Physical Sciences and Mathematics Commons^™

Covid-19 In Casinos: Analysis Of Covid-19 Contamination And Spread With Economic Impact Assessment, Anastasia (Stasi) D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Abstract:

The COVID-19 pandemic caused tremendous disruption for casinos, with the virus causing various lengths of shutdowns, capacity restrictions, and social distancing strategies such as machine removals or section closures. Although most of the world has now eased off these measures, it is important to review lessons learned to understand, and better prepare for similar circumstances in the future. We present Monte Carlo slot floor simulation software customized to simulate players spreading COVID-19 on the slot floor. We simulate the amount of touch surface contamination; the number of potential surface contact exposure events per day, and a proximity exposures statistic …

Trajectory Analysis For Driving Safety Quantification, Michael I. Chang

UNLV Theses, Dissertations, Professional Papers, and Capstones

In order to evaluate the efficacy of the skid recovery exercise in the Driver’s Edge teenage driving program, a process is established to determine the trajectories of vehicles from recorded videos, compare them in terms of similarity through dynamic time warping (DTW), and then analyze the similarity measurements to assess whether the program has a significant effect on driving ability by repeated measures analysis of variance (rANOVA). The video is analyzed by Harris corner detection and Lucas-Kanade optical flow method to ascertain the vehicle trajectories. A homography is then estimated to translate coordinates from video into real-world. The instructor and …

Some Graph Laplacians And Variational Methods Applied To Partial Differential Equations On Graphs, Daniel Anthony Corral

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation we will be examining partial differential equations on graphs. We start by presenting some basic graph theory topics and graph Laplacians with some minor original results. We move on to computing original Jost graph Laplacians of friendly labelings of various finite graphs. We then continue on to a host of original variational problems on a finite graph. The first variational problem is an original basic minimization problem. Next, we use the Lagrange multiplier approach to the Kazdan-Warner equation on a finite graph, our original results generalize those of Dr. Grigor’yan, Dr. Yang, and Dr. Lin. Then we …

A Survey Of The Br´Ezis-Nirenberg Problem And Related Theorems, Edward Huynh

UNLV Theses, Dissertations, Professional Papers, and Capstones

Nonlinear elliptic partial differential equations on bounded domains arise in several different areas of mathematics that include geometry, mathematical physics, and the calculus of variations. The Br ́ezis-Nirenberg problem is concerned with a boundary-value problem that is intimately connected to the existence of positive solutions of the Yamabe problem, of non-minimal solutions to Yang-Mills functionals, and of extremal functions to several important inequalities. Results on existence and uniqueness have been obtained in cases when the exponent is sub-critical, but such results have not been obtained when the exponent is critical due to a lack of compactness. The earliest results obtained …

Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …

Evaluating The Behaviour Of Centrally Perforated Unreinforced Masonry Walls: Applications Of Numerical Analysis, Machine Learning, And Stochastic Methods, Mohsen Khaleghi, Javid Salimi, Visar Farhangi, Mohammad Javad Moradi, Moses Karakouzian

Civil and Environmental Engineering and Construction Faculty Research

The presence of openings greatly affects the response of unreinforced masonry (URM) walls. This topic greatly attracts the attention of many researchers. Perforated unreinforced masonry (PURM) walls under in-plane loads through the truss discretization method (TDM) along with several machine learning approaches such as Multilayer perceptron (MLP), Group of Method Data Handling (GMDH), and Radial basis function (RBF) are described in this paper. A new method named Multi-pier (MP) that is fast and accurate, is used to determine the behavior of PURM walls. The results of the MP method are expressed as a ratio of lateral load-bearing capacity and initial …

Modeling Covid-19 Infection Rates Using Sir And Arima Models, Janelle Domantay, Ilya Pivavaruk, Victor Taksheyev

Undergraduate Research Symposium Posters

With the onset of the COVID-19 pandemic, it has become of increasing interest to both monitor and predict the growth of its infection rates. In order to analyze the accuracy of epidemiological prediction, we consider two different models for prediction, the Susceptible Infected and Removed (SIR), and Autoregressive Integrated Moving Average (ARIMA) models. Using a dataset of Clark County COVID-19 infections, we create various ARIMA and SIR models that attempt to predict the progression of COVID-19 infections whilst comparing these predictions to the dataset. We observed that the ARIMA model performed more accurately overall, having a much lower Root Mean …

The Pencil Code, A Modular Mpi Code For Partial Differential Equations And Particles: Multipurpose And Multiuser-Maintained, The Pencil Code Collaboration, Chao-Chin Yang

Physics & Astronomy Faculty Research

The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) (A. Brandenburg & Dobler, 2010) to meteorological cloud microphysics (Li et al., 2017) and engineering applications in combustion (Babkovskaia et al., 2011). Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to …

Two New Finite Element Schemes And Their Analysis For Modeling Of Wave Propagation In Graphene, Jichun Li

Mathematical Sciences Faculty Research

© 2020 The Author(s) In this paper, we investigate a system of governing equations for modeling wave propagation in graphene. Compared to our previous work (Yang et al., 2020), here we re-investigate the governing equations by eliminating two auxiliary unknowns from the original model. A totally new stability for the model is established for the first time. Since the finite element scheme proposed in Yang et al. (2020) is only first order in time, here we propose two new schemes with second order convergence in time for the simplified modeling equations. Discrete stabilities inheriting exactly the same form as the …

Computational Study Of The Time Relaxation Model With High Order Deconvolution Operator, Jeffrey Belding, Monika Neda, Fran Pahlevani

Mathematical Sciences Faculty Research

This paper presents a computational investigation for a time relaxation regularization of Navier–Stokes equations known as Time Relaxation Model, TRM, and its corresponding sensitivity equations. The model generates a regularization based on both filtering and deconvolution. We discretize the equations of TRM and the corresponding sensitivity equations using finite element in space and Crank–Nicolson in time. The step problem and the shear layer roll-up benchmark is used to computationally test the performance of TRM across different orders of deconvolution operator as well as the sensitivity of the shear layer computations of the model with respect to the variation of time …

Recent Advances In Computational Mathematics And Applications, Eric Machorro, Jichun Li, Monika Neda, Pengtao Sun, Hongtao Yang

Mathematical Sciences Faculty Research

No abstract provided.

Correlation Coefficients For A Study With Repeated Measures, Guogen Shan, Hua Zhang, Tao Jiang

Environmental & Occupational Health Faculty Publications

Repeated measures are increasingly collected in a study to investigate the trajectory of measures over time. One of the first research questions is to determine the correlation between two measures. The following five methods for correlation calculation are compared: (1) Pearson correlation; (2) correlation of subject means; (3) partial correlation for subject effect; (4) partial correlation for visit effect; and (5) a mixed model approach. Pearson correlation coefficient is traditionally used in a cross-sectional study. Pearson correlation is close to the correlations computed from mixed-effects models that consider the correlation structure, but Pearson correlation may not be theoretically appropriate in …

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 …

An Application Of Conformal Mapping To The Boundary Element Method For Unconfined Steady Seepage With A Phreatic Surface, Jorge Eduardo Reyes

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, numerical results using the Boundary Element Method (BEM) for groundwater flow in a domain with a boundary that contains numerous singularities with a phreatic surface are developed. The flow in the domain is modeled using Darcy’s law for a homogeneous isotropic porous medium. The boundary conditions are a combination of Dirichlet and Neumann with the phreatic surface having both boundary conditions. Exact solutions by Conformal Mapping for simplified domains with the same singularity as the original domain allow for modifications to the BEM resulting in an improvement to the numerical solution.

An iterative process is used to …

Numerical Analysis And Fluid Flow Modeling Of Incompressible Navier-Stokes Equations, Tahj Hill

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Navier-Stokes equations (NSE) are an essential set of partial differential equations for governing the motion of fluids. In this paper, we will study the NSE for an incompressible flow, one which density ρ = ρ0 is constant.

First, we will present the derivation of the NSE and discuss solutions and boundary conditions for the equations. We will then discuss the Reynolds number, a dimensionless number that is important in the observations of fluid flow patterns. We will study the NSE at various Reynolds numbers, and use the Reynolds number to write the NSE in a nondimensional form.

We will …

Numerical Study In The Conservative Arbitrary Lagrangian-Eulerian (Ale) Method For An Unsteady Stokes/Parabolic Interface Problem With Jump Coefficients And A Moving Interface, Michael Joseph Ramirez

UNLV Theses, Dissertations, Professional Papers, and Capstones

Towards numerical analyses for fluid-structure interaction (FSI) problems in the future, in this thesis the arbitrary Lagrangian-Eulerian (ALE) finite element method within a conservative form is developed and analyzed for a linearized FSI problem - an unsteady Stokes/parabolic interface problem with jump coefficients and moving interface, and the corresponding mixed finite element approximation is developed and analyzed for both semi- and fully discrete schemes based upon the so-called conservative formulation. In terms of a novel H1-projection technique, their stability and optimal convergence properties are obtained for approximating the real solution equipped with lower regularity.

Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee

UNLV Gaming Research & Review Journal

There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of these strategies would require a book-length manuscript. Instead, a hand-rank table, which fits on a single page and reproduces the optimal strategy perfectly, was found for Jacks or Better as early as the mid 1990s. Is there a systematic way to derive such a hand-rank table? We show that there is indeed, and it involves finding the exact optimal …

Comparison Principle For Stochastic Heat Equation On Rd, Le Chen, Jingyu Huang

Mathematical Sciences Faculty Research

We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on Rd (∂∂t−12Δ)u(t,x)=ρ(u(t,x))M˙(t,x), for measure-valued initial data, where M˙ is a spatially homogeneous Gaussian noise that is white in time and ρ is Lipschitz continuous. ... (See full text for complete abstract)

Inferring The Distribution Of Selective Effects From A Time Inhomogeneous Model, Amei Amei, Shilei Zhour

Mathematical Sciences Faculty Research

We have developed a Poisson random field model for estimating the distribution of selective effects of newly arisen nonsynonymous mutations that could be observed as polymorphism or divergence in samples of two related species under the assumption that the two species populations are not at mutation-selection-drift equilibrium. The model is applied to 91Drosophila genes by comparing levels of polymorphism in an African population of D. melanogaster with divergence to a reference strain of D. simulans. Based on the difference of gene expression level between testes and ovaries, the 91 genes were classified as 33 male-biased, 28 female-biased, and 30 sex-unbiased …

Estimation Of The Parameters In A Spatial Regressive-Autoregressive Model Using Ord's Eigenvalue Method, Sajib Mahmud Mahmud Tonmoy

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, we study one of Ord's (1975) global spatial regression models.

Ord considered spatial regressive-autoregressive models to describe the interaction

between location and a response variable in the presence of several covariates. He also

developed a practical estimation method for the parameters of this regression model

using the eigenvalues of a weight matrix that captures the contiguity of locations.

We review the theoretical aspects of his estimation method and implement it in the

statistical package R.

We also implement Ord's methods on the Columbus, Ohio, crime data set from the

year 1980, which involves the crime rate of …

Probabilistic Interpretation Of Solutions Of Linear Ultraparabolic Equations, Michael D. Marcozzi

Mathematical Sciences Faculty Research

We demonstrate the existence, uniqueness and Galerkin approximatation of linear ultraparabolic terminal value/infinite-horizon problems on unbounded spatial domains. Furthermore, we provide a probabilistic interpretation of the solution in terms of the expectation of an associated ultradiffusion process.

Conformal Mapping Improvement Of The Boundary Element Method Solution For Underground Water Flow In A Domain With A Very Singular Boundary, Megan Romero

UNLV Theses, Dissertations, Professional Papers, and Capstones

Numerical solutions using a Boundary Element Method (BEM) for a confined flow in a very singular finite domain are developed. Typically, in scientific journal publications, authors avoid domains with many and more malignant singularities due to the extremely big and difficult to estimate errors in the numerical calculations. Using exact Conformal Mapping solutions for simplified domains with the same singularity as in the original domain, this problem can be solved numerically with improvements introduced by Conformal Mapping solutions. Firstly, to experiment with improving the BEM solution by Conformal Mapping, a domain inside a rectangle is considered. The exact solution inside …

Fundamental Tradeoffs In Estimation Of Finite-State Hidden Markov Models, Justin Le

UNLV Theses, Dissertations, Professional Papers, and Capstones

Hidden Markov models (HMMs) constitute a broad and flexible class of statistical models that are widely used in studying processes that evolve over time and are only observable through the collection of noisy data. Two problems are essential to the use of HMMs: state estimation and parameter estimation. In state estimation, an algorithm estimates the sequence of states of the process that most likely generated a certain sequence of observations in the data. In parameter estimation, an algorithm computes the probability distributions that govern the time-evolution of states and the sampling of data. Although algorithms for the two problems are …

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 …

Numerical Methods For Option Pricing Under The Two-Factor Models, Jiacheng Cai

UNLV Theses, Dissertations, Professional Papers, and Capstones

Pricing options under multi-factor models are challenging and important problems for financial applications. In particular, the closed form solutions are not available for the American options and some European options, and the correlations between factors increase the complexity and difficulty for the formulations and implements of the numerical methods.

In this dissertation, we first introduce a general transformation to decouple correlated stochastic processes governed by a system of stochastic differential equations. Then we apply the transformation to the popular two-factor models: the two-asset model, the stochastic volatility model, and the stochastic interest rate models. Based on our new formulations, we …

Diffusive Logistic Equations With Harvesting And Heterogeneity Under Strong Growth Rate, Saeed Shabani Rokn-E-Vafa, Hossein T. Tehrani

Mathematical Sciences Faculty Research

We consider the equation −Δu=au−b(x)u2−ch(x) in Ω,u=0 on ∂Ω, where Ω is a smooth bounded domain in RN, b(x) and h(x) are nonnegative functions, and there exists Ω0⊂⊂Ω such that {x:b(x)=0}=Ω¯¯¯0. We investigate the existence of positive solutions of this equation for c large under the strong growth rate assumption a≥λ1(Ω0), where λ1(Ω0) is the first eigenvalue of the −Δ in Ω0 with Dirichlet boundary condition. We show that if h≡0 in Ω∖Ω¯¯¯0, then our equation has a unique positive solution for all c large, provided that a is in a right neighborhood of λ1(Ω0). For this purpose, we prove …

Self-Correcting Kelly Strategies For Skeptical Traders, Aaron C. Brown

International Conference on Gambling & Risk Taking

The Kelly criterion gives the appropriate bet size in idealized situations with known parameters. In financial trading situations parameters are generally unknown and the mathematical assumptions underlying the Kelly proof are not met precisely. Moreover a risk manager typically must cooperate with a trader who may be skeptical about both the Kelly criterion specifically and the concept of mathematical optimization of bet size in general.

This presentation tackles the problem of designing a Kelly-based system for setting trade risk management parameters that is both self-correcting (the system delivers good results even if initial parameter are misestimated or parameters change) and …

Optimizing The Mix Of Games And Their Locations On The Casino Floor, Jason D. Fiege, Anastasia D. Baran

International Conference on Gambling & Risk Taking

We present a mathematical framework and computational approach that aims to optimize the mix and locations of slot machine types and denominations, plus other games to maximize the overall performance of the gaming floor. This problem belongs to a larger class of spatial resource optimization problems, concerned with optimizing the allocation and spatial distribution of finite resources, subject to various constraints. We introduce a powerful multi-objective evolutionary optimization and data-modelling platform, developed by the presenter since 2002, and show how this software can be used for casino floor optimization. We begin by extending a linear formulation of the casino floor …

Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, Anastasia D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single …

On The Scattering Of An Acoustic Plane Wave By A Soft Prolate Spheroid, Joseph Michael Borromeo

UNLV Theses, Dissertations, Professional Papers, and Capstones

This thesis solves the scattering problem in which an acoustic plane wave of propagation number K1 is scattered by a soft prolate spheroid. The interior field of the scatterer is characterized by a propagation number K2, while the field radiated by the scatterer is characterized by the propagation number K3. The three fields and their normal derivatives satisfy boundary conditions at the surface of the scatterer. These boundary conditions involve six complex parameters depending on the propagation numbers. The scattered wave also satisfies the Sommerfeld radiation condition at infinity. Through analytical methods, series representations are constructed for the interior field …