Scientific

This talk introduces a probabilistic approach to numerically compute geometric convergence rates in discrete or continuous stochastic systems. Choosing appropriate coupling mechanisms and combining them together, works well in many settings, especially in high-dimensions. Using this approach, it is observed that the rate of geometric ergodicity of a randomly perturbed system can, to some extent, reveal the degree of chaoticity of the unperturbed system. Potential applications of the coupling method and the visualization of higher dimensional non-convex functions, e.g., the loss functions of neural networks, will be discussed.

Comparisons are constantly being made between the 1918 influenza pandemic and the present COVID-19 pandemic. We will discuss our previous work on influenza pandemics, and the tools we have used to understand the temporal patterns of those outbreaks. Applying similar tools to the COVID-19 pandemic is easier in some respects and harder in others. We will describe our current approach to modelling the spread of COVID-19, and some of the challenges and limitations of epidemic forecasting.

See attached PDF

Measuring the impact of scientific articles is important for evaluating the research output of individual scientists, academic institutions, and journals. While citations are raw data for constructing impact measures, there exist biases and potential issues if factors affecting citation patterns are not properly accounted for. In this work, we address the problem of field variation and introduce an article-level metric useful for evaluating individual articles’ visibility. This measure derives from joint probabilistic modeling of the content in the articles and the citations among them using latent Dirichlet allocation (LDA) and the mixed membership stochastic blockmodel (MMSB). Our proposed model provides a visibility metric for individual articles adjusted for field variation in citation rates, a structural understanding of citation behavior in different fields, and article recommendations that take into account article visibility and citation patterns.

Accessibility is a fundamental tool when working with partially hyperbolic systems. For instance, in the 1970s it was used as a tool to show certain systems were transitive, and in the 1990s it was used to establish stable ergodicity. We will review the general notion and how it applies in these settings. We will also review the result from 2003 by Dolgopyat and Wilkinson on the C^1 density of stably transitive systems.