Clustering in complex directed networks

Flickering in Information Spreading Precedes Critical Transitions in Financial Markets

As many complex dynamical systems, financial markets exhibit sudden changes or tipping points that can turn into systemic risk. This paper aims at building and validating a new class of early warning signals of critical transitions. We base our analysis on information spreading patterns in dynamic temporal networks, where nodes are connected by short-term causality. Before a tipping point occurs, we observe flickering in information spreading, as measured by clustering coefficients. Nodes rapidly switch between "being in" and "being out" the information diffusion process. Concurrently, stock markets start to desynchronize. To capture these features, we build two early warning indicators based on the number of regime switches, and on the time between two switches. We divide our data into two sub-samples. Over the first one, using receiver operating curve, we show that we are able to detect a tipping point about one year before it occurs. For instance, our empirical model perfectly predicts the Global Financial Crisis. Over the second sub-sample, used as a robustness check, our two statistical metrics also capture, to a large extent, the 2016 financial turmoil. Our results suggest that our indicators have informational content about a future tipping point, and have therefore strong policy implications.

Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits

Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical circuits. To integrate these properties from anatomy and physiology, and to elucidate the links between them, we develop a novel cortical circuit model that captures a range of realistic features of synaptic connectivity. We show that the model accounts for the emergence of higher-order connectivity structures, including highly connected hub neurons that form an interconnected rich-club. The circuit model exhibits a rich repertoire of dynamical activity states, ranging from asynchronous to localized and global propagating wave states. We find that around the transition between asynchronous and localized propagating wave states, our model quantitatively reproduces a variety of major empirical findings regarding neural spatiotemporal dynamics, which otherwise remain disjointed in existing studies. These dynamics include diverse coupling (correlation) between spiking activity of individual neurons and the population, dynamical wave patterns with variable speeds and precise temporal structures of neural spikes. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to the diverse population coupling. These findings establish an integrated account of structural connectivity and activity dynamics of local cortical circuits, and provide new insights into understanding their working mechanisms.

To integrate essential anatomical and physiological properties of local cortical circuits and to elucidate mechanistic links between them, we develop a novel circuit model capturing key synaptic connectivity features. We show that the model explains the emergence of a range of connectivity patterns such as rich-club connectivity, and gives rise to a rich repertoire of cortical states. We identify both the anatomical and physiological mechanisms underlying the transition of these cortical states, and show that our model reconciles an otherwise disparate set of key physiological findings on neural activity dynamics. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to diverse neural population correlations as observed recently. Our model thus provides a framework for integrating and explaining a variety of neural connectivity properties and spatiotemporal activity dynamics observed in experimental studies, and provides novel experimentally testable predictions.

Abiotic stress induced miRNA-TF-gene regulatory network: A structural perspective

MicroRNAs (miRNAs) and transcription factors (TFs) are the largest families of trans-acting gene regulatory species, which are pivotal players in a complex regulatory network. Recently, extensive research on miRNAs and TFs in agriculture has identified these trans-acting regulatory species, as an effective tool for engineering new crop cultivars to increase yield and quality as well tolerance to environmental stresses but our knowledge of regulatory network is still not sufficient to decipher the exact mechanism. In the current work, stress-specific TF-miRNA-gene network was built for Arabidopsis under drought, cold, salt and waterlogging stress using data from reliable publically available databases; and transcriptome and degradome sequence data analysis by meta-analysis approach. Further network analysis elucidated significantly dense, scale-free, small world and hierarchical backbone of interactions. The various centrality measures highlighted several genes/TF/miRNAs as potential targets for tolerant variety cultivation. This comprehensive regulatory information will accelerate the advancement of current understanding on stress specific transcriptional and post-transcriptional regulatory mechanism and has promising utilizations for experimental biologist who are intended to improve plant crop performance under multiple Abiotic stress environments.

Hyper-Frequency Network Topology Changes During Choral Singing

Choral singing requires the coordination of physiological subsystems within and across individuals. Previously, we suggested that the choir functions as a superordinate system that imposes boundary conditions on the dynamic features of the individual singers and found reliable differences in the network topography by analyzing within- and cross-frequency couplings (WFC and CFC, respectively). Here, we further refine our analyses to investigate hyper-frequency network (HFN) topology structures (i.e., the layout or arrangement of connections) using a graph-theoretical approach. In a sample of eleven singers and one conductor engaged in choral singing (aged between 23 and 56 years, and including five men and seven women), we calculated phase coupling (WFC and CFC) between respiratory, cardiac, and vocalizing subsystems across ten frequencies of interest. All these couplings were used for construction of HFN with nodes being a combination of frequency components and subsystems across choir participants. With regard to the network topology measures, we found that clustering coefficients (CCs) as well as local and global efficiency were highest and characteristic path lengths, correspondingly, were shortest when the choir sang a canon in parts as compared to singing it in unison. Furthermore, these metrics revealed a significant relationship to individual heart rate, as an indicator of arousal, and to an index of heart rate variability indicated by the LF/HF ratio (low and high frequency, respectively), and reflecting the balance between sympathetic and parasympathetic activity. In addition, we found that the CC and local efficiency for groups singing the same canon part were higher than for groups of singers constructed randomly post hoc, indicating stronger neighbor–neighbor connections in the former. We conclude that network topology dynamics are a crucial determinant of group behavior and may represent a potent biomarker for social interaction.

Macroscopic Cluster Organizations Change the Complexity of Neural Activity

In this study, simulations are conducted using a network model to examine how the macroscopic network in the brain is related to the complexity of activity for each region. The network model is composed of multiple neuron groups, each of which consists of spiking neurons with different topological properties of a macroscopic network based on the Watts and Strogatz model. The complexity of spontaneous activity is analyzed using multiscale entropy, and the structural properties of the network are analyzed using complex network theory. Experimental results show that a macroscopic structure with high clustering and high degree centrality increases the firing rates of neurons in a neuron group and enhances intraconnections from the excitatory neurons to inhibitory neurons in a neuron group. As a result, the intensity of the specific frequency components of neural activity increases. This decreases the complexity of neural activity. Finally, we discuss the research relevance of the complexity of the brain activity.

Transient seizure onset network for localization of epileptogenic zone: effective connectivity and graph theory-based analyses of ECoG data in temporal lobe epilepsy

OBJECTIVE

Abnormal and dynamic epileptogenic networks cause difficulties for clinical epileptologists in the localization of the seizure onset zone (SOZ) and the epileptogenic zone (EZ) in preoperative assessments of patients with refractory epilepsy. The aim of this study is to investigate the characteristics of time-varying effective connectivity networks in various non-seizure and seizure periods, and to propose a quantitative approach for accurate localization of SOZ and EZ.

METHODS

We used electrocorticogram recordings in the temporal lobe and hippocampus from seven patients with temporal lobe epilepsy to characterize the effective connectivity dynamics at a high temporal resolution using the full-frequency adaptive directed transfer function (ffADTF) measure and five graph metrics, i.e., the out-degree (OD), closeness centrality (CC), betweenness centrality (BC), clustering coefficient (C), and local efficiency (LE). The ffADTF effective connectivity network was calculated and described in five frequency bands (δ, θ, α, β, and γ) and five seizure periods (pre-seizure, early seizure, mid-seizure, late seizure, and post-seizure). The cortical areas with high values of graph metrics in the transient seizure onset network were compared with the SOZ and EZ identified by clinical epileptologists and the results of epilepsy resection surgeries.

RESULTS

Origination and propagation of epileptic activity were observed in the high time resolution ffADTF effective connectivity network throughout the entire seizure period. The seizure-specific transient seizure onset ffADTF network that emerged at seizure onset time remained for approximately 20-50 ms with strong connections generated from both SOZ and EZ. The values of graph metrics in the SOZ and EZ were significantly larger than that in the other cortical areas. More cortical areas with the highest mean of graph metrics were the same as the clinically determined SOZ in the low-frequency δ and θ bands and in Engel Class I patients than in higher frequency α, β, and γ bands and in Engel Class II and III patients. The OD and C were more likely to localize the SOZ and EZ than CC, BC, and LE in the transient seizure onset network.

CONCLUSION

The high temporal resolution ffADTF effective connectivity analysis combined with the graph theoretical analysis helps us to understand how epileptic activity is generated and propagated during the seizure period. The newly discovered seizure-specific transient seizure onset network could be an important biomarker and a promising tool for more precise localization of the SOZ and EZ in preoperative evaluations.

Mean-field analysis of directed modular networks

We considered a modular network with a binomial degree distribution and related the analytical relationships of the network properties (modularity, average clustering coefficient, and small-worldness) with structural parameters that define the network, i.e., number of nodes, number of modules, average node degree, and ratio of intra-modular to total connections. Even though modular networks are universally found in real-world systems and are consequently of broad interest in complex network science, the relationship between network properties and structural parameters has not yet been formulated. Here, we show that a series of equations for predicting the network properties can be related using a mean-field connectivity matrix that is defined on the basis of the structural parameters in the network generation algorithm. The theoretical results are then compared with values calculated numerically using the original connectivity matrix and are found to agree well, except when the connections between modules are sparse. Representation of the structure of the network using simple parameters is expected to be conducive for elucidating the structure-dynamics relationship.

Graph Energies of Egocentric Networks and Their Correlation with Vertex Centrality Measures

Graph energy is the energy of the matrix representation of the graph, where the energy of a matrix is the sum of singular values of the matrix. Depending on the definition of a matrix, one can contemplate graph energy, Randić energy, Laplacian energy, distance energy, and many others. Although theoretical properties of various graph energies have been investigated in the past in the areas of mathematics, chemistry, physics, or graph theory, these explorations have been limited to relatively small graphs representing chemical compounds or theoretical graph classes with strictly defined properties. In this paper we investigate the usefulness of the concept of graph energy in the context of large, complex networks. We show that when graph energies are applied to local egocentric networks, the values of these energies correlate strongly with vertex centrality measures. In particular, for some generative network models graph energies tend to correlate strongly with the betweenness and the eigencentrality of vertices. As the exact computation of these centrality measures is expensive and requires global processing of a network, our research opens the possibility of devising efficient algorithms for the estimation of these centrality measures based only on local information.

Assortative mixing in spatially-extended networks

We focus on spatially-extended networks during their transition from short-range connectivities to a scale-free structure expressed by heavy-tailed degree-distribution. In particular, a model is introduced for the generation of such graphs, which combines spatial growth and preferential attachment. In this model the transition to heterogeneous structures is always accompanied by a change in the graph's degree-degree correlation properties: while high assortativity levels characterize the dominance of short distance couplings, long-range connectivity structures are associated with small amounts of disassortativity. Our results allow to infer that a disassortative mixing is essential for establishing long-range links. We discuss also how our findings are consistent with recent experimental studies of 2-dimensional neuronal cultures.

A simple computer vision pipeline reveals the effects of isolation on social interaction dynamics in Drosophila

Isolation profoundly influences social behavior in all animals. In humans, isolation has serious effects on health. Drosophila melanogaster is a powerful model to study small-scale, temporally-transient social behavior. However, longer-term analysis of large groups of flies is hampered by the lack of effective and reliable tools. We built a new imaging arena and improved the existing tracking algorithm to reliably follow a large number of flies simultaneously. Next, based on the automatic classification of touch and graph-based social network analysis, we designed an algorithm to quantify changes in the social network in response to prior social isolation. We observed that isolation significantly and swiftly enhanced individual and local social network parameters depicting near-neighbor relationships. We explored the genome-wide molecular correlates of these behavioral changes and found that whereas behavior changed throughout the six days of isolation, gene expression alterations occurred largely on day one. These changes occurred mostly in metabolic genes, and we verified the metabolic changes by showing an increase of lipid content in isolated flies. In summary, we describe a highly reliable tracking and analysis pipeline for large groups of flies that we use to unravel the behavioral, molecular and physiological impact of isolation on social network dynamics in Drosophila.

Social isolation severely affects the behavior and physiology of social animals, including humans. The fruit fly is a powerful model for studying the mechanisms of development, health and disease and is also used to study social behaviors such as mating and aggression. However, these studies are limited to examining few individuals for shorts amounts of time, due to the lack of effective computational tools for the analysis of large groups over prolonged time. To overcome this hurdle, we built a new behavioral arena and developed new software that accurately tracks many flies simultaneously over long time periods. The arena is cheap and easy to build and the software works with low resolution videos. Using these improved tools, we studied social isolation in groups of male flies. We found that isolation caused flies to form stronger interactions with neighboring flies in their social network. These behavioral changes were preceded by transient changes in the expression of metabolism genes and eventually resulted in isolated flies accumulating fat, as has been previously observed in studies in mice and humans. Our study opens the door for the use of fruit flies in future studies of social isolation.

Exploring the Neuroplastic Effects of Biofeedback Training on Smokers

Smoking and stress cooccur in different stages of a nicotine addiction cycle, affecting brain function and showing additive impact on different physiological responses. Resting-state functional connectivity has shown potential in identifying these alterations. Nicotine addiction has been associated with detrimental effects on functional integrity of the central nervous system, including the organization of resting-state networks. Prolonged stress may result in enhanced activation of the default mode network (DMN). Considering that biofeedback has shown promise in alleviating physiological manifestations of stress, we aimed to explore the possible neuroplastic effects of biofeedback training on smokers. Clinical, behavioral, and neurophysiological (resting-state EEG) data were collected from twenty-seven subjects before and after five sessions of skin temperature training. DMN functional cortical connectivity was investigated. While clinical status remained unaltered, the degree of nicotine dependence and psychiatric symptoms were significantly improved. Significant changes in DMN organization and network properties were not observed, except for a significant increase of information flow from the right ventrolateral prefrontal cortex and right temporal pole cortex towards other DMN components. Biofeedback aiming at stress alleviation in smokers could play a protective role against maladaptive plasticity of connectivity. Multiple sessions, individualized interventions and more suitable methods to promote brain plasticity, such as neurofeedback training, should be considered.

Estimating the impact of structural directionality: How reliable are undirected connectomes?

Directionality is a fundamental feature of network connections. Most structural brain networks are intrinsically directed because of the nature of chemical synapses, which comprise most neuronal connections. Because of the limitations of noninvasive imaging techniques, the directionality of connections between structurally connected regions of the human brain cannot be confirmed. Hence, connections are represented as undirected, and it is still unknown how this lack of directionality affects brain network topology. Using six directed brain networks from different species and parcellations (cat, mouse, C. elegans, and three macaque networks), we estimate the inaccuracies in network measures (degree, betweenness, clustering coefficient, path length, global efficiency, participation index, and small-worldness) associated with the removal of the directionality of connections. We employ three different methods to render directed brain networks undirected: (a) remove unidirectional connections, (b) add reciprocal connections, and (c) combine equal numbers of removed and added unidirectional connections. We quantify the extent of inaccuracy in network measures introduced through neglecting connection directionality for individual nodes and across the network. We find that the coarse division between core and peripheral nodes remains accurate for undirected networks. However, hub nodes differ considerably when directionality is neglected. Comparing the different methods to generate undirected networks from directed ones, we generally find that the addition of reciprocal connections (false positives) causes larger errors in graph-theoretic measures than the removal of the same number of directed connections (false negatives). These findings suggest that directionality plays an essential role in shaping brain networks and highlight some limitations of undirected connectomes.

Functional Brain Connectivity during Multiple Motor Imagery Tasks in Spinal Cord Injury

Reciprocal communication of the central and peripheral nervous systems is compromised during spinal cord injury due to neurotrauma of ascending and descending pathways. Changes in brain organization after spinal cord injury have been associated with differences in prognosis. Changes in functional connectivity may also serve as injury biomarkers. Most studies on functional connectivity have focused on chronic complete injury or resting-state condition. In our study, ten right-handed patients with incomplete spinal cord injury and ten age- and gender-matched healthy controls performed multiple visual motor imagery tasks of upper extremities and walking under high-resolution electroencephalography recording. Directed transfer function was used to study connectivity at the cortical source space between sensorimotor nodes. Chronic disruption of reciprocal communication in incomplete injury could result in permanent significant decrease of connectivity in a subset of the sensorimotor network, regardless of positive or negative neurological outcome. Cingulate motor areas consistently contributed the larger outflow (right) and received the higher inflow (left) among all nodes, across all motor imagery categories, in both groups. Injured subjects had higher outflow from left cingulate than healthy subjects and higher inflow in right cingulate than healthy subjects. Alpha networks were less dense, showing less integration and more segregation than beta networks. Spinal cord injury patients showed signs of increased local processing as adaptive mechanism. This trial is registered with NCT02443558.

Functional triplet motifs underlie accurate predictions of single-trial responses in populations of tuned and untuned V1 neurons

Visual stimuli evoke activity in visual cortical neuronal populations. Neuronal activity can be selectively modulated by particular visual stimulus parameters, such as the direction of a moving bar of light, resulting in well-defined trial averaged tuning properties. However, given any single stimulus parameter, a large number of neurons in visual cortex remain unmodulated, and the role of this untuned population is not well understood. Here, we use two-photon calcium imaging to record, in an unbiased manner, from large populations of layer 2/3 excitatory neurons in mouse primary visual cortex to describe co-varying activity on single trials in neuronal populations consisting of both tuned and untuned neurons. Specifically, we summarize pairwise covariability with an asymmetric partial correlation coefficient, allowing us to analyze the resultant population correlation structure, or functional network, with graph theory. Using the graph neighbors of a neuron, we find that the local population, including both tuned and untuned neurons, are able to predict individual neuron activity on a moment to moment basis, while also recapitulating tuning properties of tuned neurons. Variance explained in total population activity scales with the number of neurons imaged, demonstrating larger sample sizes are required to fully capture local network interactions. We also find that a specific functional triplet motif in the graph results in the best predictions, suggesting a signature of informative correlations in these populations. In summary, we show that unbiased sampling of the local population can explain single trial response variability as well as trial-averaged tuning properties in V1, and the ability to predict responses is tied to the occurrence of a functional triplet motif.

Controllability Analysis of A Gene Network for Arabidopsis thaliana Reveals Characteristics of Functional Gene Families

Based on structural controllability of complex networks and a constructed gene network with 9241 nodes for Arabidopsis thaliana, we classified nodes into five categories via their roles in control or node deletion, including indispensable, neutral, dispensable, driver and critical driver nodes. The indispensable nodes can increase the number of drivers after deletion, which are never drivers or critical drivers. About 10% nodes are indispensable. However, more than 60% nodes are neutral ones. More than 62% nodes are drivers, and indicates the gene network is very difficult to be fully controlled. Gene Ontology (GO) enrichment analysis reveals that different sets of nodes have preferred biological functions and processes.The indispensable nodes are significantly enriched as essential genes, drought responsive and abscisic acid (ABA) independent genes, transcriptional factors (TFs), core cell cycle genes, ABA and Gibberellin (GA) related genes. The critical drivers are enriched as receptor kinase-like genes, while shorted in WRKY TFs and functional genes that are enriched in the indispensable nodes. Robustness analysis based on node and edge additions, edge rewiring indicate the obtained conclusions are robust to network perturbations. Our investigations clarify control roles of some gene families and provide potential implications for identifying functional genes in other plant species, such as drought responsive genes and TFs.

Predicting species emergence in simulated complex pre-biotic networks

An intriguing question in evolution is what would happen if one could "replay" life's tape. Here, we explore the following hypothesis: when replaying the tape, the details ("decorations") of the outcomes would vary but certain "invariants" might emerge across different life-tapes sharing similar initial conditions. We use large-scale simulations of an in silico model of pre-biotic evolution called GARD (Graded Autocatalysis Replication Domain) to test this hypothesis. GARD models the temporal evolution of molecular assemblies, governed by a rates matrix (i.e. network) that biases different molecules' likelihood of joining or leaving a dynamically growing and splitting assembly. Previous studies have shown the emergence of so called compotypes, i.e., species capable of replication and selection response. Here, we apply networks' science to ascertain the degree to which invariants emerge across different life-tapes under GARD dynamics and whether one can predict these invariant from the chemistry specification alone (i.e. GARD's rates network representing initial conditions). We analysed the (complex) rates' network communities and asked whether communities are related (and how) to the emerging species under GARD's dynamic, and found that the communities correspond to the species emerging from the simulations. Importantly, we show how to use the set of communities detected to predict species emergence without performing any simulations. The analysis developed here may impact complex systems simulations in general.

Different Topological Properties of EEG-Derived Networks Describe Working Memory Phases as Revealed by Graph Theoretical Analysis

Several non-invasive imaging methods have contributed to shed light on the brain mechanisms underlying working memory (WM). The aim of the present study was to depict the topology of the relevant EEG-derived brain networks associated to distinct operations of WM function elicited by the Sternberg Item Recognition Task (SIRT) such as encoding, storage, and retrieval in healthy, middle age (46 ± 5 years) adults. High density EEG recordings were performed in 17 participants whilst attending a visual SIRT. Neural correlates of WM were assessed by means of a combination of EEG signal processing methods (i.e., time-varying connectivity estimation and graph theory), in order to extract synthetic descriptors of the complex networks underlying the encoding, storage, and retrieval phases of WM construct. The group analysis revealed that the encoding phase exhibited a significantly higher small-world topology of EEG networks with respect to storage and retrieval in all EEG frequency oscillations, thus indicating that during the encoding of items the global network organization could “optimally” promote the information flow between WM sub-networks. We also found that the magnitude of such configuration could predict subject behavioral performance when memory load increases as indicated by the negative correlation between Reaction Time and the local efficiency values estimated during the encoding in the alpha band in both 4 and 6 digits conditions. At the local scale, the values of the degree index which measures the degree of in- and out- information flow between scalp areas were found to specifically distinguish the hubs within the relevant sub-networks associated to each of the three different WM phases, according to the different role of the sub-network of regions in the different WM phases. Our findings indicate that the use of EEG-derived connectivity measures and their related topological indices might offer a reliable and yet affordable approach to monitor WM components and thus theoretically support the clinical assessment of cognitive functions in presence of WM decline/impairment, as it occurs after stroke.

Decoding the different states of visual attention using functional and effective connectivity features in fMRI data

The present paper concentrates on the impact of visual attention task on structure of the brain functional and effective connectivity networks using coherence and Granger causality methods. Since most studies used correlation method and resting-state functional connectivity, the task-based approach was selected for this experiment to boost our knowledge of spatial and feature-based attention. In the present study, the whole brain was divided into 82 sub-regions based on Brodmann areas. The coherence and Granger causality were applied to construct functional and effective connectivity matrices. These matrices were converted into graphs using a threshold, and the graph theory measures were calculated from it including degree and characteristic path length. Visual attention was found to reveal more information during the spatial-based task. The degree was higher while performing a spatial-based task, whereas characteristic path length was lower in the spatial-based task in both functional and effective connectivity. Primary and secondary visual cortex (17 and 18 Brodmann areas) were highly connected to parietal and prefrontal cortex while doing visual attention task. Whole brain connectivity was also calculated in both functional and effective connectivity. Our results reveal that Brodmann areas of 17, 18, 19, 46, 3 and 4 had a significant role proving that somatosensory, parietal and prefrontal regions along with visual cortex were highly connected to other parts of the cortex during the visual attention task. Characteristic path length results indicated an increase in functional connectivity and more functional integration in spatial-based attention compared with feature-based attention. The results of this work can provide useful information about the mechanism of visual attention at the network level.

Structure constrained by metadata in networks of chess players

Chess is an emblematic sport that stands out because of its age, popularity and complexity. It has served to study human behavior from the perspective of a wide number of disciplines, from cognitive skills such as memory and learning, to aspects like innovation and decision-making. Given that an extensive documentation of chess games played throughout history is available, it is possible to perform detailed and statistically significant studies about this sport. Here we use one of the most extensive chess databases in the world to construct two networks of chess players. One of the networks includes games that were played over-the-board and the other contains games played on the Internet. We study the main topological characteristics of the networks, such as degree distribution and correlations, transitivity and community structure. We complement the structural analysis by incorporating players’ level of play as node metadata. Although both networks are topologically different, we show that in both cases players gather in communities according to their expertise and that an emergent rich-club structure, composed by the top-rated players, is also present.

Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space

Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level definition of the ‘function’ of a motif, in terms of two fundamental properties of its dynamical state space as a Boolean network. One is the basin entropy, which is a complexity measure of the dynamics of Boolean networks. The other is the diversity of cyclic attractor lengths that a given motif can produce. Using these two measures, we examine all 104 topologically distinct three-node motifs and show that the structural properties of a motif, such as the presence of feedback loops and feed-forward loops, predict fundamental characteristics of its dynamical state space, which in turn determine aspects of its functional versatility. We also show that these higher-level properties have a direct bearing on real regulatory networks, as both basin entropy and cycle length diversity show a close correspondence with the prevalence, in neural and genetic regulatory networks, of the 13 connected motifs without self-interactions that have been studied extensively in the literature.

Applying graphs and complex networks to football metric interpretation

This work presents a methodology for analysing the interactions between players in a football team, from the point of view of graph theory and complex networks. We model the complex network of passing interactions between players of a same team in 32 official matches of the Liga de Fútbol Profesional (Spain), using a passing/reception graph. This methodology allows us to understand the play structure of the team, by analysing the offensive phases of game-play. We utilise two different strategies for characterising the contribution of the players to the team: the clustering coefficient, and centrality metrics (closeness and betweenness). We show the application of this methodology by analyzing the performance of a professional Spanish team according to these metrics and the distribution of passing/reception in the field. Keeping in mind the dynamic nature of collective sports, in the future we will incorporate metrics which allows us to analyse the performance of the team also according to the circumstances of game-play and to different contextual variables such as, the utilisation of the field space, the time, and the ball, according to specific tactical situations.

Spatio-Temporal Patterns of the International Merger and Acquisition Network

This paper analyses the world web of mergers and acquisitions (M&As) using a complex network approach. We use data of M&As to build a temporal sequence of binary and weighted-directed networks for the period 1995–2010 and 224 countries (nodes) connected according to their M&As flows (links). We study different geographical and temporal aspects of the international M&A network (IMAN), building sequences of filtered sub-networks whose links belong to specific intervals of distance or time. Given that M&As and trade are complementary ways of reaching foreign markets, we perform our analysis using statistics employed for the study of the international trade network (ITN), highlighting the similarities and differences between the ITN and the IMAN. In contrast to the ITN, the IMAN is a low density network characterized by a persistent giant component with many external nodes and low reciprocity. Clustering patterns are very heterogeneous and dynamic. High-income economies are the main acquirers and are characterized by high connectivity, implying that most countries are targets of a few acquirers. Like in the ITN, geographical distance strongly impacts the structure of the IMAN: link-weights and node degrees have a non-linear relation with distance, and an assortative pattern is present at short distances.

Sensitivity of directed networks to the addition and pruning of edges and vertices

Directed networks have various topologically different extensive components, in contrast to a single giant component in undirected networks. We study the sensitivity (response) of the sizes of these extensive components in directed complex networks to the addition and pruning of edges and vertices. We introduce the susceptibility, which quantifies this sensitivity. We show that topologically different parts of a directed network have different sensitivity to the addition and pruning of edges and vertices and, therefore, they are characterized by different susceptibilities. These susceptibilities diverge at the critical point of the directed percolation transition, signaling the appearance (or disappearance) of the giant strongly connected component in the infinite size limit. We demonstrate this behavior in randomly damaged real and synthetic directed complex networks, such as the World Wide Web, Twitter, the Caenorhabditis elegans neural network, directed Erdős-Rényi graphs, and others. We reveal a nonmonotonic dependence of the sensitivity to random pruning of edges or vertices in the case of C. elegans and Twitter that manifests specific structural peculiarities of these networks. We propose the measurements of the susceptibilities during the addition or pruning of edges and vertices as a new method for studying structural peculiarities of directed networks.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Brain Interaction during Cooperation: Evaluating Local Properties of Multiple-Brain Network

Subjects’ interaction is the core of most human activities. This is the reason why a lack of coordination is often the cause of missing goals, more than individual failure. While there are different subjective and objective measures to assess the level of mental effort required by subjects while facing a situation that is getting harder, that is, mental workload, to define an objective measure based on how and if team members are interacting is not so straightforward. In this study, behavioral, subjective and synchronized electroencephalographic data were collected from couples involved in a cooperative task to describe the relationship between task difficulty and team coordination, in the sense of interaction aimed at cooperatively performing the assignment. Multiple-brain connectivity analysis provided information about the whole interacting system. The results showed that averaged local properties of a brain network were affected by task difficulty. In particular, strength changed significantly with task difficulty and clustering coefficients strongly correlated with the workload itself. In particular, a higher workload corresponded to lower clustering values over the central and parietal brain areas. Such results has been interpreted as less efficient organization of the network when the subjects’ activities, due to high workload tendencies, were less coordinated.

Australia's regional innovation systems: inter-industry interaction in innovative activities in three Australian territories

Regional specifics reveal in differences in economic activity and structure, the institutional, socio-economic and cultural environment and not least in the capability of regions to create new knowledge and to generate innovations. Focusing on the regional level, this paper for three Australian territories (New South Wales, Victoria and Queensland) explores patterns of innovative activities in their private business sectors. Furthermore, these patterns are compared to specifics of each region's economic structure. We make use of input-output-based innovation flow networks, which are directed and weighted instead of binary. The value added of the proposed analysis is that we are able to trace a variety of different aspects related to the structure of innovative activities for each territory. It gets evident that mostly innovative activities in each territory are not strong in 'niche' branches but in fields of intense economic activity, signalising the high path-dependency of innovative activities in a specific geographical environment.

Mapping functional connectivity of bursting neuronal networks

Using single-cell laser scanning photostimulation (LSPS) combined with broad-field calcium imaging, we measured the functional connectivity of neuronal cultures before and after the developmental appearance of network bursting. From these data, network properties were determined for these relatively large neuronal networks. Based on these properties, we found that although 'small-world' network behavior existed throughout this time period, only average node degree and global efficiency correlate with the development of network bursting while clustering and local efficiency remained relatively constant.

The left middle temporal gyrus in the middle of an impaired social-affective communication network in social anxiety disorder

BACKGROUND

Previous studies on patients diagnosed with social anxiety disorder (SAD) reported changed patterns of the resting-state functional connectivity network (rs-FCN) between the prefrontal cortices and other prefrontal, amygdalar or striatal regions. Using a graph theory approach, this study explored the modularity-based community profile and patterns of inter-/intra-modular communication for the rs-FCN in SAD.

METHODS

In total, for 28 SAD patients and 27 healthy controls (HC), functional magnetic resonance imaging (fMRI) data were acquired in resting-state and subjected to a graph theory analysis.

RESULTS

The within-module degree z-score for a hub region [out of a total of 10 hub regions ranked using the participation coefficient] named left middle temporal gyrus was impaired in SAD compared to HC, proportional to the severity of clinician-scored and patient-reported functional impairment in SAD.

LIMITATIONS

Most of participants included in this study were undergraduate students in their early-to-mid 20's.

CONCLUSIONS

This study showed the importance of functional communication from the left middle temporal gyrus with other opercular-insular-subcortical regions for better objective functioning and lesser subjective disability in SAD.

Emergence of ultrafast sparsely synchronized rhythms and their responses to external stimuli in an inhomogeneous small-world complex neuronal network

We consider an inhomogeneous small-world network (SWN) composed of inhibitory short-range (SR) and long-range (LR) interneurons, and investigate the effect of network architecture on emergence of synchronized brain rhythms by varying the fraction of LR interneurons p_long. The betweenness centralities of the LR and SR interneurons (characterizing the potentiality in controlling communication between other interneurons) are distinctly different. Hence, in view of the betweenness, SWNs we consider are inhomogeneous, unlike the "canonical" Watts-Strogatz SWN with nearly the same betweenness centralities. For small p_long, the load of communication traffic is much concentrated on a few LR interneurons. However, as p_long is increased, the number of LR connections (coming from LR interneurons) increases, and then the load of communication traffic is less concentrated on LR interneurons, which leads to better efficiency of global communication between interneurons. Sparsely synchronized rhythms are thus found to emerge when passing a small critical value p_long^(c)(≃0.16). The population frequency of the sparsely synchronized rhythm is ultrafast (higher than 100 Hz), while the mean firing rate of individual interneurons is much lower (∼30 Hz) due to stochastic and intermittent neural discharges. These dynamical behaviors in the inhomogeneous SWN are also compared with those in the homogeneous Watts-Strogatz SWN, in connection with their network topologies. Particularly, we note that the main difference between the two types of SWNs lies in the distribution of betweenness centralities. Unlike the case of the Watts-Strogatz SWN, dynamical responses to external stimuli vary depending on the type of stimulated interneurons in the inhomogeneous SWN. We consider two cases of external time-periodic stimuli applied to sub-populations of the LR and SR interneurons, respectively. Dynamical responses (such as synchronization suppression and enhancement) to these two cases of stimuli are studied and discussed in relation to the betweenness centralities of stimulated interneurons, representing the effectiveness for transfer of stimulation effect in the whole network.

Automated network analysis to measure brain effective connectivity estimated from EEG data of patients with alcoholism

OBJECTIVE

Detection and diagnosis based on extracting features and classification using electroencephalography (EEG) signals are being studied vigorously. A network analysis of time series EEG signal data is one of many techniques that could help study brain functions. In this study, we analyze EEG to diagnose alcoholism.

APPROACH

We propose a novel methodology to estimate the differences in the status of the brain based on EEG data of normal subjects and data from alcoholics by computing many parameters stemming from effective network using Granger causality.

MAIN RESULTS

Among many parameters, only ten parameters were chosen as final candidates. By the combination of ten graph-based parameters, our results demonstrate predictable differences between alcoholics and normal subjects. A support vector machine classifier with best performance had 90% accuracy with sensitivity of 95.3%, and specificity of 82.4% for differentiating between the two groups.

Structural connectome topology relates to regional BOLD signal dynamics in the mouse brain

Brain dynamics are thought to unfold on a network determined by the pattern of axonal connections linking pairs of neuronal elements; the so-called connectome. Prior work has indicated that structural brain connectivity constrains pairwise correlations of brain dynamics ("functional connectivity"), but it is not known whether inter-regional axonal connectivity is related to the intrinsic dynamics of individual brain areas. Here we investigate this relationship using a weighted, directed mesoscale mouse connectome from the Allen Mouse Brain Connectivity Atlas and resting state functional MRI (rs-fMRI) time-series data measured in 184 brain regions in eighteen anesthetized mice. For each brain region, we measured degree, betweenness, and clustering coefficient from weighted and unweighted, and directed and undirected versions of the connectome. We then characterized the univariate rs-fMRI dynamics in each brain region by computing 6930 time-series properties using the time-series analysis toolbox, hctsa. After correcting for regional volume variations, strong and robust correlations between structural connectivity properties and rs-fMRI dynamics were found only when edge weights were accounted for, and were associated with variations in the autocorrelation properties of the rs-fMRI signal. The strongest relationships were found for weighted in-degree, which was positively correlated to the autocorrelation of fMRI time series at time lag τ = 34 s (partial Spearman correlation ρ=0.58), as well as a range of related measures such as relative high frequency power (f > 0.4 Hz: ρ=-0.43). Our results indicate that the topology of inter-regional axonal connections of the mouse brain is closely related to intrinsic, spontaneous dynamics such that regions with a greater aggregate strength of incoming projections display longer timescales of activity fluctuations.

Spatial confluence of psychological and anatomical network constructs in the human brain revealed by a mass meta-analysis of fMRI activation

It is well-known that the brain's activity is organized into networks but it is unclear how many networks exist. Additionally, there is also a risk of ambiguity since different names for the same network are frequently reported in the literature. In this study, we employed a mass meta-analysis of fMRI data associated with network constructs originating from both psychology and neuroscience. Based on the results from the meta-analysis, we derived a spatial similarity map between all construct terms, showing that the brain's networks cluster hierarchically into several levels. The results presented are useful as a first step in developing a unified terminology for large-scale brain network and a platform for a queryable network atlas.

Identifying topological motif patterns of human brain functional networks

Recent imaging connectome studies demonstrated that the human functional brain network follows an efficient small-world topology with cohesive functional modules and highly connected hubs. However, the functional motif patterns that represent the underlying information flow remain largely unknown. Here, we investigated motif patterns within directed human functional brain networks, which were derived from resting-state functional magnetic resonance imaging data with controlled confounding hemodynamic latencies. We found several significantly recurring motifs within the network, including the two-node reciprocal motif and five classes of three-node motifs. These recurring motifs were distributed in distinct patterns to support intra- and inter-module functional connectivity, which also promoted integration and segregation in network organization. Moreover, the significant participation of several functional hubs in the recurring motifs exhibited their critical role in global integration. Collectively, our findings highlight the basic architecture governing brain network organization and provide insight into the information flow mechanism underlying intrinsic brain activities. Hum Brain Mapp 38:2734-2750, 2017. © 2017 Wiley Periodicals, Inc.

Edge anisotropy and the geometric perspective on flow networks

Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding the existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.

Clustering coefficient and periodic orbits in flow networks

We show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e., graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions, identifies approximate locations of periodic trajectories in the flow system. This is true for steady flows and for periodic ones in which the time interval τ used to construct the network is the period of the flow or a multiple of it. In other situations, the clustering coefficient still identifies cyclic motion between regions of the fluid. Besides the fluid context, these ideas apply equally well to general dynamical systems. By varying the value of τ used to construct the network, a kind of spectroscopy can be performed so that the observation of high values of mean clustering at a value of τ reveals the presence of periodic orbits of period 3τ, which impact phase space significantly. These results are illustrated with examples of increasing complexity, namely, a steady and a periodically perturbed model two-dimensional fluid flow, the three-dimensional Lorenz system, and the turbulent surface flow obtained from a numerical model of circulation in the Mediterranean sea.

Tracking the Evolution of Infrastructure Systems and Mass Responses Using Publically Available Data

Networks can evolve even on a short-term basis. This phenomenon is well understood by network scientists, but receive little attention in empirical literature involving real-world networks. On one hand, this is due to the deceitfully fixed topology of some networks such as many physical infrastructures, whose evolution is often deemed unlikely to occur in short term; on the other hand, the lack of data prohibits scientists from studying subjects such as social networks that seem likely to evolve on a short-term basis. We show that both networks-the infrastructure network and social network-are able to demonstrate evolutionary dynamics at the system level even in the short-term, characterized by shifting between different phases as predicted in network science. We develop a methodology of tracking the evolutionary dynamics of the two networks by incorporating flows and the microstructure of networks such as motifs. This approach is applied to the human interaction network and two transportation networks (subway and taxi) in the context of Hurricane Sandy, using publically available Twitter data and transportation data. Our result shows that significant changes in the system-level structure of networks can be detected on a continuous basis. This result provides a promising channel for real-time tracking in the future.

Graph Theoretic and Motif Analyses of the Hippocampal Neuron Type Potential Connectome

We computed the potential connectivity map of all known neuron types in the rodent hippocampal formation by supplementing scantly available synaptic data with spatial distributions of axons and dendrites from the open-access knowledge base Hippocampome.org. The network that results from this endeavor, the broadest and most complete for a mammalian cortical region at the neuron-type level to date, contains more than 3200 connections among 122 neuron types across six subregions. Analyses of these data using graph theory metrics unveil the fundamental architectural principles of the hippocampal circuit. Globally, we identify a highly specialized topology minimizing communication cost; a modular structure underscoring the prominence of the trisynaptic loop; a core set of neuron types serving as information-processing hubs as well as a distinct group of particular antihub neurons; a nested, two-tier rich club managing much of the network traffic; and an innate resilience to random perturbations. At the local level, we uncover the basic building blocks, or connectivity patterns, that combine to produce complex global functionality, and we benchmark their utilization in the circuit relative to random networks. Taken together, these results provide a comprehensive connectivity profile of the hippocampus, yielding novel insights on its functional operations at the computationally crucial level of neuron types.

Topology, Cross-Frequency, and Same-Frequency Band Interactions Shape the Generation of Phase-Amplitude Coupling in a Neural Mass Model of a Cortical Column

Phase-amplitude coupling (PAC), a type of cross-frequency coupling (CFC) where the phase of a low-frequency rhythm modulates the amplitude of a higher frequency, is becoming an important indicator of information transmission in the brain. However, the neurobiological mechanisms underlying its generation remain undetermined. A realistic, yet tractable computational model of the phenomenon is thus needed. Here we analyze a neural mass model of a cortical column, comprising fourteen neuronal populations distributed across four layers (L2/3, L4, L5 and L6). A control analysis showed that the conditional transfer entropy (cTE) measure is able to correctly estimate the flow of information between neuronal populations. Then, we computed cTE from the phases to the amplitudes of the oscillations generated in the cortical column. This approach provides information regarding directionality by distinguishing PAC from APC (amplitude-phase coupling), i.e. the information transfer from amplitudes to phases, and can be used to estimate other types of CFC such as amplitude-amplitude coupling (AAC) and phase-phase coupling (PPC). While experiments often only focus on one or two PAC combinations (e.g., theta-gamma or alpha-gamma), we found that a cortical column can simultaneously generate almost all possible PAC combinations, depending on connectivity parameters, time constants, and external inputs. PAC interactions with and without an anatomical equivalent (direct and indirect interactions, respectively) were analyzed. We found that the strength of PAC between two populations was strongly correlated with the strength of the effective connections between the populations and, on average, did not depend on whether the PAC connection was direct or indirect. When considering a cortical column circuit as a complex network, we found that neuronal populations making indirect PAC connections had, on average, higher local clustering coefficient, efficiency, and betweenness centrality than populations making direct connections and populations not involved in PAC connections. This suggests that their interactions were more effective when transmitting information. Since approximately 60% of the obtained interactions represented indirect connections, our results highlight the importance of the topology of cortical circuits for the generation of the PAC phenomenon. Finally, our results demonstrated that indirect PAC interactions can be explained by a cascade of direct CFC and same-frequency band interactions, suggesting that PAC analysis of experimental data should be accompanied by the estimation of other types of frequency interactions for an integrative understanding of the phenomenon.

Structure and Topology Dynamics of Hyper-Frequency Networks during Rest and Auditory Oddball Performance

Resting-state and task-related recordings are characterized by oscillatory brain activity and widely distributed networks of synchronized oscillatory circuits. Electroencephalographic recordings (EEG) were used to assess network structure and network dynamics during resting state with eyes open and closed, and auditory oddball performance through phase synchronization between EEG channels. For this assessment, we constructed a hyper-frequency network (HFN) based on within- and cross-frequency coupling (WFC and CFC, respectively) at 10 oscillation frequencies ranging between 2 and 20 Hz. We found that CFC generally differentiates between task conditions better than WFC. CFC was the highest during resting state with eyes open. Using a graph-theoretical approach (GTA), we found that HFNs possess small-world network (SWN) topology with a slight tendency to random network characteristics. Moreover, analysis of the temporal fluctuations of HFNs revealed specific network topology dynamics (NTD), i.e., temporal changes of different graph-theoretical measures such as strength, clustering coefficient, characteristic path length (CPL), local, and global efficiency determined for HFNs at different time windows. The different topology metrics showed significant differences between conditions in the mean and standard deviation of these metrics both across time and nodes. In addition, using an artificial neural network approach, we found stimulus-related dynamics that varied across the different network topology metrics. We conclude that functional connectivity dynamics (FCD), or NTD, which was found using the HFN approach during rest and stimulus processing, reflects temporal and topological changes in the functional organization and reorganization of neuronal cell assemblies.

Detecting causality in policy diffusion processes

A universal question in network science entails learning about the topology of interaction from collective dynamics. Here, we address this question by examining diffusion of laws across US states. We propose two complementary techniques to unravel determinants of this diffusion process: information-theoretic union transfer entropy and event synchronization. In order to systematically investigate their performance on law activity data, we establish a new stochastic model to generate synthetic law activity data based on plausible networks of interactions. Through extensive parametric studies, we demonstrate the ability of these methods to reconstruct networks, varying in size, link density, and degree heterogeneity. Our results suggest that union transfer entropy should be preferred for slowly varying processes, which may be associated with policies attending to specific local problems that occur only rarely or with policies facing high levels of opposition. In contrast, event synchronization is effective for faster enactment rates, which may be related to policies involving Federal mandates or incentives. This study puts forward a data-driven toolbox to explain the determinants of legal activity applicable to political science, across dynamical systems, information theory, and complex networks.

Higher-Order Synaptic Interactions Coordinate Dynamics in Recurrent Networks

Linking synaptic connectivity to dynamics is key to understanding information processing in neocortex. Circuit dynamics emerge from complex interactions of interconnected neurons, necessitating that links between connectivity and dynamics be evaluated at the network level. Here we map propagating activity in large neuronal ensembles from mouse neocortex and compare it to a recurrent network model, where connectivity can be precisely measured and manipulated. We find that a dynamical feature dominates statistical descriptions of propagating activity for both neocortex and the model: convergent clusters comprised of fan-in triangle motifs, where two input neurons are themselves connected. Fan-in triangles coordinate the timing of presynaptic inputs during ongoing activity to effectively generate postsynaptic spiking. As a result, paradoxically, fan-in triangles dominate the statistics of spike propagation even in randomly connected recurrent networks. Interplay between higher-order synaptic connectivity and the integrative properties of neurons constrains the structure of network dynamics and shapes the routing of information in neocortex.