“Structures built from a very large number of units can exhibit sharp transitions from one state to another state, which physicists call phase transitions,” said Cowan, a Professor in Mathematics and Neurology at Chicago. “Strange and interesting things happen in the neighborhood of a phase transition.”
When liquids undergo phase transitions, they evaporate into gas or freeze into ice. When the brain undergoes a phase transition, it moves from random to patterned activity. “The brain at rest produces random activity,” Cowan said, or what physicists call “Brownian motion.”
Although the bulk of his work involves deriving equations, Cowan’s findings mesh well with laboratory data generated on the cerebral cortex and electroencephalograms. His latest findings show that the same mathematical tools physicists use to describe the behavior of subatomic particles and the dynamics of liquids and solids can now be applied to understanding how the brain generates its various rhythms.
These include the delta waves generated during sleep, the alpha waves of the visual brain, and the gamma waves, discovered during the last decade, which seem related to information processing. “The resting state of brain activity seems to have a statistical structure that’s characteristic of a certain kind of phase transition,” Cowan said. “The brain likes to sit there because that’s the place where information processing is optimized.”
Cowan organized a session for AAAS on Mathematics and the Brain, which will take place from 8:30 to 10 a.m. EST Saturday, Feb. 16. He also will participate in a news briefing on the topic at 3 p.m. EST Friday, Feb. 15. Joining him at both events will be mathematician Nancy Kopell of Boston University and computational neuroscientist Tomaso Poggio of the Massachusetts Institute of Technology.
At this stage of his research, Cowan said it would be premature and speculative for him to try to relate how phase transitions in the brain might relate to neurological conditions or states of human consciousness. “That’s for the future,” he said.
Another component of his latest research is the close relationship between spontaneous pattern formation in brain circuits and in chemical reaction networks. In this research, he shows how mathematics can help explain visual hallucinations and how the visual cortex obtained its stripes, which are visible to the naked eye when removed from cadavers.
“This line of research on pattern formation can be traced back to Alan Turing, who also founded the modern science of computation,” said Terrence Sejnowski of the Salk Institute for Biological Studies in La Jolla, Calif., who is a leading specialist in computational neurobiology.
Cowan’s quest to understand the brain’s workings using numerical methods spans more than four decades. Along the way he has collaborated with a series of Ph.D. students and colleagues in physics, mathematics, biology and neuroscience.
In 1972, he and postdoctoral fellow Hugh Wilson, now of Canada’s York University, formulated a set of equations that could describe the dynamics of neural networks. Now called “Wilson-Cowan equations,” they became a mainstay of neural network research. “But I always knew that those equations were inadequate, so I kept thinking about them,” Cowan said.
Then in 1985, he ran across an article in a Japanese journal that described a statistical physics approach to chemical reaction networks. “It took me years to understand how to use these tools for biological networks,” he said. “It so happens that there is an analogy between the behavior of chemical reaction networks and neural networks.”
His research career began in 1962, when as a graduate student in electrical engineering, he worked with the founders of neural network theory. These included Norbert Wiener, who died in 1964, before they could work jointly on the problem that Cowan continues to address.
“I didn’t really understand what he was saying to me until I worked it out myself. He was one of the great mathematicians of the 20th century,” Cowan said.
Steve Koppes | EurekAlert!
New survey hints at exotic origin for the Cold Spot
26.04.2017 | Royal Astronomical Society
NASA's Fermi catches gamma-ray flashes from tropical storms
25.04.2017 | NASA/Goddard Space Flight Center
More and more automobile companies are focusing on body parts made of carbon fiber reinforced plastics (CFRP). However, manufacturing and repair costs must be further reduced in order to make CFRP more economical in use. Together with the Volkswagen AG and five other partners in the project HolQueSt 3D, the Laser Zentrum Hannover e.V. (LZH) has developed laser processes for the automatic trimming, drilling and repair of three-dimensional components.
Automated manufacturing processes are the basis for ultimately establishing the series production of CFRP components. In the project HolQueSt 3D, the LZH has...
Reflecting the structure of composites found in nature and the ancient world, researchers at the University of Illinois at Urbana-Champaign have synthesized thin carbon nanotube (CNT) textiles that exhibit both high electrical conductivity and a level of toughness that is about fifty times higher than copper films, currently used in electronics.
"The structural robustness of thin metal films has significant importance for the reliable operation of smart skin and flexible electronics including...
The nearby, giant radio galaxy M87 hosts a supermassive black hole (BH) and is well-known for its bright jet dominating the spectrum over ten orders of magnitude in frequency. Due to its proximity, jet prominence, and the large black hole mass, M87 is the best laboratory for investigating the formation, acceleration, and collimation of relativistic jets. A research team led by Silke Britzen from the Max Planck Institute for Radio Astronomy in Bonn, Germany, has found strong indication for turbulent processes connecting the accretion disk and the jet of that galaxy providing insights into the longstanding problem of the origin of astrophysical jets.
Supermassive black holes form some of the most enigmatic phenomena in astrophysics. Their enormous energy output is supposed to be generated by the...
The probability to find a certain number of photons inside a laser pulse usually corresponds to a classical distribution of independent events, the so-called...
Microprocessors based on atomically thin materials hold the promise of the evolution of traditional processors as well as new applications in the field of flexible electronics. Now, a TU Wien research team led by Thomas Müller has made a breakthrough in this field as part of an ongoing research project.
Two-dimensional materials, or 2D materials for short, are extremely versatile, although – or often more precisely because – they are made up of just one or a...
20.04.2017 | Event News
18.04.2017 | Event News
03.04.2017 | Event News
26.04.2017 | Life Sciences
26.04.2017 | Physics and Astronomy
26.04.2017 | Earth Sciences