College of Engineering News

Raissa D'Souza and Charles Brummitt Publish in PNAS

Posted on: March 12, 2012

Raissa D'Souza, an associate professor with joint appointments in the UC Davis Department of Computer Science and the Department of Mechanical and Aerospace Engineering, has published a paper, "Suppressing Cascades of Load in Interdependent Networks," in the February 21, 2012, "Early Edition" of the Proceedings of the National Academy of Sciences. D'Souza and third-year Ph.D. student Charles Brummitt have achieved an important "proof of concept" in the relatively innovative fields of network theory and network science.

Network theory has become a vital field of analysis, as the world has become increasingly dependent on inter-related networks that cross cultural and geographical boundaries.

"Think about buying something online," D'Souza suggests. "I go to the Web, which relies on the physical Internet — the cables and wires — which in turn rely on the electrical grid, which in turn relies on water distribution networks, for cooling. Such collections of networks are fundamental to modern society, but we don't understand the consequences of all the interactions."

The best-known paradigm to illustrate interdependence, the Bak-Tang-Wiesenfeld "sand pile model," dates back to 1987. In one basic example, each node in an interdependent cluster has a capacity for holding so many grains of sand (representing load or stress). Grains of sand are dropped randomly on these nodes; whenever one node exceeds its capacity, it topples and dumps all its sand onto its neighbors, which may in turn have too much sand and topple, and so forth. The model demonstrates that a single grain of sand can cause an avalanche (cascade) of topplings.

Real-world examples of "cascade shocks" abound: some easily recognized, others more subtle. Roughly five million people in Southern California, Arizona and Mexico lost power on September 8, 2011; the outtage, attributed to human error, was trigged by a single utility employee working at a substation in Arizona. The April 2010 eruption of Iceland's Eyjafjallajökull volcano radically polluted the air space across western and northern Europe, which shut down air traffic for a week, which prompted hotel and rental car prices to escalate, while also stressing the telecom networks.

Perhaps because of such mishaps, the few existing studies published thus far — most visibly, in a February 2010 issue of Nature — have focused exclusively on the negative aspects of interdependent networks, and the fact that interdependence can cause a system to fail more easily.

D'Souza and Brummitt, in contrast, have shown that a certain degree of interdependence — not too little, not too much — can produce a stable equilibrium. Some interconnectivity can be beneficial to an individual network, since the "partner network" acts as a reservoir for extra load. The goal, moving forward, is to explore increasingly complex mathematical models in order to fine-tune this "sweet spot" not only for individual grids, but also for coupled grids and entire systems of grids.

D'Souza also stresses a key difference between this approach and the study published in Nature. "They looked at a network whose physical infrastructure was being destroyed by a cataclysmic event such as an earthquake or hurricane. We're focusing more about the dynamic process taking place on top of networks during normal operating times, where — for example — lines get tripped on the power grid because of too much demand."

D'Souza also is an external faculty member at New Mexico's Santa Fe Institute. In that capacity, she'll be involved with an upcoming two-day workshop on networks and the power grid, taking place May 17-18 at the Institute's Center for Complex Systems. "We'll team up network theory experts with the engineers who design control systems for new smart grids, along with some power grid operators and some policy makers. The goal is to find a middle ground."

Network interdependence isn't confined to power grids, of course; the models also are applicable in many other realms, including finance. D'Souza and Brummitt are aware of a study being conducted by a group that includes Nobel laureate Joseph Stiglitz. "They found the same result that we did,” D'Souza explains, “that there's a 'sweet spot,' and that a little bit of inter-dependence actually reduces systemic risk in financial markets. That's important, because up until now, the entire financial world viewed participation in a network only negatively, in terms of having to absorb others' failures."

Thus far, however, that financial study remains a working paper; D'Souza and Brummitt are the first to publish their results. "Our work now will be a guideline," D'Souza says. "It brings a new perspective to the table."

Little imagination is necessary to see that this perspective becomes more relevant by the day.

"Different systems that used to be isolated — in different parts of the world, or in different parts of the human existence — are becoming more interdependent," Brummitt concludes. "This requires the sort of models that we're studying, in order to better address the question of how interdependent we should be."

Proceedings of the National Academy of Sciences:http://www.pnas.org/content/early/2012/02/15/1110586109.abstract
Raissa D'Souza: http://mae.ucdavis.edu/dsouza/