KI-Net: "Kinetic description of emerging challenges in multiscale problems
of natural sciences"

a new NSF Research Network in Mathematical Sciences



Winter School: An introduction to kinetic models in the emergence of
complex behavior in social and economic systems
Feb 18 - 21, 2013 The University of Texas at Austin
The Institute for Computational Engineering and Sciences


These are graduate level short courses in an introductory series of
lectures  on the derivation, analysis and simulations of network
structures and kinetic aspects of complex systems models. Such models
appear in problems that range from traffic, flocking dynamics, supply
chain networks, information exchange or  more general dynamics in
networks.  One of the goals consists into looking at the derivations and
dynamics of  statistical transients or flows in discrete and continuous
probabilistic settings that give rise to statistical transport models.


For information go to
http://www.ki-net.umd.edu/


Kinetic theory for the emergence of complex behavior in social and
economic systems
Feb 21 - 24, 2013 Arizona State University
Center for Social Dynamics and Complexity


Kinetic theory describes the stochastic interaction of many particles or
agents via high dimensional evolution equations of probability densities.
Computationally tractable, low dimensional equations for macroscopic
observables (emergence) are obtained via asymptotics for large time scales
and many agents. This follows the recipe of Boltzmann's kinetic gas
theory, leading to the basic equations of gas dynamics in the limit.
	 

	In the social science context, this methodology has been extended from
simple gas molecules to birds and fish to describe flocking, and to
opinions to describe the evolution of rumors in a crowd. The main
advantage of this theory is that in its core it is an accurate, analytic
and explicit first principle theory and, when it works, it allows for an
analytic description of Agent Based Simulations (ABS).  It may also be
used to relate popular aggregate models like population models in the
social sciences or diffusion models in economy to their microscopic
origins.
	 

	Applying such methods in biology is well within the experience of most
applied mathematicians - they typically know physics and therefore have an
idea what the interesting questions for a fish swarm are. This is less the
case for simulation models in social science and economics. As a result,
mathematical applications in social sciences are often not very relevant
and seem to be staying at a descriptive qualitative level. In essence the
theory for emergent social phenomena is just emerging and the relationship
between model, their purpose  and data is unresolved.


For information go to
http://www.ki-net.umd.edu/