Mathematical foundations of neuroscience
G. Bard Ermentrout,David Terman +1 more
- 01 Jan 2010
- Vol. 35
TL;DR: The Hodgkin-Huxley Equations are applied to the model of Neuronal Networks to describe the “spatially distributed” networks.
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Abstract: The Hodgkin-Huxley Equations.- Dendrites.- Dynamics.- The Variety of Channels.- Bursting Oscillations.- Propagating Action Potentials.- Synaptic Channels.- Neural Oscillators: Weak Coupling.- Neuronal Networks: Fast/Slow Analysis.- Noise.- Firing Rate Models.- Spatially Distributed Networks.
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Estimating individual firing frequencies in a multiple spike train record.
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TL;DR: The proposed method is based on the presence of the refractory period in neuronal firing, however, its precise value is not required and can be used for an inference about the refectory period itself.
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Gualtiero Piccinini
- 12 Nov 2020
TL;DR: Copyright page extracts information about Oxford University Press and its copyright policies. It includes the address and registration information for the press, as well as restrictions on reproduction and distribution.
Bifurcations in a forced Wilson-Cowan neuron pair
TL;DR: In this paper , the authors investigate bifurcations of periodic solutions observed in the forced Wilson-Cowan neuron pair by both the brute-force computation and the shooting method.
References
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TL;DR: In this article, the authors investigated the relationship between certain classes of ordered small categories, introduced by Charles Ehresmann in the course of his work on local structures, and the class of U -semiabundant semigroups, first studied by El-Qallali and by de Barros.
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Expansions, free inverse semigroups, and Schützenberger product
Stuart W. Margolis,J.E Pin +1 more
TL;DR: In this article, the authors present a new construction of the free inverse monoid on a set X. Contrary to previous constructions of [9, 11], their construction is symmetric and originates from classical ideas of language theory.
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