Publication
A. A. Lazar
Population Encoding with Hodgkin-Huxley Neurons
IEEE Transactions on Information Theory , Volume 56 , Number 2 , pp. 821-837 , February 2010 , Special Issue on Molecular Biology and Neuroscience
Keywords:- hodgkin–huxley neurons input–output (i/o) equivalence neural encoding population encoding reproducing kernel hilbert spaces splines stimulus reconstruction time encoding time decoding
BibTex DOI PDF
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.
Population Encoding with Hodgkin-Huxley Neurons
IEEE Transactions on Information Theory , Volume 56 , Number 2 , pp. 821-837 , February 2010 , Special Issue on Molecular Biology and Neuroscience
Keywords:- hodgkin–huxley neurons input–output (i/o) equivalence neural encoding population encoding reproducing kernel hilbert spaces splines stimulus reconstruction time encoding time decoding
BibTex DOI PDF
Reference
@article{LAZ10a,
author = "A. A. Lazar",
title = "Population Encoding with Hodgkin-Huxley Neurons",
year = 2010,
journal = "IEEE Transactions on Information Theory",
volume = 56,
number = 2,
pages = "821-837",
month = "Feb",
keywords = "hodgkin–huxley neurons, input–output (i/o) equivalence, neural encoding, population encoding, reproducing kernel hilbert spaces, splines, stimulus reconstruction, time encoding, time decoding"
}