Since the discovery of electrical activity of the brain, electroencephalographic (EEG) recordings constitute one of the most popular techniques of brain research. However, EEG signals are highly nonstationary and one should expect that averages of the cross-correlation coefficient, which may take positive and negative values with equal probability, (almost) vanish when estimated over long data segments. Instead, we found that the average zero-lag cross-correlation matrix estimated with a running window over the whole night of sleep EEGs, or of resting state during eyes-open and eyes-closed conditions of healthy subjects shows a characteristic correlation pattern containing pronounced nonzero values. A similar correlation structure has already been encountered in scalp EEG signals containing focal onset seizures. Therefore, we conclude that this structure is independent of the physiological state. Because of its pronounced similarity across subjects, we believe that it depicts a generic feature of the brain dynamics. Namely, we interpret this pattern as a manifestation of a dynamical ground state of the brain activity, necessary to preserve an efficient operational mode, or, expressed in terms of dynamical system theory, we interpret it as a "shadow" of the evolution on (or close to) an attractor in phase space. Nonstationary dynamical aspects of higher cerebral processes should manifest in deviations from this stable pattern. We confirm this hypothesis through a correlation analysis of EEG recordings of 10 healthy subjects during night sleep, 20 recordings of 9 epilepsy patients, and 42 recordings of 21 healthy subjects in resting state during eyes-open and eyes-closed conditions. In particular, we show that the estimation of deviations from the stationary correlation structures provides a more significant differentiation of physiological states and more homogeneous results across subjects.

Currently, research in physiology focuses on molecular mechanisms underlying the functioning of living organisms. Reductionist strategies are used to decompose systems into their components and to measure changes of physiological variables between experimental conditions. However, how these isolated physiological variables translate into the emergence -and collapse- of biological functions of the organism as a whole is often a less tractable question. To generate a useful representation of physiology as a system, known and unknown interactions between heterogeneous physiological components must be taken into account. In this work we use a Complex Inference Networks approach to build physiological networks from biomarkers. We employ two unrelated databases to generate Spearman correlation matrices of 81 and 54 physiological variables, respectively, including endocrine, mechanic, biochemical, anthropometric, physiological, and cellular variables. From these correlation matrices we generated physiological networks by selecting a p-value threshold indicating statistically significant links. We compared the networks from both samples to show which features are robust and representative for physiology in health. We found that although network topology is sensitive to the p-value threshold, an optimal value may be defined by combining criteria of stability of topological features and network connectedness. Unsupervised community detection algorithms allowed to obtain functional clusters that correlate well with current medical knowledge. Finally, we describe the topology of the physiological networks, which lie between random and ordered structural features, and may reflect system robustness and adaptability. Modularity of physiological networks allows to explore functional clusters that are consistent even when considering different physiological variables. Altogether Complex Inference Networks from biomarkers provide an efficient implementation of a systems biology approach that is visually understandable and robust. We hypothesize that physiological networks allow to translate concepts such as homeostasis into quantifiable properties of biological systems useful for determination and quantification of health and disease.

The characterization of the functional network of the brain dynamics has become a prominent tool to illuminate novel aspects of brain functioning. Due to its excellent time resolution, such research is oftentimes based on electroencephalographic recordings (EEG). However, a particular EEG-reference might cause crucial distortions of the spatiotemporal interrelation pattern and may induce spurious correlations as well as diminish genuine interrelations originally present in the dataset. Here we investigate in which manner correlation patterns are affected by a chosen EEG reference. To this end we evaluate the influence of 7 popular reference schemes on artificial recordings derived from well controlled numerical test frameworks. In this respect we are not only interested in the deformation of spatial interrelations, but we test additionally in which way the time evolution of the functional network, estimated via some bi-variate interrelation measures, gets distorted. It turns out that the median reference as well as the global average show the best performance in most situations considered in the present study. However, if a collective brain dynamics is present, where most of the signals get correlated, these schemes may also cause crucial deformations of the functional network, such that the parallel use of different reference schemes seems advisable.

Both parametric and non-parametric approaches to time-series analysis have advantages and drawbacks. Parametric methods, although powerful and widely used, can yield inconsistent results due to the oversimplification of the observed phenomena. They require the setting of arbitrary constants for their creation and refinement, and, although these constants relate to assumptions about the observed systems, it can lead to erroneous results when treating a very complex problem with a sizable list of unknowns. Their non-parametric counterparts, instead, are more widely applicable but present a higher detrimental sensitivity to noise and low density in the data. For the case of approximately periodic phenomena, such as human actigraphic time series, parametric methods are widely used and concepts such as acrophase are key in chronobiology, especially when studying healthy and diseased human populations. In this work, we present a non-parametric method of analysis of actigraphic time series from insomniac patients and healthy age-matched controls. The method is fully data-driven, reproduces previous results in the context of activity offset delay and, crucially, extends the concept of acrophase not only to circadian but also for ultradian spectral components.