Harmonic fractal transformation for modeling complex neuronal effects: from bursting and noise shaping to waveform sensitivity and noise-induced subthreshold spiking
This provides a novel approach for modeling neuronal functionality, potentially impacting neuroscience and signal processing, though it appears incremental as it builds on existing transformation concepts.
The authors tackled the problem of modeling complex neuronal effects by proposing the first fractal frequency mapping, which replicates phenomena like bursting, noise shaping, and noise-induced subthreshold spiking, enabling high sensitivity detection and robustness to noise.
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.