Shevtsov: Teaching Modeling To First-Year Life Science Students: The Ucsc Experience, 2024 University of California, Santa Cruz

#### Shevtsov: Teaching Modeling To First-Year Life Science Students: The Ucsc Experience, Martin H. Weissman

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Modeling Opioid Addiction In Hand Surgery Patients, 2024 University of Portland

#### Modeling Opioid Addiction In Hand Surgery Patients, Eli Goldwyn, Grace Bowman, Kathryn Montovan, Julie Blackwood

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Relative Equilibria Of Pinwheel Point Mass Systems In A Planar Gravitational Field, 2024 Wayzata High School, Minnesota

#### Relative Equilibria Of Pinwheel Point Mass Systems In A Planar Gravitational Field, Ritwik Gaur

*Rose-Hulman Undergraduate Mathematics Journal*

In this paper, we consider a planar case of the full two-body problem (F2BP) where one body is a pinwheel (four point masses connected via two perpendicular massless rods) and the other is a point mass. Relative equilibria (RE) are defined to be ordered pairs (*r*, *θ*) such that there exists a rotating reference frame under which the two bodies are in equilibrium when the distance between the point mass and the center of the pinwheel is *r* and the angle of the pinwheel within its orbit is *θ*. We prove that relative equilibria exist for …

Categorical Chain Conditions For Étale Groupoid Algebras, 2024 The Graduate Center, City University of New York

#### Categorical Chain Conditions For Étale Groupoid Algebras, Sunil Philip

*Dissertations, Theses, and Capstone Projects*

Let R be a unital commutative ring and G an ample groupoid. Using the topology of the groupoid G, Steinberg defined an étale groupoid algebra RG. These étale groupoid algebras generalize various algebras, including group algebras, commutative algebras over a field generated by idempotents, traditional groupoid algebras, Leavitt path algebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg later characterized the classical chain conditions for étale groupoid algebras. In this work, we characterize categorically noetherian and artinian, locally noetherian and artinian, and semisimple étale groupoid algebras, thereby generalizing existing results for Leavitt path algebras and introducing new results for inverse …

A Measure Of Interactive Complexity In Network Models, 2024 Binghamton University

#### A Measure Of Interactive Complexity In Network Models, Will Deter

*Northeast Journal of Complex Systems (NEJCS)*

This work presents an innovative approach to understanding and measuring complexity in network models. We revisit several classic characterizations of complexity and propose a novel measure that represents complexity as an interactive process. This measure incorporates transfer entropy and Jensen-Shannon divergence to quantify both the information transfer within a system and the dynamism of its constituents’ state changes. To validate our measure, we apply it to several well-known simulation models implemented in Python, including: two models of residential segregation, Conway’s Game of Life, and the Susceptible-Infected-Susceptible (SIS) model. Our results reveal varied trajectories of complexity, demonstrating the efficacy and sensitivity …

Data-Driven Model Reduction Strategies For Dynamical Systems, 2024 University of Tennessee, Knoxville

#### Data-Driven Model Reduction Strategies For Dynamical Systems, Talha Ahmed

*Doctoral Dissertations*

Many physically occurring phenomena are nonlinear in nature and can be understood through dynamical systems theory which describes how the state of the particular system evolves in time. However, it is generally cumbersome to analyze these processes in depth because of the nonlinearities in the mathematical model or large sets of equations. Model reduction strategies are employed for such nonlinear processes to reduce the model dimensionality and approximate the full model dynamics. In this study, we focus on data driven model reduction strategies for various biological systems where only observable data is available and illustrate their efficacy.

Our first work …

Bifurcations And Resultants For Rational Maps And Dynatomic Modular Curves In Positive Characteristic, 2024 The Graduate Center, City University of New York

#### Bifurcations And Resultants For Rational Maps And Dynatomic Modular Curves In Positive Characteristic, Colette Lapointe

*Dissertations, Theses, and Capstone Projects*

No abstract provided.

Exploring The Mandelbrot Set, 2024 Stephen F. Austin State University

#### Exploring The Mandelbrot Set, James Shirley

*Electronic Theses and Dissertations*

The Mandelbrot set is a mathematical mystery. Finding its home somewhere be-

tween holomorphic dynamics and complex analysis, the Mandelbrot set showcases

its usefulness in fields across the many realms of math—ranging from physics to nu-

merical methods and even biology. While typically defined in terms of its bounded

sequences, this thesis intends to illuminate the Mandelbrot set as a type of param-

eterization of connectivity itself, specifically that of complex-valued rational maps

of the form z → z² + c. This fully illustrated guide to the Mandelbrot set merges

the worlds of intuition and theory with a series of …

Modeling The Neutral Densities Of Sparc Using A Python Version Of Kn1d, 2024 William & Mary

#### Modeling The Neutral Densities Of Sparc Using A Python Version Of Kn1d, Gwendolyn R. Galleher

*Undergraduate Honors Theses*

Currently, neutral recycling is a crucial contributor to fueling the plasma within tokamaks. However, Commonwealth Fusion System’s SPARC Tokamak is expected to be more opaque to neutrals. Thus, we anticipate that the role of neutral recycling in fueling will decrease. Since SPARC is predicted to have a groundbreaking fusion power gain ratio of Q ≈ 10, we must have a concrete understanding of the opacity

and whether or not alternative fueling practices must be included. To develop said understanding, we produced neutral density profiles via KN1DPy, a 1D kinetic neutral transport code for atomic and molecular hydrogen in an ionizing …

Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, 2024 Kennesaw State University

#### Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad

*Dissertations*

The high prevalence of dental caries among children and adolescents, especially those from lower socio-economic backgrounds, is a significant nationwide health concern. Early prevention, such as dental sealants and fluoride varnish (FV), is essential, but access to this care remains limited and disparate. In this research, a national dataset is utilized to assess sealants' reach and effectiveness in preventing tooth decay, particularly focusing on 2nd molars that emerge during early adolescence, a current gap in the knowledge base. FV is recommended to be delivered during medical well-child visits to children who are not seeing a dentist. Challenges and facilitators in …

Birkhoff Summation Of Irrational Rotations: A Surprising Result For The Golden Mean, 2024 Portland State University

#### Birkhoff Summation Of Irrational Rotations: A Surprising Result For The Golden Mean, Heather Moore

*University Honors Theses*

This thesis presents a surprising result that the difference in a certain sums of constant rotations by the golden mean approaches *exactly* 1/5. Specifically, we focus on the Birkhoff sums of these rotations, with the number of terms equal to squared Fibonacci numbers. The proof relies on the properties of continued fraction approximants, Vajda's identity and the explicit formula for the Fibonacci numbers.

A Causal Inference Approach For Spike Train Interactions, 2024 The Graduate Center, City University of New York

#### A Causal Inference Approach For Spike Train Interactions, Zach Saccomano

*Dissertations, Theses, and Capstone Projects*

Since the 1960s, neuroscientists have worked on the problem of estimating synaptic properties, such as connectivity and strength, from simultaneously recorded spike trains. Recent years have seen renewed interest in the problem coinciding with rapid advances in experimental technologies, including an approximate exponential increase in the number of neurons that can be recorded in parallel and perturbation techniques such as optogenetics that can be used to calibrate and validate causal hypotheses about functional connectivity. This thesis presents a mathematical examination of synaptic inference from two perspectives: (1) using in vivo data and biophysical models, we ask in what cases the …

Exploring Sigmoidal Bounded Confidence Models With Mean Field Methods, 2024 Claremont Colleges

#### Exploring Sigmoidal Bounded Confidence Models With Mean Field Methods, Tian Dong

*HMC Senior Theses*

Mathematicians use models of opinion dynamics to describe how opinions in a group of people change over time, which can yield insight into mechanisms behind phenomena like polarization and consensus. In these models, mathematicians represent the community as a graph, where nodes represent agents and edges represent possible interactions. Opinion updates are modeled with a system of differential equations (ODEs). Our work focuses on the sigmoidal bounded confidence model (SBCM), where agents update their opinion toward a weighted average of their neighbors' opinions by weighting similar opinions more heavily. Using tools developed in physics (mean-field theory), we derive a continuity …

Super Hiper Funcion Y Super Hiper Estructura Y Sus Correspondientes Super Hiper Funcion Neutrosofica Y Super Hiper Estructura Neutrosofica, 2024 University of New Mexico

#### Super Hiper Funcion Y Super Hiper Estructura Y Sus Correspondientes Super Hiper Funcion Neutrosofica Y Super Hiper Estructura Neutrosofica, Florentin Smarandache

*Branch Mathematics and Statistics Faculty and Staff Publications*

El *n-ésimo *Conjunto Potencia de un Conjunto {o *Pn(S)*} describe mejor nuestro mundo real, porque un sistema S (que puede ser una empresa, institución, asociación, país, sociedad, conjunto de objetos/plantas/animales/seres, conjunto de conceptos/ideas/proposiciones, etc.) está formado por subsistemas, que a su vez están formados por sub-subsistemas, y así sucesivamente. Demostramos que la Super Hiper Función es una generalización de la Función clásica, Super Función y la Hiper Función. Y el Super Hiper Álgebra, Super Hiper Gráfico son parte de la Super Hiper Estructura. Casi todas las estructuras en nuestro mundo real son Super Hiper Estructuras Neutrosóficas ya que tienen …

Advanced Techniques In Time Series Forecasting: From Deterministic Models To Deep Learning, 2024 West Virginia University

#### Advanced Techniques In Time Series Forecasting: From Deterministic Models To Deep Learning, Xue Bai

*Graduate Theses, Dissertations, and Problem Reports*

This dissertation discusses three instances of temporal prediction, applied to population dynamics and deep learning.

In population modeling, dynamic processes are frequently represented by systems of differential equations, allowing for the analysis of various phenomena. The first application explores modeling cloned hematopoiesis in chronic myeloid leukemia (CML) via a nonlinear system of differential equations. By tracking the evolution of different cell compartments, including cycling and quiescent stem cells, progenitor cells, differentiated cells, and terminally differentiated cells, the model captures the transition from normal hematopoiesis to the chronic and accelerated-acute phases of CML. Three distinct non-zero steady states are identified, representing …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, 2024 Wilfrid Laurier University

#### 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 …

Self-Exciting Point Processes In Real Estate, 2024 Wilfrid Laurier University

#### Self-Exciting Point Processes In Real Estate, Ian Fraser

*Theses and Dissertations (Comprehensive)*

This thesis introduces a novel approach to analyzing residential property sales through the lens of stochastic processes by employing point processes. Herein, property sales are treated as point patterns, using self-exciting point process models and a variety of statistical tools to uncover underlying patterns in the data. Key findings include the identification and explanation of clustering in both space and time, and the efficacy of a temporal Hawkes process with a sinusoidal background in predicting home sale occurrences. The temporal analysis starts by employing the state of art techniques for time series data like regression, autoregressive, and autoregressive integrated moving …

Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, 2024 University at Albany, State University of New York

#### Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, Felipe Xavier Costa

*Electronic Theses & Dissertations (2024 - present)*

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, …

Reducing Food Scarcity: The Benefits Of Urban Farming, 2023 Brigham Young University

#### Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

*Journal of Nonprofit Innovation*

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Convolution And Autoencoders Applied To Nonlinear Differential Equations, 2023 East Tennessee State University

#### Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye

*Electronic Theses and Dissertations*

Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …