Comprehensive Exam CMSE Sean Cottrell
Department of Computational Mathematics, Science & Engineering
Michigan State University
Comprehensive Exam Notice
4/6/2026, 10:30am at Stem Building Room 3106
Zoom link: https://msu.zoom.us/j/9645485999
Passcode: 096348
Title:
A Survey of Mathematical Methods in Single Cell Omics Data Analysis and Future Perspectives
By: Sean Cottrell
Abstract
The rapid advancement of single-cell and spatial transcriptomics technologies has generated unprecedented volumes of high-dimensional, multi-sample and multi-modal biological data, creating an urgent need for principled computational methods capable of integrating, representing, and analyzing these complex datasets. While deep learning approaches have achieved considerable success in single-cell data processing, they typically operate as black-box models whose learned representations lack explicit mathematical semantics, making it difficult to ascertain why particular patterns emerge. Mathematical frameworks drawing from optimal transport, multilinear algebra, and algebraic topology offer a complementary alternative. In this survey, we present formulations of these mathematical frameworks in the context of single-cell and spatial omics data analysis. We focus specifically on how these perspectives compose into a cohesive analytical pipeline addressing a specific sequence of problems: identification of cross-dataset couplings of cells, batch-corrected population scale data integration, and principled feature selection and biomarker identification, with downstream applications in drug repurposing. This compositional perspective highlights not only the individual utility of each framework but also the synergies that emerge when they are deployed in sequence.
Committee:
Longxiu Huang
Guo-Wei Wei
Yuying Xie
Ekaterina Rapinchuk
