Fractional differentiation by neocortical pyramidal neurons

By Brian Nils Lundstrom, M. Higgs, W. Spain, Adrienne L. Fairhall. Nature Neuroscience, 2008

665 citations recorded by the source corpus.

Neural systems adapt to changes in stimulus statistics. However, it is not known how stimuli with complex temporal dynamics drive the dynamics of adaptation and the resulting firing rate. For single neurons, it has often been assumed that adaptation has a single time scale. We found that single rat neocortical pyramidal neurons adapt with a time scale that depends on the time scale of changes in stimulus statistics. This multiple time scale adaptation is consistent with fractional order differentiation, such that the neuron's firing rate is a fractional derivative of slowly varying stimulus parameters. Biophysically, even though neuronal fractional differentiation effectively yields adaptation with many time scales, we found that its implementation required only a few properly balanced known adaptive mechanisms. Fractional differentiation provides single neurons with a fundamental and general computation that can contribute to efficient information processing, stimulus anticipation and frequency-independent phase shifts of oscillatory neuronal firing.

Subfields: Cellular and Molecular Neuroscience, Cognitive Neuroscience, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/22fe8a384e78d81187ef37de318df46a8e322c18

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Citations in the corpus

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Measuring memory with the order of fractional derivative (2013, background): “2, equation (6) fits the test data very well.”
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Inferring Network Dynamics and Neuron Properties from Population Recordings (2011, background): “, 1988; Marom, 2009), including also additional adaptation and recovery mechanisms (La Camera et al., 2006; Lundstrom et al., 2008).”
Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions☆ (2011, background): “In the recent paper [25] it has been pointed out that fractional differentiation provides neurons with a fundamental and general computation ability that can contribute to efficient information processing, stimulus anticipation and frequency-independent phase shifts of oscillatory neuronal firing, e”
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Necessary and Sucient Conditions for the Fractional Gagliardo-Nirenberg Inequalities and Applications to Navier-Stokes and Generalized Boson Equations (2011, neutral): “[20, 41].”