In science we have what are called "laws", be them Newton's Laws of Motion or Archimedes' Principle, because these mathematical expressions describe systems in a rigid set of boundaries, essentially helping predict how these systems will behave in the future. What about overly complex, highly dynamic systems; could we use a single mathematical equation to predict outcomes for such systems? An University of Sussex-led study found a mathematical equation that may help predict calamities such as financial crashes in economic systems and epileptic seizures in the brain.

The team of neuroscientists led by Dr Lionel Barnett sought to mathematically describe how various parts of a systems simultaneously behave differently, while still being integrated (the parts depend on each other). Collaborating with scientists at the University's Sackler Centre for Consciousness Science and the Centre for Research in Complex Systems at Charles Sturt University in Australia, the team used mathematics and detailed computer simulations to show that a measure of 'information flow' reaches a peak just before a system moves from a healthy state to an unhealthy state.

This is known as a 'phase transition' and in real world systems these can have huge implications, like epileptic seizures or financial market crashes. Predicting such events in the past had been extremely difficult to undertake. Barnett and colleagues, however, showed for the first time that their method can reliably predict phase transitions in a physics standard system - so-called Ising models.

" This conjecture is verified for a ferromagnetic 2D lattice Ising model with Glauber dynamics and a transfer entropy-based measure of systemwide information flow. Implications of the conjecture are considered, in particular, that for a complex dynamical system in the process of transitioning from disordered to ordered dynamics (a mechanism implicated, for example, in financial market crashes and the onset of some types of epileptic seizures); information dynamics may be able to predict an imminent transition," reads the paper's abstract.

"The key insight in the paper is that the dynamics of complex systems – like the brain and the economy – depend on how their elements causally influence each other; in other words, how information flows between them. And that this information flow needs to be measured for the system as a whole, and not just locally between its various parts," Dr. Barnett said.

It will be interesting to see how University of Susses researchers' method fairs with complex real world system, and to which degree their equation can reliably predict when a phase transition will occur.

Professor Anil Seth, Co-Director of the Sackler Centre, says: "The implications of the work are far-reaching. If the results generalise to other real-world systems, we might have ways of predicting calamitous events before they happen, which would open the possibility for intervention to prevent the transition from occurring."

"For example, the ability to predict the imminent onset of an epileptic seizure could allow a rapid medical intervention (perhaps via brain stimulation) which would change the course of the dynamics and prevent the seizure. And if similar principles apply to financial markets, climate systems, and even immune systems, similar interventions might be possible. Further research is needed to explore these exciting possibilities."

The findings were published in the journal *Physical Review Letters*.