Modeling And Analysis Of Electric Signal In Neurons,
2025
Utah State University
Modeling And Analysis Of Electric Signal In Neurons, Kevin J. Roberts
All Graduate Reports and Creative Projects, Fall 2023 to Present
Neurons in humans and other species transmit information by sending electric signals via axons. This process relies on the generation and propagation of action potentials—rapid changes in the membrane potential of the axon. Understanding the mechanisms of action potentials, including how they are generated and influenced by the axon geometry and material parameters, is crucial for gaining insight into neurological diseases such as Alzheimer’s and Multiple Sclerosis (diseases highly correlated to demyelination). In this work, we review and summarize mathematical models for signal transmission–including the classical Hodgkin-Huxley model, the Single Cable (SC) model, and the Double Cable (DC) model. We …
Role Of Competition In Avoiding Social Collapse,
2025
Utah State University
Role Of Competition In Avoiding Social Collapse, Gabriel M. Tonks
All Graduate Reports and Creative Projects, Fall 2023 to Present
Historical examples suggest that isolated, resource-scarce societies are prone to increased hostility and social disasters. The research in this report explores the role of intrasocietal competition in avoiding resource collapse. Two resource-consumer models are proposed with competition which depends on the level of available resources. One of these models is selected for in-depth analysis, and the region in the parameter space where saddle-node bifurcations emerge is computed numerically. The effects of environmental noise on resource growth are simulated, showing that the increased noise usually has negative long-term effects which might be mitigated via increased consumer competition.
Universal Systems Simulation Via Constraint Hypergraphs With Applications To Digital Twins,
2025
Clemson University
Universal Systems Simulation Via Constraint Hypergraphs With Applications To Digital Twins, John Morris
All Dissertations
The characterization of systems encompasses a variety of modeling frameworks designed to capture specific behaviors and components of various system domains. Whatever the framework, the core elements of a system representation are the information of the system and a description of how that information is related. The relations in deterministic systems are functions, which, when composed to form executable processes, can be used to simulate system data. A declarative modeling framework is one that encodes mechanisms for preparing these simulations within the model structure, allowing an external agent to form the execution processes required for a given context. To date, …
The Odds Don’T Lie: Mathematical Reasoning And Societal Ignorance In Don’T Look Up,
2025
West Morris Central High School
The Odds Don’T Lie: Mathematical Reasoning And Societal Ignorance In Don’T Look Up, Nysa Vedwan, Shane Carey
LASER Journal
In Adam McKay’s 2021 satirical sci-fi movie Don’t Look Up, two astronomers discover a comet heading directly toward Earth. Despite overwhelming evidence and near-certainty of global extinction, their warnings are ignored and ridiculed. This paper discusses the mathematical and scientific foundations of the movie’s social and political reception, and specifically focuses on orbital prediction and probabilistic modeling as they relate to public understanding of risk. This paper shows how data is often undermined by political and social dynamics, by connecting the fictional events of the movie with real-world crises like the COVID-19 pandemic and the climate emergency. In Don’t Look …
Computational Models For Pre-Lens Tear Film Drug Concentration Dynamics With Drug Supply From A Contact Lens And Drug Exchange During Blinking,
2025
George Mason University
Computational Models For Pre-Lens Tear Film Drug Concentration Dynamics With Drug Supply From A Contact Lens And Drug Exchange During Blinking, Mazen A. Althobaiti
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Metapopulation Model To Evaluate C.Difficile Potential Vaccine Interventions.,
2025
Illinois State University
Metapopulation Model To Evaluate C.Difficile Potential Vaccine Interventions., Archana Neupane Timsina
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Following Carbon: Pathway And Flux Representations Of Ecosystems,
2025
University of Georgia
Following Carbon: Pathway And Flux Representations Of Ecosystems, Caner Kazanci
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Exploring Solutions To Food Addiction Challenges Using Mathematical Modeling, Simulation, And Analysis Applying Optimal Control Theory,
2025
University of Maryland at College Park
Exploring Solutions To Food Addiction Challenges Using Mathematical Modeling, Simulation, And Analysis Applying Optimal Control Theory, Dia Bonsu, Padmanabhan Seshaiyer, Alonso Ogueda-Oliva
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling The Cancer Cell Growth Predictions Based On Classical Mathematical Models With Physics-Informed Neural Network,
2025
Jarvis Christian University
Modeling The Cancer Cell Growth Predictions Based On Classical Mathematical Models With Physics-Informed Neural Network, Widodo Samyono
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
[Project Insight] Applications Of Physics Informed Neural Networks For Incorporating Human Behavior Into Epidemiological Models,
2025
George Mason University
[Project Insight] Applications Of Physics Informed Neural Networks For Incorporating Human Behavior Into Epidemiological Models, Alonso Gabriel Ogueda Oliva
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Can We End The Hiv Epidemic In The U.S.? Linking Clinical And National Surveillance Data Through Multiscale Modeling From Patients To Populations,
2025
Florida Atlantic University
Can We End The Hiv Epidemic In The U.S.? Linking Clinical And National Surveillance Data Through Multiscale Modeling From Patients To Populations, Necibe Tuncer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Quantification Of Parameters To Predict The Rupture Of Intracranial Saccular Aneurysms Using Physics Informed Neural Networks,
2025
George Mason University
Quantification Of Parameters To Predict The Rupture Of Intracranial Saccular Aneurysms Using Physics Informed Neural Networks, Alonso Gabriel Ogueda, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Sustainable Insecticide Spraying Strategy For Long-Term Chagas Disease Vector Control,
2025
Pennsylvania Western University
Sustainable Insecticide Spraying Strategy For Long-Term Chagas Disease Vector Control, Bismark Oduro
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Understanding The Spread Of Black Sigatoka Disease: A Deterministic And Stochastic Modeling Approach,
2025
Utah State University
Understanding The Spread Of Black Sigatoka Disease: A Deterministic And Stochastic Modeling Approach, Bernard Asamoah Afful, Luis F. Gordillo
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Stabilized Weak-Gradient Discontinuous Finite Elements With Optimal Error Estimates For Second-Order Elliptic Pdes,
2025
Department of Mathematics, College of Computing and Mathematical Sciences, Khalifa University of Science and Technology, P.O. Box: 127788, Abu Dhabi, United Arab Emirates
Stabilized Weak-Gradient Discontinuous Finite Elements With Optimal Error Estimates For Second-Order Elliptic Pdes, Aymen Laadhari
Mathematical Modelling and Numerical Simulation with Applications
This work introduces an accurate finite element approach employing a new stabilized discrete weak gradient, designed for second-order elliptic problems on arbitrary conforming meshes. We formulate the approach within a discontinuous Galerkin framework and derive a consistent and coercive bilinear form. Appropriate error analysis on a model problem confirms optimal convergence. Building on the core analysis, we extend the method to more challenging settings, including time-dependent heterogeneous scenarios and a biophysically realistic optimal-control model of photobleaching in the budding yeast cell. We further illustrate the versatility of the weak-gradient construction by applying it to an unsteady level-set equation relevant to …
High-Order Adaptive Solutions For Coupled Fractional Riccati Equations Via Daubechies Redundant Frames,
2025
Department of Mathematics, Zayed University, Abu Dhabi, United Arab Emirates
High-Order Adaptive Solutions For Coupled Fractional Riccati Equations Via Daubechies Redundant Frames, Mutaz Mohammad, Alexander Trounev
Mathematical Modelling and Numerical Simulation with Applications
Coupled fractional Riccati equations play a fundamental role in modeling complex systems with memory effects and anomalous diffusion, frequently arising in engineering, control theory, finance, and quantum mechanics. Their analytical and numerical treatment remains highly challenging due to the nonlocal nature of fractional-order derivatives and the presence of nonlinear coupling terms. This study introduces an adaptive numerical framework that combines the Caputo fractional derivative with redundant Daubechies wavelet frames. The method leverages multi-resolution analysis, compact support, and controlled redundancy to achieve accurate approximation of both localized and global solution features, particularly in scenarios characterized by singular behavior and long-range memory …
The Consideration Of Two Scalarization Methods For The Multi-Objective Nurse-To-Patient Assignment Problem,
2025
Department of Industrial and Entrepreneurial Engineering and Engineering Management, Western Michigan University, Kalamazoo, 49008-5336, MI, USA
The Consideration Of Two Scalarization Methods For The Multi-Objective Nurse-To-Patient Assignment Problem, Ilgın Acar, Steven E. Butt, Aydın Sipahioğlu, İslam Altın
Mathematical Modelling and Numerical Simulation with Applications
In this research, the application of two scalarization methods, namely the conic scalarization method and the $\varepsilon$-constraint method, is investigated within the context of a multi-objective optimization problem. These methods are used to address the challenge of assigning nurses to patients on a hospital unit during a shift. The two objective functions of this assignment problem are based on patient workload metrics and unit-related travel distance measures. The proposed solution approach demonstrates the ability to generate solutions that eluded the previous mathematical programming techniques that relied on simplistic weightings of conflicting objective functions. In addition, it is found that the …
Solution Of Fractional Order Diffusion Equations With Clique Neural Network,
2025
Distance Education Center, Agri Ibrahim Cecen University, Agri, Türkiye
Solution Of Fractional Order Diffusion Equations With Clique Neural Network, Merve Zeynep Kaya, Mesut Karabacak, Ercan Çelik
Mathematical Modelling and Numerical Simulation with Applications
In this paper, the clique artificial neural network method is used to solve the fractional diffusion equation, which is a subclass of partial differential equations. The clique neural network architecture is constructed using input, hidden, and output layers. Several degrees of clique polynomials were used as activation functions, and the output layer was obtained by multiplying them with weight coefficients. Subsequently, the optimization equation was derived, and the exact solution, numerical solution, and error function graphs were obtained using a specialized algorithm. Analysis of the results demonstrates that the clique artificial neural network method provides quicker and more accurate results …
Some New Three-Term Conjugate Gradient Methods For Riemannian Optimization With Application To The Gough-Stewart Platform,
2025
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok, Thailand
Some New Three-Term Conjugate Gradient Methods For Riemannian Optimization With Application To The Gough-Stewart Platform, Nasiru Salihu, Poom Kumam, Lin Wang, Sani Salisu
Mathematical Modelling and Numerical Simulation with Applications
Three-term conjugate gradient (TTCG) methods have been extensively studied for optimization within Euclidean geometry, with some inherently satisfying the sufficient descent property, thus enhancing their theoretical superiority. However, other TTCG methods have been developed that incorporate restarting the search direction, simplify the steepest descent approach, or rely on the convexity assumptions of f to establish their convergence results. This paper introduces the Riemannian three-term conjugate gradient (RTTCG) methods. The search direction in these RTTCG methods consistently satisfies the sufficient descent condition, regardless of the line search employed, and does so without requiring a restart mechanism. By utilizing retraction and vector …
(Si15-068) Advanced Numerical Methods For The Solution Of Nonlinear Fisher Equation,
2025
National Institute of Technology
(Si15-068) Advanced Numerical Methods For The Solution Of Nonlinear Fisher Equation, Vikash Vimal, Richa Kumari, Ashish Awasthi
Applications and Applied Mathematics: An International Journal (AAM)
This paper examines the use of advanced numerical techniques to approximate solutions of the Fisher equation with higher-order accuracy. This technique integrates the method of lines with a strong stability-preserving Runge–Kutta scheme of orders four and five stages (SSPRK-54) for the numerical formulation. This scheme is then tested on two examples and the results show that it is more efficient than existing methods and requires less computing power. These equations are widely used across scientific and engineering disciplines, with particular relevance in biomedical studies, such as estimating the boundary size of tumors. The difficulties arising from their nonlinear nature are …
