The Battle Against Malaria: A Teachable Moment, 2017 Schoolcraft College

#### The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

*Journal of Humanistic Mathematics*

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to ...

Control Uniqueness In Reconstructability Analysis, 2016 Portland State University

#### Control Uniqueness In Reconstructability Analysis, Martin Zwick

*Martin Zwick*

When the reconstructability analysis of a directed system yields a structure in which a generated variable appears in more than one subsystem, information from all of the subsystems can be used in modeling the relationship between generating and generated variables. The conceptualization and procedure proposed here is discussed in relation to Klir's concept of control uniqueness.

Multi-Level Decomposition Of Probalistic Relations, 2016 Portland State University

#### Multi-Level Decomposition Of Probalistic Relations, Stanislaw Grygiel, Martin Zwick, Marek Perkowski

*Martin Zwick*

Two methods of decomposition of probabilistic relations are presented in this paper. They consist of splitting relations (blocks) into pairs of smaller blocks related to each other by new variables generated in such a way so as to minimize a cost function which depends on the size and structure of the result. The decomposition is repeated iteratively until a stopping criterion is met. Topology and contents of the resulting structure develop dynamically in the decomposition process and reflect relationships hidden in the data.

Review Of: Charles R. Bennett, Risks In The Environment: How To Assess Them, 2016 University of New Hampshire

#### Review Of: Charles R. Bennett, Risks In The Environment: How To Assess Them, Penny Dean

*RISK: Health, Safety & Environment*

Review of: Charles R. Bennett, Risks in the Environment: How to Assess Them (Burloak Publications 1996). Appendices, references for the appendices, prologue. ISBN 0-9680438-0-1 [305 pp. Paper $23.95. 277 Belvenia Rd., Burlington, Ontario.]

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, 2016 Washington University in St. Louis

#### A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

*Doctor of Business Administration Dissertations*

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with ...

Newsvendor Models With Monte Carlo Sampling, 2016 East Tennessee State University

#### Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

*Electronic Theses and Dissertations*

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected proﬁt. Finally, this method will be used ...

Advanced Sequential Monte Carlo Methods And Their Applications To Sparse Sensor Network For Detection And Estimation, 2016 University of Tennessee, Knoxville

#### Advanced Sequential Monte Carlo Methods And Their Applications To Sparse Sensor Network For Detection And Estimation, Kai Kang

*Doctoral Dissertations*

The general state space models present a flexible framework for modeling dynamic systems and therefore have vast applications in many disciplines such as engineering, economics, biology, etc. However, optimal estimation problems of non-linear non-Gaussian state space models are analytically intractable in general. Sequential Monte Carlo (SMC) methods become a very popular class of simulation-based methods for the solution of optimal estimation problems. The advantages of SMC methods in comparison with classical filtering methods such as Kalman Filter and Extended Kalman Filter are that they are able to handle non-linear non-Gaussian scenarios without relying on any local linearization techniques. In this ...

Numerical Solutions Of Stochastic Differential Equations, 2016 University of Tennessee, Knoxville

#### Numerical Solutions Of Stochastic Differential Equations, Liguo Wang

*Doctoral Dissertations*

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by Brownian motions or the general Levy processes. There are two types of convergence for a numerical solution of a stochastic differential equation, the strong convergence and the weak convergence. We first introduce the strong convergence of the tamed Euler-Maruyama scheme under non-globally Lipschitz conditions, which allow the polynomial growth for the drift and diffusion coefficients. Then we prove a new weak convergence theorem given that the drift and diffusion coefficients of the stochastic differential equation are only twice continuously differentiable with bounded derivatives up to ...

Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, 2016 University of Georgia

#### Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, Noah Giansiracusa

*Journal of Humanistic Mathematics*

This review-essay on the mother-and-daughter collaboration *Math on Trial* stems from my recent experience using this book as the basis for a college freshman seminar on the interactions between math and law. I discuss the strengths and weaknesses of this book as an accessible introduction to this enigmatic yet deeply important topic. For those considering teaching from this text (a highly recommended endeavor) I offer some curricular suggestions.

Simple Tools With Nontrivial Implications For Assessment Of Hypothesis-Evidence Relationships: The Interrogator’S Fallacy, 2016 Hofstra University

#### Simple Tools With Nontrivial Implications For Assessment Of Hypothesis-Evidence Relationships: The Interrogator’S Fallacy, Justus R. Riek

*Journal of Humanistic Mathematics*

This paper takes a mathematical analysis technique derived from the Interrogator’s Fallacy (in a legal context), expands upon it to identify a set of three interrelated probabilistic tools with wide applicability, and demonstrates their ability to assess hypothesis-evidence relationships associated with important problems

Markov Chain Analysis Of Noise And Restart In Stochastic Local Search, 2016 Carnegie Mellon University

#### Markov Chain Analysis Of Noise And Restart In Stochastic Local Search, Ole J. Mengshoel, Youssef Ahres, Tong Yu

*Ole J Mengshoel*

Octahedral Dice, 2016 Butler University

#### Octahedral Dice, Todd Estroff, Jeremiah Farrell

*Jeremiah Farrell*

All five Platonic solids have been used as random number generators in games involving chance with the cube being the most popular. Martin Gardenr, in his article on dice (MG 1977) remarks: "Why cubical?... It is the easiest to make, its six sides accomodate a set of numbers neither too large nor too small, and it rolls easily enough but not too easily."

Gardner adds that the octahedron has been the next most popular as a randomizer. We offer here several problems and games using octahedral dice. The first two are extensions from Gardner's article. All answers will be ...

Thinking Poker Through Game Theory, 2016 California State University, San Bernardino

#### Thinking Poker Through Game Theory, Damian Palafox

*Electronic Theses, Projects, and Dissertations*

Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be ...

Elements Of The Mathematical Formulation Of Quantum Mechanics, 2016 Washington University in Saint Louis

#### Elements Of The Mathematical Formulation Of Quantum Mechanics, Keunjae Go

*Senior Honors Papers / Undergraduate Theses*

In this paper, we will explore some of the basic elements of the mathematical formulation of quantum mechanics. In the first section, I will list the motivations for introducing a probability model that is quite different from that of the classical probability theory, but still shares quite a few significant commonalities. Later in the paper, I will discuss the quantum probability theory in detail, while paying a brief attention to some of the axioms (by Birkhoff and von Neumann) that illustrate both the commonalities and differences between classical mechanics and quantum mechanics. This paper will end with a presentation of ...

On A Multiple-Choice Guessing Game, 2016 Bethel College - Mishawaka

#### On A Multiple-Choice Guessing Game, Ryan Cushman, Adam J. Hammett

*The Research and Scholarship Symposium*

We consider the following game (a generalization of a binary version explored by Hammett and Oman): the first player (“Ann”) chooses a (uniformly) random integer from the first n positive integers, which is not revealed to the second player (“Gus”). Then, Gus presents Ann with a k-option multiple choice question concerning the number she chose, to which Ann truthfully replies. After a predetermined number m of these questions have been asked, Gus attempts to guess the number chosen by Ann. Gus wins if he guesses Ann’s number. Our goal is to determine every m-question algorithm which maximizes the probability ...

Models For Hsv Shedding Must Account For Two Levels Of Overdispersion, 2016 University of Washington - Seattle Campus

#### Models For Hsv Shedding Must Account For Two Levels Of Overdispersion, Amalia Magaret

*UW Biostatistics Working Paper Series*

We have frequently implemented crossover studies to evaluate new therapeutic interventions for genital herpes simplex virus infection. The outcome measured to assess the efficacy of interventions on herpes disease severity is the viral shedding rate, defined as the frequency of detection of HSV on the genital skin and mucosa. We performed a simulation study to ascertain whether our standard model, which we have used previously, was appropriately considering all the necessary features of the shedding data to provide correct inference. We simulated shedding data under our standard, validated assumptions and assessed the ability of 5 different models to reproduce the ...

A New Right Tailed Test Of The Ratio Of Variances, 2016 University of North Florida

#### A New Right Tailed Test Of The Ratio Of Variances, Elizabeth Rochelle Lesser

*UNF Theses and Dissertations*

It is important to be able to compare variances efficiently and accurately regardless of the parent populations. This study proposes a new right tailed test for the ratio of two variances using the Edgeworth’s expansion. To study the Type I error rate and Power performance, simulation was performed on the new test with various combinations of symmetric and skewed distributions. It is found to have more controlled Type I error rates than the existing tests. Additionally, it also has sufficient power. Therefore, the newly derived test provides a good robust alternative to the already existing methods.

Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, 2016 Humboldt State University

#### Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, Steven T. Margell

*Theses*

In this thesis several novel techniques are developed to simulate fusion events in an isotropic, electrostatic three-dimensional Deuterium-Tritium plasma. These techniques allow us to accurately predict three-dimensional collision events with a one-dimensional model while simultaneously reducing compute time via a nearest neighbor algorithm. Furthermore, a fusion model based on first principles is developed that yields an average fusion reactivity which correlates well with empirical results.

Stochastic Network Design: Models And Scalable Algorithms, 2016 University of Massachusetts - Amherst

#### Stochastic Network Design: Models And Scalable Algorithms, Xiaojian Wu

*Doctoral Dissertations May 2014 - current*

Many natural and social phenomena occur in networks. Examples include the spread of information, ideas, and opinions through a social network, the propagation of an infectious disease among people, and the spread of species within an interconnected habitat network. The ability to modify a phenomenon towards some desired outcomes has widely recognized benefits to our society and the economy. The outcome of a phenomenon is largely determined by the topology or properties of its underlying network. A decision maker can take *management actions *to modify a network and, therefore, change the outcome of the phenomenon. A management action is an ...

A Novel Method For Assessing Co-Monotonicity: An Interplay Between Mathematics And Statistics With Applications, 2015 The University of Western Ontario

#### A Novel Method For Assessing Co-Monotonicity: An Interplay Between Mathematics And Statistics With Applications, Danang T. Qoyyimi

*Electronic Thesis and Dissertation Repository*

Numerous problems in econometrics, insurance, reliability engineering, and statistics rely on the assumption that certain functions are monotonic, which may or may not be true in real life scenarios. To satisfy this requirement, from the theoretical point of view, researchers frequently model the underlying phenomena using parametric and semi-parametric families of functions, thus effectively specifying the required shapes of the functions. To tackle these problems in a non-parametric way, when the shape cannot be specified explicitly but only estimated approximately, we suggest indices for measuring the lack of monotonicity in functions. We investigate properties of these indices and offer convenient ...