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 ...

Using Probabilistic Approach To Joint Clustering And Statistical Inference: Analytics For Big Investment Data, 2016 University of Massachusetts Medical School

#### Using Probabilistic Approach To Joint Clustering And Statistical Inference: Analytics For Big Investment Data, Hua Fang, Honggang Wang, Chonggang Wang, Mahmoud Daneshmand

*Hua Julia Fang*

This paper proposes a Contrarian Probabilistic Model (CPM) to evaluate the effectiveness of contrarians' investment in preferred stocks using big data from Tradeline. CPM accommodates the unique features of investment data which are often correlated, nested, heterogeneous, non-normal with missing values. The clustering and statistical inference are integrated in CPM, which enables joint investment behavior trajectory pattern recognition and risk analyses based on the entire variance-covariance structure between and within clusters. The empirical study using CPM provides a finer and comprehensive evaluation of contrarian investment in preferred stocks. Two distinctive investment behavior trajectory clusters were identified, showing a few high-risk-seeking ...

Cutoff For Lamplighter Markov Chains On Prisms, 2016 Bard College

#### Cutoff For Lamplighter Markov Chains On Prisms, Zexi Song

*Senior Projects Spring 2016*

A Markov chain is said to have a cutoff if its convergence to stationary distribution exhibits a sharp threshold. In this senior project we want to determine whether lamplighter Markov chains with prisms as underlying graphs have a cutoff. Lamplighter chains describe the stochastic process of a random walk on a graph along with the mixing of {0, 1} configurations over all vertices. A prism is defined as the Cartesian product of a cycle and a path. We provide bounds of the cover time of random walk on prisms. We run computer simulations to investigate the topic empirically. We also ...

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 ...

Probabilistic Reasoning In Cosmology, 2015 The University of Western Ontario

#### Probabilistic Reasoning In Cosmology, Yann Benétreau-Dupin

*Electronic Thesis and Dissertation Repository*

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology.

The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such ...

Tropical Cyclone Wind Hazard Assessment For Southeast Part Of Coastal Region Of China, 2015 The University of Western Ontario

#### Tropical Cyclone Wind Hazard Assessment For Southeast Part Of Coastal Region Of China, Sihan Li

*Electronic Thesis and Dissertation Repository*

Tropical cyclone (TC) or typhoon wind hazard and risk are significant for China. The return period value of the maximum typhoon wind speed is used to characterize the typhoon wind hazard and assign wind load in building design code. Since the historical surface observations of typhoon wind speed are often scarce and of short period, the typhoon wind hazard assessment is often carried out using the wind field model and TC track model. For a few major cities in the coastal region of mainland China, simple or approximated wind field models and a circular subregion method (CSM) have been used ...

Numerical Approximation Of Stochastic Differential Equations Driven By Levy Motion With Infinitely Many Jumps, 2015 University of Tennessee - Knoxville

#### Numerical Approximation Of Stochastic Differential Equations Driven By Levy Motion With Infinitely Many Jumps, Ernest Jum

*Doctoral Dissertations*

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by pure jump Levy processes with infinite jump activity. Examples include, the class of stochastic differential equations driven by stable and tempered stable Levy processes, which are suited for modeling of a wide range of heavy tail phenomena. We replace the small jump part of the driving Levy process by a suitable Brownian motion, as proposed by Asmussen and Rosinski, which results in a jump-diffusion equation. We obtain L^{p} [the space of measurable functions with a finite p-norm], for p greater than or equal to ...

Numerical Methods For Deterministic And Stochastic Phase Field Models Of Phase Transition And Related Geometric Flows, 2015 University of Tennessee - Knoxville

#### Numerical Methods For Deterministic And Stochastic Phase Field Models Of Phase Transition And Related Geometric Flows, Yukun Li

*Doctoral Dissertations*

This dissertation consists of three integral parts with each part focusing on numerical approximations of several partial differential equations (PDEs). The goals of each part are to design, to analyze and to implement continuous or discontinuous Galerkin finite element methods for the underlying PDE problem.

Part One studies discontinuous Galerkin (DG) approximations of two phase field models, namely, the Allen-Cahn and Cahn-Hilliard equations, and their related curvature-driven geometric problems, namely, the mean curvature flow and the Hele-Shaw flow. We derive two discrete spectrum estimates, which play an important role in proving the sharper error estimates which only depend on a ...

Propagating Lyapunov Functions To Prove Noise-Induced Stabilization, 2015 Valparaiso University

#### Propagating Lyapunov Functions To Prove Noise-Induced Stabilization, Tiffany Kolba, Avanti Athreya, Jonathan Mattingly

*Tiffany N Kolba*

No abstract provided.

Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, 2015 University of Bucharest

#### Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, Catalin Barboianu

*UNLV Gaming Research & Review Journal*

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of mathematical modeling, arguing that such non-standard knowledge ...

The Relationship Between Self-Determination And Client Outcomes Among The Homeless, 2015 California State University - San Bernardino

#### The Relationship Between Self-Determination And Client Outcomes Among The Homeless, Samuel M. Hanna

*Electronic Theses, Projects, and Dissertations*

This paper has attempted to determine if there is a significant relationship between self-determination and client outcomes among the homeless. The study has been based upon the conceptual framework set forth in Self-Determination Theory. The purpose of the study was to explore the relationship between self-determination and client outcomes among the homeless. Using a data collection instrument, based on empirically validated instrumentation, clients from several homeless service providers in the City of San Bernardino were assessed for the level of self-determination and autonomy support they experience within these agencies. Outcome measures included such things as whether the client was going ...

Estimated Probability Of Becoming A Case Of Drug Dependence In Relation To Duration Of Drug-Taking Experience: A Function Approach, 2015 Michigan State University

#### Estimated Probability Of Becoming A Case Of Drug Dependence In Relation To Duration Of Drug-Taking Experience: A Function Approach, Olga Vsevolozhskaya, James Anthony

*Olga A. Vsevolozhskaya*

Measured as elapsed time from first use to dependence syndrome onset, the estimated 'induction interval' for cocaine clearly is short relative to the cannabis interval, but little is known about risk of becoming dependent when use persists. Published estimates for this facet of drug dependence epidemiology are from life histories elicited years after first use. To improve estimation, we turn to new data from nationally representative samples of newly incident drug users identified via probability sampling and confidential computer-assisted self-interviews for the National Surveys on Drug Use and Health, 2004-2013. Standardized modules assess first and most recent use, and dependence ...

Video Event Understanding With Pattern Theory, 2015 University of South Florida

#### Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su

*MODVIS Workshop*

We propose a combinatorial approach built on Grenander’s pattern theory to generate semantic interpretations of video events of human activities. The basic units of representations, termed generators, are linked with each other using pairwise connections, termed bonds, that satisfy predefined relations. Different generators are specified for different levels, from (image) features at the bottom level to (human) actions at the highest, providing a rich representation of items in a scene. The resulting configurations of connected generators provide scene interpretations; the inference goal is to parse given video data and generate high-probability configurations. The probabilistic structures are imposed using energies ...

Spatially Random Processes In One-Dimensional Maps: The Logistic Map And The Arnold Circle Map, 2015 University of Colorado Boulder

#### Spatially Random Processes In One-Dimensional Maps: The Logistic Map And The Arnold Circle Map, An T. Le

*Applied Mathematics Graduate Theses & Dissertations*

One way to model in-situ remediation of contaminated groundwater is to consider spatially random processes in nonlinear systems. Groundwater remediation often requires injecting an aquifer with treatment solution, where degradation reactions break down the toxins. As the treatment solution and contaminated water flow through the aquifer, their movement is limited by the types of sediment found in the aquifer, which act as spatial barriers to mixing. The onset of chaos in this system implies the two solutions are well mixed, and thus the contaminants are rendered inert. The spatially random processes explored in this thesis are meant to mimic the ...

Assessing The Probability That A Finding Is Genuine For Large-Scale Genetic Association Studies, 2015 University of Connecticut

#### Assessing The Probability That A Finding Is Genuine For Large-Scale Genetic Association Studies, Chia-Ling Kuo, Olga Vsevolozhskaya, Dmitri Zaykin

*Olga A. Vsevolozhskaya*

Genetic association studies routinely involve massive numbers of statistical tests accompanied by P-values. Whole genome sequencing technologies increased the potential number of tested variants to tens of millions. The more tests are performed, the smaller P-value is required to be deemed significant. However, a small P-value is not equivalent to small chances of a spurious finding and significance thresholds may fail to serve as efficient filters against false results. While the Bayesian approach can provide a direct assessment of the probability that a finding is spurious, its adoption in association studies has been slow, due in part to the ubiquity ...

Boundary Problems For One And Two Dimensional Random Walks, 2015 Western Kentucky University

#### Boundary Problems For One And Two Dimensional Random Walks, Miky Wright

*Masters Theses & Specialist Projects*

This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with ...