The relation between large-scale brain structure and function is an outstanding open problem in neuroscience. We approach this problem by studying the dynamical regime under which realistic spatio-temporal patterns of brain activity emerge from the empirically derived network of human brain neuroanatomical connections. The results show that critical dynamics unfolding on the structural connectivity of the human brain allow the recovery of many key experimental findings obtained with functional Magnetic Resonance Imaging (fMRI), such as divergence of the correlation length, anomalous scaling of correlation fluctuations, and the emergence of large-scale resting state networks.Understanding the relation between brain architecture and function is a central question in neuroscience. In that direction, important efforts over recent years have been devoted to map the large-scale structure of the human cortex, including attempts to build brain structural connectivity matrices from imaging data. An example is the connectivity matrix of the entire human brain, recently derived from fiber densities measured between a large number (500-4000) of homogeneously distributed brain regions [1]. This and related work encompasses a large collaborative project dubbed the brain "connectome" [3], whose ultimate goal is to understand in detail the architecture of whole-brain connectivity. However, "like genes, structural connections alone are powerless", thus "the connectome must be expressed in dynamic neural activity to be effective in behavior and cognition" [2]. The results presented in this Letter show that very relevant aspects of brain dynamics can be predicted from the structure provided that the underlying dynamics are critical.To guide our comparison with available experimental results, we choose to concentrate on robust findings concerning brain dynamics. Specifically, we ask how spontaneous brain dynamics at the large scale organize into the relatively few spatio-temporal patterns revealed experimentally in recent years [4]. This is important because a wide range of experiments using functional Magnetic Resonance Imaging (fMRI) have emphasized that these spatial clusters of coherent activity, termed Resting State Networks (RSN) [5], are specifically associated with neuronal systems responsible for sensory, cognitive and behavioural functions [6]. Furthermore, the pattern of correlations in these networks has been shown to change with various cognitive and pathophysiological conditions [4]. Of interest here are studies showing that the RSN activity exhibits peculiar scaling properties, resembling dynamics near the critical point of a second order phase transition [7][8][9], consistent with evidence showing that the brain at rest is near a critical point [10]. These empirical findings are in line with computational modeling results [11][12][13].Here we study whether a simple dynamical model running over the empirical structure of neuroanatomical connections [1] suffices to replicate the aforementioned fundamental features of ...

Abstract. We discuss a Bayesian model selection approach to high dimensional data in the deep under sampling regime. The data is based on a representation of the possible discrete states s, as defined by the observer, and it consists of M observations of the state. This approach shows that, for a given sample size M , not all states observed in the sample can be distinguished. Rather, only a partition of the sampled states s can be resolved. Such partition defines an emergent classification q s of the states that becomes finer and finer as the sample size increases, through a process of symmetry breaking between states. This allows us to distinguish between the resolution of a given representation of the observer defined states s, which is given by the entropy of s, and its relevance which is defined by the entropy of the partition q s . Relevance has a non-monotonic dependence on resolution, for a given sample size. In addition, we characterise most relevant samples and we show that they exhibit power law frequency distributions, generally taken as signatures of "criticality". This suggests that "criticality" reflects the relevance of a given representation of the states of a complex system, and does not necessarily require a specific mechanism of self-organisation to a critical point.

Human brain dynamics and functional connectivity fluctuate over a range of temporal scales in coordination with internal states and environmental demands. However, the neurobiological significance and consequences of functional connectivity dynamics during rest have not yet been established. We show that the coarse-grained clustering of whole-brain dynamic connectivity measured with magnetic resonance imaging reveals discrete patterns (dynamic connectivity states) associated with wakefulness and sleep. We validate this using EEG in healthy subjects and patients with narcolepsy and by matching our results with previous findings in a large collaborative database. We also show that drowsiness may account for previous reports of metastable connectivity states associated with different levels of functional integration. This implies that future studies of transient functional connectivity must independently monitor wakefulness. We conclude that a possible neurobiological significance of dynamic connectivity states, computed at a sufficiently coarse temporal scale, is that of fluctuations in wakefulness.