Mutual information (MI) is a useful information-theoretic measure to quantify the statistical dependence between two random variables: X and Y. Often, we are interested in understanding how the dependence between X and Y in one set of samples compares to another. Although the dependence between X and Y in each set of samples can be measured separately using MI, these estimates cannot be compared directly if they are based on samples from a non-stationary distribution. Here, we propose an alternative measure for characterising how the dependence between X and Y as defined by one set of samples is expressed in another, cross MI. We present a comprehensive set of simulation studies sampling data with X-Y dependencies to explore this measure. Finally, we discuss how this relates to measures of model fit in linear regression, and some future applications in neuroimaging data analysis.

Neuronal activity is organized in collective patterns that are critical for information coding, generation, and communication between neural populations. These patterns are often described in terms of synchrony, oscillations, and phase relationships. Many methods have been proposed for the quantification of these collective states of dynamic neuronal organization. However, it is difficult to determine which method is best suited for which experimental setting and research question. This choice is further complicated by the fact that most methods are sensitive to a combination of synchrony, oscillations, and other factors; in addition, some of them display systematic biases that can complicate their interpretation. To address these challenges, we adopt a highly comparative approach, whereby spike trains are represented by a diverse library of measures. This enables unsupervised or supervised analysis in the space of measures, or in that of spike trains. We compile a battery of 122 measures of synchrony, oscillations, and phase relationships, complemented with 9 measures of spiking intensity and variability. We first apply them to sets of synthetic spike trains with known statistical properties, and show that all measures are confounded by extraneous factors such as firing rate or population frequency, but to different extents. Then, we analyze spike trains recorded in different species-rat, mouse, and monkey-and brain areas-primary sensory cortices and hippocampus-and show that our highly comparative approach provides a high-dimensional quantification of collective network activity that can be leveraged for both unsupervised and supervised characterization of firing patterns. Overall, the highly comparative approach provides a detailed description of the empirical properties of multineuron spike train analysis methods, including practical guidelines for their use in experimental settings, and advances our understanding of neuronal coordination and coding.

Previous research has examined resting electroencephalographic (EEG) data to explore brain activity related to meditation. However, previous research has mostly examined power in different frequency bands. The practical objective of this study was to comprehensively test whether other types of time-series analysis methods are better suited to characterize brain activity related to meditation. To achieve this, we compared >7000 time-series features of the EEG signal to comprehensively characterize brain activity differences in meditators, using many measures that are novel in meditation research. Eyes-closed resting-state EEG data from 49 meditators and 46 non-meditators was decomposed into the top eight principal components (PCs). We extracted 7381 time-series features from each PC and each participant and used them to train classification algorithms to identify meditators. Highly differentiating individual features from successful classifiers were analysed in detail. Only the third PC (which had a central-parietal maximum) showed above-chance classification accuracy (67%, pFDR = 0.007), for which 405 features significantly distinguished meditators (all pFDR < 0.05). Top-performing features indicated that meditators exhibited more consistent statistical properties across shorter subsegments of their EEG time-series (higher stationarity) and displayed an altered distributional shape of values about the mean. By contrast, classifiers trained with traditional band-power measures did not distinguish the groups (pFDR > 0.05). Our novel analysis approach suggests the key signatures of meditators’ brain activity are higher temporal stability and a distribution of time-series values suggestive of longer, larger, or more frequent non-outlying voltage deviations from the mean within the third PC of their EEG data. The higher temporal stability observed in this EEG component might underpin the higher attentional stability associated with meditation. The novel time-series properties identified here have considerable potential for future exploration in meditation research and the analysis of neural dynamics more broadly.

The brain's complex distributed dynamics are typically quantified using a limited set of manually selected statistical properties, leaving the possibility that alternative dynamical properties may outperform those reported for a given application. Here, we address this limitation by systematically comparing diverse, interpretable features of both intra-regional activity and inter-regional functional coupling from resting-state functional magnetic resonance imaging (rs-fMRI) data, demonstrating our method using case-control comparisons of four neuropsychiatric disorders. Our findings generally support the use of linear time-series analysis techniques for rs-fMRI case-control analyses, while also identifying new ways to quantify informative dynamical fMRI structures. While simple statistical representations of fMRI dynamics performed surprisingly well (e.g., properties within a single brain region), combining intra-regional properties with inter-regional coupling generally improved performance, underscoring the distributed, multifaceted changes to fMRI dynamics in neuropsychiatric disorders. The comprehensive, data-driven method introduced here enables systematic identification and interpretation of quantitative dynamical signatures of multivariate time-series data, with applicability beyond neuroimaging to diverse scientific problems involving complex time-varying systems.

Capturing the dynamical properties of time series concisely as interpretable feature vectors can enable efficient clustering and classification for time-series applications across science and industry. Selecting an appropriate feature-based representation of time series for a given application can be achieved through systematic comparison across a comprehensive time-series feature library, such as those in the hctsa toolbox. However, this approach is computationally expensive and involves evaluating many similar features, limiting the widespread adoption of feature-based representations of time series for real-world applications. In this work, we introduce a method to infer small sets of time-series features that (i) exhibit strong classification performance across a given collection of time-series problems, and (ii) are minimally redundant. Applying our method to a set of 93 time-series classification datasets (containing over 147,000 time series) and using a filtered version of the hctsa feature library (4791 features), we introduce a set of 22 CAnonical Time-series CHaracteristics, catch22 , tailored to the dynamics typically encountered in time-series data-mining tasks. This dimensionality reduction, from 4791 to 22, is associated with an approximately 1000-fold reduction in computation time and near linear scaling with time-series length, despite an average reduction in classification accuracy of just 7%. catch22 captures a diverse and interpretable signature of time series in terms of their properties, including linear and non-linear autocorrelation, successive differences, value distributions and outliers, and fluctuation scaling properties. We provide an efficient implementation of catch22 , accessible from many programming environments, that facilitates feature-based time-series analysis for scientific, industrial, financial and medical applications using a common language of interpretable time-series properties.

Studies of nervous system connectivity, in a wide variety of species and at different scales of resolution, have identified several highly conserved motifs of network organization. One such motif is a heterogeneous distribution of connectivity across neural elements, such that some elements act as highly connected and functionally important network hubs. These brain network hubs are also densely interconnected, forming a so-called rich club. Recent work in mouse has identified a distinctive transcriptional signature of neural hubs, characterized by tightly coupled expression of oxidative metabolism genes, with similar genes characterizing macroscale inter-modular hub regions of the human cortex. Here, we sought to determine whether hubs of the neuronal C. elegans connectome also show tightly coupled gene expression. Using open data on the chemical and electrical connectivity of 279 C. elegans neurons, and binary gene expression data for each neuron across 948 genes, we computed a correlated gene expression score for each pair of neurons, providing a measure of their gene expression similarity. We demonstrate that connections between hub neurons are the most similar in their gene expression while connections between nonhubs are the least similar. Genes with the greatest contribution to this effect are involved in glutamatergic and cholinergic signaling, and other communication processes. We further show that coupled expression between hub neurons cannot be explained by their neuronal subtype (i.e., sensory, motor, or interneuron), separation distance, chemically secreted neurotransmitter, birth time, pairwise lineage distance, or their topological module affiliation. Instead, this coupling is intrinsically linked to the identity of most hubs as command interneurons, a specific class of interneurons that regulates locomotion. Our results suggest that neural hubs may possess a distinctive transcriptional signature, preserved across scales and species, that is related to the involvement of hubs in regulating the higher-order behaviors of a given organism.

A highly comparative, feature-based approach to time series classification is introduced that uses an extensive database of algorithms to extract thousands of interpretable features from time series. These features are derived from across the scientific time-series analysis literature, and include summaries of time series in terms of their correlation structure, distribution, entropy, stationarity, scaling properties, and fits to a range of time-series models. After computing thousands of features for each time series in a training set, those that are most informative of the class structure are selected using greedy forward feature selection with a linear classifier. The resulting feature-based classifiers automatically learn the differences between classes using a reduced number of time-series properties, and circumvent the need to calculate distances between time series. Representing time series in this way results in orders of magnitude of dimensionality reduction, allowing the method to perform well on very large data sets containing long time series or time series of different lengths. For many of the data sets studied, classification performance exceeded that of conventional instance-based classifiers, including one nearest neighbor classifiers using euclidean distances and dynamic time warping and, most importantly, the features selected provide an understanding of the properties of the data set, insight that can guide further scientific investigation.

Circadian rhythms are fundamental to life. In mammals, these rhythms are generated by pacemaker neurons in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN is remarkably consistent in structure and function between species, yet mammalian rest/activity patterns are extremely diverse, including diurnal, nocturnal, and crepuscular behaviors. Two mechanisms have been proposed to account for this diversity: (i) modulation of SCN output by downstream nuclei, and (ii) direct effects of light on activity. These two mechanisms are difficult to disentangle experimentally and their respective roles remain unknown. To address this, we developed a computational model to simulate the two mechanisms and their influence on temporal niche. In our model, SCN output is relayed via the subparaventricular zone (SPZ) to the dorsomedial hypothalamus (DMH), and thence to ventrolateral preoptic nuclei (VLPO) and lateral hypothalamus (LHA). Using this model, we generated rich phenotypes that closely resemble experimental data. Modulation of SCN output at the SPZ was found to generate a full spectrum of diurnal-to-nocturnal phenotypes. Intriguingly, we also uncovered a novel mechanism for crepuscular behavior: if DMH/VLPO and DMH/LHA projections act cooperatively, daily activity is unimodal, but if they act competitively, activity can become bimodal. In addition, we successfully reproduced diurnal/nocturnal switching in the rodent Octodon degu using coordinated inversions in both masking and circadian modulation. Finally, the model correctly predicted the SCN lesion phenotype in squirrel monkeys: loss of circadian rhythmicity and emergence of ∼4-h sleep/wake cycles. In capturing these diverse phenotypes, the model provides a powerful new framework for understanding rest/activity patterns and relating them to underlying physiology. Given the ubiquitous effects of temporal organization on all aspects of animal behavior and physiology, this study sheds light on the physiological changes required to orchestrate adaptation to various temporal niches.