Community detection in complex networks using extremal optimization

Insights from graph theory on the morphologies of actomyosin networks with multilinkers

Quantifying the influence of microscopic details on the dynamics of development of the overall structure of a filamentous network is important in a number of biologically relevant contexts, but it is not obvious what order parameters can be used to adequately describe this complex process. In this paper we investigated the role of multivalent actin-binding proteins (ABPs) in reorganizing actin filaments into higher-order complex networks via a computer model of semiflexible filaments. We characterize the importance of local connectivity among actin filaments, as well as the global features of actomyosin networks. We first map the networks into local graph representations and then, using principles from network-theory order parameters, combine properties from these representations to gain insight into the heterogeneous morphologies of actomyosin networks at a global level. We find that ABPs with a valency greater than 2 promote filament bundles and large filament clusters to a much greater extent than bivalent multilinkers. We also show that active myosinlike motor proteins promote the formation of dendritic branches from a stalk of actin bundles. Our work motivates future studies to embrace network theory as a tool to characterize complex morphologies of actomyosin detected by experiments, leading to a quantitative understanding of the role of ABPs in manipulating the self-assembly of actin filaments into unique architectures that underlie the structural scaffold of a cell relating to its mobility and shape.

Path-based extensions of local link prediction methods for complex networks

Link prediction in a complex network is a problem of fundamental interest in network science and has attracted increasing attention in recent years. It aims to predict missing (or future) links between two entities in a complex system that are not already connected. Among existing methods, local similarity indices are most popular that take into account the information of common neighbours to estimate the likelihood of existence of a connection between two nodes. In this paper, we propose global and quasi-local extensions of some commonly used local similarity indices. We have performed extensive numerical simulations on publicly available datasets from diverse domains demonstrating that the proposed extensions not only give superior performance, when compared to their respective local indices, but also outperform some of the current, state-of-the-art, local and global link-prediction methods.

Latent Poisson models for networks with heterogeneous density

Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense, for example, with a few nodes connecting to a large fraction of the rest of the network, or with small groups of nodes with a large probability of connections between them. Here we show how latent Poisson models that generate hidden multigraphs can be effective at capturing this density heterogeneity, while being more tractable mathematically than some of the alternatives that model simple graphs directly. We show how these latent multigraphs can be reconstructed from data on simple graphs, and how this allows us to disentangle disassortative degree-degree correlations from the constraints of imposed degree sequences, and to improve the identification of community structure in empirically relevant scenarios.

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.

Identifying Influencers in Social Networks

Social network analysis is a multidisciplinary research covering informatics, mathematics, sociology, management, psychology, etc. In the last decade, the development of online social media has provided individuals with a fascinating platform of sharing knowledge and interests. The emergence of various social networks has greatly enriched our daily life, and simultaneously, it brings a challenging task to identify influencers among multiple social networks. The key problem lies in the various interactions among individuals and huge data scale. Aiming at solving the problem, this paper employs a general multilayer network model to represent the multiple social networks, and then proposes the node influence indicator merely based on the local neighboring information. Extensive experiments on 21 real-world datasets are conducted to verify the performance of the proposed method, which shows superiority to the competitors. It is of remarkable significance in revealing the evolutions in social networks and we hope this work will shed light for more and more forthcoming researchers to further explore the uncharted part of this promising field.

Characterization of network complexity by communicability sequence entropy and associated Jensen-Shannon divergence

Characterizing the structural complexity of networks is a major challenging work in network science. However, a valid measure to quantify network complexity remains unexplored. Although the entropy of various network descriptors and algorithmic complexity have been selected in the previous studies to do it, most of these methods only contain local information of the network, so they cannot accurately reflect the global structural complexity of the network. In this paper, we propose a statistical measure to characterize network complexity from a global perspective, which is composed of the communicability sequence entropy of the network and the associated Jensen-Shannon divergence. We study the influences of the topology of the synthetic networks on the complexity measure. The results show that networks with strong heterogeneity, strong degree-degree correlation, and a certain number of communities have a relatively large complexity. Moreover, by studying some real networks and their corresponding randomized network models, we find that the complexity measure is a monotone increasing function of the order of the randomized network, and the ones of real networks are larger complexity-values compared to all corresponding randomized networks. These results indicate that the complexity measure is sensitive to the changes of the basic topology of the network and increases with the increase of the external constraints of the network, which further proves that the complexity measure presented in this paper can effectively represent the topological complexity of the network.

Dimension Reduction and Clustering Models for Single-Cell RNA Sequencing Data: A Comparative Study

With recent advances in single-cell RNA sequencing, enormous transcriptome datasets have been generated. These datasets have furthered our understanding of cellular heterogeneity and its underlying mechanisms in homogeneous populations. Single-cell RNA sequencing (scRNA-seq) data clustering can group cells belonging to the same cell type based on patterns embedded in gene expression. However, scRNA-seq data are high-dimensional, noisy, and sparse, owing to the limitation of existing scRNA-seq technologies. Traditional clustering methods are not effective and efficient for high-dimensional and sparse matrix computations. Therefore, several dimension reduction methods have been introduced. To validate a reliable and standard research routine, we conducted a comprehensive review and evaluation of four classical dimension reduction methods and five clustering models. Four experiments were progressively performed on two large scRNA-seq datasets using 20 models. Results showed that the feature selection method contributed positively to high-dimensional and sparse scRNA-seq data. Moreover, feature-extraction methods were able to promote clustering performance, although this was not eternally immutable. Independent component analysis (ICA) performed well in those small compressed feature spaces, whereas principal component analysis was steadier than all the other feature-extraction methods. In addition, ICA was not ideal for fuzzy C-means clustering in scRNA-seq data analysis. K-means clustering was combined with feature-extraction methods to achieve good results.

Detecting multiple communities using quantum annealing on the D-Wave system

A very important problem in combinatorial optimization is the partitioning of a network into communities of densely connected nodes; where the connectivity between nodes inside a particular community is large compared to the connectivity between nodes belonging to different ones. This problem is known as community detection, and has become very important in various fields of science including chemistry, biology and social sciences. The problem of community detection is a twofold problem that consists of determining the number of communities and, at the same time, finding those communities. This drastically increases the solution space for heuristics to work on, compared to traditional graph partitioning problems. In many of the scientific domains in which graphs are used, there is the need to have the ability to partition a graph into communities with the "highest quality" possible since the presence of even small isolated communities can become crucial to explain a particular phenomenon. We have explored community detection using the power of quantum annealers, and in particular the D-Wave 2X and 2000Q machines. It turns out that the problem of detecting at most two communities naturally fits into the architecture of a quantum annealer with almost no need of reformulation. This paper addresses a systematic study of detecting two or more communities in a network using a quantum annealer.

Community Detection Based on a Preferential Decision Model

The research on complex networks is a hot topic in many fields, among which community detection is a complex and meaningful process, which plays an important role in researching the characteristics of complex networks. Community structure is a common feature in the network. Given a graph, the process of uncovering its community structure is called community detection. Many community detection algorithms from different perspectives have been proposed. Achieving stable and accurate community division is still a non-trivial task due to the difficulty of setting specific parameters, high randomness and lack of ground-truth information. In this paper, we explore a new decision-making method through real-life communication and propose a preferential decision model based on dynamic relationships applied to dynamic systems. We apply this model to the label propagation algorithm and present a Community Detection based on Preferential Decision Model, called CDPD. This model intuitively aims to reveal the topological structure and the hierarchical structure between networks. By analyzing the structural characteristics of complex networks and mining the tightness between nodes, the priority of neighbor nodes is chosen to perform the required preferential decision, and finally the information in the system reaches a stable state. In the experiments, through the comparison of eight comparison algorithms, we verified the performance of CDPD in real-world networks and synthetic networks. The results show that CDPD not only has better performance than most recent algorithms on most datasets, but it is also more suitable for many community networks with ambiguous structure, especially sparse networks.

Reliability-based topology design for large-scale networks

Network topology has a critical effect on its reliability. Due to the complexity of networks, how to design a more reliable network topology is one of the fascinating and significant challenges. In this paper, inspired by the multi-scale model of biological systems which range from gene to individual cells, and up to the individual organism, we provide a novel method to design a reliable topology of large-scale networks. By means of fractal theory and its application in complex networks, a network topology can be described as consisting of the superposition of basic units, called fractal-cells, which are made up of several components and their connections. Based on this fractal-cell structure, we find that a fractal-cell network has structural similarity with its primitive structure, and then develop a method to build a reliable topology which is generated from a primitive ring structure. Numerical simulation compared with the existing methods and performing on real networks show that our proposed method is effective.

Macro- and mesoscale pattern interdependencies in complex networks

Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other arrangements-e.g. nestedness or core-periphery-have been studied in parallel, but to a much lesser extent. However, empirical evidence increasingly suggests that characterizing a network with a unique pattern typology may be too simplistic, since a system can integrate properties from distinct organizations at different scales. Here, we explore the relationship between some of these different organizational patterns: two at the mesoscale (modularity and in-block nestedness); and one at the macroscale (nestedness). We show experimentally and analytically that nestedness imposes bounds to modularity, with exact analytical results in idealized scenarios. Specifically, we show that nestedness and modularity are interdependent. Furthermore, we analytically evidence that in-block nestedness provides a natural combination between nested and modular networks, taking structural properties of both. Far from a mere theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent that modularity and nestedness are known to place heavy dynamical effects on processes, such as species abundances and stability in ecology.

The effect of dimerization on the activation and conformational dynamics of adenosine A1 receptor

The adenosine A1 receptor (A1R) is one of four adenosine receptors in humans, which are involved in the function of the cardiovascular, respiratory and central nervous systems. Experimental results indicate that A1R can form a homodimer and that the protomer-protomer interaction in the A1R dimer is related to certain pharmacological characteristics of A1R activation. In this work, we performed docking, metadynamics simulation, conventional molecular dynamics simulations, Gaussian-accelerated molecular dynamics simulations, potential of mean force calculations, dynamic cross-correlation motions analysis and community network analysis to study the binding mode of 5'-N-ethylcarboxamidoadenosine (NECA) to A1R and the effect of dimerization on the activation of A1R. Our results show that NECA binds to A1R in a similar mode to adenosine in the A1R crystal structure and NECA in the A2AR crystal structure. The A1R homodimer can be activated by one or two agonists with NECA occupying its orthosteric pockets in one (which we call the NECA-A1R system) or both protomers (which we call the dNECA-A1R system). In the NECA-A1R system, activation is predicated in the protomer without NECA bound. In the dNECA-A1R system, only one protomer achieves the active state. These findings suggest an asymmetrical activation mechanism of the homodimer and a negative cooperativity between the two protomers. We envision that our results may further facilitate the drug development of A1R.

Multiplex communities and the emergence of international conflict

Advances in community detection reveal new insights into multiplex and multilayer networks. Less work, however, investigates the relationship between these communities and outcomes in social systems. We leverage these advances to shed light on the relationship between the cooperative mesostructure of the international system and the onset of interstate conflict. We detect communities based upon weaker signals of affinity expressed in United Nations votes and speeches, as well as stronger signals observed across multiple layers of bilateral cooperation. Communities of diplomatic affinity display an expected negative relationship with conflict onset. Ties in communities based upon observed cooperation, however, display no effect under a standard model specification and a positive relationship with conflict under an alternative specification. These results align with some extant hypotheses but also point to a paucity in our understanding of the relationship between community structure and behavioral outcomes in networks.

Weighted h-index for Identifying Influential Spreaders

In this paper, we propose weighted h-index h w and h-index strength s h to measure spreading capability and identify the most influential spreaders. Experimental results on twelve real networks reveal that s h was more accurate and more monotonic than h w and four previous measures in ranking the spreading influence of a node evaluated by the single seed SIR spreading model. We point out that the questions of how to improve monotonicity and how to determine a proper neighborhood range are two interesting future directions.

Reduced network extremal ensemble learning (RenEEL) scheme for community detection in complex networks

We introduce an ensemble learning scheme for community detection in complex networks. The scheme uses a Machine Learning algorithmic paradigm we call Extremal Ensemble Learning. It uses iterative extremal updating of an ensemble of network partitions, which can be found by a conventional base algorithm, to find a node partition that maximizes modularity. At each iteration, core groups of nodes that are in the same community in every ensemble partition are identified and used to form a reduced network. Partitions of the reduced network are then found and used to update the ensemble. The smaller size of the reduced network makes the scheme efficient. We use the scheme to analyze the community structure in a set of commonly studied benchmark networks and find that it outperforms all other known methods for finding the partition with maximum modularity.

Online division of labour: emergent structures in Open Source Software

The development Open Source Software fundamentally depends on the participation and commitment of volunteer developers to progress on a particular task. Several works have presented strategies to increase the on-boarding and engagement of new contributors, but little is known on how these diverse groups of developers self-organise to work together. To understand this, one must consider that, on one hand, platforms like GitHub provide a virtually unlimited development framework: any number of actors can potentially join to contribute in a decentralised, distributed, remote, and asynchronous manner. On the other, however, it seems reasonable that some sort of hierarchy and division of labour must be in place to meet human biological and cognitive limits, and also to achieve some level of efficiency. These latter features (hierarchy and division of labour) should translate into detectable structural arrangements when projects are represented as developer-file bipartite networks. Thus, in this paper we analyse a set of popular open source projects from GitHub, placing the accent on three key properties: nestedness, modularity and in-block nestedness -which typify the emergence of heterogeneities among contributors, the emergence of subgroups of developers working on specific subgroups of files, and a mixture of the two previous, respectively. These analyses show that indeed projects evolve into internally organised blocks. Furthermore, the distribution of sizes of such blocks is bounded, connecting our results to the celebrated Dunbar number both in off- and on-line environments. Our conclusions create a link between bio-cognitive constraints, group formation and online working environments, opening up a rich scenario for future research on (online) work team assembly (e.g. size, composition, and formation). From a complex network perspective, our results pave the way for the study of time-resolved datasets, and the design of suitable models that can mimic the growth and evolution of OSS projects.

Reliable Link Inference for Network Data With Community Structures

Complex systems are often characterized by complex networks with links and entities. However, in many complex systems such as protein-protein interaction networks, recommender systems, and online communities, their links are hard to reveal directly, but they can be inaccurately observed by multiple data collection platforms or by a data collection platform at different times. Then, the links of the systems are inferred by the integration of the collected observations. As those data collection platforms are usually distributed over a large area and in different fields, their observations are unreliable and sensitive to the potential structures of the systems. In this paper, we consider the link inference problem in network data with community structures, in which the reliability of data collection platforms is unknown a priori and the link errors and reliability of platforms' observations are heterogeneous to the underlying community structures of the systems. We propose an expectation maximization algorithm for link inference in a network system with community structures (EMLIC). The EMLIC algorithm is also used to infer the link errors and reliability of platforms' observations in different communities. Experimental results on both synthetic data and eight real-world network data demonstrate that our algorithm is able to achieve lower link errors than the existing reliable link inference algorithms when the network data have community structures.

Link prediction in recommender systems with confidence measures

The link prediction aims at predicting missing or future links in networks, which provides theoretical significance and extensive applications in the related field. However, the degree of confidence in the prediction results has not been fully discussed in related works. In this article, we propose a similarity confidence coefficient and a confidence measure for link prediction. The former is used to balance the reliability of similarity calculation results, which might be untrustworthy due to the information asymmetry in the calculation, and also makes it easier to achieve the optimal accuracy with a smaller number of neighbors. The latter is used to quantify our confidence in the prediction results of each prediction. The experimental results based on the Movie-Lens data set show that prediction accuracy is improved when the similarity between the nodes is corrected by the similarity confidence coefficient. Second, the experiments also confirm that the confidence degree of the link prediction results can be measured quantitatively. Our research indicates that the confidence level on each prediction is determined by the amount of data used in the corresponding calculation, which can be measured quantitatively.

Detecting modular brain states in rest and task

The human brain is a dynamic networked system that continually reconfigures its functional connectivity patterns over time. Thus, developing approaches able to adequately detect fast brain dynamics is critical. Of particular interest are the methods that analyze the modular structure of brain networks, that is, the presence of clusters of regions that are densely interconnected. In this paper, we propose a novel framework to identify fast modular states that dynamically fluctuate over time during rest and task. We started by demonstrating the feasibility and relevance of this framework using simulated data. Compared with other methods, our algorithm was able to identify the simulated networks with high temporal and spatial accuracies. We further applied the proposed framework on MEG data recorded during a finger movement task, identifying modular states linking somatosensory and primary motor regions. The algorithm was also performed on dense-EEG data recorded during a picture naming task, revealing the subsecond transition between several modular states that relate to visual processing, semantic processing, and language. Next, we tested our method on a dataset of resting-state dense-EEG signals recorded from 124 patients with Parkinson's disease. Results disclosed brain modular states that differentiate cognitively intact patients, patients with moderate cognitive deficits, and patients with severe cognitive deficits. Our new approach complements classical methods, offering a new way to track the brain modular states, in healthy subjects and patients, on an adequate task-specific timescale.

On neighbourhood degree sequences of complex networks

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in complex networks. We consider how to explicitly characterise important physical concepts such as similarity, heterogeneity and organization in these sequences, as well as updating the notion of hierarchical complexity to reflect previously unnoticed organizational principles. We also point out that neighbourhood degree sequences are related to a powerful subtree kernel for unlabeled graph classification. We study these newly defined sequence properties in a comprehensive array of graph models and over 200 real-world networks. We find that these indices are neither highly correlated with each other nor with classical network indices. Importantly, the sequences of a wide variety of real world networks are found to have greater similarity and organisation than is expected for networks of their given degree distributions. Notably, while biological, social and technological networks all showed consistently large neighbourhood similarity and organisation, hierarchical complexity was not a consistent feature of real world networks. Neighbourhood degree sequences are an interesting tool for describing unique and important characteristics of complex networks.

The application of degree related clustering coefficient in estimating the link predictability and predicting missing links of networks

Though a lot of valuable algorithms of link prediction have been created, it is still difficult to improve the accuracy of link prediction for some networks. Such difficulties may be due to the intrinsic topological features of these networks. To reveal the correlation between the network topology and the link predictability, we generate a group of artificial networks by keeping some structural features of an initial seed network. Based on these artificial networks and some real networks, we find that five topological measures including clustering coefficient, structural consistency, random walk entropy, network diameter, and average path length significantly show their impact on the link predictability. Then, we define a topological score that combines these important topological features. Specifically, it is an integration of structural consistency with degree-related clustering coefficient defined in this work. This topological score exhibits high correlation with the link predictability. Finally, we propose an algorithm for link prediction based on this topological score. Our experiment on eight real networks verifies good performance of this algorithm in link prediction, which supports the reasonability of the new topological score. This work could be insightful for the study of the link predictability.

Topological and functional comparison of community detection algorithms in biological networks

Background

Community detection algorithms are fundamental tools to uncover important features in networks. There are several studies focused on social networks but only a few deal with biological networks. Directly or indirectly, most of the methods maximize modularity, a measure of the density of links within communities as compared to links between communities.

Results

Here we analyze six different community detection algorithms, namely, Combo, Conclude, Fast Greedy, Leading Eigen, Louvain and Spinglass, on two important biological networks to find their communities and evaluate the results in terms of topological and functional features through Kyoto Encyclopedia of Genes and Genomes pathway and Gene Ontology term enrichment analysis. At a high level, the main assessment criteria are 1) appropriate community size (neither too small nor too large), 2) representation within the community of only one or two broad biological functions, 3) most genes from the network belonging to a pathway should also belong to only one or two communities, and 4) performance speed. The first network in this study is a network of Protein-Protein Interactions (PPI) in Saccharomyces cerevisiae (Yeast) with 6532 nodes and 229,696 edges and the second is a network of PPI in Homo sapiens (Human) with 20,644 nodes and 241,008 edges. All six methods perform well, i.e., find reasonably sized and biologically interpretable communities, for the Yeast PPI network but the Conclude method does not find reasonably sized communities for the Human PPI network. Louvain method maximizes modularity by using an agglomerative approach, and is the fastest method for community detection. For the Yeast PPI network, the results of Spinglass method are most similar to the results of Louvain method with regard to the size of communities and core pathways they identify, whereas for the Human PPI network, Combo and Spinglass methods yield the most similar results, with Louvain being the next closest.

Conclusions

For Yeast and Human PPI networks, Louvain method is likely the best method to find communities in terms of detecting known core pathways in a reasonable time.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2746-0) contains supplementary material, which is available to authorized users.

Non-Negative Matrix Factorizations for Multiplex Network Analysis

Networks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monoplex) networks. However, with the advent of relational data with multiple modalities, multiplex networks, i.e., networks composed of multiple layers representing different aspects of relations, have emerged. Consequently, community detection in multiplex network, i.e., detecting clusters of nodes shared by all layers, has become a new challenge. In this paper, we propose Network Fusion for Composite Community Extraction (NF-CCE), a new class of algorithms, based on four different non-negative matrix factorization models, capable of extracting composite communities in multiplex networks. Each algorithm works in two steps: first, it finds a non-negative, low-dimensional feature representation of each network layer; then, it fuses the feature representation of layers into a common non-negative, low-dimensional feature representation via collective factorization. The composite clusters are extracted from the common feature representation. We demonstrate the superior performance of our algorithms over the state-of-the-art methods on various types of multiplex networks, including biological, social, economic, citation, phone communication, and brain multiplex networks.

From Louvain to Leiden: guaranteeing well-connected communities

Community detection is often used to understand the structure of large and complex networks. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. To address this problem, we introduce the Leiden algorithm. We prove that the Leiden algorithm yields communities that are guaranteed to be connected. In addition, we prove that, when the Leiden algorithm is applied iteratively, it converges to a partition in which all subsets of all communities are locally optimally assigned. Furthermore, by relying on a fast local move approach, the Leiden algorithm runs faster than the Louvain algorithm. We demonstrate the performance of the Leiden algorithm for several benchmark and real-world networks. We find that the Leiden algorithm is faster than the Louvain algorithm and uncovers better partitions, in addition to providing explicit guarantees.

Disclosing the Template-Induced Misfolding Mechanism of Tau Protein by Studying the Dissociation of the Boundary Chain from the Formed Tau Fibril Based on a Steered Molecular Dynamics Simulation

The level of tau aggregation into neurofibrillary tangles, including paired helical filament (PHF) and straight filament (SF), is closely associated with Alzheimer's disease. Despite the pathological importance of misfolding and aggregation of tau, the corresponding mechanism remains unclear. Therefore, to uncover the misfolding mechanism of the tau monomer upon induction of formed PHF and SF, in this study, a conventional molecular dynamics simulation combined with a steered molecular dynamics simulation was performed to study the dissociation of the boundary chain. Interestingly, our results show that the dissociation mechanisms of the boundary chain in PHF and SF are different. In PHF, the boundary chain begins to dissociate from regions β2 and β3 and ends at β8. However, in SF, it is simultaneously dissociated from β1 and β8 and ends at β5. The dissociation of the boundary chain is the reverse of template-induced misfolding of the monomer. Therefore, we can deduce the misfolding mechanism of the monomer upon induction of the template. For PHF, β8 first interacts with the template by hydrophobic interaction. Then β7, β6, β5, β4, and β1 sequentially bind to the template by electrostatic and hydrophobic interactions. After β1 binds to the template, β2 and β3 very quickly bind to the template through hydrophobic interaction. For SF, β5 of the monomer first interacts with the template by electrostatic attraction. Then β4 and β6, β3 and β7, and β2 and β8 bind to the template in turn. Finally, β1 and β8 are fully bound to the template by hydrophobic interaction. The obtained results will be vital for understanding the earlier events during misfolding and aggregation of tau.

A nature inspired modularity function for unsupervised learning involving spatially embedded networks

The quality of network clustering is often measured in terms of a commonly used metric known as "modularity". Modularity compares the clusters found in a network to those present in a random graph (a "null model"). Unfortunately, modularity is somewhat ill suited for studying spatially embedded networks, since a random graph contains no basic geometrical notions. Regardless of their distance, the null model assigns a nonzero probability for an edge to appear between any pair of nodes. Here, we propose a variant of modularity that does not rely on the use of a null model. To demonstrate the essentials of our method, we analyze networks generated from granular ensemble. We show that our method performs better than the most commonly used Newman-Girvan (NG) modularity in detecting the best (physically transparent) partitions in those systems. Our measure further properly detects hierarchical structures, whenever these are present.

Co-Association Matrix-Based Multi-Layer Fusion for Community Detection in Attributed Networks

Community detection is a challenging task in attributed networks, due to the data inconsistency between network topological structure and node attributes. The problem of how to effectively and robustly fuse multi-source heterogeneous data plays an important role in community detection algorithms. Although some algorithms taking both topological structure and node attributes into account have been proposed in recent years, the fusion strategy is simple and usually adopts the linear combination method. As a consequence of this, the detected community structure is vulnerable to small variations of the input data. In order to overcome this challenge, we develop a novel two-layer representation to capture the latent knowledge from both topological structure and node attributes in attributed networks. Then, we propose a weighted co-association matrix-based fusion algorithm (WCMFA) to detect the inherent community structure in attributed networks by using multi-layer fusion strategies. It extends the community detection method from a single-view to a multi-view style, which is consistent with the thinking model of human beings. Experiments show that our method is superior to the state-of-the-art community detection algorithms for attributed networks.

First-year development of modules and hubs in infant brain functional networks

The human brain develops rapidly in the first postnatal year, in which rewired functional brain networks could shape later behavioral and cognitive performance. Resting-state functional magnetic resonances imaging (rs-fMRI) and complex network analysis have been widely used for characterizing the developmental brain functional connectome. Yet, such studies focusing on the first year of postnatal life are still very limited. Leveraging normally developing longitudinal infant rs-fMRI scans from neonate to one year of age, we investigated how brain functional networks develop at a fine temporal scale (every 3 months). Considering challenges in the infant fMRI-based network analysis, we developed a novel algorithm to construct the robust, temporally consistent and modular structure augmented group-level network based on which functional modules were detected at each age. Our study reveals that the brain functional network is gradually subdivided into an increasing number of functional modules accompanied by the strengthened intra- and inter-modular connectivities. Based on the developing modules, we found connector hubs (the high-centrality regions connecting different modules) emerging and increasing, while provincial hubs (the high-centrality regions connecting regions in the same module) diminishing. Further region-wise longitudinal analysis validates that different hubs have distinct developmental trajectories of the intra- and inter-modular connections suggesting different types of role transitions in network, such as non-hubs to hubs or provincial hubs to connector hubs et al. All findings indicate that functional segregation and integration are both increased in the first year of postnatal life. The module reorganization and hub transition lead to more efficient brain networks, featuring increasingly segregated modular structure and more connector hubs. This study provides the first comprehensive report of the development of functional brain networks at a 3-month interval throughout the first postnatal year of life, which provides essential information to the future neurodevelopmental and developmental disorder studies.

Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation

We investigate transition to synchronization in the Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage (f) of higher degree nodes of the network are assumed to be correlated with their degrees and that of the remaining nodes are drawn from some standard distribution, namely, Lorentz distribution. The effects of variation of f and phase frustration parameter α on transition to synchronization are investigated in detail. Self-consistent equations involving critical coupling strength (λ_c) and group angular velocity (Ω_c) at the onset of synchronization have been derived analytically in the thermodynamic limit. For the detailed investigation, we considered the SK model on scale-free (SF) as well as Erdős-Rényi (ER) networks. Interestingly, explosive synchronization (ES) has been observed in both networks for different ranges of values of α and f. For SF networks, as the value of f is set within 10%≤f≤70%, the range of the values of α for existence of the ES is greatly enhanced compared to the fully degree-frequency correlated case when scaling exponent γ<3. ES is also observed in SF networks with γ>3, which is never observed in fully degree-frequency correlated environment. On the other hand, for random networks, ES observed is in a narrow window of α when the value of f is taken within 30%≤f≤50%. In all the cases, critical coupling strengths for transition to synchronization computed from the analytically derived self-consistent equations show a very good agreement with the numerical results. Finally, we observe ES in the metabolic network of the roundworm Caenorhabditis elegans in partially degree-frequency correlated environment.

Generating symmetric graphs

Symmetry in graphs which describe the underlying topology of networked dynamical systems plays an essential role in the emergence of clusters of synchrony. Many real networked systems have a very large number of symmetries. Often one wants to test new results on large sets of random graphs that are representative of the real networks of interest. Unfortunately, existing graph generating algorithms will seldom produce graphs with any symmetry and much less ones with desired symmetry patterns. Here, we present an algorithm that is able to generate graphs with any desired symmetry pattern. The algorithm can be coupled with other graph generating algorithms to tune the final graph's properties of interest such as the degree distribution.

Structure and dynamical behavior of non-normal networks

We analyze a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behavior, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. In addition, eigenvalues may become extremely sensible to noise and have a diminished physical meaning. We identify structural properties of networks that are associated with non-normality and propose simple models to generate networks with a tunable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality and propose their potential use in the context of the stability of complex ecosystems.