Interconnection of all things challenges the traditional communication methods,and Semantic Communication and Computing(SCC)will become new solutions.It is a challenging task to accurately detect,extract,and represent...Interconnection of all things challenges the traditional communication methods,and Semantic Communication and Computing(SCC)will become new solutions.It is a challenging task to accurately detect,extract,and represent semantic information in the research of SCC-based networks.In previous research,researchers usually use convolution to extract the feature information of a graph and perform the corresponding task of node classification.However,the content of semantic information is quite complex.Although graph convolutional neural networks provide an effective solution for node classification tasks,due to their limitations in representing multiple relational patterns and not recognizing and analyzing higher-order local structures,the extracted feature information is subject to varying degrees of loss.Therefore,this paper extends from a single-layer topology network to a multi-layer heterogeneous topology network.The Bidirectional Encoder Representations from Transformers(BERT)training word vector is introduced to extract the semantic features in the network,and the existing graph neural network is improved by combining the higher-order local feature module of the network model representation network.A multi-layer network embedding algorithm on SCC-based networks with motifs is proposed to complete the task of end-to-end node classification.We verify the effectiveness of the algorithm on a real multi-layer heterogeneous network.展开更多
This paper studies the target controllability of multilayer complex networked systems,in which the nodes are highdimensional linear time invariant(LTI)dynamical systems,and the network topology is directed and weighte...This paper studies the target controllability of multilayer complex networked systems,in which the nodes are highdimensional linear time invariant(LTI)dynamical systems,and the network topology is directed and weighted.The influence of inter-layer couplings on the target controllability of multi-layer networks is discussed.It is found that even if there exists a layer which is not target controllable,the entire multi-layer network can still be target controllable due to the inter-layer couplings.For the multi-layer networks with general structure,a necessary and sufficient condition for target controllability is given by establishing the relationship between uncontrollable subspace and output matrix.By the derived condition,it can be found that the system may be target controllable even if it is not state controllable.On this basis,two corollaries are derived,which clarify the relationship between target controllability,state controllability and output controllability.For the multi-layer networks where the inter-layer couplings are directed chains and directed stars,sufficient conditions for target controllability of networked systems are given,respectively.These conditions are easier to verify than the classic criterion.展开更多
In last decade,due to that the popularity of the internet, data-central traffic kept growing,some emerging networking requirements have been posed on the todays telecommunication networks,especially in the area of n...In last decade,due to that the popularity of the internet, data-central traffic kept growing,some emerging networking requirements have been posed on the todays telecommunication networks,especially in the area of network survivability.Obviously,as a key networking problem,network reliability will be more and more important.The integration of different technologies such as ATM,SDH,and WDM in multilayer transport networks raises many questions regarding the coordination of the individual network layers.This problem is referred as multilayer network survivability.The integrated multilayer network survivability is investingated as well as the representation of an interworking strategy between different single layer survivability schemes in IP via generalized multi-protocol label switching over optical network.展开更多
With the continuous development of mobile communications and Internet technologies,the marketing model of the communications industry has shifted from calling-based to social APP-based personalized recommendations.In ...With the continuous development of mobile communications and Internet technologies,the marketing model of the communications industry has shifted from calling-based to social APP-based personalized recommendations.In order to improve the accuracy of recommendation,this paper proposes a recommendation algorithm for social analysis.Empirical data was firstly used to construct a“user-APP”two-layer communication network model,and then the traditional collaborative filtering recommendation technology was integrated to reconstruct similar users and similar APP network model.The bipartite graph weight distribution method was taken to recommend targets in the obtained network model.The experimental simulation shows that,in view of the characteristics of the twolayer communication network,compared with the traditional recommendation algorithm,the algorithm effectively improves the accuracy of the score prediction.展开更多
Intraocular pressure(IOP)is a key parameter to diagnose glaucoma disease and assess the treatment effect of cornea after refractive surgery.Current refractive surgeries inevitably change the configuration of the corne...Intraocular pressure(IOP)is a key parameter to diagnose glaucoma disease and assess the treatment effect of cornea after refractive surgery.Current refractive surgeries inevitably change the configuration of the cornea,making it difficult to measure IOP accurately using conventional methods.The prediction method proposed in this article can accurately measure the IOP after refractive surgery.In this study,firstly,the finite element models of cornea free of IOP depicted by various vertex height,thickness,and radius are established,and the deformation of the cornea under different IOP is predicted.Based on the dataset obtained from the numerical simulations and the multi-layer perceptron neural network algorithm,two prediction models for the vertex height and thickness of the cornea free of IOP and for the configuration under IOP are developed,and a prediction method for IOP is then proposed by combining the two models.Following the similar way,two prediction models respectively for the parameters of the presumptive initial configuration of the cornea to undergo refractive surgery and for those of the cornea after surgery are constructed,and a prediction method for IOP of cornea after the surgery is presented.The validity of the prediction methods for regular IOP and that after refractive surgery is demonstrated using the clinical data from some volunteers.The proposed methods provide an efficient prediction method for regular IOP and that after refractive surgery.展开更多
The key parameters that characterize the morphological quality of multi-layer and multi-pass metal laser deposited parts are the surface roughness and the error between the actual printing height and the theoretical m...The key parameters that characterize the morphological quality of multi-layer and multi-pass metal laser deposited parts are the surface roughness and the error between the actual printing height and the theoretical model height.The Taguchi method was employed to establish the correlations between process parameter combinations and multi-objective characterization of metal deposition morphology(height error and roughness).Results show that using the signal-to-noise ratio and grey relational analysis,the optimal parameter combination for multi-layer and multi-pass deposition is determined as follows:laser power of 800 W,powder feeding rate of 0.3 r/min,step distance of 1.6 mm,and scanning speed of 20 mm/s.Subsequently,a Genetic Bayesian-back propagation(GB-BP)network is constructed to predict multi-objective responses.Compared with the traditional back propagation network,the GB-back propagation network improves the prediction accuracy of height error and surface roughness by 43.14%and 71.43%,respectively.This network can accurately predict the multi-objective characterization of morphological quality of multi-layer and multi-pass metal deposited parts.展开更多
High-entropy oxides(HEOs)exhibit great potential as supercapacitor electrode materials,but their practical application is hindered by inherent challenges such as structural instability,insufficient conductivity,and di...High-entropy oxides(HEOs)exhibit great potential as supercapacitor electrode materials,but their practical application is hindered by inherent challenges such as structural instability,insufficient conductivity,and difficulties in regulating oxygen vacancies.To overcome these limitations,we present a dual-defect engineering strategy:tailoring the elemental composition of FeZnCuCoNi-based HEOs to generate abundant oxygen vacancies,and constructing a hierarchical,3D multi-shell porous network structure via an in situ template method.Density functional theory calculations reveal that high-entropy lattice distortion significantly enhances oxygen vacancy concentration while reducing charge transfer barriers.Additionally,the multi-layered eggshell morphology creates interconnected ion diffusion pathways,shortens ion transport distances,and reinforces mechanical integrity.The optimized HEO electrode demonstrates remarkable electrochemical performance,achieving a specific capacitance of 641 F g⁻¹at 1 A g⁻¹,with a 92% electric double-layer contribution at 50 mV s⁻¹.The assembled asymmetric supercapacitor delivers an energy density of 36.7 Wh kg⁻¹ at a power density of 800 W kg⁻¹,while maintaining 92% of its initial capacity after 10000 charge-discharge cycles.Mechanistic studies indicate that oxygen vacancies optimize hydroxyl adsorption kinetics,facilitating surface charge transfer,while the hierarchical porous structure effectively mitigates volumetric expansion stress via a 3D ion transport network.This work offers a strategic framework for designing next-generation high-entropy energy storage materials by providing a synergy between atomic-scale electronic tuning and mesoscale structural design.展开更多
Heat conduction in multi-layered geomaterials was a pervasive phenomenon in various engineering applications,such as nuclear waste repositories,energy piles,and abandoned oil wells.The incomplete contact between adjac...Heat conduction in multi-layered geomaterials was a pervasive phenomenon in various engineering applications,such as nuclear waste repositories,energy piles,and abandoned oil wells.The incomplete contact between adjacent geomaterials will impede the heat transfer at interfaces,known as the interfacial thermal resistance effect.In this regard,a two-dimensional axisymmetric mathematical model for transient heat conduction in multi-layered geomaterials with interfacial thermal resistance was established.Employing Green's function formalism,the thermal transport system was mathematically resolved through a closed-form analytical solution that provides continuum-level characterization of thermal evolution across all spatial-temporal coordinates.A numerical model for threelayered geomaterials and a benchmark test for double-layered geomaterials were constructed to verify the analytical solution.Finally,the solution was applied to simulate the temperature evolutions in a nuclear waste repository with three-and four-layered barrier systems with interfacial thermal resistance.The results indicated that the existence of interfacial thermal resistance caused heat accumulation at interfaces,thereby resulting in an increase in overall temperature within the repository.Moreover,the temperature rises in the bentonite block layer and bentonite granule layer were obviously greater than that in the surrounding rock.Due to the interfacial thermal resistance effect,a notable temperature difference was observed at the interfaces.Specifically,for every increment of 0.03(K m2)/W in interfacial thermal resistance,the temperature difference increased by 1.5℃.A comparative analysis of temperature fieldsin repositories with three-and four-layered barrier systems revealed that the gap between the canister and bentonite block significantlyaffects the peak temperature in the buffer layer.展开更多
Crossflow vortices induced transition is one of the most important instability types in supersonic aircraft boundary layers.While the traditional linear stability theory(LST)-based eN method demonstrates satisfactory ...Crossflow vortices induced transition is one of the most important instability types in supersonic aircraft boundary layers.While the traditional linear stability theory(LST)-based eN method demonstrates satisfactory predictive capabilities for this kind of transition,its practical implementation faces inherent limitations:the requirement of first-and second-order wallnormal derivatives of boundary layer velocityemperature profiles,the need for initial eigenvalue guesses,and the computational burden of solving eigenvalue problems.To address these challenges,this study develops a multi-layer perceptron(MLP)model tailored for linear stability analysis of three-dimensional compressible boundary layers based on the artificially defined quasi-three-dimensional non-similar boundary layer solutions.The boundary layer edge flow parameters and perturbation characteristics are mapped to eigenvalues or local growth rates of the envelop curves through fully connected layers.This architecture eliminates the need for computing wall-normal derivatives of velocityemperature profiles,initial eigenvalue estimation,and direct eigenvalue problem solving.Extensive validation across varying operational conditions and geometries(airfoils and swept wings)demonstrates exceptional agreement between the MLP’s predictions(eigenvalues and disturbance amplification factors)and traditional LST results.Furthermore,the model’s transition prediction capability is rigorously verified using National Aeronautics and Space Administration’s supersonic swept-wing crossflow-dominated transition benchmark,incorporating both stability analysis and flight test data.Results confirm the model is an efficient and reliable computational framework for transition prediction in three-dimensional finite-span wings.展开更多
The growing incidence of cyberattacks necessitates a robust and effective Intrusion Detection Systems(IDS)for enhanced network security.While conventional IDSs can be unsuitable for detecting different and emerging at...The growing incidence of cyberattacks necessitates a robust and effective Intrusion Detection Systems(IDS)for enhanced network security.While conventional IDSs can be unsuitable for detecting different and emerging attacks,there is a demand for better techniques to improve detection reliability.This study introduces a new method,the Deep Adaptive Multi-Layer Attention Network(DAMLAN),to boost the result of intrusion detection on network data.Due to its multi-scale attention mechanisms and graph features,DAMLAN aims to address both known and unknown intrusions.The real-world NSL-KDD dataset,a popular choice among IDS researchers,is used to assess the proposed model.There are 67,343 normal samples and 58,630 intrusion attacks in the training set,12,833 normal samples,and 9711 intrusion attacks in the test set.Thus,the proposed DAMLAN method is more effective than the standard models due to the consideration of patterns by the attention layers.The experimental performance of the proposed model demonstrates that it achieves 99.26%training accuracy and 90.68%testing accuracy,with precision reaching 98.54%on the training set and 96.64%on the testing set.The recall and F1 scores again support the model with training set values of 99.90%and 99.21%and testing set values of 86.65%and 91.37%.These results provide a strong basis for the claims made regarding the model’s potential to identify intrusion attacks and affirm its relatively strong overall performance,irrespective of type.Future work would employ more attempts to extend the scalability and applicability of DAMLAN for real-time use in intrusion detection systems.展开更多
The plastic strain accumulation results of the multi-layered wrapped pressure vessel liner during long-term service are an important basis for its safety performance evaluation.However,the complex welds distributed on...The plastic strain accumulation results of the multi-layered wrapped pressure vessel liner during long-term service are an important basis for its safety performance evaluation.However,the complex welds distributed on the liner bring challenges to the calculation of plastic cumulative strain.To this end,a novel hybrid deep learning framework is proposed for the efficient and precise prediction of ratcheting behavior in the liner welds of multilayered pressure vessels.By employing a BiLSTM network to extract bidirectional temporal dependencies from the strain history and incorporating a Multi-Head Attention(MHA)mechanism for adaptive feature weighting,the proposed method effectively addresses the difficulty of modeling cumulative effects in long-sequence ratcheting data.Firstly,asymmetric cyclic loading experiments were conducted on various welded joints and base metals to reveal the evolutionary laws of ratcheting behavior and construct a training dataset.The results show that the ratcheting strain evolution of different structural specimens shows the typical‘two-stage’characteristics,and the ratcheting strain accumulation on the base metal is significantly higher than that of the weld structure specimen.The proposed deep learning model can not only accurately capture the‘two-stage’evolution of ratcheting strain,but also directly use the base metal data to accurately predict the ratcheting strain accumulation in different weld parts,avoiding the complex parameter calibration process of the traditional constitutive model.It provides technical support for the integrity assessment and online monitoring of the complex weld structure of multi-layered pressure vessels.展开更多
Low Earth Orbit(LEO)mega-constellation networks,exemplified by Starlink,are poised to play a pivotal role in future mobile communication networks,due to their low latency and high capacity.With the massively deployed ...Low Earth Orbit(LEO)mega-constellation networks,exemplified by Starlink,are poised to play a pivotal role in future mobile communication networks,due to their low latency and high capacity.With the massively deployed satellites,ground users now can be covered by multiple visible satellites,but also face complex handover issues with such massive high-mobility satellites in multi-layer.The end-to-end routing is also affected by the handover behavior.In this paper,we propose an intelligent handover strategy dedicated to multi-layer LEO mega-constellation networks.Firstly,an analytic model is utilized to rapidly estimate the end-to-end propagation latency as a key handover factor to construct a multi-objective optimization model.Subsequently,an intelligent handover strategy is proposed by employing the Dueling Double Deep Q Network(D3QN)-based deep reinforcement learning algorithm for single-layer constellations.Moreover,an optimal crosslayer handover scheme is proposed by predicting the latency-jitter and minimizing the cross-layer overhead.Simulation results demonstrate the superior performance of the proposed method in the multi-layer LEO mega-constellation,showcasing reductions of up to 8.2%and 59.5%in end-to-end latency and jitter respectively,when compared to the existing handover strategies.展开更多
Physics-informed neural networks(PINNs)have prevailed as differentiable simulators to investigate flow in porous media.Despite recent progress PINNs have achieved,practical geotechnical scenarios cannot be readily sim...Physics-informed neural networks(PINNs)have prevailed as differentiable simulators to investigate flow in porous media.Despite recent progress PINNs have achieved,practical geotechnical scenarios cannot be readily simulated because conventional PINNs fail in discontinuous heterogeneous porous media or multi-layer strata when labeled data are missing.This work aims to develop a universal network structure to encode the mass continuity equation and Darcy’s law without labeled data.The finite element approximation,which can decompose a complex heterogeneous domain into simpler ones,is adopted to build the differentiable network.Without conventional DNNs,physics-encoded finite element network(PEFEN)can avoid spectral bias and learn high-frequency functions with sharp/steep gradients.PEFEN rigorously encodes Dirichlet and Neumann boundary conditions without training.Benefiting from its discretized formulation,the discontinuous heterogeneous hydraulic conductivity is readily embedded into the network.Three typical cases are reproduced to corroborate PEFEN’s superior performance over conventional PINNs and the PINN with mixed formulation.PEFEN is sparse and demonstrated to be capable of dealing with heterogeneity with much fewer training iterations(less than 1/30)than the improved PINN with mixed formulation.Thus,PEFEN saves energy and contributes to low-carbon AI for science.The last two cases focus on common geotechnical settings of impermeable sheet pile in singlelayer and multi-layer strata.PEFEN solves these cases with high accuracy,circumventing costly labeled data,extra computational burden,and additional treatment.Thus,this study warrants the further development and application of PEFEN as a novel differentiable network in porous flow of practical geotechnical engineering.展开更多
Accurate prediction of stress evolution induced by production pressure depletion after hydraulic fracturing is essential for efficient development of stacked continental shale reservoirs.This study establishes a three...Accurate prediction of stress evolution induced by production pressure depletion after hydraulic fracturing is essential for efficient development of stacked continental shale reservoirs.This study establishes a three-dimensional stress sensitivity and flow coupling framework to characterize intra-layer and interlayer stress evolution during shale oil development.A 3D discrete fracture network(DFN)integrating hydraulic and natural fractures was reconstructed from microseismic data obtained during multi-layer fracturing.Based on this,a stress sensitivity model for interbedded sandstone-shale reservoirs and a V-shaped well layout flow model was developed to simulate single-layer(three-well)and three-layer(nine-well)production scenarios.The reconstructed fracture network revealed that hydraulic fractures propagate laterally away from the zipper fracturing side and vertically upward toward low-pressure zones.During multi-layer development on Platform H,fracture intersections between the middle and adjacent layers produced 0-3 MPa pore pressure interference under different production schedules,indicating the need for optimized inter-well and interlayer spacing.Sandstone layers,characterized by higher permeability and porosity,exhibited a greater increase in horizontal stress difference(2.61 MPa)than shale layers(<0.5 MPa).Stress reorientation angles ranged from 5°to 38°in shale and from 16°to 64°in sandstone layers.These results demonstrate that well spacing should be larger in sandstone layers,whereas infill drilling is more suitable within shale intervals.The proposed modeling and analysis approach provides a theoretical and technical basis for optimizing well pattern deployment and maximizing energy utilization in shale oil reservoir development.展开更多
6G is desired to support more intelligence networks and this trend attaches importance to the self-healing capability if degradation emerges in the cellular networks.As a primary component of selfhealing networks,faul...6G is desired to support more intelligence networks and this trend attaches importance to the self-healing capability if degradation emerges in the cellular networks.As a primary component of selfhealing networks,fault detection is investigated in this paper.Considering the fast response and low timeand-computational consumption,it is the first time that the Online Broad Learning System(OBLS)is applied to identify outages in cellular networks.In addition,the Automatic-constructed Online Broad Learning System(AOBLS)is put forward to rationalize its structure and consequently avoid over-fitting and under-fitting.Furthermore,a multi-layer classification structure is proposed to further improve the classification performance.To face the challenges caused by imbalanced data in fault detection problems,a novel weighting strategy is derived to achieve the Multilayer Automatic-constructed Weighted Online Broad Learning System(MAWOBLS)and ensemble learning with retrained Support Vector Machine(SVM),denoted as EMAWOBLS,for superior treatment with this imbalance issue.Simulation results show that the proposed algorithm has excellent performance in detecting faults with satisfactory time usage.展开更多
Network models adeptly capture heterogeneities in individual interactions,making them well-suited for describing a wide range of real-world and virtual connections,including information diffusion,behavioural tendencie...Network models adeptly capture heterogeneities in individual interactions,making them well-suited for describing a wide range of real-world and virtual connections,including information diffusion,behavioural tendencies,and disease dynamic fluctuations.However,there is a notable methodological gap in existing studies examining the interplay between physical and virtual interactions and the impact of information dissemination and behavioural responses on disease propagation.We constructed a three-layer(information,cognition,and epidemic)network model to investigate the adoption of protective behaviours,such as wearing masks or practising social distancing,influenced by the diffusion and correction of misinformation.We examined five key events influencing the rate of information spread:(i)rumour transmission,(ii)information suppression,(iii)renewed interest in spreading misinformation,(iv)correction of misinformation,and(v)relapse to a stifler state after correction.We found that adopting information-based protection behaviours is more effective in mitigating disease spread than protection adoption induced by neighbourhood interactions.Specifically,our results show that warning and educating individuals to counter misinformation within the information network is a more effective strategy for curbing disease spread than suspending gossip spreaders from the network.Our study has practical implications for developing strategies to mitigate the impact of misinformation and enhance protective behavioural responses during disease outbreaks.展开更多
The rapid growth of Internet of things devices and the emergence of rapidly evolving network threats have made traditional security assessment methods inadequate.Federated learning offers a promising solution to exped...The rapid growth of Internet of things devices and the emergence of rapidly evolving network threats have made traditional security assessment methods inadequate.Federated learning offers a promising solution to expedite the training of security assessment models.However,ensuring the trustworthiness and robustness of federated learning under multi-party collaboration scenarios remains a challenge.To address these issues,this study proposes a shard aggregation network structure and a malicious node detection mechanism,along with improvements to the federated learning training process.First,we extract the data features of the participants by using spectral clustering methods combined with a Gaussian kernel function.Then,we introduce a multi-objective decision-making approach that combines data distribution consistency,consensus communication overhead,and consensus result reliability in order to determine the final network sharing scheme.Finally,by integrating the federated learning aggregation process with the malicious node detection mechanism,we improve the traditional decentralized learning process.Our proposed ShardFed algorithm outperforms conventional classification algorithms and state-of-the-art machine learning methods like FedProx and FedCurv in convergence speed,robustness against data interference,and adaptability across multiple scenarios.Experimental results demonstrate that the proposed approach improves model accuracy by up to 2.33%under non-independent and identically distributed data conditions,maintains higher performance with malicious nodes containing poisoned data ratios of 20%–50%,and significantly enhances model resistance to low-quality data.展开更多
The remaining useful life prediction of rolling bearing is vital in safety and reliability guarantee.In engineering scenarios,only a small amount of bearing performance degradation data can be obtained through acceler...The remaining useful life prediction of rolling bearing is vital in safety and reliability guarantee.In engineering scenarios,only a small amount of bearing performance degradation data can be obtained through accelerated life testing.In the absence of lifetime data,the hidden long-term correlation between performance degradation data is challenging to mine effectively,which is the main factor that restricts the prediction precision and engineering application of the residual life prediction method.To address this problem,a novel method based on the multi-layer perception neural network and bidirectional long short-term memory network is proposed.Firstly,a nonlinear health indicator(HI)calculation method based on kernel principal component analysis(KPCA)and exponential weighted moving average(EWMA)is designed.Then,using the raw vibration data and HI,a multi-layer perceptron(MLP)neural network is trained to further calculate the HI of the online bearing in real time.Furthermore,The bidirectional long short-term memory model(BiLSTM)optimized by particle swarm optimization(PSO)is used to mine the time series features of HI and predict the remaining service life.Performance verification experiments and comparative experiments are carried out on the XJTU-SY bearing open dataset.The research results indicate that this method has an excellent ability to predict future HI and remaining life.展开更多
Explosive synchronization(ES)is a kind of first-order jump phenomenon that exists in physical and biological systems.In recent years,researchers have focused on ES between single-layer and multi-layer networks.Most re...Explosive synchronization(ES)is a kind of first-order jump phenomenon that exists in physical and biological systems.In recent years,researchers have focused on ES between single-layer and multi-layer networks.Most research on complex networks with delay has focused on single-layer or double-layer networks,multi-layer networks are seldom explored.In this paper,we propose a Kuramoto model of frequency weights in multi-layer complex networks with delay and star connections between layers.Through theoretical analysis and numerical verification,the factors affecting the backward critical coupling strength are analyzed.The results show that the interaction between layers and the average node degree has a direct effect on the backward critical coupling strength of each layer network.The location of the delay,the size of the delay,the number of network layers,the number of nodes,and the network topology are revealed to have no direct impact on the backward critical coupling strength of the network.Delay is introduced to explore the influence of delay and other related parameters on ES.展开更多
Explosive synchronization(ES)is a first-order transition phenomenon that is ubiquitous in various physical and biological systems.In recent years,researchers have focused on explosive synchronization in a single-layer...Explosive synchronization(ES)is a first-order transition phenomenon that is ubiquitous in various physical and biological systems.In recent years,researchers have focused on explosive synchronization in a single-layer network,but few in multi-layer networks.This paper proposes a frequency-weighted Kuramoto model in multi-layer complex networks with star connection between layers and analyzes the factors affecting the backward critical coupling strength by both theoretical analysis and numerical validation.Our results show that the backward critical coupling strength of each layer network is influenced by the inter-layer interaction strength and the average degree.The number of network layers,the number of nodes,and the network topology can not directly affect the synchronization of the network.Enhancing the inter-layer interaction strength can prevent the emergence of explosive synchronization and increasing the average degree can promote the generation of explosive synchronization.展开更多
基金supported by National Natural Science Foundation of China(62101088,61801076,61971336)Natural Science Foundation of Liaoning Province(2022-MS-157,2023-MS-108)+1 种基金Key Laboratory of Big Data Intelligent Computing Funds for Chongqing University of Posts and Telecommunications(BDIC-2023-A-003)Fundamental Research Funds for the Central Universities(3132022230).
摘要Interconnection of all things challenges the traditional communication methods,and Semantic Communication and Computing(SCC)will become new solutions.It is a challenging task to accurately detect,extract,and represent semantic information in the research of SCC-based networks.In previous research,researchers usually use convolution to extract the feature information of a graph and perform the corresponding task of node classification.However,the content of semantic information is quite complex.Although graph convolutional neural networks provide an effective solution for node classification tasks,due to their limitations in representing multiple relational patterns and not recognizing and analyzing higher-order local structures,the extracted feature information is subject to varying degrees of loss.Therefore,this paper extends from a single-layer topology network to a multi-layer heterogeneous topology network.The Bidirectional Encoder Representations from Transformers(BERT)training word vector is introduced to extract the semantic features in the network,and the existing graph neural network is improved by combining the higher-order local feature module of the network model representation network.A multi-layer network embedding algorithm on SCC-based networks with motifs is proposed to complete the task of end-to-end node classification.We verify the effectiveness of the algorithm on a real multi-layer heterogeneous network.
基金supported by the National Natural Science Foundation of China (U1808205)Hebei Natural Science Foundation (F2000501005)。
摘要This paper studies the target controllability of multilayer complex networked systems,in which the nodes are highdimensional linear time invariant(LTI)dynamical systems,and the network topology is directed and weighted.The influence of inter-layer couplings on the target controllability of multi-layer networks is discussed.It is found that even if there exists a layer which is not target controllable,the entire multi-layer network can still be target controllable due to the inter-layer couplings.For the multi-layer networks with general structure,a necessary and sufficient condition for target controllability is given by establishing the relationship between uncontrollable subspace and output matrix.By the derived condition,it can be found that the system may be target controllable even if it is not state controllable.On this basis,two corollaries are derived,which clarify the relationship between target controllability,state controllability and output controllability.For the multi-layer networks where the inter-layer couplings are directed chains and directed stars,sufficient conditions for target controllability of networked systems are given,respectively.These conditions are easier to verify than the classic criterion.
摘要In last decade,due to that the popularity of the internet, data-central traffic kept growing,some emerging networking requirements have been posed on the todays telecommunication networks,especially in the area of network survivability.Obviously,as a key networking problem,network reliability will be more and more important.The integration of different technologies such as ATM,SDH,and WDM in multilayer transport networks raises many questions regarding the coordination of the individual network layers.This problem is referred as multilayer network survivability.The integrated multilayer network survivability is investingated as well as the representation of an interworking strategy between different single layer survivability schemes in IP via generalized multi-protocol label switching over optical network.
基金This work was supported by the National Science Foundation of China(No.61763041)and the Science Found of Qinghai Province(No.2020-GX-112).
摘要With the continuous development of mobile communications and Internet technologies,the marketing model of the communications industry has shifted from calling-based to social APP-based personalized recommendations.In order to improve the accuracy of recommendation,this paper proposes a recommendation algorithm for social analysis.Empirical data was firstly used to construct a“user-APP”two-layer communication network model,and then the traditional collaborative filtering recommendation technology was integrated to reconstruct similar users and similar APP network model.The bipartite graph weight distribution method was taken to recommend targets in the obtained network model.The experimental simulation shows that,in view of the characteristics of the twolayer communication network,compared with the traditional recommendation algorithm,the algorithm effectively improves the accuracy of the score prediction.
基金supported by Central guidance for local scientific and technological development funding projects(Grant No.2024ZY01057)。
摘要Intraocular pressure(IOP)is a key parameter to diagnose glaucoma disease and assess the treatment effect of cornea after refractive surgery.Current refractive surgeries inevitably change the configuration of the cornea,making it difficult to measure IOP accurately using conventional methods.The prediction method proposed in this article can accurately measure the IOP after refractive surgery.In this study,firstly,the finite element models of cornea free of IOP depicted by various vertex height,thickness,and radius are established,and the deformation of the cornea under different IOP is predicted.Based on the dataset obtained from the numerical simulations and the multi-layer perceptron neural network algorithm,two prediction models for the vertex height and thickness of the cornea free of IOP and for the configuration under IOP are developed,and a prediction method for IOP is then proposed by combining the two models.Following the similar way,two prediction models respectively for the parameters of the presumptive initial configuration of the cornea to undergo refractive surgery and for those of the cornea after surgery are constructed,and a prediction method for IOP of cornea after the surgery is presented.The validity of the prediction methods for regular IOP and that after refractive surgery is demonstrated using the clinical data from some volunteers.The proposed methods provide an efficient prediction method for regular IOP and that after refractive surgery.
基金National Natural Science Foundation of China(52175237)。
摘要The key parameters that characterize the morphological quality of multi-layer and multi-pass metal laser deposited parts are the surface roughness and the error between the actual printing height and the theoretical model height.The Taguchi method was employed to establish the correlations between process parameter combinations and multi-objective characterization of metal deposition morphology(height error and roughness).Results show that using the signal-to-noise ratio and grey relational analysis,the optimal parameter combination for multi-layer and multi-pass deposition is determined as follows:laser power of 800 W,powder feeding rate of 0.3 r/min,step distance of 1.6 mm,and scanning speed of 20 mm/s.Subsequently,a Genetic Bayesian-back propagation(GB-BP)network is constructed to predict multi-objective responses.Compared with the traditional back propagation network,the GB-back propagation network improves the prediction accuracy of height error and surface roughness by 43.14%and 71.43%,respectively.This network can accurately predict the multi-objective characterization of morphological quality of multi-layer and multi-pass metal deposited parts.
基金funding provided by Guangxi Natural Science Foundation(grant number 2021GXNSFFA196002)the Natural Sciences and Engineering Research Council of Canada(RGPIN-2022-03129)the University of Toronto.
摘要High-entropy oxides(HEOs)exhibit great potential as supercapacitor electrode materials,but their practical application is hindered by inherent challenges such as structural instability,insufficient conductivity,and difficulties in regulating oxygen vacancies.To overcome these limitations,we present a dual-defect engineering strategy:tailoring the elemental composition of FeZnCuCoNi-based HEOs to generate abundant oxygen vacancies,and constructing a hierarchical,3D multi-shell porous network structure via an in situ template method.Density functional theory calculations reveal that high-entropy lattice distortion significantly enhances oxygen vacancy concentration while reducing charge transfer barriers.Additionally,the multi-layered eggshell morphology creates interconnected ion diffusion pathways,shortens ion transport distances,and reinforces mechanical integrity.The optimized HEO electrode demonstrates remarkable electrochemical performance,achieving a specific capacitance of 641 F g⁻¹at 1 A g⁻¹,with a 92% electric double-layer contribution at 50 mV s⁻¹.The assembled asymmetric supercapacitor delivers an energy density of 36.7 Wh kg⁻¹ at a power density of 800 W kg⁻¹,while maintaining 92% of its initial capacity after 10000 charge-discharge cycles.Mechanistic studies indicate that oxygen vacancies optimize hydroxyl adsorption kinetics,facilitating surface charge transfer,while the hierarchical porous structure effectively mitigates volumetric expansion stress via a 3D ion transport network.This work offers a strategic framework for designing next-generation high-entropy energy storage materials by providing a synergy between atomic-scale electronic tuning and mesoscale structural design.
基金supported by the National Natural Science Foundation of China(Grant Nos.52378354 and 12572457)the Talent Research Initiation Foundation of Nanjing Institute of Technology(Grant No.YKJ202323).
摘要Heat conduction in multi-layered geomaterials was a pervasive phenomenon in various engineering applications,such as nuclear waste repositories,energy piles,and abandoned oil wells.The incomplete contact between adjacent geomaterials will impede the heat transfer at interfaces,known as the interfacial thermal resistance effect.In this regard,a two-dimensional axisymmetric mathematical model for transient heat conduction in multi-layered geomaterials with interfacial thermal resistance was established.Employing Green's function formalism,the thermal transport system was mathematically resolved through a closed-form analytical solution that provides continuum-level characterization of thermal evolution across all spatial-temporal coordinates.A numerical model for threelayered geomaterials and a benchmark test for double-layered geomaterials were constructed to verify the analytical solution.Finally,the solution was applied to simulate the temperature evolutions in a nuclear waste repository with three-and four-layered barrier systems with interfacial thermal resistance.The results indicated that the existence of interfacial thermal resistance caused heat accumulation at interfaces,thereby resulting in an increase in overall temperature within the repository.Moreover,the temperature rises in the bentonite block layer and bentonite granule layer were obviously greater than that in the surrounding rock.Due to the interfacial thermal resistance effect,a notable temperature difference was observed at the interfaces.Specifically,for every increment of 0.03(K m2)/W in interfacial thermal resistance,the temperature difference increased by 1.5℃.A comparative analysis of temperature fieldsin repositories with three-and four-layered barrier systems revealed that the gap between the canister and bentonite block significantlyaffects the peak temperature in the buffer layer.
基金supported by the National Natural Science Foundation of China(Grant Nos.52372362 and 12102361)the Natural Science Basic Research Program of Shaanxi(Grant No.2025JCJCQN-071)+1 种基金the Zhejiang Provincial Natural Science Foundation of China(Grant No.LR25A020001)the Fundamental Research Funds for the Central Universities(Grant No.G2024KY0615).
摘要Crossflow vortices induced transition is one of the most important instability types in supersonic aircraft boundary layers.While the traditional linear stability theory(LST)-based eN method demonstrates satisfactory predictive capabilities for this kind of transition,its practical implementation faces inherent limitations:the requirement of first-and second-order wallnormal derivatives of boundary layer velocityemperature profiles,the need for initial eigenvalue guesses,and the computational burden of solving eigenvalue problems.To address these challenges,this study develops a multi-layer perceptron(MLP)model tailored for linear stability analysis of three-dimensional compressible boundary layers based on the artificially defined quasi-three-dimensional non-similar boundary layer solutions.The boundary layer edge flow parameters and perturbation characteristics are mapped to eigenvalues or local growth rates of the envelop curves through fully connected layers.This architecture eliminates the need for computing wall-normal derivatives of velocityemperature profiles,initial eigenvalue estimation,and direct eigenvalue problem solving.Extensive validation across varying operational conditions and geometries(airfoils and swept wings)demonstrates exceptional agreement between the MLP’s predictions(eigenvalues and disturbance amplification factors)and traditional LST results.Furthermore,the model’s transition prediction capability is rigorously verified using National Aeronautics and Space Administration’s supersonic swept-wing crossflow-dominated transition benchmark,incorporating both stability analysis and flight test data.Results confirm the model is an efficient and reliable computational framework for transition prediction in three-dimensional finite-span wings.
基金Nourah bint Abdulrahman University for funding this project through the Researchers Supporting Project(PNURSP2025R319)Riyadh,Saudi Arabia and Prince Sultan University for covering the article processing charges(APC)associated with this publication.Special acknowledgement to Automated Systems&Soft Computing Lab(ASSCL),Prince Sultan University,Riyadh,Saudi Arabia.
摘要The growing incidence of cyberattacks necessitates a robust and effective Intrusion Detection Systems(IDS)for enhanced network security.While conventional IDSs can be unsuitable for detecting different and emerging attacks,there is a demand for better techniques to improve detection reliability.This study introduces a new method,the Deep Adaptive Multi-Layer Attention Network(DAMLAN),to boost the result of intrusion detection on network data.Due to its multi-scale attention mechanisms and graph features,DAMLAN aims to address both known and unknown intrusions.The real-world NSL-KDD dataset,a popular choice among IDS researchers,is used to assess the proposed model.There are 67,343 normal samples and 58,630 intrusion attacks in the training set,12,833 normal samples,and 9711 intrusion attacks in the test set.Thus,the proposed DAMLAN method is more effective than the standard models due to the consideration of patterns by the attention layers.The experimental performance of the proposed model demonstrates that it achieves 99.26%training accuracy and 90.68%testing accuracy,with precision reaching 98.54%on the training set and 96.64%on the testing set.The recall and F1 scores again support the model with training set values of 99.90%and 99.21%and testing set values of 86.65%and 91.37%.These results provide a strong basis for the claims made regarding the model’s potential to identify intrusion attacks and affirm its relatively strong overall performance,irrespective of type.Future work would employ more attempts to extend the scalability and applicability of DAMLAN for real-time use in intrusion detection systems.
基金supported by The Key Research and Development Program of Gansu Province—Industrial Category,China(Grant No.24YFGA018)The Science and Technology Program of the State Administration for Market Regulation of China(Grant No.2024MK129)The Gansu Provincial Department of Education:Gansu Provincial Graduate Student“Innovation Star”Project,China(Grant No.2025CXZX612).
摘要The plastic strain accumulation results of the multi-layered wrapped pressure vessel liner during long-term service are an important basis for its safety performance evaluation.However,the complex welds distributed on the liner bring challenges to the calculation of plastic cumulative strain.To this end,a novel hybrid deep learning framework is proposed for the efficient and precise prediction of ratcheting behavior in the liner welds of multilayered pressure vessels.By employing a BiLSTM network to extract bidirectional temporal dependencies from the strain history and incorporating a Multi-Head Attention(MHA)mechanism for adaptive feature weighting,the proposed method effectively addresses the difficulty of modeling cumulative effects in long-sequence ratcheting data.Firstly,asymmetric cyclic loading experiments were conducted on various welded joints and base metals to reveal the evolutionary laws of ratcheting behavior and construct a training dataset.The results show that the ratcheting strain evolution of different structural specimens shows the typical‘two-stage’characteristics,and the ratcheting strain accumulation on the base metal is significantly higher than that of the weld structure specimen.The proposed deep learning model can not only accurately capture the‘two-stage’evolution of ratcheting strain,but also directly use the base metal data to accurately predict the ratcheting strain accumulation in different weld parts,avoiding the complex parameter calibration process of the traditional constitutive model.It provides technical support for the integrity assessment and online monitoring of the complex weld structure of multi-layered pressure vessels.
基金supported by the National Natural Science Foundation of China(No.62401597)Natural Science Foundation of Hunan Province,China(No.2024JJ6469)the Research Project of National University of Defense Technology,China(No.ZK22-02).
摘要Low Earth Orbit(LEO)mega-constellation networks,exemplified by Starlink,are poised to play a pivotal role in future mobile communication networks,due to their low latency and high capacity.With the massively deployed satellites,ground users now can be covered by multiple visible satellites,but also face complex handover issues with such massive high-mobility satellites in multi-layer.The end-to-end routing is also affected by the handover behavior.In this paper,we propose an intelligent handover strategy dedicated to multi-layer LEO mega-constellation networks.Firstly,an analytic model is utilized to rapidly estimate the end-to-end propagation latency as a key handover factor to construct a multi-objective optimization model.Subsequently,an intelligent handover strategy is proposed by employing the Dueling Double Deep Q Network(D3QN)-based deep reinforcement learning algorithm for single-layer constellations.Moreover,an optimal crosslayer handover scheme is proposed by predicting the latency-jitter and minimizing the cross-layer overhead.Simulation results demonstrate the superior performance of the proposed method in the multi-layer LEO mega-constellation,showcasing reductions of up to 8.2%and 59.5%in end-to-end latency and jitter respectively,when compared to the existing handover strategies.
基金supported by the National Natural Science Foundation of China(Grant Nos.42272338 and 41827807)Department of Transportation of Zhejiang Province,China(Grant No.202213).
摘要Physics-informed neural networks(PINNs)have prevailed as differentiable simulators to investigate flow in porous media.Despite recent progress PINNs have achieved,practical geotechnical scenarios cannot be readily simulated because conventional PINNs fail in discontinuous heterogeneous porous media or multi-layer strata when labeled data are missing.This work aims to develop a universal network structure to encode the mass continuity equation and Darcy’s law without labeled data.The finite element approximation,which can decompose a complex heterogeneous domain into simpler ones,is adopted to build the differentiable network.Without conventional DNNs,physics-encoded finite element network(PEFEN)can avoid spectral bias and learn high-frequency functions with sharp/steep gradients.PEFEN rigorously encodes Dirichlet and Neumann boundary conditions without training.Benefiting from its discretized formulation,the discontinuous heterogeneous hydraulic conductivity is readily embedded into the network.Three typical cases are reproduced to corroborate PEFEN’s superior performance over conventional PINNs and the PINN with mixed formulation.PEFEN is sparse and demonstrated to be capable of dealing with heterogeneity with much fewer training iterations(less than 1/30)than the improved PINN with mixed formulation.Thus,PEFEN saves energy and contributes to low-carbon AI for science.The last two cases focus on common geotechnical settings of impermeable sheet pile in singlelayer and multi-layer strata.PEFEN solves these cases with high accuracy,circumventing costly labeled data,extra computational burden,and additional treatment.Thus,this study warrants the further development and application of PEFEN as a novel differentiable network in porous flow of practical geotechnical engineering.
基金the financial support from the National Natural Science Foundation of China(No.52504019)China Postdoctoral Science Foundation(No.2025 M772961)+1 种基金the National Science and Technology Major Project of China(No.2024ZD1404701)the State Key Laboratory of Petroleum Resources and Engineering,China University of Petroleum(Beijing)(No.PRE/open-2507)。
摘要Accurate prediction of stress evolution induced by production pressure depletion after hydraulic fracturing is essential for efficient development of stacked continental shale reservoirs.This study establishes a three-dimensional stress sensitivity and flow coupling framework to characterize intra-layer and interlayer stress evolution during shale oil development.A 3D discrete fracture network(DFN)integrating hydraulic and natural fractures was reconstructed from microseismic data obtained during multi-layer fracturing.Based on this,a stress sensitivity model for interbedded sandstone-shale reservoirs and a V-shaped well layout flow model was developed to simulate single-layer(three-well)and three-layer(nine-well)production scenarios.The reconstructed fracture network revealed that hydraulic fractures propagate laterally away from the zipper fracturing side and vertically upward toward low-pressure zones.During multi-layer development on Platform H,fracture intersections between the middle and adjacent layers produced 0-3 MPa pore pressure interference under different production schedules,indicating the need for optimized inter-well and interlayer spacing.Sandstone layers,characterized by higher permeability and porosity,exhibited a greater increase in horizontal stress difference(2.61 MPa)than shale layers(<0.5 MPa).Stress reorientation angles ranged from 5°to 38°in shale and from 16°to 64°in sandstone layers.These results demonstrate that well spacing should be larger in sandstone layers,whereas infill drilling is more suitable within shale intervals.The proposed modeling and analysis approach provides a theoretical and technical basis for optimizing well pattern deployment and maximizing energy utilization in shale oil reservoir development.
基金supported in part by the National Key Research and Development Project under Grant 2020YFB1806805partially funded through a grant from Qualcomm。
摘要6G is desired to support more intelligence networks and this trend attaches importance to the self-healing capability if degradation emerges in the cellular networks.As a primary component of selfhealing networks,fault detection is investigated in this paper.Considering the fast response and low timeand-computational consumption,it is the first time that the Online Broad Learning System(OBLS)is applied to identify outages in cellular networks.In addition,the Automatic-constructed Online Broad Learning System(AOBLS)is put forward to rationalize its structure and consequently avoid over-fitting and under-fitting.Furthermore,a multi-layer classification structure is proposed to further improve the classification performance.To face the challenges caused by imbalanced data in fault detection problems,a novel weighting strategy is derived to achieve the Multilayer Automatic-constructed Weighted Online Broad Learning System(MAWOBLS)and ensemble learning with retrained Support Vector Machine(SVM),denoted as EMAWOBLS,for superior treatment with this imbalance issue.Simulation results show that the proposed algorithm has excellent performance in detecting faults with satisfactory time usage.
基金supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq)-Brazil(Grant no.310984/2023-8)Fundação de AmparoàPesquisa do Estado de Minas Gerais(FAPEMIG)-Brazil(Grant no.APQ-01973-24)+1 种基金supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior(CAPES)-Brazil-Finance Code 001Seyed M.Moghadas acknowledges the support from Natural Sciences and Engineering Research Council of Canada(NSERC),Discovery Grant and Alliance Grant.
摘要Network models adeptly capture heterogeneities in individual interactions,making them well-suited for describing a wide range of real-world and virtual connections,including information diffusion,behavioural tendencies,and disease dynamic fluctuations.However,there is a notable methodological gap in existing studies examining the interplay between physical and virtual interactions and the impact of information dissemination and behavioural responses on disease propagation.We constructed a three-layer(information,cognition,and epidemic)network model to investigate the adoption of protective behaviours,such as wearing masks or practising social distancing,influenced by the diffusion and correction of misinformation.We examined five key events influencing the rate of information spread:(i)rumour transmission,(ii)information suppression,(iii)renewed interest in spreading misinformation,(iv)correction of misinformation,and(v)relapse to a stifler state after correction.We found that adopting information-based protection behaviours is more effective in mitigating disease spread than protection adoption induced by neighbourhood interactions.Specifically,our results show that warning and educating individuals to counter misinformation within the information network is a more effective strategy for curbing disease spread than suspending gossip spreaders from the network.Our study has practical implications for developing strategies to mitigate the impact of misinformation and enhance protective behavioural responses during disease outbreaks.
基金supported by State Grid Hebei Electric Power Co.,Ltd.Science and Technology Project,Research on Security Protection of Power Services Carried by 4G/5G Networks(Grant No.KJ2024-127).
摘要The rapid growth of Internet of things devices and the emergence of rapidly evolving network threats have made traditional security assessment methods inadequate.Federated learning offers a promising solution to expedite the training of security assessment models.However,ensuring the trustworthiness and robustness of federated learning under multi-party collaboration scenarios remains a challenge.To address these issues,this study proposes a shard aggregation network structure and a malicious node detection mechanism,along with improvements to the federated learning training process.First,we extract the data features of the participants by using spectral clustering methods combined with a Gaussian kernel function.Then,we introduce a multi-objective decision-making approach that combines data distribution consistency,consensus communication overhead,and consensus result reliability in order to determine the final network sharing scheme.Finally,by integrating the federated learning aggregation process with the malicious node detection mechanism,we improve the traditional decentralized learning process.Our proposed ShardFed algorithm outperforms conventional classification algorithms and state-of-the-art machine learning methods like FedProx and FedCurv in convergence speed,robustness against data interference,and adaptability across multiple scenarios.Experimental results demonstrate that the proposed approach improves model accuracy by up to 2.33%under non-independent and identically distributed data conditions,maintains higher performance with malicious nodes containing poisoned data ratios of 20%–50%,and significantly enhances model resistance to low-quality data.
基金supported by the National Key Research and Development Project(Grant Number 2023YFB3709601)the National Natural Science Foundation of China(Grant Numbers 62373215,62373219,62073193)+2 种基金the Key Research and Development Plan of Shandong Province(Grant Numbers 2021CXGC010204,2022CXGC020902)the Fundamental Research Funds of Shandong University(Grant Number 2021JCG008)the Natural Science Foundation of Shandong Province(Grant Number ZR2023MF100).
摘要The remaining useful life prediction of rolling bearing is vital in safety and reliability guarantee.In engineering scenarios,only a small amount of bearing performance degradation data can be obtained through accelerated life testing.In the absence of lifetime data,the hidden long-term correlation between performance degradation data is challenging to mine effectively,which is the main factor that restricts the prediction precision and engineering application of the residual life prediction method.To address this problem,a novel method based on the multi-layer perception neural network and bidirectional long short-term memory network is proposed.Firstly,a nonlinear health indicator(HI)calculation method based on kernel principal component analysis(KPCA)and exponential weighted moving average(EWMA)is designed.Then,using the raw vibration data and HI,a multi-layer perceptron(MLP)neural network is trained to further calculate the HI of the online bearing in real time.Furthermore,The bidirectional long short-term memory model(BiLSTM)optimized by particle swarm optimization(PSO)is used to mine the time series features of HI and predict the remaining service life.Performance verification experiments and comparative experiments are carried out on the XJTU-SY bearing open dataset.The research results indicate that this method has an excellent ability to predict future HI and remaining life.
摘要Explosive synchronization(ES)is a kind of first-order jump phenomenon that exists in physical and biological systems.In recent years,researchers have focused on ES between single-layer and multi-layer networks.Most research on complex networks with delay has focused on single-layer or double-layer networks,multi-layer networks are seldom explored.In this paper,we propose a Kuramoto model of frequency weights in multi-layer complex networks with delay and star connections between layers.Through theoretical analysis and numerical verification,the factors affecting the backward critical coupling strength are analyzed.The results show that the interaction between layers and the average node degree has a direct effect on the backward critical coupling strength of each layer network.The location of the delay,the size of the delay,the number of network layers,the number of nodes,and the network topology are revealed to have no direct impact on the backward critical coupling strength of the network.Delay is introduced to explore the influence of delay and other related parameters on ES.
摘要Explosive synchronization(ES)is a first-order transition phenomenon that is ubiquitous in various physical and biological systems.In recent years,researchers have focused on explosive synchronization in a single-layer network,but few in multi-layer networks.This paper proposes a frequency-weighted Kuramoto model in multi-layer complex networks with star connection between layers and analyzes the factors affecting the backward critical coupling strength by both theoretical analysis and numerical validation.Our results show that the backward critical coupling strength of each layer network is influenced by the inter-layer interaction strength and the average degree.The number of network layers,the number of nodes,and the network topology can not directly affect the synchronization of the network.Enhancing the inter-layer interaction strength can prevent the emergence of explosive synchronization and increasing the average degree can promote the generation of explosive synchronization.