Abstract:
We first introduce the mathematical concepts of ``elementary processes'' and ``pure kinetic species'' in the counting of populations of individuals in terms of continuous time, integer valued Markov chains, an approach dates back to D. G. Kendall, J. E. Moyal, and J. Keizer. We illustrate how R. A. Fisher's Fundamental Theorem of Natural Selection arises naturally in this setting. We then show that from the theory of probability and beyond the theory of fluctuations, the large deviations description provides a novel "energetic, informatic, and causal" narrative in addition to the usual population dynamic description. We apply this idea to show Gibbs' chemical thermodynamics as an emergent phenomenon of chemical kinematics. This theory generalizes Gibbs' theory to isothermal nonequilibrium living systems such as single cells.
Professor Qian (Q=Ch) received his B.A. in Astrophysics from Peking University in China, and his Ph.D. in Biochemistry and Biophysics from Washington University School of Medicine in St. Louis. Subsequently, he worked as postdoctoral researcher at University of Oregon and Caltech on biophysical chemistry and mathematical biology. Before joining the University of Washington, he was an assistant professor of Biomathematics at UCLA School of Medicine. From 1992-1994, he was a fellow with the Program in Mathematics and Molecular Biology (PMMB), a NSF-funded multi-university consortium. He was elected a fellow of the American Physical Society in 2010.
Professor Qian's main research interest is the mathematical approach to and physical understanding of biological systems, especially in terms of stochastic mathematics and nonequilibrium statistical physics. In recent years, he has been particularly interested in a nonlinear, stochastic, open system approach to cellular dynamics. Similar population dynamic approach can be applied to other complex systems and processes, such as those in ecology, infection epidemics, and economics. He believes his recent work on the statistical thermodynamic laws of general Markov processes can have applications in ecomomic dynamics and theory of values. In his research on cellular biology, his recent interest is in isogenetic variations and possible pre-genetic biochemical origins of oncogenesis.
