Abstract
Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings.
Highlights
Non-stationary time series are very common in physical and biological systems
Approaches to the analysis of time series in dynamic scenarios have been developed in a wide range of areas such as geophysics (e.g. [1,2] and references therein), econometrics [3] or human neurophysiology [4] to name just a few
Trial-totrial variability has been observed in multiple modalities of neural recordings [5,7,13,14,15,16,17] and it has been studied using a variety of techniques ranging from multivariate statistics to informationtheoretic approaches (e.g. [7,18,19,20])
Summary
Non-stationary time series are very common in physical and biological systems. approaches to the analysis of time series in dynamic scenarios have been developed in a wide range of areas such as geophysics (e.g. [1,2] and references therein), econometrics [3] or human neurophysiology [4] to name just a few. Approaches to the analysis of time series in dynamic scenarios have been developed in a wide range of areas such as geophysics Responses of the brain to the same stimulus typically vary across multiple instances of the same experiment (trials) [5,6,7,8,9,10,11,12]. Trial-totrial variability has been observed in multiple modalities of neural recordings [5,7,13,14,15,16,17] and it has been studied using a variety of techniques ranging from multivariate statistics to informationtheoretic approaches Despite the large number of studies over recent decades, the dynamical substrate of such observed variability is largely unknown [5,13]
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