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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Citations
Optimal entrainment for removal of pinned spiral waves.
TL;DR: In this paper , a phase-based reduction technique is used to solve an optimal control problem to yield a time-varying external voltage gradient that can synchronize a collection of spiral waves that are pinned to a set of heterogeneous obstacles.
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Well-posedness and stability of stochastic evolution equations arising from neuroscience
Jennifer Krüger
- 01 Jan 2017
TL;DR: The main criterion, the so-called absolute continuity condition, is introduced and proven to guarantee the uniqueness of deterministic as well as stochastic mild solutions and it is shown that on finite domain suitably chosen Hilbert space-valued additive noise is able to regularise the equation without any further conditions.
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The neuronal response at extended timescales: a linearized spiking input-output relation.
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TL;DR: A linearized spiking Input–Output (I/O) relation can be derived semi-analytically, relating input spike trains to output spikes based on known biophysical properties, and enables a biophysical neuron model to be fit so it reproduces experimentally observed temporal firing statistics on days-long experiments.
Neural energy computations based on Hodgkin-Huxley models bridge abnormal neuronal activities and energy consumption patterns of major depressive disorder
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TL;DR: The model in this paper was the first neural network energy computational model for MDD, which showed success in explaining its dynamical mechanisms with an energy consumption perspective, and showed a promising pipeline to use an energy methodology for studying other neuropsychiatric disorders.
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