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Noise Sustained Patterns: Fluctuations and Nonlinearities, World Scientific Lecture Notes in Physics, World Scientific (2003).

"Markus Loecher has written a vivid and timely review of a rapidly emerging area with implications for many fields. Noise Sustained Patterns describes, in a clear and tutorial way, how random processes can actually lead to the emergence of order in nonlinear systems."

Prof. Frank Moss
Curators' Professor
Center for Neurodynamics
University of Missouri St Louis

"The book "Noise Sustained Patterns" by Markus Loecher is a speedy but profound introduction into the Emerging field of stochastic pattern formation. The author emphasizes the interdisciplinarity of the interaction between noise and nonlinear dynamics by providing various applications in economics, traffic systems, neural networks and many other areas. He treats analytical as well as numerical and experimental aspects. The book is a quick and useful introduction into the subject and it is fun to read. The broad collection of non-physical examples makes it interesting to read also for scientists already familiar with stochastic dynamics."

Prof. L. Schimansky-Geier
Chair, Center for Stochastic Processes
Physics Dept.
Humbold University Berlin

“This book provides an excellent overview of noise-induced-spatio-temporal phenomena in a variety of contexts, ranging from fluid dynamics, semiconductor devices and statistical mechanics to biophysics, traffic flows and game theory ... With almost 300 references it provides a good summary of the current literature on the impact of noise upon the emergence ad sustenance of patterns. It should provide a unique tool for researchers wanting to have a quick overview of this field.”

Mathematical Reviews

Noise On The Brain

(16 June 1998)
"The random fluctuations of noise generally add unwanted messiness to a signal. But sometimes noise can actually pump up small signals and make them detectable. Now physicists, reporting in the current issue of Physical Review Letters, have built an electronic model demonstrating how noise might play a key role in communication among neurons in the brain, by helping to push signals from cell to cell.

When background noise and a faint signal have similar frequency components, the two add constructively and can crank up the signal's strength. Scientists first noticed these "stochastic resonances" 20 years ago as peaks in the annual global climate temperatures brought out by the "noise" of variations in solar radiation. Since then, signals buoyed by noise have been spotted in biological, electrical, and chemical systems.

To study the role of noise in systems--like the brain--that consist of many linked components, Markus Löcher, David Cigna, and Earle Hunt, physicists at Ohio University in Athens, wired up an electronic circuit using 32 diodes. Diodes act a bit like dams: the signal can pass through one only if it is above a certain threshold. In earlier work, the team had shown that adding noise to the circuit as a whole could amplify signals in all elements at once. But they wondered if adding noise to each diode could also create a sort of domino effect and help an individual signal jump from one element in the circuit to another.

To find out, the team rigged the diodes so that they acted as high dams, completely blocking the passage of the signal. Then they added a bit of noise to the signal before it passed through each diode. The team discovered that a controlled amount of noise gave the signal enough energy to push itself across from one diode to the next, despite the barriers. Too little noise, says Löcher, and the signal doesn't make it. Too much noise distorts and corrupts the signal.

The way a signal propagates through this electronic circuit and through brain cells is very similar, says Peter Jung, a physicist at Ohio University. "It shows that the mechanism of noise-supported transmission is very general, which is very interesting." Brain diseases like epilepsy, he says, may well be related to some sort of imbalance in the noise-assisted communication between brain cells."
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