Deterministic characteristics of spontaneous activity detected by multi-fractal analysis in a spiking neural network with long-tailed distributions of synaptic weights

Abstract

Cortical neural networks maintain autonomous electrical activity called spontaneous activity that represents the brain's dynamic internal state even in the absence of sensory stimuli. The spatio-temporal complexity of spontaneous activity is strongly related to perceptual, learning, and cognitive brain functions; multi-fractal analysis can be utilized to evaluate the complexity of spontaneous activity. Recent studies have shown that the deterministic dynamic behavior of spontaneous activity especially reflects the topological neural network characteristics and changes of neural network structures. However, it remains unclear whether multi-fractal analysis, recently widely utilized for neural activity, is effective for detecting the complexity of the deterministic dynamic process. To verify this point, we focused on the log-normal distribution of excitatory postsynaptic potentials (EPSPs) to evaluate the multi-fractality of spontaneous activity in a spiking neural network with a log-normal distribution of EPSPs. We found that the spiking activities exhibited multi-fractal characteristics. Moreover, to investigate the presence of a deterministic process in the spiking activity, we conducted a surrogate data analysis against the time-series of spiking activity. The results showed that the spontaneous spiking activity included the deterministic dynamic behavior. Overall, the combination of multi-fractal analysis and surrogate data analysis can detect deterministic complex neural activity. The multi-fractal analysis of neural activity used in this study could be widely utilized for brain modeling and evaluation methods for signals obtained by neuroimaging modalities.

Keywords: Complexity; Fluctuation; Log-normal distribution; Spiking neural network; Spontaneous activity.

Fig. 1

Characteristics of spiking activities in spiking neural networks with log-normal. a Raster plot. b Time series of spiking rate. c Power spectrum of spiking rate

Fig. 2

Multi-fractal analysis for the original time-series of spiking rate $r_E$ Hz and its iterative amplitude-adjusted Fourier-transformed (IAAFT) surrogate time-series in the log-normal and normal distributions for spontaneous. Singularity spectrum D(h) for the time series of spiking rate in the excitatory neural population as a function of the Hölder exponent h (upper parts). The horizontal and vertical error bars indicate standard deviations of h and D(h) from 11 trials, respectively. The 1st and 2nd cumulants of the singularity spectrum ($c_1$ and $c_2$) in 11 trials (lower parts)