The UCLA multimodal connectivity database: a web-based platform for brain connectivity matrix sharing and analysis

A hierarchy index for networks in the brain reveals a complex entangled organizational structure

Networks involved in information processing often have their nodes arranged hierarchically, with the majority of connections occurring in adjacent levels. However, despite being an intuitively appealing concept, the hierarchical organization of large networks, such as those in the brain, is difficult to identify, especially in absence of additional information beyond that provided by the connectome. In this paper, we propose a framework to uncover the hierarchical structure of a given network, that identifies the nodes occupying each level as well as the sequential order of the levels. It involves optimizing a metric that we use to quantify the extent of hierarchy present in a network. Applying this measure to various brain networks, ranging from the nervous system of the nematode Caenorhabditis elegans to the human connectome, we unexpectedly find that they exhibit a common network architectural motif intertwining hierarchy and modularity. This suggests that brain networks may have evolved to simultaneously exploit the functional advantages of these two types of organizations, viz., relatively independent modules performing distributed processing in parallel and a hierarchical structure that allows sequential pooling of these multiple processing streams. An intriguing possibility is that this property we report may be common to information processing networks in general.

Determinants of multimodal fake review generation in China's E-commerce platforms

This paper develops a theoretical model of determinants influencing multimodal fake review generation using the theories of signaling, actor-network, motivation, and human-environment interaction hypothesis. Applying survey data from users of China's three leading E-commerce platforms (Taobao, Jingdong, and Pinduoduo), we adopt structural equation modeling, machine learning technique, and Bayesian complex networks analysis to perform factor identification, path analysis, feature factor importance ranking, regime division, and network centrality analysis of full sample, male sample, and female sample to reach the following conclusions: (1) platforms' multimodal recognition and governance capabilities exert significant negative moderating effects on merchants' information behavior, while it shows no apparent moderating effect on users' information behavior; users' emotional venting, perceived value, reward mechanisms, and subjective norms positively influence multimodal fake review generation through perceptual behavior control; (2) feature factors of multimodal fake review generation can be divided into four regimes, i.e., regime 1 includes reward mechanisms and perceived social costs, indicating they are key feature factors of multimodal fake review generation; merchant perception impact is positioned in regime 2, signifying its pivotal role in multimodal fake review generation; regime 3 includes multimodal recognition and governance capabilities, supporting/disparaging merchants, and emotional venting; whereas user perception impact is positioned in regime 4, indicating its weaker influence on multimodal fake review generation; (3) both in full sample, male sample, and female sample, reward mechanisms play a crucial role in multimodal fake review generation; perceived value, hiring review control agency, multimodal recognition and governance capabilities exhibit a high degree of correlation; however, results of network centrality analysis also exhibit heterogeneity between male and female samples, i.e., male sample has different trends in closeness centrality values and betweenness centrality values than female sample. This indicates that determinants influencing multimodal fake review generation are complex and interconnected.

Eigenmode-based approach reveals a decline in brain structure-function liberality across the human lifespan

While brain function is supported and constrained by the underlying structure, the connectome-based link estimated by current approaches is either relatively moderate or accompanied by high model complexity, with the essential principles underlying structure-function coupling remaining elusive. Here, by proposing a mapping method based on network eigendecomposition, we present a concise and strong correspondence between structure and function. We show that the explanation of functional connectivity can be significantly improved by incorporating interactions between different structural eigenmodes. We also demonstrate the pronounced advantage of the present mapping in capturing individual-specific information with simple implementation. Applying our methodology to the human lifespan, we find that functional diversity decreases with age, with functional interactions increasingly dominated by the leading functional mode. We also find that structure-function liberality weakens with age, which is driven by the decreases in functional components that are less constrained by anatomy, while the magnitude of structure-aligned components is preserved. Overall, our work enhances the understanding of structure-function coupling from a collective, connectome-oriented perspective and promotes a more refined identification of functional portions relevant to human aging, holding great potential for mechanistic insights into individual differences associated with cognition, development, and neurological disorders.

Vizaj-A free online interactive software for visualizing spatial networks

In many fields of science and technology we are confronted with complex networks. Making sense of these networks often require the ability to visualize and explore their intermingled structure consisting of nodes and links. To facilitate the identification of significant connectivity patterns, many methods have been developed based on the rearrangement of the nodes so as to avoid link criss-cross. However, real networks are often embedded in a geometrical space and the nodes code for an intrinsic physical feature of the system that one might want to preserve. For these spatial networks, it is therefore crucial to find alternative strategies operating on the links and not on the nodes. Here, we introduce Vizaj a javascript web application to render spatial networks based on optimized geometrical criteria that reshape the link profiles. While optimized for 3D networks, Vizaj can also be used for 2D networks and offers the possibility to interactively customize the visualization via several controlling parameters, including network filtering and the effect of internode distance on the link trajectories. Vizaj is further equipped with additional options allowing to improve the final aesthetics, such as the color/size of both nodes and links, zooming/rotating/translating, and superimposing external objects. Vizaj is an open-source software which can be freely downloaded and updated via a github repository. Here, we provide a detailed description of its main features and algorithms together with a guide on how to use it. Finally, we validate its potential on several synthetic and real spatial networks from infrastructural to biological systems. We hope that Vizaj will help scientists and practitioners to make sense of complex networks and provide aesthetic while informative visualizations.

An Empirical Bayes Approach to Shrinkage Estimation on the Manifold of Symmetric Positive-Definite Matrices

The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of problems. Nonetheless, research on shrinkage estimation for manifold-valued data is scarce. In this article, we propose shrinkage estimators for the parameters of the Log-Normal distribution defined on the manifold of N × N symmetric positive-definite matrices. For this manifold, we choose the Log-Euclidean metric as its Riemannian metric since it is easy to compute and has been widely used in a variety of applications. By using the Log-Euclidean distance in the loss function, we derive a shrinkage estimator in an analytic form and show that it is asymptotically optimal within a large class of estimators that includes the MLE, which is the sample Fréchet mean of the data. We demonstrate the performance of the proposed shrinkage estimator via several simulated data experiments. Additionally, we apply the shrinkage estimator to perform statistical inference in both diffusion and functional magnetic resonance imaging problems.

rs-fMRI and machine learning for ASD diagnosis: a systematic review and meta-analysis

Autism Spectrum Disorder (ASD) diagnosis is still based on behavioral criteria through a lengthy and time-consuming process. Much effort is being made to identify brain imaging biomarkers and develop tools that could facilitate its diagnosis. In particular, using Machine Learning classifiers based on resting-state fMRI (rs-fMRI) data is promising, but there is an ongoing need for further research on their accuracy and reliability. Therefore, we conducted a systematic review and meta-analysis to summarize the available evidence in the literature so far. A bivariate random-effects meta-analytic model was implemented to investigate the sensitivity and specificity across the 55 studies that offered sufficient information for quantitative analysis. Our results indicated overall summary sensitivity and specificity estimates of 73.8% and 74.8%, respectively. SVM stood out as the most used classifier, presenting summary estimates above 76%. Studies with bigger samples tended to obtain worse accuracies, except in the subgroup analysis for ANN classifiers. The use of other brain imaging or phenotypic data to complement rs-fMRI information seems promising, achieving higher sensitivities when compared to rs-fMRI data alone (84.7% versus 72.8%). Finally, our analysis showed AUC values between acceptable and excellent. Still, given the many limitations indicated in our study, further well-designed studies are warranted to extend the potential use of those classification algorithms to clinical settings.

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.

A hands-on tutorial on network and topological neuroscience

The brain is an extraordinarily complex system that facilitates the optimal integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging at different scales and from numerous modalities. With that comes the need for sophisticated tools for analysis. The field of network neuroscience has been trying to tackle these challenges, and graph theory has been one of its essential branches through the investigation of brain networks. Recently, topological data analysis has gained more attention as an alternative framework by providing a set of metrics that go beyond pairwise connections and offer improved robustness against noise. In this hands-on tutorial, our goal is to provide the computational tools to explore neuroimaging data using these frameworks and to facilitate their accessibility, data visualisation, and comprehension for newcomers to the field. We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses the 1000 Functional Connectomes Project dataset. Moreover, we would like to highlight one part of our notebook dedicated to the realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pairwise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.

Connectomic analysis of Alzheimer's disease using percolation theory

Alzheimer's disease (AD) is a severe neurodegenerative disorder that affects a growing worldwide elderly population. Identification of brain functional biomarkers is expected to help determine preclinical stages for targeted mechanistic studies and development of therapeutic interventions to deter disease progression. Connectomic analysis, a graph theory-based methodology used in the analysis of brain-derived connectivity matrices was used in conjunction with percolation theory targeted attack model to investigate the network effects of AD-related amyloid deposition. We used matrices derived from resting-state functional magnetic resonance imaging collected on mice with extracellular amyloidosis (TgCRND8 mice, n = 17) and control littermates (n = 17). Global, nodal, spatial, and percolation-based analysis was performed comparing AD and control mice. These data indicate a short-term compensatory response to neurodegeneration in the AD brain via a strongly connected core network with highly vulnerable or disconnected hubs. Targeted attacks demonstrated a greater vulnerability of AD brains to all types of attacks and identified progression models to mimic AD brain functional connectivity through betweenness centrality and collective influence metrics. Furthermore, both spatial analysis and percolation theory identified a key disconnect between the anterior brain of the AD mice to the rest of the brain network.

Autism Spectrum Disorder Studies Using fMRI Data and Machine Learning: A Review

Machine learning methods have been frequently applied in the field of cognitive neuroscience in the last decade. A great deal of attention has been attracted to introduce machine learning methods to study the autism spectrum disorder (ASD) in order to find out its neurophysiological underpinnings. In this paper, we presented a comprehensive review about the previous studies since 2011, which applied machine learning methods to analyze the functional magnetic resonance imaging (fMRI) data of autistic individuals and the typical controls (TCs). The all-round process was covered, including feature construction from raw fMRI data, feature selection methods, machine learning methods, factors for high classification accuracy, and critical conclusions. Applying different machine learning methods and fMRI data acquired from different sites, classification accuracies were obtained ranging from 48.3% up to 97%, and informative brain regions and networks were located. Through thorough analysis, high classification accuracies were found to usually occur in the studies which involved task-based fMRI data, single dataset for some selection principle, effective feature selection methods, or advanced machine learning methods. Advanced deep learning together with the multi-site Autism Brain Imaging Data Exchange (ABIDE) dataset became research trends especially in the recent 4 years. In the future, advanced feature selection and machine learning methods combined with multi-site dataset or easily operated task-based fMRI data may appear to have the potentiality to serve as a promising diagnostic tool for ASD.

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.

Energy constraints on brain network formation

Energy constraints are a fundamental limitation of the brain, which is physically embedded in a restricted space. The collective dynamics of neurons through connections enable the brain to achieve rich functionality, but building connections and maintaining activity come at a high cost. The effects of reducing these costs can be found in the characteristic structures of the brain network. Nevertheless, the mechanism by which energy constraints affect the organization and formation of the neuronal network in the brain is unclear. Here, it is shown that a simple model based on cost minimization can reproduce structures characteristic of the brain network. With reference to the behavior of neurons in real brains, the cost function was introduced in an activity-dependent form correlating the activity cost and the wiring cost as a simple ratio. Cost reduction of this ratio resulted in strengthening connections, especially at highly activated nodes, and induced the formation of large clusters. Regarding these network features, statistical similarity was confirmed by comparison to connectome datasets from various real brains. The findings indicate that these networks share an efficient structure maintained with low costs, both for activity and for wiring. These results imply the crucial role of energy constraints in regulating the network activity and structure of the brain.

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.

Brain dynamics and structure-function relationships via spectral factorization and the transfer function

It is shown how the brain's linear transfer function provides a means to systematically analyze brain connectivity and dynamics, and to infer connectivity, eigenmodes, and activity measures such as spectra, evoked responses, coherence, and causality, all of which are widely used in brain monitoring. In particular, the Wilson spectral factorization algorithm is outlined and used to efficiently obtain linear transfer functions from experimental two-point correlation functions. The algorithm is tested on a series of brain-like structures of increasing complexity which include time delays, asymmetry, two-dimensionality, and complex network connectivity. These tests are used to verify the algorithm is suitable for application to brain dynamics, specify sampling requirements for experimental time series, and to verify that its runtime is short enough to obtain accurate results for systems of similar size to current experiments. The results can equally well be applied to inference of the transfer function in complex linear systems other than brains.

The structure dilemma in biological and artificial neural networks

Brain research up to date has revealed that structure and function are highly related. Thus, for example, studies have repeatedly shown that the brains of patients suffering from schizophrenia or other diseases have a different connectome compared to healthy people. Apart from stochastic processes, however, an inherent logic describing how neurons connect to each other has not yet been identified. We revisited this structural dilemma by comparing and analyzing artificial and biological-based neural networks. Namely, we used feed-forward and recurrent artificial neural networks as well as networks based on the structure of the micro-connectome of C. elegans and of the human macro-connectome. We trained these diverse networks, which markedly differ in their architecture, initialization and pruning technique, and we found remarkable parallels between biological-based and artificial neural networks, as we were additionally able to show that the dilemma is also present in artificial neural networks. Our findings show that structure contains all the information, but that this structure is not exclusive. Indeed, the same structure was able to solve completely different problems with only minimal adjustments. We particularly put interest on the influence of weights and the neuron offset value, as they show a different adaption behaviour. Our findings open up new questions in the fields of artificial and biological information processing research.

Unique scales preserve self-similar integrate-and-fire functionality of neuronal clusters

Brains demonstrate varying spatial scales of nested hierarchical clustering. Identifying the brain's neuronal cluster size to be presented as nodes in a network computation is critical to both neuroscience and artificial intelligence, as these define the cognitive blocks capable of building intelligent computation. Experiments support various forms and sizes of neural clustering, from handfuls of dendrites to thousands of neurons, and hint at their behavior. Here, we use computational simulations with a brain-derived fMRI network to show that not only do brain networks remain structurally self-similar across scales but also neuron-like signal integration functionality ("integrate and fire") is preserved at particular clustering scales. As such, we propose a coarse-graining of neuronal networks to ensemble-nodes, with multiple spikes making up its ensemble-spike and time re-scaling factor defining its ensemble-time step. This fractal-like spatiotemporal property, observed in both structure and function, permits strategic choice in bridging across experimental scales for computational modeling while also suggesting regulatory constraints on developmental and evolutionary "growth spurts" in brain size, as per punctuated equilibrium theories in evolutionary biology.

Importance of self-connections for brain connectivity and spectral connectomics

Spectral analysis and neural field theory are used to investigate the role of local connections in brain connectivity matrices (CMs) that quantify connectivity between pairs of discretized brain regions. This work investigates how the common procedure of omitting such self-connections (i.e., the diagonal elements of CMs) in published studies of brain connectivity affects the properties of functional CMs (fCMs) and the mutually consistent effective CMs (eCMs) that correspond to them. It is shown that retention of self-connections in the fCM calculated from two-point activity covariances is essential for the fCM to be a true covariance matrix, to enable correct inference of the direct total eCMs from the fCM, and to ensure their compatibility with it; the deCM and teCM represent the strengths of direct connections and all connections between points, respectively. When self-connections are retained, inferred eCMs are found to have net inhibitory self-connections that represent the local inhibition needed to balance excitation via white matter fibers at longer ranges. This inference of spatially unresolved connectivity exemplifies the power of spectral connectivity methods, which also enable transformation of CMs to compact diagonal forms that allow accurate approximation of the fCM and total eCM in terms of just a few modes, rather than the full [Formula: see text] CM entries for connections between N brain regions. It is found that omission of fCM self-connections affects both local and long-range connections in eCMs, so they cannot be omitted even when studying the large-scale. Moreover, retention of local connections enables inference of subgrid short-range inhibitory connectivity. The results are verified and illustrated using the NKI-Rockland dataset from the University of Southern California Multimodal Connectivity Database. Deletion of self-connections is common in the field; this does not affect case-control studies but the present results imply that such fCMs must have self-connections restored before eCMs can be inferred from them.

Synergistic information in a dynamical model implemented on the human structural connectome reveals spatially distinct associations with age

We implement the dynamical Ising model on the large-scale architecture of white matter connections of healthy subjects in the age range 4-85 years, and analyze the dynamics in terms of the synergy, a quantity measuring the extent to which the joint state of pairs of variables is projected onto the dynamics of a target one. We find that the amount of synergy in explaining the dynamics of the hubs of the structural connectivity (in terms of degree strength) peaks before the critical temperature, and can thus be considered as a precursor of a critical transition. Conversely, the greatest amount of synergy goes into explaining the dynamics of more central nodes. We also find that the aging of structural connectivity is associated with significant changes in the simulated dynamics: There are brain regions whose synergy decreases with age, in particular the frontal pole, the subcallosal area, and the supplementary motor area; these areas could then be more likely to show a decline in terms of the capability to perform higher order computation (if structural connectivity was the sole variable). On the other hand, several regions in the temporal cortex show a positive correlation with age in the first 30 years of life, that is, during brain maturation.

Finding Community of Brain Networks Based on Neighbor Index and DPSO with Dynamic Crossover

Background: :

The brain networks can provide us an effective way to analyze brain function and brain disease detection. In brain networks, there exist some import neural unit modules, which contain meaningful biological insights.

Objective::

Therefore, we need to find the optimal neural unit modules effectively and efficiently.

Method::

In this study, we propose a novel algorithm to find community modules of brain networks by combining Neighbor Index and Discrete Particle Swarm Optimization (DPSO) with dynamic crossover, abbreviated as NIDPSO. The differences between this study and the existing ones lie in that NIDPSO is proposed first to find community modules of brain networks, and dose not need to predefine and preestimate the number of communities in advance.

Results: :

We generate a neighbor index table to alleviate and eliminate ineffective searches and design a novel coding by which we can determine the community without computing the distances amongst vertices in brain networks. Furthermore, dynamic crossover and mutation operators are designed to modify NIDPSO so as to alleviate the drawback of premature convergence in DPSO.

Conclusion:

The numerical results performing on several resting-state functional MRI brain networks demonstrate that NIDPSO outperforms or is comparable with other competing methods in terms of modularity, coverage and conductance metrics.

Finding Community Modules for Brain Networks Combined Uniform Design with Fruit Fly Optimization Algorithm

There are a huge amount of neural units in brain networks. Some of the neural units have tight connection and form neural unit modules. These unit modules are helpful to the disease detection and target therapy. A good method can find neural unit modules accurately and effectively. The study proposes a new algorithm to analyze a brain network and obtain its neural unit modules. The proposed algorithm combines the uniform design and the fruit fly optimization algorithm (FOA); therefore, we called it as UFOA. It makes the utmost of their respective merits of the uniform design and the FOA, so as to acquire the feasible solutions scattered uniformly over the vector domain and find the optimal solution as quickly as possible. When compared with other existing methods, FOA and the uniform design are integrated first, and UFOA is first utilized to find unit modules from brain networks. 37 TD resting-state functional MRI brain networks are used to testify the performance of UFOA. The obtained experimental results manifest that UFOA is clearly superior to the other five methods in terms of modularity, and is comparable with the other five methods in terms of conductance. Additionally, the comparative analysis of UFOA and FOA also demonstrates that the uniform design brings benefit to the improvement of UFOA.

Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches

Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. ​Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks.

Topics and trends in artificial intelligence assisted human brain research

Artificial intelligence (AI) assisted human brain research is a dynamic interdisciplinary field with great interest, rich literature, and huge diversity. The diversity in research topics and technologies keeps increasing along with the tremendous growth in application scope of AI-assisted human brain research. A comprehensive understanding of this field is necessary to assess research efficacy, (re)allocate research resources, and conduct collaborations. This paper combines the structural topic modeling (STM) with the bibliometric analysis to automatically identify prominent research topics from the large-scale, unstructured text of AI-assisted human brain research publications in the past decade. Analyses on topical trends, correlations, and clusters reveal distinct developmental trends of these topics, promising research orientations, and diverse topical distributions in influential countries/regions and research institutes. These findings help better understand scientific and technological AI-assisted human brain research, provide insightful guidance for resource (re)allocation, and promote effective international collaborations.

Principles of Mutual Information Maximization and Energy Minimization Affect the Activation Patterns of Large Scale Networks in the Brain

Successive patterns of activation and deactivation in local areas of the brain indicate the mechanisms of information processing in the brain. It is possible that this process can be optimized by principles, such as the maximization of mutual information and the minimization of energy consumption. In the present paper, I showed evidence for this argument by demonstrating the correlation among mutual information, the energy of the activation, and the activation patterns. Modeling the information processing based on the functional connectome datasets of the human brain, I simulated information transfer in this network structure. Evaluating the statistical quantities of the different network states, I clarified the correlation between them. First, I showed that mutual information and network energy have a close relationship, and that the values are maximized and minimized around a same network state. This implies that there is an optimal network state in the brain that is organized according to the principles regarding mutual information and energy. On the other hand, the evaluation of the network structure revealed that the characteristic network structure known as the criticality also emerges around this state. These results imply that the characteristic features of the functional network are also affected strongly by these principles. To assess the functional aspects of this state, I investigated the output activation patterns in response to random input stimuli. Measuring the redundancy of the responses in terms of the number of overlapping activation patterns, the results indicate that there is a negative correlation between mutual information and the redundancy in the patterns, suggesting that there is a trade-off between communication efficiency and robustness due to redundancy, and the principles of mutual information and network energy are important to network formation and its function in the human brain.

A network clustering based feature selection strategy for classifying autism spectrum disorder

BACKGROUND

Advanced non-invasive neuroimaging techniques offer new approaches to study functions and structures of human brains. Whole-brain functional networks obtained from resting state functional magnetic resonance imaging has been widely used to study brain diseases like autism spectrum disorder (ASD). Auto-classification of ASD has become an important issue. Existing classification methods for ASD are based on features extracted from the whole-brain functional networks, which may be not discriminant enough for good performance.

METHODS

In this study, we propose a network clustering based feature selection strategy for classifying ASD. In our proposed method, we first apply symmetric non-negative matrix factorization to divide brain networks into four modules. Then we extract features from one of four modules called default mode network (DMN) and use them to train several classifiers for ASD classification.

RESULTS

The computational experiments show that our proposed method achieves better performances than those trained with features extracted from the whole brain network.

CONCLUSION

It is a good strategy to train the classifiers for ASD based on features from the default mode subnetwork.

Finding Community Modules of Brain Networks Based on PSO with Uniform Design

The brain has the most complex structures and functions in living organisms, and brain networks can provide us an effective way for brain function analysis and brain disease detection. In brain networks, there exist some important neural unit modules, which contain many meaningful biological insights. It is appealing to find the neural unit modules and obtain their affiliations. In this study, we present a novel method by integrating the uniform design into the particle swarm optimization to find community modules of brain networks, abbreviated as UPSO. The difference between UPSO and the existing ones lies in that UPSO is presented first for detecting community modules. Several brain networks generated from functional MRI for studying autism are used to verify the proposed algorithm. Experimental results obtained on these brain networks demonstrate that UPSO can find community modules efficiently and outperforms the other competing methods in terms of modularity and conductance. Additionally, the comparison of UPSO and PSO also shows that the uniform design plays an important role in improving the performance of UPSO.

Network curvature as a hallmark of brain structural connectivity

Although brain functionality is often remarkably robust to lesions and other insults, it may be fragile when these take place in specific locations. Previous attempts to quantify robustness and fragility sought to understand how the functional connectivity of brain networks is affected by structural changes, using either model-based predictions or empirical studies of the effects of lesions. We advance a geometric viewpoint relying on a notion of network curvature, the so-called Ollivier-Ricci curvature. This approach has been proposed to assess financial market robustness and to differentiate biological networks of cancer cells from healthy ones. Here, we apply curvature-based measures to brain structural networks to identify robust and fragile brain regions in healthy subjects. We show that curvature can also be used to track changes in brain connectivity related to age and autism spectrum disorder (ASD), and we obtain results that are in agreement with previous MRI studies.

The brain can often continue to function despite lesions in many areas, but damage to particular locations may have serious effects. Here, the authors use the concept of Ollivier-Ricci curvature to investigate the robustness of brain networks.

Topological phase transitions in functional brain networks

Functional brain networks are often constructed by quantifying correlations between time series of activity of brain regions. Their topological structure includes nodes, edges, triangles, and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process data sets under this perspective. In parallel, topology has proven essential for understanding fundamental questions in physics. Here we report the discovery of topological phase transitions in functional brain networks by merging concepts from TDA, topology, geometry, physics, and network theory. We show that topological phase transitions occur when the Euler entropy has a singularity, which remarkably coincides with the emergence of multidimensional topological holes in the brain network. The geometric nature of the transitions can be interpreted, under certain hypotheses, as an extension of percolation to high-dimensional objects. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives toward establishing reliable topological and geometrical markers for group and possibly individual differences in functional brain network organization.

Spectral peculiarity and criticality of a human connectome

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms. Considering the network evolution induced by the preference of 3-cycles formation, we discovered that for macaque and human connectomes the evolution with the conservation of local clusterization is crucial, while for primitive organisms the conservation of averaged clusterization is sufficient. Investigating for the first time the level spacing distribution of the spectrum of human connectome Laplacian matrix, we explicitly demonstrate that the spectral statistics corresponds to the critical regime, which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides strong support for debated statement of the brain criticality.

Network structural dependency in the human connectome across the life-span

Principles of network topology have been widely studied in the human connectome. Of particular interest is the modularity of the human brain, where the connectome is divided into subnetworks from which changes with development, aging or disease can be investigated. We present a weighted network measure, the Network Dependency Index (NDI), to identify an individual region’s importance to the global functioning of the network. Importantly, we utilize NDI to differentiate four subnetworks (Tiers) in the human connectome following Gaussian mixture model fitting. We analyze the topological aspects of each subnetwork with respect to age and compare it to rich club-based subnetworks (rich club, feeder, and seeder). Our results first demonstrate the efficacy of NDI to identify more consistent, central nodes of the connectome across age groups, when compared with the rich club framework. Stratifying the connectome by NDI led to consistent subnetworks across the life-span, revealing distinct patterns associated with age where, for example, the key relay nuclei and cortical regions are contained in a subnetwork with highest NDI. The divisions of the human connectome derived from our data-driven NDI framework have the potential to reveal topological alterations described by network measures through the life-span.

Brain connectomic associations with traditional Chinese medicine diagnostic classification of major depressive disorder: a diffusion tensor imaging study

Background

Major depressive disorder (MDD) is highly heterogeneous in pathogenesis and manifestations. Further classification may help characterize its heterogeneity. We previously have shown differential metabolomic profiles of traditional Chinese medicine (TCM) diagnostic subtypes of MDD. We further determined brain connectomic associations with TCM subtypes of MDD.

Methods

In this naturalistic study, 44 medication-free patients with a recurrent depressive episode were classified into liver qi stagnation (LQS, n = 26) and Heart and Spleen Deficiency (HSD, n = 18) subtypes according to TCM diagnosis. Healthy subjects (n = 28) were included as controls. Whole-brain white matter connectivity was analyzed on diffusion tensor imaging.

Results

The LQS subtype showed significant differences in multiple network metrics of the angular gyrus, middle occipital gyrus, calcarine sulcus, and Heschl's gyrus compared to the other two groups. The HSD subtype had markedly greater regional connectivity of the insula, parahippocampal gyrus, and posterior cingulate gyrus than the other two groups, and microstructural abnormalities of the frontal medial orbital gyrus and middle temporal pole. The insular betweenness centrality was strongly inversely correlated with the severity of depression and dichotomized the two subtypes at the optimal cutoff value with acceptable sensitivity and specificity.

Conclusions

The LQS subtype is mainly characterized by aberrant connectivity of the audiovisual perception-related temporal-occipital network, whereas the HSD subtype is more closely associated with hyperconnectivity and microstructural abnormalities of the limbic-paralimbic network. Insular connectivity may serve a biomarker for TCM-based classification of depression.Trial registration Registered at http://www.clinicaltrials.gov (NCT02346682) on January 27, 2015.

Evolutionary expansion of connectivity between multimodal association areas in the human brain compared with chimpanzees

The development of complex cognitive functions during human evolution coincides with pronounced encephalization and expansion of white matter, the brain's infrastructure for region-to-region communication. We investigated adaptations of the human macroscale brain network by comparing human brain wiring with that of the chimpanzee, one of our closest living primate relatives. White matter connectivity networks were reconstructed using diffusion-weighted MRI in humans (n = 57) and chimpanzees (n = 20) and then analyzed using network neuroscience tools. We demonstrate higher network centrality of connections linking multimodal association areas in humans compared with chimpanzees, together with a more pronounced modular topology of the human connectome. Furthermore, connections observed in humans but not in chimpanzees particularly link multimodal areas of the temporal, lateral parietal, and inferior frontal cortices, including tracts important for language processing. Network analysis demonstrates a particularly high contribution of these connections to global network integration in the human brain. Taken together, our comparative connectome findings suggest an evolutionary shift in the human brain toward investment of neural resources in multimodal connectivity facilitating neural integration, combined with an increase in language-related connectivity supporting functional specialization.

Making Sense of Connectivity

In addition to the assessment of local alterations of specific brain regions, the investigation of entire networks with in vivo neuroimaging techniques has gained increasing attention. In general, connectivity analysis refers to the investigation of links between brain regions, with the aim to characterize their interactions and information transfer. These may represent or relate to different physiological characteristics (structural, functional, or metabolic information) and can be calculated across different levels of granularity (2 regions vs whole brain). In this article, we provide an overview of different connectivity analysis approaches with interpretations and limitations as well as examples in pharmacological imaging and clinical applications. Structural connectivity obtained from diffusion MRI enables the reconstruction of neuronal fiber tracts. These physical links represent major constraints of functional connections, which are in turn defined as correlations between signal time courses. In addition, molecular connectivity approaches based on PET imaging enable the assessment of interregional associations of metabolic demands and neurotransmitter systems. Application of these approaches in clinical investigations has demonstrated novel alterations in various neurological and psychiatric disorders on a network level. Future work should aim for the combined assessment of multiple imaging modalities and to establish robust biomarkers for clinical use. These advancements will further improve the biological interpretation of connectivity metrics and networks of the human brain.

Dysautonomia is associated with structural and functional alterations in Parkinson disease

Objective

To investigate whether the presence of autonomic dysfunction is associated with white matter and functional connectivities and the level of cognitive performance in patients with de novo Parkinson disease (PD).

Methods

Seventy-five patients with de novo PD underwent a comprehensive autonomic function test and were classified into 2 groups according to the Composite Autonomic Severity Score (CASS; 30 with moderate to severe autonomic dysfunction [CASS 4–10, PD-AUT+] and 45 without significant autonomic dysfunction [CASS 0–3, PD-AUT−]). Network-based statistics and a graph theoretical analysis were performed to assess the interregional white matter connectivity using diffusion tensor imaging. We also performed analyses of resting-state functional connectivity and compared cognitive performance between the 2 groups.

Results

There were no significant differences in demographic characteristics and vascular risk factors between the PD-AUT+ and PD-AUT− groups. The PD-AUT+ group showed poorer cognitive performance on frontal/executive function than the PD-AUT− group. The PD-AUT+ group exhibited severely disrupted white matter connectivity in both fronto-subcortical and posterior cortical regions, which was well correlated with the severity of autonomic dysfunction assessed by the CASS. In addition, functional connectivity within the executive control network and dorsal attention network negatively correlated with the CASS.

Conclusions

Our results suggest that autonomic dysfunction is associated with disrupted white matter and functional brain connectivity as well as cognitive impairment in de novo patients with PD.

MultiLink Analysis: Brain Network Comparison via Sparse Connectivity Analysis

The analysis of the brain from a connectivity perspective is revealing novel insights into brain structure and function. Discovery is, however, hindered by the lack of prior knowledge used to make hypotheses. Additionally, exploratory data analysis is made complex by the high dimensionality of data. Indeed, to assess the effect of pathological states on brain networks, neuroscientists are often required to evaluate experimental effects in case-control studies, with hundreds of thousands of connections. In this paper, we propose an approach to identify the multivariate relationships in brain connections that characterize two distinct groups, hence permitting the investigators to immediately discover the subnetworks that contain information about the differences between experimental groups. In particular, we are interested in data discovery related to connectomics, where the connections that characterize differences between two groups of subjects are found. Nevertheless, those connections do not necessarily maximize the accuracy in classification since this does not guarantee reliable interpretation of specific differences between groups. In practice, our method exploits recent machine learning techniques employing sparsity to deal with weighted networks describing the whole-brain macro connectivity. We evaluated our technique on functional and structural connectomes from human and murine brain data. In our experiments, we automatically identified disease-relevant connections in datasets with supervised and unsupervised anatomy-driven parcellation approaches and by using high-dimensional datasets.

From Matrices to Knowledge: Using Semantic Networks to Annotate the Connectome

The connectome is regarded as the key to brain function in health and disease. Structural and functional neuroimaging enables us to measure brain connectivity in the living human brain. The field of connectomics describes the connectome as a mathematical graph with its connection strengths being represented by connectivity matrices. Graph theory algorithms are used to assess the integrity of the graph as a whole and to reveal brain network biomarkers for brain diseases; however, the faulty wiring of single connections or subnetworks as the structural correlate for neurological or mental diseases remains elusive. We describe a novel approach to represent the knowledge of human brain connectivity by a semantic network – a formalism frequently used in knowledge management to describe the semantic relations between objects. In our novel approach, objects are brain areas and connectivity is modeled as semantic relations among them. The semantic network turns the graph of the connectome into an explicit knowledge base about which brain areas are interconnected. Moreover, this approach can semantically enrich the measured connectivity of an individual subject by the semantic context from ontologies, brain atlases and molecular biological databases. Integrating all measurements and facts into one unified feature space enables cross-modal comparisons and analyses. We used a query mechanism for semantic networks to extract functional, structural and transcriptome networks. We found that in general higher structural and functional connectivity go along with a lower differential gene expression among connected brain areas; however, subcortical motor areas and limbic structures turned out to have a localized high differential gene expression while being strongly connected. In an additional explorative use case, we could show a localized high availability of fkbp5, gmeb1, and gmeb2 genes at a connection hub of temporo-limbic brain networks. Fkbp5 is known for having a role in stress-related psychiatric disorders, while gmeb1 and gmeb2 encode for modulator proteins of the glucocorticoid receptor, a key receptor in the hormonal stress system. Semantic networks tremendously ease working with multimodal neuroimaging and neurogenetics data and may reveal relevant coincidences between transcriptome and connectome networks.

Subject specificity of the correlation between large-scale structural and functional connectivity

Structural connectivity (SC), the physical pathways connecting regions in the brain, and functional connectivity (FC), the temporal coactivations, are known to be tightly linked. However, the nature of this relationship is still not understood. In the present study, we examined this relation more closely in six separate human neuroimaging datasets with different acquisition and preprocessing methods. We show that using simple linear associations, the relation between an individual's SC and FC is not subject specific for five of the datasets. Subject specificity of SC-FC fit is achieved only for one of the six datasets, the multimodal Glasser Human Connectome Project (HCP) parcellated dataset. We show that subject specificity of SC-FC correspondence is limited across datasets due to relatively small variability between subjects in SC compared with the larger variability in FC.

Multiplex core-periphery organization of the human connectome

What is the core of the human brain is a fundamental question that has been mainly addressed by studying the anatomical connections between differently specialized areas, thus neglecting the possible contributions from their functional interactions. While many methods are available to identify the core of a network when connections between nodes are all of the same type, a principled approach to define the core when multiple types of connectivity are allowed is still lacking. Here, we introduce a general framework to define and extract the core-periphery structure of multi-layer networks by explicitly taking into account the connectivity patterns at each layer. We first validate our algorithm on synthetic networks of different size and density, and with tunable overlap between the cores at different layers. We then use our method to merge information from structural and functional brain networks, obtaining in this way an integrated description of the core of the human connectome. Results confirm the role of the main known cortical and subcortical hubs, but also suggest the presence of new areas in the sensori-motor cortex that are crucial for intrinsic brain functioning. Taken together these findings provide fresh evidence on a fundamental question in modern neuroscience and offer new opportunities to explore the mesoscale properties of multimodal brain networks.

Information-Based Principle Induces Small-World Topology and Self-Organized Criticality in a Large Scale Brain Network

The information processing in the large scale network of the human brain is related to its cognitive functions. Due to requirements for adaptation to changing environments under biological constraints, these processes in the brain can be hypothesized to be optimized. The principles based on the information optimization are expected to play a central role in affecting the dynamics and topological structure of the brain network. Recent studies on the functional connectivity between brain regions, referred to as the functional connectome, reveal characteristics of their networks, such as self-organized criticality of brain dynamics and small-world topology. However, these important attributes are established separately, and their relations to the principle of the information optimization are unclear. Here, we show that the maximization principle of the mutual information entropy induces the optimal state, at which the small-world network topology and the criticality in the activation dynamics emerge. Our findings, based on the functional connectome analyses, show that according to the increasing mutual information entropy, the coactivation pattern converges to the state of self-organized criticality, and a phase transition of the network topology, which is responsible for the small-world topology, arises simultaneously at the same point. The coincidence of these phase transitions at the same critical point indicates that the criticality of the dynamics and the phase transition of the network topology are essentially rooted in the same phenomenon driven by the mutual information maximization. As a consequence, the two different attributes of the brain, self-organized criticality and small-world topology, can be understood within a unified perspective under the information-based principle. Thus, our study provides an insight into the mechanism underlying the information processing in the brain.

Warnings and caveats in brain controllability

A recent article by Gu et al. (Nat. Commun. 6, 2015) proposed to characterize brain networks, quantified using anatomical diffusion imaging, in terms of their "controllability", drawing on concepts and methods of control theory. They reported that brain activity is controllable from a single node, and that the topology of brain networks provides an explanation for the types of control roles that different regions play in the brain. In this work, we first briefly review the framework of control theory applied to complex networks. We then show contrasting results on brain controllability through the analysis of five different datasets and numerical simulations. We find that brain networks are not controllable (in a statistical significant way) by one single region. Additionally, we show that random null models, with no biological resemblance to brain network architecture, produce the same type of relationship observed by Gu et al. between the average/modal controllability and weighted degree. Finally, we find that resting state networks defined with fMRI cannot be attributed specific control roles. In summary, our study highlights some warning and caveats in the brain controllability framework.

The effect of the total small vessel disease burden on the structural brain network

Different cerebral small vessel disease (SVD) lesion types have been shown to disrupt structural brain network individually. Considering that they often coexist, we investigated the relation between their collective effect using the recently proposed total SVD score and structural brain network on MRI in 95 patients with first transient ischemic attack (TIA) or ischemic stroke. Fifty-nine patients with and 36 without any SVD lesions were included. The total SVD score was recorded. Diffusion tensor imaging was performed to estimate structural brain connections for subsequent brain connectivity analysis. The global efficiency and characteristic path length of the structural brain network are respectively lower and higher due to SVD. Lower nodal efficiency is also found in the insular, precuneus, supplementary motor area, paracentral lobule, putamen and hippocampus. The total SVD score is correlated with global network measures, the local clustering coefficient and nodal efficiency of hippocampus, and the nodal efficiency of paracentral lobule. We have successfully demonstrated that the disruption of global and local structural brain networks are associated with the increase in the overall SVD severity or burden of patients with TIA or first-time stroke.

Platform for systems medicine research and diagnostic applications in psychotic disorders-The METSY project

Psychotic disorders are associated with metabolic abnormalities including alterations in glucose and lipid metabolism. A major challenge in the treatment of psychosis is to identify patients with vulnerable metabolic profiles who may be at risk of developing cardiometabolic co-morbidities. It is established that both central and peripheral metabolic organs use lipids to control energy balance and regulate peripheral insulin sensitivity. The endocannabinoid system, implicated in the regulation of glucose and lipid metabolism, has been shown to be dysregulated in psychosis. It is currently unclear how these endocannabinoid abnormalities relate to metabolic changes in psychosis. Here we review recent research in the field of metabolic co-morbidities in psychotic disorders as well as the methods to study them and potential links to the endocannabinoid system. We also describe the bioinformatics platforms developed in the EU project METSY for the investigations of the biological etiology in patients at risk of psychosis and in first episode psychosis patients. The METSY project was established with the aim to identify and evaluate multi-modal peripheral and neuroimaging markers that may be able to predict the onset and prognosis of psychiatric and metabolic symptoms in patients at risk of developing psychosis and first episode psychosis patients. Given the intrinsic complexity and widespread role of lipid metabolism, a systems biology approach which combines molecular, structural and functional neuroimaging methods with detailed metabolic characterisation and multi-variate network analysis is essential in order to identify how lipid dysregulation may contribute to psychotic disorders. A decision support system, integrating clinical, neuropsychological and neuroimaging data, was also developed in order to aid clinical decision making in psychosis. Knowledge of common and specific mechanisms may aid the etiopathogenic understanding of psychotic and metabolic disorders, facilitate early disease detection, aid treatment selection and elucidate new targets for pharmacological treatments.

Resting State fMRI Functional Connectivity-Based Classification Using a Convolutional Neural Network Architecture

Machine learning techniques have become increasingly popular in the field of resting state fMRI (functional magnetic resonance imaging) network based classification. However, the application of convolutional networks has been proposed only very recently and has remained largely unexplored. In this paper we describe a convolutional neural network architecture for functional connectome classification called connectome-convolutional neural network (CCNN). Our results on simulated datasets and a publicly available dataset for amnestic mild cognitive impairment classification demonstrate that our CCNN model can efficiently distinguish between subject groups. We also show that the connectome-convolutional network is capable to combine information from diverse functional connectivity metrics and that models using a combination of different connectivity descriptors are able to outperform classifiers using only one metric. From this flexibility follows that our proposed CCNN model can be easily adapted to a wide range of connectome based classification or regression tasks, by varying which connectivity descriptor combinations are used to train the network.

The significance of negative correlations in brain connectivity

Understanding the modularity of functional magnetic resonance imaging (fMRI)-derived brain networks or "connectomes" can inform the study of brain function organization. However, fMRI connectomes additionally involve negative edges, which may not be optimally accounted for by existing approaches to modularity that variably threshold, binarize, or arbitrarily weight these connections. Consequently, many existing Q maximization-based modularity algorithms yield variable modular structures. Here, we present an alternative complementary approach that exploits how frequent the blood-oxygen-level-dependent (BOLD) signal correlation between two nodes is negative. We validated this novel probability-based modularity approach on two independent publicly-available resting-state connectome data sets (the Human Connectome Project [HCP] and the 1,000 functional connectomes) and demonstrated that negative correlations alone are sufficient in understanding resting-state modularity. In fact, this approach (a) permits a dual formulation, leading to equivalent solutions regardless of whether one considers positive or negative edges; (b) is theoretically linked to the Ising model defined on the connectome, thus yielding modularity result that maximizes data likelihood. Additionally, we were able to detect novel and consistent sex differences in modularity in both data sets. As data sets like HCP become widely available for analysis by the neuroscience community at large, alternative and perhaps more advantageous computational tools to understand the neurobiological information of negative edges in fMRI connectomes are increasingly important.

Consensus clustering approach to group brain connectivity matrices

A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease. The method can be summarized as follows: (a) define, for each node, a distance matrix for the set of subjects by comparing the connectivity pattern of that node in all pairs of subjects; (b) cluster the distance matrix for each node; (c) build the consensus network from the corresponding partitions; and (d) extract groups of subjects by finding the communities of the consensus network thus obtained. Different from the previous implementations of consensus clustering, we thus propose to use the consensus strategy to combine the information arising from the connectivity patterns of each node. The proposed approach may be seen either as an exploratory technique or as an unsupervised pretraining step to help the subsequent construction of a supervised classifier. Applications on a toy model and two real datasets show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.

Brain Modulyzer: Interactive Visual Analysis of Functional Brain Connectivity

We present Brain Modulyzer, an interactive visual exploration tool for functional magnetic resonance imaging (fMRI) brain scans, aimed at analyzing the correlation between different brain regions when resting or when performing mental tasks. Brain Modulyzer combines multiple coordinated views-such as heat maps, node link diagrams and anatomical views-using brushing and linking to provide an anatomical context for brain connectivity data. Integrating methods from graph theory and analysis, e.g., community detection and derived graph measures, makes it possible to explore the modular and hierarchical organization of functional brain networks. Providing immediate feedback by displaying analysis results instantaneously while changing parameters gives neuroscientists a powerful means to comprehend complex brain structure more effectively and efficiently and supports forming hypotheses that can then be validated via statistical analysis. To demonstrate the utility of our tool, we present two case studies-exploring progressive supranuclear palsy, as well as memory encoding and retrieval.

Network component analysis reveals developmental trajectories of structural connectivity and specific alterations in autism spectrum disorder

The structural organization of the brain can be characterized as a hierarchical ensemble of segregated modules linked by densely interconnected hub regions that facilitate distributed functional interactions. Disturbances to this network may be an important marker of abnormal development. Recently, several neurodevelopmental disorders, including autism spectrum disorder (ASD), have been framed as disorders of connectivity but the full nature and timing of these disturbances remain unclear. In this study, we use non-negative matrix factorization, a data-driven, multivariate approach, to model the structural network architecture of the brain as a set of superposed subnetworks, or network components. In an openly available dataset of 196 subjects scanned between 5 and 85 years we identify a set of robust and reliable subnetworks that develop in tandem with age and reflect both anatomically local and long-range, network hub connections. In a second experiment, we compare network components in a cohort of 51 high-functioning ASD adolescents to a group of age-matched controls. We identify a specific subnetwork representing an increase in local connection strength in the cingulate cortex in ASD (t = 3.44, P < 0.001). This work highlights possible long-term implications of alterations to the developmental trajectories of specific cortical subnetworks. Hum Brain Mapp 38:4169-4184, 2017. © 2017 Wiley Periodicals, Inc.

A distribution model of functional connectome based on criticality and energy constraints

The analysis of the network structure of the functional connectivity data constructed from fMRI images provides basic information about functions and features of the brain activity. We focus on the two features which are considered as relevant to the brain activity, the criticality and the constraint regarding energy consumptions. Within a wide variety of complex systems, the critical state occurs associated with a phase transition between distinct phases, random one and order one. Although the hypothesis that human brain activity is also in a state of criticality is supported by some experimental results, it still remains controversial. One issue is that experimental distributions exhibit deviations from the power law predicted by the criticality. Based on the assumption that constraints on brain from the biological costs cause these deviations, we derive a distribution model. The evaluation using the information criteria indicates an advantage of this model in fitting to experimental data compared to other representative distribution models, the truncated power law and the power law. Our findings also suggest that the mechanism underlying this model is closely related to the cost effective behavior in human brain with maximizing the network efficiency for the given network cost.