Texas A&M University
Title: Mathematics of some novel imaging techniques
The talk will provide a excursion into the mathematics of
hybrid imaging, reconstructions with internal information, and
time permitting (unlikely) Compton camera imaging.
University of Washington
Title: Mathematicothermodynamics: Stochastic Laws and Emergent Behavior of Population Kinetic Systems
Abstract: There is a growing awareness toward a slow shifting in the foundation of the thermodynamic laws, from several macroscopic, empirical postulates concerning heat as a form of random mechanical motions, to derivable mathematical theorems based on stochastic dynamics of mesoscopic systems. It becomes increasingly clear that a stochastic dynamic description of the Nature is a very effective mathematical representation of the Reality. In this talk, I shall first introduce mathematicothermodynamics as a set of mathematical results in stochastic processes. The result is then applied to complex chemical kinetic systems. Via the limit by merely taking the molecular numbers to be infinite, we are able to derive J. W. Gibbs' macroscopic isothermal equilibrium chemical thermodynamics, as well as generalize it to mesoscopic nonequilibrium systems such as biological cells.
University of Maryland
Title: Short-Range Interactions and the Emergence of Higher-Order Patterns
A fascinating aspect in collective dynamics is
self-organization: ants form colonies, birds flock,
mobile networks coordinate a rendezvous and human crowds reach a consensus.
We discuss the large-time, large-crowd flocking behavior of different
models for collective dynamics driven by alignment.
In particular, we address the central question how short-range
interactions lead, over time,
to the emergence of long-range, higher-order patterns in one- and