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.

Modeling Topology and Nonlinear Dynamical Behavior of the Weighted Scale-Free Networks

An improved weighted scale-free network, which has two evolution mechanisms： topological growth and strength dynamics, has been introduced. The topology structure of the model will be explored in details in this work. The evolution driven mechanism of Olami-Feder Christensen （OFC） model is added to our model to study the self-organlzed criticality and the dynamical behavior. We also.consider attack mechanism and the study of the model with attack is also investigated in this paper. We tlnd there are differences between the model with attack and without attack.

Relaxation Dynamics in Condensation on Weighted Scale-Free Networks

Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E 74 （2006） 036101] and here we focus on its evolutionary process of phase transition. In order to show how the weighted transport influences the dynamical properties, we study the relaxation dynamics in a zero range process on weighted scale-free networks. We find that there is a hierarchical relaxation dynamics in the evolution and there is a scaling relation between the relaxation time and the jumping exponent. The relaxation dynamics can be illustrated by a mean-field equation. The theoretical predictions are confirmed by our numerical simulations.

Improving consensual performance of multi-agent systems in weighted scale-free networks

This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is deter：mined by the relative degree of the involved nodes. It shows that the asymmetry of interactions has a great effect on the consensus. Especially, when the interactions are dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.

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).

Structural Characteristics and Evolution of a Weighted Sino-US Container Shipping Network

This study selected the Sino-US route data from the top 30 global container liner companies between December 1,2019,and December 29,2019,as the data source utilizing the complex network research methodology.It constructs a Sino-US container shipping network through voyage weighting and analyzes the essential structural characteristics to explore the network’s complex structural fea-tures.The network’s evolution is examined from three perspectives,namely,time,space,and event influence,aiming to comprehens-ively explore the network’s evolution mechanism.The results revealed that:1)the weighted Sino-US container shipping network exhib-its small-world and scale-free properties.Key hub ports in the United States include NEW YORK NY,SAVANNAH GA,LOS ANGELES CA,and OAKLAND CA,whereas SHANGHAI serving as the hub port in China.The geographical distribution of these hub ports is uneven.2)Concerning the evolution of the weighted Sino-US container shipping network,from a temporal perspective,the evolution of the regional structure of the entire Sino-US region and the Inland United States is in a stage of radiative expansion and de-velopment,with a need for further enhancement in competitiveness and development speed.The evolution of the regional structure of southern China and Europe is transitioning from the stage of radiative expansion and development to an advanced equilibrium stage.The shipping development in Northern China,the Western and Eastern United States,and Asia is undergoing significant changes but faces challenges of fierce competition and imbalances.From a spatial perspective,the rationality and effectiveness of the improved weighted Barrat-Barthelemy-Vespignani(BBV)model are confirmed through theoretical derivation.The applicability of the improved evolution model is verified by simulating the evolution of the weighted Sino-US container shipping network.From an event impact per-spective,the Corona Virus Disease 2019(COVID-19)pandemic has not fundamentally affected the spatial pattern of the weighted Sino-US container shipping network but has significantly impacted the network’s connectivity.The network lacks sufficient resilience and stability in emergency situations.3)Based on the analysis of the structural characteristics and evolution of the weighted Sino-US con-tainer shipping network,recommendations for network development are proposed from three aspects:emphasizing the development of hub ports,focusing on the balanced development of the network,and optimizing the layout of Chinese ports.

Exploration of the efficacy and mechanism of treating head wind disease with the combination change of ginger volatile oil and gingerol by using content-weighted network pharmacology technology

Background:Exploring the efficacy,potential components,and mechanism of the combination of ginger essential oil and gingerols in the treatment of head wind disease based on network pharmacology technology with content weight.Methods:The experimental groups were divided into:0:10,1:4,1:2,1:1,2:1,4:1,10:0.The relative content(Ri)of the chemical constituents of ginger's volatile oil was determined using gas chromatography-mass spectrometry(GC-MS).Additionally,the physicochemical and biological property parameters(LogP,MDCK,PPB,MW)of the components were considered.To assess the quantitative effect of the components,a grading score was performed,and the quantitative effect index(Ki)was calculated.Subsequently,the target effect index(Ti)was calculated by combining the component-target matching score(Fit score).Using these calculations,the target effect score A was determined under the influence of multiple components targeting different targets.Key targets with A≥1000 were identified.To predict the targets related to head wind disease,the Comparative Toxicogenomics Database(https://ctdbase.org/),Gene Cards(https://www.genecards.org/),and Disgenet database(https://www.disgenet.org/)were utilized.The key targets,obtained from different proportions of ginger's volatile oil and gingerol,were intersected with the predicted targets.This facilitated network pharmacological analysis and verification of the efficacy.Results:The content of volatile oil in ginger demonstrated an impact on key targets associated with the volatile oil group.Each specific combination of volatile oil consistently activated distinct pathways,with variations stemming from changes in content.Experimental testing revealed that different combinations of ginger's volatile oil and gingerol effectively alleviated migraine symptoms in rats.Conclusion:Through the application of content-weighted network pharmacology technology and pharmacodynamic verification,it was determined that altering the ratio between ginger's volatile oil and gingerol leads to variations in potential targets and pathways,consequently impacting its efficacy.

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.

Research on Node Classification Based on Joint Weighted Node Vectors

Node of network has lots of information, such as topology, text and label information. Therefore, node classification is an open issue. Recently, one vector of node is directly connected at the end of another vector. However, this method actually obtains the performance by extending dimensions and considering that the text and structural information are one-to-one, which is obviously unreasonable. Regarding this issue, a method by weighting vectors is proposed in this paper. Three methods, negative logarithm, modulus and sigmoid function are used to weight-trained vectors, then recombine the weighted vectors and put them into the SVM classifier for evaluation output. By comparing three different weighting methods, the results showed that using negative logarithm weighting achieved better results than the other two using modulus and sigmoid function weighting, and was superior to directly concatenating vectors in the same dimension.

Role-Based Network Embedding via Quantum Walk with Weighted Features Fusion

Role-based network embedding aims to embed role-similar nodes into a similar embedding space,which is widely used in graph mining tasks such as role classification and detection.Roles are sets of nodes in graph networks with similar structural patterns and functions.However,the rolesimilar nodes may be far away or even disconnected from each other.Meanwhile,the neighborhood node features and noise also affect the result of the role-based network embedding,which are also challenges of current network embedding work.In this paper,we propose a Role-based network Embedding via Quantum walk with weighted Features fusion(REQF),which simultaneously considers the influence of global and local role information,node features,and noise.Firstly,we capture the global role information of nodes via quantum walk based on its superposition property which emphasizes the local role information via biased quantum walk.Secondly,we utilize the quantum walkweighted characteristic function to extract and fuse features of nodes and their neighborhood by different distributions which contain role information implicitly.Finally,we leverage the Variational Auto-Encoder(VAE)to reduce the effect of noise.We conduct extensive experiments on seven real-world datasets,and the results show that REQF is more effective at capturing role information in the network,which outperforms the best baseline by up to 14.6% in role classification,and 23% in role detection on average.

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.

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.

Immunization for scale-free networks by random walker

Based on the random walk and the intentional random walk, we propose two types of immunization strategies which require only local connectivity information. On several typical scale-free networks, we demonstrate that these strategies can lead to the eradication of the epidemic by immunizing a small fraction of the nodes in the networks. Particularly, the immunization strategy based on the intentional random walk is extremely efficient for the assortatively mixed networks.

Weighted average consensus problem in networks of agents with diverse time-delays

This paper studies the weighted average consensus problem for networks of agents with fixed directed asymmetric unbalance information exchange topology. We suppose that the classical distributed consensus protocol is destroyed by diverse time-delays which include communication time-delay and self time-delay. Based on the generalized Nyquist stability criterion and the Gerschgorin disk theorem, some sufficient conditions for the consensus of multi-agent systems are obtained. And we give the expression of the weighted average consensus value for our consensus protocol. Finally, numerical examples are presented to illustrate the theoretical results.

Weighted Evolving Networks with Self-organized Communities

In order to describe the self-organization of communities in the evolution of weighted networks, we propose a new evolving model for weighted community-structured networks with the preferential mechanisms functioned in different levels according to community sizes and node strengths, respectively. Theoretical analyses and numerical simulations show that our model captures power-law distributions of community sizes, node strengths, and link weights, with tunable exponents of v ≥ 1, γ 〉 2, and α 〉 2, respectively, sharing large clustering coefficients and scaling clustering spectra, and covering the range from disassortative networks to assortative networks. Finally, we apply our new model to the scientific co-authorship networks with both their weighted and unweighted datasets to verify its effectiveness.

Comparison of Artificial Neural Networks,Geographically Weighted Regression and Cokriging Methods for Predicting the Spatial Distribution of Soil Macronutrients(N,P,and K)

Soil macronutrients(i.e. nitrogen(N), phosphorus(P), and potassium(K)) are important soils components and knowing the spatial distribution of these parameters are necessary at precision agriculture. The purpose of this study was to evaluate the feasibility of different methods such as artificial neural networks(ANN) and two geostatistical methods(geographically weighted regression(GWR) and cokriging(CK)) to estimate N, P and K contents. For this purpose, soil samples were taken from topsoil(0–30 cm) at 106 points and analyzed for their chemical and physical parameters. These data were divided into calibration(n = 84) and validation(n = 22). Chemical and physical variables including clay, p H and organic carbon(OC) were used as auxiliary soil variables to estimate the N, P and K contents. Results showed that the ANN model(with coefficient of determination R^2 = 0.922 and root mean square error RMSE = 0.0079%) was more accurate compared to the CK model(with R^2 = 0.612 and RMSE = 0.0094%), and the GWR model(with R^2 = 0.872 and RMSE = 0.0089%) to estimate the N variable. The ANN model estimated the P with the RMSE of 3.630 ppm, which was respectively 28.93% and 20.00% less than the RMSE of 4.680 ppm and 4.357 ppm from the CK and GWR models. The estimated K by CK, GWR and ANN models have the RMSE of 76.794 ppm, 75.790 ppm and 52.484 ppm. Results indicated that the performance of the CK model for estimation of macro nutrients(N, P and K) was slightly lower than the GWR model. Also, the accuracy of the ANN model was higher than CK and GWR models, which proved to be more effective and reliable methods for estimating macro nutrients.

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.

Distributed event region fault-tolerance based on weighted distance for wireless sensor networks

Event region detection is the important application for wireless sensor networks（WSNs）, where the existing faulty sensors would lead to drastic deterioration of network quality of service.Considering single-moment nodes fault-tolerance, a novel distributed fault-tolerant detection algorithm named distributed fault-tolerance based on weighted distance（DFWD） is proposed, which exploits the spatial correlation among sensor nodes and their redundant information.In sensor networks, neighborhood sensor nodes will be endowed with different relative weights respectively according to the distances between them and the central node.Having syncretized the weighted information of dual-neighborhood nodes appropriately, it is reasonable to decide the ultimate status of the central sensor node.Simultaneously, readings of faulty sensors would be corrected during this process.Simulation results demonstrate that the DFWD has a higher fault detection accuracy compared with other algorithms, and when the sensor fault probability is 10%, the DFWD can still correct more than 91% faulty sensor nodes, which significantly improves the performance of the whole sensor network.

Epidemic spreading in scale-free networks including the effect of individual vigilance

In this paper, we study the epidemic spreading in scale-flee networks and propose a new susceptible-infected- recovered （SIR） model that includes the effect of individual vigilance. In our model, the effective spreading rate is dynamically adjusted with the time evolution at the vigilance period. Using the mean-field theory, an analytical result is derived. It shows that individual vigilance has no effect on the epidemic threshold. The numerical simulations agree well with the analytical result. Purthermore, we investigate the effect of individual vigilance on the epidemic spreading speed. It is shown that individual vigilance can slow the epidemic spreading speed effectively and delay the arrival of peak epidemic infection.

Cascading failure in the wireless sensor scale-free networks

In the practical wireless sensor networks （WSNs）, the cascading failure caused by a failure node has serious impact on the network performance. In this paper, we deeply research the cascading failure of scale-free topology in WSNs. Firstly, a cascading failure model for scale-free topology in WSNs is studied. Through analyzing the influence of the node load on cascading failure, the critical load triggering large-scale cascading failure is obtained. Then based on the critical load, a control method for cascading failure is presented. In addition, the simulation experiments are performed to validate the effectiveness of the control method. The results show that the control method can effectively prevent cascading failure.