It has been said that complexity lies between order and disorder. In the case of brain activity, and physiology in general, complexity issues are being considered with increased emphasis. We sought to identify features of brain organization that are optimal for sensory processing, and that may guide the emergence of cognition and consciousness, by analysing neurophysiological recordings in conscious and unconscious states. We find a surprisingly simple result: normal wakeful states are characterised by the greatest number of possible configurations of interactions between brain networks, representing highest entropy values. Therefore, the information content is larger in the network associated to conscious states, suggesting that consciousness could be the result of an optimization of information processing. These findings encapsulate three main current theories of cognition, as discussed in the text, and more specifically the conceptualization of consciousness in terms of brain complexity. We hope our study represents the preliminary attempt at finding organising principles of brain function that will help to guide in a more formal sense inquiry into how consciousness arises from the organization of matter

Quantification of complexity in neurophysiological signals has been studied using different methods, especially those from information or dynamical system theory. These studies have revealed a dependence on different states of consciousness, and in particular that wakefulness is characterized by a greater complexity of brain signals, perhaps due to the necessity for the brain to handle varied sensorimotor information. Thus, these frameworks are very useful in attempts to quantify cognitive states. We set out to analyze different types of signals obtained from scalp electroencephalography (EEG), intracranial EEG and magnetoencephalography recording in subjects during different states of consciousness: resting wakefulness, different sleep stages and epileptic seizures. The signals were analyzed using a statistical (permutation entropy) and a deterministic (permutation Lempel-Ziv complexity) analytical method. The results are presented in complexity versus entropy graphs, showing that the values of entropy and complexity of the signals tend to be greatest when the subjects are in fully alert states, falling in states with loss of awareness or consciousness. These findings were robust for all three types of recordings. We propose that the investigation of the structure of cognition using the frameworks of complexity will reveal mechanistic aspects of brain dynamics associated not only with altered states of consciousness but also with normal and pathological conditions.

Mounting evidence suggests that during conscious states, the electrodynamics of the cortex are poised near a critical point or phase transition and that this near-critical behavior supports the vast flow of information through cortical networks during conscious states. Here, we empirically identify a mathematically specific critical point near which waking cortical oscillatory dynamics operate, which is known as the edge-of-chaos critical point, or the boundary between stability and chaos. We do so by applying the recently developed modified 0-1 chaos test to electrocorticography (ECoG) and magnetoencephalography (MEG) recordings from the cortices of humans and macaques across normal waking, generalized seizure, anesthesia, and psychedelic states. Our evidence suggests that cortical information processing is disrupted during unconscious states because of a transition of low-frequency cortical electric oscillations away from this critical point; conversely, we show that psychedelics may increase the information richness of cortical activity by tuning low-frequency cortical oscillations closer to this critical point. Finally, we analyze clinical electroencephalography (EEG) recordings from patients with disorders of consciousness (DOC) and show that assessing the proximity of slow cortical oscillatory electrodynamics to the edge-of-chaos critical point may be useful as an index of consciousness in the clinical setting.

We seek general principles of the structure of the cellular collective activity associated with conscious awareness. Can we obtain evidence for features of the optimal brain organization that allows for adequate processing of stimuli and that may guide the emergence of cognition and consciousness? Analysing brain recordings in conscious and unconscious states, we followed initially the classic approach in physics when it comes to understanding collective behaviours of systems composed of a myriad of units: the assessment of the number of possible configurations (microstates) that the system can adopt, for which we use a global entropic measure associated with the number of connected brain regions. Having found maximal entropy in conscious states, we then inspected the microscopic nature of the configurations of connections using an adequate complexity measure, and found higher complexity in states characterised not only by conscious awareness but also by subconscious cognitive processing, such as sleep stages. Our observations indicate that conscious awareness is associated with maximal global (macroscopic) entropy and with the short time scale (microscopic) complexity of the configurations of connected brain networks in pathological unconscious states (seizures and coma), but the microscopic view captures the high complexity in physiological unconscious states (sleep) where there is information processing. As such, our results support the global nature of conscious awareness, as advocated by several theories of cognition. We thus hope that our studies represent preliminary steps to reveal aspects of the structure of cognition that leads to conscious awareness.

Abstract. In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of 'symbols', as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discretestate sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach -of a permutation procedure and a complexity analysis -is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach.

A possible framework to characterize nervous system dynamics and its organization in conscious and unconscious states is introduced, derived from a high level perspective on the coordinated activity of brain cell ensembles. Some questions are best addressable in a global framework and here we build on past observations about the structure of configurations of brain networks in conscious and unconscious states and about neurophysiological results. Aiming to bind some results together into some sort of coherence with a central theme, the scenario that emerges underscores the crucial importance of the creation and dissipation of energy gradients in brain cellular ensembles resulting in maximization of the configurations in the functional connectivity among those networks that favor conscious awareness and healthy conditions. These considerations are then applied to indicate approaches that can be used to improve neuropathological syndromes.

This paper addresses a fundamental question, are eyes closed and eyes open resting states equivalent baseline conditions, or do they have consistently different electrophysiological signatures? We compare the functional connectivity patterns in an eyes closed resting state with an eyes open resting state to investigate the alpha desynchronization hypothesis. The change in functional connectivity from eyes closed to eyes open, is here, for the first time, studied with intracranial recordings. We perform network connectivity analysis in iEEG and we find that phase-based connectivity is sensitive to the transition from eyes closed to eyes open only in interhemispheral and frontal electrodes. Power based connectivity, on the other hand, consistently discriminates between the two conditions in temporal and interhemispheral electrodes. Additionally, we provide a calculation for the wiring cost, defined in terms of the connectivity between electrodes weighted by distance. We find that the wiring cost variation from eyes closed to eyes open is sensitive to the eyes closed and eyes open conditions. We extend the standard network-based approach using the filtration method from algebraic topology which does not rely on the threshold selection problem. Both the wiring cost measure defined here and this novel methodology provide a new avenue for understanding the electrophysiology of resting state.

A possible framework to characterise nervous system dynamics and its organization in conscious and unconscious states is introduced, derived from a high level perspective on the coordinated activity of brain cell ensembles. Some questions are best addressable in a global framework and here we build on past observations about the structure of configurations of brain networks in conscious and unconscious states and about neurophysiological results. Aiming to bind some results together into some sort of coherence with a central theme, the scenario that emerges underscores the crucial importance of the creation and dissipation of energy gradients in brain cellular ensembles resulting in maximisation of the configurations in the functional connectivity among those networks that favour conscious awareness and healthy conditions. These considerations are then applied to indicate approaches that can be used to improve neuropathological syndromes.