Exploring brain function from anatomical connectivity

Identifying individual's distractor suppression using functional connectivity between anatomical large-scale brain regions

Distractor suppression (DS) is crucial in goal-oriented behaviors, referring to the ability to suppress irrelevant information. Current evidence points to the prefrontal cortex as an origin region of DS, while subcortical, occipital, and temporal regions are also implicated. The present study aimed to examine the contribution of communications between these brain regions to visual DS. To do it, we recruited two independent cohorts of participants for the study. One cohort participated in a visual search experiment where a salient distractor triggering distractor suppression to measure their DS and the other cohort filled out a Cognitive Failure Questionnaire to assess distractibility in daily life. Both cohorts collected resting-state functional magnetic resonance imaging (rs-fMRI) data to investigate function connectivity (FC) underlying DS. First, we generated predictive models of the DS measured in visual search task using resting-state functional connectivity between large anatomical regions. It turned out that the models could successfully predict individual's DS, indicated by a significant correlation between the actual and predicted DS (r = 0.32, p < 0.01). Importantly, Prefrontal-Temporal, Insula-Limbic and Parietal-Occipital connections contributed to the prediction model. Furthermore, the model could also predict individual's daily distractibility in the other independent cohort (r = -0.34, p < 0.05). Our findings showed the efficiency of the predictive models of distractor suppression encompassing connections between large anatomical regions and highlighted the importance of the communications between attention-related and visual information processing regions in distractor suppression. Current findings may potentially provide neurobiological markers of visual distractor suppression.

An integrative dynamical perspective for graph theory and the analysis of complex networks

Built upon the shoulders of graph theory, the field of complex networks has become a central tool for studying real systems across various fields of research. Represented as graphs, different systems can be studied using the same analysis methods, which allows for their comparison. Here, we challenge the widespread idea that graph theory is a universal analysis tool, uniformly applicable to any kind of network data. Instead, we show that many classical graph metrics-including degree, clustering coefficient, and geodesic distance-arise from a common hidden propagation model: the discrete cascade. From this perspective, graph metrics are no longer regarded as combinatorial measures of the graph but as spatiotemporal properties of the network dynamics unfolded at different temporal scales. Once graph theory is seen as a model-based (and not a purely data-driven) analysis tool, we can freely or intentionally replace the discrete cascade by other canonical propagation models and define new network metrics. This opens the opportunity to design-explicitly and transparently-dedicated analyses for different types of real networks by choosing a propagation model that matches their individual constraints. In this way, we take stand that network topology cannot always be abstracted independently from network dynamics but shall be jointly studied, which is key for the interpretability of the analyses. The model-based perspective here proposed serves to integrate into a common context both the classical graph analysis and the more recent network metrics defined in the literature which were, directly or indirectly, inspired by propagation phenomena on networks.

Integration and segregation manifolds in the brain ensure cognitive flexibility during tasks and rest

Adapting to a constantly changing environment requires the human brain to flexibly switch among many demanding cognitive tasks, processing both specialized and integrated information associated with the activity in functional networks over time. In this study, we investigated the nature of the temporal alternation between segregated and integrated states in the brain during rest and six cognitive tasks using functional MRI. We employed a deep autoencoder to explore the 2D latent space associated with the segregated and integrated states. Our results show that the integrated state occupies less space in the latent space manifold compared to the segregated states. Moreover, the integrated state is characterized by lower entropy of occupancy than the segregated state, suggesting that integration plays a consolidating role, while segregation may serve as cognitive expertness. Comparing rest and the tasks, we found that rest exhibits higher entropy of occupancy, indicating a more random wandering of the mind compared to the expected focus during task performance. Our study demonstrates that both transient, short-lived integrated and segregated states are present during rest and task performance, flexibly switching between them, with integration serving as information compression and segregation related to information specialization.

Inhibitory neurons control the consolidation of neural assemblies via adaptation to selective stimuli

Brain circuits display modular architecture at different scales of organization. Such neural assemblies are typically associated to functional specialization but the mechanisms leading to their emergence and consolidation still remain elusive. In this paper we investigate the role of inhibition in structuring new neural assemblies driven by the entrainment to various inputs. In particular, we focus on the role of partially synchronized dynamics for the creation and maintenance of structural modules in neural circuits by considering a network of excitatory and inhibitory [Formula: see text]-neurons with plastic Hebbian synapses. The learning process consists of an entrainment to temporally alternating stimuli that are applied to separate regions of the network. This entrainment leads to the emergence of modular structures. Contrary to common practice in artificial neural networks-where the acquired weights are typically frozen after the learning session-we allow for synaptic adaptation even after the learning phase. We find that the presence of inhibitory neurons in the network is crucial for the emergence and the post-learning consolidation of the modular structures. Indeed networks made of purely excitatory neurons or of neurons not respecting Dale's principle are unable to form or to maintain the modular architecture induced by the stimuli. We also demonstrate that the number of inhibitory neurons in the network is directly related to the maximal number of neural assemblies that can be consolidated, supporting the idea that inhibition has a direct impact on the memory capacity of the neural network.

The association between genetic variations and morphology-based brain networks changes in Alzheimer's disease

Alzheimer's disease (AD) is a highly heritable disease. The morphological changes of cortical cortex (such as, cortical thickness and surface area) in AD always accompany by the change of the functional connectivity to other brain regions and influence the short- and long-range brain network connections, causing functional deficits of AD. In this study, the first hypothesis is that genetic variations might affect morphology-based brain networks, leading to functional deficits; the second hypothesis is that protein-protein interaction (PPI) between the candidate proteins and known interacting proteins to AD might exist and influence AD. 600 470 variants and structural magnetic resonance imaging scans from 175 AD patients and 214 healthy controls were obtained from the Alzheimer's Disease Neuroimaging Initiative-1 database. A co-sparse reduced-rank regression model was fit to study the relationship between non-synonymous mutations and morphology-based brain networks. After that, PPIs between selected genes and BACE1, an enzyme that was known to be related to AD, are explored by using molecular dynamics (MD) simulation and co-immunoprecipitation (Co-IP) experiments. Eight genes affecting morphology-based brain networks were identified. The results of MD simulation showed that the PPI between TGM4 and BACE1 was the strongest among them and its interaction was verified by Co-IP. Hence, gene variations influence morphology-based brain networks in AD, leading to functional deficits. This finding, validated by MD simulation and Co-IP, suggests that the effect is robust.

Neuroscience and Network Dynamics Toward Brain-Inspired Intelligence

This article surveys the interdisciplinary research of neuroscience, network science, and dynamic systems, with emphasis on the emergence of brain-inspired intelligence. To replicate brain intelligence, a practical way is to reconstruct cortical networks with dynamic activities that nourish the brain functions, instead of using only artificial computing networks. The survey provides a complex network and spatiotemporal dynamics (abbr. network dynamics) perspective for understanding the brain and cortical networks and, furthermore, develops integrated approaches of neuroscience and network dynamics toward building brain-inspired intelligence with learning and resilience functions. Presented are fundamental concepts and principles of complex networks, neuroscience, and hybrid dynamic systems, as well as relevant studies about the brain and intelligence. Other promising research directions, such as brain science, data science, quantum information science, and machine behavior are also briefly discussed toward future applications.

Modes of cognition: Evidence from metastable brain dynamics

Managing cognitive load depends on adequate resource allocation by the human brain through the engagement of metastable substates, which are large-scale functional networks that change over time. We employed a novel analysis method, deep autoencoder dynamical analysis (DADA), with 100 healthy adults selected from the Human Connectome Project (HCP) data set in rest and six cognitive tasks. The deep autoencoder of DADA described seven recurrent stochastic metastable substates from the functional connectome of BOLD phase coherence matrices. These substates were significantly differentiated in terms of their probability of appearance, time duration, and spatial attributes. We found that during different cognitive tasks, there was a higher probability of having more connected substates dominated by a high degree of connectivity in the thalamus. In addition, compared with those during tasks, resting brain dynamics have a lower level of predictability, indicating a more uniform distribution of metastability between substates, quantified by higher entropy. These novel findings provide empirical evidence for the philosophically motivated cognitive theory, suggesting on-line and off-line as two fundamentally distinct modes of cognition. On-line cognition refers to task-dependent engagement with the sensory input, while off-line cognition is a slower, environmentally detached mode engaged with decision and planning. Overall, the DADA framework provides a bridge between neuroscience and cognitive theory that can be further explored in the future.

Functional Connectivity of the Brain Across Rodents and Humans

Resting-state functional magnetic resonance imaging (rs-fMRI), which measures the spontaneous fluctuations in the blood oxygen level-dependent (BOLD) signal, is increasingly utilized for the investigation of the brain's physiological and pathological functional activity. Rodents, as a typical animal model in neuroscience, play an important role in the studies that examine the neuronal processes that underpin the spontaneous fluctuations in the BOLD signal and the functional connectivity that results. Translating this knowledge from rodents to humans requires a basic knowledge of the similarities and differences across species in terms of both the BOLD signal fluctuations and the resulting functional connectivity. This review begins by examining similarities and differences in anatomical features, acquisition parameters, and preprocessing techniques, as factors that contribute to functional connectivity. Homologous functional networks are compared across species, and aspects of the BOLD fluctuations such as the topography of the global signal and the relationship between structural and functional connectivity are examined. Time-varying features of functional connectivity, obtained by sliding windowed approaches, quasi-periodic patterns, and coactivation patterns, are compared across species. Applications demonstrating the use of rs-fMRI as a translational tool for cross-species analysis are discussed, with an emphasis on neurological and psychiatric disorders. Finally, open questions are presented to encapsulate the future direction of the field.

Reorganization of rich clubs in functional brain networks of dementia with Lewy bodies and Alzheimer's disease

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DLB and AD had the different functional reorganization patterns.

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Rich club nodes increased in frontal-parietal network in patients with DLB.

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The rich club nodes in temporal lobe decreased and those in cerebellum increased for AD.

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Compared with HC, rich club connectivity was enhanced in the DLB and AD groups.

The purpose of this study was to reveal the patterns of reorganization of rich club organization in brain functional networks in dementia with Lewy bodies (DLB) and Alzheimer’s disease (AD). The study found that the rich club node shifts from sensory/somatomotor network to fronto-parietal network in DLB. For AD, the rich club nodes switch between the temporal lobe with obvious structural atrophy and the frontal lobe, parietal lobe and cerebellum with relatively preserved structure and function. In addition, compared with healthy controls, rich club connectivity was enhanced in the DLB and AD groups. The connection strength of DLB patients was related to cognitive assessment. In conclusion, we revealed the different functional reorganization patterns of DLB and AD. The conversion and redistribution of rich club members may play a causal role in disease-specific outcomes. It may be used as a potential biomarker to provide more accurate prevention and treatment strategies.

Gyral Hinges Account for the Highest Cost and the Highest Communication Capacity in a Corticocortical Network

Prior studies reported the global structure of brain networks exhibits the "small-world" and "rich-world" attributes. However, the underlying structural and functional architecture highlighted by these graph theory findings hasn't been explicitly related to the morphology of the cortex. This could be attributed to the lower resolution of used folding patterns, such as gyro-sulcal patterns. By defining a novel gyral folding pattern, termed gyral hinge (GH), which is the conjunction of ordinary gyri from multiple directions, we found GHs possess the highest length and cost in the white matter fiber connective network, and the shortest paths in the network tend to travel through GHs in their middle part. Based on these findings, we would hypothesize GHs could reside in the centers of a network core, thereby accounting for the highest cost and the highest communication capacity in a corticocortical network. The following results further support our hypothesis: 1) GHs possess stronger functional network integration capacity. 2) Higher cost is found on the connection with GHs to hinges and GHs to GHs. 3) Moving GHs introduces higher extra network cost. Our findings and hypotheses could reveal a profound relationship among the cortical folding patterns, axonal wiring architectures, and brain functions.

Loss of consciousness reduces the stability of brain hubs and the heterogeneity of brain dynamics

Low-level states of consciousness are characterized by disruptions of brain activity that sustain arousal and awareness. Yet, how structural, dynamical, local and network brain properties interplay in the different levels of consciousness is unknown. Here, we study fMRI brain dynamics from patients that suffered brain injuries leading to a disorder of consciousness and from healthy subjects undergoing propofol-induced sedation. We show that pathological and pharmacological low-level states of consciousness display less recurrent, less connected and more segregated synchronization patterns than conscious state. We use whole-brain models built upon healthy and injured structural connectivity to interpret these dynamical effects. We found that low-level states of consciousness were associated with reduced network interactions, together with more homogeneous and more structurally constrained local dynamics. Notably, these changes lead the structural hub regions to lose their stability during low-level states of consciousness, thus attenuating the differences between hubs and non-hubs brain dynamics.

López-González et al study the fMRI brain dynamics and their underlying mechanism from patients that suffered brain injuries leading to a disorder of consciousness as well as from healthy subjects undergoing propofol-induced sedation. They show that pathological and pharmacological low-level states of consciousness display disrupted synchronization patterns, higher constraint to the anatomy and a loss of heterogeneity and stability in the structural hubs compared to conscious states.

Columnar grouping preserves synchronization in neuronal networks with distance-dependent time delays

Neuronal connectivity at the cellular level in the cerebral cortex is far from random, with characteristics that point to a hierarchical design with intricately connected neuronal clusters. Here we investigate computationally the effects of varying neuronal cluster connectivity on network synchronization for two different spatial distributions of clusters: one where clusters are arranged in columns in a grid and the other where neurons from different clusters are spatially intermixed. We characterize each case by measuring the degree of neuronal spiking synchrony as a function of the number of connections per neuron and the degree of intercluster connectivity. We find that in both cases as the number of connections per neuron increases, there is an asynchronous to synchronous transition dependent only on intrinsic parameters of the biophysical model. We also observe in both cases that with very low intercluster connectivity clusters have independent firing dynamics yielding a low degree of synchrony. More importantly, we find that for a high number of connections per neuron but intermediate intercluster connectivity, the two spatial distributions of clusters differ in their response where the clusters in a grid have a higher degree of synchrony than the clusters that are intermixed.

Marmoset Brain ISH Data Revealed Molecular Difference Between Cortical Folding Patterns

Literature studies have demonstrated the structural, connectional, and functional differences between cortical folding patterns in mammalian brains, such as convex and concave patterns. However, the molecular underpinning of such convex/concave differences remains largely unknown. Thanks to public access to a recently released set of marmoset whole-brain in situ hybridization data by RIKEN, Japan; this data's accessibility empowers us to improve our understanding of the organization, regulation, and function of genes and their relation to macroscale metrics of brains. In this work, magnetic resonance imaging and diffusion tensor imaging macroscale neuroimaging data in this dataset were used to delineate convex/concave patterns in marmoset and to examine their structural features. Machine learning and visualization tools were employed to investigate the possible transcriptome difference between cortical convex and concave patterns. Experimental results demonstrated that a collection of genes is differentially expressed in convex and concave patterns, and their expression profiles can robustly characterize and differentiate the two folding patterns. More importantly, neuroscientific interpretations of these differentially expressed genes, as well as axonal guidance pathway analysis and gene enrichment analysis, offer novel understanding of structural and functional differences between cortical folding patterns in different regions from a molecular perspective.

Signature of consciousness in brain-wide synchronization patterns of monkey and human fMRI signals

During the sleep-wake cycle, the brain undergoes profound dynamical changes, which manifest subjectively as transitions between conscious experience and unconsciousness. Yet, neurophysiological signatures that can objectively distinguish different consciousness states based are scarce. Here, we show that differences in the level of brain-wide signals can reliably distinguish different stages of sleep and anesthesia from the awake state in human and monkey fMRI resting state data. Moreover, a whole-brain computational model can faithfully reproduce changes in global synchronization and other metrics such as functional connectivity, structure-function relationship, integration and segregation across vigilance states. We demonstrate that the awake brain is close to a Hopf bifurcation, which naturally coincides with the emergence of globally correlated fMRI signals. Furthermore, simulating lesions of individual brain areas highlights the importance of connectivity hubs in the posterior brain and subcortical nuclei for maintaining the model in the awake state, as predicted by graph-theoretical analyses of structural data.

The Emerging Role of Biomarkers in Adaptive Modulation of Clinical Brain Stimulation

Therapeutic brain stimulation has proven efficacious for treatment of nervous system diseases, exerting widespread influence via disease-specific neural networks. Activation or suppression of neural networks could theoretically be assessed by either clinical symptom modification (ie, tremor, rigidity, seizures) or development of specific biomarkers linked to treatment of symptomatic disease states. For example, biomarkers indicative of disease state could aid improved intraoperative localization of electrode position, optimize device efficacy or efficiency through dynamic control, and eventually serve to guide automatic adjustment of stimulation settings. Biomarkers to control either extracranial or intracranial stimulation span from continuous physiological brain activity, intermittent pathological activity, and triggered local phenomena or potentials, to wearable devices, blood flow, biochemical or cardiac signals, temperature perturbations, optical or magnetic resonance imaging changes, or optogenetic signals. The goal of this review is to update new approaches to implement control of stimulation through relevant biomarkers. Critical questions include whether adaptive systems adjusted through biomarkers can optimize efficiency and eventually efficacy, serve as inputs for stimulation adjustment, and consequently broaden our fundamental understanding of abnormal neural networks in pathologic states. Neurosurgeons are at the forefront of translating and developing biomarkers embedded within improved brain stimulation systems. Thus, criteria for developing and validating biomarkers for clinical use are important for the adaptation of device approaches into clinical practice.

Model-based whole-brain effective connectivity to study distributed cognition in health and disease

Neuroimaging techniques are now widely used to study human cognition. The functional associations between brain areas have become a standard proxy to describe how cognitive processes are distributed across the brain network. Among the many analysis tools available, dynamic models of brain activity have been developed to overcome the limitations of original connectivity measures such as functional connectivity. This goes in line with the many efforts devoted to the assessment of directional interactions between brain areas from the observed neuroimaging activity. This opinion article provides an overview of our model-based whole-brain effective connectivity to analyze fMRI data, while discussing the pros and cons of our approach with respect to other established approaches. Our framework relies on the multivariate Ornstein-Uhlenbeck (MOU) process and is thus referred to as MOU-EC. Once tuned, the model provides a directed connectivity estimate that reflects the dynamical state of BOLD activity, which can be used to explore cognition. We illustrate this approach using two applications on task-evoked fMRI data. First, as a connectivity measure, MOU-EC can be used to extract biomarkers for task-specific brain coordination, understood as the patterns of areas exchanging information. The multivariate nature of connectivity measures raises several challenges for whole-brain analysis, for which machine-learning tools present some advantages over statistical testing. Second, we show how to interpret changes in MOU-EC connections in a collective and model-based manner, bridging with network analysis. Our framework provides a comprehensive set of tools that open exciting perspectives to study distributed cognition, as well as neuropathologies.

Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Cross-Species Evidence of Interplay Between Neural Connectivity at the Micro- and Macroscale of Connectome Organization in Human, Mouse, and Rat Brain

The mammalian brain describes a multiscale system. At the microscale, axonal, dendritic, and synaptic elements ensure neuron-to-neuron communication, and at the macroscale, large-scale projections form the anatomical wiring for communication between cortical areas. Although it is clear that both levels of neural organization play a crucial role in brain functioning, their interaction is not extensively studied. Connectome studies of the mammalian brain in cat, macaque, and human have recently shown that regions with larger and more complex pyramidal cells to have more macroscale corticocortical connections. In this study, we aimed to further validate these cross-scale findings in the human, mouse, and rat brain. We combined neuron reconstructions from the NeuroMorpho.org neuroarchitecture database with macroscale connectivity data derived from connectome mapping by means of tract-tracing (rat, mouse) and in vivo diffusion magnetic resonance imaging (human). Across these three mammalian species, we show cortical variation in neural organization to be associated with features of macroscale connectivity, with cortical variation in neuronal complexity explaining significant proportions of cortical variation in the number of white matter projections of cortical areas. Our findings converge on the notion of a relationship between features of micro- and macroscale neural connectivity to form a central aspect of mammalian neural architecture.

Altered structural and functional brain network overall organization predict human intertemporal decision-making

Intertemporal decision-making is naturally ubiquitous to us: individuals always make a decision with different consequences occurring at different moments. These choices are invariably involved in life-changing outcomes regarding marriage, education, fertility, long-term well-being, and even public policy. Previous studies have clearly uncovered the neurobiological mechanism of the intertemporal decision in the schemes of regional location or sub-network. However, it still remains unclear how to characterize intertemporal behavior with multimodal whole-brain network metrics to date. Here, we combined diffusion tensor image and resting-state functional connectivity MRI technology, in conjunction with graph-theoretical analysis, to explore the link between topological properties of integrated structural and functional whole-brain networks and intertemporal decision-making. Graph-theoretical analysis illustrated that the participants with steep discounting rates exhibited the decreased global topological organizations including small-world and rich-club regimes in both functional and structural connectivity networks, and reflected the dreadful local topological dynamics in the modularity of functional connectome. Furthermore, in the cross-modalities configuration, the same relationship was predominantly observed for the coupling of structural-functional connectivity as well. Above topological metrics are commonly indicative of the communication pattern of simultaneous global and local parallel information processing, and it thus reshapes our accounts on intertemporal decision-making from functional regional/sub-network scheme to multimodal brain overall organization.

Comprehensive computational modelling of the development of mammalian cortical connectivity underlying an architectonic type principle

The architectonic type principle relates patterns of cortico-cortical connectivity to the relative architectonic differentiation of cortical regions. One mechanism through which the observed close relation between cortical architecture and connectivity may be established is the joint development of cortical areas and their connections in developmental time windows. Here, we describe a theoretical exploration of the possible mechanistic underpinnings of the architectonic type principle, by performing systematic computational simulations of cortical development. The main component of our in silico model was a developing two-dimensional cortical sheet, which was gradually populated by neurons that formed cortico-cortical connections. To assess different explanatory mechanisms, we varied the spatiotemporal trajectory of the simulated neurogenesis. By keeping the rules governing axon outgrowth and connection formation constant across all variants of simulated development, we were able to create model variants which differed exclusively by the specifics of when and where neurons were generated. Thus, all differences in the resulting connectivity were due to the variations in spatiotemporal growth trajectories. Our results demonstrated that a prescribed targeting of interareal connection sites was not necessary for obtaining a realistic replication of the experimentally observed relation between connection patterns and architectonic differentiation. Instead, we found that spatiotemporal interactions within the forming cortical sheet were sufficient if a small number of empirically well-grounded assumptions were met, namely planar, expansive growth of the cortical sheet around two points of origin as neurogenesis progressed, stronger architectonic differentiation of cortical areas for later neurogenetic time windows, and stochastic connection formation. Thus, our study highlights a potential mechanism of how relative architectonic differentiation and cortical connectivity become linked during development. We successfully predicted connectivity in two species, cat and macaque, from simulated cortico-cortical connection networks, which further underscored the general applicability of mechanisms through which the architectonic type principle can explain cortical connectivity in terms of the relative architectonic differentiation of cortical regions.

Multimodal Connectomics in Psychiatry: Bridging Scales From Micro to Macro

The human brain is a highly complex system, with a large variety of microscale cellular morphologies and macroscale global properties. Working at multiple scales, it forms an efficient system for processing and integration of multimodal information. Studies have repeatedly demonstrated strong associations between modalities of both microscales and macroscales of brain organization. These consistent observations point toward potential common organization principles where regions with a microscale architecture supportive of a larger computational load have more and stronger connections in the brain network on the macroscale. Conversely, disruptions observed on one organizational scale could modulate the other. First neuropsychiatric micro-macro comparisons in, among other conditions, Alzheimer's disease and schizophrenia, have, for example, shown overlapping alterations across both scales. We give an overview of recent findings on associations between microscale and macroscale organization observed in the healthy brain, followed by a summary of microscale and macroscale findings reported in the context of brain disorders. We conclude with suggestions for future multiscale connectome comparisons linking multiple scales and modalities of organization and suggest how such comparisons could contribute to a more complete fundamental understanding of brain organization and associated disease-related alterations.

Analysis of fMRI data using noise-diffusion network models: a new covariance-coding perspective

Since the middle of the 1990s, studies of resting-state fMRI/BOLD data have explored the correlation patterns of activity across the whole brain, which is referred to as functional connectivity (FC). Among the many methods that have been developed to interpret FC, a recently proposed model-based approach describes the propagation of fluctuating BOLD activity within the recurrently connected brain network by inferring the effective connectivity (EC). In this model, EC quantifies the strengths of directional interactions between brain regions, viewed from the proxy of BOLD activity. In addition, the tuning procedure for the model provides estimates for the local variability (input variances) to explain how the observed FC is generated. Generalizing, the network dynamics can be studied in the context of an input-output mapping-determined by EC-for the second-order statistics of fluctuating nodal activities. The present paper focuses on the following detection paradigm: observing output covariances, how discriminative is the (estimated) network model with respect to various input covariance patterns? An application with the model fitted to experimental fMRI data-movie viewing versus resting state-illustrates that changes in local variability and changes in brain coordination go hand in hand.

Effective Subnetwork Topology for Synchronizing Interconnected Networks of Coupled Phase Oscillators

A system consisting of interconnected networks, or a network of networks (NoN), appears diversely in many real-world systems, including the brain. In this study, we consider NoNs consisting of heterogeneous phase oscillators and investigate how the topology of subnetworks affects the global synchrony of the network. The degree of synchrony and the effect of subnetwork topology are evaluated based on the Kuramoto order parameter and the minimum coupling strength necessary for the order parameter to exceed a threshold value, respectively. In contrast to an isolated network in which random connectivity is favorable for achieving synchrony, NoNs synchronize with weaker interconnections when the degree distribution of subnetworks is heterogeneous, suggesting the major role of the high-degree nodes. We also investigate a case in which subnetworks with different average natural frequencies are coupled to show that direct coupling of subnetworks with the largest variation is effective for synchronizing the whole system. In real-world NoNs like the brain, the balance of synchrony and asynchrony is critical for its function at various spatial resolutions. Our work provides novel insights into the topological basis of coordinated dynamics in such networks.

Biomarkers and Stimulation Algorithms for Adaptive Brain Stimulation

The goal of this review is to describe in what ways feedback or adaptive stimulation may be delivered and adjusted based on relevant biomarkers. Specific treatment mechanisms underlying therapeutic brain stimulation remain unclear, in spite of the demonstrated efficacy in a number of nervous system diseases. Brain stimulation appears to exert widespread influence over specific neural networks that are relevant to specific disease entities. In awake patients, activation or suppression of these neural networks can be assessed by either symptom alleviation (i.e., tremor, rigidity, seizures) or physiological criteria, which may be predictive of expected symptomatic treatment. Secondary verification of network activation through specific biomarkers that are linked to symptomatic disease improvement may be useful for several reasons. For example, these biomarkers could aid optimal intraoperative localization, possibly improve efficacy or efficiency (i.e., reduced power needs), and provide long-term adaptive automatic adjustment of stimulation parameters. Possible biomarkers for use in portable or implanted devices span from ongoing physiological brain activity, evoked local field potentials (LFPs), and intermittent pathological activity, to wearable devices, biochemical, blood flow, optical, or magnetic resonance imaging (MRI) changes, temperature changes, or optogenetic signals. First, however, potential biomarkers must be correlated directly with symptom or disease treatment and network activation. Although numerous biomarkers are under consideration for a variety of stimulation indications the feasibility of these approaches has yet to be fully determined. Particularly, there are critical questions whether the use of adaptive systems can improve efficacy over continuous stimulation, facilitate adjustment of stimulation interventions and improve our understanding of the role of abnormal network function in disease mechanisms.

Robustness and efficiency in interconnected networks with changes in network assortativity

In this study, the effect of assortativity on the robustness and efficiency of interconnected networks was investigated. This involved constructing a network that possessed the desired degree of assortativity. Additionally, an interconnected network was constructed wherein the assortativity between component networks possessed the desired value. With respect to single networks, the results indicated that a decrease in assortativity provided low hop length, high information diffusion efficiency, and distribution of communication load on edges. The study also revealed that excessive assortativity led to poor network performance. In the study, the assortativity between networks was defined and the following results were demonstrated: assortative connections between networks lowered the average hop length and enhanced information diffusion efficiency, whereas disassortative connections between networks distributed the communication loads of internetwork links and enhanced robustness. Furthermore, it is necessary to carefully adjust assortativity based on the node degree distribution of networks. Finally, the application of the results to the design of robust and efficient information networks was discussed.

Functional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs

The large-scale structural ingredients of the brain and neural connectomes have been identified in recent years. These are, similar to the features found in many other real networks: the arrangement of brain regions into modules and the presence of highly connected regions (hubs) forming rich-clubs. Here, we examine how modules and hubs shape the collective dynamics on networks and we find that both ingredients lead to the emergence of complex dynamics. Comparing the connectomes of C. elegans, cats, macaques and humans to surrogate networks in which either modules or hubs are destroyed, we find that functional complexity always decreases in the perturbed networks. A comparison between simulated and empirically obtained resting-state functional connectivity indicates that the human brain, at rest, lies in a dynamical state that reflects the largest complexity its anatomical connectome can host. Last, we generalise the topology of neural connectomes into a new hierarchical network model that successfully combines modular organisation with rich-club forming hubs. This is achieved by centralising the cross-modular connections through a preferential attachment rule. Our network model hosts more complex dynamics than other hierarchical models widely used as benchmarks.

Disrupted structural and functional rich club organization of the brain connectome in patients with generalized tonic-clonic seizure

Network studies have demonstrated that a small set of highly connected regions may play a central role in global information integration, together forming a rich club organization. Given that generalized tonic-clonic seizure (GTCS) has been conceptualized as a network disorder, we hypothesized that the rich club disturbances may be related to the network abnormalities of GTCS. Here, we used graph theoretical analysis to investigate the rich club organization of both structural and functional connectome in patients with GTCS (n = 50) and healthy controls (n = 60). We further measured the level of global efficiency and clustering in rich club and non-rich club organization. We, respectively, identified a small number of highly connected hubs as rich club organization from structural and functional networks. Patients were found to exhibit significantly reduced rich club connectivity among the central hubs. Meanwhile, both structural and functional network showed changed levels of global efficiency and clustering of rich club organization in GTCS. Furthermore, in patients, lower levels of rich club connectivity were found to be correlated with longer duration of illness and seizure frequency. Together, these findings suggest that GTCS is characterized by a selective disruption of rich club organization due to the long-term injurious effects of epileptic actions on the central hub regions, which potentially contribute to a reduced level of brain integration capacity among different functional domains and an added effect of illness on a preexisting vulnerability. Our findings emphasize a central role for abnormal rich club organization in the pathophysiological mechanism underlying GTCS. Hum Brain Mapp 37:4487-4499, 2016. © 2016 Wiley Periodicals, Inc.

Robust Multiobjective Controllability of Complex Neuronal Networks

This paper addresses robust multiobjective identification of driver nodes in the neuronal network of a cat's brain, in which uncertainties in determination of driver nodes and control gains are considered. A framework for robust multiobjective controllability is proposed by introducing interval uncertainties and optimization algorithms. By appropriate definitions of robust multiobjective controllability, a robust nondominated sorting adaptive differential evolution (NSJaDE) is presented by means of the nondominated sorting mechanism and the adaptive differential evolution (JaDE). The simulation experimental results illustrate the satisfactory performance of NSJaDE for robust multiobjective controllability, in comparison with six statistical methods and two multiobjective evolutionary algorithms (MOEAs): nondominated sorting genetic algorithms II (NSGA-II) and nondominated sorting composite differential evolution. It is revealed that the existence of uncertainties in choosing driver nodes and designing control gains heavily affects the controllability of neuronal networks. We also unveil that driver nodes play a more drastic role than control gains in robust controllability. The developed NSJaDE and obtained results will shed light on the understanding of robustness in controlling realistic complex networks such as transportation networks, power grid networks, biological networks, etc.

Topological organization of connectivity strength in the rat connectome

The mammalian brain is a complex network of anatomically interconnected regions. Animal studies allow for an invasive measurement of the connections of these networks at the macroscale level by means of neuronal tracing of axonal projections, providing a unique opportunity for the formation of detailed 'connectome maps'. Here we analyzed the macroscale connectome of the rat brain, including detailed information on the macroscale interregional pathways between 67 cortical and subcortical regions as provided by the high-quality, open-access BAMS-II database on rat brain anatomical projections, focusing in particular on the non-uniform distribution of projection strength across pathways. First, network analysis confirmed a small-world, modular and rich club organization of the rat connectome; findings in clear support of previous studies on connectome organization in other mammalian species. More importantly, analyzing network properties of different connection weight classes, we extend previous observations by showing that pathways with different topological roles have significantly different levels of connectivity strength. Among other findings, intramodular connections are shown to display a higher connectivity strength than intermodular connections and hub-to-hub rich club connections are shown to include significantly stronger pathways than connections spanning between peripheral nodes. Furthermore, we show evidence indicating that edges of different weight classes display different topological structures, potentially suggesting varying roles and origins of pathways in the mammalian brain network.

Comparative Connectomics

We introduce comparative connectomics, the quantitative study of cross-species commonalities and variations in brain network topology that aims to discover general principles of network architecture of nervous systems and the identification of species-specific features of brain connectivity. By comparing connectomes derived from simple to more advanced species, we identify two conserved themes of wiring: the tendency to organize network topology into communities that serve specialized functionality and the general drive to enable high topological integration by means of investment of neural resources in short communication paths, hubs, and rich clubs. Within the space of wiring possibilities that conform to these common principles, we argue that differences in connectome organization between closely related species support adaptations in cognition and behavior.

Chimera-like States in Modular Neural Networks

Chimera states, namely the coexistence of coherent and incoherent behavior, were previously analyzed in complex networks. However, they have not been extensively studied in modular networks. Here, we consider a neural network inspired by the connectome of the C. elegans soil worm, organized into six interconnected communities, where neurons obey chaotic bursting dynamics. Neurons are assumed to be connected with electrical synapses within their communities and with chemical synapses across them. As our numerical simulations reveal, the coaction of these two types of coupling can shape the dynamics in such a way that chimera-like states can happen. They consist of a fraction of synchronized neurons which belong to the larger communities, and a fraction of desynchronized neurons which are part of smaller communities. In addition to the Kuramoto order parameter ρ, we also employ other measures of coherence, such as the chimera-like χ and metastability λ indices, which quantify the degree of synchronization among communities and along time, respectively. We perform the same analysis for networks that share common features with the C. elegans neural network. Similar results suggest that under certain assumptions, chimera-like states are prominent phenomena in modular networks, and might provide insight for the behavior of more complex modular networks.

Effect of intermodular connection on fast sparse synchronization in clustered small-world neural networks

We consider a clustered network with small-world subnetworks of inhibitory fast spiking interneurons and investigate the effect of intermodular connection on the emergence of fast sparsely synchronized rhythms by varying both the intermodular coupling strength J(inter) and the average number of intermodular links per interneuron M(syn)(inter). In contrast to the case of nonclustered networks, two kinds of sparsely synchronized states such as modular and global synchronization are found. For the case of modular sparse synchronization, the population behavior reveals the modular structure, because the intramodular dynamics of subnetworks make some mismatching. On the other hand, in the case of global sparse synchronization, the population behavior is globally identical, independently of the cluster structure, because the intramodular dynamics of subnetworks make perfect matching. We introduce a realistic cross-correlation modularity measure, representing the matching degree between the instantaneous subpopulation spike rates of the subnetworks, and examine whether the sparse synchronization is global or modular. Depending on its magnitude, the intermodular coupling strength J(inter) seems to play "dual" roles for the pacing between spikes in each subnetwork. For large J(inter), due to strong inhibition it plays a destructive role to "spoil" the pacing between spikes, while for small J(inter) it plays a constructive role to "favor" the pacing between spikes. Through competition between the constructive and the destructive roles of J(inter), there exists an intermediate optimal J(inter) at which the pacing degree between spikes becomes maximal. In contrast, the average number of intermodular links per interneuron M(syn)(inter) seems to play a role just to favor the pacing between spikes. With increasing M(syn)(inter), the pacing degree between spikes increases monotonically thanks to the increase in the degree of effectiveness of global communication between spikes. Furthermore, we employ the realistic sub- and whole-population order parameters, based on the instantaneous sub- and whole-population spike rates, to determine the threshold values for the synchronization-unsynchronization transition in the sub- and whole populations, and the degrees of global and modular sparse synchronization are also measured in terms of the realistic sub- and whole-population statistical-mechanical spiking measures defined by considering both the occupation and the pacing degrees of spikes. It is expected that our results could have implications for the role of the brain plasticity in some functional behaviors associated with population synchronization.

Effects of bursting dynamic features on the generation of multi-clustered structure of neural network with symmetric spike-timing-dependent plasticity learning rule

In this paper, the generation of multi-clustered structure of self-organized neural network with different neuronal firing patterns, i.e., bursting or spiking, has been investigated. The initially all-to-all-connected spiking neural network or bursting neural network can be self-organized into clustered structure through the symmetric spike-timing-dependent plasticity learning for both bursting and spiking neurons. However, the time consumption of this clustering procedure of the burst-based self-organized neural network (BSON) is much shorter than the spike-based self-organized neural network (SSON). Our results show that the BSON network has more obvious small-world properties, i.e., higher clustering coefficient and smaller shortest path length than the SSON network. Also, the results of larger structure entropy and activity entropy of the BSON network demonstrate that this network has higher topological complexity and dynamical diversity, which benefits for enhancing information transmission of neural circuits. Hence, we conclude that the burst firing can significantly enhance the efficiency of clustering procedure and the emergent clustered structure renders the whole network more synchronous and therefore more sensitive to weak input. This result is further confirmed from its improved performance on stochastic resonance. Therefore, we believe that the multi-clustered neural network which self-organized from the bursting dynamics has high efficiency in information processing.

Between-network connectivity occurs in brain regions lacking layer IV input

To better understand the cortical circuitry underlying connectivity between large-scale neural networks, we develop a novel, data-driven approach to identify potential integration subregions. Between-network connectivity (BNC) associated with any anatomical region is the amount of connectivity between that point and all large-scale networks, as measured using simple and multiple correlations. It is straightforward to calculate and applicable to functional networks identified using independent components analysis. We calculated BNC for all fMRI voxels within the brain and compared the results to known regional cytoarchitectural patterns. Based on previous observations of the relationship between macroscopic connectivity and microscopic cytoarchitecture, we predicted that areas with high BNC will be located in paralimbic subregions with an undifferentiated laminar structure. Results suggest that the anterior insula and dorsal posterior cingulate cortices play prominent roles in information integration. Cytoarchitecturely, these areas show agranular or dysgranular cytologies with absent or disrupted cortical layer IV. Since layer IV is the primary recipient of feed-forward thalamocortical connections, and due to the exclusive nature of driving connections to this layer, we suggest that the absence of cortical layer IV might allow for information to be exchanged across networks, and is an organizational characteristic of brain-subregions serving as inter-network communication hubs.

Phase synchronization of coupled bursting neurons and the generalized Kuramoto model

Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal models of bursting neurons must include both effects. We considered one of these models and its relation with a generalized Kuramoto model, thanks to the definition of a geometrical phase for bursting and a corresponding frequency. We considered neuronal networks with different connection topologies and investigated the transition from a non-synchronized to a partially phase-synchronized state as the coupling strength is varied. The numerically determined critical coupling strength value for this transition to occur is compared with theoretical results valid for the generalized Kuramoto model.

Linking macroscale graph analytical organization to microscale neuroarchitectonics in the macaque connectome

Macroscale connectivity of the mammalian brain has been shown to display several characteristics of an efficient communication network architecture. In parallel, at the microscopic scale, histological studies have extensively revealed large interregional variation in cortical neural architectonics. However, how these two "scales" of cerebrum organization are linked remains an open question. Collating and combining data across multiple studies on the cortical cytoarchitecture of the macaque cortex with information on macroscale anatomical wiring derived from tract tracing studies, this study focuses on examining the interplay between macroscale organization of the macaque connectome and microscale cortical neuronal architecture. Our findings show that both macroscale degree as well as the topological role in the overall network are related to the level of neuronal complexity of cortical regions at the microscale, showing (among several effects) a positive overall association between macroscale degree and metrics of microscale pyramidal complexity. Macroscale hub regions, together forming a densely interconnected "rich club," are noted to display a high level of neuronal complexity, findings supportive of a high level of integrative neuronal processes to occur in these regions. Together, we report on cross-scale observations that jointly suggest that a region's microscale neuronal architecture is tuned to its role in the global brain network.

Synchronization of bursting Hodgkin-Huxley-type neurons in clustered networks

We considered a clustered network of bursting neurons described by the Huber-Braun model. In the upper level of the network we used the connectivity matrix of the cat cerebral cortex network, and in the lower level each cortex area (or cluster) is modelled as a small-world network. There are two different coupling strengths related to inter- and intracluster dynamics. Each bursting cycle is composed of a quiescent period followed by a rapid chaotic sequence of spikes, and we defined a geometric phase which enables us to investigate the onset of synchronized bursting, as the state in which the neuron start bursting at the same time, whereas their spikes may remain uncorrelated. The bursting synchronization of a clustered network has been investigated using an order parameter and the average field of the network in order to identify regimes in which each cluster may display synchronized behavior, whereas the overall network does not. We introduce quantifiers to evaluate the relative contribution of each cluster in the partial synchronized behavior of the whole network. Our main finding is that we typically observe in the clustered network not a complete phase synchronized regime but instead a complex pattern of partial phase synchronization in which different cortical areas may be internally synchronized at distinct phase values, hence they are not externally synchronized, unless the coupling strengths are too large.

Structural and functional aspects relating to cost and benefit of rich club organization in the human cerebral cortex

Recent findings have demonstrated that a small set of highly connected brain regions may play a central role in enabling efficient communication between cortical regions, together forming a densely interconnected "rich club." However, the density and spatial layout of the rich club also suggest that it constitutes a costly feature of brain architecture. Here, combining anatomical T1, diffusion tensor imaging, magnetic transfer imaging, and functional MRI, several aspects of structural and functional connectivity of the brain's rich club were examined. Our findings suggest that rich club regions and rich club connections exhibit high levels of wiring volume, high levels of white matter organization, high levels of metabolic energy usage, long maturational trajectories, more variable regional time series, and more inter-regional functional couplings. Taken together, these structural and functional measures extend the notion that rich club organization represents a high-cost feature of brain architecture that puts a significant strain on brain resources. The high cost of the rich club may, however, be offset by significant functional benefits that the rich club confers to the brain network as a whole.

Neurophysiological correlates of eye movement desensitization and reprocessing sessions: preliminary evidence for traumatic memories integration

We have investigated the potential role of eye movement desensitization and reprocessing (EMDR) in enhancing the integration of traumatic memories by measuring EEG coherence, power spectra and autonomic variables before (pre-EMDR) and after (post-EMDR) EMDR sessions during the recall of patient's traumatic memory. Thirteen EMDR sessions of six patients with post-traumatic stress disorder were recorded. EEG analyses were conducted by means of the standardized Low Resolution Electric Tomography (sLORETA) software. Power spectra, EEG coherence and heart rate variability (HRV) were compared between pre- and post-EMDR sessions. After EMDR, we observed a significant increase of alpha power in the left inferior temporal gyrus (T = 3.879; P = 0.041) and an increased EEG coherence in beta band between C3 and T5 electrodes (T = 6.358; P < 0.001). Furthermore, a significant increase of HRV in the post-EMDR sessions was also observed (pre-EMDR: 6.38 ± 6.83; post-EMDR: 2.46 ± 2.95; U-Test = 45, P = 0.043). Finally, the values of lagged coherence were negatively associated with subjective units of disturbance (r(24) = -0.44, P < 0.05) and positively associated with parasympathetic activity (r(24) = 0.40, P < 0.05). Our results suggest that EMDR leads to an integration of dissociated aspects of traumatic memories and, consequently, a decrease of hyperarousal symptoms [Correction made here after initial publication].

Network hubs in the human brain

Virtually all domains of cognitive function require the integration of distributed neural activity. Network analysis of human brain connectivity has consistently identified sets of regions that are critically important for enabling efficient neuronal signaling and communication. The central embedding of these candidate 'brain hubs' in anatomical networks supports their diverse functional roles across a broad range of cognitive tasks and widespread dynamic coupling within and across functional networks. The high level of centrality of brain hubs also renders them points of vulnerability that are susceptible to disconnection and dysfunction in brain disorders. Combining data from numerous empirical and computational studies, network approaches strongly suggest that brain hubs play important roles in information integration underpinning numerous aspects of complex cognitive function.

A predictive model of the cat cortical connectome based on cytoarchitecture and distance

Information processing in the brain is strongly constrained by anatomical connectivity. However, the principles governing the organization of corticocortical connections remain elusive. Here, we tested three models of relationships between the organization of cortical structure and features of connections linking 49 areas of the cat cerebral cortex. Factors taken into account were relative cytoarchitectonic differentiation (‘structural model’), relative spatial position (‘distance model’), or relative hierarchical position (‘hierarchical model’) of the areas. Cytoarchitectonic differentiation and spatial distance (themselves uncorrelated) correlated strongly with the existence of inter-areal connections, whereas no correlation was found with relative hierarchical position. Moreover, a strong correlation was observed between patterns of laminar projection origin or termination and cytoarchitectonic differentiation. Additionally, cytoarchitectonic differentiation correlated with the absolute number of corticocortical connections formed by areas, and varied characteristically between different cortical subnetworks, including a ‘rich-club’ module of hub areas. Thus, connections between areas of the cat cerebral cortex can, to a large part, be explained by the two independent factors of relative cytoarchitectonic differentiation and spatial distance of brain regions. As both the structural and distance model were originally formulated in the macaque monkey, their applicability in another mammalian species suggests a general principle of global cortical organization.

Synchronization and stochastic resonance of the small-world neural network based on the CPG

According to biological knowledge, the central nervous system controls the central pattern generator (CPG) to drive the locomotion. The brain is a complex system consisting of different functions and different interconnections. The topological properties of the brain display features of small-world network. The synchronization and stochastic resonance have important roles in neural information transmission and processing. In order to study the synchronization and stochastic resonance of the brain based on the CPG, we establish the model which shows the relationship between the small-world neural network (SWNN) and the CPG. We analyze the synchronization of the SWNN when the amplitude and frequency of the CPG are changed and the effects on the CPG when the SWNN's parameters are changed. And we also study the stochastic resonance on the SWNN. The main findings include: (1) When the CPG is added into the SWNN, there exists parameters space of the CPG and the SWNN, which can make the synchronization of the SWNN optimum. (2) There exists an optimal noise level at which the resonance factor Q gets its peak value. And the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the noise intensity. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.

Rich club organization supports a diverse set of functional network configurations

Brain function relies on the flexible integration of a diverse set of segregated cortical modules, with the structural connectivity of the brain being a fundamentally important factor in shaping the brain's functional dynamics. Following up on macroscopic studies showing the existence of centrally connected nodes in the mammalian brain, combined with the notion that these putative brain hubs may form a dense interconnected 'rich club' collective, we hypothesized that brain connectivity might involve a rich club type of architecture to promote a repertoire of different and flexibly accessible brain functions. With the rich club suggested to play an important role in global brain communication, examining the effects of a rich club organization on the functional repertoire of physical systems in general, and the brain in particular, is of keen interest. Here we elucidate these effects using a spin glass model of neural networks for simulating stable configurations of cortical activity. Using simulations, we show that the presence of a rich club increases the set of attractors and hence the diversity of the functional repertoire over and above the effects produced by scale free type topology alone. Within the networks' overall functional repertoire rich nodes are shown to be important for enabling a high level of dynamic integrations of low-degree nodes to form functional networks. This suggests that the rich club serves as an important backbone for numerous co-activation patterns among peripheral nodes of the network. In addition, applying the spin glass model to empirical anatomical data of the human brain, we show that the positive effects on the functional repertoire attributed to the rich club phenomenon can be observed for the brain as well. We conclude that a rich club organization in network architectures may be crucial for the facilitation and integration of a diverse number of segregated functions.

The Laplacian spectrum of neural networks

The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks. Many popular graph metrics, however, encode average properties of individual network elements. Complementing these "conventional" graph metrics, the eigenvalue spectrum of the normalized Laplacian describes a network's structure directly at a systems level, without referring to individual nodes or connections. In this paper, the Laplacian spectra of the macroscopic anatomical neuronal networks of the macaque and cat, and the microscopic network of the Caenorhabditis elegans were examined. Consistent with conventional graph metrics, analysis of the Laplacian spectra revealed an integrative community structure in neural brain networks. Extending previous findings of overlap of network attributes across species, similarity of the Laplacian spectra across the cat, macaque and C. elegans neural networks suggests a certain level of consistency in the overall architecture of the anatomical neural networks of these species. Our results further suggest a specific network class for neural networks, distinct from conceptual small-world and scale-free models as well as several empirical networks.

Disentangling different types of El Niño episodes by evolving climate network analysis

Complex network theory provides a powerful toolbox for studying the structure of statistical interrelationships between multiple time series in various scientific disciplines. In this work, we apply the recently proposed climate network approach for characterizing the evolving correlation structure of the Earth's climate system based on reanalysis data for surface air temperatures. We provide a detailed study of the temporal variability of several global climate network characteristics. Based on a simple conceptual view of red climate networks (i.e., networks with a comparably low number of edges), we give a thorough interpretation of our evolving climate network characteristics, which allows a functional discrimination between recently recognized different types of El Niño episodes. Our analysis provides deep insights into the Earth's climate system, particularly its global response to strong volcanic eruptions and large-scale impacts of different phases of the El Niño Southern Oscillation.

Rich club organization and intermodule communication in the cat connectome

Macroscopic brain networks have been shown to display several properties of an efficient communication architecture. In light of global communication, the formation of a densely connected neural "rich club" of hubs is of particular interest, because brain hubs have been suggested to play a key role in enabling short communication pathways within neural networks. Here, analyzing the cat connectome as reconstructed from tract tracing data (Scannell et al., 1995), we provide several lines of evidence of an important role of the structural rich club to interlink functional domains. First, rich club hub nodes were found to be mostly present at the boundaries between functional communities and well represented among intermodule hubs, displaying a diverse connectivity profile. Second, rich club connections, linking nodes of the rich club, and feeder connections, linking non-rich club nodes to rich club nodes, were found to comprise 86% of the intermodule connections, whereas local connections between peripheral nodes mostly spanned between nodes of the same functional community. Third, almost 90% of all intermodule communication paths were found to follow a sequence or "path motif" that involved rich club or feeder edges and thus traversed a rich club node. Together, our findings provide evidence of the structural rich club to form a central infrastructure for intermodule communication in the brain.

Large-scale network organization in the avian forebrain: a connectivity matrix and theoretical analysis

Many species of birds, including pigeons, possess demonstrable cognitive capacities, and some are capable of cognitive feats matching those of apes. Since mammalian cortex is laminar while the avian telencephalon is nucleated, it is natural to ask whether the brains of these two cognitively capable taxa, despite their apparent anatomical dissimilarities, might exhibit common principles of organization on some level. Complementing recent investigations of macro-scale brain connectivity in mammals, including humans and macaques, we here present the first large-scale "wiring diagram" for the forebrain of a bird. Using graph theory, we show that the pigeon telencephalon is organized along similar lines to that of a mammal. Both are modular, small-world networks with a connective core of hub nodes that includes prefrontal-like and hippocampal structures. These hub nodes are, topologically speaking, the most central regions of the pigeon's brain, as well as being the most richly connected, implying a crucial role in information flow. Overall, our analysis suggests that indeed, despite the absence of cortical layers and close to 300 million years of separate evolution, the connectivity of the avian brain conforms to the same organizational principles as the mammalian brain.

Connectivity-driven coherence in complex networks

We study the emergence of coherence in complex networks of mutually coupled nonidentical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, the isolated dynamics of the elements, and the coupling function. These findings predict that in random graphs the enhancement of coherence is proportional to the mean degree. In locally connected networks, coherence is no longer controlled by the mean degree but rather by how the mean degree scales with the network size. In these networks, even when the coherence is absent, adding a fraction s of random connections leads to an enhancement of coherence proportional to s. Our results provide a way to control the emergent properties by the manipulation of the dynamics of the elements and the network connectivity.