No abstract

Functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites. Analysis of the resulting networks in different tasks shows that (a) the distribution of functional connections, and the probability of finding a link versus distance are both scale-free, (b) the characteristic path length is small and comparable with those of equivalent random networks, and (c) the clustering coefficient is orders of magnitude larger than those of equivalent random networks. All these properties, typical of scale-free small-world networks, reflect important functional information about brain states.

Entropy is a dimensionless quantity that is used for measuring uncertainty about the state of a system but it can also imply physical qualities, where high entropy is synonymous with high disorder. Entropy is applied here in the context of states of consciousness and their associated neurodynamics, with a particular focus on the psychedelic state. The psychedelic state is considered an exemplar of a primitive or primary state of consciousness that preceded the development of modern, adult, human, normal waking consciousness. Based on neuroimaging data with psilocybin, a classic psychedelic drug, it is argued that the defining feature of “primary states” is elevated entropy in certain aspects of brain function, such as the repertoire of functional connectivity motifs that form and fragment across time. Indeed, since there is a greater repertoire of connectivity motifs in the psychedelic state than in normal waking consciousness, this implies that primary states may exhibit “criticality,” i.e., the property of being poised at a “critical” point in a transition zone between order and disorder where certain phenomena such as power-law scaling appear. Moreover, if primary states are critical, then this suggests that entropy is suppressed in normal waking consciousness, meaning that the brain operates just below criticality. It is argued that this entropy suppression furnishes normal waking consciousness with a constrained quality and associated metacognitive functions, including reality-testing and self-awareness. It is also proposed that entry into primary states depends on a collapse of the normally highly organized activity within the default-mode network (DMN) and a decoupling between the DMN and the medial temporal lobes (which are normally significantly coupled). These hypotheses can be tested by examining brain activity and associated cognition in other candidate primary states such as rapid eye movement (REM) sleep and early psychosis and comparing these with non-primary states such as normal waking consciousness and the anaesthetized state.

A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brains hundred billion neurons and hundred trillion synapses manage to produce such a range of cortical configurations in a flexible manner remains a fundamental problem in neuroscience. One plausible solution is the involvement of universal mechanisms of emergent complex phenomena evident in dynamical systems poised near a critical point of a second-order phase transition. We review recent theoretical and empirical results supporting the notion that the brain is naturally poised near criticality, as well as its implications for better understanding of the brain.Understanding the brain is among the most challenging problems to which a physicist can be attracted. As a system with an astronomical number of elements, each one known to have plenty of nonlinearities, the brain exhibits collective dynamics that in many aspects resemble some of the classic problems well studied in statistical physics. The contradiction, and the provoking point in these notes, is that only a minority of the publications in the field today are concerned with the understanding of the brain dynamics as a collective process. To the contrary, the great majority of the work explains the brain through explicit or implicit connectionist paradigms. In our opinion there is a need to reflect and recognize to what degree these collectivist-connectionist views imply more than just a semantic difference, and that its adequate resolution holds the key to resolve some of the more puzzling questions about the brain. We review key results on emergent complex neural dynamics over the past few years. From the outset it should be noted that the intentionally provoking nature of these notes naturally induces a strong bias regarding cited publications; consequently this is neither a fair, nor historically correct, exhaustive or updated review of the relevant literature. Another cautionary note is that being a subject at the fringe of disciplines, physicists and biologists alike, will encounter boring passages on their most familiar topics. Nevertheless, for the sake of clarity, and with the forgiveness of the readers, we will proceed to (even excessively) define each issue at hand. What are the issues?Understanding human behavior and cognition requires the description of the laws of the underlying neural collective phenomena, the patterns of spatio-temporal brain activity. Formal approaches to study collective phenomena are one of the classical topics at the center of statistical physics, with recent novel and successful applications in diverse areas such as genetics, ecology, computer science, social and economic settings [1][2][3][4][5][6][7][8][9][10][11][12][13]. While in all these fields there is a clear transfer of methods and ideas from statistical physics, a similar flow has only recently started to impact neuroscience.The main issue addressed here belongs to the under the rug class of problems in the field,...