Math and Stats Student Colloquium (Sep 11)
Join us on Thursday, September 11, from 4-5 pm in IES 123. as we have three talks on exciting math topics given by our math students. The speakers will be Delaney Rager, Amanda Newton, and Avery Boland. See the abstracts below.
Delaney Rager
Title: A Modified Chaos Game Optimization Algorithm
Abstract: The Chaos Game Optimization (CGO) is a metaheuristic algorithm that was proposed by Azizi and Talatahari in 2020 to solve optimization problems. Traditionally, chaos games are random and iterative processes that form fractals when played. The CGO is based on some principles of chaos games in which the configuration of fractals alongside the fractals self-similarity issues are in perspective. This game theory-based algorithm formulation has been novel when solving multidimensional objective functions and displayed promising results. This project implements a corrected and improved version of the CGO algorithm and tests it with functions of varying dimensions. It also introduces new and more practical stopping criteria to address the limitations of traditional methods like relative error and a fixed number of iterations. Ultimately, this work provides a robust and efficient framework for applying the CGO to complex optimization problems, demonstrating its enhanced performance through automated analysis of objective functions.
Amanda Newton
Title: Using MOOSE for Crystal Plasticity Simulations of RMPEAs
Abstract: As advancements in nuclear reactor and jet engine technologies have advanced, the materials used in their construction have needed to withstand higher temperatures. The alloys that have traditionally been used for these applications, largely Nickel based alloys, have reached their operational limits. Refractory multiple principal elemental alloys (RMPEAs) have been proposed for development for this purpose and have shown promising mechanical properties in theoretical studies. Specifically, the behavior of RMPEAs can be studied using Finite Element Method (FEM) for crystal plasticity (CP), which determines the plastic deformation of RMPEAs on the meso-scale, providing stress-strain curves and stress distributions, building upon a CP hierarchical model. MOOSE is a software that implements this.
Avery Boland
Title: Quality Assessment in Deformable Image Registration
Abstract: Deformable image registration (DIR) is routinely applied in radiotherapy planning and adaptive workflow. However, quality assurance (QA) remains challenging in the absence of physician-drawn contours or anatomical landmarks. While industry guidance emphasizes independent QA of DIR, widely used metrics are reference-based and often inapplicable in real-world clinical settings without manual contours. To confront this issue, we introduce the Medical Image Registration QA Toolkit (MIRQAT), an open-source, Python-based framework that computes and visualizes contour-free DIR performance quality metrics and generates standardized and reproducible QA reports for evaluating DIR algorithms and workflows. MIRQAT accepts 3D medical images with optional deformation vector fields (DVFs) from any DIR software, or generates DVFs using built-in registration algorithms. MIRQAT provides a comprehensive framework for contour-free DIR QA by integrating transparent metrics, interpretable visualizations, and reproducible reporting. It complements reference-based evaluation and enables efficient, routine auditing of registration workflows in both clinical and research settings where manual contours are unavailable.
Join us on Thursday, September 11, from 4-5 pm in IES 123. as we have three talks on exciting math topics given by our math students. The speakers will be Delaney Rager, Amanda Newton, and Avery Boland. See the abstracts below.
Delaney Rager
Title: A Modified Chaos Game Optimization Algorithm
Abstract: The Chaos Game Optimization (CGO) is a metaheuristic algorithm that was proposed by Azizi and Talatahari in 2020 to solve optimization problems. Traditionally, chaos games are random and iterative processes that form fractals when played. The CGO is based on some principles of chaos games in which the configuration of fractals alongside the fractals self-similarity issues are in perspective. This game theory-based algorithm formulation has been novel when solving multidimensional objective functions and displayed promising results. This project implements a corrected and improved version of the CGO algorithm and tests it with functions of varying dimensions. It also introduces new and more practical stopping criteria to address the limitations of traditional methods like relative error and a fixed number of iterations. Ultimately, this work provides a robust and efficient framework for applying the CGO to complex optimization problems, demonstrating its enhanced performance through automated analysis of objective functions.
Amanda Newton
Title: Using MOOSE for Crystal Plasticity Simulations of RMPEAs
Abstract: As advancements in nuclear reactor and jet engine technologies have advanced, the materials used in their construction have needed to withstand higher temperatures. The alloys that have traditionally been used for these applications, largely Nickel based alloys, have reached their operational limits. Refractory multiple principal elemental alloys (RMPEAs) have been proposed for development for this purpose and have shown promising mechanical properties in theoretical studies. Specifically, the behavior of RMPEAs can be studied using Finite Element Method (FEM) for crystal plasticity (CP), which determines the plastic deformation of RMPEAs on the meso-scale, providing stress-strain curves and stress distributions, building upon a CP hierarchical model. MOOSE is a software that implements this.
Avery Boland
Title: Quality Assessment in Deformable Image Registration
Abstract: Deformable image registration (DIR) is routinely applied in radiotherapy planning and adaptive workflow. However, quality assurance (QA) remains challenging in the absence of physician-drawn contours or anatomical landmarks. While industry guidance emphasizes independent QA of DIR, widely used metrics are reference-based and often inapplicable in real-world clinical settings without manual contours. To confront this issue, we introduce the Medical Image Registration QA Toolkit (MIRQAT), an open-source, Python-based framework that computes and visualizes contour-free DIR performance quality metrics and generates standardized and reproducible QA reports for evaluating DIR algorithms and workflows. MIRQAT accepts 3D medical images with optional deformation vector fields (DVFs) from any DIR software, or generates DVFs using built-in registration algorithms. MIRQAT provides a comprehensive framework for contour-free DIR QA by integrating transparent metrics, interpretable visualizations, and reproducible reporting. It complements reference-based evaluation and enables efficient, routine auditing of registration workflows in both clinical and research settings where manual contours are unavailable.