Reconstruction of Underlying Nonlinear Deterministic Dynamics Embedded in Noisy Spike Trains

Abstract

An experimentally recorded time series formed by the exact times of occurrence of the neuronal spikes (spike train) is likely to be affected by observational noise that provokes events mistakenly confused with neuronal discharges, as well as missed detection of genuine neuronal discharges. The points of the spike train may also suffer a slight jitter in time due to stochastic processes in synaptic transmission and to delays in the detecting devices. This study presents a procedure aimed at filtering the embedded noise (denoising the spike trains) the spike trains based on the hypothesis that recurrent temporal patterns of spikes are likely to represent the robust expression of a dynamic process associated with the information carried by the spike train. The rationale of this approach is tested on simulated spike trains generated by several nonlinear deterministic dynamical systems with embedded observational noise. The application of the pattern grouping algorithm (PGA) to the noisy time series allows us to extract a set of points that form the reconstructed time series. Three new indices are defined for assessment of the performance of the denoising procedure. The results show that this procedure may indeed retrieve the most relevant temporal features of the original dynamics. Moreover, we observe that additional spurious events affect the performance to a larger extent than the missing of original points. Thus, a strict criterion for the detection of spikes under experimental conditions, thus reducing the number of spurious spikes, may raise the possibility to apply PGA to detect endogenous deterministic dynamics in the spike train otherwise masked by the observational noise.

Expressive power of first-order recurrent neural networks determined by their attractor dynamics

“…They have also been observed in neural network simulations at various scales [28,55], in particular as the outcome of evolvable changes in synaptic weights determined by simple learning rules [29]. Furthermoore, the association between attractor dynamics and repeating firing patterns has been demonstrated in nonlinear dynamical systems [3,4] and in simulations of large scale neuronal networks [28,29]. Hence, it is important to consider the spatiotemporal patterns not at all as kind of Morse-code messages, but rather as the witness of an underlying dynamics -the attractor dynamics -which is assumed to be a key feature of neural coding.…”

“…Various experimental studies suggest that specific attractor dynamics [20,21,56] as well as spatiotemporal pattern of discharges, i.e., ordered and precise interspike interval relationships [2,49,51,53,54,57], are likely to be significantly involved in the processing and coding of information in the brain. Moreover, the association between attractor dynamics and spatiotemporal patterns has been demonstrated in nonlinear dynamical systems [3,4] and in simulations of large scale neuronal networks [28,29]. Spatiotemporal patterns are therefore assumed to be the witnesses of an underlying attractor dynamics -which itself would be a key feature of neural coding.…”

Characterization of the causality between spike trains with permutation conditional mutual information

“…The missing and extra spikes arise as spurious points in the spike trains, primarily caused by spikes that are not fired by the recorded neuron but by other external processes involving the discharges of other neurons, errors in the spike sorting procedure, electrical artifacts, etc. [19,63].…”

Complexity in Neurology and Psychiatry

“…Particularly sophisticated methods have been developed by Martínez-Montes et al [5] on the basis of combined EEG and functional magnetic resonance imaging recordings for spatiotemporal characterisation of brain networks. Asai and Villa [6] describe a new method for the detection of recurrent temporal patterns in noisy spike trains as a robust expression of the underlying dynamics. The linear autoregressive models of Olbrich and Achermann [7] are specifically developed for the analysis of the temporal organisation of sleep spindles and slow waves in the EEG.…”