Quantifying the Predictability of Visual Scanpaths Using Active Information Storage

On the potential of transfer entropy in turbulent dynamical systems

Information theory (IT) provides tools to estimate causality between events, in various scientific domains. Here, we explore the potential of IT-based causality estimation in turbulent (i.e. chaotic) dynamical systems and investigate the impact of various hyperparameters on the outcomes. The influence of Markovian orders, i.e. the time lags, on the computation of the transfer entropy (TE) has been mostly overlooked in the literature. We show that the history effect remarkably affects the TE estimation, especially for turbulent signals. In a turbulent channel flow, we compare the TE with standard measures such as auto- and cross-correlation, showing that the TE has a dominant direction, i.e. from the walls towards the core of the flow. In addition, we found that, in generic low-order vector auto-regressive models (VAR), the causality time scale is determined from the order of the VAR, rather than the integral time scale. Eventually, we propose a novel application of TE as a sensitivity measure for controlling computational errors in numerical simulations with adaptive mesh refinement. The introduced indicator is fully data-driven, no solution of adjoint equations is required, with an improved convergence to the accurate function of interest. In summary, we demonstrate the potential of TE for turbulence, where other measures may only provide partial information.

Information theoretic evidence for layer- and frequency-specific changes in cortical information processing under anesthesia

Nature relies on highly distributed computation for the processing of information in nervous systems across the entire animal kingdom. Such distributed computation can be more easily understood if decomposed into the three elementary components of information processing, i.e. storage, transfer and modification, and rigorous information theoretic measures for these components exist. However, the distributed computation is often also linked to neural dynamics exhibiting distinct rhythms. Thus, it would be beneficial to associate the above components of information processing with distinct rhythmic processes where possible. Here we focus on the storage of information in neural dynamics and introduce a novel spectrally-resolved measure of active information storage (AIS). Drawing on intracortical recordings of neural activity in ferrets under anesthesia before and after loss of consciousness (LOC) we show that anesthesia- related modulation of AIS is highly specific to different frequency bands and that these frequency-specific effects differ across cortical layers and brain regions. We found that in the high/low gamma band the effects of anesthesia result in AIS modulation only in the supergranular layers, while in the alpha/beta band the strongest decrease in AIS can be seen at infragranular layers. Finally, we show that the increase of spectral power at multiple frequencies, in particular at alpha and delta bands in frontal areas, that is often observed during LOC ('anteriorization') also impacts local information processing-but in a frequency specific way: Increases in isoflurane concentration induced a decrease in AIS in the alpha frequencies, while they increased AIS in the delta frequency range < 2Hz. Thus, the analysis of spectrally-resolved AIS provides valuable additional insights into changes in cortical information processing under anaesthesia.

Measuring inter- and intra-individual differences in visual scan patterns in a driving simulator experiment using active information storage

Scan pattern analysis has been discussed as a promising tool in the context of real-time gaze-based applications. In particular, information-theoretic measures of scan path predictability, such as the gaze transition entropy (GTE), have been proposed for detecting relevant changes in user state or task demand. These measures model scan patterns as first-order Markov chains, assuming that only the location of the previous fixation is predictive of the next fixation in time. However, this assumption may not be sufficient in general, as recent research has shown that scan patterns may also exhibit more long-range temporal correlations. Thus, we here evaluate the active information storage (AIS) as a novel information-theoretic approach to quantifying scan path predictability in a dynamic task. In contrast to the GTE, the AIS provides means to statistically test and account for temporal correlations in scan path data beyond the previous last fixation. We compare AIS to GTE in a driving simulator experiment, in which participants drove in a highway scenario, where trials were defined based on an experimental manipulation that encouraged the driver to start an overtaking maneuver. Two levels of difficulty were realized by varying the time left to complete the task. We found that individual observers indeed showed temporal correlations beyond a single past fixation and that the length of the correlation varied between observers. No effect of task difficulty was observed on scan path predictability for either AIS or GTE, but we found a significant increase in predictability during overtaking. Importantly, for participants for which the first-order Markov chain assumption did not hold, this was only shown using AIS but not GTE. We conclude that accounting for longer time horizons in scan paths in a personalized fashion is beneficial for interpreting gaze pattern in dynamic tasks.