GENESIS: a system for simulating neural networks
Advances in neural information processing systems 1
Multiple channels and calcium dynamics
Methods in neuronal modeling
Analysis of neural excitability and oscillations
Methods in neuronal modeling
Associative memory in a network of biological neurons
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
Reduction of conductance-based neuron models
Biological Cybernetics
What matters in neuronal locking?
Neural Computation
Resonance of a Stochastic Spiking Neuron Mimicking the Hodgkin-Huxley Model
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Spike and Burst Synchronization in a Detailed Cortical Network Model with I-F Neurons
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Markov Chain Model Approximating the Hodgkin-Huxley Neuron
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Clustering within Integrate-and-Fire Neurons for Image Segmentation
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Split-Precharge Differential Noise-Immune Threshold Logic Gate (SPD-NTL)
IWANN '03 Proceedings of the 7th International Work-Conference on Artificial and Natural Neural Networks: Part II: Artificial Neural Nets Problem Solving Methods
Evolving Spiking Neural Parameters for Behavioral Sequences
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
The spike response model: a framework to predict neuronal spike trains
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
The learning of moment neuronal networks
Neurocomputing
Applying the multivariate time-rescaling theorem to neural population models
Neural Computation
Improved similarity measures for small sets of spike trains
Neural Computation
Estimation of time-dependent input from neuronal membrane potential
Neural Computation
Improved dimensionally-reduced visual cortical network using stochastic noise modeling
Journal of Computational Neuroscience
Computational Intelligence and Neuroscience - Special issue on Selected Papers from the 4th International Conference on Bioinspired Systems and Cognitive Signal Processing
A Modified Spiking Neuron that Involves Derivative of the State Function at Firing Time
Neural Processing Letters
A nonlinear autoregressive Volterra model of the Hodgkin---Huxley equations
Journal of Computational Neuroscience
Reliability of spike and burst firing in thalamocortical relay cells
Journal of Computational Neuroscience
Hi-index | 0.00 |
It is generally believed that a neuron is a threshold element that fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the four-dimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The first-order term is linear in the input and its kernel has the typical form of an elementary postsynaptic potential. Higher-order kernels take care of nonlinear interactions between input spikes. In contrast to the standard Volterra expansion, the kernels depend on the firing time of the most recent output spike. In particular, a zero-order kernel that describes the shape of the spike and the typical after-potential is included. Our model neuron fires if the membrane voltage, given by the truncated response kernel expansion, crosses a threshold. The threshold model is tested on a spike train generated by the Hodgkin-Huxley model with a stochastic input current. We find that the threshold model predicts 90 percent of the spikes correctly. Our results show that, to good approximation, the description of a neuron as a threshold element can indeed be justified.