Whether you are attempting to predict a climate catastrophe or mental health crisis, mathematics tells us to search for fluctuations.
Changes in data, from wildlife population to anxiety levels, may be an early warning signal that a system is reaching a critical threshold, often known as a tipping point, during which those changes may speed up and even develop into irreversible.
But which data points matter most? And that are simply just noise?
A brand new algorithm developed by University at Buffalo researchers can discover essentially the most predictive data points that a tipping point is near. Detailed in Nature Communications, this theoretical framework uses the ability of stochastic differential equations to watch the fluctuation of knowledge points, or nodes, after which determine which ought to be used to calculate an early warning signal.
Simulations confirmed this method was more accurate at predicting theoretical tipping points than randomly choosing nodes.
“Every node is somewhat noisy — in other words, it changes over time — but some may change earlier and more drastically than others when a tipping point is near. Choosing the precise set of nodes may improve the standard of the early warning signal, in addition to help us avoid wasting resources observing uninformative nodes,” says the study’s lead creator, Naoki Masuda, PhD, professor and director of graduate studies within the UB Department of Mathematics, throughout the College of Arts and Sciences.
The study was co-authored by Neil Maclaren, a postdoctoral research associate within the Department of Mathematics, and Kazuyuki Aihara, executive director of the International Research Center for Neurointelligence on the University of Tokyo.
The work was supported by the National Science Foundation and the Japan Science and Technology Agency.
Warning signals connected via networks
The algorithm is exclusive in that it fully incorporates network science into the method. While early warning signals have been applied to ecology and psychology for the last twenty years, little research has focused on how those signals are connected inside a network, Masuda says.
Consider depression. Recent research has considered it and other mental disorders as a network of symptoms influencing one another by creating feedback loops. A lack of appetite could mean the onset of 5 other symptoms within the near future, depending on how close those symptoms are on the network.
“As a network scientist, I felt network science could offer a novel or maybe even improved approach to early warning signals,” Masuda says.
By thoroughly considering systems as networks, researchers found that simply choosing the nodes with highest fluctuations was not one of the best strategy. That is because some chosen nodes could also be too closely related to other chosen nodes.
“Even when we mix two nodes with nice early warning signals, we do not necessarily get a more accurate signal. Sometimes combining a node with an excellent signal and one other node with a mid-quality signal actually gives us a greater signal,” Masuda says.
While the team validated the algorithm with numerical simulations, they are saying it may possibly readily be applied to actual data since it doesn’t require information in regards to the network structure itself; it only requires two different states of the networked system to find out an optimal set of nodes.
“The following steps can be to collaborate with domain experts akin to ecologists, climate scientists and medical doctors to further develop and test the algorithm with their empirical data and get insights into their problems,” Masuda says.
