Exploring the Role of Matrices in Analyzing Neural Networks and their Connectivity (Prof. Sima Ahsani)

2 students are sought for a project on “Exploring the Role of Matrices in Analyzing Neural Networks and their Connectivity” with Prof. Sima Ahsani that will begin on 6/1/2024 and last for 10 weeks

Project Description:

This is an interdisciplinary field that merges mathematics, computer science, and neuroscience, providing a comprehensive understanding of mathematical concepts and their practical applications in studying neural networks and connectivity among brain regions. It offers valuable insights into brain function and analysis methodologies. This study is structured into three phases. Phase 1 includes mathematics for machine learning, Phase 2, simultaneously with Phase 1, encompasses programming, preferably using Python, and Phase 3 integrates the knowledge gained from Phases 1 and 2 to analyze real-world fMRI data. The latter phase seeks to enhance our understanding of brain function and cognitive processes through empirical analysis.

Prerequisites

Calculus I and II, basic Linear Algebra knowledge, and basic programming skills.

Special Comments

If students don’t have linear algebra knowledge or programming skills, they will be required to learn during the Winter semester as a directed study officially or unofficially.

Project Information

Estimated Start Date: 6/1/2024

Estimated End Date: 8/9/2024

Maximum number of students sought: 2

Contact Information: Prof. Sima Ahsani (sahsani@wlu.edu)

Energy-Driven Pattern Formation (Prof. Chong Wang)

1 student is sought for a project on “Energy-Driven Pattern Formation” with Prof. Chong Wang that will begin on 6/3/2024 and last for 9 weeks

Project Description:

This project explores energy-driven pattern formation in complex physical and biological systems com- posed of multiple constituents. The total energy within these systems comprises two distinct parts. The first part, known as the local terms, promotes large regions with minimum interfaces. Conversely, the second part, referred to as the nonlocal terms, favors small regions. Exquisitely structured patterns arise as the balance of these two parts. These phenomena are observed in various instances such as the morphological phases seen in block copolymers, animal coats, and skin pigmentation.

Prerequisites

MATH 332 – Ordinary Differential Equations

Special Comments

No

Project Information

Estimated Start Date: 6/3/2024

Estimated End Date: 8/2/2024

Maximum number of students sought: 1

Contact Information: Prof. Chong Wang (cwang@wlu.edu)