People spend hours a day interacting in online settings, ranging from social media sites to a broad range of digital communities designed for work, education and entertainment. Such systems are generally intended to elicit particular activities or forms of engagement, yet we have relatively little understanding of the resulting behaviors or of how system design may contribute to those behaviors. This talk will discuss work that aims to develop models of human behavior in online settings, both to inform system design but also to address fundamental questions in the social sciences.
One of the characteristic features of life — specificity — emerges in metabolism, information transfer from DNA to protein, embryology, immunology and virtually every other process. Its explanation on the molecular level is thermodynamic stability and structural complementarity. Yet one disturbing issue persists: the protein and nucleic acid sequences coding for that specificity are generally too small to distinguish actual partners from competitors. Similarly, protein degradation conveys specificity through very short sequences. The process is so kinetically complex that bulk kinetic experiments and a few molecular structures are insufficient to explain how specificity is achieved. Using single molecule kinetic measurements, we have deconvolved much of that specificity.
Since at least the time when it was understood that the circumference of a circle is pi multiplied by its diameter, the applications of mathematics have raced on far ahead of the foundations of the subject itself. By considering a variety of examples, principally from the 19th century, we will explore the tension between mathematics and its applications, and reasons why it remains a valuable and rewarding occupation to develop the necessary framework for existing and “well understood” theories.
Topology, the “rubber sheet geometry”, studies properties that do not change when objects are pulled and stretched. Accepting somewhat fuzzy input, it is the part of mathematics typically applied when qualitative conclusions are reached. However, it has a quantitative aspect important in understanding singularities, and potentially, high-dimensional noisy data and aspects of large-scale geometry of networks. Prof. Weinberger will discuss a variety of phenomena that arise or are illuminated by tracking of the complexity of geometric constructions.
Simulating quantum mechanics on classical computers appears at first to require exponential computational resources, yet at the same time rapid progress is being made in accurate simulations of the quantum properties of realistic materials. How is this discrepancy resolved?