As the nation and the world become increasingly dependent on complex networks ranging from the Internet to electrical grids and centralized computing systems, understanding how these systems operate is of paramount importance. To address this issue, researchers in Lawrence Berkeley National Laboratory's Computational Research Division (CRD) will lead two projects funded at a total of $3.5M million under a U.S. Department of Energy (DOE) program to study the mathematical challenges involved in improving our understanding of complex, interconnected systems such as computer networks.

The DOE program, called Mathematics for Complex, Interconnected Distributed Systems, was established to "support basic research in mathematical models, methods and tools for the modeling, simulation and analysis of complex, distributed, interconnected systems." The projects are funded through the Applied Mathematics Program within DOE's Office of Advanced Scientific Computing Research

"The Internet is probably the most complex artifact ever created by humans and today it has a profound effect on society," said Steven Hofmeyr, a computer scientist in Berkeley La'’s Computational Research Division and leader of one of the two projects. "Networks also play an increasingly critical role in support of DOE research, so gaining a better understanding of their characteristics is important."

Hofmeyr's project, co-led by Stephanie Forrest of the University of New Mexico (UNM), will develop a software program for modeling various aspects of networks. Although a number of programs exist for modeling complex systems, they are too generic for understanding a system as complex as the Internet. The challenge is to develop a method that is not so simple that it isn't useful, but not so complex that it';s difficult to understand. What makes the Internet so complex is the incredible number of nodes and their linked relationships, which are far from uniform. For example, a few prominent sites (like Google) have huge numbers of incoming links, whereas the majority of sites on the web have very few links. To develop a model that accurately captures the characteristics of a very complex system, Hofmeyr's project will comprise three components: Geography, Economics and Traffic.

In terms of geography, each node or site is a distinct location and they all exist on a grid connected by the networks comprising the Internet. The project will model the routing of traffic, including web traffic and email, as it is routed at the autonomous systems level by network operators, such as telecoms, across the Internet, from one location to another. Each autonomous system is modeled as an economic entity, distributed across a grid (capturing the geography aspect). Each agent earns money by routing traffic, and spends money to expand its capacity and geographic distribution. Thus the network grows. The model will also address different time scales, from very short times for traffic to long-term economics.

The second project to be funded at Berkeley Lab is "A Mathematical and Data-Driven Approach to Intrusion Detection for High-Performance Computing." According to David Bailey, the chief technologist for Berkeley Lab's CRD and lead for the project, the team will apply known mathematical and statistical techniques to analyze the access and use of high-performance computer systems. As part of the project, the team will investigate some new promising techniques that potentially might be more effective, incorporating machine learning and statistical techniques. Sean Peisert, a member of the LBNL team and an adjunct professor at UC Davis, said the project will involve a lot of forensic analysis of data. One of the challenges, Peisert said, is that most of the tools now used for such analysis were developed for tasks other than forensics, making it difficult to accurately analyze what's there.

"By using mathematical methods to develop new rules, much as it is in the physical world where fire researchers have gone from 'firefighting' to studying the nature of fire and combustible objects, we want to develop better methods for detection and prevention," Peisert said.