Projects

We are an interdisciplinary research group in the Mathematics Department at Trinity Washington University. We use mathematical and computational tools and theoretical biophysics principles to study neuron morphology, behavioral disorders and pathology, and mathematics pedagogy at the college level. Our core work uses mathematical framework from biological scaling theory to establish a unifying biophysical model describing the relationship between neuron structure and function and apply machine learning methods to our model and experimental data to classify between cell types and understand the functional differences causing differences in structure between the different types. Our current projects build on this work on scaling theory in nervous systems and extend it in new directions. Currently, we have three main directions of our work:​

1. Behavioral Disorders: We aim to understand the pathology of behavioral disorders, and to this end, we apply machine learning classification methods to analyze data from neuronal and glial cells from animal models of behavioral disorders. We are currently looking at data from mouse models of anxiety disorder and using our functionally relevant structural parameters to distinguish these data from control group data. We are interested in extending our analysis to include new datasets and welcome collaborations and information about morphological datasets you might be aware of. 

2. Encyclopedia and Coloring Book: We aim to create a comprehensive encyclopedia of human neuron cell types, using characteristic scaling ratios and branching generations (leaf numbers) and assuming self-similarity to create fractal patterns representing the diversity of cell types observed in the human brain. This encyclopedia will be unique, as it will also function as a coloring book for children and adults alike to learn about the brain while using art and coloring as a tool to calm their own brains.  This project involves mathematical and biophysical theory, computation, and art and design skills. We are lucky to have mathematicians who are also artists on our team, and we welcome input and expertise from those with more art and design experience.     

3. Pedagogy Research: A major part of our work is improving mathematics teaching at the undergraduate level, promoting more inclusivity and bridging the gap between skills taught in the classroom and skills required to participate in effective research. To this end, we are designing courses at Trinity Washington University that incorporate project-based learning into mathematics education and integrating emerging technological tools into the learning process to encourage mindful use of these tools to enhance the thinking and learning process rather than to substitute it. These methods are incorporated into the design of both upper level and lower level mathematical courses, examining their usefulness in teaching both mathematics majors and non-majors, aiming to promote mathematical thinking in those who might not already see the relevance of mathematics in their own lives. We are collecting quantitative and qualitative data from these classrooms and analyzing the results to assess the effectiveness of our methods and revise them as necessary.