A surge of recent research in machine learning and statistics has developed new techniques for finding patterns of words in document collections using hierarchical probabilistic models. These models are called "topic models" because the word patterns often reflect the underlying topics that are combined to form the documents; however topic models also naturally apply also such data as images and biological sequences.

After reviewing the basics of topic modeling, I will describe two related lines of research in this field, which extend the current state of the art.

First, I will describe probabilistic models designed to capture the dynamics of topics as they evolve over time. Many document collections change over time: scientific articles, emails, and search queries reflect evolving content, and it is important to model the corresponding evolution of the underlying topics.

Second, I will describe a probabilistic topic model which can capture correlations between the hidden topics. Previous models assume that the occurrence of the different topics are independent. In many document collections, however, the presence of a topic may be correlated with the presence of another. For example, a document about sports is more likely to also be about health than international finance.

In addition to giving quantitative, predictive models of a corpus, topic models provide a qualitative window into the structure of a large document collection. This allows a user to explore a corpus in a topic-guided fashion. I will demonstrate the capabilities of these new models on the archives of the journal Science, founded in 1880 by Thomas Edison. The models are built on the noisy text from JSTOR, an online scholarly journal archive, resulting from an optical character recognition engine run over the original bound journals.

(joint work with M. Jordan, A. Ng, and J. Lafferty)

The design and processing of materials with novel physical and mechanical properties requires a fundamental understanding of the connections between processing, microstructure, and properties. For example, mechanical properties in pure metals and alloys can be varied by manipulating the polycrystalline grain size or the size of the compositional domains through heat treatment, while elastic strain provides a way to tune the optical properties of self-assembled quantum dots during growth. In an analogous manner, the biological function of cell membranes is strongly affected by the details of the local "microstructure".

Typically, microstructural evolution takes place across multiple length and time scales, ranging from atomistic to mesoscopic ones. In this talk I will describe our recent efforts in developing physically-based, coarse-grained continuum models, which bridge the atomistic and mesoscopic scales, to elucidate lateral organization and non-equilibrium dynamics of heterogeneous lipid bilayers. In particular, I will focus on spatially organized, dynamic heterogeneities in the local lipid composition ("lipid rafts") which have been implicated in many important cellular processes including signal transduction, membrane trafficking, cytoskeleton organization, and pathogen entry.