Physical Sciences and Mathematics Commons^™

Localized Collocation Meshless Method For Modeling Transdermal Pharmacokinetics In Multiphase Skin Structures, Eduardo Divo

Math Department Colloquium Series

The human skin has a complicated structure with many multi-scale, biophysical effects impacting the propagation of skin-injected substances, such as partitioning, metabolic reactions, adsorption and elimination. An extended version of Fick’s second law governing the process of the compound diffusion in various skin layer is employed in the current work by considering the conservation of mass of the substance and the metabolic reaction of the substance in viable skin. Additionally, a model assuming linear coupling between the substance concentrations that are bound and unbound with blood was developed. Using such a model, a set of coupled partial differential equations are …

Resource Optimization For Air Mobility Under Emergency Situations, Yongxin (Jack) Liu

Math Department Colloquium Series

This project aims to improve air traffic management in emergencies. We first developed a GRU neural network to forecast weather-related airport capacity constraints using historical data, underscoring the value of real-time data analysis. We then optimized emergency evacuation air travel using Particle Swarm Optimization, demonstrating the ability to quickly aggregate evacuation flight resources cost-effectively. Finally, we provided a hybrid model combining a genetic algorithm with a neural network for evacuation planning, we show that neural network can be integrated accelerate genetic algorithms for efficient and performance assured system optimization.

Transfer Learning In The Era Of Foundational Models: Application To Diagnosis In Rheumatology, Prashant Shekhar

Math Department Colloquium Series

Problems with current synovitis grading procedures

• There has been a lack of reliability in grading these images in the medical community due to a lack of universally accepted diagnostic criteria [Momtazmanesh et al., 2022]
• The human/machine variability creates an additional challenge in an efficient automated scoring system [Ranganath et al., 2022]
• There is a lack of consistency between doctors in grading these images [Momtazmanesh et al., 2022]

Understanding Collective Performance: Human Factors And Team Science, Joseph Keebler

Math Department Colloquium Series

This talk will focus on modern issues with team science. Joe will discuss a variety of projects he's been involved with aimed at improving teamwork in complex sociotechnical systems including military, aviation, and healthcare. He will discuss major theoretical facets of teamwork and provide evidence-based best practices that were utilized to improve teams in applied settings.

Modeling And Estimation Of A Continuous Flexible Structure Using The Theory Of Functional Connections, Riccardo Bevilacqua

Math Department Colloquium Series

This talk presents a novel method for modeling and estimating the dynamics of a continuous structure based on a limited number of noisy measurements. The goal is reached using a Kalman filter in synergy with the recently developed mathematical framework known as the Theory of Functional Connections (TFC). The TFC allows to derive a functional expression capable of representing the entire space of the functions that satisfy a given set of linear and, in some cases, nonlinear constraints. The proposed approach exploits the possibilities offered by the TFC to derive an approximated dynamical model for the flexible system using the …

Privacy-Preserving Federated Learning, Dumindu Samaraweera

Math Department Colloquium Series

AI's applicability across diverse fields is hindered by data sensitivity, privacy concerns, and limited training data availability. Federated Learning (FL) addresses this challenge by enabling collaborative machine learning while preserving data privacy. FL allows clients to engage in model training with their local data, avoiding centralized storage. However, even with FL, security threats persist, jeopardizing model integrity and client data privacy. In this presentation, we will explore our latest findings in this area of research, safeguarding sensitive data from attacks through techniques like secure multiparty computation, homomorphic encryption, and differential privacy within the FL framework, enhancing data protection, and expanding …

A Low-Complexity Algorithm To Determine Spacecraft Trajectories, Sirani Perera

Math Department Colloquium Series

The growing traffic within the Cislunar region has created a need for computationally effective methods to obtain the trajectories of spacecraft in the Cislunar region. By developing algorithms with low time and arithmetic complexities, we can effectively address these needs.

In this talk, we will present a mathematical model that uses interpolation and boundary conditions to obtain trajectories for satellites based on the principles of three-body dynamics. Following the model, we propose a low- complexity algorithm to generate satellite trajectories. Once the algorithm is proposed, we will apply it to the relevant periodic orbits in the Cislunar region. Finally, we …