Multiscale temporal neural dynamics predict performance in a complex sensorimotor task.

Ongoing neuronal oscillations are pivotal in brain functioning and are known to influence subjects' performance. This modulation is usually studied on short time scales whilst multiple time scales are rarely considered. In our study we show that Long-Range Temporal Correlations (LRTCs) estimated from the amplitude of EEG oscillations over a range of time-scales predict performance in a complex sensorimotor task, based on Brain-Computer Interfacing (BCI). Our paradigm involved eighty subjects generating covert motor responses to dynamically changing visual cues and thus controlling a computer program through the modulation of neuronal oscillations. The neuronal dynamics were estimated with multichannel EEG. Our results show that: (a) BCI task accuracy may be predicted on the basis of LRTCs measured during the preceding training session, and (b) this result was not due to signal-to-noise ratio of the ongoing neuronal oscillations. Our results provide direct empirical evidence in addition to previous theoretical work suggesting that scale-free neuronal dynamics are important for optimal brain functioning.

Power-law dynamics in neuronal and behavioral data introduce spurious correlations.

Relating behavioral and neuroimaging measures is essential to understanding human brain function. Often, this is achieved by computing a correlation between behavioral measures, e.g., reaction times, and neurophysiological recordings, e.g., prestimulus EEG alpha-power, on a single-trial-basis. This approach treats individual trials as independent measurements and ignores the fact that data are acquired in a temporal order. It has already been shown that behavioral measures as well as neurophysiological recordings display power-law dynamics, which implies that trials are not in fact independent. Critically, computing the correlation coefficient between two measures exhibiting long-range temporal dependencies may introduce spurious correlations, thus leading to erroneous conclusions about the relationship between brain activity and behavioral measures. Here, we address data-analytic pitfalls which may arise when long-range temporal dependencies in neural as well as behavioral measures are ignored. We quantify the influence of temporal dependencies of neural and behavioral measures on the observed correlations through simulations. Results are further supported in analysis of real EEG data recorded in a simple reaction time task, where the aim is to predict the latency of responses on the basis of prestimulus alpha oscillations. We show that it is possible to "predict" reaction times from one subject on the basis of EEG activity recorded in another subject simply owing to the fact that both measures display power-law dynamics. The same is true when correlating EEG activity obtained from different subjects. A surrogate-data procedure is described which correctly tests for the presence of correlation while controlling for the effect of power-law dynamics.

The effect of linear mixing in the EEG on Hurst exponent estimation.

Although the long-range temporal correlation (LRTC) of the amplitude fluctuations of neuronal EEG/MEG oscillations is widely acknowledged, the majority of studies to date have been performed in sensor space, disregarding the mixing effects implied by volume conduction and confounding noise. While the effect of mixing on the evaluation of evoked responses and connectivity measures has been extensively studied, there are, to date, no studies reporting on the differences in the values of the estimated Hurst exponents when moving between sensor and source space representations of the multivariate data or on the effect of noise. Such differences, if not duly acknowledged, may lead to erroneous data interpretations. We show in simulations and in theory that measuring Hurst exponents in sensor space may lead to an incomplete picture of the LRTC properties of the underlying data and that noise may significantly bias the estimate of the Hurst exponent of the underlying signal. Moreover, these predictions are confirmed in real data, where we analyze the amplitude dynamics of neuronal oscillations in the resting state from EEG data. By moving either to an independent components representation or to a source representation which maximizes the signal to noise ratio in the alpha frequency range, we observe greater variance, skewness and kurtosis over measured Hurst exponents than in sensor space. We confirm the suitability of conventional source separation methodology by introducing a novel algorithm HeMax which obtains a source maximizing the Hurst exponent in the amplitude dynamics of narrow band oscillations. Our findings imply that the long-range correlative properties of the EEG should be studied in source space, in such a way that the SNR is maximized, or at least with spatial decomposition techniques approximating source activities, rather than in sensor space.

Causal Learning via Manifold Regularization.

This paper frames causal structure estimation as a machine learning task. The idea is to treat indicators of causal relationships between variables as 'labels' and to exploit available data on the variables of interest to provide features for the labelling task. Background scientific knowledge or any available interventional data provide labels on some causal relationships and the remainder are treated as unlabelled. To illustrate the key ideas, we develop a distance-based approach (based on bivariate histograms) within a manifold regularization framework. We present empirical results on three different biological data sets (including examples where causal effects can be verified by experimental intervention), that together demonstrate the efficacy and general nature of the approach as well as its simplicity from a user's point of view.

Long-range temporal correlations in neural narrowband time-series arise due to critical dynamics.

We show theoretically that the hypothesis of criticality as a theory of long-range fluctuation in the human brain may be distinguished from the theory of passive filtering on the basis of macroscopic neuronal signals such as the electroencephalogram, using novel theory of narrowband amplitude time-series at criticality. Our theory predicts the division of critical activity into meta-universality classes. As a consequence our analysis shows that experimental electroencephalography data favours the hypothesis of criticality in the human brain.

Prediction and Quantification of Individual Athletic Performance of Runners.

We present a novel, quantitative view on the human athletic performance of individual runners. We obtain a predictor for running performance, a parsimonious model and a training state summary consisting of three numbers by application of modern validation techniques and recent advances in machine learning to the thepowerof10 database of British runners' performances (164,746 individuals, 1,417,432 performances). Our predictor achieves an average prediction error (out-of-sample) of e.g. 3.6 min on elite Marathon performances and 0.3 seconds on 100 metres performances, and a lower error than the state-of-the-art in performance prediction (30% improvement, RMSE) over a range of distances. We are also the first to report on a systematic comparison of predictors for running performance. Our model has three parameters per runner, and three components which are the same for all runners. The first component of the model corresponds to a power law with exponent dependent on the runner which achieves a better goodness-of-fit than known power laws in the study of running. Many documented phenomena in quantitative sports science, such as the form of scoring tables, the success of existing prediction methods including Riegel's formula, the Purdy points scheme, the power law for world records performances and the broken power law for world record speeds may be explained on the basis of our findings in a unified way. We provide strong evidence that the three parameters per runner are related to physiological and behavioural parameters, such as training state, event specialization and age, which allows us to derive novel physiological hypotheses relating to athletic performance. We conjecture on this basis that our findings will be vital in exercise physiology, race planning, the study of aging and training regime design.

Robust Statistical Detection of Power-Law Cross-Correlation.

We show that widely used approaches in statistical physics incorrectly indicate the existence of power-law cross-correlations between financial stock market fluctuations measured over several years and the neuronal activity of the human brain lasting for only a few minutes. While such cross-correlations are nonsensical, no current methodology allows them to be reliably discarded, leaving researchers at greater risk when the spurious nature of cross-correlations is not clear from the unrelated origin of the time series and rather requires careful statistical estimation. Here we propose a theory and method (PLCC-test) which allows us to rigorously and robustly test for power-law cross-correlations, correctly detecting genuine and discarding spurious cross-correlations, thus establishing meaningful relationships between processes in complex physical systems. Our method reveals for the first time the presence of power-law cross-correlations between amplitudes of the alpha and beta frequency ranges of the human electroencephalogram.

Explorative data analysis for changes in neural activity.

Neural recordings are non-stationary time series, i.e. their properties typically change over time. Identifying specific changes, e.g., those induced by a learning task, can shed light on the underlying neural processes. However, such changes of interest are often masked by strong unrelated changes, which can be of physiological origin or due to measurement artifacts. We propose a novel algorithm for disentangling such different causes of non-stationarity and in this manner enable better neurophysiological interpretation for a wider set of experimental paradigms. A key ingredient is the repeated application of Stationary Subspace Analysis (SSA) using different temporal scales. The usefulness of our explorative approach is demonstrated in simulations, theory and EEG experiments with 80 brain-computer interfacing subjects.

Feature extraction for change-point detection using stationary subspace analysis.

Detecting changes in high-dimensional time series is difficult because it involves the comparison of probability densities that need to be estimated from finite samples. In this paper, we present the first feature extraction method tailored to change-point detection, which is based on an extended version of stationary subspace analysis. We reduce the dimensionality of the data to the most nonstationary directions, which are most informative for detecting state changes in the time series. In extensive simulations on synthetic data, we show that the accuracy of three change-point detection algorithms is significantly increased by a prior feature extraction step. These findings are confirmed in an application to industrial fault monitoring.