Universality and scaling in complex networks from periods of Chinese history.

Critical physical systems with large numbers of molecules can show universal and scaling behaviors. It is of interest to know whether human societies with large numbers of people can show the same behaviors. Here, we use network theory to analyze Chinese history in periods 209 BCE-23 CE and 515-618 CE) related to the Western Han-Xin Dynasty and the late Northern Wei-Sui Dynasty, respectively.

Dependence of extreme events on spatial location.

To model the dependence of extreme events on locations, we consider extreme events of Brownian particles in a potential. We find that barring the exception of very large potentials and/or very small regions, in general, the probability of extreme events increases with the potential. Our approach is general and can be useful for studying several complex systems.

Physical mechanism for biopolymers to aggregate and maintain in non-equilibrium states.

Many human or animal diseases are related to aggregation of proteins. A viable biological organism should maintain in non-equilibrium states. How protein aggregate and why biological organisms can maintain in non-equilibrium states are not well understood.

Stochastic dynamical model for stock-stock correlations.

We propose a model of coupled random walks for stock-stock correlations. The walks in the model are coupled via a mechanism that the displacement (price change) of each walk (stock) is activated by the price gradients over some underlying network. We assume that the network has two underlying structures, describing the correlations among the stocks of the whole market and among those within individual groups, respectively, each with a coupling parameter controlling the degree of correlation.