Time Scale Separation In Life-Long Ovarian Follicles Population Dynamics Model, 2024 INRAE, CNRS, Université de Tours, PRC, 37380, Nouzilly, France

#### Time Scale Separation In Life-Long Ovarian Follicles Population Dynamics Model, Romain Yvinec, Frédérique Clément, Guillaume Ballif

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Multi-Type Branching Processes In Time-Varying Environments, 2024 Columbia University

#### Multi-Type Branching Processes In Time-Varying Environments, Arash Jamshidpey

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Exchangeability And A Model Of Biological Evolution, 2024 University of Connecticut

#### 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.

Modeling Human Temporal Eeg Responses To Vr Visual Stimuli, 2024 Virginia Commonwealth University

#### Modeling Human Temporal Eeg Responses To Vr Visual Stimuli, Richard R. Foster, Connor Delaney, Dean J. Krusienski, Cheng Ly

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Improved Rational Approximation Of Near-To-Far Propagation Kernels For The Wave Equation, 2024 University of New Mexico

#### 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. …

Assessing Reproducibility Of Brain-Behavior Associations Using Bootstrap Aggregation Methods, 2024 Washington University in St. Louis

#### Assessing Reproducibility Of Brain-Behavior Associations Using Bootstrap Aggregation Methods, Zhetao Chen

*Arts & Sciences Electronic Theses and Dissertations*

在本论文中，随着越来越多地利用静息态功能连接 MRI (rs-fcMRI) 将神经活动与病理状况联系起来，我们面临着对此类数据可靠性的普遍担忧。我们的探索集中于提高人类连接组计划（HCP）数据集框架内大脑行为关联的可重复性。我们采用两种不同的引导聚合方法来研究功能连接可靠性的增强：使用循环块引导（CBB）的单独时间序列装袋和使用线性支持向量回归（LSVR）模型的主题级装袋。我们对 CBB 个体时间序列 bagging 的调查表明，这种方法并不能显着增强大脑行为关联的可重复性。这一发现指出了实现可靠的功能连接措施的复杂性以及某些聚合方法在克服这一挑战方面的局限性。相比之下，我们的学科水平考试 通过 LSVR 模型装袋呈现出更有希望的结果。这种方法显着增强了分析之间模型权重的可靠性，证明了其在提高数据稳健性和可重复性方面的功效。两种方法的这种不同影响强调了适当的分析策略在提高神经影像数据可靠性方面的关键作用。通过描述这两种方法的结果，本论文有助于对神经影像领域的数据可靠性进行更广泛的讨论。它强调了在不同数据集上持续进行方法创新和验证的必要性，以提高 rs-fcMRI 研究的可靠性和可解释性。

Capturing Higher-Order Relationships Through Information Decomposition, 2024 Washington University – McKelvey School of Engineering

#### Capturing Higher-Order Relationships Through Information Decomposition, Aobo Lyu

*McKelvey School of Engineering Theses & Dissertations*

Mutual information between two random variables is a well-studied notion, whose understanding is fairly complete. Mutual information between one random variable and a pair of other random variables, however, is a far more involved notion. Specifically, Shannon's mutual information does not capture fine-grained interactions between those three variables, resulting in limited insights in complex systems. To capture these fine-grained higher-order interactions among variables, Williams and Beer proposed a framework called Partial Information Decomposition (PID) to decompose this mutual information to *information atoms*, called unique, redundant, and synergistic, and proposed several operational axioms that these atoms must satisfy. This conceptual …

Statistical Approaches For The Early Detection Of Colorectal Cancer Using Longitudinal Biomarkers, 2024 Southern Methodist University

#### Statistical Approaches For The Early Detection Of Colorectal Cancer Using Longitudinal Biomarkers, Emily Berry

*Statistical Science Theses and Dissertations*

*Colorectal cancer (CRC) is the third leading cause of cancer-related death in the United **States [45]. CRC is believed to advance from adenomatous polyps creating a unique opportunity **for both early detection and cancer prevention [4, 23]. Like other diseases, CRC **screening reduces mortality by detecting cancer at earlier, more treatable stages; however, **it can also reduce incidence through the removal of precancerous lesions [4]. As a result, **screening is recommended for average-risk adults ≥ 45 years of age and includes a variety **of tests [4, 12]. Despite alternate screening options, colonoscopy capacity is often cited as **a barrier to …*

Robust Prediction Of Charpy Toughness Of Additively Manufactured Kovar Using Deep Convolutional Neural Networks, 2024 University of New Mexico - Main Campus

#### 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 …

The Performance Of Arima And Arfima In Modelling The Exchange Rate Of Nigeria Currency To Other Currencies, 2024 Department of Mathematics, Tai Solarin University of Education Ijagun Ogun State Nigeria.

#### The Performance Of Arima And Arfima In Modelling The Exchange Rate Of Nigeria Currency To Other Currencies, Adewole Ayoade I.

*Al-Bahir Journal for Engineering and Pure Sciences*

Economic performance of a nation depends majorly on the stability of foreign exchange rate; the economic viability hangs on the exchange rate of local currencies against other currencies across the globe. Box – Jenkins Approach was employed to model the Naira exchange rate to other major currencies using Autoregressive Integrated Moving Average (ARIMA) and The autoregressive fractional integral moving average (ARFIMA) models. This studies aimed on measuring forecast ability of Autoregressive Integrated Moving Average (ARIMA) (p,d,q) and autoregressive fractional integral moving average (ARFIMA) (p, fd, q) models for stationary type series that exhibit features of Long memory properties. Results indicate …

Significant Predictors Of Suicide Rates In The United States: A Multiple Regression Analysis, 2024 Stevenson University

#### Significant Predictors Of Suicide Rates In The United States: A Multiple Regression Analysis, Alexa L. Darak, Gary Popoli

*Undergraduate Research Journal for the Human Sciences*

Inspired by Stack's (2021) research, this study investigated the influence of 19 variables on suicide rates across all 50 United States. The variables included political party, gun ownership, registered guns, religion, alcohol consumption, state safety, depression, marriage, divorce, domestic violence, race, mean elevation, and region. Regression analyses revealed that gun ownership significantly impacts suicide rates, with stricter firearm laws correlating with lower suicide rates. Other crucial contributors to suicide risk were alcohol consumption, domestic violence, marital status, divorce, mean elevation, and political party affiliation. The five most statistically significant predictor variables were gun ownership, divorce rates, percentage of White individuals, …

Testing The Hypothesis That Tennis Points Are Independent And Identically Distributed Using Statistical Methods, 2024 Liberty University

#### Testing The Hypothesis That Tennis Points Are Independent And Identically Distributed Using Statistical Methods, Ernesto Ugona Santana

*Senior Honors Theses*

Most research on the probability of winning a tennis match is based on the assumption that the points are independent and identically distributed, treating each point as a Bernoulli trial with fixed probability of success. This assumption, however, seems to contradict experience. Players' performance appears to fluctuate as the match progresses due to the psychological effect of past performance. To test this counterintuitive yet central assumption, previous research has attempted to test the independence hypothesis. However, there exists a research gap in evaluating the identicality-of-distribution hypothesis, a question of broader scope than that of independence. Hence, the purpose of this …

The Relationship Between Amygdala And Orbitofrontal Cortex Volume In The Context Of Oppositional Defiant Disorder, 2024 University of Connecticut

#### The Relationship Between Amygdala And Orbitofrontal Cortex Volume In The Context Of Oppositional Defiant Disorder, Rahul Alla

*Honors Scholar Theses*

Disobedient and rebellious attitude in children is on the rise and this type of behavior is categorized as Oppositional Defiant Disorder (ODD). ODD in children can be identified as a persistent pattern of angry or irritable mood, argumentative or defiant behavior or vindictiveness toward others according to the Diagnostic and Statistical Manual (DSM-5, Fifth Edition) of Mental Disorders.1 Children with ODD typically have difficulty regulating and processing their emotions. Issues with regulating emotions is defined as the process by which individuals “influence which emotions they have, when they have them, and how they experience and express them”.2 Dysregulation of emotions …

A Spatial Decision Support System For Rent Estimation Of Retail Spaces In Manhattan Using Geographically Weighted Regression And Spatial Regression, 2024 CUNY Hunter College

#### A Spatial Decision Support System For Rent Estimation Of Retail Spaces In Manhattan Using Geographically Weighted Regression And Spatial Regression, Andie M. Migden Miller

*Theses and Dissertations*

This report outlines an automated, three-phase Spatial Decision Support System that creates models to estimate rent of retail spaces across Manhattan. First, enrich data with predictors. Second, optimize spatially aware neighborhood-level models by combining GWR, spatial regression, and non-spatial regression. Finally, visualize results in an Esri-based WebApp.

Calculations From On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, 2024 Utah State University

#### 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.

Markov Chain Model Of Three-Dimensional Daphnia Magna Movement, 2024 University of Wisconsin-Milwaukee

#### Markov Chain Model Of Three-Dimensional Daphnia Magna Movement, Helen L. Kafka

*Theses and Dissertations*

Daphnia magna make turns through an antennae-whipping action. This action occursevery few seconds, hence, during the intervening time, the animal either remains in place or continues movement roughly along its current course. We view their movement in three dimensions. We divide the movement in the three dimensions into the movement on a two-dimensional lattice and the movement between the different planes. For the movement on the lattice, we construct a second-order Markov chain model to make predictions about which region of the lattice the animal moves to based on where it was at the last two time points. The movement …

Utilizing Arma Models For Non-Independent Replications Of Point Processes, 2024 University of Wisconsin-Milwaukee

#### Utilizing Arma Models For Non-Independent Replications Of Point Processes, Lucas M. Fellmeth

*Theses and Dissertations*

The use of a functional principal component analysis (FPCA) approach for estimatingintensity functions from prior work allows us to obtain component scores of replicated point processes under the assumption of independent replications. We show these component scores can be modeled using classical autoregressive moving average (ARMA) models, thus allowing us to also apply the FPCA model to non-independent replications. The Divvy bike-sharing system in the city of Chicago is showcased as an application.

Bayesian Change Point Detection In Segmented Multi-Group Autoregressive Moving-Average Data For The Study Of Covid-19 In Wisconsin, 2024 University of Wisconsin-Milwaukee

#### Bayesian Change Point Detection In Segmented Multi-Group Autoregressive Moving-Average Data For The Study Of Covid-19 In Wisconsin, Russell Latterman

*Theses and Dissertations*

Changepoint detection involves the discovery of abrupt fluctuations in population dynamics over time. We take a Bayesian approach to estimating points in time at which the parameters of an autoregressive moving average (ARMA) change, applying a Markov chain Monte Carlo method. We specifically assume that data may originate from one of two groups. We provide estimates of all multi-group parameters of a model of this form for both simulated and real-world data sets. We include a provision to resolve the problem of confounding ARMA parameter estimates and variance of segment data. We apply our model to identify points in time …

An Improved Bayesian Pick-The-Winner (Ibpw) Design For Randomized Phase Ii Clinical Trials, 2024 Weill Cornell Medicine

#### An Improved Bayesian Pick-The-Winner (Ibpw) Design For Randomized Phase Ii Clinical Trials, Wanni Lei, Maosen Peng, Xi K. Zhou

*COBRA Preprint Series*

Phase II clinical trials play a pivotal role in drug development by screening a large number of drug candidates to identify those with promising preliminary efficacy for phase III testing. Trial designs that enable efficient decision-making with small sample sizes and early futility stopping while controlling for type I and II errors in hypothesis testing, such as Simon’s two-stage design, are preferred. Randomized multi-arm trials are increasingly used in phase II settings to overcome the limitations associated with using historical controls as the reference. However, how to effectively balance efficiency and accurate decision-making continues to be an important research topic. …

Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, 2024 Air Force Institute of Technology

#### 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 …