Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events

Abstract

Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate.

Mathematical modeling and optimization for real life phenomena

“…For example, the inter-spike interval distribution display temporally heterogeneous patterns, which cannot be simply interpreted as a random or regular process. Numerous studies have addressed temporal correlations between bursty spikes using approaches such as the non-renewal process (Shahi et al, 2016), intensity functions with voltage-dependent terms . /fncom.…”

Burst and Memory-aware Transformer: capturing temporal heterogeneity

“…For example, the inter-spike interval distribution display temporally heterogeneous patterns, which cannot be simply interpreted as a random or regular process. Numerous studies have addressed temporal correlations between bursty spikes using approaches such as the non-renewal process (Shahi et al, 2016 ), intensity functions with voltage-dependent terms (Yamauchi et al, 2011 ), and transitions between burst and non-burst states (Dashevskiy and Cymbalyuk, 2018 ). To quantify temporal heterogeneity, two commonly employed single-value metrics are burstiness and memory coefficient.…”