Reduction of the Hodgkin-Huxley Equations to a Single-Variable Threshold Model

By Werner M. Kistler, Wulfram Gerstner, J. van Hemmen. 1997

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Citations in the corpus

Deep learning in neural networks: An overview (2014, methodology): “Many computational models of such spiking neurons have been proposed and analyzed (e.g., Gerstner and van Hemmen, 1992; Zipser et al., 1993; Stemmler, 1996; Tsodyks et al., 1996; Maex and Orban, 1996; Maass, 1996, 1997; Kistler et al., 1997; Amit and Brunel, 1997; Kempter et al., 1999; Song et al., ”
Stochastic Integrate and Fire Models: a review on mathematical methods and their applications (2011, methodology): “ studies on networks. Indeed, although the stochastic LIF models are simpliﬁed representations of the cells, they are considered good descriptors of the neuron spiking activity (cf. for example [69], [73]). Though some criticisms have appeared, showing some lacks in the ﬁt of experimental data (cf. ”
Global solvability of a networked integrate-and-fire model of McKean–Vlasov type (2012, methodology): “Here Iexti (t) represents the external input current to the neuron, ηi(t) is the noise (a white noise) which is importantly supposed to be independent from neuron to neuron, and the constants λ, β, α and σ are chosen according to experimental data.”
Improving Generalization in Meta Reinforcement Learning using Learned Objectives (2019, background): “…tasks (reward functions) as well as environments (e.g. different Atari games) has been shown previously in the context of transfer learning (Kistler et al., 1997; Parisotto et al., 2015; Rusu et al., 2016; 2019; Nichol et al., 2018) and meta-critic learning across tasks (Sung et al., 2017).”
Modeling Synaptic Plasticity in Conjunction with the Timing of Pre- and Postsynaptic Action Potentials (2000, methodology): “Depending on the choice for 2 and g, the spike-response model can reproduce the standard integrate-and-re model or even mimic complex HodgkinHuxley-type neuron models (Kistler et al., 1997).”
SPIKING NEURON MODELS Single Neurons , Populations , Plasticity (2002, methodology): “This interpretation has motivated the name ‘Spike Response Model’, SRM for short (Gerstner, 1995; Kistler et al., 1997).”
A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input (2006, background): “The truncation of this expansion beyond the first-order kernel has been shown to be equivalent to a form of the leaky integrate-and-fire neuron model (Kistler et al. 1997), namely the spike response model (Gerstner 1995).”
Artificial Neural Networks-Based Machine Learning for Wireless Networks: A Tutorial (2017, methodology): “e are many models to describe the spiking neurons such as Hodgkin-Huxley model in [106], integrate-and-ﬁre model in [107], theta model in [108], Lzhikevich model in [109], and spike response model in [110]. The most common spiking neuron models are based on the integrate-and-ﬁre and leaky-integrate-”
Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. (2005, result): “…and comparison with previously published results (Jolivet et al. 2004), we also used a single performance measure, the coincidence factor (cid:9) , deﬁned in Kistler et al. (1997), ranging from 0 to 1, which is, for small E and M, related to the previous two measures by (cid:9) (cid:2) 1 (cid”
Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking (2000, methodology): “To a very good approximation, the Hodgkin-Huxley model can also be mapped to a response kernel description (Kistler et al., 1997).”
Machine Learning for Wireless Networks with Artificial Intelligence: A Tutorial on Neural Networks (2017, methodology): “There are many models to describe the spiking neurons such as Hodgkin-Huxley model in [106], integrate-and-fire model in [107], theta model in [108], Lzhikevich model in [109], and spike response model in [110].”
Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. (2004, methodology): “A slightly different analytical approach leads to the Spike Response Model (SRM) that we discuss in the second subsection.”