Single equation proposed to predict strength of ecosystems, power grids, internet, and other systems — ScienceDaily

Whether a transformer in a power grid caught fire, a species disappeared from an ecosystem, or a city street was flooded, many systems can absorb a certain amount of disruption. But how dangerous is a single failure to weaken the network? And how much damage can it do before it collapses? Network scientist Jianxi Gao is building tools that can answer these questions, regardless of the nature of the system.

Dr. said. . Gao, associate professor of computer science at Rensselaer Polytechnic, who received the CAREER Award from the National Science Foundation for addressing the problem. “The computational tools we are building will make it possible to assess the resilience of any system. With this, we can predict and prevent failure.”

Dr. Zhao said imagine the effects of climate change on the ecosystem. Species that cannot adapt will dwindle to extinction, perhaps driving a string of other species, which eat the first, to the brink of extinction as well. With climate changing, and pressure on species increasing, Dr. Zhao wants the ability to predict the impact of those dwindling populations on the rest of the ecosystem.

Resilience prediction begins by designating the system as a network, a graph in which players (animal, neuron, power plant) relate to the relationships between them, and how this relationship affects both the players and the network in general. In one visualization of a network, each player is a point, or node, connected to the other players by links that represent the relationship between them – think about who eats who in the forest and how this affects the total population of each species, or how the information transmitted affects Through the social networking site for opinions. Over time, the system changes, with some nodes appearing or disappearing, the links getting stronger or weaker or the relationship with each other changing as the system as a whole responds to this change.

Mathematically, the variable network can be described by a series of paired nonlinear equations. And while equations have been developed to map networks in many fields, predicting the resilience of complex networks or systems with missing information overwhelms the current capability of even the most powerful supercomputers.

“We are very limited in what we can do with current methods. Even if the network is not very large, we may be able to use a computer to solve the pairwise equations, but we cannot simulate many different failure scenarios,” Dr. Zhao said.

Dr. Zhao first proposed a preliminary solution to the problem in a research paper published in 2016 in temper nature. In that paper, he and colleagues declare that current analytical tools are insufficient because they are designed for smaller models with few interacting components, as opposed to the wide networks we want to understand. The authors propose a new set of tools, designed for complex networks, capable of first determining the normality and control parameters of the network, and then breaking down the behavior of different networks into a single solvable global function.

Tools provided in temper nature The paper worked with strict assumptions on a network in which all information is known – all nodes and all connections and interactions between those nodes and links. In the new work, Dr. Zhao wants to extend the single overarching equation to networks where some information is missing. The tools it develops will estimate the missing information—missing nodes and links, and the relationships between them—based on what is already known. Dr. Zhao said this approach reduces accuracy somewhat, but allows for a much greater reward than what was lost.

“For a network of millions or even billions of nodes, I will only be able to use one equation to estimate the macroscopic behavior of the network. Of course, I will lose some information, some accuracy, but capture the most important dynamics or properties of the whole system,” said Dr. Gao. “Right now, people can’t do that. They can’t test the system, find where it gives way, and better yet, improve it so it doesn’t fail.”

“The ability to analyze and anticipate vulnerabilities across a variety of network types gives us a tremendous amount of power to protect vulnerable networks and ecosystems before they fail,” said Kurt Brennemann, Dean of the Rensselaer College of Science. “This is the kind of game-changing work, and this CAREER award is recognition of that potential. We congratulate Jianxi and expect great things from his research.”

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