Math may help predict calamities

Scientists, including one of Indian-origin, have developed a mathematical equation that may help predict calamities such as financial crashes in economic systems and epileptic seizures in the brain.
If the principle is generalised in other real-world complex systems, such as climate change or disease control, it could open up the possibility of catastrophes being averted before they happen, researchers said.
Researchers led by The University of Sussex 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.
Such "phase transitions" are common in many real systems, and are often highly significant: epileptic seizures and financial market crashes are just two examples of transitions.

Until now, though, ways to predict these transitions in advance have been lacking, researchers said.
Previous measures, which peak at the transition itself, have been of no use for purposes of prediction, they said.

"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," lead researcher Dr Lionel Barnett said.

Essentially this means finding a way to characterise, mathematically, the extent to which the parts of a complex system are simultaneously segregated and integrated.
Researchers managed to do just this, and to show for the first time that their measure reliably predicts phase transitions in standard systems.
"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," Professor Anil Seth, Co-Director of the Sackler Centre, said.
"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," said Seth.
The study was published in the journal Physics Review Letters.