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J Neurophysiol (April 26, 2006). doi:10.1152/jn.00134.2006
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Submitted on February 8, 2006
Accepted on April 23, 2006

Models and Properties of Power-Law Adaptation in Neural Systems

Patrick James Drew1* and Larry F. Abbott2

1 Neurobiology Section, Division of Biological Sciences, University of California, San Diego, La Jolla, California, United States
2 Center for Neurobiology and Behavior, Department of Physiology and Cellular Biophysics, Columbia University College of Physicians and Surgeons, New York, New York, United States

* To whom correspondence should be addressed. E-mail: pjdrew{at}ucsd.edu.

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.




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