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 …

An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, 2023 University of Alabama, Tuscaloosa

#### 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 …

Data-Driven Exploration Of Coarse-Grained Equations: Harnessing Machine Learning, 2023 The University of Western Ontario

#### Data-Driven Exploration Of Coarse-Grained Equations: Harnessing Machine Learning, Elham Kianiharchegani

*Electronic Thesis and Dissertation Repository*

In scientific research, understanding and modeling physical systems often involves working with complex equations called Partial Differential Equations (PDEs). These equations are essential for describing the relationships between variables and their derivatives, allowing us to analyze a wide range of phenomena, from fluid dynamics to quantum mechanics. Traditionally, the discovery of PDEs relied on mathematical derivations and expert knowledge. However, the advent of data-driven approaches and machine learning (ML) techniques has transformed this process. By harnessing ML techniques and data analysis methods, data-driven approaches have revolutionized the task of uncovering complex equations that describe physical systems. The primary goal in …

Balancing Sustainability, Profitability, And Resiliency In A 2-Prey, 1-Predator System, 2023 United States Air Force Academy

#### Balancing Sustainability, Profitability, And Resiliency In A 2-Prey, 1-Predator System, Jacob Kahn

*Mathematica Militaris*

Management decisions on sustainable harvesting of any species in our marine ecosystems benefit from mathematical modeling and simulations due to the underlying complex ecological interactions between species. Using basic mathematical analysis and numerical simulation tools, we consider the problem of investigating the maximum sustainable yield (MSY) and the maximum economic yield (MEY) when harvesting in a fishery system consisting of one predator and two competing prey species. Results show that the harvesting effort required to achieve MEY is less than what is needed to achieve MSY. This implies that increasing harvesting effort beyond what is needed to reach MEY will …

(R2033) Resonant Curve Due To Perturbations Of Geo-Synchronous Satellite Including Effect Of Earth’S Equatorial Ellipticity, 2023 University of Delhi

#### (R2033) Resonant Curve Due To Perturbations Of Geo-Synchronous Satellite Including Effect Of Earth’S Equatorial Ellipticity, Sushil Yadav, Mukesh Kumar, Virendra Kumar

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

In this paper, we have investigated resonant curve due to frequencies − angular rate of rotation of the Earth and the rate of change of Earth’s equatorial ellipticity parameter. Perturbation equations are used to convert the non-linear equations of motion of geo-synchronous satellite to the linear form. With the help of graphs, we have shown the effect of Earth’s equatorial ellipticity parameter on oscillatory amplitude and variation in orbital radius of satellite. By defining different perturbations, we have also drawn resonant curve due to frequencies steady-state orbital angular rate of satellite and the rate of change of Earth’s equatorial ellipticity …

(R1954) Fractional Order On Modeling The Transmission Of Devastative Covid-19 Infection: Efficacy Of Vaccination, 2023 Deshbandhu College, University of Delhi

#### (R1954) Fractional Order On Modeling The Transmission Of Devastative Covid-19 Infection: Efficacy Of Vaccination, Ashutosh Rajput, Tanvi ., Rajiv Aggarwal, Arpana Sharma, Shiv Kumar Sahdev, Manoj Kumar, Jaimala .

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

The second wave of COVID-19 is an unprecedented condition in India and began in mid February 2021. Individuals who were already suffering from other comorbidities were found with lung infection, and hence, the number of disease induced deaths were rising faster during the second wave in relation to the first wave. This paper has proposed a mathematical model with fractional order derivatives by correlating the model based number of infectives with the real number of infectives in India. For the system of fractional differential equations, a disease-free state has been computed and proved to be locally asymptotically stable with certain …

Complex-Valued Approach To Kuramoto-Like Oscillators, 2023 The University of Western Ontario

#### Complex-Valued Approach To Kuramoto-Like Oscillators, Jacqueline Bao Ngoc Doan

*Electronic Thesis and Dissertation Repository*

The Kuramoto Model (KM) is a nonlinear model widely used to model synchrony in a network of oscillators – from the synchrony of the flashing fireflies to the hand clapping in an auditorium. Recently, a modification of the KM (complex-valued KM) was introduced with an analytical solution expressed in terms of a matrix exponential, and consequentially, its eigensystem. Remarkably, the analytical KM and the original KM bear significant similarities, even with phase lag introduced, despite being determined by distinct systems. We found that this approach gives a geometric perspective of synchronization phenomena in terms of complex eigenmodes, which in turn …

Modeling The Immune Response To Immunotherapy And Triple Negative Breast Cancer In Mice, 2023 Florida State University

#### Modeling The Immune Response To Immunotherapy And Triple Negative Breast Cancer In Mice, Dayton J. Syme, Angelica Davenport, Yun Lu, Anna G. Sorace, Nicholas G. Cogan

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Generalized Differential Equation Models For Disease Interventions: A Novel Approach For Predicting Sexually Transmitted Disease Outbreaks, 2023 Siena College

#### Generalized Differential Equation Models For Disease Interventions: A Novel Approach For Predicting Sexually Transmitted Disease Outbreaks, Scott Greenhalgh

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Modeling The Dynamics Of Alcohol-Marijuana Co-Abuse In Virginia, 2023 Norfolk State University

#### Modeling The Dynamics Of Alcohol-Marijuana Co-Abuse In Virginia, Ana L. Vivas-Barber, James Tipton, Sujan Pant, Anne Fernando

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Mathematical Model For Wound Healing In Reef-Building Coral Pocillopora Damicornis, 2023 Virginia Commonwealth University

#### A Mathematical Model For Wound Healing In Reef-Building Coral Pocillopora Damicornis, Quintessa Hay, Luke Gardner, Eunice Pak, Liza M. Roger, Rebecca A. Segal, Anna Shaw, Nastassja A. Lewinski, Angela M. Reynolds

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Adaptive Multirate Infinitesimal Time Integration, 2023 Southern Methodist University

#### Adaptive Multirate Infinitesimal Time Integration, Alex Fish

*Mathematics Theses and Dissertations*

As multiphysics simulations grow in complexity and application scientists desire more accurate results, computational costs increase greatly. Time integrators typically cater to the most restrictive physical processes of a given simulation\add{,} which can be unnecessarily computationally expensive for the less restrictive physical processes. Multirate time integrators are a way to combat this increase in computational costs by efficiently solving systems of ordinary differential equations that contain physical processes which evolve at different rates by assigning different time step sizes to the different processes. Adaptivity is a technique for further increasing efficiency in time integration by automatically growing and shrinking the …

An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, 2023 Utah State University

#### An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones

*All Graduate Plan B and other Reports, Spring 1920 to Spring 2023*

Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory …

From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, 2023 University of Richmond

#### From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, Rilyn Mckallip

*Honors Theses*

Antibiotics are used in poultry production as prophylaxis, curative treatment, and growth promotion. The first use is as prophylaxis, or prevention of common bacterial diseases. The crowded conditions in concentrated animal feeding operations necessitate management of infectious disease to ensure overall animal health and the profitability of such operations. In these farms, between 20,000 and 125,000 birds are raised in shed-like enclosures [3], with an average of less than one square foot of space per chicken [34]. Antibiotics are currently used in chicken farms to manage and prevent common bacterial diseases such as respiratory and digestive tract infections, as well …

Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, 2023 Harvard University

#### Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov

*CODEE Journal*

An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …

A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, 2023 Utah Tech University

#### A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, Gregory Schmidt, Benjamin Whipple, Vinodh Chellamuthu, Xiaoxia Xie

*Spora: A Journal of Biomathematics*

The dengue virus is a serious concern in many parts of the world, including Brazil. As data indicates, a prominent vector for dengue is the mosquito *Aedes aegypti*. By using the dengue incidence records from the Brazilian SINAN database, we estimate the population of *A. aegypti* within the city of Rio de Janeiro. Using historical climate data for Rio de Janeiro and the computed population estimates, we extend an existing model for the population dynamics of mosquitoes to incorporate precipitation in aquatic stages of development for *A. aegypti*.

Swarm Intelligence For Solving Some Nonlinear Differential Equations, 2023 Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Egypt

#### Swarm Intelligence For Solving Some Nonlinear Differential Equations, Ahmed Elzaghal, Mohammed Mohammed Elgamal, Ahmed H. Eltanboly

*Mansoura Engineering Journal*

The Euler method is a well-known numerical technique employed for solving initial value problems of ordinary differential equations. The solution obtained through Euler's method is subject to significant inaccuracies, which tend to amplify with each successive iteration. The Particle Swarm Optimization (PSO) algorithm is a highly effective method for finding optimal solutions to both linear and nonlinear optimization problems. In this particular investigation, the PSO technique was utilized to solve initial value problems associated with ordinary differential equations. The Euler method, on the other hand, employs equidistant grid points to approximate solutions, which can result in significant errors and a …

Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, 2023 Claremont Colleges

#### Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen

*HMC Senior Theses*

Although women have made progress in entering positions in academia and

industry, they are still underrepresented at the highest levels of leadership.

Two factors that may contribute to this leaky pipeline are gender bias,

the tendency to treat individuals differently based on the person’s gender

identity, and homophily, the tendency of people to want to be around those

who are similar to themselves. Here, we present a multilayer network model

of gender representation in professional hierarchies that incorporates these

two factors. This model builds on previous work by Clifton et al. (2019), but

the multilayer network framework allows us to …

Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, 2023 Virginia Commonwealth University

#### Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer

*Theses and Dissertations*

Axisymmetric Drop Shape Analysis (ADSA) is a technique commonly used to determine surface or interfacial tension. Applications of traditional ASDA methods to process analytical technologies are limited by computational speed and image quality. Here, we address these limitations using a novel machine learning approach to analysis. With a convolutional neural network (CNN), we were able to achieve an experimental fit precision of (+/-) 0.122 mN/m in predicting the surface tension of drop images at a rate of 1.5 ms^-1 versus 7.7 s^-1, which is more than 5,000 times faster than the traditional method. The results are validated on real images …

Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, 2023 University of Malawi

#### Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove

*Biological Sciences Faculty Publications*

Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the …