Numerical Analysis and Computation Commons^™

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 …

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.

Convolutional Neural Network-Based Gene Prediction Using Buffalograss As A Model System, Michael Morikone

Complex Biosystems PhD Program: Dissertations

The task of gene prediction has been largely stagnant in algorithmic improvements compared to when algorithms were first developed for predicting genes thirty years ago. Rather than iteratively improving the underlying algorithms in gene prediction tools by utilizing better performing models, most current approaches update existing tools through incorporating increasing amounts of extrinsic data to improve gene prediction performance. The traditional method of predicting genes is done using Hidden Markov Models (HMMs). These HMMs are constrained by having strict assumptions made about the independence of genes that do not always hold true. To address this, a Convolutional Neural Network (CNN) …

Modeling Nonsegmented Negative-Strand Rna Virus (Nnsv) Transcription With Ejective Polymerase Collisions And Biased Diffusion, Felipe-Andres Piedra

Research Symposium

Background: The textbook model of NNSV transcription predicts a gene expression gradient. However, multiple studies show non-gradient gene expression patterns or data inconsistent with a simple gradient. Regarding the latter, several studies show a dramatic decrease in gene expression over the last two genes of the respiratory syncytial virus (RSV) genome (a highly studied NNSV). The textbook model cannot explain these phenomena.

Methods: Computational models of RSV and vesicular stomatitis virus (VSV – another highly studied NNSV) transcription were written in the Python programming language using the Scientific Python Development Environment. The model code is freely available on GitHub: …

An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel O. Adara, Roger B. Sidje

Northeast Journal of Complex Systems (NEJCS)

Among numerical techniques used to facilitate the analysis of biochemical reactions, we can use the method of moments to directly approximate statistics such as the mean numbers of molecules. The method is computationally viable in time and memory, compared to solving the chemical master equation (CME) which is notoriously expensive. In this study, we apply the method of moments to a chemical system with a constant rate representing a vascular endothelial growth factor (VEGF) model, as well as another system with time-dependent propensities representing the susceptible, infected, and recovered (SIR) model with periodic contact rate. We assess the accuracy of …

Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison Of Brain- Cousens And Cedergreen Models For A Biochemical Dataset, Venkat D. Abbaraju, Tamaraty L. Robinson, Brian P. Weiser

Rowan-Virtua School of Osteopathic Medicine Faculty Scholarship

Biphasic, non-sigmoidal dose-response relationships are frequently observed in biochemistry and pharmacology, but they are not always analyzed with appropriate statistical methods. Here, we examine curve fitting methods for “hormetic” dose-response relationships where low and high doses of an effector produce opposite responses. We provide the full dataset used for modeling, and we provide the code for analyzing the dataset in SAS using two established mathematical models of hormesis, the Brain-Cousens model and the Cedergreen model. We show how to obtain and interpret curve parameters such as the ED50 that arise from modeling, and we discuss how curve parameters might change …

A Comparison Of Computational Perfusion Imaging Techniques, Shaharina Shoha

Masters Theses & Specialist Projects

Dynamic contrast agent magnetic resonance perfusion imaging plays a vital role in various medical applications, including tumor grading, distinguishing between tumor types, guiding procedures, and evaluating treatment efficacy. Extracting essential biological parameters, such as cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT), from acquired imaging data is crucial for making critical treatment decisions. However, the accuracy of these parameters can be compromised by the inherent noise and artifacts present in the source images.

This thesis focuses on addressing the challenges associated with parameter estimation in dynamic contrast agent magnetic resonance perfusion imaging. Specifically, we aim …

Pathogen Emergence As Complex Biological Invasion: Lessons From Dynamical Systems Modeling, Sudam Surasinghe, Marisabel Rodriguez, Victor Meszaros, Jane Molofsky, Salvador Almagro-Moreno, Brandon Ogbunugafor

Northeast Journal of Complex Systems (NEJCS)

Infectious disease emergence has become the target of cross-disciplinary efforts
that aim to understand and predict the shape of outbreaks. The many challenges
involved with the prediction of disease emergence events is a characteristic that in-
fectious diseases share with biological invasions in many subfields of ecology (e.g.,
how certain plants are able to successfully invade a new niche). Like infectious
diseases, biological invasions by plants and animals involve interactions between
agents (pathogens and plants in their respective cases) and a recipient niche. In
this study, we examine the problem of pathogen emergence through the lens of a
framework first …

Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe

Master's Theses

In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …

Stochastic Gradient Descent Method For A Parameter Identification Problem In Elasticity Imaging, Basca Jadamba

Biology and Medicine Through Mathematics Conference

No abstract provided.

Quantifying The Carbon Stored And Sequestered By The Trees On Pomona College’S Campus, Paola A. Giron-Carson

Scripps Senior Theses

We are experiencing a climate crisis that must be confronted with strategic mitigation. Pomona College contributes to the climate crisis through its emissions for which there is a baseline record. However there is no baseline record of the climate mitigation currently performed by the trees on Pomona’s campus through carbon storage. This study seeks to determine a current baseline quantity of carbon stored and sequestrated by Pomona’s trees as well as possible courses of climate mitigation for Pomona College to take. Initial information gathering was conducted through interviews with several stakeholders. This study was conducted using data collected prior to …

Modeling Vascular Diffusion Of Oxygen In Breast Cancer, Tina Giorgadze

Senior Projects Spring 2023

Oxygen is a vital nutrient necessary for tumor cells to survive and proliferate. Oxygen is diffused from our blood vessels into the tissue, where it is consumed by our cells. This process can be modeled by partial differential equations with sinks and sources. This project focuses on adding an oxygen diffusion module to an existing 3D agent-based model of breast cancer developed in Dr. Norton’s lab. The mathematical diffusion module added to an existing agent-based model (ABM) includes deriving the 1-dimensional and multi-dimensional diffusion equations, implementing 2D and 3D oxygen diffusion models into the ABM, and numerically evaluating those equations …

Mathematical Modeling Of Brain Cancer Growth Using A Level-Set Method, Gbocho M. Terasaki

Biology and Medicine Through Mathematics Conference

No abstract provided.

Olfactory Bulb Processing Of Ortho Versus Retronasal Odors, Michelle F. Craft, Andrea Barreiro, Shree Gautam, Woodrow Shew, Cheng Ly

Biology and Medicine Through Mathematics Conference

No abstract provided.

Inferring Dynamics Of Biological Systems, Tracey G. Oellerich

Biology and Medicine Through Mathematics Conference

No abstract provided.

Bistability And Switching Behavior In Moving Animal Groups, Daniel Strömbom, Stephanie Nickerson, Catherine Futterman, Alyssa Difazio, Cameron Costello, Kolbjørn Tunstrøm

Northeast Journal of Complex Systems (NEJCS)

Moving animal groups such as schools of fish and flocks of birds frequently switch between different group structures. Standard models of collective motion have been used successfully to explain how stable groups form via local interactions between individuals, but they are typically unable to produce groups that exhibit spontaneous switching. We are only aware of one model, constructed for barred flagtail fish that are known to rely on alignment and attraction to organize their collective motion, that has been shown to generate this type of behavior in 2D (or 3D). Interestingly, another species of fish, golden shiners, do exhibit switching …

Grizzly Bears Mortalities And The Survival Of The Species, Courtney Swanson

Senior Seminars and Capstones

In this paper we aim to understand what is happening in the grizzly bear population mortalities from the year 2010 to 2020. We are performing Classical and Regression Tree (CART) methods and Correspondence Analysis on data provided by the U.S. Geological Survey (USGS). We found certain variables in the data set to be important through CART methods. Correspondence Analysis then allowed us to compare these variables to determine their relationships and association to one another. Most of the grizzly bear deaths are human caused and mainly over land and resources such as food and habitat. This aligns with some of …

An Examination Of Fontan Circulation Using Differential Equation Models And Numerical Methods, Vanessa Maybruck

Honors Student Research

Certain congenital heart defects can lead to the development of only a single pumping chamber, or ventricle, in the heart instead of the usual two ventricles. Individuals with this defect undergo a corrective, three-part surgery, the third step of which is the Fontan procedure, but as the patients age, their cardiovascular health will likely deteriorate. Using computational fluid dynamics and differential equations, Fontan circulation can be modeled to investigate why the procedure fails and how Fontan failure can be maximally prevented. Borrowing from well-established literature on RC circuits, the differential equation models simulate systemic blood flow in a piecewise, switch-like …

Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley

Electronic Theses and Dissertations

Systems of ordinary differential equations (ODEs) may be used to model a wide variety of real-world phenomena in biology and engineering. Classical sensitivity theory is well-established and concerns itself with quantifying the responsiveness of such models to changes in parameter values. By performing a sensitivity analysis, a variety of insights can be gained into a model (and hence, the real-world system that it represents); in particular, the information gained can uncover a system's most important aspects, for use in design, control or optimization of the system. However, while the results of such analysis are desirable, the approach that classical theory …

Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman

Pitzer Senior Theses

This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …

Mathematical Modelling And In Silico Experimentation To Estimate The Quantity Of Covid-19 Infected Individuals In Tijuana, México, Karla A. Encinas, Luis N. Coria, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

Department of Mathematics: Dissertations, Theses, and Student Research

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …

Mathematical Modeling For Studying The Sustainability Of Plants Subject To The Stress Of Two Distinct Herbivores, B. Chen-Charpentier, M. C.A. Leite, O. Gaoue, F. B. Agusto

Applications and Applied Mathematics: An International Journal (AAM)

Viability of plants, especially endangered species, are usually affected by multiple stressors, including insects, herbivores, environmental factors and other plant species. We present new mathematical models, based on systems of ordinary differential equations, of two distinct herbivore species feeding (two stressors) on the same plant species. The new feature is the explicit functional form modeling the simultaneous feedback interactions (synergistic or additive or antagonistic) between the three species in the ecosystem. The goal is to investigate whether the coexistence of the plant and both herbivore species is possible (a sustainable system) and under which conditions sustainability is feasible. Our theoretical …

Parallel-In-Time Simulation Of Biofluids, Weifan Liu, Minghao Rostami

Biology and Medicine Through Mathematics Conference

No abstract provided.

On The Properties Of Solutions Of A Cross-Diffusion System With Nonlinear Boundary Flux, Zafar Rakhmonov, Jasur Urunbaev, Bobur Allaberdiyev

Scientific Journal of Samarkand University

In this paper, based on a self-similar analysis and the method of standard equations, the properties of a nonlinear cross-diffusion system coupled via nonlocal boundary conditions are studied. We are investigated the qualitative properties of solutions of a nonlinear system of parabolic equations of cross-diffusion in a medium coupled with nonlinear boundary conditions. It is proved that for certain values of the numerical parameters of the nonlinear cross-diffusion system of parabolic equations coupled via nonlinear boundary conditions, they may not have global solutions in time. Based on a self-similar analysis and the principle of comparing solutions, a critical exponent of …

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson

Department of Mathematics: Dissertations, Theses, and Student Research

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual …

Sperm Motility In Groups, Julie Simons

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.