A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks

Stimulus type shapes the topology of cellular functional networks in mouse visual cortex

On the timescale of sensory processing, neuronal networks have relatively fixed anatomical connectivity, while functional interactions between neurons can vary depending on the ongoing activity of the neurons within the network. We thus hypothesized that different types of stimuli could lead those networks to display stimulus-dependent functional connectivity patterns. To test this hypothesis, we analyzed single-cell resolution electrophysiological data from the Allen Institute, with simultaneous recordings of stimulus-evoked activity from neurons across 6 different regions of mouse visual cortex. Comparing the functional connectivity patterns during different stimulus types, we made several nontrivial observations: (1) while the frequencies of different functional motifs were preserved across stimuli, the identities of the neurons within those motifs changed; (2) the degree to which functional modules are contained within a single brain region increases with stimulus complexity. Altogether, our work reveals unexpected stimulus-dependence to the way groups of neurons interact to process incoming sensory information.

Response inhibition in premotor cortex corresponds to a complex reshuffle of the mesoscopic information network

Recent studies have explored functional and effective neural networks in animal models; however, the dynamics of information propagation among functional modules under cognitive control remain largely unknown. Here, we addressed the issue using transfer entropy and graph theory methods on mesoscopic neural activities recorded in the dorsal premotor cortex of rhesus monkeys. We focused our study on the decision time of a Stop-signal task, looking for patterns in the network configuration that could influence motor plan maturation when the Stop signal is provided. When comparing trials with successful inhibition to those with generated movement, the nodes of the network resulted organized into four clusters, hierarchically arranged, and distinctly involved in information transfer. Interestingly, the hierarchies and the strength of information transmission between clusters varied throughout the task, distinguishing between generated movements and canceled ones and corresponding to measurable levels of network complexity. Our results suggest a putative mechanism for motor inhibition in premotor cortex: a topological reshuffle of the information exchanged among ensembles of neurons.

Fibration symmetry-breaking supports functional transitions in a brain network engaged in language

In his book 'A Beautiful Question' 1, physicist Frank Wilczek argues that symmetry is 'nature's deep design,' governing the behavior of the universe, from the smallest particles to the largest structures 1-4. While symmetry is a cornerstone of physics, it has not yet been found widespread applicability to describe biological systems 5, particularly the human brain. In this context, we study the human brain network engaged in language and explore the relationship between the structural connectivity (connectome or structural network) and the emergent synchronization of the mesoscopic regions of interest (functional network). We explain this relationship through a different kind of symmetry than physical symmetry, derived from the categorical notion of Grothendieck fibrations 6. This introduces a new understanding of the human brain by proposing a local symmetry theory of the connectome, which accounts for how the structure of the brain's network determines its coherent activity. Among the allowed patterns of structural connectivity, synchronization elicits different symmetry subsets according to the functional engagement of the brain. We show that the resting state is a particular realization of the cerebral synchronization pattern characterized by a fibration symmetry that is broken 7 in the transition from rest to language. Our findings suggest that the brain's network symmetry at the local level determines its coherent function, and we can understand this relationship from theoretical principles.

Systematic evaluation of fMRI data-processing pipelines for consistent functional connectomics

Functional interactions between brain regions can be viewed as a network, enabling neuroscientists to investigate brain function through network science. Here, we systematically evaluate 768 data-processing pipelines for network reconstruction from resting-state functional MRI, evaluating the effect of brain parcellation, connectivity definition, and global signal regression. Our criteria seek pipelines that minimise motion confounds and spurious test-retest discrepancies of network topology, while being sensitive to both inter-subject differences and experimental effects of interest. We reveal vast and systematic variability across pipelines' suitability for functional connectomics. Inappropriate choice of data-processing pipeline can produce results that are not only misleading, but systematically so, with the majority of pipelines failing at least one criterion. However, a set of optimal pipelines consistently satisfy all criteria across different datasets, spanning minutes, weeks, and months. We provide a full breakdown of each pipeline's performance across criteria and datasets, to inform future best practices in functional connectomics.

Scaling theory of fractal complex networks

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes with which we cover the network when determining its box dimension. This approach-grounded in both scaling theory of phase transitions and renormalization group theory-leads to the consistent scaling theory of fractal complex networks, which complements the collection of scaling exponents with several new ones and reveals various relationships between them. We propose the introduction of two classes of exponents: microscopic and macroscopic, characterizing the local structure of fractal complex networks and their global properties, respectively. Interestingly, exponents from both classes are related to each other and only a few of them (three out of seven) are independent, thus bridging the local self-similarity and global scale-invariance in fractal networks. We successfully verify our findings in real networks situated in various fields (information-the World Wide Web, biological-the human brain, and social-scientific collaboration networks) and in several fractal network models.

Small vessel disease and cognitive reserve oppositely modulate global network redundancy and cognitive function: A study in middle-to-old aged community participants

Cerebral small vessel disease (SVD) can disrupt the global brain network and lead to cognitive impairment. Conversely, cognitive reserve (CR) can improve one's cognitive ability to handle damaging effects like SVD, partly by optimizing the brain network's organization. Understanding how SVD and CR collectively influence brain networks could be instrumental in preventing cognitive impairment. Recently, brain redundancy has emerged as a critical network protective metric, providing a nuanced perspective of changes in network organization. However, it remains unclear how SVD and CR affect global redundancy and subsequently cognitive function. Here, we included 121 community-dwelling participants who underwent neuropsychological assessments and a multimodal MRI examination. We visually examined common SVD imaging markers and assessed lifespan CR using the Cognitive Reserve Index Questionnaire. We quantified the global redundancy index (RI) based on the dynamic functional connectome. We then conducted multiple linear regressions to explore the specific cognitive domains related to RI and the associations of RI with SVD and CR. We also conducted mediation analyses to explore whether RI mediated the relationships between SVD, CR, and cognition. We found negative correlations of RI with the presence of microbleeds (MBs) and the SVD total score, and a positive correlation of RI with leisure activity-related CR (CRI-leisure). RI was positively correlated with memory and fully mediated the relationships between the MBs, CRI-leisure, and memory. Our study highlights the potential benefits of promoting leisure activities and keeping brain redundancy for memory preservation in older adults, especially those with SVD.

Longitudinal Functional Connectome in Pediatric Concussion: An Advancing Concussion Assessment in Pediatrics Study

Advanced magnetic resonance imaging (MRI) techniques indicate that concussion (i.e., mild traumatic brain injury) disrupts brain structure and function in children. However, the functional connectivity of brain regions within global and local networks (i.e., functional connectome) is poorly understood in pediatric concussion. This prospective, longitudinal study addressed this gap using data from the largest neuroimaging study of pediatric concussion to date to study the functional connectome longitudinally after concussion as compared with mild orthopedic injury (OI). Children and adolescents (n = 967) 8-16.99 years with concussion or mild OI were recruited from pediatric emergency departments within 48 h post-injury. Pre-injury and 1-month post-injury symptom ratings were used to classify concussion with or without persistent symptoms based on reliable change. Subjects completed a post-acute (2-33 days) and chronic (3 or 6 months via random assignment) MRI scan. Graph theory metrics were derived from 918 resting-state functional MRI scans in 585 children (386 concussion/199 OI). Linear mixed-effects modeling was performed to assess group differences over time, correcting for multiple comparisons. Relative to OI, the global clustering coefficient was reduced at 3 months post-injury in older children with concussion and in females with concussion and persistent symptoms. Time post-injury and sex moderated group differences in local (regional) network metrics of several brain regions, including degree centrality, efficiency, and clustering coefficient of the angular gyrus, calcarine fissure, cuneus, and inferior occipital, lingual, middle occipital, post-central, and superior occipital gyrus. Relative to OI, degree centrality and nodal efficiency were reduced post-acutely, and nodal efficiency and clustering coefficient were reduced chronically after concussion (i.e., at 3 and 6 months post-injury in females; at 6 months post-injury in males). Functional network alterations were more robust and widespread chronically as opposed to post-acutely after concussion, and varied by sex, age, and symptom recovery at 1-month post-injury. Local network segregation reductions emerged globally (across the whole brain network) in older children and in females with poor recovery chronically after concussion. Reduced functioning between neighboring regions could negatively disrupt specialized information processing. Local network metric alterations were demonstrated in several posterior regions that are involved in vision and attention after concussion relative to OI. This indicates that functioning of superior parietal and occipital regions could be particularly susceptibile to the effects of concussion. Moreover, those regional alterations were especially apparent at later time periods post-injury, emerging after post-concussive symptoms resolved in most and persisted up to 6 months post-injury, and differed by biological sex. This indicates that neurobiological changes continue to occur up to 6 months after pediatric concussion, although changes emerge earlier in females than in males. Changes could reflect neural compensation mechanisms.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Dissecting muscle synergies in the task space

The muscle synergy is a guiding concept in motor control research that relies on the general notion of muscles 'working together' towards task performance. However, although the synergy concept has provided valuable insights into motor coordination, muscle interactions have not been fully characterised with respect to task performance. Here, we address this research gap by proposing a novel perspective to the muscle synergy that assigns specific functional roles to muscle couplings by characterising their task-relevance. Our novel perspective provides nuance to the muscle synergy concept, demonstrating how muscular interactions can 'work together' in different ways: (1) irrespective of the task at hand but also (2) redundantly or (3) complementarily towards common task-goals. To establish this perspective, we leverage information- and network-theory and dimensionality reduction methods to include discrete and continuous task parameters directly during muscle synergy extraction. Specifically, we introduce co-information as a measure of the task-relevance of muscle interactions and use it to categorise such interactions as task-irrelevant (present across tasks), redundant (shared task information), or synergistic (different task information). To demonstrate these types of interactions in real data, we firstly apply the framework in a simple way, revealing its added functional and physiological relevance with respect to current approaches. We then apply the framework to large-scale datasets and extract generalizable and scale-invariant representations consisting of subnetworks of synchronised muscle couplings and distinct temporal patterns. The representations effectively capture the functional interplay between task end-goals and biomechanical affordances and the concurrent processing of functionally similar and complementary task information. The proposed framework unifies the capabilities of current approaches in capturing distinct motor features while providing novel insights and research opportunities through a nuanced perspective to the muscle synergy.

Mosaic: in-memory computing and routing for small-world spike-based neuromorphic systems

The brain's connectivity is locally dense and globally sparse, forming a small-world graph-a principle prevalent in the evolution of various species, suggesting a universal solution for efficient information routing. However, current artificial neural network circuit architectures do not fully embrace small-world neural network models. Here, we present the neuromorphic Mosaic: a non-von Neumann systolic architecture employing distributed memristors for in-memory computing and in-memory routing, efficiently implementing small-world graph topologies for Spiking Neural Networks (SNNs). We've designed, fabricated, and experimentally demonstrated the Mosaic's building blocks, using integrated memristors with 130 nm CMOS technology. We show that thanks to enforcing locality in the connectivity, routing efficiency of Mosaic is at least one order of magnitude higher than other SNN hardware platforms. This is while Mosaic achieves a competitive accuracy in a variety of edge benchmarks. Mosaic offers a scalable approach for edge systems based on distributed spike-based computing and in-memory routing.

Fractal Geometry Meets Computational Intelligence: Future Perspectives

Characterizations in terms of fractals are typically employed for systems with complex and multiscale descriptions. A prominent example of such systems is provided by the human brain, which can be idealized as a complex dynamical system made of many interacting subunits. The human brain can be modeled in terms of observable variables together with their spatio-temporal-functional relations. Computational intelligence is a research field bridging many nature-inspired computational methods, such as artificial neural networks, fuzzy systems, and evolutionary and swarm intelligence optimization techniques. Typical problems faced by means of computational intelligence methods include those of recognition, such as classification and prediction. Although historically conceived to operate in some vector space, such methods have been recently extended to the so-called nongeometric spaces, considering labeled graphs as the most general example of such patterns. Here, we suggest that fractal analysis and computational intelligence methods can be exploited together in neuroscience research. Fractal characterizations can be used to (i) assess scale-invariant properties and (ii) offer numeric, feature-based representations to complement the usually more complex pattern structures encountered in neurosciences. Computational intelligence methods could be used to exploit such fractal characterizations, considering also the possibility to perform data-driven analysis of nongeometric input spaces, therby overcoming the intrinsic limits related to Euclidean geometry.

Fractals in Neuroanatomy and Basic Neurosciences: An Overview

The introduction of fractal geometry to the neurosciences has been a major paradigm shift over the last decades as it has helped overcome approximations and limitations that occur when Euclidean and reductionist approaches are used to analyze neurons or the entire brain. Fractal geometry allows for quantitative analysis and description of the geometric complexity of the brain, from its single units to the neuronal networks.As illustrated in the second section of this book, fractal analysis provides a quantitative tool for the study of the morphology of brain cells (i.e., neurons and microglia) and its components (e.g., dendritic trees, synapses), as well as the brain structure itself (cortex, functional modules, neuronal networks). The self-similar logic which generates and shapes the different hierarchical systems of the brain and even some structures related to its "container," that is, the cranial sutures on the skull, is widely discussed in the following chapters, with a link between the applications of fractal analysis to the neuroanatomy and basic neurosciences to the clinical applications discussed in the third section.

The Structure of Hippocampal CA1 Interactions Optimizes Spatial Coding across Experience

Although much is known about how single neurons in the hippocampus represent an animal's position, how circuit interactions contribute to spatial coding is less well understood. Using a novel statistical estimator and theoretical modeling, both developed in the framework of maximum entropy models, we reveal highly structured CA1 cell-cell interactions in male rats during open field exploration. The statistics of these interactions depend on whether the animal is in a familiar or novel environment. In both conditions the circuit interactions optimize the encoding of spatial information, but for regimes that differ in the informativeness of their spatial inputs. This structure facilitates linear decodability, making the information easy to read out by downstream circuits. Overall, our findings suggest that the efficient coding hypothesis is not only applicable to individual neuron properties in the sensory periphery, but also to neural interactions in the central brain.SIGNIFICANCE STATEMENT Local circuit interactions play a key role in neural computation and are dynamically shaped by experience. However, measuring and assessing their effects during behavior remains a challenge. Here, we combine techniques from statistical physics and machine learning to develop new tools for determining the effects of local network interactions on neural population activity. This approach reveals highly structured local interactions between hippocampal neurons, which make the neural code more precise and easier to read out by downstream circuits, across different levels of experience. More generally, the novel combination of theory and data analysis in the framework of maximum entropy models enables traditional neural coding questions to be asked in naturalistic settings.

Multifractality of Complex Networks Is Also Due to Geometry: A Geometric Sandbox Algorithm

Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity, which often manifests itself in a fractal or even multifractal structure. As a generalization of fractal analysis, the multifractal analysis of complex networks is a useful tool for identifying and quantitatively describing the spatial hierarchy of both theoretical and numerical fractal patterns. Nowadays, there are many methods of multifractal analysis. However, all these methods take into account only the fact of connection between nodes (and eventually the weight of edges) and do not take into account the real positions (coordinates) of nodes in space. However, intuition suggests that the geometry of network nodes' position should have a significant impact on the true fractal structure. Many networks identified in nature (e.g., air connection networks, energy networks, social networks, mountain ridge networks, networks of neurones in the brain, and street networks) have their own often unique and characteristic geometry, which is not taken into account in the identification process of multifractality in commonly used methods. In this paper, we propose a multifractal network analysis method that takes into account both connections between nodes and the location coordinates of nodes (network geometry). We show the results for different geometrical variants of the same network and reveal that this method, contrary to the commonly used method, is sensitive to changes in network geometry. We also carry out tests for synthetic as well as real-world networks.

Identifying the Neural Bases of Math Competence Based on Structural and Functional Properties of the Human Brain

Human populations show large individual differences in math performance and math learning abilities. Early math skill acquisition is critical for providing the foundation for higher quantitative skill acquisition and succeeding in modern society. However, the neural bases underlying individual differences in math competence remain unclear. Modern neuroimaging techniques allow us to not only identify distinct local cortical regions but also investigate large-scale neural networks underlying math competence both structurally and functionally. To gain insights into the neural bases of math competence, this review provides an overview of the structural and functional neural markers for math competence in both typical and atypical populations of children and adults. Although including discussion of arithmetic skills in children, this review primarily focuses on the neural markers associated with complex math skills. Basic number comprehension and number comparison skills are outside the scope of this review. By synthesizing current research findings, we conclude that neural markers related to math competence are not confined to one particular region; rather, they are characterized by a distributed and interconnected network of regions across the brain, primarily focused on frontal and parietal cortices. Given that human brain is a complex network organized to minimize the cost of information processing, an efficient brain is capable of integrating information from different regions and coordinating the activity of various brain regions in a manner that maximizes the overall efficiency of the network to achieve the goal. We end by proposing that frontoparietal network efficiency is critical for math competence, which enables the recruitment of task-relevant neural resources and the engagement of distributed neural circuits in a goal-oriented manner. Thus, it will be important for future studies to not only examine brain activation patterns of discrete regions but also examine distributed network patterns across the brain, both structurally and functionally.

Stimulus-dependent functional network topology in mouse visual cortex

Information is processed by networks of neurons in the brain. On the timescale of sensory processing, those neuronal networks have relatively fixed anatomical connectivity, while functional connectivity, which defines the interactions between neurons, can vary depending on the ongoing activity of the neurons within the network. We thus hypothesized that different types of stimuli, which drive different neuronal activities in the network, could lead those networks to display stimulus-dependent functional connectivity patterns. To test this hypothesis, we analyzed electrophysiological data from the Allen Brain Observatory, which utilized Neuropixels probes to simultaneously record stimulus-evoked activity from hundreds of neurons across 6 different regions of mouse visual cortex. The recordings had single-cell resolution and high temporal fidelity, enabling us to determine fine-scale functional connectivity. Comparing the functional connectivity patterns observed when different stimuli were presented to the mice, we made several nontrivial observations. First, while the frequencies of different connectivity motifs (i.e., the patterns of connectivity between triplets of neurons) were preserved across stimuli, the identities of the neurons within those motifs changed. This means that functional connectivity dynamically changes along with the input stimulus, but does so in a way that preserves the motif frequencies. Secondly, we found that the degree to which functional modules are contained within a single brain region (as opposed to being distributed between regions) increases with increasing stimulus complexity. This suggests a mechanism for how the brain could dynamically alter its computations based on its inputs. Altogether, our work reveals unexpected stimulus-dependence to the way groups of neurons interact to process incoming sensory information.

Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

Understanding how different areas of the human brain communicate with each other is a crucial issue in neuroscience. The concepts of structural, functional and effective connectivity have been widely exploited to describe the human connectome, consisting of brain networks, their structural connections and functional interactions. Despite high-spatial-resolution imaging techniques such as functional magnetic resonance imaging (fMRI) being widely used to map this complex network of multiple interactions, electroencephalographic (EEG) recordings claim high temporal resolution and are thus perfectly suitable to describe either spatially distributed and temporally dynamic patterns of neural activation and connectivity. In this work, we provide a technical account and a categorization of the most-used data-driven approaches to assess brain-functional connectivity, intended as the study of the statistical dependencies between the recorded EEG signals. Different pairwise and multivariate, as well as directed and non-directed connectivity metrics are discussed with a pros-cons approach, in the time, frequency, and information-theoretic domains. The establishment of conceptual and mathematical relationships between metrics from these three frameworks, and the discussion of novel methodological approaches, will allow the reader to go deep into the problem of inferring functional connectivity in complex networks. Furthermore, emerging trends for the description of extended forms of connectivity (e.g., high-order interactions) are also discussed, along with graph-theory tools exploring the topological properties of the network of connections provided by the proposed metrics. Applications to EEG data are reviewed. In addition, the importance of source localization, and the impacts of signal acquisition and pre-processing techniques (e.g., filtering, source localization, and artifact rejection) on the connectivity estimates are recognized and discussed. By going through this review, the reader could delve deeply into the entire process of EEG pre-processing and analysis for the study of brain functional connectivity and learning, thereby exploiting novel methodologies and approaches to the problem of inferring connectivity within complex networks.

The Entangled Brain

The Entangled Brain (Pessoa, L., 2002. MIT Press) promotes the idea that we need to understand the brain as a complex, entangled system. Why does the complex systems perspective, one that entails emergent properties, matter for brain science? In fact, many neuroscientists consider these ideas a distraction. We discuss three principles of brain organization that inform the question of the interactional complexity of the brain: (1) massive combinatorial anatomical connectivity; (2) highly distributed functional coordination; and (3) networks/circuits as functional units. To motivate the challenges of mapping structure and function, we discuss neural circuits illustrating the high anatomical and functional interactional complexity typical in the brain. We discuss potential avenues for testing for network-level properties, including those relying on distributed computations across multiple regions. We discuss implications for brain science, including the need to characterize decentralized and heterarchical anatomical-functional organization. The view advocated has important implications for causation, too, because traditional accounts of causality provide poor candidates for explanation in interactionally complex systems like the brain given the distributed, mutual, and reciprocal nature of the interactions. Ultimately, to make progress understanding how the brain supports complex mental functions, we need to dissolve boundaries within the brain-those suggested to be associated with perception, cognition, action, emotion, motivation-as well as outside the brain, as we bring down the walls between biology, psychology, mathematics, computer science, philosophy, and so on.

Investigating cognitive neuroscience theories of human intelligence: A connectome-based predictive modeling approach

Central to modern neuroscientific theories of human intelligence is the notion that general intelligence depends on a primary brain region or network, engaging spatially localized (rather than global) neural representations. Recent findings in network neuroscience, however, challenge this assumption, providing evidence that general intelligence may depend on system-wide network mechanisms, suggesting that local representations are necessary but not sufficient to account for the neural architecture of human intelligence. Despite the importance of this key theoretical distinction, prior research has not systematically investigated the role of local versus global neural representations in predicting general intelligence. We conducted a large-scale connectome-based predictive modeling study (N = 297), administering resting-state fMRI and a comprehensive cognitive battery to evaluate the efficacy of modern neuroscientific theories of human intelligence, including spatially localized theories (Lateral Prefrontal Cortex Theory, Parieto-Frontal Integration Theory, and Multiple Demand Theory) and recent global accounts (Process Overlap Theory and Network Neuroscience Theory). The results of our study demonstrate that general intelligence can be predicted by local functional connectivity profiles but is most robustly explained by global profiles of whole-brain connectivity. Our findings further suggest that the improved efficacy of global theories is not reducible to a greater strength or number of connections, but instead results from considering both strong and weak connections that provide the basis for intelligence (as predicted by the Network Neuroscience Theory). Our results highlight the importance of considering local neural representations in the context of a global information-processing architecture, suggesting future directions for theory-driven research on system-wide network mechanisms underlying general intelligence.

Omnipresence of the sensorimotor-association axis topography in the human connectome

Low-dimensional representations are increasingly used to study meaningful organizational principles within the human brain. Most notably, the sensorimotor-association axis consistently explains the most variance in the human connectome as its so-called principal gradient, suggesting that it represents a fundamental organizational principle. While recent work indicates these low dimensional representations are relatively robust, they are limited by modeling only certain aspects of the functional connectivity structure. To date, the majority of studies have restricted these approaches to the strongest connections in the brain, treating weaker or negative connections as noise despite evidence of meaningful structure among them. The present work examines connectivity gradients of the human connectome across a full range of connectivity strengths and explores the implications for outcomes of individual differences, identifying potential dependencies on thresholds and opportunities to improve prediction tasks. Interestingly, the sensorimotor-association axis emerged as the principal gradient of the human connectome across the entire range of connectivity levels. Moreover, the principal gradient of connections at intermediate strengths encoded individual differences, better followed individual-specific anatomical features, and was also more predictive of intelligence. Taken together, our results add to evidence of the sensorimotor-association axis as a fundamental principle of the brain's functional organization, since it is evident even in the connectivity structure of more lenient connectivity thresholds. These more loosely coupled connections further appear to contain valuable and potentially important information that could be used to improve our understanding of individual differences, diagnosis, and the prediction of treatment outcomes.

Network evolution of regional brain volumes in young children reflects neurocognitive scores and mother's education

The maturation of regional brain volumes from birth to preadolescence is a critical developmental process that underlies emerging brain structural connectivity and function. Regulated by genes and environment, the coordinated growth of different brain regions plays an important role in cognitive development. Current knowledge about structural network evolution is limited, partly due to the sparse and irregular nature of most longitudinal neuroimaging data. In particular, it is unknown how factors such as mother's education or sex of the child impact the structural network evolution. To address this issue, we propose a method to construct evolving structural networks and study how the evolving connections among brain regions as reflected at the network level are related to maternal education and biological sex of the child and also how they are associated with cognitive development. Our methodology is based on applying local Fréchet regression to longitudinal neuroimaging data acquired from the RESONANCE cohort, a cohort of healthy children (245 females and 309 males) ranging in age from 9 weeks to 10 years. Our findings reveal that sustained highly coordinated volume growth across brain regions is associated with lower maternal education and lower cognitive development. This suggests that higher neurocognitive performance levels in children are associated with increased variability of regional growth patterns as children age.

Test-retest reliability of modular-relevant analysis in brain functional network

Introduction

The human brain could be modeled as a complex network via functional magnetic resonance imaging (fMRI), and the architecture of these brain functional networks can be studied from multiple spatial scales with different graph theory tools. Detecting modules is an important mesoscale network measuring approach that has provided crucial insights for uncovering how brain organizes itself among different functional subsystems. Despite its successful application in a wide range of brain network studies, the lack of comprehensive reliability assessment prevents its potential extension to clinical trials.

Methods

To fill this gap, this paper, using resting-state test-retest fMRI data, systematically explored the reliabilities of five popular network metrics derived from modular structure. Considering the repeatability of network partition depends heavily on network size and module detection algorithm, we constructed three types of brain functional networks for each subject by using a set of coarse-to-fine brain atlases and adopted four methods for single-subject module detection and twelve methods for group-level module detection.

Results

The results reported moderate-to-good reliability in modularity, intra- and inter-modular functional connectivities, within-modular degree and participation coefficient at both individual and group levels, indicating modular-relevant network metrics can provide robust evaluation results. Further analysis identified the significant influence of module detection algorithm and node definition approach on reliabilities of network partitions and its derived network analysis results.

Discussion

This paper provides important guidance for choosing reliable modular-relevant network metrics and analysis strategies in future studies.

May the 4C's be with you: an overview of complexity-inspired frameworks for analysing resting-state neuroimaging data

Competing and complementary models of resting-state brain dynamics contribute to our phenomenological and mechanistic understanding of whole-brain coordination and communication, and provide potential evidence for differential brain functioning associated with normal and pathological behaviour. These neuroscientific theories stem from the perspectives of physics, engineering, mathematics and psychology and create a complicated landscape of domain-specific terminology and meaning, which, when used outside of that domain, may lead to incorrect assumptions and conclusions within the neuroscience community. Here, we review and clarify the key concepts of connectivity, computation, criticality and coherence-the 4C's-and outline a potential role for metastability as a common denominator across these propositions. We analyse and synthesize whole-brain neuroimaging research, examined through functional magnetic imaging, to demonstrate that complexity science offers a principled and integrated approach to describe, and potentially understand, macroscale spontaneous brain functioning.

A New Method of Quantifying the Complexity of Fractal Networks

There is a large body of research devoted to identifying the complexity of structures in networks. In the context of network theory, a complex network is a graph with nontrivial topological features—features that do not occur in simple networks, such as lattices or random graphs, but often occur in graphs modeling real systems. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks, such as computer networks and logistic transport networks. Transport is of great importance for the economic and cultural cooperation of any country with other countries, the strengthening and development of the economic management system, and in solving social and economic problems. Provision of the territory with a well-developed transport system is one of the factors for attracting population and production, serving as an important advantage for locating productive forces and providing an integration effect. In this paper, we introduce a new method for quantifying the complexity of a network based on presenting the nodes of the network in Cartesian coordinates, converting to polar coordinates, and calculating the fractal dimension using the ReScaled ranged (R/S) method. Our results suggest that this approach can be used to determine complexity for any type of network that has fixed nodes, and it presents an application of this method in the public transport system.

A More Female-Characterized Resting-State Brain: Graph Similarity Analyses of Sex Influence on the Human Brain Intrinsic Functional Network

It remains unclear whether human species exhibits sexual dimorphism in brain activities, and how the dimorphisms associated with sex-characterized behaviors. Here, in a large dataset from Human Connectome Project, we investigated sex differences of resting-state network structure by using local and global network graph similarity analysis. The "typical male" and "typical female" resting-state networks were highly similar. However, we found significant inter-sex difference in all local brain networks compared with sex-label permutations. The global and many local network topologies showed significant higher intra-female similarity, while males' network topologies were more dissimilar to each other. Additionally, by using global graph similarity analysis, we found that female individuals whose brain network were more similar to the average pattern present lower social-related anger, lower social distress and better companionships, while similar effects were not detected for males. Our study confirms the existence of sex-related resting-state network topology. Female's intrinsic brain is closer to a typical pattern than male's, and they may more fulfill the "similarity breeds connection" principle in building social ties.

Network medicine in ovarian cancer: topological properties to drug discovery

Network medicine provides network theoretical tools, methods and properties to study underlying laws governing human interactome to identify disease states and disease complexity leading to drug discovery. Within this framework, we investigated the topological properties of ovarian cancer network (OCN) and the roles of hubs to understand OCN organization to address disease states and complexity. The OCN constructed from the experimentally verified genes exhibits fractal nature in the topological properties with deeply rooted functional communities indicating self-organizing behavior. The network properties at all levels of organization obey one parameter scaling law which lacks centrality lethality rule. We showed that $\langle k\rangle $ can be taken as a scaling parameter, where, power law exponent can be estimated from the ratio of network diameters. The betweenness centrality $C_B$ shows two distinct behaviors one shown by high degree hubs and the other by segregated low degree nodes. The $C_B$ power law exponent is found to connect the exponents of distributions of high and low degree nodes. OCN showed the absence of rich-club formation which leads to the missing of a number of attractors in the network causing formation of weakly tied diverse functional modules to keep optimal network efficiency. In OCN, provincial and connector hubs, which includes identified key regulators, take major responsibility to keep the OCN integrity and organization. Further, most of the key regulators are found to be over expressed and positively correlated with immune infiltrates. Finally, few potential drugs are identified related to the key regulators.

Characteristic functional cores revealed by hyperbolic disc embedding and k-core percolation on resting-state fMRI

Hyperbolic disc embedding and k-core percolation reveal the hierarchical structure of functional connectivity on resting-state fMRI (rsfMRI). Using 180 normal adults’ rsfMRI data from the human connectome project database, we visualized inter-voxel relations by embedding voxels on the hyperbolic space using the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{S}}^{1} /{\mathbb{H}}^{2}$$\end{document}S1/H2 model. We also conducted k-core percolation on 30 participants to investigate core voxels for each individual. It recursively peels the layer off, and this procedure leaves voxels embedded in the center of the hyperbolic disc. We used independent components to classify core voxels, and it revealed stereotypes of individuals such as visual network dominant, default mode network dominant, and distributed patterns. Characteristic core structures of resting-state brain connectivity of normal subjects disclosed the distributed or asymmetric contribution of voxels to the k_max-core, which suggests the hierarchical dominance of certain IC subnetworks characteristic of subgroups of individuals at rest.

Telling functional networks apart using ranked network features stability

Over the past few years, it has become standard to describe brain anatomical and functional organisation in terms of complex networks, wherein single brain regions or modules and their connections are respectively identified with network nodes and the links connecting them. Often, the goal of a given study is not that of modelling brain activity but, more basically, to discriminate between experimental conditions or populations, thus to find a way to compute differences between them. This in turn involves two important aspects: defining discriminative features and quantifying differences between them. Here we show that the ranked dynamical stability of network features, from links or nodes to higher-level network properties, discriminates well between healthy brain activity and various pathological conditions. These easily computable properties, which constitute local but topographically aspecific aspects of brain activity, greatly simplify inter-network comparisons and spare the need for network pruning. Our results are discussed in terms of microstate stability. Some implications for functional brain activity are discussed.

A network information theoretic framework to characterise muscle synergies in space and time

Objective Current approaches to muscle synergy extraction rely on linear dimensionality reduction algorithms that make specific assumptions on the underlying signals. However, to capture nonlinear time varying, large-scale but also muscle-specific interactions, a more generalised approach is required. Approach Here we developed a novel framework for muscle synergy extraction that relaxes model assumptions by using a combination of information- and network theory and dimensionality reduction. We first quantify informational dynamics between muscles, time-samples or muscle-time pairings using a novel mutual information formulation. We then model these pairwise interactions as multiplex networks and identify modules representing the network architecture. We employ this modularity criterion as the input parameter for dimensionality reduction, which verifiably extracts the identified modules, and also to characterise salient structures within each module. Main results This novel framework captures spatial, temporal and spatiotemporal interactions across two benchmark datasets of reaching movements, producing distinct spatial groupings and both tonic and phasic temporal patterns. Readily interpretable muscle synergies spanning multiple spatial and temporal scales were identified, demonstrating significant task dependence, ability to capture trial-to-trial fluctuations and concordance across participants. Furthermore, our framework identifies submodular structures that represent the distributed networks of co-occurring signal interactions across scales. Significance The capabilities of this framework are illustrated through the concomitant continuity with previous research and novelty of the insights gained. Several previous limitations are circumvented including the extraction of functionally meaningful and multiplexed pairwise muscle couplings under relaxed model assumptions. The extracted synergies provide a holistic view of the movement while important details of task performance are readily interpretable. The identified muscle groupings transcend biomechanical constraints and the temporal patterns reveal characteristics of fundamental motor control mechanisms. We conclude that this framework opens new opportunities for muscle synergy research and can constitute a bridge between existing models and recent network-theoretic endeavours.

Increased network centrality of the anterior insula in early abstinence from alcohol

Abnormal resting‐state functional connectivity, as measured by functional magnetic resonance imaging (MRI), has been reported in alcohol use disorders (AUD), but findings are so far inconsistent. Here, we exploited recent developments in graph‐theoretical analyses, enabling improved resolution and fine‐grained representation of brain networks, to investigate functional connectivity in 35 recently detoxified alcohol dependent patients versus 34 healthy controls. Specifically, we focused on the modular organization, that is, the presence of tightly connected substructures within a network, and on the identification of brain regions responsible for network integration using an unbiased approach based on a large‐scale network composed of more than 600 a priori defined nodes. We found significant reductions in global connectivity and region‐specific disruption in the network topology in patients compared with controls. Specifically, the basal brain and the insular–supramarginal cortices, which form tightly coupled modules in healthy subjects, were fragmented in patients. Further, patients showed a strong increase in the centrality of the anterior insula, which exhibited stronger connectivity to distal cortical regions and weaker connectivity to the posterior insula. Anterior insula centrality, a measure of the integrative role of a region, was significantly associated with increased risk of relapse. Exploratory analysis suggests partial recovery of modular structure and insular connectivity in patients after 2 weeks. These findings support the hypothesis that, at least during the early stages of abstinence, the anterior insula may drive exaggerated integration of interoceptive states in AUD patients with possible consequences for decision making and emotional states and that functional connectivity is dynamically changing during treatment.

Modular community structure of the face network supports face recognition

Face recognition is dependent on computations conducted in specialized brain regions and the communication among them, giving rise to the face-processing network. We examined whether modularity of this network may underlie the vast individual differences found in human face recognition abilities. Modular networks, characterized by strong within and weaker between-network connectivity, were previously suggested to promote efficacy and reduce interference among cognitive systems and also correlated with better cognitive abilities. The study was conducted in a large sample (n = 409) with diffusion-weighted imaging, resting-state fMRI, and a behavioral face recognition measure. We defined a network of face-selective regions and derived a novel measure of communication along with structural and functional connectivity among them. The modularity of this network was positively correlated with recognition abilities even when controlled for age. Furthermore, the results were specific to the face network when compared with the place network or to spatially permuted null networks. The relation to behavior was also preserved at the individual-edge level such that a larger correlation to behavior was found within hemispheres and particularly within the right hemisphere. This study provides the first evidence of modularity-behavior relationships in the domain of face processing and more generally in visual perception.

Mapping covariance in brain FDG uptake to structural connectivity

PURPOSE

Inter-subject covariance of regional 18F-fluorodeoxyglucose (FDG) PET measures (FDG_cov) as proxy of brain connectivity has been gaining an increasing acceptance in the community. Yet, it is still unclear to what extent FDG_cov is underlied by actual structural connectivity via white matter fiber tracts. In this study, we quantified the degree of spatial overlap between FDG_cov and structural connectivity networks.

METHODS

We retrospectively analyzed neuroimaging data from 303 subjects, both patients with suspected neurodegenerative disorders and healthy individuals. For each subject, structural magnetic resonance, diffusion tensor imaging, and FDG-PET data were available. The images were spatially normalized to a standard space and segmented into 62 anatomical regions using a probabilistic atlas. Sparse inverse covariance estimation was employed to estimate FDG_cov. Structural connectivity was measured by streamline tractography through fiber assignment by continuous tracking.

RESULTS

For the whole brain, 55% of detected connections were found to be convergent, i.e., present in both FDG_cov and structural networks. This metric for random networks was significantly lower, i.e., 12%. Convergent were 80% of intralobe connections and only 30% of interhemispheric interlobe connections.

CONCLUSION

Structural connectivity via white matter fiber tracts is a relevant substrate of FDG_cov, underlying around a half of connections at the whole brain level. Short-range white matter tracts appear to be a major substrate of intralobe FDG_cov connections.

Connectivity of EEG synchronization networks increases for Parkinson's disease patients with freezing of gait

Freezing of gait (FoG), a paroxysmal gait disturbance commonly experienced by patients with Parkinson's disease (PD), is characterized by sudden episodes of inability to generate effective forward stepping. Recent studies have shown an increase in beta frequency of local-field potentials in the basal-ganglia during FoG, however, comprehensive research on the synchronization between different brain locations and frequency bands in PD patients is scarce. Here, by developing tools based on network science and non-linear dynamics, we analyze synchronization networks of electroencephalography (EEG) brain waves of three PD patient groups with different FoG severity. We find higher EEG amplitude synchronization (stronger network links) between different brain locations as PD and FoG severity increase. These results are consistent across frequency bands (theta, alpha, beta, gamma) and independent of the specific motor task (walking, still standing, hand tapping) suggesting that an increase in severity of PD and FoG is associated with stronger EEG networks over a broad range of brain frequencies. This observation of a direct relationship of PD/FoG severity with overall EEG synchronization together with our proposed EEG synchronization network approach may be used for evaluating FoG propensity and help to gain further insight into PD and the pathophysiology leading to FoG.

The functional brain favours segregated modular connectivity at old age unless affected by neurodegeneration

Brain's modular connectivity gives this organ resilience and adaptability. The ageing process alters the organised modularity of the brain and these changes are further accentuated by neurodegeneration, leading to disorganisation. To understand this further, we analysed modular variability-heterogeneity of modules-and modular dissociation-detachment from segregated connectivity-in two ageing cohorts and a mixed cohort of neurodegenerative diseases. Our results revealed that the brain follows a universal pattern of high modular variability in metacognitive brain regions: the association cortices. The brain in ageing moves towards a segregated modular structure despite presenting with increased modular heterogeneity-modules in older adults are not only segregated, but their shape and size are more variable than in young adults. In the presence of neurodegeneration, the brain maintains its segregated connectivity globally but not locally, and this is particularly visible in dementia with Lewy bodies and Parkinson's disease dementia; overall, the modular brain shows patterns of differentiated pathology.

Principles and open questions in functional brain network reconstruction

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

The unbalanced reorganization of weaker functional connections induces the altered brain network topology in schizophrenia

Network neuroscience shed some light on the functional and structural modifications occurring to the brain associated with the phenomenology of schizophrenia. In particular, resting-state functional networks have helped our understanding of the illness by highlighting the global and local alterations within the cerebral organization. We investigated the robustness of the brain functional architecture in 44 medicated schizophrenic patients and 40 healthy comparators through an advanced network analysis of resting-state functional magnetic resonance imaging data. The networks in patients showed more resistance to disconnection than in healthy controls, with an evident discrepancy between the two groups in the node degree distribution computed along a percolation process. Despite a substantial similarity of the basal functional organization between the two groups, the expected hierarchy of healthy brains' modular organization is crumbled in schizophrenia, showing a peculiar arrangement of the functional connections, characterized by several topologically equivalent backbones. Thus, the manifold nature of the functional organization's basal scheme, together with its altered hierarchical modularity, may be crucial in the pathogenesis of schizophrenia. This result fits the disconnection hypothesis that describes schizophrenia as a brain disorder characterized by an abnormal functional integration among brain regions.

The modulation of brain network integration and arousal during exploration

There is growing interest in how neuromodulators shape brain networks. Recent neuroimaging studies provide evidence that brainstem arousal systems, such as the locus coeruleus-norepinephrine system (LC-NE), influence functional connectivity and brain network topology, suggesting they have a role in flexibly reconfiguring brain networks in order to adapt behavior and cognition to environmental demands. To date, however, the relationship between brainstem arousal systems and functional connectivity has not been assessed within the context of a task with an established relationship between arousal and behavior, with most prior studies relying on incidental variations in arousal or pharmacological manipulation and static brain networks constructed over long periods of time. These factors have likely contributed to a heterogeneity of effects across studies. To address these issues, we took advantage of the association between LC-NE-linked arousal and exploration to probe the relationships between exploratory choice, arousal—as measured indirectly via pupil diameter—and brain network dynamics. Exploration in a bandit task was associated with a shift toward fewer, more weakly connected modules that were more segregated in terms of connectivity and topology but more integrated with respect to the diversity of cognitive systems represented in each module. Functional connectivity strength decreased, and changes in connectivity were correlated with changes in pupil diameter, in line with the hypothesis that brainstem arousal systems influence the dynamic reorganization of brain networks. More broadly, we argue that carefully aligning dynamic network analyses with task designs can increase the temporal resolution at which behaviorally- and cognitively-relevant modulations can be identified, and offer these results as a proof of concept of this approach.

Spike signal transmission between modules and the predictability of spike activity in modular neuronal networks

Modularity is a common feature of the nervous system across species and scales. Although it has been qualitatively investigated in network science, very little is known about how it affects spike signal transmission in neuronal networks at the mesoscopic level. Here, a neuronal network model is built to simulate dynamic interactions among different modules of neuronal networks. This neuronal network model follows the organizational principle of modular structure. The neurons can generate spikes like biological neurons, and changes in the strength of synaptic connections conform to the STDP learning rule. Based on this neuronal network model, we first quantitatively studied whether and to what extent the connectivity within and between modules can affect spike signal transmission, and found that spike signal transmission heavily depends on the connectivity between modules, but has little to do with the connectivity within modules. More importantly, we further found that the spike activity of a module can be predicted according to the spike activities of its adjacent modules through building a resting-state functional connectivity matrix.

Promises and pitfalls of topological data analysis for brain connectivity analysis

Developing sensitive and reliable methods to distinguish normal and abnormal brain states is a key neuroscientific challenge. Topological Data Analysis, despite its relative novelty, already generated many promising applications, including in neuroscience. We conjecture its prominent tool of persistent homology may benefit from going beyond analysing structural and functional connectivity to effective connectivity graphs capturing the direct causal interactions or information flows. Therefore, we assess the potential of persistent homology to directed brain network analysis by testing its discriminatory power in two distinctive examples of disease-related brain connectivity alterations: epilepsy and schizophrenia. We estimate connectivity from functional magnetic resonance imaging and electrophysiology data, employ Persistent Homology and quantify its ability to distinguish healthy from diseased brain states by applying a support vector machine to features quantifying persistent homology structure. We show how this novel approach compares to classification using standard undirected approaches and original connectivity matrices. In the schizophrenia classification, topological data analysis generally performs close to random, while classifications from raw connectivity perform substantially better; potentially due to topographical, rather than topological, specificity of the differences. In the easier task of seizure discrimination from scalp electroencephalography data, classification based on persistent homology features generally reached comparable performance to using raw connectivity, albeit with typically smaller accuracies obtained for the directed (effective) connectivity compared to the undirected (functional) connectivity. Specific applications for topological data analysis may open when direct comparison of connectivity matrices is unsuitable - such as for intracranial electrophysiology with individual number and location of measurements. While standard homology performed overall better than directed homology, this could be due to notorious technical problems of accurate effective connectivity estimation.

Computationally efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive for MFA of large-scale networks with tens of millions of nodes. It is also not clear whether MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of networks, our CESA employs the compressed sparse row format of the adjacency matrix and the breadth-first search technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. Then the CESA is demonstrated to be effective, efficient, and feasible through the MFA results of (u,v)-flower model networks from the fifth to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

Monolingual and bilingual language networks in healthy subjects using functional MRI and graph theory

Bilingualism requires control of multiple language systems, and may lead to architectural differences in language networks obtained from clinical fMRI tasks. Emerging connectivity metrics such as k-core may capture these differences, highlighting crucial network components based on resiliency. We investigated the influence of bilingualism on clinical fMRI language tasks and characterized bilingual networks using connectivity metrics to provide a patient care benchmark. Sixteen right-handed subjects (mean age 42-years; nine males) without neurological history were included: eight native English-speaking monolinguals and eight native Spanish-speaking (L1) bilinguals with acquired English (L2). All subjects underwent fMRI with gold-standard clinical language tasks. Starting from active clusters on fMRI, we inferred the persistent functional network across subjects and ran centrality measures to characterize differences. Our results demonstrated a persistent network "core" consisting of Broca's area, the pre-supplementary motor area, and the premotor area. K-core analysis showed that Wernicke's area was engaged by the "core" with weaker connection in L2 than L1.

Preserved fractal character of structural brain networks is associated with covert consciousness after severe brain injury

•

We study structural brain networks in patients with disorders of consciousness (DOC)

•

Structural brain networks are less fractal (self-similar) in patients than controls.

•

Preserved fractal dimension is associated with covert consciousness in DOC patients.

Self-similarity is ubiquitous throughout natural phenomena, including the human brain. Recent evidence indicates that fractal dimension of functional brain networks, a measure of self-similarity, is diminished in patients diagnosed with disorders of consciousness arising from severe brain injury. Here, we set out to investigate whether loss of self-similarity is observed in the structural connectome of patients with disorders of consciousness. Using diffusion MRI tractography from N = 11 patients in a minimally conscious state (MCS), N = 10 patients diagnosed with unresponsive wakefulness syndrome (UWS), and N = 20 healthy controls, we show that fractal dimension of structural brain networks is diminished in DOC patients. Remarkably, we also show that fractal dimension of structural brain networks is preserved in patients who exhibit evidence of covert consciousness by performing mental imagery tasks during functional MRI scanning. These results demonstrate that differences in fractal dimension of structural brain networks are quantitatively associated with chronic loss of consciousness induced by severe brain injury, highlighting the close connection between structural organisation of the human brain and its ability to support cognitive function.

Detecting network anomalies using Forman-Ricci curvature and a case study for human brain networks

We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (adhd). We express the task for finding changes as a network anomaly detection problem on temporal networks. We propose the use of a curvature measure based on the Forman–Ricci curvature, which expresses higher-order correlations among two connected nodes. Our theoretical result on comparing this Forman–Ricci curvature with another well-known notion of network curvature, namely the Ollivier–Ricci curvature, lends further justification to the assertions that these two notions of network curvatures are not well correlated and therefore one of these curvature measures cannot be used as an universal substitute for the other measure. Our experimental results indicate nine critical edges whose curvature differs dramatically in brains of adhd patients compared to healthy brains. The importance of these edges is supported by existing neuroscience evidence. We demonstrate that comparative analysis of curvature identifies changes that more traditional approaches, for example analysis of edge weights, would not be able to identify.

A Fast Transform for Brain Connectivity Difference Evaluation

Anatomical and dynamical connectivity are essential to healthy brain function. However, quantifying variations in connectivity across conditions or between patient populations and appraising their functional significance are highly non-trivial tasks. Here we show that link ranking differences induce specific geometries in a convenient auxiliary space that are often easily recognisable at mere eye inspection. Link ranking can also provide fast and reliable criteria for network reconstruction parameters for which no theoretical guideline has been proposed.

Heritability of brain resilience to perturbation in humans

Resilience is the capacity of complex systems to persist in the face of external perturbations and retain their functional properties and performance. In the present study, we investigated how individual variations in brain resilience, which might influence response to stress, aging and disease, are influenced by genetics and/or the environment, with potential implications for the implementation of resilience-boosting interventions. Resilience estimates were derived from in silico lesioning of either brain regions or functional connections constituting the connectome of healthy individuals belonging to two different large and unique datasets of twins, specifically: 463 individual twins from the Human Connectome Project and 453 individual twins from the Colorado Longitudinal Twin Study. As has been reported previously, moderate heritability was found for several topological indexes of brain efficiency and modularity. Importantly, evidence of heritability was found for resilience measures based on removal of brain connections rather than specific single regions, suggesting that genetic influences on resilience are preferentially directed toward region-to-region communication rather than local brain activity. Specifically, the strongest genetic influence was observed for moderately weak, long-range connections between a specific subset of functional brain networks: the Default Mode, Visual and Sensorimotor networks. These findings may help identify a link between brain resilience and network-level alterations observed in neurological and psychiatric diseases, as well as inform future studies investigating brain shielding interventions against physiological and pathological perturbations.

Percolation of heterogeneous flows uncovers the bottlenecks of infrastructure networks

Whether it be the passengers’ mobility demand in transportation systems, or the consumers’ energy demand in power grids, the primary purpose of many infrastructure networks is to best serve this flow demand. In reality, the volume of flow demand fluctuates unevenly across complex networks while simultaneously being hindered by some form of congestion or overload. Nevertheless, there is little known about how the heterogeneity of flow demand influences the network flow dynamics under congestion. To explore this, we introduce a percolation-based network analysis framework underpinned by flow heterogeneity. Thereby, we theoretically identify bottleneck links with guaranteed decisive impact on how flows are passed through the network. The effectiveness of the framework is demonstrated on large-scale real transportation networks, where mitigating the congestion on a small fraction of the links identified as bottlenecks results in a significant network improvement.

Infrastructure networks are characterized by fluctuations of flow demand between different points and temporal congestion or overload on flow pathways. Hamedmoghadam et al. identify congestion bottlenecks in networks relevant to communication, transportation, water supply, and power distribution.