Weighted Adjacency Matrix Research Articles

A Deep Learning Approach Using Graph Neural Networks for Anomaly Detection in Air Quality Data Considering Spatiotemporal Correlations

The ambient air pollution problem has become more severe as the social economy develops. Abnormal event detection in air quality data can prevent property loss and protect human health. The majority of existing anomaly detection models in air quality data are based on a single variable or a single monitoring station, ignoring spatial correlation and multivariate features of regional air pollutant concentrations. To address the aforementioned issues, this paper proposes a new deep learning approach that combines spatial correlation and temporal correlation of air quality data to detect air quality anomalies. The essential idea of this approach is to use the correlation degree between node information to fuse the spatial correlational feature and temporal correlational feature of air quality data to construct spatiotemporal graph structure data, which are used for anomaly detection in air quality data. In this proposed approach, (1) the weighted adjacency matrix is established to characterize the spatial correlation, and the feature matrix is constructed to characterize the temporal correlation; (2) changes in node information are transformed into changes in edge weights using the correlation degree between node information, and spatiotemporal graph structure data are constructed to characterize the spatiotemporal correlation; and (3) an advanced deep learning model, Context augmented Graph Autoencoder (Con-GAE), is utilized to handle the above spatiotemporal graph structure data and detect abnormal air quality events. The efficiency of the approach is demonstrated by anomaly detection on synthetic test sets produced from real-world datasets.

Software Knowledge Entity Relation Extraction with Entity-Aware and Syntactic Dependency Structure Information

Software knowledge community contains a large scale of software knowledge entities with complex structure and rich semantic relations. Semantic relation extraction of software knowledge entities is a critical task for software knowledge graph construction, which has an important impact on knowledge graph based tasks such as software document generation and software expert recommendation. Due to the problems of entity sparsity, relation ambiguity, and the lack of annotated dataset in user-generated content of software knowledge community, it is difficult to apply existing methods of relation extraction in the software knowledge domain. To address these issues, we propose a novel software knowledge entity relation extraction model which incorporates entity-aware information with syntactic dependency information. Bidirectional Gated Recurrent Unit (Bi-GRU) and Graph Convolutional Networks (GCN) are used to learn the features of contextual semantic representation and syntactic dependency representation, respectively. To obtain more syntactic dependency information, a weight graph convolutional network based on Newton’s cooling law is constructed by calculating a weight adjacency matrix. Specifically, an entity-aware attention mechanism is proposed to integrate the entity information and syntactic dependency information to improve the prediction performance of the model. Experiments are conducted on a dataset which is constructed based on texts of the StackOverflow and show that the proposed model has better performance than the benchmark models.

Approaching Disordered Quantum Dot Systems by Complex Networks with Spatial and Physical-Based Constraints.

This paper focuses on modeling a disordered system of quantum dots (QDs) by using complex networks with spatial and physical-based constraints. The first constraint is that, although QDs (=nodes) are randomly distributed in a metric space, they have to fulfill the condition that there is a minimum inter-dot distance that cannot be violated (to minimize electron localization). The second constraint arises from our process of weighted link formation, which is consistent with the laws of quantum physics and statistics: it not only takes into account the overlap integrals but also Boltzmann factors to include the fact that an electron can hop from one QD to another with a different energy level. Boltzmann factors and coherence naturally arise from the Lindblad master equation. The weighted adjacency matrix leads to a Laplacian matrix and a time evolution operator that allows the computation of the electron probability distribution and quantum transport efficiency. The results suggest that there is an optimal inter-dot distance that helps reduce electron localization in QD clusters and make the wave function better extended. As a potential application, we provide recommendations for improving QD intermediate-band solar cells.

A zero forcing technique for bounding sums of eigenvalue multiplicities

Given a graph G, one may ask: “What sets of eigenvalues are possible over all weighted adjacency matrices of G?” (The weight of an edge is positive or negative, while the diagonal entries can be any real numbers.) This is known as the Inverse Eigenvalue Problem for graphs (IEPG). A mild relaxation of this question considers the multiplicity list instead of the exact eigenvalues themselves. That is, given a graph G on n vertices and an ordered partition m=(m1,…,mℓ) of n, is there a weighted adjacency matrix where the i-th distinct eigenvalue has multiplicity mi? This is known as the ordered multiplicity IEPG. Recent work solved the ordered multiplicity IEPG for all graphs on 6 vertices.In this work, we develop zero forcing methods for the ordered multiplicity IEPG in a multitude of different contexts. Namely, we utilize zero forcing parameters on powers of graphs to achieve bounds on consecutive multiplicities. We are able to provide general bounds on sums of multiplicities of eigenvalues for graphs. This includes new bounds on the sums of multiplicities of consecutive eigenvalues as well as more specific bounds for trees. Using these results, we verify the previous results above regarding the IEPG on six vertices. In addition, applying our techniques to skew-symmetric matrices, we are able to determine all possible ordered multiplicity lists for skew-symmetric matrices for connected graphs on five vertices.

FLAME: long-read bioinformatics tool for comprehensive spliceome characterization.

Comprehensive characterization of differentially spliced RNA transcripts with nanopore sequencing is limited by bioinformatics tools that are reliant on existing annotations. We have developed FLAME, a bioinformatics pipeline for alternative splicing analysis of gene-specific or transcriptome-wide long-read sequencing data. FLAME is a Python-based tool aimed at providing comprehensible quantification of full-length splice variants, reliable de novo recognition of splice sites and exons, and representation of consecutive exon connectivity in the form of a weighted adjacency matrix. Notably, this workflow circumvents issues related to inadequate reference annotations and allows for incorporation of short-read sequencing data to improve the confidence of nanopore sequencing reads. In this study, the Epstein-Barr virus long noncoding RNA RPMS1 was used to demonstrate the utility of the pipeline. RPMS1 is ubiquitously expressed in Epstein-Barr virus associated cancer and known to undergo ample differential splicing. To fully resolve the RPMS1 spliceome, we combined gene-specific nanopore sequencing reads from a primary gastric adenocarcinoma and a nasopharyngeal carcinoma cell line with matched publicly available short-read sequencing data sets. All previously reported splice variants, including putative ORFs, were detected using FLAME. In addition, 32 novel exons, including two intron retentions and a cassette exon, were discovered within the RPMS1 gene.

Fixed-time consensus of nonlinear multi-agent systems with stochastically switching topologies

In this paper, the fixed-time consensus issue of nonlinear multi-agent systems with general time-varying topologies and stochastically switching topologies is investigated. Firstly, for the case of general time-varying topologies, an appropriate nonlinear control protocol is proposed, the sufficient criterion for fixed-time consensus is derived by utilising the method basing on the scramblingness property of the system's weighted adjacency matrix. Then, based on the derived general theorem, the case of stochastically switching topologies is investigated. We mainly focus on the scenarios of (i) independent and identically distributed switching topologies and (ii) Markovian switching topologies. For both scenarios, it is proved that, if the probability of a scrambling weighted adjacency matrix is nonzero, then the fixed-time consensus can be realised almost surely when the involved control parameters are properly selected. Some simulations are presented at last to verify the obtained theorems.

FC 101PROTEOMIC PROFILE OF MESOTHELIAL EXOSOMES ISOLATED FROM PERITONEAL DIALYSIS EFFLUENT OF CHILDREN WITH FOCAL SEGMENTAL GLOMERULOSCLEROSIS

Abstract Background and Aims Peritoneal dialysis (PD) is the worldwide preferred dialysis treatment for children affected by end stage kidney disease. However, due to the unphysiological composition of PD fluids, the peritoneal mesothelium of these patients may undergo structural and functional alterations, which may cause fibrosis. Several factors may accelerate this process and primary kidney disease may have a causative role. In particular, patients affected by corticosteroid resistant focal segmental glomerulosclerosis (FSGS), a rare glomerular disease leading to nephrotic syndrome, seems more prone to develop peritoneal fibrosis. The mechanism causing this predisposition is still unrecognized. To better define this condition, we carried out, for the first time, a new comprehensive comparative proteomic mass spectrometry analysis of mesothelial exosomes from peritoneal dialysis effluent (PDE). Method We enrolled 12 paediatric patients on PD. Half of them affected by FSGS and the others affected by other disorders (NO FSGS). Exosomes from mesothelial peritoneal cells were isolated by centrifugation and, using a biotinylated antibody and streptavidin magnetic beads. Exosome size was determined by dynamic light scattering, and antigen profile of exosomes was assayed by western blot. Mass spectrometry data were analyzed by unsupervised hierarchical clustering using multidimensional scaling, in order to identify outliers and dissimilarity between samples. The normalized data were used to construct a co-expression network using the weighted gene co-expression network analysis (WGCNA). A weighted adjacency matrix was constructed, and transformed into a topological overlap matrix, which measures the network connectivity of all proteins. To identify the relationship between each module and each clinical trait, we used module eigengenes (MEs) and calculated the correlation between MEs and the clinical traits. To identify the hub proteins of modules that maximize the discrimination between FSGS and NO FSGS samples, we applied T-test, and non-linear support vector machine (SVM) learning. Finally, gene set enrichment analysis was done to build a functional proteins network based on their Gene Ontology (GO) annotations extracted from the Gene Ontology Consortium. Results Our omic study demonstrated that SVM allowed a complete distinction of the whole proteomic exosome mesothelial content of FSGS versus NO FSGS (100% accuracy). Out of the 2490 identified proteins, 40% (995) were involved in endothelial to mesenchymal transition /fibrosis and in the TGF-B pathway. The WGCNA analysis highlighted a total of 40 proteins were that maximize the discrimination between FSGS and NO FSGS patients (Figure 1A). Their expression profile is reported in a heatmap diagram (Figure 1B). Additionally, we performed GO enrichment analysis (Figure 2) and the algorithm identified that some of the discriminative proteins (TIMP1, CTHRC1, SPARC, CHMP4B, COL5A2, ANXA13, FNC2 and CENP-E) were also highly correlated to the peritoneal dialysis vintage, fibrosis, EMT and PM disease. Conclusion Our data demonstrated, for the first time, that mesothelial cells of FSGS are more prone to activate a pro-fibrotic machinery with exosomes having a primary role in this process. Moreover, they indicated that identified FSGS-associated element in mesothelial exosome protein could be employed as potential new biomarkers of mesothelial integrity. Finally, results highlighted that FSGS should be treated with more biocompatible dialysis solution, reduce the length of time on PD and personalize type and regimens of PD to minimize the risk of rapid loss of peritoneal membrane.

A deep learning approach using graph convolutional networks for slope deformation prediction based on time-series displacement data

Slope deformation prediction is crucial for early warning of slope failure, which can prevent property damage and save human life. Existing predictive models focus on predicting the displacement of a single monitoring point based on time series data, without considering spatial correlations among monitoring points, which makes it difficult to reveal the displacement changes in the entire monitoring system and ignores the potential threats from nonselected points. To address the above problem, this paper presents a novel deep learning method for predicting the slope deformation, by considering the spatial correlations between all points in the entire displacement monitoring system. The essential idea behind the proposed method is to predict the slope deformation based on the global information (i.e., the correlated displacements of all points in the entire monitoring system), rather than based on the local information (i.e., the displacements of a specified single point in the monitoring system). In the proposed method, (1) a weighted adjacency matrix is built to interpret the spatial correlations between all points, (2) a feature matrix is assembled to store the time-series displacements of all points, and (3) one of the state-of-the-art deep learning models, i.e., T-GCN, is developed to process the above graph-structured data consisting of two matrices. The effectiveness of the proposed method is verified by performing predictions based on a real dataset. The proposed method can be applied to predict time-dependency information in other similar geohazard scenarios, based on time-series data collected from multiple monitoring points.

Technology Forecasting based on Topic Analysis and Social Network Analysis: A Case Study Focusing on Gene Editing Patents

Technology forecasting research is an indispensable means to master the development trend of technology and provide decision support for scientific research management. For patent documents, it does not provide keyword information, which makes the keyword based technology prediction method have some limitations in revealing research content and hidden topics in specific fields. In order to better reflect the technical information in the patent, this paper combines topic analysis and social network analysis to study the development trends of gene editing technology. First, the patent data of gene editing technology is collected from Derwent Innovations Index. Secondly, text mining software is adopted to draw a network graph of topic words, combined with Inverse Document Frequency (IDF) to construct a weighted adjacency matrix, and Social Network Analysis is used to obtain the degree of centrality of technical topic words. Finally, the technological trends of gene editing technology is explored by identifying the core themes of gene editing, highlighting themes and emerging themes, and some meaningful conclusions are also obtained. Based on the analysis results, this study finds that the development of gene editing technology is limited by factors such as ethics, law and cellular pollution. In addition, future research directions will be more inclined to optimize the safety and efficiency of gene editing technology.

Quantum search of matching on signed graphs

We construct a quantum searching model of a signed edge driven by a quantum walk. The time evolution operator of this quantum walk provides a weighted adjacency matrix induced by the assignment of a sign to each edge. This sign can be regarded as so-called the edge coloring. Then as an application, under an arbitrary edge coloring which gives a matching on a complete graph on $$n+1$$ vertices we consider a quantum search of a colored edge from the edge set of the complete graph. We show that this quantum walk finds a colored edge within the time complexity of $$O(n^{\frac{2-\alpha }{2}})$$ with probability $$1-o(1)$$ , while the corresponding random walk on the line graph finds them within the time complexity of $$O(n^{2-\alpha })$$ if we set the number of the edges of the matching by $$t=O(n^{\alpha })$$ for $$0 \le \alpha \le 1$$ red with $$t \le \frac{n}{2}$$ .

Cospectrality preserving graph modifications and eigenvector properties via walk equivalence of vertices

Originating from spectral graph theory, cospectrality is a powerful generalization of exchange symmetry and can be applied to all real-valued symmetric matrices. Two vertices of an undirected graph with real edge weights are cospectral if and only if the underlying weighted adjacency matrix M fulfills [Mk]u,u=[Mk]v,v for all non-negative integer k, and as a result any eigenvector ϕ of M has (or, in the presence of degeneracies, can be chosen to have) definite parity on u and v. We here show that the powers of a matrix with cospectral vertices induce further local relations on its eigenvectors, and also can be used to design cospectrality preserving modifications. To this end, we introduce the concept of walk equivalence of cospectral vertices with respect to walk multiplets which are special vertex subsets of a graph. Walk multiplets allow for systematic and flexible modifications of a graph with a given cospectral pair while preserving this cospectrality. The set of modifications includes the addition and removal of both vertices and edges, such that the underlying topology of the graph can be altered. In particular, we prove that any new vertex connected to a walk multiplet by suitable connection weights becomes a so-called unrestricted substitution point (USP), meaning that any arbitrary graph may be connected to it without breaking cospectrality. Also, suitable interconnections between walk multiplets within a graph are shown to preserve the associated cospectrality. Importantly, we demonstrate that the walk equivalence of cospectral vertices u,v imposes a local structure on every eigenvector ϕ obeying ϕu=±ϕv≠0 (in the case of degeneracies, a specific choice of the eigenvector basis is needed). Our work paves the way for flexibly exploiting hidden structural symmetries in the design of generic complex network-like systems.

Trees with extremal spectral radius of weighted adjacency matrices among trees weighted by degree-based indices

For a graph G=(V,E) and i,j∈V, denote by di, dj the degrees of vertices i, j in G. Let f(di,dj)>0 be a function symmetric in i and j. Define a matrix Af(G), called the weighted adjacency matrix of G, with the ij-entry Af(G)(i,j)=f(di,dj) if i∼j and Af(G)(i,j)=0 otherwise. In this paper, we find the extremal trees with the largest radius of Af when f(x,y) is increasing and convex in variable x. We also find the extremal tree with the smallest radius of Af when f(x,y) has a form P(x,y) or P(x,y), where P(x,y) is a symmetric polynomial with nonnegative coefficients and zero constant term. This paper tries to unify the spectral study of weighted adjacency matrices of graphs weighted by some topological indices.

Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links.

This paper focuses on modeling a disorder ensemble of quantum dots (QDs) as a special kind of Random Geometric Graphs (RGG) with weighted links. We compute any link weight as the overlap integral (or electron probability amplitude) between the QDs (=nodes) involved. This naturally leads to a weighted adjacency matrix, a Laplacian matrix, and a time evolution operator that have meaning in Quantum Mechanics. The model prohibits the existence of long-range links (shortcuts) between distant nodes because the electron cannot tunnel between two QDs that are too far away in the array. The spatial network generated by the proposed model captures inner properties of the QD system, which cannot be deduced from the simple interactions of their isolated components. It predicts the system quantum state, its time evolution, and the emergence of quantum transport when the network becomes connected.

A novel weighted graph representation-based method for structural topology optimization

This paper proposes a novel weighted graph representation for structural topology optimization. Based on the graph theory, a weighted adjacency matrix is first introduced to collect the connectivity information and the corresponding width value of the edges. Accordingly, each edge with different width is symbolized as a rectangle to represent the mapped topology for a regular meshed design domain. To reduce the computational cost, an improved differential evolution (DE) process with a dual self-adaptive mutation operator which is named as the DSADE is proposed to utilize as an optimizer. Finally, three classical numerical tests are carried out. The results indicate that the present method can effectively deal with a series of structural topology optimization problem with different boundary constraints. In addition, by comparing with the related methods in literatures, it is found that the present method can achieve an optimized solution without complex initial definitions.

Exploring the dependence structure among Chinese firms in the 5G industry

PurposeThis study aims to explore the dependence structure among Chinese firms across the emerging 5G industry at different stages and to provide some strategic insights for market participants.Design/methodology/approachThis study adopt macroeconomic fundamentals and the log-returns of 45 listed firms in the Chinese 5G industry to construct the weighted adjacency matrix by measuring the correlation parameters and then use the triangulated maximally filtered graph (TMFG) algorithm to construct the dependence network. It analyses the topological structure of the constructed networks to obtain the dependence characteristics for each firm in the whole industrial supply chain at different levels.FindingsThe empirical results provide a comprehensive and concise snapshot of the industrial structure, across the whole 5G industry at different levels, rather than just a “one-to-one” pattern. Specifically, the dependence characteristics of different firms are heterogeneous, and most firms are highly connected with partners in the whole industrial supply chain, whereas a few firms that are weakly connected. Those closely connected firms are usually in the midstream. In addition, compared with firms at different levels, downstream firms usually have closer dependencies and stronger influence capabilities.Practical implicationsRegulators not only should promote stability development for those firms most intensely connected with whole industry chain but also protect those firms with weak link in the whole industry chain. Investors should better understand the embedded ties among different firms to obtain effective market information and can select multiple firms with fewer connections as backup to conduct joint investment for risk mitigation. Mangers should give priority to the central players/firms in the whole industrial supply chain and establish the alliances with closely connected firms.Originality/valueThis study contributes to both the information system and operation management literature by constructing a new network method, Copula-TMFG, to capture the dependence structure among Chinese firms in 5G industry, empirically providing some strategic insights for 5G industry stakeholders, such as regulators, investors and managers.

Exact Recovery of Community Detection in k-Partite Graph Models with Applications to Learning Electric Potentials in Electric Networks

We study the vertex classification problem on a graph whose vertices are in $$k\ (k\ge 2)$$ different communities, edges are only allowed between distinct communities, and the number of vertices in different communities are not necessarily equal. The observation is a weighted adjacency matrix, perturbed by a scalar multiple of the Gaussian Orthogonal Ensemble (GOE), or Gaussian Unitary Ensemble (GUE) matrix. For the exact recovery of the maximum likelihood estimation (MLE) with various weighted adjacency matrices, we prove sharp thresholds of the intensity $$\sigma $$ of the Gaussian perturbation. Roughly speaking, when $$\sigma $$ is below (resp. above) the threshold, exact recovery of MLE occurs with probability tending to 1 (resp. 0) as the size of the graph goes to infinity. These weighted adjacency matrices may be considered as natural models for the electric network. Surprisingly, these thresholds of $$\sigma $$ do not depend on whether the sample space for MLE is restricted to such classifications that the number of vertices in each group is equal to the true value. In contrast to the $${{\mathbb {Z}}}_2$$ -synchronization, a new complex version of the semi-definite programming (SDP) is designed to efficiently implement the community detection problem when the number of communities k is greater than 2, and a common region (independent of k) for $$\sigma $$ such that SDP exactly recovers the true classification is obtained.

Learning Dynamic Relationships for Facial Expression Recognition Based on Graph Convolutional Network.

Facial action units (AUs) analysis plays an important role in facial expression recognition (FER). Existing deep spectral convolutional networks (DSCNs) have made encouraging performance for FER based on a set of facial local regions and a predefined graph structure. However, these regions do not have close relationships to AUs, and DSCNs cannot model the dynamic spatial dependencies of these regions for estimating different facial expressions. To tackle these issues, we propose a novel double dynamic relationships graph convolutional network (DDRGCN) to learn the strength of the edges in the facial graph by a trainable weighted adjacency matrix. We construct facial graph data by 20 regions of interest (ROIs) guided by different facial AUs. Furthermore, we devise an efficient graph convolutional network in which the inherent dependencies of vertices in the facial graph can be learned automatically during network training. Notably, the proposed model only has 110K parameters and 0.48MB model size, which is significantly less than most existing methods. Experiments on four widely-used FER datasets demonstrate that the proposed dynamic relationships graph network achieves superior results compared to existing light-weight networks, not just in terms of accuracy but also model size and speed.

Statistical Graph Signal Recovery Using Variational Bayes

This brief investigates the problem of Graph Signal Recovery (GSR) when the topology of the graph is not known in advance. In this brief, the elements of the weighted adjacency matrix is statistically related to normal distribution and the graph signal is assumed to be Gaussian Markov Random Field (GMRF). Then, the problem of GSR is solved by a Variational Bayes (VB) algorithm in a Bayesian manner by computing the posteriors in a closed form. The posteriors of the elements of weighted adjacency matrix are proved to have a new distribution which we call it Generalized Compound Confluent Hypergeometric (GCCH) distribution. Moreover, the variance of the noise is estimated by calculating its posterior via VB. The simulation results on synthetic and real-world data shows the superiority of the proposed Bayesian algorithm over some state-of-the-art algorithms in recovering the graph signal.

Trophic Ecology of Seahorse Key, Florida: A Unique Bird-Snake Interaction Network Analysis

In 2015 the entire breeding colony of nesting waterbirds on Seahorse Key (Florida, U.S.A.) unexpectedly abandoned the island and have not returned. These birds have a unique trophic relationship with a sympatric cottonmouth snake (Agkistrodon conanti) population, as well as potentially important positions within the entire insular food web. Species-interaction network analysis was used to compare two trophic networks; pre- and post-abandonment. Trophic data were used to create a weighted adjacency matrix for each network and the resulting network metrics were compared using the network analysis software package UCINET and visualized using NetDraw. Results for the pre-abandonment network indicated a large, complex, diffuse network with low centrality and seven sub-networks. Several species of colonial nesting birds were identified as holding important positions within the network for resource transfer from marine and intertidal environments to terrestrial trophic guilds, particularly to the snakes. Post-abandonment analysis showed the network significantly fractured with the terrestrial trophic guild that includes the snakes being smaller, more isolated and potentially less stable.

Trophic Ecology of Seahorse Key, Florida: A Unique Bird-Snake Interaction Network Analysis

In 2015 the entire breeding colony of nesting waterbirds on Seahorse Key (Florida, U.S.A.) unexpectedly abandoned the island and have not returned. These birds have a unique trophic relationship with a sympatric cottonmouth snake (Agkistrodon conanti) population, as well as potentially important positions within the entire insular food web. Species-interaction network analysis was used to compare two trophic networks; pre- and post-abandonment. Trophic data were used to create a weighted adjacency matrix for each network and the resulting network metrics were compared using the network analysis software package UCINET and visualized using NetDraw. Results for the pre-abandonment network indicated a large, complex, diffuse network with low centrality and seven sub-networks. Several species of colonial nesting birds were identified as holding important positions within the network for resource transfer from marine and intertidal environments to terrestrial trophic guilds, particularly to the snakes. Post-abandonment analysis showed the network significantly fractured with the terrestrial trophic guild that includes the snakes being smaller, more isolated and potentially less stable.