Networks, Power Laws and Phase Transitions
Raissa D'Souza presents Networks, Power Laws and Phase Transitions
| What | Seminar |
|---|---|
| When |
2005-10-27 04:10 PM
2005-10-27 05:00 PM
October 27, 2005 from 04:10 pm to 05:00 pm |
| Where | PES 3001 |
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Raissa D'Souza from the Center for Computational Science and Engineering at UC Davis will give a seminar titled Networks, Power Laws and Phase Transitions. All are invited to attend.
We are beginning to understand how pervasive network structures are in natural and engineered systems, and to formulate mathematical theories of network growth. A common observation in technological, biological and social networks is the existence of "scale-free" probability distributions, and of phase transitions (abrupt changes in behavior, such as the emergence of a giant connected core). Mathematical models of random graphs based on the paradigm of preferential attachment (PA) have been used extensively to model network growth as they reproduce some of the observed scale-free properties. Furthermore, PA has a long tradition of use from economics to biology, where it is taken as a fundamental axiom. Rather than assuming PA, we begin with a more basic mechanism, of competition between opposing forces, and show that PA can arise as the solution to the optimization problem. In addition, certain aspects of Internet growth, that have not been captured by previous models, emerge from our framework. This talk will begin by surveying characteristic structures for different types of networks. Then our optimization model of "competition induced preferential attachment" will be presented, along with how PA emerges. Time permitting, I will digress to a discussion of phase transitions, and present a computational study of "traffic" on a lattice, which shows a sharp transition from free flowing to fully jammed. It is a simple model whose behavior remained elusive for over a decade.