Harmonic fractal transformation for modeling complex neuronal effects: from bursting and noise shaping to waveform sensitivity and noise-induced subthreshold spiking

TL;DR

This paper introduces a novel fractal frequency mapping technique that models complex neuronal effects, enabling sensitive detection, noise robustness, and spike formation through spectral recomposition, offering new insights into neuronal functionality.

Contribution

It presents the first fractal frequency mapping method that replicates neuronal effects by nonlinear spectral recomposition, differing from traditional filtering approaches.

Findings

Enables high sensitivity detection and noise robustness.

Induces noise-induced signal amplification.

Models neuronal functionality as spectrum summation over nonlinear transformations.

Abstract

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.