Growth and Phase Transitions in Isolated and Interacting Networks


October 7, 2009


Networks with complex structures and functions are pervasive in the modern world, spanning social, biological and technological systems. One feature common to many such networks is a broad variation in the number of edges incident to each node, and growth by preferential attachment, whereby the rich get richer, has been assumed as an explanatory axiom. I will show that an underlying local optimization mechanism can in fact give rise to preferential attachment. Another complex feature of evolving networks is that exhibit phase transitions, such as the sudden emergence of large-scale connectivity. I show that a variant of the classic Erdos-Renyi model of network formation (using the power of two choices) can alter the location and also the nature of the phase transition, making for an explosive onset of connectivity. Finally, in the past ten years a general theory of networks has been developing, but it applies only to isolated networks. In reality, individual networks are increasingly interdependent (e.g., the Internet and the power grid, globalization of financial markets and of social networks). I show that interactions between different types of networks can actually lower the critical threshold, allowing large-scale connectivity to be achieved with fewer overall connections, with implications for the spread of disease across geographic regions and the design of simple communications networks.


Raissa D'Souza

Raissa D’Souza is a statistical physicist working at the interface of physics and computer science. She studies the dynamical evolution of nonlinear, nonequilibrium systems. Much of the emphasis is on developing discrete computer models of microscopic physical phenomena in the context of thermodynamics of pattern formation. In addition to modeling patterns forming in nature, these models allow us to explore how we might implement a computation with a discrete dynamical system.
Raissa is currently a postdoctoral research scientist at Bell Labs, in Murray Hill, New Jersey, where she holds a joint appointment between the Theoretical Physics Research and the Fundamental Mathematics Research groups. She is also a postdoctoral member of the DIMACS center at Rutgers University and a Fellow-at-Large at the Santa Fe Institute. Raissa received a B.S. in physics from the University of Illinois, and a Ph.D. in Condensed Matter Physics from the Massachusetts Institute of Technology. She has received various honors and awards, including the Vasquez Thesis Award from MIT, and has given invited lectures at places such as Cornell University, Los Alamos National Lab, Exxon Research, and University of Illinois.
Raissa also is keenly interested in finding the intersections amongst different human cultures and societies, and has made a few forays into social policy. She was raised in the United States and South America, and has traveled extensively throughout Asia. These days, when not at work, her latest passion is technical climbing on rock slabs.