Mapping dynamical systems: New algorithm infers hypergraph structure from time-series data without prior knowledge

In a community, pairs of particular person components, or nodes, join to one another; these connections can signify a sprawling system with myriad particular person hyperlinks. A hypergraph goes deeper: It offers researchers a solution to mannequin complicated, dynamical methods the place interactions amongst three or extra people—and even amongst teams of people—could play an vital half.

As a substitute of edges that join pairs of nodes, it’s primarily based on hyperedges that join teams of nodes. Hypergraphs can signify higher-order interactions that signify collective behaviors like swarming in fish, birds, or bees, or processes within the mind.

Scientists often use a hypergraph model to foretell dynamic behaviors. However the reverse drawback is attention-grabbing, too. What if researchers can observe the dynamics however haven’t got entry to a dependable mannequin? Yuanzhao Zhang, an SFI Complexity Postdoctoral Fellow, has a solution.

In a paper published in Nature Communications, Zhang and his collaborators describe a novel algorithm that may infer the construction of a hypergraph utilizing solely the noticed dynamics.

Their algorithm makes use of time-series knowledge—observations collected at even intervals over a interval—to assemble hypergraphs (and different representations of higher-order interactions) that produce the noticed patterns. It may be utilized to any dataset assumed to have some underlying mathematical construction, Zhang says. Time-series knowledge are helpful for finding out the unfold of illness or the habits of monetary markets, biological systems, and lots of different conditions.

Notably, the strategy solely requires the info; it does not require prior data concerning the system or how particular person nodes behave. “That’s the main advantage,” Zhang says. “It opens up a lot more possibilities, and you can apply it to systems for which you don’t know the underlying dynamics.”

He factors to mind perform for example. Researchers can gather observational time-series knowledge, however they do not have a great mannequin for the way every part matches collectively. “Obviously we cannot cut open our brains and see what’s actually going on,” he says. “But we can learn something by looking at data from brain recordings.”

Within the new paper, Zhang and his collaborators verified their strategy by testing it on time-series knowledge, guaranteeing that it produced a recognized underlying construction. Then, they utilized it to electroencephalogram (EEG) knowledge collected from greater than 100 human topics. An EEG measures electrical activity in varied areas of the mind over time, collected by way of sensors caught to an individual’s scalp. The ensuing report appears to be like like a collection of waves.

Most recognized connections within the mind are pairwise, connecting one mind area to a different. Nevertheless, utilizing their new algorithm, Zhang and his collaborators unearthed a hypergraph mannequin that precisely captured connections within the EEG knowledge amongst three or extra areas. That means higher-order interactions play an vital and underappreciated function in shaping macroscopic patterns of mind exercise.

The researchers used their mannequin to establish probably the most frequent varieties of interactions amongst mind areas. “What’s actually attention-grabbing is that the highest six distinguished hyperedges all pointed towards the prefrontal cortex, which is understood to be one of many data processing hubs within the mind,” Zhang says.

The present work can infer a mannequin of some hundred nodes; sooner or later, he hopes to scale as much as bigger networks.