Population Encoding With Hodgkin–Huxley Neurons

Lazar, Aurel A.

doi:10.1109/tit.2009.2037040

Cited by 31 publications

(28 citation statements)

References 34 publications

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“…Lazar and Pnevmatikakis (2008a) have developed conditions under which a bandlimited input of the IF neuron can be reconstructed perfectly. The result has been extended to other TEMs, such as populations of IF neurons Pnevmatikakis, 2008a, Lazar andSlutskiy, 2014c), IF neurons with refractory period (Lazar, 2004), leaky IF (LIF) neurons (Lazar, 2005), Hodgkin-Huxley neurons (Lazar, 2010) and asynchronous sigma-delta modulators (ASDMs) (Lazar and Tóth, 2004b). …”

Section: Time Encoding and Decoding In Bandlimited And Shift-invarianmentioning

confidence: 93%

“…The following lemma proves that a Hodgkin-Huxley neuron with multiplicative coupling and an ideal IF neuron with variable threshold sequence {δ k+1 − δ k } k∈Z are inputoutput equivalent, i.e., they both trigger the same spike sequence {t k } k∈Z when presented with the same input u (Lazar, 2010).…”

Section: The Hodgkin-huxley Neuronmentioning

confidence: 99%

“…Reconstruction algorithms have been designed for the bandlimited inputs of linear (Lazar and Pnevmatikakis, 2008a) as well as nonlinear (Lazar and Slutskiy, 2014c) filter banks in cascade with ensembles of ideal IF neurons, ideal IF neurons with refractory period (Lazar, 2004), leaky IF (LIF) neurons (Lazar, 2005), populations of LIF neurons with random thresholds , as well as populations of Hodgkin-Huxley neurons (Lazar, 2007(Lazar, , 2010. Florescu and Coca (2015) have introduced a new reconstruction algorithm for ideal IF neurons that redefines IF time encoding as a uniform sampling problem.…”

Section: Time Encoding and Decoding In Bandlimited Spacesmentioning

confidence: 99%

“…A Hodgkin-Huxley neuron stimulated via multiplicative coupling by input function u is described by (Lazar, 2007) (Lazar, 2010).…”

Section: The Hodgkin-huxley Neuronmentioning

confidence: 99%

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Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Florescu¹

2017

Springer Theses

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To my family iii The third problem addressed in this work is given by the need of developing neuromorphic engineering circuits that perform mathematical computations in the spike domain.In this respect, this thesis developed a new representation between the time encoded input and output of a linear filter, where the TEM is represented by an ideal IF neuron. A new practical algorithm is developed based on this representation. The proposed algorithm is significantly faster than the alternative approach, which involves reconstructing the input, simulating the linear filter, and subsequently encoding the resulting output into a spike train.

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Section: Time Encoding and Decoding In Bandlimited And Shift-invarianmentioning

confidence: 93%

Section: The Hodgkin-huxley Neuronmentioning

confidence: 99%

Section: Time Encoding and Decoding In Bandlimited Spacesmentioning

confidence: 99%

“…A Hodgkin-Huxley neuron stimulated via multiplicative coupling by input function u is described by (Lazar, 2007) (Lazar, 2010).…”

Section: The Hodgkin-huxley Neuronmentioning

confidence: 99%

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Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Florescu¹

2017

Springer Theses

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“…The set of stochastic differential equations (SDEs) below represent their stochastic counterpart (Lazar, 2010):…”

Section: Modeling Nonlinear Neural Circuits Stimuli and Noisementioning

confidence: 99%

Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources

Lazar

Zhou

2014

Front. Comput. Neurosci.

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We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The dendritic stimulus processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

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Phase‐response curves of ion channel gating kinetics

Schleimer

Schreiber

2018

Math Methods in App Sciences

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Reduced models of single-neuron dynamics are widely used to characterize neuronal properties such as stimulus encoding and a cell's contribution to network function. Low-dimensional phase oscillator models based on phase-response curves, in particular, permit to capture the essence of a neuron's input-output dynamics at the level of spike times from high-dimensional conductance-based neuron models. In principle, these phase models allow for a direct translation of perturbations in the state variables (such as changes in specific ion channel conductances and kinetics) to shifts in the timing of spikes. Previous mathematical work, however, has predominantly focused on voltage and current perturbations and less on perturbations occurring in any of the involved kinetic equations of ionic channels. Here, we provide the means to mathematically relate properties in these variables to the phase-dependent voltage dynamics. Specifically, we derive the vector of phase-response curves near two different onset bifurcations: the physiologically prominent saddle node on invariant cycle bifurcation as well as the saddle-node loop bifurcation. We demonstrate that, locally around the saddle node, the tangent space of the isochrons is spanned by the strongly stable manifold of the saddle node. This finding enables us to quantitatively relate perturbations in the gating kinetics of ion channels to the resulting changes in spike timing. These results lay the methodological foundation for future quantitative analyses of the impact of specific biophysical channel properties on spike timing, including, but not limited to, channel noise. KEYWORDSconductance-based neuron model, gating kinetics, homoclinic orbits to a saddle node, isochrons, phase-response curves, saddle-node loop, saddle node on invariant cycle, semistable manifold, strongly stable manifold 8844

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Population Encoding With Hodgkin–Huxley Neurons

Cited by 31 publications

References 34 publications

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources

Phase‐response curves of ion channel gating kinetics

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