Analysis of neural excitability and oscillations
Methods in neuronal modeling
Weakly connected neural networks
Weakly connected neural networks
Spikes: exploring the neural code
Spikes: exploring the neural code
On the difference between two widely publicized methods for analyzing oscillator phase behavior
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Computation in a single Neuron: Hodgkin and Huxley revisited
Neural Computation
Computation of the Phase Response Curve: A Direct Numerical Approach
Neural Computation
Reconstruction of sensory stimuli encoded with integrate-and-fire neurons with random thresholds
EURASIP Journal on Advances in Signal Processing - Special issue on statistical signal processing in neuroscience
Consistent recovery of sensory stimuli encoded with MIMO neural circuits
Computational Intelligence and Neuroscience - Special issue on signal processing for neural spike trains
Multichannel time encoding with integrate-and-fire neurons
Neurocomputing
A simple model of spike processing
Neurocomputing
Information theory in neuroscience
Journal of Computational Neuroscience
Channel identification machines
Computational Intelligence and Neuroscience
Functional identification of spike-processing neural circuits
Neural Computation
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The recovery of (weak) stimuli encoded with a population of Hodgkin-Huxley neurons is investigated. In the absence of a stimulus, the Hodgkin-Huxley neurons are assumed to be tonically spiking. The methodology employed calls for 1) finding an input-output (I/O) equivalent description of the Hodgkin-Huxley neuron and 2) devising a recovery algorithm for stimuli encoded with the I/O equivalent neuron(s). A Hodgkin-Huxley neuron with multiplicative coupling is I/O equivalent with an Integrate-and-Fire neuron with a variable threshold sequence. For bandlimited stimuli a perfect recovery of the stimulus can be achieved provided that a Nyquist-type rate condition is satisfied. A Hodgkin-Huxley neuron with additive coupling and deterministic conductances is first-order I/O equivalent with a Project-Integrate-and-Fire neuron that integrates a projection of the stimulus on the phase response curve. The stimulus recovery is formulated as a spline interpolation problem in the space of finite length bounded energy signals. A Hodgkin-Huxley neuron with additive coupling and stochastic conductances is shown to be first-order I/O equivalent with a Project-Integrate-and-Fire neuron with random thresholds. For stimuli modeled as elements of Sobolev spaces the reconstruction algorithm minimizes a regularized quadratic optimality criterion. Finally, all previous recovery results of stimuli encoded with Hodgkin-Huxley neurons with multiplicative and additive coupling, and deterministic and stochastic conductances are extended to stimuli encoded with a population of Hodgkin-Huxley neurons.