Assess the resilience of complex networks


Newswise – TROY, NY – Whether a transformer catches fire in an electrical grid, a species disappears from an ecosystem, or water floods a city street, many systems can absorb a certain amount of disturbance. But how much does a single failure weaken the network? And how much damage can he take before tipping over into collapse? Network scientist Jianxi Gao builds tools capable of answering these questions, whatever the nature of the system.

“After a certain point, the damage to a system is so severe that it causes catastrophic failure. But the events leading to a loss of resilience in a system are rarely predictable and often irreversible. So it’s hard to avoid a collapse, ”said Dr Gao, assistant professor of computer science at the Rensselaer Polytechnic Institute, which received a prestigious CAREER award from the National Science Foundation for tackling the problem. “The mathematical tools that we are building will allow us to assess the resilience of any system. And with this, we can predict and prevent failures.

Imagine the effects of climate change on an ecosystem, said Dr Gao. A species that cannot adapt will shrink to extinction, possibly leading to a cascade of other species, which eat first, on the brink of extinction as well. As the climate changes and more species are stressed, Dr. Gao wants to be able to predict the impact of these declining populations on the rest of the ecosystem.

Predicting resilience begins by mapping the system as a network, a graph in which the actors (an animal, a neuron, a power plant) are connected by the relationships between them, and how this relationship affects each of the actors and the network in his outfit. In a visualization of a network, each of the actors is a point, a node, connected to other actors by links that represent the relationship between them – think about who eats who in a forest and how this affects the overall population of each. species, or how information circulating on a social networking site influences opinions. Over time the system changes with some nodes appearing or disappearing, the links strengthen or weaken or change relationship with each other as the system as a whole reacts to this change.

“We are very limited in what we can do with existing methods. Even though the network is not that big, maybe we can use the computer to solve the coupled equations, but we can’t simulate many different failure scenarios, ”Dr Gao said.

Dr Gao launched a preliminary solution to the problem in a 2016 article published in Nature. In that article, he and his colleagues said that the existing analytical tools are insufficient because they were designed for smaller models with few interacting components, as opposed to the large networks that we want to understand. The authors proposed a new set of tools, designed for complex networks, capable of first identifying the natural state and control parameters of the network, and then grouping the behavior of different networks into a single solvable universal function. .

The tools presented in the Nature paper worked with strict assumptions about a network where all information is known – all nodes, all links, and the interactions between those nodes and those links. In the new work, Dr Gao wants to extend the One Universal Equation to networks where certain information is missing. The tools he is developing will make it possible to estimate the missing information – the missing nodes and links, and the relationships between them – on the basis of what is already known. The approach reduces accuracy somewhat, but allows for a much greater reward than what is lost, Dr Gao said.

“For a network of millions or even billions of nodes, I could use a single equation to estimate the macroscopic behavior of the network. Of course, I’m going to lose some information, some precision, but I’m capturing the dynamics or the most important properties of the whole system, ”Dr Gao said. “Right now people can’t do that. They can’t test the system, find out where it is failing, and better yet, improve it so that it doesn’t fail.

“The ability to analyze and predict weaknesses on a variety of types of networks gives us a great deal of power to protect vulnerable networks and ecosystems before they fail,” said Curt Breneman, Dean of the Rensselaer School of Science. “It’s the kind of work that changes the game, and this CAREER award is recognition of that potential. We congratulate Jianxi and expect great things from his research.

CAREER: Network resilience: theories, algorithms and applicationsIs funded by a grant of $ 576,000 from the National Science Foundation.

About the Rensselaer Polytechnic Institute

Founded in 1824, the Rensselaer Polytechnic Institute is the first technological research university in the United States. Rensselaer encompasses five schools, 34 research centers, over 145 academic programs, including 25 new programs, and a vibrant community of over 7,600 students and over 104,000 living alumni. Rensselaer’s faculty and alumni include more than 145 members of the National Academy, six members of the National Inventors Hall of Fame, six winners of the National Medal of Technology, five winners of the National Medal of Science and one award winner. Nobel Prize in Physics. With nearly 200 years of experience in advancing scientific and technological knowledge, Rensselaer remains focused on solving global challenges with a spirit of ingenuity and collaboration. For more information, please visit


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