Diffusion processes are probably the most studied dynamics on networks, e.g., disease spread, influence maximization, opinion formation, just to name a few. However, a few gaps still exist between the literature and real systems. First, the underlying network structure is not always known. Second, the network structure affects and is affected by the diffusion processes simultaneously. With collaborators from math, stats, physics, and social sciences, I have been developing a series of theoretical models and methods to address these issues, and use them to quantify the self-reinforcing dynamics in the real world.

Can We Agree on Science? Evidence from Book Co-Purchase Data, F. Dokshin, J. A. Evans, M. Macy, F. Shi, Y. Shi in preparation

Social Clustering in Epidemic Spread on Coevolving Networks, H.-W. Lee, N. Malik, F. Shi, and P. J. Mucha in preparation

Multiopinion coevolving voter model with infinitely many phase transitions, F. Shi, P.J. Mucha, R. Durrett PRE

Graph fission in an evolving voter model, R. Durrett, J. P. Gleeson, A. L. Lloyd, P. J. Mucha, F. Shi, D. Sivakoff, J. E. S. Socolar, C. Varghese PNAS

Diffusion through Information networks, S. S. Bhamidi, P. J. Mucha, A. Nobel, J. Wilson, F. Shi Master's Thesis

Although computers excel at computing, they can hardly perform deduction, reasoning and creation. To make a real intelligent machine, with progresses in machine learning algorithms we also need a quantitative understanding of our knowledge and a systematic theory of how knowledge is generated, dissimilated, and digested into common sense. My collaborators and I are taking a step towards this direction, studying how people search in the space of knowledge and make discoveries. With a systematic understanding of the knowledge generating process, we will be able to measure the efficiency of current practices, identify optimal evolution paths, and ultimately, “train” machines to explore and test hypotheses.

Weaving the Fabric of Science: Dynamic network models of science’s unfolding structure, F. Shi, J. G. Foster, and J. A. Evans Social Networks

Nanoscopic to microscopic particles of high aspect ratio have sparked a considerable amount of interest as their inclusions into host materials are found to dramatically enhance the electrical, thermal and mechanical properties of the origin materials even at a low concentration. Using stochastical PDE, network methods, and numerical analysis, my collaborators and I have been studing electrical and mechanical percolations of rod-like systems with anisotropic orientations induced by processing history.

Dielectric And Charge Storage Anisotropy And Scaling Be-havior Of Shear-Induced 3d Nano-Rod Composite Films, S. Wang, F. Shi, M. G. Forest, P. J. Mucha in preparation

Network-based assessments of percolation-induced current distributions in sheared rod macromolecular dispersions, F. Shi, S. Wang, M.G. Forest, P.J. Mucha, R. Zhou SIAM: MMS

Percolation-induced exponential scaling in the large current tails of random resistor networks, F. Shi, S. Wang, M.G. Forest, P.J. Mucha SIAM: MMS

My research on biological systems has split into two lines.

Collaborating with biologists and mathematicians, I have developed stochastic differential equantions and simulation tools for diffusion-limited antibody-virus interactions in human mucus, which provide a theoretical framework for studying how virus-specific antibodies reduce HIV infection by binding to and trapping viruses in cervi-covaginal mucus. The second line investigates gene interactions and combines machine learning with network science to identify interaction patterns and generate hypotheses for lab experiments.

Modeling of virion collisions in cervicovaginal mucus reveals limits on agglutination as the protective mechanism of secretory immunoglobulin A, A. Chen, S. A. McKinley, F. Shi, S. Wang, P. J. Mucha, D. Harit, M. G. Forest, S. K. Lai PLoS ONE

Modeling Neutralization Kinetics of HIV by Broadly Neutralizing Monoclonal Antibodies in Genital Secretions Coating the Cervicovaginal Mucosa, S.A. McKinley, A. Chen, F. Shi, S. Wang, P.J. Mucha, M.G. Forest, S.K. Lai PLoS ONE

Transient Antibody-Mucin Interactions Produce a Dynamic Molecular Shield against Viral Invasion, A. Chen, S.A. McKinley, S. Wang, F. Shi, P.J. Mucha, M.G. Forest, S.K. Lai Biophys J

Information Monitoring in Routing Networks, D. Burstein, F. Kentner, J. Kun, F. Shi under review arxiv

A Network Analysis on the Stability of Power Grids, Y. Chen, M. G. Forest, G. Lin, P. J. Mucha, S. Wang, F. Shi Technical Report

My interest in finance was intrigued by the 27th Annual Workshop on Mathematical Problems in Industry. The project of my team was to estimate the likelihood of a rare event, i.e., failure of serious losses in a portfolio, using importance sampling and Milestoning. Extended from the project, I later developed a Gaussian mixture model for portfolio loss and a Gibbs sampler algorithm for inference, as a course project. Recently I have started serious studies on finance. My collaborators from finance and I are mining high-frequency stock trading data to investigate causes and predictors for flash crashes of the market.

Investor Sentiment and Stock Market Activity, X. Yang, F. Shi, J. A. Evans, B. Lv under review

An empirical study on the risk evaluation of stock portfolios: fast computation of loss distributions using Gibbs sampler and importance sampling, Technical Report

Fast Computation of Loss Distributions for Credit Portfolios (with Standard & Poor’s Financial Services LLC), The finacial math group Technical Report