Numerical Analysis and Computation Commons^™

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 …

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, 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, 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, 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 …

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, 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 …

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 …

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. …

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 …

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 …

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, 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 …

Utilizing Non-Negative Least Squares For Data-Driven Discovery Of Dynamics, Tracey G. Oellerich

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Parameter Estimation In Epidemiological And Climate Models Using Ensemble Smoothing With Multiple Data Assimilation, Emmanuel Fleurantin

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Thoracoabdominal Asynchrony In A Virtual Preterm Infant: Computational Modeling And Analysis, Richard R. Foster, Bradford Smith, Laura Ellwein Fix

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Minimization Of Diet For Optimum Consumption Using Linear Programming, Nita Ngozi Ezekwem, Aditi Ghosh

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Single And Multiple Pacemaker Interaction In Jellyfish Locomotion, Alexander Hoover

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.