Statistics and Probability Commons^™

Effect Of Phylogeny Misestimation On Estimating Trait Evolution Parameters, Tabytha Ariel Perez

Mathematics & Statistics ETDs

Biologists are interested in estimating trait evolution models from phylogenies. However, phylogenies are imperfectly estimated, generally from DNA sequence data. In this study, true phylogenies are simulated to understand whether errors in phylogeny estimation affect inference of the trait evolution model. Given the tree, DNA sequences as well as traits are then simulated from the true phylogeny; both are simulated independently from the other. After the simulation, the DNA sequences were used to estimate trees using the UPGMA method without utilizing the trait information. The estimated trees combined with the traits are used to infer the evolutionary trait models, specifically …

Derivation And Analysis Of A Discrete Predator–Prey Model, Sabrina H. Streipert, Gail S.K. Wolkowicz, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We derive a discrete predator–prey model from first principles, assuming that the prey population grows to carrying capacity in the absence of predators and that the predator population requires prey in order to grow. The proposed derivation method exploits a technique known from economics that describes the relationship between continuous and discrete compounding of bonds. We extend standard phase plane analysis by introducing the next iterate root-curve associated with the nontrivial prey nullcline. Using this curve in combination with the nullclines and direction field, we show that the prey-only equilibrium is globally asymptotic stability if the prey consumption-energy rate of …

Error Estimate Of A Decoupled Numerical Scheme For The Cahn-Hilliard-Stokes-Darcy System, Wenbin Chen, Shufen Wang, Yichao Zhang, Daozhi Han, Cheng Wang, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We analyze a fully discrete finite element numerical scheme for the Cahn-Hilliard-Stokes-Darcy system that models two-phase flows in coupled free flow and porous media. To avoid a well-known difficulty associated with the coupling between the Cahn-Hilliard equation and the fluid motion, we make use of the operator-splitting in the numerical scheme, so that these two solvers are decoupled, which in turn would greatly improve the computational efficiency. The unique solvability and the energy stability have been proved in Chen et al. (2017, Uniquely solvable and energy stable decoupled numerical schemes for the Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry. …

Numerical Solutions To The Robin Inverse Problem With Nonnegativity Constraints, Weifu Fang, Fu-Rong Lin

Mathematics and Statistics Faculty Publications

We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.

Applications Of Machine Learning Algorithms In Materials Science And Bioinformatics, Mohammed Quazi

Mathematics & Statistics ETDs

The piezoelectric response has been a measure of interest in density functional theory (DFT) for micro-electromechanical systems (MEMS) since the inception of MEMS technology. Piezoelectric-based MEMS devices find wide applications in automobiles, mobile phones, healthcare devices, and silicon chips for computers, to name a few. Piezoelectric properties of doped aluminum nitride (AlN) have been under investigation in materials science for piezoelectric thin films because of its wide range of device applicability. In this research using rigorous DFT calculations, high throughput ab-initio simulations for 23 AlN alloys are generated.

This research is the first to report strong enhancements of piezoelectric properties …

Data-Driven Analytical Predictive Modeling For Pancreatic Cancer, Financial & Social Systems, Aditya Chakraborty

USF Tampa Graduate Theses and Dissertations

Pancreatic cancer is one of the most deathly disease and becoming an increasingly commoncause of cancer mortality. It continues giving rise to massive challenges to clinicians and cancer researchers. The combined five-year survival rate for pancreatic cancer is extremely low, about 5 to 10 percent, owing to the fact that a large number of the patients are diagnosed at stage IV when the disease has metastasized. Our study investigates if there exists any statistical significant difference between the median survival times and also the survival probabilities of male and female pancreatic cancer patients at different cancer stages, and irrespective of …

Sparse Spectral-Tau Method For The Two-Dimensional Helmholtz Problem Posed On A Rectangular Domain, Gabriella M. Dalton

Mathematics & Statistics ETDs

Within recent decades, spectral methods have become an important technique in numerical computing for solving partial differential equations. This is due to their superior accuracy when compared to finite difference and finite element methods. For such spectral approximations, the convergence rate is solely dependent on the smoothness of the solution yielding the potential to achieve spectral accuracy. We present an iterative approach for solving the two-dimensional Helmholtz problem posed on a rectangular domain subject to Dirichlet boundary conditions that is well-conditioned, low in memory, and of sub-quadratic complexity. The proposed approach spectrally approximates the partial differential equation by means of …

(R1881) Impatient Customers In Queueing System With Optional Vacation Policies And Power Saving Mode, Poonam Gupta, Rajni Gupta, Sangeeta Malik

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, a queueing system with two optional vacation policies, power-saving mode under reneging and retention of reneged customers in both vacations is analyzed. If the server is free, it chooses either of the vacations, classical vacation or working vacation. During vacations, the customers may get impatient due to delays and may leave the system, but they are retained in the system with some convincing mechanisms. On vacation completion, if the system is empty, the server is turned off to facilitate better utilization of the resources. Some of the operating system characteristics are derived using the probability generating functions …

Nonoscillatory Solutions Of Higher-Order Fractional Differential Equations, Martin Bohner, Said R. Grace, Irena Jadlovská, Nurten Kılıç

Mathematics and Statistics Faculty Research & Creative Works

This paper deals with the asymptotic behavior of the nonoscillatory solutions of a certain forced fractional differential equations with positive and negative terms, involving the Caputo fractional derivative. The results obtained are new and generalize some known results appearing in the literature. Two examples are also provided to illustrate the results.

Analysis Of Ibnr Liabilities With Interevent Times Depending On Claim Counts, Daniel J. Geiger, Akim Adekpedjou

Mathematics and Statistics Faculty Research & Creative Works

We extend a recently proposed stochastic loss reserving model for liabilities from incurred but not reported (IBNR) micro-level claims. We propose viewing the number of claims from an event as a measure of catastrophic severity. This view covers catastrophes with arbitrarily many classes of magnitude. Our Markovian model allows the time between disasters to depend on the previous event's level of severity. Simultaneously, we let the discount rate vary in the same manner. First, we find the moments of IBNR liabilities in our model. Then, we permit a later time horizon for IBNR claims when considered jointly with incurred and …

Joint Control Of Manufacturing And Onsite Microgrid System Via Novel Neural-Network Integrated Reinforcement Learning Algorithms, Jiaojiao Yang, Zeyi Sun, Wenqing Hu, Louis Steinmeister

Mathematics and Statistics Faculty Research & Creative Works

Microgrid is a promising technology of distributed energy supply system, which consists of storage devices, generation capacities including renewable sources, and controllable loads. It has been widely investigated and applied for residential and commercial end-use customers as well as critical facilities. In this paper, we propose a joint state-based dynamic control model on microgrids and manufacturing systems where optimal controls for both sides are implemented to coordinate the energy demand and supply so that the overall production cost can be minimized considering the constraint of production target. Markov Decision Process (MDP) is used to formulate the decision-making procedure. The main …

Characterization Of A Family Of Rotationally Symmetric Spherical Quadrangulations, Lowell Abrams, Daniel Slilaty

Mathematics and Statistics Faculty Publications

A spherical quadrangulation is an embedding of a graph G in the sphere in which each facial boundary walk has length four. Vertices that are not of degree four in G are called curvature vertices. In this paper we classify all spherical quadrangulations with n-fold rotational symmetry (n ≥ 3) that have minimum degree 3 and the least possible number of curvature vertices, and describe all such spherical quadrangulations in terms of nets of quadrilaterals. The description reveals that such rotationally symmetric quadrangulations necessarily also have a pole-exchanging symmetry.

Data Ethics: An Investigation Of Data, Algorithms, And Practice, Gabrialla S. Cockerell

Honors Projects

This paper encompasses an examination of defective data collection, algorithms, and practices that continue to be cycled through society under the illusion that all information is processed uniformly, and technological innovation consistently parallels societal betterment. However, vulnerable communities, typically the impoverished and racially discriminated, get ensnared in these harmful cycles due to their disadvantages. Their hindrances are reflected in their information due to the interconnectedness of data, such as race being highly correlated to wealth, education, and location. However, their information continues to be analyzed with the same measures as populations who are not significantly affected by racial bias. Not …

Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Combining Cardiac Monitoring With Actigraphy Aids Nocturnal Arousal Detection During Ambulatory Sleep Assessment In Insomnia, Lara Rösler, Glenn Van Der Lande, Jeanne Leerssen, Austin G. Vandegriffe, Oti Lakbila-Kamal, Jessica C. Foster-Dingley, Anne C.W. Albers, Eus J.W. Van Someren

Mathematics and Statistics Faculty Research & Creative Works

Study Objectives: The objective assessment of insomnia has remained difficult. Multisensory devices collecting heart rate (HR) and motion are regarded as the future of ambulatory sleep monitoring. Unfortunately, reports on altered average HR or heart rate variability (HRV) during sleep in insomnia are equivocal. Here, we evaluated whether the objective quantification of insomnia improves by assessing state-related changes in cardiac measures. Methods: We recorded electrocardiography, posture, and actigraphy in 33 people without sleep complaints and 158 patients with mild to severe insomnia over 4 d in their home environment. At the microscale, we investigated whether HR changed with proximity to …

Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County, Cassie Dibenedetti, Kate Rosello

Undergraduate Research and Scholarship Symposium

Auberle social services is opening the Family Healing Center (FHC), a level 3.5 treatment program in Pittsburgh, PA that provides housing and 24-hour support for families struggling with opioid addiction. We partnered with Auberle to study characteristics of individuals receiving level 3.5 treatment and to determine whether longer treatment lengths correlate with fewer adverse outcomes. We obtained data from the Allegheny County Department of Human Services on 2,016 individuals admitted to level 3.5 treatment in 2019. The data included birth year, race, gender, admittance date, discharge date, and Children Youth and Family (CYF) incidents before and after treatment. We categorized …

A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman

USF Tampa Graduate Theses and Dissertations

The goal of the current research project is the formulation of a method for the estimation and modeling of additive stochastic processes with both linear- and cycle-type trend components as well as a relatively robust noise component in the form of Levy processes. Most of the research in stochastic processes tends to focus on cases where the process is stationary, a condition that cannot be assumed for the model above due to the presence of the cyclical sub-component in the overall additive process. As such, we outline a number of relevant theoretical and applied topics, such as stochastic processes and …

Anticipating Stochastic Integrals And Related Linear Stochastic Differential Equations, Sudip Sinha

LSU Doctoral Dissertations

Itô’s stochastic calculus revolutionized the field of stochastic analysis and has found numerous applications in a wide variety of disciplines. Itô’s theory, even though quite general, cannot handle anticipating stochastic processes as integrands. There have been considerable efforts within the mathematical community to extend Itô’s calculus to account for anticipation. The Ayed–Kuo integral — introduced in 2008 — is one of the most recent developments. It is arguably the most accessible among the theories extending Itô’s calculus — relying solely on probabilistic methods. In this dissertation, we look at the recent advances in this area, highlighting our contributions. First, we …

Machine Learning In Support Of Student Success, Rachel Rucker

Undergraduate Research Conference

Our goal is to predict whether a student will finish the semester on academic probation by mid-term using university data.

Eigenfunction Restriction Estimates For Curves With Nonvanishing Geodesic Curvatures In Compact Riemannian Surfaces With Nonpositive Sectional Curvatures, Chamsol Park

Mathematics & Statistics ETDs

For 2 ≤ p < 4, we study the Lp norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact 2-dimensional Riemannian manifolds. Burq, G\´erard, and Tzvetkov [12], and Hu [21] found eigenfunction restriction estimates for a curve with nonvanishing geodesic curvatures. We will explain how the proof of the known estimates helps us to consider the case where the given smooth compact Riemannian manifold has nonpositive sectional curvatures. For p = 4, we will also obtain a logarithmic analogous estimate, by using arguments in Xi and Zhang [37], Sogge [33], and Bourgain [10]. At the end of this dissertation, we will talk about a future work, which is a follow up study for higher dimensional analogues of the above curve cases.

General Stochastic Calculus And Applications, Pujan Shrestha

LSU Doctoral Dissertations

In 1942, K. Itô published his pioneering paper on stochastic integration with respect to Brownian motion. This work led to the framework for Itô calculus. Note that, Itô calculus is limited in working with knowledge from the future. There have been many generalizations of the stochastic integral in being able to do so. In 2008, W. Ayed and H.-H. Kuo introduced a new stochastic integral by splitting the integrand into the adaptive part and the counterpart called instantly independent. In this doctoral work, we conduct deeper research into the Ayed–Kuo stochastic integral and corresponding anticipating stochastic calculus.

We provide a …

Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano

Electrical and Computer Engineering ETDs

Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …

Hypothesis Testing Of Student's Mathematical Performance In Relation To The Covid-19 Pandemic, Elizabeth Foster

Mathematics Senior Capstone Papers

The COVID-19 Pandemic affected everyone, especially schools and education due to the rapid switch from traditional face-to-face classes to online and hybrid classes. The goal of this study is to see how the pandemic affected students’ grades during distance learning when compared to before. Using hypothesis testing, we will analyze data from 13 sections of MATH 243 classes to determine if the averages went down during the pandemic, specifically in hybrid class settings. Based on the raw data of the test grades in relation to the COVID-19 Pandemic, a significant difference can be found in test scores before and during …

Factors That Relate To Academic Excellence, Matthew Lemoine

Mathematics Senior Capstone Papers

The American College Testing (ACT) provides university admissions offices a look into a student’s academic ability so that the university can determine admittance and scholarships. The premise of this study is to see whether this is the most effective way to determine academic ability, using the Logistic Regression Model. The data was collected from October 21, 2021 to December 31, 2021 at Louisiana Tech University. Using the Logistic Regression Model, predictions of academic excellence are obtained based on the parameters outlined in this paper. After the parameters for the Logistic Regression Model are calculated, conclusions can be drawn that the …

Statistical Analysis Of Home-Field Advantage In European Soccer, Francisco Simoncini

Mathematics Senior Capstone Papers

Home-field advantage in the sports world is commonly known as a huge factor in determining the final score of any sports game. By using a one-tailed, two-sample t-test, I am analyzing how playing at home generally affects a European soccer team’s performance. I am looking at how these performances are affected across three domestic leagues in Europe. I predict that when teams play at home, there will be a significant difference in their win ratio and goals scored.

Flood Risk Prediction In Southern Louisiana Using Support Vector Machines, Claire Dorsett

Mathematics Senior Capstone Papers

Flooding in Southern Louisiana is a growing concern as violent weather becomes more frequent. According to the Environmental Protection Agency (EPA), Louisiana soils have become drier and annual rainfall trends have increased, which may lead to more severe flooding in the coming years. In light of this change in weather trends, flood prediction has become increasingly important for the public’s safety. The focus of this paper is to apply the Support Vector Machine (SVM), a machine learning technique, to classify flood risks based on water gage height, wind speed and direction, and time of the year. In this paper, the …

A New Application Of The Central Limit Theorem, Kenneth Winters

Selected Honors Theses

This paper discusses the Central Limit Theorem (CLT) and its applications. The paper gives an introduction to what the CLT is and how it can be applied to real life. Additionally, the paper gives a conceptual understanding of the theorem through various examples and visuals. The paper discusses the applications of the CLT in fields such as computer science, psychology, and political science. The author then suggests a new mathematical theorem as an application of the CLT and provides a proof of the theorem. The new theorem relates to expected value and probabilities of random variables and provides a link …

Program Review: Mathematics And Statistics Department, Katherine Kime, University Of Nebraska At Kearney Department Of Mathematics And Statistics Faculty & Staff

Academic Program Reviews

No abstract provided.

Session 5: Equipment Finance Credit Risk Modeling - A Case Study In Creative Model Development & Nimble Data Engineering, Edward Krueger, Landon Thompson, Josh Moore

SDSU Data Science Symposium

This presentation will focus first on providing an overview of Channel and the Risk Analytics team that performed this case study. Given that context, we’ll then dive into our approach for building the modeling development data set, techniques and tools used to develop and implement the model into a production environment, and some of the challenges faced upon launch. Then, the presentation will pivot to the data engineering pipeline. During this portion, we will explore the application process and what happens to the data we collect. This will include how we extract & store the data along with how it …

Periodicity On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

In this work, we formulate the definition of periodicity for functions defined on isolated time scales. The introduced definition is consistent with the known formulations in the discrete and quantum calculus settings. Using the definition of periodicity, we discuss the existence and uniqueness of periodic solutions to a family of linear dynamic equations on isolated time scales. Examples in quantum calculus and for mixed isolated time scales are presented.