Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering, September 1, 2003 - June 30, 2004

Winter 2004

IMA Tutorial:

Robustness and the Internet: Design, Evolution, and Theoretical Foundations

February 8, 2004

Organizers:

Walter Willinger
AT&T Labs - Research
walter@research.att.com
http://www.research.att.com/~walter/

and

John Doyle
California Institute of Technology
doyle@cds.caltech.edu
http://www.cds.caltech.edu/~doyle/home.htm

This tutorial uses the Internet as starting point for a scientific exploration of the broader issues of robustness in complex systems throughout technology and biology. In most of these systems, complexity is driven by the need for robustness to uncertainty in their environments and components far more than by basic functionality. At the same time, most of this complexity tends to be hidden, deliberately creating the illusion of superficially simple systems, which has encouraged the development of specious theories.

The objective of this tutorial is to outline an emerging theoretical foundation for the Internet that provides a sound framework for understanding both success and shortcomings of existing Internet technologies, offers alternative protocols for identified problems, guides the rational design for future evolution of ubiquitous networking, and suggests what new mathematics and technology will be needed for developing a useful, general theory of complex systems.

Abstracts

Antonis Papachristodoulou (California Institute of Technology) antonis@its.caltech.edu

Robustness in Complex Systems: Theoretical Foundations II

Ordinary or Functional differential equations with uncertain parameters can be used to model a variety of systems. Analysis usually proceeds by further simplification to the investigation of the linearizations of these models, or a series of assumptions that result in conservativeness or may be misleading. This methodology offers scalability, but the conclusions are only locally correct. Investigating the properties of the system at the nonlinear level with delays is usually cumbersome. Using the Sum of Squares decomposition, we will build a framework for the algorithmic analysis of nonlinear ordinary and functional differential equations, taking examples from network congestion control.

LIST OF CONFIRMED PARTICIPANTS