Proof-Of-Concept For Converging Beam Small Animal Irradiator, 2024 The Texas Medical Center Library

#### Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

*Dissertations & Theses (Open Access)*

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

Modeling An Infection Outbreak With Quarantine: The Sibkr Model, 2024 The Ohio State University

#### Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein

*Rose-Hulman Undergraduate Mathematics Journal*

Influenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based …

Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, 2024 St. Mary's University

#### Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine

*Honors Program Theses and Research Projects*

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …

Homotopy Perturbation Laplace Method For Boundary Value Problems, 2024 Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan

#### Homotopy Perturbation Laplace Method For Boundary Value Problems, Mubashir Qayyum, Khadim Hussain

*International Journal of Emerging Multidisciplinaries: Mathematics*

Most of the real situations are typically modeled as differential equations (DEs). Accurate solutions of such equations is one of the objective of researchers for the analysis and predictions in the physical systems. Typically, pure numerical approaches are utilized for the solution of such problems. These methods are usually consistent, but due to discretization and round-off errors, accuracy can be compromised. Also, pure numerical schemes may be computationally expensive and have large memory requirement. Due to this reason, current manuscript proposed a hybrid methodology by combining homotopy perturbation method (HPM) with Laplace transformation. This scheme provides excellent accuracy in less …

A Novel Fuzzy Time Series Forecasting Method Based On Probabilistic Fuzzy Set And Cpbd Approach, 2024 Shri Ram Murti Smarak College of Engineering and Technology

#### A Novel Fuzzy Time Series Forecasting Method Based On Probabilistic Fuzzy Set And Cpbd Approach, Krishna Kumar Gupta, Suneet Saxena

*Applications and Applied Mathematics: An International Journal (AAM)*

Probabilistic fuzzy set is used to model the non-probabilistic and probabilistic uncertainties simultaneously in the system. This study proposes a cumulative probability-based discretization and probabilistic fuzzy set based novel fuzzy time series forecasting method. It also proposes a novel discretization approach based on cumulative probability to tackle the probabilistic uncertainty in partitioning of datasets. Gaussian probability distribution function has been used to construct probabilistic fuzzy set. The advantage of the proposed work is that it addresses the uncertainties due to randomness and fuzziness simultaneously and also improves accuracy rate in time series forecasting. A proposed forecasting method is applied on …

New Algorithmic Support For The Fundamental Theorem Of Algebra, 2024 The Graduate Center, City University of New York

#### New Algorithmic Support For The Fundamental Theorem Of Algebra, Vitaly Zaderman

*Dissertations, Theses, and Capstone Projects*

Univariate polynomial root-finding is a venerated subjects of Mathematics and Computational Mathematics studied for four millenia. In 1924 Herman Weyl published a seminal root-finder and called it an algorithmic proof of the Fundamental Theorem of Algebra. Steve Smale in 1981 and Arnold Schonhage in 1982 proposed to classify such algorithmic proofs in terms of their computational complexity. This prompted extensive research in 1980s and 1990s, culminated in a divide-and-conquer polynomial root-finder by Victor Pan at ACM STOC 1995, which used a near optimal number of bit-operations. The algorithm approximates all roots of a polynomial p almost as fast as one …

Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, 2024 University of Tennessee, Knoxville

#### Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Steven M. Wise, Evan Habbershaw

*Faculty Publications and Other Works -- Mathematics*

In this second progress report we expand upon our previous report and preliminary work. Specifically, we review some work on the numerical solution of single- and multi-species BGK-type kinetic equations of particle transport. Such equations model the motion of fluid particles via a density field when the kinetic theory of rarefied gases must be used in place of the continuum limit Navier-Stokes and Euler equations. The BGK-type equations describe the fluid in terms of phase space variables, and, in three space dimensions, require 6 independent phase-space variables (3 for space and 3 for velocity) for each species for accurate simulation. …

Utilization Of Adomain Decomposition Method And Laplace Transform To Study Fractional Kdv And Fractional Benjamin Models Via Caputo Fractional Operator, 2024 Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan

#### Utilization Of Adomain Decomposition Method And Laplace Transform To Study Fractional Kdv And Fractional Benjamin Models Via Caputo Fractional Operator, Muhammad Sohail, Hina Younis

*International Journal of Emerging Multidisciplinaries: Mathematics*

In the present study, we implement Adomian decomposition method (ADM) to solve fractional potential Korteweg-de Vries (p-KdV) and Benjamin models. The investigated approach is a hybrid of the Adomian decomposition method and the Laplace transform, and the fractional operator developed by Caputo has been utilized in the present research. In a vast accessible domain, the proposed solution tackle impacts and regulates the gained conclusions. Additionally, it provides a simple technique for determining the point of convergence region of the derived result. To ensure that the LADM is realistic and dependable, mathematical simulations for each equation were run, and the results …

Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, 2024 Brown University

#### Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum

*CODEE Journal*

Common mechanistic models include Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models. These models in their basic forms have generally failed to capture the nature of the COVID-19 pandemic's multiple waves and do not take into account public policies such as social distancing, mask mandates, and the ``Stay-at-Home'' orders implemented in early 2020. While the Susceptible-Vaccinated-Infected-Recovered-Deceased (SVIRD) model only adds two more compartments to the SIR model, the inclusion of time-dependent parameters allows for the model to better capture the first two waves of the COVID-19 pandemic when surveillance testing was common practice for a large portion of the population. We find …

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 …

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, 2024 Department of mathematics and engineering physics, faculty of engineering, Mansoura University, Mansoura, Egypt

#### A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

*Mansoura Engineering Journal*

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

Simulation Of Multi-Variable Converters Using The Linear Interpolation Method, 2023 Tashkent State Technical University. Address: 2 Universitetskaya st., 100095, Tashkent city, Republic of Uzbekistan. E – mail: informtgtu@mail.ru.

#### Simulation Of Multi-Variable Converters Using The Linear Interpolation Method, Miraziz Vorisovich Sagatov

*Chemical Technology, Control and Management*

*In this work, based on the theory of barycentric coordinates and simplexes, a linear interpolation method is proposed for modeling and controlling the operation of multiparameter converters. It has been determined that the linear interpolation method minimizes the structural diagram of a computing device, which makes it possible to more accurately determine the metrological characteristics of multiparameter measuring transducers and offer effective methods and means for processing primary measurement information. A theorem has been proven about a linear interpolating polynomial of a function of many variables, which will allow us to judge the property of linearization of multidimensional quantities from …*

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 …

High-Performance Computing In Covariant Loop Quantum Gravity, 2023 The University of Western Ontario

#### High-Performance Computing In Covariant Loop Quantum Gravity, Pietropaolo Frisoni

*Electronic Thesis and Dissertation Repository*

This Ph.D. thesis presents a compilation of the scientific papers I published over the last three years during my Ph.D. in loop quantum gravity (LQG). First, we comprehensively introduce spinfoam calculations with a practical pedagogical paper. We highlight LQG's unique features and mathematical formalism and emphasize the computational complexities associated with its calculations. The subsequent articles delve into specific aspects of employing high-performance computing (HPC) in LQG research. We discuss the results obtained by applying numerical methods to studying spinfoams' infrared divergences, or ``bubbles''. This research direction is crucial to define the continuum limit of LQG properly. We investigate the …

New Preconditioned Conjugate Gradient Methods For Some Structured Problems In Physics, 2023 Clemson University

#### New Preconditioned Conjugate Gradient Methods For Some Structured Problems In Physics, Tianqi Zhang

*All Dissertations*

This dissertation concerns the development and analysis of new preconditioned conjugate gradient (PCG) algorithms for three important classes of large-scale and complex physical problems characterized by special structures. We propose several new iterative methods for solving the eigenvalue problem or energy minimization problem, which leverage the unique structures inherent in these problems while preserving the underlying physical properties. The new algorithms enable more efficient and robust large-scale modeling and simulations in many areas, including condensed matter physics, optical properties of materials, stabilities of dynamical systems arising from control problems, and many more. Some methods are expected to be applicable to …

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, 2023 University of Nebraska-Lincoln

#### Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

*Department of Mathematics: Dissertations, Theses, and Student Research*

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …

Controlled Manipulation And Transport By Microswimmers In Stokes Flows, 2023 Clemson University

#### Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt

*All Dissertations*

Remotely actuated microscale swimming robots have the potential to revolutionize many aspects of biomedicine. However, for the longterm goals of this field of research to be achievable, it is necessary to develop modelling, simulation, and control strategies which effectively and efficiently account for not only the motion of individual swimmers, but also the complex interactions of such swimmers with their environment including other nearby swimmers, boundaries, other cargo and passive particles, and the fluid medium itself. The aim of this thesis is to study these problems in simulation from the perspective of controls and dynamical systems, with a particular focus …

Memory Network-Based Interpreter Of User Preferences In Content-Aware Recommender Systems, 2023 Singapore Management University

#### Memory Network-Based Interpreter Of User Preferences In Content-Aware Recommender Systems, Nhu Thuat Tran, Hady W. Lauw

*Research Collection School Of Computing and Information Systems*

This article introduces a novel architecture for two objectives recommendation and interpretability in a unified model. We leverage textual content as a source of interpretability in content-aware recommender systems. The goal is to characterize user preferences with a set of human-understandable attributes, each is described by a single word, enabling comprehension of user interests behind item adoptions. This is achieved via a dedicated architecture, which is interpretable by design, involving two components for recommendation and interpretation. In particular, we seek an interpreter, which accepts holistic user’s representation from a recommender to output a set of activated attributes describing user preferences. …

Series Expansions Of Lambert W And Related Functions, 2023 Western University

#### Series Expansions Of Lambert W And Related Functions, Jacob Imre

*Electronic Thesis and Dissertation Repository*

In the realm of multivalued functions, certain specimens run the risk of being elementary or complex

to a fault. The Lambert $W$ function serves as a middle ground in a way, being non-representable by elementary

functions yet admitting several properties which have allowed for copious research. $W$ utilizes the

inverse of the elementary function $xe^x$, resulting in a multivalued function with non-elementary

connections between its branches. $W_k(z)$, the solution to the equation $z=W_k(z)e^{W_k(z)}$

for a "branch number" $k \in \Z$, has both asymptotic and Taylor series for its various branches.

In recent years, significant effort has been dedicated to exploring …

Thermodynamic Laws Of Billiards-Like Microscopic Heat Conduction Models, 2023 University of Massachusetts Amherst

#### Thermodynamic Laws Of Billiards-Like Microscopic Heat Conduction Models, Ling-Chen Bu

*Doctoral Dissertations*

In this thesis, we study the mathematical model of one-dimensional microscopic heat conduction of gas particles, applying both both analytical and numerical approaches. The macroscopic law of heat conduction is the renowned Fourier’s law J = −k∇T, where J is the local heat flux density, T(x, t) is the temperature gradient, and k is the thermal conductivity coefficient that characterizes the material’s ability to conduct heat. Though Fouriers’s law has been discovered since 1822, the thorough understanding of its microscopic mechanisms remains challenging [3] (2000). We assume that the microscopic model of heat conduction is a hard ball system. The …