Applied Math Seminar-Applications of Persistent Spectral Graph in COVID-19

Time: Friday, Dec. 9th. 3:30-4:30 pm

Place: Zoom

Zoom link: https://gwu-edu.zoom.us/j/95630895609

Speaker: Rui Wang, Michigan State University

Title: Applications of Persistent Spectral Graph in COVID-19

Abstract: Persistent spectral graph is a new paradigm for the multiscale analysis of the topological invariants and geometric shapes of high-dimensional datasets. Motivated by the success of persistent homology and multiscale graphs in dealing with complex biomolecular data, we construct a family of spectral graphs. Specifically, families of persistent Laplacian matrices (PLMs) corresponding to various topological dimensions are constructed by continuously increasing a filtration parameter. The harmonic spectra from the null spaces of PLMs can capture the topological structures, whereas the non-harmonic spectra of PLMs characterize the additional geometric shape of a given high-dimensional data. In addition, we developed an open-source package called HERMES that can provide an efficient and robust tool to calculate the multidimensional harmonic and non-harmonic spectra of PLMs. This enables broad real-world applications in biology, medicine, and engineering. During the COVID-19 pandemic, we developed a Math-AI model by integrating persistent spectral graphs, genomics, biophysics, experimental data, and deep learning to forecast the mutational impacts on COVID-19 vaccines, anti-body drugs, and diagnostics. Our model has accurately forecasted the incoming dominance of Omicron, Omicron BA.2, and BA.4/BA.5 variants one or two months ahead.