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Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang 2021 East Tennessee State University

Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

Electronic Theses and Dissertations

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to ...


Improving Bayesian Graph Convolutional Networks Using Markov Chain Monte Carlo Graph Sampling, Aneesh Komanduri 2021 University of Arkansas, Fayetteville

Improving Bayesian Graph Convolutional Networks Using Markov Chain Monte Carlo Graph Sampling, Aneesh Komanduri

Computer Science and Computer Engineering Undergraduate Honors Theses

In the modern age of social media and networks, graph representations of real-world phenomena have become incredibly crucial. Often, we are interested in understanding how entities in a graph are interconnected. Graph Neural Networks (GNNs) have proven to be a very useful tool in a variety of graph learning tasks including node classification, link prediction, and edge classification. However, in most of these tasks, the graph data we are working with may be noisy and may contain spurious edges. That is, there is a lot of uncertainty associated with the underlying graph structure. Recent approaches to modeling uncertainty have been ...


Markov Chains And Their Applications, Fariha Mahfuz 2021 University of Texas at Tyler

Markov Chains And Their Applications, Fariha Mahfuz

Math Theses

Markov chain is a stochastic model that is used to predict future events. Markov chain is relatively simple since it only requires the information of the present state to predict the future states. In this paper we will go over the basic concepts of Markov Chain and several of its applications including Google PageRank algorithm, weather prediction and gamblers ruin.

We examine on how the Google PageRank algorithm works efficiently to provide PageRank for a Google search result. We also show how can we use Markov chain to predict weather by creating a model from real life data.


Predicting Tumor Response To Radiotherapy Based On Estimation Of Non-Treatment Parameters, Yutian Huang, Allison L. Lewis 2021 Lafayette College

Predicting Tumor Response To Radiotherapy Based On Estimation Of Non-Treatment Parameters, Yutian Huang, Allison L. Lewis

Spora: A Journal of Biomathematics

Though clinicians can now collect detailed information about a variety of tumor characteristics as a tumor evolves, it remains difficult to predict the efficacy of a given treatment prior to administration. Additionally, the process of data collection may be invasive and expensive. Thus, the creation of a framework for predicting patient response to treatment using only information collected prior to the start of treatment could be invaluable. In this study, we employ ordinary differential equation models for tumor growth and utilize synthetic data from a cellular automaton model for calibration. We investigate which parameters have the most influence upon treatment ...


Continuous-Time Controlled Branching Processes, Ines Garcia, George Yanev, Manuel Molina, Nikolay Yanev, Miguel Velasco 2021 University of Extremadura, Spain

Continuous-Time Controlled Branching Processes, Ines Garcia, George Yanev, Manuel Molina, Nikolay Yanev, Miguel Velasco

Mathematical and Statistical Sciences Faculty Publications and Presentations

Controlled branching processes with continuous time are introduced and limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.


Evaluation Of Individual And Ensemble Probabilistic Forecasts Of Covid-19 Mortality In The Us, Estee Y. Cramer, Velma K. Lopez, Jarad Niemi, Glover E. George, Jeffrey C. Cegan, Ian D. Dettwiller, William P. England, Matthew W. Farthing, Robert H. Hunter, Brandon Lafferty, Igor Linkov, Michael L. Mayo, Matthew D. Parno, Michael A. Rowland, Benjamin D. Trump, Lily Wang, Lei Gao, Zhiling Gu, Myungjin Kim, Yueying Wang, Jo W. Walker, Rachel B. Slayton, Michael Johansson, Matthew Biggerstaff, et al. 2021 University of Massachusetts

Evaluation Of Individual And Ensemble Probabilistic Forecasts Of Covid-19 Mortality In The Us, Estee Y. Cramer, Velma K. Lopez, Jarad Niemi, Glover E. George, Jeffrey C. Cegan, Ian D. Dettwiller, William P. England, Matthew W. Farthing, Robert H. Hunter, Brandon Lafferty, Igor Linkov, Michael L. Mayo, Matthew D. Parno, Michael A. Rowland, Benjamin D. Trump, Lily Wang, Lei Gao, Zhiling Gu, Myungjin Kim, Yueying Wang, Jo W. Walker, Rachel B. Slayton, Michael Johansson, Matthew Biggerstaff, Et Al.

Statistics Publications

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. In 2020, the COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized hundreds of thousands of specific predictions from more than 50 different academic, industry, and independent research groups. This manuscript systematically evaluates 23 models that regularly submitted forecasts of ...


The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications, Zhenxian Gong 2021 The University of Western Ontario

The Mean-Reverting 4/2 Stochastic Volatility Model: Properties And Financial Applications, Zhenxian Gong

Electronic Thesis and Dissertation Repository

Financial markets and instruments are continuously evolving, displaying new and more refined stylized facts. This requires regular reviews and empirical evaluations of advanced models. There is evidence in literature that supports stochastic volatility models over constant volatility models in capturing stylized facts such as "smile" and "skew" presented in implied volatility surfaces. In this thesis, we target commodity and volatility index markets, and develop a novel stochastic volatility model that incorporates mean-reverting property and 4/2 stochastic volatility process. Commodities and volatility indexes have been proved to be mean-reverting, which means their prices tend to revert to their long term ...


Predicting The Number Of Future Events, Qinglong Tian, Fanqi Meng, Daniel J. Nordman, William Q. Meeker 2021 Iowa State University

Predicting The Number Of Future Events, Qinglong Tian, Fanqi Meng, Daniel J. Nordman, William Q. Meeker

Statistics Publications

This paper describes prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Examples include the prediction of warranty returns and the prediction of the number of future product failures that could cause serious threats to property or life. Important decisions such as whether a product recall should be mandated are often based on such predictions. Data, generally right-censored (and sometimes left truncated and right-censored), are used to estimate the parameters of a time-to-event distribution. This distribution can then be used to predict the number of events over future periods of ...


Design Project: Smart Headband, John Michel, Jack Durkin, Noah Lewis 2021 The University of Akron

Design Project: Smart Headband, John Michel, Jack Durkin, Noah Lewis

Williams Honors College, Honors Research Projects

Concussion in sports is a prevalent medical issue. It can be difficult for medical professionals to diagnose concussions. With the fast pace nature of many sports, and the damaging effects of concussions, it is important that any concussion risks are assessed immediately. There is a growing trend of wearable technology that collects data such as steps and provides the wearer with in-depth information regarding their performance. The Smart Headband project created a wearable that can record impact data and provide the wearer with a detailed analysis on their risk of sustaining a concussion. The Smart Headband uses accelerometers and gyroscopes ...


Analysis And Implementation Of The Maximum Likelihood Expectation Maximization Algorithm For Find, Angus Boyd Jameson 2020 University of New Hampshire

Analysis And Implementation Of The Maximum Likelihood Expectation Maximization Algorithm For Find, Angus Boyd Jameson

Student Research Projects

This thesis presents an organized explanation and breakdown of the Maximum Likelihood Expectation Maximization image reconstruction algorithm. This background research was used to develop a means of implementing the algorithm into the imaging code for UNH's Field Deployable Imaging Neutron Detector to improve its ability to resolve complex neutron sources. This thesis provides an overview for this implementation scheme, and include the results of a couple of reconstruction tests for the algorithm. A discussion is given on the current state of the algorithm and its integration with the neutron detector system, and suggestions are given for how the work ...


Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev 2020 The University of Texas Rio Grande Valley

Exponential And Hypoexponential Distributions: Some Characterizations, George Yanev

Mathematical and Statistical Sciences Faculty Publications and Presentations

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some n ≥ 2, X1, X2, . . . , Xn are independent copies of a random variable X with unknown distribution F and a specific linear combination of Xj ’s has hypoexponential distribution, then F is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently by Arnold and Villaseñor (2013 ...


A Brief On Characteristic Functions, Austin G. Vandegriffe 2020 Missouri University of Science and Technology

A Brief On Characteristic Functions, Austin G. Vandegriffe

Graduate Student Research & Creative Works

Characteristic functions (CFs) are often used in problems involving convergence in distribution, independence of random variables, infinitely divisible distributions, and stochastics. The most famous use of characteristic functions is in the proof of the Central Limit Theorem, also known as the Fundamental Theorem of Statistics. Though less frequent, CFs have also been used in problems of nonparametric time series analysis and in machine learning. Moreover, CFs uniquely determine their distribution, much like the moment generating functions (MGFs), but the major difference is that CFs always exists, whereas MGFs can fail, e.g. the Cauchy distribution. This makes CFs more robust ...


A Brief On Optimal Transport, Austin G. Vandegriffe 2020 Missouri University of Science and Technology

A Brief On Optimal Transport, Austin G. Vandegriffe

Graduate Student Research & Creative Works

Optimal transport is an interesting and exciting application of measure theory to optimization and analysis. In the following, I will bring you through a detailed treatment of random variable couplings, transport plans, basic properties of transport plans, and finishing with the Wasserstein distance on spaces of probability measures with compact support. No detail is left out in this presentation, but some results have further generality and more intricate consequences when tools like measure disintegration are used. But this is left for future work.


Concerns In Id'ing A Suitable Distribution, Necip Doganaksoy, Gerald J. Hahn, William Q. Meeker 2020 Siena College School of Business

Concerns In Id'ing A Suitable Distribution, Necip Doganaksoy, Gerald J. Hahn, William Q. Meeker

Statistics Publications

Analysis of product lifetime data generally requires fitting a suitable distribution to the data at hand. The fitted distribution is used to estimate quantities of interest, such as the fraction of product failing after various times in service and selected distribution percentiles (for example, the estimated time by which 1% of the product population is expected to fail).


Stochastic Analysis And Statistical Inference For Seir Models Of Infectious Diseases, Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Anuj Mubayi 2020 PRECISIONheor

Stochastic Analysis And Statistical Inference For Seir Models Of Infectious Diseases, Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Anuj Mubayi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Direct Questioning Of Sensitive Topics In Public Health Studies: A Simulation Study, Jessica K. Fox, Evrim Oral 2020 LSU Health Sciences Center, School of Public Health, Biostatistics Program

Direct Questioning Of Sensitive Topics In Public Health Studies: A Simulation Study, Jessica K. Fox, Evrim Oral

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman 2020 University of Washington, Tacoma

Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman

Access*: Interdisciplinary Journal of Student Research and Scholarship

The history of wagering predictions and their impact on wide reaching disciplines such as statistics and economics dates to at least the 1700’s, if not before. Predicting the outcomes of sports is a multibillion-dollar business that capitalizes on these tools but is in constant development with the addition of big data analytics methods. Sportsline.com, a popular website for fantasy sports leagues, provides odds predictions in multiple sports, produces proprietary computer models of both winning and losing teams, and provides specific point estimates. To test likely candidates for inclusion in these prediction algorithms, the authors developed a computer model ...


Task Interrupted By A Poisson Process, Jarrett Christopher Nantais 2020 University of Windsor

Task Interrupted By A Poisson Process, Jarrett Christopher Nantais

Major Papers

We consider a task which has a completion time T (if not interrupted), which is a random variable with probability density function (pdf) f(t), t>0. Before it is complete, the task may be interrupted by a Poisson process with rate lambda. If that happens, then the task must begin again, with the same completion time random variable T, but with a potentially different realization. These interruptions can reoccur, until eventually the task is finished, with a total time of W. In this paper, we will find the Laplace Transform of W in several special cases.


Video Game Genre Classification Based On Deep Learning, Yuhang Jiang 2020 Western Kentucky University

Video Game Genre Classification Based On Deep Learning, Yuhang Jiang

Masters Theses & Specialist Projects

Video games have played a more and more important role in our life. While the genre classification is a deeply explored research subject by leveraging the strength of deep learning, the automatic video game genre classification has drawn little attention in academia. In this study, we compiled a large dataset of 50,000 video games, consisting of the video game covers, game descriptions and the genre information. We explored three approaches for genre classification using deep learning techniques. First, we developed five image-based models utilizing pre-trained computer vision models such as MobileNet, ResNet50 and Inception, based on the game covers ...


Maximum Entropy Classification For Record Linkage, Danhyang Lee, Li-Chun Zhang, Jae Kwang Kim 2020 University of Alabama

Maximum Entropy Classification For Record Linkage, Danhyang Lee, Li-Chun Zhang, Jae Kwang Kim

Statistics Publications

By record linkage one joins records residing in separate files which are believed to be related to the same entity. In this paper we approach record linkage as a classification problem, and adapt the maximum entropy classification method in text mining to record linkage, both in the supervised and unsupervised settings of machine learning. The set of links will be chosen according to the associated uncertainty. On the one hand, our framework overcomes some persistent theoretical flaws of the classical approach pioneered by Fellegi and Sunter (1969); on the other hand, the proposed algorithm is scalable and fully automatic, unlike ...


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