用分形频域变换模拟神经元复杂行为，实现噪声增强与敏感检测。
Harmonic fractal transformation for modeling complex neuronal effects: from bursting and noise shaping to waveform sensitivity and noise-induced subthreshold spiking
- 提出分形频谱重组方法，非线性变换频率域生成新谐波分量
- 在共振频率处激发尖峰，实现对微弱信号的高灵敏度检测
- 适用于需要噪声增强的神经计算场景，如生物神经建模
我们提出了首个分形频率映射方法，以简洁形式即可复现复杂的神经元效应。与传统滤波器按权重抑制或放大输入频谱成分不同，该变换通过分形重组输入频谱，激发新的谐波成分，在最优采样共振频率处形成尖峰。这使得系统具备高灵敏度检测能力、抗噪鲁棒性及噪声诱导的信号放大特性。所提出的模型表明，神经功能可被视作频谱在非线性变换频率域上的线性叠加。
原文摘要 · Abstract (English)
We propose the first fractal frequency mapping, which in a simple form enables to replicate complex neuronal effects. Unlike the conventional filters, which suppress or amplify the input spectral components according to the filter weights, the transformation excites novel components by a fractal recomposition of the input spectra resulting in a formation of spikes at resonant frequencies that are optimal for sampling. This enables high sensitivity detection, robustness to noise and noise-induced signal amplification. The proposed model illustrates that a neuronal functionality can be viewed as a linear summation of spectrum over nonlinearly transformed frequency domain.
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