By Peter Arhem, Hans Liljenstrom, Clas Blomberg
The most objective of this learn is to elevate and discover the fascinating difficulties of noise and chaos within the worried approach. It examines questions comparable to: what sensible position do fluctuations in neural structures play?; are there chaotic procedures within the brain?; what's the neural code, and the way strong is it in the direction of noise?; and are there mechanisms which can keep an eye on noise and chaos?
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Additional info for Disorder Versus Order in Brain Function: Essays in Theoretical Neurobiology
Moss, F. Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature 373, 33-36 (1995). 27 Wilson, M. A. & Bower, J. M. The simulation of large-scale neural networks. In: Methods of Neuronal Modeling: From Synapses to Networks C. Koch and I. Segev, eds. (MIT Press, Cambridge, MA, 1989). Wu, X. & Liljenstrom, H. Regulating the nonlinear dynamics of olfactory cortex. Network: Comp. Neur. Syst 5, 47-60 (1994). 28 Chapter 2 A PRIMER ON NOISE AND CHAOS C. BLOMBERG 1 Introduction As discussed in Chapter 1, the basic concepts related to irregular and disordered processes do not tell anything about their generation.
Standard concepts in the analysis of random (noise) processes are autocorrelation and spectral functions. Autocorrelation for a random process x(t), is as well known defined as an average of x at two different times: C(t) =< x(to)x(to+t) >. The spectral function is in principle the Fourier transform of the autocorrelation function. White noise means that the values at two different times are totally uncorrelated, thus the autocorrelation is a delta function, expressed in (2). The spectral function is then constant over all frequencies.
Freeman, W. J. Random activity at the microscopic neural level in cortex ("noise") sustains and is regulated by low-dimensional dynamics of macroscopic cortical activity ("chaos"). Int. J. Neur. Syst. 7, 473-480 (1996). , Spano, M. , Ditto, W. , & Weiss, J. , Controlling cardiac chaos. Science 257, 1230- 1235 (1992). , Briggs, M. , Francis, M. , Sengers, J. , Gammon, R. , Dorfman, J. R. & Calabrese, R. V. Experimental evidence for microscopic chaos, Nature 394, 865-868 (1998). Gutman, G. A. & K.
Disorder Versus Order in Brain Function: Essays in Theoretical Neurobiology by Peter Arhem, Hans Liljenstrom, Clas Blomberg