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.

中文翻译：

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使用霍奇金-赫胥黎神经元进行种群编码

研究了用一群霍奇金-赫胥黎神经元编码的（弱）刺激的恢复。在没有刺激的情况下，霍奇金-赫胥黎神经元被假定为紧张刺激。所采用的方法要求 1) 找到 Hodgkin-Huxley 神经元的输入-输出 (I/O) 等效描述，以及 2) 为用 I/O 等效神经元编码的刺激设计恢复算法。具有乘法耦合的 Hodgkin-Huxley 神经元与具有可变阈值序列的 Integrate-and-Fire 神经元的 I/O 等效。对于带限刺激，只要满足奈奎斯特型速率条件，就可以实现刺激的完美恢复。具有加性耦合和确定性电导的 Hodgkin-Huxley 神经元与 Project-Integrate-and-Fire 神经元的一阶 I/O 等效，后者在相位响应曲线上集成了刺激的投影。刺激恢复被表述为有限长度有界能量信号空间中的样条插值问题。具有加性耦合和随机电导的 Hodgkin-Huxley 神经元与具有随机阈值的 Project-Integrate-and-Fire 神经元的一阶 I/O 等效。对于建模为 Sobolev 空间元素的刺激，重建算法最小化正则化二次最优性标准。最后，用具有乘法和加法耦合的霍奇金-赫胥黎神经元编码的刺激的所有先前恢复结果，