Statistics and Probability Commons^™

Stability Of Quantum Computers, Samudra Dasgupta

Doctoral Dissertations

Quantum computing faces a persistent challenge with noise. This dissertation addresses the fundamental question of how to define and differentiate computational accuracy, result reproducibility, output stability, and device reliability amidst spatio-temporal non-stationarity in quantum registers. It explores characterizing spatial and temporal noise statistics, estimating performance limits via characterization data, mitigating time-varying quantum noise with adaptive algorithms, and understanding trade-offs when using unreliable devices. Sources of noise include interaction between qubits and the environment, as well as imperfections in implementing quantum logic gates, leading to decoherence (the loss of coherence) in quantum states. Quantum states' survival is brief, making reliable output …

On A Multivalued Prescribed Mean Curvature Problem And Inclusions Defined On Dual Spaces, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

This article addresses two main objectives. First, it establishes a functional analytic framework and presents existence results for a quasilinear inclusion describing a prescribed mean curvature problem with homogeneous Dirichlet boundary conditions, involving a multivalued lower order term. The formulation of the problem is done in the space of functions with bounded variation. The second objective is to introduce a general existence theory for inclusions defined on nonreflexive Banach spaces, which is specifically applicable to the aforementioned prescribed mean curvature problem. This problem can be formulated as a multivalued variational inequality in the space of functions with bounded variation, which, …

Tropical Fish Study In Tahiti, French Polynesia, Miranda Brainard, Caitlyn Swango, Paityn Houglan, Richard Londraville

Williams Honors College, Honors Research Projects

In May of 2023, I embarked on an exciting research journey to Moorea, French Polynesia, alongside fellow students and faculty members from the University of Akron and Syracuse University. This expedition was part of the university-sponsored Tropical Vertebrate Biology course, where we delved into the exploration of various tropical species inhabiting the island, including sea urchins, geckos, and my primary focus, the blackspotted rockskipper.

My research team, composed of my co-authors and me, was particularly intrigued by the unique refuge-seeking behavior displayed by blackspotted rockskippers. These amphibious fish are renowned for their remarkable ability to inhabit tide pools and rocky …

Formulating An Efficient Statistical Test Using The Goodness Of Fit Approach With Applications To Real-Life Data, S. A. Qaid, S. E. Abo Youssef Prof., Mahmoud Mansour

Basic Science Engineering

Statistical tests are very important for researchers to make decisions. In particular, when the tests are non-parametric, they are of greater importance because they can be applied to a wide range of data sets regardless of knowing the distribution of these data. Researchers are therefore racing to obtain efficient tests for making good decisions based on the results of these tests. In this study, NBU (2)L was used based on the goodness of fit approach to present an efficient statistical test. The efficiency of the proposed test was computed, and the results were compared to those of other tests. Critical …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Interpretable Word-Level Sentiment Analysis With Attention-Based Multiple Instance Classification Models, Chenyu Yang

Statistical Science Theses and Dissertations

In this study, our main objective is to tackle the black-box nature of popular machine learning models in sentiment analysis and enhance model interpretability. We aim to gain more insight into the decision-making process of sentiment analysis models, which is often obscure in those complex models. To achieve this goal, we introduce two word-level sentiment analysis models.

The first model is called the attention-based multiple instance classification (AMIC) model. It combines the transparent model structure of multiple instance classification and the self-attention mechanism in deep learning to incorporate the contextual information from documents. As demonstrated by a wine review dataset …

Climate Change Impact On Bridge Scour Risk In Ny State: A Gis-Based Risk Analysis Model, Muhammad Hassan Butt

Publications and Research

Bridge scour, the primary cause of bridge failure in the United States, escalates post-severe storms, necessitating effective mitigation. This study employs a GIS-based risk analysis model to assess climate change's impact on bridge scour and associated risks in New York State. Data from the National Bridge Inventory, climate hazard maps, and geospatial data are integrated.

Teaching Reproducibility To First Year College Students: Reflections From An Introductory Data Science Course, Brennan L. Bean

Journal on Empowering Teaching Excellence

Access the online Pressbooks version of this article here.

Modern technology threatens traditional modes of classroom assessment by providing students with automated ways to write essays and take exams. At the same time, modern technology continues to expand the accessibility of computational tools that promise to increase the potential scope and quality of class projects. This paper presents a case study where students are asked to complete a “reproducible” final project in an introductory data science course using the R programming language. A reproducible project is one where an instructor can easily regenerate the results and conclusions from the submitted …

Analyzing The Efficacy Of Covid-19 Travel Bans: A Regression Analysis Approach, Mallory Kochanek

Honors Projects

Some might associate the term ‘public health’ with the pandemic that occurred in 2020. COVID-19 spread like most have never seen in their lifetime. It is useful to look at the effectiveness of the travel re- strictions in mitigating the spread of the global pandemic. Using linear regression and network regression, we obtain parameter estimates to determine the relation of predictors, such as network effect, percentage of urban population and GDP, on the COVID-19 incidence rate for the months January to April of 2020. Linear regression does not ac- count for the correlation structure of the data. Network regression, on …

Interactions Between Sediment Mechanical Structure And Infaunal Community Structure Following Physical Disturbance, William Cyrus Roger Clemo

Theses and Dissertations

Shallow, river-influenced coastal sediments are important for global carbon storage and nutrient cycling and provide a habitat for diverse communities of invertebrates (infauna). Elevated bed shear stress from extreme storms can resuspend, transport, and deposit sediments, disrupting the cohesive structure of muds, and sorting and depositing sand eroded from beaches. These physical disruptions can also resuspend or smother infauna, decreasing abundances and changing community structure. Infaunal activities such as burrowing, tube construction, and feeding can impact sediment structure and stability. However, little is known about how physical disturbance impacts short and long-term sediment habitat suitability and whether disturbance-tolerant infauna influence …

An Ensemble Approach For Mapping Snow Water Equivalent In Utah, Logan Schneider

All Graduate Theses and Dissertations, Fall 2023 to Present

Mountain snowpack is an important resource for water management planning in Utah. Snow water equivalent (SWE) is the amount of water contained in a snowpack. A few organizations predict SWE throughout the United States but struggle making accurate predictions in mountainous regions. Weather stations provide accurate measurements of SWE but have limited spatial coverage that hinders the ability to make accurate estimates statewide. This thesis examines the accuracy of current models and proposes using local weather measurements to improve upon national level predictions. An R statistical software package named rsnodas implements this process while allowing the public access to a …

Random Variable Spaces: Mathematical Properties And An Extension To Programming Computable Functions, Mohammed Kurd-Misto

Computational and Data Sciences (PhD) Dissertations

This dissertation aims to extend the boundaries of Programming Computable Functions (PCF) by introducing a novel collection of categories referred to as Random Variable Spaces. Originating as a generalization of Quasi-Borel Spaces, Random Variable Spaces are rigorously defined as categories where objects are sets paired with a collection of random variables from an underlying measurable space. These spaces offer a theoretical foundation for extending PCF to natively handle stochastic elements.

The dissertation is structured into seven chapters that provide a multi-disciplinary background, from PCF and Measure Theory to Category Theory with special attention to Monads and the Giry Monad. The …

The Private Pilot Check Ride: Applying The Spacing Effect Theory To Predict Time To Proficiency For The Practical Test, Michael Scott Harwin

Theses and Dissertations

This study examined the relationship between a set of targeted factors and the total flight time students needed to become ready to take the private pilot check ride. The study was grounded in Ebbinghaus’s (1885/1913/2013) forgetting curve theory and spacing effect, and Ausubel’s (1963) theory of meaningful learning. The research factors included (a) training time to proficiency, which represented the number of training days needed to become check-ride ready; (b) flight training program (Part 61 vs. Part 141); (c) organization offering the training program (2- or 4-year college/university vs. FBO); (d) scheduling policy (mandated vs. student-driven); and demographical variables, which …

Data Quality Checks: Implementation With Popular Data Collection Crowdsourcing Platforms, James Down, Gregory Balkcom, Kristine Duncan, Ngan (An) Truong, Andrew Lewis

Symposium of Student Scholars

The utilization of online crowdsourcing platforms for data collection has increased over the past two decades in the field of public health due to the ease of use, the cost-saving benefits, the speed of the data collection process, and the accessibility of a potentially true representative population. Although these platforms offer many advantages to researchers, significant drawbacks exist, such as poor data quality, that threaten the reliability and validity of the study. Previous studies have examined data quality concerns, but differences in results arise due to variations in study designs, disciplinary contexts, and the platforms being investigated. Therefore, this study …

The Impacts Of The Covid-19 Pandemic On Mental Health Across Different Genders And Sexualities, Jiale Zhu, Jonas Katona

Undergraduate Research Journal for the Human Sciences

Current studies report an increase in psychological distress as a result of the COVID-19 pandemic. This study is interested in examining mental health disparities and how the COVID-19 pandemic has disproportionately impacted marginalized groups—and more specifically, those identified by sex, gender, and sexuality—compared with the general population. This study also considers the effects and ramifications of different policy measures taken during the course of the pandemic. We perform exploratory data modeling and analysis on several important and publicly available datasets taken during the pandemic on mental health and COVID-19 infection data across various identity groups to look for significant disparities, …

Expansionary Fiscal Contraction Hypothesis: An Evidence From Pakistan, Aisha Irum

CBER Conference

The fiscal sector in Pakistan has been facing mule-layered challenges over several years. One of the reasons is the stubborn and unproductive nature of its public expenditure, and the other one is the lower tax revenues. This issue of hovering fiscal deficit is mostly dealt with the tools of fiscal contraction/austerity which can have a potential impact on the private sector of the economy. Thus, the question which has been addressed in this study is whether the Expansionary Fiscal Contraction (EFC) hypothesis holds in case of Pakistan. Fiscal contraction episodes have been identified using growth in the growth rates of …

Probability Distributions Arising In Connection With The Inspection Paradox For Bernoulli Trials., James E. Marengo, Anne Marino Himes, W. Cade Reinberger, David L. Farnsworth

Articles

In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.

Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako

Doctoral Dissertations

This dissertation is in the field of Nonparametric Derivative Estimation using
Penalized Splines. It is conducted in two parts. In the first part, we study the L2
convergence rates of estimating derivatives of mean regression functions using penalized splines. In 1982, Stone provided the optimal rates of convergence for estimating derivatives of mean regression functions using nonparametric methods. Using these rates, Zhou et. al. in their 2000 paper showed that the MSE of derivative estimators based on regression splines approach zero at the optimal rate of convergence. Also, in 2019, Xiao showed that, under some general conditions, penalized spline estimators …

Multi-Arm Randomized Control Trials In Inflammatory Bowel Disease: A Literature Review And An Illustration Of Methods For Analysis, Sahiba Saini

Electronic Thesis and Dissertation Repository

This thesis aimed to review the literature on multiple-arm randomized control trials in inflammatory bowel disease (IBD) and to illustrate how to analyze these trials, focusing on appropriately controlling the type 1 error rates. The literature review found 247 trials published from the inception of each database to April 2014, of which 122 (49%) trials were multiple-arm trials and of those, 59 (48%) trials were on ulcerative colitis and 63 (52%) on Crohn’s disease. A published assessment tool was adopted to assess whether controlling of Type I error rates was needed. Despite the common use of this trial design and …

Baa-Ttling Sore Mouth In Sheep With Mathematical Modeling, David C. Elzinga, W. Christopher Strickland

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.