Models of neural computation: Difference between revisions

Revision as of 08:58, 13 January 2013

Revision as of 21:40, 23 June 2013

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==Introduction==

Due to the complexity of nervous system behavior, the associated experimental error bounds are ill-defined, but the relative merit of the different [[scientific model|models]] of a particular subsystem can be compared according to how closely they reproduce real-world behaviors or respond to specific input signals. In the closely related field of computational [[neuroethology]], the practice is to include the environment in the model in such a way that the [[Control theory#Closed-loop_transfer_functionloop transfer function|loop is closed]]. In the cases where competing models are unavailable, or where only gross responses have been measured or quantified, a clearly formulated model can guide the scientist in designing experiments to probe biochemical mechanisms or network connectivity.

In all but the simplest cases, the mathematical equations that form the basis of a model cannot be solved exactly. Nevertheless, computer technology, sometimes in the form of specialized software or hardware architectures, allow scientists to perform iterative calculations and search for plausible solutions. A computer chip or a robot that can interact with the natural environment in ways akin to the original organism is one embodiment of a useful model. The ultimate measure of success is however the ability to make testable predictions.

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====Cross-correlation in sound localization: Jeffress model====

According to Jeffress,<ref>Jeffress, L.A., 1948. A place theory of sound localization. ''Journal of Comparative and Physiological Psychology 41'', 35–39.</ref> in order to compute the ___location of a sound source in space from [[interaural time difference]]s, an auditory system relies on [[delay line]]s: the induced signal from an [[ipsilateral]] auditory receptor to a particular neuron is delayed for the same time as it takes for the original sound to go in space from that ear to the other. Each postsynaptic cell is differently delayed and thus specific for a particular inter-aural time difference. This theory is equivalent to the mathematical procedure of [[cross-correlation]].

Following Fischer and Anderson,<ref>Brian J. Fischer and Charles H. Anderson, 2004. A computational model of sound localization in the barn owl ''Neurocomputing" 58–60 (2004) 1007–1012</ref> the response of the postsynaptic neuron to the signals from the left and right ears is given by

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===Neurophysiological metronomes: neural circuits for pattern generation===

Mutually [[inhibitory]] processes are ana unifying motif of all [[central pattern generator]]s. This has been demonstrated in the stomatogastric (STG) nervous system of crayfish and lobsters.<ref>Michael P. Nusbaum and Mark P. Beenhakker, A small-systems approach to motor pattern generation, Nature 417, 343–350 (16 May 2002)</ref> Two and three-cell oscillating networks based on the STG have been constructed which are amenable to mathematical analysis, and which depend in a simple way on on synaptic strengths and overall activity, presumably the knobs on these things.<ref>Cristina Soto-Treviño, Kurt A. Thoroughman and Eve Marder, L. F. Abbott, 2006. Activity-dependent modification of inhibitory synapses in models of rhythmic neural networks Nature Vol 4 No 3 2102–2121</ref> The mathematics involved is the theory of [[dynamical systems]].

===Anti-Hebbian adaptation: spike-timing dependent plasticity===

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==External links==

* [http://home.earthlink.net/~perlewitz/sftwr.html Computational Neuroscience – Software ] – A list of commonly used modelling tools.

* [http://www.proberts.net/research/ Neural Dynamics at NSI ] – Web page of Patrick D Roberts at the Neurological Sciences Institute

* [http://www.dickinson.caltech.edu/ Dickinson Lab ] – Web page of the Dickinson group at Caltech which studies flight control in ''Drosophila''

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