Fig. 1: Multifractal analysis of spiking dynamics as a tool to infer functional network topology.

Although it is well established that connectivity patterns (a) shape spiking dynamics of neurons (b) in brain circuits, inferring the connectivity from neuronal activity is fraught with challenges. We ask if specific features of spiking dynamics are diagnostic for the topological features that determine the circuit’s computations and function (c). d–f Multifractal analysis of spiking dynamics. Recurrent networks are characterized by propagation of signals in intricate loops with different lengths, which give rise to spiking dynamics with multiscale temporal characteristics and multifractal properties. We hypothesize that the higher-order statistics of spiking activity of individual neurons carry a signature of the network’s topological features, adequate for identifying key architectural differences across circuits. We show that the generalized Hurst exponents with different orders (q) efficiently capture the diagnostic higher-order spiking statistics. To calculate Hurst exponents for a neuron, we measure its successive interspike intervals (d) and use detrended fluctuation analysis to calculate the multifractal properties not captured by the first-order and second-order moments (e). Interspike intervals of real neurons exhibit nontrivial higher-order statistics over multiple timescales, reflected by a non-linear dependence of the q-order Hurst exponent as a function of the q-th magnification factor (f). This non-linear dependence (blue) is markedly different from the trend expected for a Poisson process. The example for a single neuron in (d–f) is recorded from the macaque motor cortex (adopted from ref. ⁴²).