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J Neurophysiol 96: 826-833, 2006. First published April 26, 2006; doi:10.1152/jn.00134.2006
0022-3077/06 $8.00
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Models and Properties of Power-Law Adaptation in Neural Systems

Patrick J. Drew and L. F. Abbott

Neurobiology Section 0357, Division of Biology, University of California at San Diego, La Jolla, California; and Center for Neurobiology and Behavior, Department of Physiology and Cellular Biophysics, Columbia University College of Physicians and Surgeons, New York, New York

Submitted 8 February 2006; accepted in final form 23 April 2006

Many biological systems exhibit complex temporal behavior that cannot be adequately characterized by a single time constant. This dynamics, observed from single channels up to the level of human psychophysics, is often better described by power-law rather than exponential dependences on time. We develop and study the properties of neural models with scale-invariant, power-law adaptation and contrast them with the more commonly studied exponential case. Responses of an adapting firing-rate model to constant, pulsed, and oscillating inputs in both the power-law and exponential cases are considered. We construct a spiking model with power-law adaptation based on a nested cascade of processes and show that it can be "programmed" to produce a wide range of time delays. Finally, within a network model, we use power-law adaptation to reproduce long-term features of the tilt aftereffect.


Address for reprint requests and other correspondence: P. J. Drew, Neurobiology Section 0357, Division of Biology, University of California at San Diego, 9500 Gilman Dr., La Jolla, CA 92093 (E-mail: pjdrew{at}biomail.ucsd.edu)




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