Publication

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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.

Reference

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@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"
}