Entropy-based link prediction in weighted networks

Information entropy has been proved to be an effective tool to quantify the structural importance of complex networks.In a previous work [Xu et al. Physica A, 456 294（2016）], we measure the contribution of a path in link prediction with information entropy. In this paper, we further quantify the contribution of a path with both path entropy and path weight,and propose a weighted prediction index based on the contributions of paths, namely weighted path entropy（WPE）, to improve the prediction accuracy in weighted networks. Empirical experiments on six weighted real-world networks show that WPE achieves higher prediction accuracy than three other typical weighted indices.

Detecting and describing the modular structures of weighted networks

In the functional properties of complex networks, modules play a central role. In this paper, we propose a new method to detect and describe the modular structures of weighted networks. In order to test the proposed method, as an example, we use our method to analyse the structural properties of the Chinese railway network. Here, the stations are regarded as the nodes and the track sections are regarded as the links. Rigorous analysis of the existing data shows that using the proposed algorithm, the nodes of network can be classified naturally. Moreover, there are several core nodes in each module. Remarkably, we introduce the correlation function Grs, and use it to distinguish the different modules in weighted networks.

Screening biomarkers for spinal cord injury using weighted gene co-expression network analysis and machine learning

Immune changes and inflammatory responses have been identified as central events in the pathological process of spinal co rd injury.They can greatly affect nerve regeneration and functional recovery.However,there is still limited understanding of the peripheral immune inflammato ry response in spinal cord inju ry.In this study.we obtained microRNA expression profiles from the peripheral blood of patients with spinal co rd injury using high-throughput sequencing.We also obtained the mRNA expression profile of spinal cord injury patients from the Gene Expression Omnibus(GEO)database(GSE151371).We identified 54 differentially expressed microRNAs and 1656 diffe rentially expressed genes using bioinformatics approaches.Functional enrichment analysis revealed that various common immune and inflammation-related signaling pathways,such as neutrophil extracellular trap formation pathway,T cell receptor signaling pathway,and nuclear factor-κB signal pathway,we re abnormally activated or inhibited in spinal cord inju ry patient samples.We applied an integrated strategy that combines weighted gene co-expression network analysis,LASSO logistic regression,and SVM-RFE algorithm and identified three biomarke rs associated with spinal cord injury:ANO10,BST1,and ZFP36L2.We verified the expression levels and diagnostic perfo rmance of these three genes in the original training dataset and clinical samples through the receiver operating characteristic curve.Quantitative polymerase chain reaction results showed that ANO20 and BST1 mRNA levels were increased and ZFP36L2 mRNA was decreased in the peripheral blood of spinal cord injury patients.We also constructed a small RNA-mRNA interaction network using Cytoscape.Additionally,we evaluated the proportion of 22 types of immune cells in the peripheral blood of spinal co rd injury patients using the CIBERSORT tool.The proportions of naive B cells,plasma cells,monocytes,and neutrophils were increased while the proportions of memory B cells,CD8^(+)T cells,resting natural killer cells,resting dendritic cells,and eosinophils were markedly decreased in spinal cord injury patients increased compared with healthy subjects,and ANO10,BST1 and ZFP26L2we re closely related to the proportion of certain immune cell types.The findings from this study provide new directions for the development of treatment strategies related to immune inflammation in spinal co rd inju ry and suggest that ANO10,BST2,and ZFP36L2 are potential biomarkers for spinal cord injury.The study was registe red in the Chinese Clinical Trial Registry(registration No.ChiCTR2200066985,December 12,2022).

Generating weighted community networks based on local events

Many realistic networks have community structures, namely, a network consists of groups of nodes within which links are dense but among which links are sparse. This paper proposes a growing network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Also, it utilizes the preferential attachment for building connections determined by nodes＇ strengths, which evolves dynamically during the growth of the system. The resulting network reflects the intrinsic community structure with generalized power-law distributions of nodes＇ degrees and strengths.

Predictive Characteristics of Co-authorship Networks: Comparing the Unweighted, Weighted, and Bipartite Cases

Purpose： This study aims to answer the question to what extent different types of networks can be used to predict future co-authorship among authors.Design/methodology/approach： We compare three types ot networks： unwelgntea networks, in which a link represents a past collaboration; weighted networks, in which links are weighted by the number of joint publications; and bipartite author-publication networks. The analysis investigates their relation to positive stability, as well as their potential in predicting links in future versions of the co-authorship network. Several hypotheses are tested.Findings： Among other results, we find that weighted networks do not automatically lead to better predictions. Bipartite networks, however, outperform unweighted networks in almost all cases. Research limitations： Only two relatively small case studies are considered Practical implications： The study suggests that future link prediction studies on networks should consider using the bipartite network as a training network. Originality/value： This is the first systematic comparison of unweighted, weighted, and bipartite training networks in link prediction.

Malicious Code Modeling and Analysis in Weighted Scale-Free Networks

We study the detailed malicious code propagating process in scale-free networks with link weights that denotes traffic between two nodes. It is found that the propagating velocity reaches a peak rapidly then decays in a power-law form, which is different from the well-known result in unweighted network case. Simulation results show that the nodes with larger strength are preferential to be infected, but the hierarchical dynamics are not clearly found. The simulation results also show that larger dispersion of weight of networks leads to slower propagating, which indicates that malicious code propagates more quickly in unweighted scale-free networks than in weighted scale-free networks under the same condition. These results show that not only the topology of networks but also the link weights affect the malicious propagating process.

Hash function construction using weighted complex dynamical networks

A novel scheme to construct a hash function based on a weighted complex dynamical network （WCDN） generated from an original message is proposed in this paper. First, the original message is divided into blocks. Then, each block is divided into components, and the nodes and weighted edges are well defined from these components and their relations. Namely, the WCDN closely related to the original message is established. Furthermore, the node dynamics of the WCDN are chosen as a chaotic map. After chaotic iterations, quantization and exclusive-or operations, the fixed-length hash value is obtained. This scheme has the property that any tiny change in message can be diffused rapidly through the WCDN, leading to very different hash values. Analysis and simulation show that the scheme possesses good statistical properties, excellent confusion and diffusion, strong collision resistance and high efficiency.

Weighted gene co-expression network analysis reveals similarities and differences of molecular features between dilated and ischemic cardiomyopathies

Cardiomyopathies represent the most common clinical and genetic heterogeneous group of diseases that affect the heart function.Though progress has been made to elucidate the process,molecular mechanisms of different classes of cardiomyopathies remain elusive.This paper aims to describe the similarities and differences in molecular features of dilated cardiomyopathy(DCM)and ischemic cardiomyopathy(ICM).We firstly detected the co-expressed modules using the weighted gene co-expression network analysis(WGCNA).Significant modules associated with DCM/ICM were identified by the Pearson correlation coefficient(PCC)between the modules and the phenotype of DCM/ICM.The differentially expressed genes in the modules were selected to perform functional enrichment.The potential transcription factors(TFs)prediction was conducted for transcription regulation of hub genes.Apoptosis and cardiac conduction were perturbed in DCM and ICM,respectively.TFs demonstrated that the biomarkers and the transcription regulations in DCM and ICM were different,which helps make more accurate discrimination between them at molecular levels.In conclusion,comprehensive analyses of the molecular features may advance our understanding of DCM and ICM causes and progression.Thus,this understanding may promote the development of innovative diagnoses and treatments.

Scaling of weighted spectral distribution in weighted small-world networks

Many real-world systems can be modeled by weighted small-world networks with high clustering coefficients. Recent studies for rigorously analyzing the weighted spectral distribution（W SD） have focused on unweighted networks with low clustering coefficients. In this paper, we rigorously analyze the W SD in a deterministic weighted scale-free small-world network model and find that the W SD grows sublinearly with increasing network order（i.e., the number of nodes） and provides a sensitive discrimination for each input of this model. This study demonstrates that the scaling feature of the W SD exists in the weighted network model which has high and order-independent clustering coefficients and reasonable power-law exponents.

Integrating Local Closure Coefficient into Weighted Networks for Link Prediction

Triadic closure is a simple and fundamental kind of link formulation mechanism in network.Local closure coefficient(LCC),a new network property,is to measure the triadic closure with respect to the fraction of length-2 paths for link prediction.In this paper,a weighted format of LCC(WLCC)is introduced to measure the weighted strength of local triadic structure,and a statistic similari-ty-based link prediction metric is proposed to incorporate the definition of WLCC.To prove the metrics effectiveness and scalability,the WLCC formula-tion was further investigated under weighted local Naive Bayes(WLNB)link prediction framework.Finally,extensive experimental studies was conducted with weighted baseline metrics on various public network datasets.The results demonstrate the merits of the proposed metrics in comparison with the weighted baselines.

Exploring the mechanism of Guizhi decoction’s“Jun-Chen-Zuo-Shi”in treating plant nervous disorders based on weighted network pharmacology and molecular docking techniques

Objective:To explore the mechanism of Guizhi decoction’s“Jun-Chen-Zuo-Shi”in treating plant nervous disorders based on network pharmacology and molecular docking methods.Methods:The main active ingredients of Guizhi decoction were screened from the Traditional Chinese Medicine Systems Pharmacology Database and Analysis Platform(TCMSP),and plant nervous disorder-related targets were screened from the Gene Cards database,OMIM database,and PharmGKB database.The intersection of the two was obtained.The intersection targets were used to draw a protein interaction network and a“Traditional Chinese Medicine-active ingredient-target”network using the STRING database and Cytoscape 3.9.1.The nodes in the“Traditional Chinese Medicine-active ingredient-target”network were weighted according to the“Jun-Chen-Zuo-Shi”principle.Kyoto Encyclopedia of Genes and Genomes,and gene ontology enrichment analysis were performed on the intersection targets.Molecular docking was used to verify the affinity between core targets and key ingredients.Results:A total of 225 effective components of Guizhi decoction were screened,among which 127 components could bind to 160 common targets and play a therapeutic role.The common targets were mainly enriched in 2785 gene ontology entries and 189 Kyoto Encyclopedia of Genes and Genomes pathways.Molecular docking confirmed that core targets could spontaneously bind to key ingredients.Conclusion:The key targets for the treatment of plant nervous disorders by Guizhi decoction are MAPK1,TP53,RB1,STAT3,MAPK3,MAPK14,etc.,which reflect the characteristics of the synergistic mechanism of traditional Chinese medicine with multiple components,targets,and pathways through the regulation of inflammatory signal pathways and oxidative stress processes.

Identification of key genes underlying clinical features of hepatocellular carcinoma based on weighted gene co‑expression network analysis and bioinformatics analysis

Objective: To identify module genes that are closely related to clinical features of hepatocellular carcinoma (HCC) by weighted gene co‑expression network analysis, and to provide a reference for early clinical diagnosis and treatment. Methods: GSE84598 chip data were downloaded from the GEO database, and module genes closely related to the clinical features of HCC were extracted by comprehensive weighted gene co‑expression network analysis. Hub genes were identified through protein interaction network analysis by the maximum clique centrality (MCC) algorithm;Finally, the expression of hub genes was validated by TCGA database and the Kaplan Meier plotter online database was used to evaluate the prognostic relationship between hub genes and HCC patients. Results: By comparing the gene expression data between HCC tissue samples and normal liver tissue samples, a total of 6 262 differentially expressed genes were obtained, of which 2 207 were upregulated and 4 055 were downregulated. Weighted gene co‑expression network analysis was applied to identify 120 genes of key modules. By intersecting with the differentially expressed genes, 115 candidate hub genes were obtained. The results of enrichment analysis showed that the candidate hub genes were closely related to cell mitosis, p53 signaling pathway and so on. Further application of the MCC algorithm to the protein interaction network of 115 candidate hub genes identified five hub genes, namely NUF2, RRM2, UBE2C, CDC20 and MAD2L1. Validation of hub genes by TCGA database revealed that all five hub genes were significantly upregulated in HCC tissues compared to normal liver tissues;Moreover, survival analysis revealed that high expression of hub genes was closely associated with poor prognosis in HCC patients. Conclusions: This study identifies five hub genes by combining multiple databases, which may provide directions for the clinical diagnosis and treatment of HCC.

Identification of key genes regulating the synthesis of quercetin derivatives in Rosa roxburghii through integrated transcriptomics and metabolomics

Rosa roxburghii fruit is rich in flavonoids, but little is known about their biosynthetic pathways. In this study, we employed transcriptomics and metabolomics to study changes related to the flavonoids at five different stages of R. roxburghii fruit development. Flavonoids and the genes related to their biosynthesis were found to undergo significant changes in abundance across different developmental stages, and numerous quercetin derivatives were identified. We found three gene expression modules that were significantly associated with the abundances of the different flavonoids in R. roxburghii and identified three structural UDP-glycosyltransferase genes directly involved in the synthesis of quercetin derivatives within these modules. In addition, we found that RrBEH4, RrLBD1 and RrPIF8could significantly increase the expression of downstream quercetin derivative biosynthesis genes. Taken together,these results provide new insights into the metabolism of flavonoids and the accumulation of quercetin derivatives in R. roxburghii.

Physiological and transcriptome analyses of Chinese cabbage in response to drought stress

Chinese cabbage is an important leafy vegetable crop with high water demand and susceptibility to drought stress.To explore the molecular mechanisms underlying the response to drought,we performed a transcriptome analysis of drought-tolerant and-sensitive Chinese cabbage genotypes under drought stress,and uncovered core drought-responsive genes and key signaling pathways.A co-expression network was constructed by a weighted gene coexpression network analysis(WGCNA)and candidate hub genes involved in drought tolerance were identified.Furthermore,abscisic acid(ABA)biosynthesis and signaling pathways and their drought responses in Chinese cabbage leaves were systemically explored.We also found that drought treatment increased the antioxidant enzyme activities and glucosinolate contents significantly.These results substantially enhance our understanding of the molecular mechanisms underlying drought responses in Chinese cabbage.

Salivary metabolites are promising noninvasive biomarkers of druginduced liver injury

BACKGROUND Drug-induced liver injury(DILI)is one of the most common adverse events of medication use,and its incidence is increasing.However,early detection of DILI is a crucial challenge due to a lack of biomarkers and noninvasive tests.AIM To identify salivary metabolic biomarkers of DILI for the future development of noninvasive diagnostic tools.METHODS Saliva samples from 31 DILI patients and 35 healthy controls(HCs)were subjected to untargeted metabolomics using ultrahigh-pressure liquid chromatography coupled with tandem mass spectrometry.Subsequent analyses,including partial least squares-discriminant analysis modeling,t tests and weighted metabolite coexpression network analysis(WMCNA),were conducted to identify key differentially expressed metabolites(DEMs)and metabolite sets.Furthermore we utilized least absolute shrinkage and selection operato and random fores analyses for biomarker prediction.The use of each metabolite and metabolite set to detect DILI was evaluated with area under the receiver operating characteristic curves.RESULTS We found 247 differentially expressed salivary metabolites between the DILI group and the HC group.Using WMCNA,we identified a set of 8 DEMs closely related to liver injury for further prediction testing.Interestingly,the distinct separation of DILI patients and HCs was achieved with five metabolites,namely,12-hydroxydodecanoic acid,3-hydroxydecanoic acid,tetradecanedioic acid,hypoxanthine,and inosine(area under the curve:0.733-1).CONCLUSION Salivary metabolomics revealed previously unreported metabolic alterations and diagnostic biomarkers in the saliva of DILI patients.Our study may provide a potentially feasible and noninvasive diagnostic method for DILI,but further validation is needed.

Transglutaminase 2 serves as a pathogenic hub gene of KRAS mutant colon cancer based on integrated analysis

BACKGROUND Colon cancer is acknowledged as one of the most common malignancies worldwide,ranking third in United States regarding incidence and mortality.Notably,approximately 40%of colon cancer cases harbor oncogenic KRAS mutations,resulting in the continuous activation of epidermal growth factor receptor signaling.AIM To investigate the key pathogenic genes in KRAS mutant colon cancer holds considerable importance.METHODS Weighted gene co-expression network analysis,in combination with additional bioinformatics analysis,were conducted to screen the key factors driving the progression of KRAS mutant colon cancer.Meanwhile,various in vitro experiments were also conducted to explore the biological function of transglutaminase 2(TGM2).RESULTS Integrated analysis demonstrated that TGM2 acted as an independent prognostic factor for progression-free survival.Immunohistochemical analysis on tissue microarrays revealed that TGM2 was associated with an elevated probability of perineural invasion in patients with KRAS mutant colon cancer.Additionally,biological roles of the key gene TGM2 was also assessed,suggesting that the downregulation of TGM2 attenuated the proliferation,invasion,and migration of the KRAS mutant colon cancer cell line.CONCLUSION This study underscores the potential significance of TGM2 in the progression of KRAS mutant colon cancer.This insight not only offers a theoretical foundation for therapeutic approaches but also highlights the need for additional clinical trials and fundamental research to support our preliminary findings.

Identification of immune cell-related prognostic genes characterized by a distinct microenvironment in hepatocellular carcinoma

BACKGROUND The development and progression of hepatocellular carcinoma(HCC)have been reported to be associated with immune-related genes and the tumor microenvir-onment.Nevertheless,there are not enough prognostic biomarkers and models available for clinical use.Based on seven prognostic genes,this study calculated overall survival in patients with HCC using a prognostic survival model and revealed the immune status of the tumor microenvironment(TME).AIM To develop a novel immune cell-related prognostic model of HCC and depict the basic profile of the immune response in HCC.METHODS We obtained clinical information and gene expression data of HCC from The Cancer Genome Atlas(TCGA)and International Cancer Genome Consortium(ICGC)datasets.TCGA and ICGC datasets were used for screening prognostic genes along with developing and validating a seven-gene prognostic survival model by weighted gene coexpression network analysis and least absolute shrinkage and selection operator regression with Cox regression.The relative analysis of tumor mutation burden(TMB),TME cell infiltration,immune check-points,immune therapy,and functional pathways was also performed based on prognostic genes.RESULTS Seven prognostic genes were identified for signature construction.Survival receiver operating characteristic curve analysis showed the good performance of survival prediction.TMB could be regarded as an independent factor in HCC survival prediction.There was a significant difference in stromal score,immune score,and estimate score between the high-risk and low-risk groups stratified based on the risk score derived from the seven-gene prognostic model.Several immune checkpoints,including VTCN1 and TNFSF9,were found to be associated with the seven prognostic genes and risk score.Different combinations of checkpoint blockade targeting inhibitory CTLA4 and PD1 receptors and potential chemotherapy drugs hold great promise for specific HCC therapies.Potential pathways,such as cell cycle regulation and metabolism of some amino acids,were also identified and analyzed.CONCLUSION The novel seven-gene(CYTH3,ENG,HTRA3,PDZD4,SAMD14,PGF,and PLN)prognostic model showed high predictive efficiency.The TMB analysis based on the seven genes could depict the basic profile of the immune response in HCC,which might be worthy of clinical application.

Identification of the key genes and mechanisms associated with transcatheter arterial chemoembolisation refractoriness in hepatocellular carcinoma

BACKGROUND Transcatheter arterial embolisation(TACE)is the primary treatment for intermediate-stage hepatocellular carcinoma(HCC)patients while some HCC cases have shown resistance to TACE.AIM To investigate the key genes and potential mechanisms correlated with TACE refractoriness in HCC.METHODS The microarray datasets of TACE-treated HCC tissues,HCC and non-HCC tissues were collected by searching multiple public databases.The respective differentially expressed genes(DEGs)were attained via limma R package.Weighted gene co-expression network analysis was employed for identifying the significant modules related to TACE non-response.TACE refractoriness-related genes were obtained by intersecting up-regulated TACE-associated and HCC-associated DEGs together with the genes in significant modules related to TACE nonresponse.The key genes expression in the above two pairs of samples was compared respectively via Wilcoxon tests and standard mean differences model.The prognostic value of the key genes was evaluated by Kaplan-Meier curve.Multivariate analysis was utilised to investigate the independent prognostic factor in key genes.Single-cell RNA(scRNA)sequencing analysis was conducted to explore the cell types in HCC.TACE refractoriness-related genes activity was calculated via AUCell packages.The CellChat R package was used for the investigation of the cell–cell communication between the identified cell types.RESULTS HCC tissues of TACE non-responders(n=66)and TACE responders(n=81),HCC(n=3941)and non-HCC(n=3443)tissues were obtained.The five key genes,DLG associated protein 5(DLGAP5),Kinesin family member 20A(KIF20A),Assembly factor for spindle microtubules(ASPM),Kinesin family member 11(KIF11)and TPX2 microtubule nucleation factor(TPX2)in TACE refractoriness-related genes,were identified.The five key genes were all up-regulated in the TACE non-responders group and the HCC group.High expression of the five key genes predicted poor prognosis in HCC.Among the key genes,TPX2 was an independent prognostic factor.Four cell types,hepatocytes,embryonic stem cells,T cells and B cells,were identified in the HCC tissues.The TACE refractoriness-related genes expressed primarily in hepatocytes and embryonic stem cells.Hepatocytes,as the providers of ligands,had the strongest interaction with embryonic stem cells that provided receptors.CONCLUSION Five key genes(DLGAP5,KIF20A,ASPM,KIF11 and TPX2)were identified as promoting refractory TACE.Hepatocytes and embryonic stem cells were likely to boost TACE refractoriness.

Generalized chaos synchronization of a weighted complex network with different nodes

This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, RSssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.

Identification of key genes involved in axon regeneration and Wallerian degeneration by weighted gene co-expression network analysis

Peripheral nerve injury repair requires a certain degree of cooperation between axon regeneration and Wallerian degeneration.Therefore,investigating how axon regeneration and degeneration work together to repair peripheral nerve injury may uncover the molecular mechanisms and signal cascades underlying peripheral nerve repair and provide potential strategies for improving the low axon regeneration capacity of the central nervous system.In this study,we applied weighted gene co-expression network analysis to identify differentially expressed genes in proximal and distal sciatic nerve segments from rats with sciatic nerve injury.We identified 31 and 15 co-expression modules from the proximal and distal sciatic nerve segments,respectively.Functional enrichment analysis revealed that the differentially expressed genes in proximal modules promoted regeneration,while the differentially expressed genes in distal modules promoted neurodegeneration.Next,we constructed hub gene networks for selected modules and identified a key hub gene,Kif22,which was up-regulated in both nerve segments.In vitro experiments confirmed that Kif22 knockdown inhibited proliferation and migration of Schwann cells by modulating the activity of the extracellular signal-regulated kinase signaling pathway.Collectively,our findings provide a comparative framework of gene modules that are co-expressed in injured proximal and distal sciatic nerve segments,and identify Kif22 as a potential therapeutic target for promoting peripheral nerve injury repair via Schwann cell proliferation and migration.All animal experiments were approved by the Institutional Animal Ethics Committee of Nantong University,China(approval No.S20210322-008)on March 22,2021.