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Neuronal dynamics display a complex spatiotemporal structure involving the precise, context-dependent coordination of activation patterns across a large number of spatially distributed regions. Functional magnetic resonance imaging (fMRI) has played a central role in demonstrating the nontrivial spatial and topological structure of these interactions, but thus far has been limited in its capacity to study their temporal evolution. Here, using highresolution resting-state fMRI data obtained from the Human Connectome Project, we mapped time-resolved functional connectivity across the entire brain at a subsecond resolution with the aim of understanding how nonstationary fluctuations in pairwise interactions between regions relate to large-scale topological properties of the human brain. We report evidence for a consistent set of functional connections that show pronounced fluctuations in their strength over time. The most dynamic connections are intermodular, linking elements from topologically separable subsystems, and localize to known hubs of default mode and frontoparietal systems. We found that spatially distributed regions spontaneously increased, for brief intervals, the efficiency with which they can transfer information, producing temporary, globally efficient network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time, possibly achieving a balance between efficient information-processing and metabolic expenditure.network efficiency | dynamic connectivity | time-dependent network T he coordination of brain activity between disparate neural populations is a dynamic and context-dependent process (1-3). Although dynamic patterns of neural synchronization may be evident in time-dependent measures of functional connectivity (4, 5), the temporal stability of high-level topological properties is unknown. The topology of large-scale cortical activity-such as its efficient network layout (6), community structure (7), network hubs (8), rich-club organization (9, 10), and small worldness (11, 12)-may reflect fundamental aspects of cortical computation. Temporal fluctuations in these graph-theoretic measures may hence speak to adaptive properties of neuronal information processing.With international connectome mapping consortia such as the Human Connectome Project (HCP) (13) and the developing Human Connectome Project in full swing, resting-state functional magnetic resonance imaging (rsfMRI) data of unprecedented temporal resolution are now available to map the time-resolved properties of functional brain networks. Imaging the brain at rest reveals spontaneous low-frequency fluctuations in brain activity that are temporally correlated between functionally related regions (14-17). Interregional correlations are referred to as functional connections, and they collectively form a complex network (18). Functional brain networks are typically mapped in a timeaveraged sense, based on the assumption that functional connections remain relatively static (stationary)...

Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a comprehensive theory of brain activity and cognitive function. Modelling and analysis methods for neuroscience should aim to accommodate multiscale phenomena. Emerging research now suggests that multi-scale processes in the brain arise from so-called critical phenomena that occur very broadly in the natural world. Criticality arises in complex systems perched between order and disorder, and is marked by fluctuations that do not have any privileged spatial or temporal scale. We review the core nature of criticality, the evidence supporting its role in neural systems and its explanatory potential in brain health and disease.Keywords: Bifurcations; metastability; multistability; dynamics; power-law; cognition. Highlights Criticality is a wide-spread phenomenon in natural systems  Criticality provides a unifying framework to model and understand brain activity and cognitive function  Substantial evidence now supports the hypothesis that the brain operates near criticality  We review the role of criticality in healthy and pathological brain dynamics  Caveats and pitfalls regarding the assessment of criticality in the brain are discussed *

Background Schizophrenia is believed to result from abnormal functional integration of neural processes thought to arise from aberrant brain connectivity. However, evidence for anatomical dysconnectivity has been equivocal, and few studies have examined axonal fiber connectivity in schizophrenia at the level of whole-brain networks. Methods Cortico-cortical anatomical connectivity at the scale of axonal fiber bundles was modeled as a network. Eighty-two network nodes demarcated functionally specific cortical regions. Sixty-four direction diffusion tensor-imaging coupled with whole-brain tractography was performed to map the architecture via which network nodes were interconnected in each of 74 patients with schizophrenia and 32 age- and gender-matched control subjects. Testing was performed to identify pairs of nodes between which connectivity was impaired in the patient group. The connectional architecture of patients was tested for changes in five network attributes: nodal degree, small-worldness, efficiency, path length, and clustering. Results Impaired connectivity in the patient group was found to involve a distributed network of nodes comprising medial frontal, parietal/occipital, and the left temporal lobe. Although small-world attributes were conserved in schizophrenia, the cortex was interconnected more sparsely and up to 20% less efficiently in patients. Intellectual performance was found to be associated with brain efficiency in control subjects but not in patients. Conclusions This study presents evidence of widespread dysconnectivity in white-matter connectional architecture in a large sample of patients with schizophrenia. When considered from the perspective of recent evidence for impaired synaptic plasticity, this study points to a multifaceted pathophysiology in schizophrenia encompassing axonal as well as putative synaptic mechanisms.

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The human brain exhibits a relatively stable spatiotemporal organization that supports brain function and can be manipulated via local brain stimulation. Such perturbations to local cortical dynamics are globally integrated by distinct neural systems. However, it remains unclear how and why local changes in neural activity affect large-scale system dynamics. Here, we briefly review empirical and computational studies addressing how localized perturbations affect brain activity. We then systematically analyze a model of large-scale brain dynamics, assessing how localized changes in brain activity at the different sites affect whole-brain dynamics. We find that local stimulation induces changes in brain activity that can be summarized by relatively smooth tuning curves, which relate a region's effectiveness as a stimulation site to its position within the cortical hierarchy. Our results also support the notion that brain hubs, operating in a slower regime, are more resilient to focal perturbations and critically contribute to maintain stability in global brain dynamics. In contrast, perturbations of peripheral regions, characterized by faster activity, have greater impact on functional connectivity. As a parallel with this region-level result, we also find that peripheral systems such as the visual and sensorimotor networks were more affected by local perturbations than high-level systems such as the cingulo-opercular network. Our results highlight the importance of a periphery-tocore hierarchy to determine the effect of local stimulation on the brain network. We also provide novel resources to orient empirical work aiming at manipulating functional connectivity using noninvasive brain stimulation.3