Representing timing patterns in event space. (a) Schematics of an event for a sample unit () formed by the interevent time of unit 1 and all cross-event intervals that may influence the subsequent event of unit 1. An additional counting index is dropped for simplicity. (b) In the event space for neuron , each event is represented by a point on the manifold defined through ().

Slopes in event space yield excitatory and inhibitory synaptic interactions. (a) Schematics of a local sampling in the event space. Local samplings may be taken from regular spiking patterns or subsets of irregular spike patterns such that events are close by in event space. Taking a reference event (red dot) and linearly approximating all other events (gray dot) through () constrains existence and sign of interactions without knowing a system model. (b) Reconstruction of inhibitory (green), excitatory (orange), and absent (blue) synaptic interactions of a neuron in a random network of LIF neurons having synapses with excitatory and inhibitory neurons and a connection probability . See [] for further parameters. The red dashed lines indicate the optimal thresholds (as calculated via Otsu’s method []) to distinguish excitatory and inhibitory from absent interactions.

Revealing synaptic connections from regular to irregular spiking patterns. (a) Schematic representation of spike trains with different degrees of irregularity. To establish test statistics, the spike trains were sampled from random networks of inhibitory LIF neurons interacting via synapses with connection probability . All simulations were performed using identical time intervals of 500 s each (see [] for further settings). (b) AUC scores for two different sampling conditions: random and closest. In the random sampling paradigm, events are randomly drawn from the uniform distribution across the spike trains, while in a closest sampling paradigm, the same number of events closest to a reference event are jointly considered for reconstruction. Reconstruction quality decreases with spiking pattern irregularity for random sampling (dark gray), yet stays consistently high for closest sampling. Gray dashed line indicates random guessing.

Reconstructing large networks is computationally feasible. Reconstruction of random networks of LIF neurons with synapses and . See [] for more details. (a) Connectivity matrix excitatory (red) and inhibitory (blue) synapses. (Inset) A close-up. (b) Distribution of reconstructed excitatory (orange), absent (blue), and inhibitory (green) synapses of a single postsynaptic neuron. (c) Quality of reconstruction for individual neurons for . ESL, CCorr, MI, and STA stand for the approaches introduced here, using cross-correlations, mutual information, and spike-triggered averages, respectively. The gray dashed line stands for random guessing.