Mathematics Commons^™

Visualization Of Species Tree Likelihood Under The Multispecies Coalescent Model, Jaimasan Sutton

Mathematics & Statistics ETDs

A commonly used tool for evolutionary biologists is a phylogenetic tree that represents the ancestry of a set of species and the evolution of traits. Statistical models can be used to predict the probabilities of gene trees which represent ancestral relationships of genes sampled from species. Because of this, we are able to represent the likelihood of a species tree, which represents the evolutionary history of a set of species, as a function of the counts of gene tree topologies, where each gene tree represents the ancestry of a specific genetic locus for multiple species. Because we can represent these …

Gauss Newton Method For Solving Variational Problems Of Pdes With Neural Network Discretizaitons, Wenrui Hao, Qingguo Hong, Xianlin Jin

Mathematics and Statistics Faculty Research & Creative Works

The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differential equations by parameterizing a set of functions. Various approaches, such as the deep Ritz method and physics-informed neural networks, have been developed for numerical solutions. Training algorithms, including gradient descent and greedy algorithms, have been proposed to solve the resulting optimization problems. In this paper, we focus on the variational formulation of the problem and propose a Gauss–Newton method for computing the numerical solution. We provide a comprehensive analysis of the superlinear convergence properties …

Mathematical Modeling Of Tumor Response Dynamics To Predict Progression-Free Survival In Patients With Recurrent High-Grade Glioma, Daniel James Glazar

USF Tampa Graduate Theses and Dissertations

In this dissertation, I aim to develop a mathematical model describing tumor volume response dynamics to perform individual dynamic predictions of progression-free survival (PFS) on patients with recurrent high-grade glioma (rHGG).

Patients with rHGG have a dismal prognosis with median overall survival (OS) of <12 months and median PFS of <7 months. However, there is a wide heterogeneity in treatment responses. Therefore, to aid clinicians with making decisions to alter therapeutic protocol, I would like to predict patient-specific PFS.

To perform individual dynamic predictions, I employ the Claret tumor growth inhibition (TGI) model. I further develop this model by coupling it with two different survival models. Inter-patient heterogeneity is also taken into account through mixed effects, including covariate effects. Model PFS predictions were evaluated using receiver operating characteristic (ROC) curve analysis as well as Brier …

Stochastic Analytical Predictive Models For Life Sciences And Crop Production Process, Erasmus Tetteh-Bator

USF Tampa Graduate Theses and Dissertations

Analytical predictive modeling uses algorithm-based mathematical, probabilistic and statistical methods to anticipate future events by identifying patterns in past data. It is a technique for predicting outcomes and a key application of statistical analysis in real-world scenarios. Real data-driven predictive models in various fields, such as life sciences, economics,or production industry, help individuals and institutions make data-driven informed decisions, which is essential for business success, providing companies with a competitive edge.

One of every five adult deaths is caused by heart disease and one person dies every 33 from cardiovascular disease in the United States according to the Center for …

Supplementary Files For "Using Digitized Building And Weather Records To Improve The Accuracy Of Ground To Roof Snow Load Ratio Estimations", Gideon Parry, Brennan Bean

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Reliability targeted snow loads (RTLs) measure the weight in accumulated snow (i.e. snow load) that a roof is required to support to ensure the probability of failure is suf- ficiently low. This calculation has historically relied upon a probability distribution that characterizes the ratio between the annual maximum ground snow load to the annual max- imum roof snow load, a quantity referred to as Gr. The best available data for estimating Gr comes from Canadian case studies from the 1950s and 1960s. However, much of the data was never digitized, with only approximations of data being made available in scanned …

Nidus Idearum. Scilogs, Xiv: Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square neutrosophic matrix, neutrosophic optimization, de-neutrosophication, the n-ary soft set relationship, hypersoft set, extending the hypergroupoid to the superhypergroupoid, alternative ranking, Dezert-Smarandache Theory (DSmT), reconciliation between …

Big Two And N-Card Poker Probabilities, Brian Wu, Chai Wah Wu

Communications on Number Theory and Combinatorial Theory

Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full house. The same order is true for 7-card poker such as Texas hold'em. However, is the same true for n-card poker for larger n? We study the probability of obtaining these various hands for n-card poker for various values of n≥5. In particular, we derive closed expressions for the probabilities of flush, straight and full house and show that the probability of a flush is less than a straight …

Supplementary Files For: "Interactive Modeling Of Bear Lake Elevations In A Future Climate", Benjamin D. Shaw, Scout Jarman, Brennan Bean, Kevin R. Moon, Wei Zhang, Nathan Butler, Tommy Bolton, April Knight, Emeline Haroldsen, Abby Funk, Rebecca Higbee

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The water level, or elevation, of Bear Lake has a significant impact on agriculture, power, infrastructure, and recreation for communities around the lake. Climatological variables, such as precipitation, temperature, and snowfall, all have an impact on the elevation of Bear Lake. As the climate changes due to greenhouse gas emissions, the typical behaviors of these climate variables change, leading to new behaviors in Bear Lake elevation. Because of the importance of Bear Lake, it is vital to be able to model and understand how Bear Lake's elevation may change in the face of different climate scenarios and to gain further …

Multivalued Variational Inequalities With Generalized Fractional Φ-Laplacians, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

In this article, we examine variational inequalities of the form (Formula presented.), where (Formula presented.) is a generalized fractional (Formula presented.) -Laplace operator, K is a closed convex set in a fractional Musielak–Orlicz–Sobolev space, and (Formula presented.) is a multivalued integral operator. We consider a functional analytic framework for the above problem, including conditions on the multivalued lower order term (Formula presented.) such that the problem can be properly formulated in a fractional Musielak–Orlicz–Sobolev space, and the involved mappings have certain useful monotonicity–continuity properties. Furthermore, we investigate the existence of solutions contingent upon certain coercivity conditions.

Differential Methylation Region Detection Via An Array-Adaptive Normalized Kernelweighted Model, Daniel Alhassan, Gayla R. Olbricht, Akim Adekpedjou

Mathematics and Statistics Faculty Research & Creative Works

A differentially methylated region (DMR) is a genomic region that has significantly different methylation patterns between biological conditions. Identifying DMRs between different biological conditions is critical for developing disease biomarkers. Although methods for detecting DMRs in microarray data have been introduced, developing methods with high precision, recall, and accuracy in determining the true length of DMRs remains a challenge. In this study, we propose a normalized kernel-weighted model to account for similar methylation profiles using the relative probe distance from "nearby" CpG sites. We also extend this model by proposing an array-adaptive version in attempt to account for the differences …

(R2068) A Study To Assess The Stress On Students Of Higher Education During Covid-19 Using Fuzzy Logic System, Monika Rathore, Uday Raj Singh, Sanjeev Kumar

Applications and Applied Mathematics: An International Journal (AAM)

The COVID-19 pandemic significantly disrupted various sectors, with higher education being one of the most severely affected. Students in higher education faced numerous challenges transitioning to online learning, leading to a surge in mental health issues. The abrupt shift in the mode of education and the inability of many students to adapt exacerbated their mental health struggles. This, in turn, contributed to a notable rise in student suicide rates in India during the pandemic-induced isolation period. Addressing this critical socio-psychological issue requires effective strategies for stress detection and management. The proposed study employed the Online Education Stress Scale (Online ESS) …

Exchangeability And A Model Of Biological Evolution, Renee Haddad

Honors Scholar Theses

A sequence of random variables (RVs) is exchangeable if its distribution is invariant under permutations. For example, every sequence of independent and identically distributed (IID) RVs is exchangeable. The main result on exchangeable sequences of random variables is de Finetti's theorem, which identifies exchangeable sequences as conditionally IID. In this thesis, we explore exchangeability, provide an elementary proof of de Finetti's theorem, and present two applications: the classical Polya's urn model and a toy model for biological evolution.

Improved Rational Approximation Of Near-To-Far Propagation Kernels For The Wave Equation, Sampson Owusu

Mathematics & Statistics ETDs

The 3-space, 1-time dimensional scalar wave equation, or 3+1 wave equation, describes the propagation of scalar or acoustic waves. The unforced homogeneous equation admits a class of outgoing solutions relative to a chosen fixed center, so called “multipole” solutions. This thesis examines near-to-far signal propagation in the context of these multipole solutions. Given a time-series (history of values) for a multipole solution recorded at a radius r1, near- to-far signal propagation recovers the corresponding time-series at larger radius r2 ≫ r1. This propagation takes into account both the appropriate time delay r2 − r1 and corrections to the wave shape. …

Nidus Idearum. Scilogs, Xiii: Structure / Neutrostructure / Antistructure, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this thirteenth book of scilogs – one may find topics on Neutrosophy, Plithogeny, Physics, Mathematics, Philosophy – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. It presents new types of soft sets and new types of topologies.

Exchanging ideas with Mohammad Abobala, Ishfaq Ahmad, Ibrahim M. Almanjahie, Fatimah Alshahrani, Nizar Altounji, Muhammad Aslam, Said Broumi, Victor Christianto, R. Diksh, Feng Liu, Frank Julian Gelli, Erick Gonzalez Caballero, Riad Hamido, Yaser Al-Hasan, Ahmed Hatip, Yasin Karmouta, Nivetha Martin, Preda Mihăilescu, V. Lakshmana Gomathi Nayagam, Ze Carlos Tiago de …

Robust Prediction Of Charpy Toughness Of Additively Manufactured Kovar Using Deep Convolutional Neural Networks, Nathan R. Bianco

Mathematics & Statistics ETDs

Understanding the reason for mechanical failures of manufactured parts in their operating environments is critical to prevention of future failures. However, in-situ post-mortem evaluation of physical properties, such as fracture toughness, is time consuming and alters the condition of the material, leading to potentially misleading findings. In this study, additively manufactured test coupons were produced over a wide range of process conditions to test the impact toughness of a material. The Charpy V-Notch toughness was measured on over 200 samples alongside corresponding optical images of both sides of the fracture surface. Convolutional neural network models were trained to correlate fracture …

Calculations From On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

Mathematics and Statistics Student Research and Class Projects

In the field of nonlinear waves, particular interest is given to periodic traveling-wave solutions of nonlinear, dispersive wave equations. This thesis aims to determine the existence of periodic traveling-wave solutions for several systems of water wave equations. These systems are the Schr¨odinger KdV-KdV, Schr¨odinger BBM-BBM, Schr¨odinger KdV-BBM, and Schr¨odinger BBM-KdV systems, and the abcd-system. In particular, it is shown that periodic traveling-wave solutions exist and are explicitly given in terms of cnoidal, the Jacobi elliptic function. Certain solitary-wave solutions are also established as a limiting case of the periodic traveling-wave solutions, that is, as the elliptic modulus approaches one.

Statistical Modeling Of Right-Censored Spatial Data Using Gaussian Random Fields, Fathima Z. Sainul Abdeen, Akim Adekpedjou, Sophie Dabo Niang

Mathematics and Statistics Faculty Research & Creative Works

Consider a Fixed Number of Clustered Areas Identified by their Geographical Coordinates that Are Monitored for the Occurrences of an Event Such as a Pandemic, Epidemic, or Migration. Data Collected on Units at All Areas Include Covariates and Environmental Factors. We Apply a Probit Transformation to the Time to Event and Embed an Isotropic Spatial Correlation Function into Our Models for Better Modeling as Compared to Existing Methodologies that Use Frailty or Copula. Composite Likelihood Technique is Employed for the Construction of a Multivariate Gaussian Random Field that Preserves the Spatial Correlation Function. the Data Are Analyzed using Counting Process …

Understanding Perspectives Of Power In A College Mathematics Classroom, Laura Seeberger

Honors College Theses

Power is embedded in teacher and student actions within mathematics classrooms, whether that power is known or not. Incorporating equity and inclusiveness requires a deeper understanding of this power behind actions. In this study, we developed and administered a three part survey questioning college faculty and college students how they perceive power related to common actions within a college mathematics classroom. For example, participants were asked whether a college math teacher assigning homework increased, decreased, or did both to the teacher’s power; then whether this action increased, decreased, or did both to a student’s power. Analysis of 16 faculty and …

On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

All Graduate Theses and Dissertations, Fall 2023 to Present

A variety of physical phenomena can be modeled by systems of nonlinear, dispersive wave equations. Such examples include the propagation of a wave through a canal, deep ocean waves with small amplitude and long wavelength, and even the propagation of long-crested waves on the surface of lakes. An important task in the study of water wave equations is to determine whether a solution exists. This thesis aims to determine whether there exists solutions that both travel at a constant speed and are periodic for several systems of water wave equations. The work done in this thesis contributes to the subfields …

The Forget Time For Random Walks On Trees Of A Fixed Diameter, Lola R. Vescovo

Mathematics, Statistics, and Computer Science Honors Projects

A mixing measure is the expected length of a random walk on a graph given a set of starting and stopping conditions. We study a mixing measure called the forget time. Given a graph G, the pessimal access time for a target distribution is the expected length of an optimal stopping rule to that target distribution, starting from the worst initial vertex. The forget time of G is the smallest pessimal access time among all possible target distributions. We prove that the balanced double broom maximizes the forget time on the set of trees on n vertices with diameter …

Spatiotemporal Negative Inventory Outlier Decomposition For Supply Chain Applications In Consumer-Packaged Goods (Cpg), Hayden Mcdonald

Data Science Undergraduate Honors Theses

Coca-Cola is a popular soft drink brand with sales occurring in every Walmart store across the world, which generates large quantities of data and requires a robust supply chain system. However, the company does not currently have a sophisticated, automated, and/or prescriptive system for detecting where, when, and why inventory outages occur and applying preventative measures to avoid loss of revenue from the absence of inventory on store shelves. This thesis proposes and applies a novel, prescriptive system for this purpose. An inventory outage can be seen as a ‘negative’ statistical outlier in a time series of inventory for an …

Modeling Prices In Limit Order Book Using Univariate Hawkes Point Process, Wenqing Jiang

LSU New Orleans Theses and Dissertations

This thesis presents a time-changed geometric Brownian price model with the univariate Hawkes processes to trace the price changes in a limit order book. Limit order books are the core mechanism for trading in modern financial markets, continuously collecting outstanding buy and sell orders from market participants. The arrival of orders causes fluctuations in prices over time. A Hawkes process is a type of point process that exhibits self-exciting behavior, where the occurrence of one event increases the probability of other events happening in the near future. This makes Hawkes processes well-suited for capturing the clustered arrival patterns of orders …

A Comprehensive Uncertainty Quantification Methodology For Metrology Calibration And Method Comparison Problems Via Numeric Solutions To Maximum Likelihood Estimation And Parametric Bootstrapping, Aloka B. S. N. Dayarathne

All Graduate Theses and Dissertations, Fall 2023 to Present

In metrology, the science of measurements, straight line calibration models are frequently employed. These models help understand the instrumental response to an analyte, whose chemical constituents are unknown, and predict the analyte’s concentration in a sample. Techniques such as ordinary least squares and generalized least squares are commonly used to fit these calibration curves. However, these methods may yield biased estimates of slope and intercept when the calibrant, substance used to calibrate an analytical procedure with known chemical constituents (x-values), carries uncertainty. To address this, Ripley and Thompson (1987) proposed functional relationship estimation by maximum likelihood (FREML), which considers uncertainties …

The Future Of Brain Tumor Diagnosis: Cnn And Transfer Learning Innovations, Shengyuan Wang

Mathematics, Statistics, and Computer Science Honors Projects

For the purpose of improving patient survival rates and facilitating efficient treatment planning, brain tumors need to be identified early and accurately classified. This research investigates the application of transfer learning and Convolutional Neural Networks (CNN) to create an automated, high-precision brain tumor segmentation and classification framework. Utilizing large-scale datasets, which comprise MRI images from open-accessible archives, the model exhibits the effectiveness of the method in various kinds of tumors and imaging scenarios. Our approach utilizes transfer learning techniques along with CNN architectures strengths to tackle the intrinsic difficulties of brain tumor diagnosis, namely significant tumor appearance variability and difficult …

Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace

Electronic Theses, Projects, and Dissertations

Change point analysis is a method used to estimate the time point at which a change in the mean or variance of data occurs. It is widely used as changes appear in various datasets such as the stock market, temperature, and quality control, allowing statisticians to take appropriate measures to mitigate financial losses, operational disruptions, or other adverse impacts. In this thesis, we develop a change point detection procedure in the Inverse Gaussian (IG) model using the Modified Information Criterion (MIC). The IG distribution, originating as the distribution of the first passage time of Brownian motion with positive drift, offers …

Coarctation Duration And Severity Predict Risk Of Hypertension Precursors In A Preclinical Model And Hypertensive Status Among Patients, Arash Ghorbannia, Hilda Jurkiewicz, Lith Nasif, Abdillahi Ahmed, Jennifer Co-Vu, Mehdi Maadooliat, Ronald K. Woods, John F. Ladisa Jr.

Mathematical and Statistical Science Faculty Research and Publications

BACKGROUND:

Coarctation of the aorta (CoA) often leads to hypertension posttreatment. Evidence is lacking for the current >20 mm Hg peak-to-peak blood pressure (BP) gradient (BPGpp) guideline, which can cause aortic thickening, stiffening, and dysfunction. This study sought to find the BPGpp severity and duration that avoid persistent dysfunction in a preclinical model and test if predictors translate to hypertension status in patients with CoA.

METHODS:

Rabbits (n=75; 5–12/group) were exposed to mild, intermediate, or severe CoA (≤12, 13–19, ≥20 mm Hg BPGpp) for ≈1, 3, or 22 weeks using dissolvable and permanent sutures with thickening, stiffening, contraction, and endothelial …

Identifying Disease-Related Gene-Environment Interactions Based On Method Of Moments, Linchuan Shen

UNLV Theses, Dissertations, Professional Papers, and Capstones

Human diseases are often caused by a complex interplay of multiple factors, including genetics and environmental factors. These factors can play critical roles in the development and progression of diseases. Although genome-wide association studies (GWAS) have successfully identified many genetic variants associated with human diseases, the estimated effects of these variants are small and can explain only a relatively small portion of the heritability of the underlying diseases.

Detecting gene-environment interactions (G × E) can shed light on the biological mechanisms of diseases. However, most existing methods that investigate G × E only look at how one environmental …

Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila

Faculty Publications

This paper describes the creation of a fast, deterministic, 3D fractal cloud renderer for the AFIT Sensor and Scene Emulation Tool (ASSET). The renderer generates 3D clouds by ray marching through a volume and sampling the level-set of a fractal function. The fractal function is distorted by a displacement map, which is generated using horizontal wind data from a Global Forecast System (GFS) weather file. The vertical windspeed and relative humidity are used to mask the creation of clouds to match realistic large-scale weather patterns over the Earth. Small-scale detail is provided by the fractal functions which are tuned to …

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

A Discussion On Estimation Of The Best Constant For Spherical Restriction Inequalities, Hongyi Liu

Mathematics, Statistics, and Computer Science Honors Projects

The restriction conjecture asks for a meaningful restriction of the Fourier transform of a function to a sufficiently curved lower dimensional manifold. It then conjectures certain size estimates for this restriction in terms of the size of the original function. It has been proven in 2 dimensions, but it is open in dimensions 3 and larger, and is an area of much recent active effort. In our study, instead of aiming to prove the restriction conjecture, we target understanding its worst-case scenarios within known estimates. Specifically, we investigate the extension operator applied to antipodally concentrating profiles, examining the ratio of …