganic inhibitor is released …

Penalized Mixed-Effects Ordinal Response Models For High-Dimensional Genomic Data In Twins And Families, Amanda E. Gentry

Theses and Dissertations

The Brisbane Longitudinal Twin Study (BLTS) was being conducted in Australia and was funded by the US National Institute on Drug Abuse (NIDA). Adolescent twins were sampled as a part of this study and surveyed about their substance use as part of the Pathways to Cannabis Use, Abuse and Dependence project. The methods developed in this dissertation were designed for the purpose of analyzing a subset of the Pathways data that includes demographics, cannabis use metrics, personality measures, and imputed genotypes (SNPs) for 493 complete twin pairs (986 subjects.) The primary goal was to determine what combination of SNPs and …

Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal

Senior Independent Study Theses

The International Monetary Fund (IMF) calculates the voting power of a country by dividing the total of one member's votes by the total of all members' votes. This method of calculating the power of a state judges power as voting weight. However, voting weights are the total number of votes a country has in an institution, while voting power is the influence a country has on a policy decision. A better approach to calculate this voting power within an institution is by using voting power indices. However, literature only calculates the winning power, while voting power is defined as the …

Decoding Book Barcode Images, Yizhou Tao

CMC Senior Theses

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises, …

Positive Definite Functions And Dual Pairs Of Locally Convex Spaces, Daniel Alpay, Saak Gabriyelyan

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.

Copula Theory And Regression Analysis, Mayooran Thevaraja

All Graduate Theses, Dissertations, and Other Capstone Projects

Researchers are often interested to study in the relationships between one variable and several other variables. Regression analysis is the statistical method for investigating such relationship and it is one of the most commonly used statistical Methods in many scientific fields such as financial data analysis, medicine, biology, agriculture, economics, engineering, sociology, geology, etc. But basic form of the regression analysis, ordinary least squares is not suitable for actuarial applications because the relationships are often nonlinear and the probability distribution of the response variable may be non-Gaussian distribution. One of the method that has been successful in overcoming these challenges …

Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of …

Multiclass Classification Using Support Vector Machines, Duleep Prasanna W. Rathgamage Don

College of Graduate Studies: Theses & Dissertations

In this thesis, we discuss different SVM methods for multiclass classification and introduce the Divide and Conquer Support Vector Machine (DCSVM) algorithm which relies on data sparsity in high dimensional space and performs a smart partitioning of the whole training data set into disjoint subsets that are easily separable. A single prediction performed between two partitions eliminates one or more classes in a single partition, leaving only a reduced number of candidate classes for subsequent steps. The algorithm continues recursively, reducing the number of classes at each step until a final binary decision is made between the last two classes …