Current concepts of neural networks have emerged over two centuries of progress beginning with the neural doctrine to the idea of neural cell assemblies. Presently the model of neural networks involves distributed neural circuits of nodes, hubs, and connections that are dynamic in different states of brain function. Advances in neurophysiology, neuroimaging and the field of connectomics have given impetus to the application of mathematical concepts of graph theory. Current approaches do carry limitations and inconsistency in results achieved. We model the neural network of the brain as a directed graph and attach a matrix (called the Markov matrix) of transition probabilities (determined by the synaptic strengths) to every pair of distinct nodes giving rise to a (continuous) Markov process. We postulate that the network hubs are the nodes with the highest probabilities given by the stationary distribution of Markov theory. We also derive a new upper bound for the diameter of a graph in terms of the eigenvalues of the Markov matrix.
Human brain structural networks contain sets of centrally embedded hub regions that enable efficient information communication. However, it remains largely unknown about categories of structural brain hubs and their microstructural, functional and cognitive characteristics as well as contributions to individual identification. Here, we employed three multi-modal imaging data sets with structural MRI, diffusion MRI and resting-state functional MRI to construct individual structural brain networks, identify brain hubs based on eight commonly used graph-nodal metrics, and perform comprehensive va…
Typical brain networks consist of many peripheral regions and a few highly central ones, i.e. hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from the analysis of specific frequency components of brain activity, present peculiar architectures with unique profiles of region centrality. However, the identification of hubs in networks built from different frequency bands simultaneously is still a challenging problem, remaining largely unexplored. Here we identify each frequency component with one layer of a multiplex network a…
Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human connectome can be crucial for the brain complex dynamics. In this context, the best-connected brain areas, designated as hub nodes, play a central role in supporting integrated brain function. Here, we study the structure of simplicial complexes attached to eight global hubs in the female and male connectomes and identify the core networks among the affected bra…
We investigate how hubs of functional brain networks are modified as a result of mild cognitive impairment (MCI), a condition causing a slight but noticeable decline in cognitive abilities, which sometimes precedes the onset of Alzheimer's disease. We used magnetoencephalography (MEG) to investigate the functional brain networks of a group of patients suffering from MCI and a control group of healthy subjects, during the execution of a short-term memory task. Couplings between brain sites were evaluated using synchronization likelihood, from which a network of functional interdependencies was …
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 fin…
Understanding of normal and pathological brain function requires the identification and localization of functional connections between specialized regions. The availability of high time resolution signals of electric neuronal activity at several regions offers information for quantifying the connections in terms of information flow. When the signals cover the whole cortex, the number of connections is very large, making visualization and interpretation very difficult. We introduce here the singular value decomposition of time-lagged multiple signals, which localizes the senders, hubs, and rece…
Alzheimer's disease (AD) causes alterations of brain network structure and function. The latter consists of connectivity changes between oscillatory processes at different frequency channels. We proposed a multi-layer network approach to analyze multiple-frequency brain networks inferred from magnetoencephalographic recordings during resting-states in AD subjects and age-matched controls. Main results showed that brain networks tend to facilitate information propagation across different frequencies, as measured by the multi-participation coefficient (MPC). However, regional connectivity in AD …
The human brain network is modular--comprised of communities of tightly interconnected nodes. This network contains local hubs, which have many connections within their own communities, and connector hubs, which have connections diversely distributed across communities. A mechanistic understanding of these hubs and how they support cognition has not been demonstrated. Here, we leveraged individual differences in hub connectivity and cognition. We show that a model of hub connectivity accurately predicts the cognitive performance of 476 individuals in four distinct tasks. Moreover, there is a g…
Middle East Technical University（中东技术大学）；Indiana University（印第安纳大学）
Complex problem solving is a high level cognitive process which has been thoroughly studied over the last decade. The Tower of London (TOL) is a task that has been widely used to study problem-solving. In this study, we aim to explore the underlying cognitive network dynamics among anatomical regions of complex problem solving and its sub-phases, namely planning and execution. A new brain network construction model establishing dynamic functional brain networks using fMRI is proposed. The first step of the model is a preprocessing pipeline that manages to decrease the spatial redundancy while …
Objective: Longitudinal neuroimaging studies have demonstrated that adolescence is the crucial developmental epoch of continued brain growth and change. A large number of researchers dedicate to uncovering the mechanisms about brain maturity during adolescence. Motivated by both achievement in graph signal processing and recent evidence that some brain areas act as hubs connecting functionally specialized systems, we proposed an approach to detect these regions from spectral analysis perspective. In particular, as human brain undergoes substantial development throughout adolescence, we address…
Tulane University（杜兰大学）；University of Nebraska Medical Center（内布拉斯加大学医学中心）；Mind Research Network（心智研究网络）；Tri-institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS)（三机构神经影像与数据科学转化研究中心（TReNDS））；Georgia State University（佐治亚州立大学）；Georgia Institute of Technology（佐治亚理工学院）；Emory University（埃默里大学）
Emotion perception is essential to affective and cognitive development which involves distributed brain circuits. The ability of emotion identification begins in infancy and continues to develop throughout childhood and adolescence. Understanding the development of brain's emotion circuitry may help us explain the emotional changes observed during adolescence. Our previous study delineated the trajectory of brain functional connectivity (FC) from late childhood to early adulthood during emotion identification tasks. In this work, we endeavour to deepen our understanding from association to cau…
The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws. The modular organization, in terms of modular mass, inter-modular, and intra-modular interaction, also obeys fractal nature. The parameters which characterize topological properties of brain networks follow one parameter scaling theory in all levels of network structure which reveals the self-similar rules governing the network structure. The calculated fract…
We studied the interactions between different temporal scales of diffusion processes on complex networks and found them to be stronger in scale-free (SF) than in Erdos-Renyi (ER) networks, especially for the case of phase-amplitude coupling (PAC)-the phenomenon where the phase of an oscillatory mode modulates the amplitude of another oscillation. We found that SF networks facilitate PAC between slow and fast frequency components of the diffusion process, whereas ER networks enable PAC between slow-frequency components. Nodes contributing the most to the generation of PAC in SF networks were no…
Neural networks are composed of neurons and synapses, which are responsible for learning in a slow adaptive dynamical process. Here we experimentally show that neurons act like independent anisotropic multiplex hubs, which relay and mute incoming signals following their input directions. Theoretically, the observed information routing enriches the computational capabilities of neurons by allowing, for instance, equalization among different information routes in the network, as well as high-frequency transmission of complex time-dependent signals constructed via several parallel routes. In addi…
Subnetwork extraction using community detection methods is commonly used to study the brain's modular structure. Recent studies indicated that certain brain regions are known to interact with multiple subnetworks. However, most existing methods are mainly for non-overlapping subnetwork extraction. In this paper, we present an approach for overlapping brain subnetwork extraction using cliques, which we defined as co-activated node groups performing multiple tasks. We proposed a multisource subnetwork extraction approach based on the co-activated clique, which (1) uses task co-activation and tas…
Exploring the human brain networks during rest is a topic of great interest. Several structural and functional studies have previously been conducted to study the intrinsic brain networks. In this paper, we focus on investigating the human brain network topology using dense Electroencephalography (EEG) source connectivity approach. We applied graph theoretical methods on functional networks reconstructed from resting state data acquired using EEG in 14 healthy subjects. Our findings confirmed the existence of sets of brain regions considered as functional hubs. In particular, the isthmus cingu…
Neural networks show a progressive increase in complexity during the time course of evolution. From diffuse nerve nets in Cnidaria to modular, hierarchical systems in macaque and humans, there is a gradual shift from simple processes involving a limited amount of tasks and modalities to complex functional and behavioral processing integrating different kinds of information from highly specialized tissue. However, studies in a range of species suggest that fundamental similarities, in spatial and topological features as well as in developmental mechanisms for network formation, are retained acr…
In systems neuroscience, most models posit that brain regions communicate information under constraints of efficiency. Yet, evidence for efficient communication in structural brain networks characterized by hierarchical organization and highly connected hubs remains sparse. The principle of efficient coding proposes that the brain transmits maximal information in a metabolically economical or compressed form to improve future behavior. To determine how structural connectivity supports efficient coding, we develop a theory specifying minimum rates of message transmission between brain regions t…
In recent years numerous attempts to understand the human brain were undertaken from a network point of view. A network framework takes into account the relationships between the different parts of the system and enables to examine how global and complex functions might emerge from network topology. Previous work revealed that the human brain features 'small world' characteristics and that cortical hubs tend to interconnect among themselves. However, in order to fully understand the topological structure of hubs one needs to go beyond the properties of a specific hub and examine the various st…
Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human functional brain networks, the network structure is often inferred from functional magnetic resonance imaging (fMRI) blood oxygen level dependent (BOLD) signal. Since the BOLD signal is a proxy for neuronal activity, it is of interest to learn the latent functional network structure. Additionally, despite a core set of observations about functional networks such…
In Indian history of arts, Rasas are the aesthetics associated with any auditory, visual, literary or musical piece of art that evokes highly orchestrated emotional states. In this work, we study the functional response of the brain to movie clippings meant to evoke the Rasas through network analysis. We extract functional brain networks using coherence measures on EEG recordings of film clips from popular Indian Bollywood movies representing nine Rasas in the Indian Natyasastra. Structural and functional network measures were computed for these brain networks, averaging over a range of signif…
Recent characterisations of self-organising systems depend upon the presence of a Markov blanket: a statistical boundary that mediates the interactions between what is inside of and outside of a system. We leverage this idea to provide an analysis of partitions in neuronal systems. This is applicable to brain architectures at multiple scales, enabling partitions into single neurons, brain regions, and brain-wide networks. This treatment is based upon the canonical micro-circuitry used in empirical studies of effective connectivity, so as to speak directly to practical applications. This depend…
Michigan State University（密歇根州立大学）；California Institute of Technology（加州理工学院）；University of Pennsylvania（宾夕法尼亚大学）；University of Wisconsin（威斯康星大学）；Indiana University（印第安纳大学）
Markov Brains are a class of evolvable artificial neural networks (ANN). They differ from conventional ANNs in many aspects, but the key difference is that instead of a layered architecture, with each node performing the same function, Markov Brains are networks built from individual computational components. These computational components interact with each other, receive inputs from sensors, and control motor outputs. The function of the computational components, their connections to each other, as well as connections to sensors and motors are all subject to evolutionary optimization. Here w…
For much of biology, the manner in which genotype maps to phenotype remains a fundamental mystery. The few maps that are known tend to show modular pleiotropy: sets of phenotypes are determined by distinct sets of genes. One key map that has evaded discovery is that of the human brain's network architecture. Here, we determine the form of this map for gene coexpression and single nucleotide polymorphisms. We discover that mostly non-overlapping sets of genes encode the connectivity of brain network modules (or so-called communities), suggesting that brain network communities demarcate genetic …
Altered functional brain networks have been a typical manifestation that distinguishes major depressive disorder (MDD) patients from healthy control (HC) subjects in functional magnetic resonance imaging (fMRI) studies. Recently, rich club and diverse club metrics have been proposed for network or network neuroscience analyses. The rich club defines a set of nodes that tend to be the hubs of specific communities, and the diverse club defines the nodes that span more communities and have edges diversely distributed across different communities. Considering the heterogeneity of rich clubs and di…
At the inception of human brain mapping, two principles of functional anatomy underwrote most conceptions - and analyses - of distributed brain responses: namely functional segregation and integration. There are currently two main approaches to characterising functional integration. The first is a mechanistic modelling of connectomics in terms of directed effective connectivity that mediates neuronal message passing and dynamics on neuronal circuits. The second phenomenological approach usually characterises undirected functional connectivity (i.e., measurable correlations), in terms of intrin…
Brain networks are adaptively rewired continually, adjusting their topology to bring about functionality and efficiency in sensory, motor and cognitive tasks. In model neural network architectures, adaptive rewiring generates complex, brain-like topologies. Present models, however, cannot account for the emergence of complex directed connectivity structures. We tested a biologically plausible model of adaptive rewiring in directed networks, based on two algorithms widely used in distributed computing: advection and consensus. When both are used in combination as rewiring criteria, adaptive rew…
Labeling subtypes in a Parkinson's Cohort using Multifeatures in MRI -- Integrating Grey and White Matter Information
Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）；National Institute of Mental Health and Neurosciences（国家心理健康与神经科学研究所）；National Institute of Mental Health & Neuro Sciences（国家心理健康与神经科学研究所）；Jyoti and Bhupat Mehta School of Health Sciences and Technology, Indian Institute of Technology Guwahati（乔蒂与布帕特·梅塔健康科学与技术学院，印度理工学院古瓦哈提分校）
Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence …
Recent studies have proposed that one can summarize brain activity into dynamics among a relatively small number of hidden states and that such an approach is a promising tool for revealing brain function. Hidden Markov models (HMMs) are a prevalent approach to inferring such neural dynamics among discrete brain states. However, the impact of assuming Markovian structure in neural time series data has not been sufficiently examined. Here, to address this situation and examine the performance of the HMM, we compare the model with the Gaussian mixture model (GMM), which is with no temporal regul…
Functional brain networks exhibit dynamics on the sub-second temporal scale and are often assumed to embody the physiological substrate of cognitive processes. Here we analyse the temporal and spatial dynamics of these states, as measured by EEG, with a hidden Markov model and compare this approach to classical EEG microstate analysis. We find dominating state lifetimes of 100--150\,ms for both approaches. The state topographies show obvious similarities. However, they also feature distinct spatial and especially temporal properties. These differences may carry physiological meaningful informa…
When the human brain manifests the birth of organised communication among local and large-scale neuronal populations activity remains undescribed. We report, in resting-state EEG source-estimates of 100 infants at term age, the existence of macro-scale dynamic functional connectivity, which have rich topological organisations, distinct spectral fingerprints and scale-invariance temporal dynamics. These functional networks encompass the default mode, primary sensory-limbic system, thalamo-frontal, thalamo-sensorimotor and visual-limbic system confined in the delta and low-alpha frequency interv…
Synchronization of brain activity fluctuations is believed to represent communication between spatially distant neural processes. These inter-areal functional interactions develop in the background of a complex network of axonal connections linking cortical and sub-cortical neurons, termed the human "structural connectome". Theoretical considerations and experimental evidence support the view that the human brain can be modeled as a system operating at a critical point between ordered (sub-critical) and disordered (super-critical) phases. Here, we explore the hypothesis that pathologies result…
We investigate scaling properties of human brain functional networks in the resting-state. Analyzing network degree distributions, we statistically test whether their tails scale as power-law or not. Initial studies, based on least-squares fitting, were shown to be inadequate for precise estimation of power-law distributions. Subsequently, methods based on maximum-likelihood estimators have been proposed and applied to address this question. Nevertheless, no clear consensus has emerged, mainly because results have shown substantial variability depending on the data-set used or its resolution. …
The trajectory of an individual's recovery after traumatic brain injury (TBI) is heterogeneous, with complete recovery in some cases but persistent disability in others. We hypothesized that changes in structural brain network abnormalities guide the trajectory of an individual's recovery post-injury. Our objective was to characterize the variability in recovery post-TBI by identifying a putative neuroimaging biomarker of traumatic axonal injury (TAI) in individuals with mild TBI. We analyzed 70 T1-weighted and diffusion MRIs longitudinally collected from 35 individuals during the subacute and…
Cognition is supported by neurophysiological processes that occur both in local anatomical neighborhoods and in distributed large-scale circuits. Recent evidence from network control theory suggests that white matter pathways linking large-scale brain regions provide a critical substrate constraining the ability of single areas to affect control on those processes. Yet, no direct evidence exists for a relationship between brain network controllability and cognitive control performance. Here, we address this gap by constructing structural brain networks from diffusion tensor imaging data acquir…
Connectomics has focused primarily on the mapping of synaptic links in the brain; yet it is well established that extrasynaptic volume transmission, especially via monoamines and neuropeptides, is also critical to brain function. Here we present a draft monoamine connectome, along with a partial neuropeptide connectome, for the nematode C. elegans, based on new and published expression data for biosynthetic genes and receptors. Thus, the neuronal connectome can be represented as a multiplex network, with synaptic, gap junction, and neuromodulatory layers representing alternative modes of inter…
Network science has been extensively developed to characterize structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally obtained biological data, represent one instance of a larger number of realizations with similar intrinsic topology. A modeling approach is therefore needed to support statistical inference on the bottom-up local connectivity mechanisms influencing the formation of the estimated brain networks. We adopted a statistical model based on exponential random graph…
Recent studies have demonstrated the existence of community structure and rich club nodes, (i.e., highly interconnected, high degree hub nodes), in human brain functional networks. The cognitive relevance of the detected modules and hubs has also been demonstrated, for both task based and default mode networks, suggesting that the brain self-organizes into patterns of co-activated sets of regions for performing specific tasks or in resting state. In this paper, we report studies on the resilience or robustness of this modular structure: under systematic erosion of connectivity in the network u…
Functional magnetic resonance imaging (fMRI) has begun to narrow down the neural correlates of self-generated forms of thought, with current evidence pointing toward central roles for the default, frontoparietal, and visual networks. Recent work has linked the arising of thoughts more specifically to default network activity, but the limited temporal resolution of fMRI has precluded more detailed conclusions about where in the brain self-created mental content is generated and how this is achieved. Here I argue that the unparalleled spatiotemporal resolution of intracranial electrophysiology (…
In many realistic networks, the edges representing the interactions between the nodes are time-varying. There is growing evidence that the complex network that models the dynamics of the human brain has time-varying interconnections, i.e., the network is evolving. Based on this evidence, we construct a patient and data specific evolving network model (comprising discrete-time dynamical systems) in which epileptic seizures or their terminations in the brain are also determined by the nature of the time-varying interconnections between the nodes. A novel and unique feature of our methodology is …
University College London（伦敦大学学院）；University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）
As a relatively new field, network neuroscience has tended to focus on aggregate behaviours of the brain averaged over many successive experiments or over long recordings in order to construct robust brain models. These models are limited in their ability to explain dynamic state changes in the brain which occurs spontaneously as a result of normal brain function. Hidden Markov Models (HMMs) trained on neuroimaging time series data have since arisen as a method to produce dynamical models that are easy to train but can be difficult to fully parametrise or analyse. We propose an interpretation …
Identifying Influential nodes in Brain Networks via Self-Supervised Graph-Transformer
School of Computer Science, Northwestern Polytechnical University（西北工业大学计算机学院）；School of Life Science and Technology, University of Electronic Science and Technology of China（电子科技大学生命科学与技术学院）；School of Automation, Northwestern Polytechnical University（西北工业大学自动化学院）
Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropies have been proposed in brain network analysis. However, they are less widely used than traditional graph theoretic measures such as global and local efficiencies because either they are not well-defined on a graph or difficult to interpret its biological meaning. In this paper, we propose a new entropy-based graph invariant, called volume entropy. It measures the exponential growth rate of the number of paths in a graph, which i…
Peking University（北京大学）；Peng Cheng Laboratory（鹏城实验室）；University of Leicester（莱斯特大学）
Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how probabilistic inference can be implemented by a network of spiking neurons in the brain. Previous studies have tried to relate the inference equation of binary Markov random fields to the dynamic equation of spiking neural networks through belief propagation algorithm and reparameterization, but they are valid only for Markov random fields with limited netwo…
A Tensor Network Framework for Interpretable Graph Analysis of Brain Networks
Università degli Studi di Bari Aldo Moro（巴里阿尔多·莫罗大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Bari（意大利国家核物理研究所巴里分部）；Dipartimento di Scienze della Formazione, Psicologia, Comunicazione (For.Psi.Com.), Università degli Studi di Bari Aldo Moro（巴里阿尔多·莫罗大学教育、心理学与传播学院）；Biocruces-Bizkaia Health Research Institute（比斯开生物克鲁塞斯健康研究所）；University of the Basque Country（巴斯克大学）；IKERBASQUE Basque Foundation for Science（伊克尔巴斯奎科学巴斯克基金会）
Functional magnetic resonance imaging recordings in the resting-state (RS) from the human brain are characterized by spontaneous low-frequency fluctuations in the blood oxygenation level dependent signal that reveal functional connectivity (FC) via their spatial synchronicity. This RS study applied network analysis to compare FC between late-life depression (LLD) patients and control subjects. Raw cross-correlation matrices (CM) for LLD were characterized by higher FC. We analyzed the small-world (SW) and modular organization of these networks consisting of 110 nodes each as well as the connec…
The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs, or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings, lattices) and consider the impl…
What does it take for a system, biological or not, to have goals? Here, this question is approached in the context of in silico artificial evolution. By examining the informational and causal properties of artificial organisms ('animats') controlled by small, adaptive neural networks (Markov Brains), this essay discusses necessary requirements for intrinsic information, autonomy, and meaning. The focus lies on comparing two types of Markov Brains that evolved in the same simple environment: one with purely feedforward connections between its elements, the other with an integrated set of elemen…
Distributed networks of brain areas interact with one another in a time-varying fashion to enable complex cognitive and sensorimotor functions. Here we use novel network analysis algorithms to test the recruitment and integration of large-scale functional neural circuitry during learning. Using functional magnetic resonance imaging (fMRI) data acquired from healthy human participants, from initial training through mastery of a simple motor skill, we investigate changes in the architecture of functional connectivity patterns that promote learning. Our results reveal that learning induces an aut…
Artificial neural networks (ANNs), while exceptionally useful for classification, are vulnerable to misdirection. Small amounts of noise can significantly affect their ability to correctly complete a task. Instead of generalizing concepts, ANNs seem to focus on surface statistical regularities in a given task. Here we compare how recurrent artificial neural networks, long short-term memory units, and Markov Brains sense and remember their environments. We show that information in Markov Brains is localized and sparsely distributed, while the other neural network substrates "smear" information …
