Spectral methods for community detection and graph partitioning

Environment and traits affect parasite and host species positions but not roles in flea-mammal networks

We studied spatial variation in the effects of environment and network size on species positions and roles in multiple flea-mammal networks from four biogeographic realms. We asked whether species positions (measured as species strength [SS], the degree of interaction specialization [d'], and the eigenvector centrality [C]) or the roles of fleas and their hosts in the interaction networks: (a) are repeatable/conserved within a flea or a host species; (b) vary in dependence on environmental variables and/or network size; and (c) the effects of environment and network size on species positions or roles in the networks depend on species traits. The repeatability analysis of species position indices for 441 flea and 429 host species, occurring in at least two networks, demonstrated that the repeatability of SS, d', and C within a species was significant, although not especially high, suggesting that the indices' values were affected by local factors. The majority of flea and host species in the majority of networks demonstrated a peripheral role. A value of at least one index of species position was significantly affected by environmental variables or network size in 41 and 36, respectively, of the 52 flea and 52 host species that occurred in multiple networks. In both fleas and hosts, the occurrence of the significant effect of environment or network size on at least one index of species position, but not on a species' role in a network, was associated with some species traits.

Developmental differences in canonical cortical networks: Insights from microstructure-informed tractography

In response to a growing interest in refining brain connectivity assessments, this study focuses on integrating white matter fiber-specific microstructural properties into structural connectomes. Spanning ages 8-19 years in a developmental sample, it explores age-related patterns of microstructure-informed network properties at both local and global scales. First, the diffusion-weighted signal fraction associated with each tractography-reconstructed streamline was constructed. Subsequently, the convex optimization modeling for microstructure-informed tractography (COMMIT) approach was employed to generate microstructure-informed connectomes from diffusion MRI data. To complete the investigation, network characteristics within eight functionally defined networks (visual, somatomotor, dorsal attention, ventral attention, limbic, fronto-parietal, default mode, and subcortical networks) were evaluated. The findings underscore a consistent increase in global efficiency across child and adolescent development within the visual, somatomotor, and default mode networks (p < 0.005). Additionally, mean strength exhibits an upward trend in the somatomotor and visual networks (p < 0.001). Notably, nodes within the dorsal and ventral visual pathways manifest substantial age-dependent changes in local efficiency, aligning with existing evidence of extended maturation in these pathways. The outcomes strongly support the notion of a prolonged developmental trajectory for visual association cortices. This study contributes valuable insights into the nuanced dynamics of microstructure-informed brain connectivity throughout different developmental stages.

Network analysis of neuropsychiatric, cognitive, and functional complications of stroke: implications for novel treatment targets

AIM

Recovery from stroke is adversely affected by neuropsychiatric complications, cognitive impairment, and functional disability. Better knowledge of their mutual relationships is required to inform effective interventions. Network theory enables the conceptualization of symptoms and impairments as dynamic and mutually interacting systems. We aimed to identify interactions of poststroke complications using network analysis in diverse stroke samples.

METHODS

Data from 2185 patients were sourced from member studies of STROKOG (Stroke and Cognition Consortium), an international collaboration of stroke studies. Networks were generated for each cohort, whereby nodes represented neuropsychiatric symptoms, cognitive deficits, and disabilities on activities of daily living. Edges characterized associations between them. Centrality measures were used to identify hub items.

RESULTS

Across cohorts, a single network of interrelated poststroke complications emerged. Networks exhibited dissociable depression, apathy, fatigue, cognitive impairment, and functional disability modules. Worry was the most central symptom across cohorts, irrespective of the depression scale used. Items relating to activities of daily living were also highly central nodes. Follow-up analysis in two studies revealed that individuals who worried had more densely connected networks than those free of worry (CASPER [Cognition and Affect after Stroke: Prospective Evaluation of Risks] study: S = 9.72, P = 0.038; SSS [Sydney Stroke Study]: S = 13.56, P = 0.069).

CONCLUSION

Neuropsychiatric symptoms are highly interconnected with cognitive deficits and functional disabilities resulting from stroke. Given their central position and high level of connectedness, worry and activities of daily living have the potential to drive multimorbidity and mutual reinforcement between domains of poststroke complications. Targeting these factors early after stroke may have benefits that extend to other complications, leading to better stroke outcomes.

A Comprehensive Survey on Community Detection With Deep Learning

Detecting a community in a network is a matter of discerning the distinct features and connections of a group of members that are different from those in other communities. The ability to do this is of great significance in network analysis. However, beyond the classic spectral clustering and statistical inference methods, there have been significant developments with deep learning techniques for community detection in recent years-particularly when it comes to handling high-dimensional network data. Hence, a comprehensive review of the latest progress in community detection through deep learning is timely. To frame the survey, we have devised a new taxonomy covering different state-of-the-art methods, including deep learning models based on deep neural networks (DNNs), deep nonnegative matrix factorization, and deep sparse filtering. The main category, i.e., DNNs, is further divided into convolutional networks, graph attention networks, generative adversarial networks, and autoencoders. The popular benchmark datasets, evaluation metrics, and open-source implementations to address experimentation settings are also summarized. This is followed by a discussion on the practical applications of community detection in various domains. The survey concludes with suggestions of challenging topics that would make for fruitful future research directions in this fast-growing deep learning field.

Dysfunctions of multiscale dynamic brain functional networks in subjective cognitive decline

Subjective cognitive decline is potentially the earliest symptom of Alzheimer's disease, whose objective neurological basis remains elusive. To explore the potential biomarkers for subjective cognitive decline, we developed a novel deep learning method based on multiscale dynamical brain functional networks to identify subjective cognitive declines. We retrospectively constructed an internal data set (with 112 subjective cognitive decline and 64 healthy control subjects) to develop and internally validate the deep learning model. Conventional deep learning methods based on static and dynamic brain functional networks are compared. After the model is established, we prospectively collect an external data set (26 subjective cognitive decline and 12 healthy control subjects) for testing. Meanwhile, our method provides monitoring of the transitions between normal and abnormal (subjective cognitive decline-related) dynamical functional network states. The features of abnormal dynamical functional network states are quantified by network and variability metrics and associated with individual cognitions. Our method achieves an area under the receiver operating characteristic curve of 0.807 ± 0.046 in the internal validation data set and of 0.707 (P = 0.007) in the external testing data set, which shows improvements compared to conventional methods. The method further suggests that, at the local level, the abnormal dynamical functional network states are characterized by decreased connectivity strength and increased connectivity variability at different spatial scales. At the network level, the abnormal states are featured by scale-specifically altered modularity and all-scale decreased efficiency. Low tendencies to stay in abnormal states and high state transition variabilities are significantly associated with high general, language and executive functions. Overall, our work supports the deficits in multiscale brain dynamical functional networks detected by the deep learning method as reliable and meaningful neural alternation underpinning subjective cognitive decline.

TEE-Graph: efficient privacy and ownership protection for cloud-based graph spectral analysis

Introduction

Big graphs like social network user interactions and customer rating matrices require significant computing resources to maintain. Data owners are now using public cloud resources for storage and computing elasticity. However, existing solutions do not fully address the privacy and ownership protection needs of the key involved parties: data contributors and the data owner who collects data from contributors.

Methods

We propose a Trusted Execution Environment (TEE) based solution: TEE-Graph for graph spectral analysis of outsourced graphs in the cloud. TEEs are new CPU features that can enable much more efficient confidential computing solutions than traditional software-based cryptographic ones. Our approach has several unique contributions compared to existing confidential graph analysis approaches. (1) It utilizes the unique TEE properties to ensure contributors' new privacy needs, e.g., the right of revocation for shared data. (2) It implements efficient access-pattern protection with a differentially private data encoding method. And (3) it implements TEE-based special analysis algorithms: the Lanczos method and the Nystrom method for efficiently handling big graphs and protecting confidentiality from compromised cloud providers.

Results

The TEE-Graph approach is much more efficient than software crypto approaches and also immune to access-pattern-based attacks. Compared with the best-known software crypto approach for graph spectral analysis, PrivateGraph, we have seen that TEE-Graph has 103-105 times lower computation, storage, and communication costs. Furthermore, the proposed access-pattern protection method incurs only about 10%-25% of the overall computation cost.

Discussion

Our experimentation showed that TEE-Graph performs significantly better and has lower costs than typical software approaches. It also addresses the unique ownership and access-pattern issues that other TEE-related graph analytics approaches have not sufficiently studied. The proposed approach can be extended to other graph analytics problems with strong ownership and access-pattern protection.

Generative models for two-ground-truth partitions in networks

A myriad of approaches have been proposed to characterize the mesoscale structure of networks most often as a partition based on patterns variously called communities, blocks, or clusters. Clearly, distinct methods designed to detect different types of patterns may provide a variety of answers' to the networks mesoscale structure. Yet even multiple runs of a given method can sometimes yield diverse and conflicting results, producing entire landscapes of partitions which potentially include multiple (locally optimal) mesoscale explanations of the network. Such ambiguity motivates a closer look at the ability of these methods to find multiple qualitatively different "ground truth" partitions in a network. Here we propose the stochastic cross-block model (SCBM), a generative model which allows for two distinct partitions to be built into the mesoscale structure of a single benchmark network. We demonstrate a use case of the benchmark model by appraising the power of stochastic block models (SBMs) to detect implicitly planted coexisting bicommunity and core-periphery structures of different strengths. Given our model design and experimental setup, we find that the ability to detect the two partitions individually varies by SBM variant and that coexistence of both partitions is recovered only in a very limited number of cases. Our findings suggest that in most instances only one-in some way dominating-structure can be detected, even in the presence of other partitions. They underline the need for considering entire landscapes of partitions when different competing explanations exist and motivate future research to advance partition coexistence detection methods. Our model also contributes to the field of benchmark networks more generally by enabling further exploration of the ability of new and existing methods to detect ambiguity in the mesoscale structure of networks.

Learning to predict synchronization of coupled oscillators on randomly generated graphs

Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph structure, this is an important yet analytically intractable question in general. In this work, we take an alternative approach to the synchronization prediction problem by viewing it as a classification problem based on the fact that any given system will eventually synchronize or converge to a non-synchronizing limit cycle. By only using some basic statistics of the underlying graphs such as edge density and diameter, our method can achieve perfect accuracy when there is a significant difference in the topology of the underlying graphs between the synchronizing and the non-synchronizing examples. However, in the problem setting where these graph statistics cannot distinguish the two classes very well (e.g., when the graphs are generated from the same random graph model), we find that pairing a few iterations of the initial dynamics along with the graph statistics as the input to our classification algorithms can lead to significant improvement in accuracy; far exceeding what is known by the classical oscillator theory. More surprisingly, we find that in almost all such settings, dropping out the basic graph statistics and training our algorithms with only initial dynamics achieves nearly the same accuracy. We demonstrate our method on three models of continuous and discrete coupled oscillators-the Kuramoto model, Firefly Cellular Automata, and Greenberg-Hastings model. Finally, we also propose an "ensemble prediction" algorithm that successfully scales our method to large graphs by training on dynamics observed from multiple random subgraphs.

Higher-order brain regions show shifts in structural covariance in adolescent marmosets

Substantial progress has been made studying morphological changes in brain regions during adolescence, but less is known of network-level changes in their relationship. Here, we compare covariance networks constructed from the correlation of morphometric volumes across 135 brain regions of marmoset monkeys in early adolescence and adulthood. Substantial shifts are identified in the topology of structural covariance networks in the prefrontal cortex (PFC) and temporal lobe. PFC regions become more structurally differentiated and segregated within their own local network, hypothesized to reflect increased specialization after maturation. In contrast, temporal regions show increased inter-hemispheric covariances that may underlie the establishment of distributed networks. Regionally selective coupling of structural and maturational covariance is revealed, with relatively weak coupling in transmodal association areas. The latter may be a consequence of continued maturation within adulthood, but also environmental factors, for example, family size, affecting brain morphology. Advancing our understanding of how morphological relationships within higher-order brain areas mature in adolescence deepens our knowledge of the developing brain's organizing principles.

Ranking community detection algorithms for complex social networks using multilayer network design approach

Purpose

Community detection is a significant research field in the study of social networks and analysis because of its tremendous applicability in multiple domains such as recommendation systems, link prediction and information diffusion. The majority of the present community detection methods considers either node information only or edge information only, but not both, which can result in loss of important information regarding network structures. In real-world social networks such as Facebook and Twitter, there are many heterogeneous aspects of the entities that connect them together such as different type of interactions occurring, which are difficult to study with the help of homogeneous network structures. The purpose of this study is to explore multilayer network design to capture these heterogeneous aspects by combining different modalities of interactions in single network.

Design/methodology/approach

In this work, multilayer network model is designed while taking into account node information as well as edge information. Existing community detection algorithms are applied on the designed multilayer network to find the densely connected nodes. Community scoring functions and partition comparison are used to further analyze the community structures. In addition to this, analytic hierarchical processing-technique for order preference by similarity to ideal solution (AHP-TOPSIS)-based framework is proposed for selection of an optimal community detection algorithm.

Findings

In the absence of reliable ground-truth communities, it becomes hard to perform evaluation of generated network communities. To overcome this problem, in this paper, various community scoring functions are computed and studied for different community detection methods.

Research limitations/implications

In this study, evaluation criteria are considered to be independent. The authors observed that the criteria used are having some interdependencies, which could not be captured by the AHP method. Therefore, in future, analytic network process may be explored to capture these interdependencies among the decision attributes.

Practical implications

Proposed ranking can be used to improve the search strategy of algorithms to decrease the search time of the best fitting one according to the case study. The suggested study ranks existing community detection algorithms to find the most appropriate one.

Social implications

Community detection is useful in many applications such as recommendation systems, health care, politics, economics, e-commerce, social media and communication network.

Originality/value

Ranking of the community detection algorithms is performed using community scoring functions as well as AHP-TOPSIS methods.

Decoding the PITX2-controlled genetic network in atrial fibrillation

Atrial fibrillation (AF), the most common sustained cardiac arrhythmia and a major risk factor for stroke, often arises through ectopic electrical impulses derived from the pulmonary veins (PVs). Sequence variants in enhancers controlling expression of the transcription factor PITX2, which is expressed in the cardiomyocytes (CMs) of the PV and left atrium (LA), have been implicated in AF predisposition. Single nuclei multiomic profiling of RNA and analysis of chromatin accessibility combined with spectral clustering uncovered distinct PV- and LA-enriched CM cell states. Pitx2-mutant PV and LA CMs exhibited gene expression changes consistent with cardiac dysfunction through cell type-distinct, PITX2-directed, cis-regulatory grammars controlling target gene expression. The perturbed network targets in each CM were enriched in distinct human AF predisposition genes, suggesting combinatorial risk for AF genesis. Our data further reveal that PV and LA Pitx2-mutant CMs signal to endothelial and endocardial cells through BMP10 signaling with pathogenic potential. This work provides a multiomic framework for interrogating the basis of AF predisposition in the PVs of humans.

Extensive Chromatin Structure-Function Associations Revealed by Accurate 3D Compartmentalization Characterization

A/B compartments are observed in Hi-C data and coincide with eu/hetero-chromatin. However, many genomic regions are ambiguous under A/B compartment scheme. We develop MOSAIC (MOdularity and Singular vAlue decomposition-based Identification of Compartments), an accurate compartmental state detection scheme. MOSAIC reveals that those ambiguous regions segregate into two additional compartmental states, which typically correspond to short genomic regions flanked by long canonical A/B compartments with opposite activities. They are denoted as micro-compartments accordingly. In contrast to the canonical A/B compartments, micro-compartments cover ∼30% of the genome and are highly dynamic across cell types. More importantly, distinguishing the micro-compartments underpins accurate characterization of chromatin structure-function relationship. By applying MOSAIC to GM12878 and K562 cells, we identify CD86, ILDR1 and GATA2 which show concordance between gene expression and compartmental states beyond the scheme of A/B compartments. Taken together, MOSAIC uncovers fine-scale and dynamic compartmental states underlying transcriptional regulation and disease.

Comodularity and detection of co-communities

This paper introduces the notion of comodularity, to cocluster observations of bipartite networks into co-communities. The task of coclustering is to group together nodes of one type with nodes of another type, according to the interactions that are the most similar. The measure of comodularity is introduced to assess the strength of co-communities, as well as to arrange the representation of nodes and clusters for visualization, and to define an objective function for optimization. We demonstrate the usefulness of our proposed methodology on simulated data, and with examples from genomics and consumer-product reviews.

Spectral detection of simplicial communities via Hodge Laplacians

While the study of graphs has been very popular, simplicial complexes are relatively new in the network science community. Despite being a source of rich information, graphs are limited to pairwise interactions. However, several real-world networks such as social networks, neuronal networks, etc., involve interactions between more than two nodes. Simplicial complexes provide a powerful mathematical framework to model such higher-order interactions. It is well known that the spectrum of the graph Laplacian is indicative of community structure, and this relation is exploited by spectral clustering algorithms. Here we propose that the spectrum of the Hodge Laplacian, a higher-order Laplacian defined on simplicial complexes, encodes simplicial communities. We formulate an algorithm to extract simplicial communities (of arbitrary dimension). We apply this algorithm to simplicial complex benchmarks and to real higher-order network data including social networks and networks extracted using language or text processing tools. However, datasets of simplicial complexes are scarce, and for the vast majority of datasets that may involve higher-order interactions, only the set of pairwise interactions are available. Hence, we use known properties of the data to infer the most likely higher-order interactions. In other words, we introduce an inference method to predict the most likely simplicial complex given the community structure of its network skeleton. This method identifies as most likely the higher-order interactions inducing simplicial communities that maximize the adjusted mutual information measured with respect to ground-truth community structure. Finally, we consider higher-order networks constructed through thresholding the edge weights of collaboration networks (encoding only pairwise interactions) and provide an example of persistent simplicial communities that are sustained over a wide range of the threshold.

Spatial variation in species' roles in host-helminth networks

Species interactions may vary considerably across space as a result of spatial and environmental gradients. With respect to host-parasite interactions, this suggests that host and parasite species may play different functional roles across the different networks they occur in. Using a global occurrence database of helminth parasites, we examine the conservation of species' roles using data on host-helminth interactions from 299 geopolitical locations. Defining species' roles in a two-dimensional space which captures the tendency of species to be more densely linked within species subgroups than between subgroups, we quantified species' roles in two ways, which captured if and which species' roles are conserved by treating species' utilization of this two-dimensional space as continuous, while also classifying species into categorical roles. Both approaches failed to detect the conservation of species' roles for a single species out of over 38 000 host and helminth parasite species. Together, our findings suggest that species' roles in host-helminth networks may not be conserved, pointing to the potential role of spatial and environmental gradients, as well as the importance of the context of the local host and helminth parasite community. This article is part of the theme issue 'Infectious disease macroecology: parasite diversity and dynamics across the globe'.

Modularity in Biological Networks

Network modeling, from the ecological to the molecular scale has become an essential tool for studying the structure, dynamics and complex behavior of living systems. Graph representations of the relationships between biological components open up a wide variety of methods for discovering the mechanistic and functional properties of biological systems. Many biological networks are organized into a modular structure, so methods to discover such modules are essential if we are to understand the biological system as a whole. However, most of the methods used in biology to this end, have a limited applicability, as they are very specific to the system they were developed for. Conversely, from the statistical physics and network science perspective, graph modularity has been theoretically studied and several methods of a very general nature have been developed. It is our perspective that in particular for the modularity detection problem, biology and theoretical physics/network science are less connected than they should. The central goal of this review is to provide the necessary background and present the most applicable and pertinent methods for community detection in a way that motivates their further usage in biological research.

Consistency landscape of network communities

The concept of community detection has long been used as a key device for handling the mesoscale structures in networks. Suitably conducted community detection reveals various embedded informative substructures of network topology. However, regarding the practical usage of community detection, it has always been a tricky problem to assign a reasonable community resolution for networks of interest. Because of the absence of the unanimously accepted criterion, most of the previous studies utilized rather ad hoc heuristics to decide the community resolution. In this work, we harness the concept of consistency in community structures of networks to provide the overall community resolution landscape of networks, which we eventually take to quantify the reliability of detected communities for a given resolution parameter. More precisely, we exploit the ambiguity in the results of stochastic detection algorithms and suggest a method that denotes the relative validity of community structures in regard to their stability of global and local inconsistency measures using multiple detection processes. Applying our framework to synthetic and real networks, we confirm that it effectively displays insightful fundamental aspects of community structures.

Correspondence analysis, spectral clustering and graph embedding: applications to ecology and economic complexity

Identifying structure underlying high-dimensional data is a common challenge across scientific disciplines. We revisit correspondence analysis (CA), a classical method revealing such structures, from a network perspective. We present the poorly-known equivalence of CA to spectral clustering and graph-embedding techniques. We point out a number of complementary interpretations of CA results, other than its traditional interpretation as an ordination technique. These interpretations relate to the structure of the underlying networks. We then discuss an empirical example drawn from ecology, where we apply CA to the global distribution of Carnivora species to show how both the clustering and ordination interpretation can be used to find gradients in clustered data. In the second empirical example, we revisit the economic complexity index as an application of correspondence analysis, and use the different interpretations of the method to shed new light on the empirical results within this literature.

A gene module identification algorithm and its applications to identify gene modules and key genes of hepatocellular carcinoma

To further improve the effect of gene modules identification, combining the Newman algorithm in community detection and K-means algorithm framework, a new method of gene module identification, GCNA-Kpca algorithm, was proposed. The core idea of the algorithm was to build a gene co-expression network (GCN) based on gene expression data firstly; Then the Newman algorithm was used to initially identify gene modules based on the topology of GCN, and the number of clusters and clustering centers were determined; Finally the number of clusters and clustering centers were input into the K-means algorithm framework, and the secondary clustering was performed based on the gene expression profile to obtain the final gene modules. The algorithm took into account the role of modularity in the clustering process, and could find the optimal membership module for each gene through multiple iterations. Experimental results showed that the algorithm proposed in this paper had the best performance in error rate, biological significance and CNN classification indicators (Precision, Recall and F-score). The gene module obtained by GCNA-Kpca was used for the task of key gene identification, and these key genes had the highest prognostic significance. Moreover, GCNA-Kpca algorithm was used to identify 10 key genes in hepatocellular carcinoma (HCC): CDC20, CCNB1, EIF4A3, H2AFX, NOP56, RFC4, NOP58, AURKA, PCNA, and FEN1. According to the validation, it was reasonable to speculate that these 10 key genes could be biomarkers for HCC. And NOP56 and NOP58 are key genes for HCC that we discovered for the first time.

Order and stochasticity in the folding of individual Drosophila genomes

Mammalian and Drosophila genomes are partitioned into topologically associating domains (TADs). Although this partitioning has been reported to be functionally relevant, it is unclear whether TADs represent true physical units located at the same genomic positions in each cell nucleus or emerge as an average of numerous alternative chromatin folding patterns in a cell population. Here, we use a single-nucleus Hi-C technique to construct high-resolution Hi-C maps in individual Drosophila genomes. These maps demonstrate chromatin compartmentalization at the megabase scale and partitioning of the genome into non-hierarchical TADs at the scale of 100 kb, which closely resembles the TAD profile in the bulk in situ Hi-C data. Over 40% of TAD boundaries are conserved between individual nuclei and possess a high level of active epigenetic marks. Polymer simulations demonstrate that chromatin folding is best described by the random walk model within TADs and is most suitably approximated by a crumpled globule build of Gaussian blobs at longer distances. We observe prominent cell-to-cell variability in the long-range contacts between either active genome loci or between Polycomb-bound regions, suggesting an important contribution of stochastic processes to the formation of the Drosophila 3D genome.

Genomes are partitioned into topologically associating domains (TADs). Here the authors present single-nucleus Hi-C maps in Drosophila at 10 kb resolution, demonstrating the presence of chromatin compartments in individual nuclei, and partitioning of the genome into non-hierarchical TADs at the scale of 100 kb, which resembles population TAD profiles.

Community Detection Using Restrained Random-Walk Similarity

In this paper, we propose a restrained random-walk similarity method for detecting the community structures of graphs. The basic premise of our method is that the starting vertices of finite-length random walks are judged to be in the same community if the walkers pass similar sets of vertices. This idea is based on our consideration that a random walker tends to move in the community including the walker's starting vertex for some time after starting the walk. Therefore, the sets of vertices passed by random walkers starting from vertices in the same community must be similar. The idea is reinforced with two conditions. First, we exclude abnormal random walks. Random walks that depart from each vertex are executed many times, and vertices that are rarely passed by the walkers are excluded from the set of vertices that the walkers may pass. Second, we forcibly restrain random walks to an appropriate length. In our method, a random walk is terminated when the walker repeatedly visits vertices that they have already passed. Experiments on real-world networks demonstrate that our method outperforms previous techniques in terms of accuracy.

Non-backtracking walks reveal compartments in sparse chromatin interaction networks

Chromatin communities stabilized by protein machinery play essential role in gene regulation and refine global polymeric folding of the chromatin fiber. However, treatment of these communities in the framework of the classical network theory (stochastic block model, SBM) does not take into account intrinsic linear connectivity of the chromatin loci. Here we propose the polymer block model, paving the way for community detection in polymer networks. On the basis of this new model we modify the non-backtracking flow operator and suggest the first protocol for annotation of compartmental domains in sparse single cell Hi-C matrices. In particular, we prove that our approach corresponds to the maximum entropy principle. The benchmark analyses demonstrates that the spectrum of the polymer non-backtracking operator resolves the true compartmental structure up to the theoretical detectability threshold, while all commonly used operators fail above it. We test various operators on real data and conclude that the sizes of the non-backtracking single cell domains are most close to the sizes of compartments from the population data. Moreover, the found domains clearly segregate in the gene density and correlate with the population compartmental mask, corroborating biological significance of our annotation of the chromatin compartmental domains in single cells Hi-C matrices.

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.

The corrected gene proximity map for analyzing the 3D genome organization using Hi-C data

BACKGROUND

Genome-wide ligation-based assays such as Hi-C provide us with an unprecedented opportunity to investigate the spatial organization of the genome. Results of a typical Hi-C experiment are often summarized in a chromosomal contact map, a matrix whose elements reflect the co-location frequencies of genomic loci. To elucidate the complex structural and functional interactions between those genomic loci, networks offer a natural and powerful framework.

RESULTS

We propose a novel graph-theoretical framework, the Corrected Gene Proximity (CGP) map to study the effect of the 3D spatial organization of genes in transcriptional regulation. The starting point of the CGP map is a weighted network, the gene proximity map, whose weights are based on the contact frequencies between genes extracted from genome-wide Hi-C data. We derive a null model for the network based on the signal contributed by the 1D genomic distance and use it to "correct" the gene proximity for cell type 3D specific arrangements. The CGP map, therefore, provides a network framework for the 3D structure of the genome on a global scale. On human cell lines, we show that the CGP map can detect and quantify gene co-regulation and co-localization more effectively than the map obtained by raw contact frequencies. Analyzing the expression pattern of metabolic pathways of two hematopoietic cell lines, we find that the relative positioning of the genes, as captured and quantified by the CGP, is highly correlated with their expression change. We further show that the CGP map can be used to form an inter-chromosomal proximity map that allows large-scale abnormalities, such as chromosomal translocations, to be identified.

CONCLUSIONS

The Corrected Gene Proximity map is a map of the 3D structure of the genome on a global scale. It allows the simultaneous analysis of intra- and inter- chromosomal interactions and of gene co-regulation and co-localization more effectively than the map obtained by raw contact frequencies, thus revealing hidden associations between global spatial positioning and gene expression. The flexible graph-based formalism of the CGP map can be easily generalized to study any existing Hi-C datasets.

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

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

Spectral State Compression of Markov Processes

Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study the rank and features of Markov processes, as well as properties like representability, aggregability, and lumpability. We develop spectral methods for estimating the transition matrix of a low-rank Markov model, estimating the leading subspace spanned by Markov features, and recovering latent structures like state aggregation and lumpable partition of the state space. We prove statistical upper bounds for the estimation errors and nearly matching minimax lower bounds. Numerical studies are performed on synthetic data and a dataset of New York City taxi trips.

Telling ecological networks apart by their structure: An environment-dependent approach

The network architecture of an ecological community describes the structure of species interactions established in a given place and time. It has been suggested that this architecture presents unique features for each type of ecological interaction: e.g., nested and modular architectures would correspond to mutualistic and antagonistic interactions, respectively. Recently, Michalska-Smith and Allesina (2019) proposed a computational challenge to test whether it is indeed possible to differentiate ecological interactions based on network architecture. Contrary to the expectation, they found that this differentiation is practically impossible, moving the question to why it is not possible to differentiate ecological interactions based on their network architecture alone. Here, we show that this differentiation becomes possible by adding the local environmental information where the networks were sampled. We show that this can be explained by the fact that environmental conditions are a confounder of ecological interactions and network architecture. That is, the lack of association between network architecture and type of ecological interactions changes by conditioning on the local environmental conditions. Additionally, we find that environmental conditions are linked to the stability of ecological networks, but the direction of this effect depends on the type of interaction network. This suggests that the association between ecological interactions and network architectures exists, but cannot be fully understood without attention to the environmental conditions acting upon them.

It has been suggested that different types of species interactions lead to ecological networks with different architectures. For example, mutualistic and antagonistic interaction networks have been shown to have nested and modular architectures, respectively. Importantly, this differentiation can provide clues about the link between the dynamics and structures shaping ecological communities. Recently, Michalska-Smith and Allesina (2019) turned this assumption into a serious computational challenge for the scientific community. Here, we embrace this challenge. We confirm that network architecture alone is not enough to differentiate interaction networks. However, we show that network architectures can differentiate between mutualistic and antagonistic interaction networks by using information about their local environmental conditions. In other words, ignoring environmental information throws out the predictable patterns of network architectures along environmental gradients. Thus, this response is also a reminder that ecological networks may only make sense in the light of environmental information.

Long-range correlation in protein dynamics: Confirmation by structural data and normal mode analysis

Proteins in cellular environments are highly susceptible. Local perturbations to any residue can be sensed by other spatially distal residues in the protein molecule, showing long-range correlations in the native dynamics of proteins. The long-range correlations of proteins contribute to many biological processes such as allostery, catalysis, and transportation. Revealing the structural origin of such long-range correlations is of great significance in understanding the design principle of biologically functional proteins. In this work, based on a large set of globular proteins determined by X-ray crystallography, by conducting normal mode analysis with the elastic network models, we demonstrate that such long-range correlations are encoded in the native topology of the proteins. To understand how native topology defines the structure and the dynamics of the proteins, we conduct scaling analysis on the size dependence of the slowest vibration mode, average path length, and modularity. Our results quantitatively describe how native proteins balance between order and disorder, showing both dense packing and fractal topology. It is suggested that the balance between stability and flexibility acts as an evolutionary constraint for proteins at different sizes. Overall, our result not only gives a new perspective bridging the protein structure and its dynamics but also reveals a universal principle in the evolution of proteins at all different sizes.

The long-range correlated fluctuations are closely related to many biological processes of the proteins, such as catalysis, ligand binding, biomolecular recognition, and transportation. In this paper, we elucidate the structural origin of the long-range correlation and describe how native contact topology defines the slow-mode dynamics of the native proteins. Our result suggests an evolutionary constraint for proteins at different sizes, which may shed light on solving many biophysical problems such as structure prediction, multi-scale molecular simulations, and the design of molecular machines. Moreover, in statistical physics, as the long-range correlations are notable signs of the critical point, unveiling the origin of such criticality can extend our understanding of the organizing principle of a large variety of complex systems.

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

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

Super-resolution modularity analysis shows polyhedral caveolin-1 oligomers combine to form scaffolds and caveolae

Caveolin-1 (Cav1), the coat protein for caveolae, also forms non-caveolar Cav1 scaffolds. Single molecule Cav1 super-resolution microscopy analysis previously identified caveolae and three distinct scaffold domains: smaller S1A and S2B scaffolds and larger hemispherical S2 scaffolds. Application here of network modularity analysis of SMLM data for endogenous Cav1 labeling in HeLa cells shows that small scaffolds combine to form larger scaffolds and caveolae. We find modules within Cav1 blobs by maximizing the intra-connectivity between Cav1 molecules within a module and minimizing the inter-connectivity between Cav1 molecules across modules, which is achieved via spectral decomposition of the localizations adjacency matrix. Features of modules are then matched with intact blobs to find the similarity between the module-blob pairs of group centers. Our results show that smaller S1A and S1B scaffolds are made up of small polygons, that S1B scaffolds correspond to S1A scaffold dimers and that caveolae and hemispherical S2 scaffolds are complex, modular structures formed from S1B and S1A scaffolds, respectively. Polyhedral interactions of Cav1 oligomers, therefore, leads progressively to the formation of larger and more complex scaffold domains and the biogenesis of caveolae.

Telling ecological networks apart by their structure: A computational challenge

Ecologists have been compiling ecological networks for over a century, detailing the interactions between species in a variety of ecosystems. To this end, they have built networks for mutualistic (e.g., pollination, seed dispersal) as well as antagonistic (e.g., herbivory, parasitism) interactions. The type of interaction being represented is believed to be reflected in the structure of the network, which would differ substantially between mutualistic and antagonistic networks. Here, we put this notion to the test by attempting to determine the type of interaction represented in a network based solely on its structure. We find that, although it is easy to separate different kinds of nonecological networks, ecological networks display much structural variation, making it difficult to distinguish between mutualistic and antagonistic interactions. We therefore frame the problem as a challenge for the community of scientists interested in computational biology and machine learning. We discuss the features a good solution to this problem should possess and the obstacles that need to be overcome to achieve this goal.

Counting the number of metastable states in the modularity landscape: Algorithmic detectability limit of greedy algorithms in community detection

Modularity maximization using greedy algorithms continues to be a popular approach toward community detection in graphs, even after various better forming algorithms have been proposed. Apart from its clear mechanism and ease of implementation, this approach is persistently popular because, presumably, its risk of algorithmic failure is not well understood. This Rapid Communication provides insight into this issue by estimating the algorithmic performance limit of the stochastic block model inference using modularity maximization. This is achieved by counting the number of metastable states under a local update rule. Our results offer a quantitative insight into the level of sparsity at which a greedy algorithm typically fails.

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.

Locally Weighted Fusion of Structural and Attribute Information in Graph Clustering

Attributed graphs have attracted much attention in recent years. Different from conventional graphs, attributed graphs involve two different types of heterogeneous information, i.e., structural information, which represents the links between the nodes, and attribute information on each of the nodes. Clustering on attributed graphs usually requires the fusion of both types of information in order to identify meaningful clusters. However, most of existing works implement the combination of these two types of information in a "global" manner by treating all nodes equally and learning a global weight for the information fusion. To address this issue, this paper proposed a novel weighted K -means algorithm with "local" learning for attributed graph clustering, called adaptive fusion of structural and attribute information (Adapt-SA) and analyzed the convergence property of the algorithm. The key advantage of this model is to automatically balance the structural connections and attribute information of each node to learn a fusion weight, and get densely connected clusters with high attribute semantic similarity. Experimental study of weights on both synthetic and real-world data sets showed that the weights learned by Adapt-SA were reasonable, and they reflected which one of these two types of information was more important to decide the membership of a node. We also compared Adapt-SA with the state-of-the-art algorithms on the real-world networks with varieties of characteristics. The experimental results demonstrated that our method outperformed the other algorithms in partitioning an attributed graph into a community structure or other general structures.

Community Structure Detection Using Firefly Algorithm

This article describes how parallel to the continuous growth of the Internet, which allows people to share and collaborate more, social networks have become more attractive as a research topic in many different disciplines. Community structures are established upon interactions between people. Detection of these communities has become a popular topic in computer science. How to detect the communities is of great importance for understanding the organization and function of networks. Community detection is considered a variant of the graph partitioning problem which is NP-hard. In this article, the Firefly algorithm is used as an optimization algorithm to solve the community detection problem by maximizing the modularity measure. Firefly algorithm is a new Nature-inspired heuristic algorithm that proved its good performance in a variety of applications. Experimental results obtained from tests on real-life networks demonstrate that the authors' algorithm successfully detects the community structure.

Network community-based model reduction for vortical flows

A network community-based reduced-order model is developed to capture key interactions among coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic techniques to identify important vortical communities that are comprised of vortical elements that share similar dynamical behavior. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of these vortical interactions, the proposed methodology is applied to formulate reduced-order models for the inter-community dynamics of vortical flows, and predict lift and drag forces on bodies in wake flows. We demonstrate the capabilities of these models by accurately capturing the macroscopic dynamics of a collection of discrete point vortices, and the complex unsteady aerodynamic forces on a circular cylinder and an airfoil with a Gurney flap. The present formulation is found to be robust against simulated experimental noise and turbulence due to its integrating nature of the system reduction.

Compressing Networks with Super Nodes

Community detection is a commonly used technique for identifying groups in a network based on similarities in connectivity patterns. To facilitate community detection in large networks, we recast the network as a smaller network of ‘super nodes’, where each super node comprises one or more nodes of the original network. We can then use this super node representation as the input into standard community detection algorithms. To define the seeds, or centers, of our super nodes, we apply the ‘CoreHD’ ranking, a technique applied in network dismantling and decycling problems. We test our approach through the analysis of two common methods for community detection: modularity maximization with the Louvain algorithm and maximum likelihood optimization for fitting a stochastic block model. Our results highlight that applying community detection to the compressed network of super nodes is significantly faster while successfully producing partitions that are more aligned with the local network connectivity and more stable across multiple (stochastic) runs within and between community detection algorithms, yet still overlap well with the results obtained using the full network.

Different Anti-Vaping Campaigns Attracting the Same Opponent Community

E-cigarettes (vape) are now the most commonly used tobacco product among youth in the United States. Ads are claiming e-cigarettes help smokers quit, but most of them contain nicotine, which can cause addiction and harm the developing adolescent brain. Therefore, national, state, and local health organizations have proposed anti-vaping campaigns to warn the potential risks of e-cigarettes. However, there is some evidence that these products may reduce harm for adult users who reduce or quit combustible cigarette smoking, and with little evidence that e-cigarettes cause long-term harm, pro-vaping advocates have used this equivocal evidence base to oppose the anti-vaping media campaign messaging, generating a very high volume of oppositional messages on social media. Thus, when we analyze the feedback of anti-vaping campaigns, it is crucial to partition the audience into different clusters according to their attitudes and affiliations. Motivated by this, in this paper, we propose the "community detection on anti-vaping campaign audience" problem and design the "community detection based on social, repost and content relation, (Sorento)" algorithm to solve it. Sorento computes users' intimacy scores based on their social connections, repost relations, and content similarities. The community detection results achieved by Sorento demonstrate that though anti-vaping campaigns are proposed in different areas at different times, their opponent messages are mainly posted by the same community of pro-vapors.

Comparative analysis on the selection of number of clusters in community detection

We conduct a comparative analysis on various estimates of the number of clusters in community detection. An exhaustive comparison requires testing of all possible combinations of frameworks, algorithms, and assessment criteria. In this paper we focus on the framework based on a stochastic block model, and investigate the performance of greedy algorithms, statistical inference, and spectral methods. For the assessment criteria, we consider modularity, map equation, Bethe free energy, prediction errors, and isolated eigenvalues. From the analysis, the tendency of overfit and underfit that the assessment criteria and algorithms have becomes apparent. In addition, we propose that the alluvial diagram is a suitable tool to visualize statistical inference results and can be useful to determine the number of clusters.