Influencer identification of dynamical networks based on an information entropy dimension reduction method

Identifying critical nodes or sets in large-scale networks is a fundamental scientific problem and one of the key research directions in the fields of data mining and network science when implementing network attacks, defense, repair and control.Traditional methods usually begin from the centrality, node location or the impact on the largest connected component after node destruction, mainly based on the network structure.However, these algorithms do not consider network state changes.We applied a model that combines a random connectivity matrix and minimal low-dimensional structures to represent network connectivity.By using mean field theory and information entropy to calculate node activity,we calculated the overlap between the random parts and fixed low-dimensional parts to quantify the influence of node impact on network state changes and ranked them by importance.We applied this algorithm and the proposed importance algorithm to the overall analysis and stratified analysis of the C.elegans neural network.We observed a change in the critical entropy of the network state and by utilizing the proposed method we can calculate the nodes that indirectly affect muscle cells through neural layers.

Spontaneous Recovery in Directed Dynamical Networks

Complex networked systems,which range from biological systems in the natural world to infrastructure systems in the human-made world,can exhibit spontaneous recovery after a failure;for example,a brain may spontaneously return to normal after a seizure,and traffic flow can become smooth again after a jam.Previous studies on the spontaneous recovery of dynamical networks have been limited to undirected networks.However,most real-world networks are directed.To fill this gap,we build a model in which nodes may alternately fail and recover,and we develop a theoretical tool to analyze the recovery properties of directed dynamical networks.We find that the tool can accurately predict the final fraction of active nodes,and the prediction accuracy decreases as the fraction of bidirectional links in the network increases,which emphasizes the importance of directionality in network dynamics.Due to different initial states,directed dynamical networks may show alternative stable states under the same control parameter,exhibiting hysteresis behavior.In addition,for networks with finite sizes,the fraction of active nodes may jump back and forth between high and low states,mimicking repetitive failure-recovery processes.These findings could help clarify the system recovery mechanism and enable better design of networked systems with high resilience.

Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.

Large-scale self-normalizing neural networks

Self-normalizing neural networks(SNN)regulate the activation and gradient flows through activation functions with the self-normalization property.As SNNs do not rely on norms computed from minibatches,they are more friendly to data parallelism,kernel fusion,and emerging architectures such as ReRAM-based accelerators.However,existing SNNs have mainly demonstrated their effectiveness on toy datasets and fall short in accuracy when dealing with large-scale tasks like ImageNet.They lack the strong normalization,regularization,and expression power required for wider,deeper models and larger-scale tasks.To enhance the normalization strength,this paper introduces a comprehensive and practical definition of the self-normalization property in terms of the stability and attractiveness of the statistical fixed points.It is comprehensive as it jointly considers all the fixed points used by existing studies:the first and second moment of forward activation and the expected Frobenius norm of backward gradient.The practicality comes from the analytical equations provided by our paper to assess the stability and attractiveness of each fixed point,which are derived from theoretical analysis of the forward and backward signals.The proposed definition is applied to a meta activation function inspired by prior research,leading to a stronger self-normalizing activation function named‘‘bi-scaled exponential linear unit with backward standardized’’(bSELU-BSTD).We provide both theoretical and empirical evidence to show that it is superior to existing studies.To enhance the regularization and expression power,we further propose scaled-Mixup and channel-wise scale&shift.With these three techniques,our approach achieves 75.23%top-1 accuracy on the ImageNet with Conv MobileNet V1,surpassing the performance of existing self-normalizing activation functions.To the best of our knowledge,this is the first SNN that achieves comparable accuracy to batch normalization on ImageNet.

Dynamic Multi-Graph Spatio-Temporal Graph Traffic Flow Prediction in Bangkok:An Application of a Continuous Convolutional Neural Network

The ability to accurately predict urban traffic flows is crucial for optimising city operations.Consequently,various methods for forecasting urban traffic have been developed,focusing on analysing historical data to understand complex mobility patterns.Deep learning techniques,such as graph neural networks(GNNs),are popular for their ability to capture spatio-temporal dependencies.However,these models often become overly complex due to the large number of hyper-parameters involved.In this study,we introduce Dynamic Multi-Graph Spatial-Temporal Graph Neural Ordinary Differential Equation Networks(DMST-GNODE),a framework based on ordinary differential equations(ODEs)that autonomously discovers effective spatial-temporal graph neural network(STGNN)architectures for traffic prediction tasks.The comparative analysis of DMST-GNODE and baseline models indicates that DMST-GNODE model demonstrates superior performance across multiple datasets,consistently achieving the lowest Root Mean Square Error(RMSE)and Mean Absolute Error(MAE)values,alongside the highest accuracy.On the BKK(Bangkok)dataset,it outperformed other models with an RMSE of 3.3165 and an accuracy of 0.9367 for a 20-min interval,maintaining this trend across 40 and 60 min.Similarly,on the PeMS08 dataset,DMST-GNODE achieved the best performance with an RMSE of 19.4863 and an accuracy of 0.9377 at 20 min,demonstrating its effectiveness over longer periods.The Los_Loop dataset results further emphasise this model’s advantage,with an RMSE of 3.3422 and an accuracy of 0.7643 at 20 min,consistently maintaining superiority across all time intervals.These numerical highlights indicate that DMST-GNODE not only outperforms baseline models but also achieves higher accuracy and lower errors across different time intervals and datasets.

UAV-assisted data collection for wireless sensor networks with dynamic working modes

Wireless Sensor Network(WSN)is a cornerstone of Internet of Things(IoT)and has rich application scenarios.In this work,we consider a heterogeneous WSN whose sensor nodes have a diversity in their Residual Energy(RE).In this work,to protect the sensor nodes with low RE,we investigate dynamic working modes for sensor nodes which are determined by their RE and an introduced energy threshold.Besides,we employ an Unmanned Aerial Vehicle(UAV)to collect the stored data from the heterogeneous WSN.We aim to jointly optimize the cluster head selection,energy threshold and sensor nodes’working mode to minimize the weighted sum of energy con-sumption from the WSN and UAV,subject to the data collection rate constraint.To this end,we propose an efficient search method to search for an optimal energy threshold,and develop a penalty-based successive convex approximation algorithm to select the cluster heads.Then we present a low-complexity iterative approach to solve the joint optimization problem and discuss the implementation procedure.Numerical results justify that our proposed approach is able to reduce the energy consumption of the sensor nodes with low RE significantly and also saves energy for the whole WSN.

A Large-Scale Group Decision Making Model Based on Trust Relationship and Social Network Updating

With the development of big data and social computing,large-scale group decisionmaking(LGDM)is nowmerging with social networks.Using social network analysis(SNA),this study proposes an LGDM consensus model that considers the trust relationship among decisionmakers(DMs).In the process of consensusmeasurement:the social network is constructed according to the social relationship among DMs,and the Louvain method is introduced to classify social networks to form subgroups.In this study,the weights of each decision maker and each subgroup are computed by comprehensive network weights and trust weights.In the process of consensus improvement:A feedback mechanism with four identification and two direction rules is designed to guide the consensus of the improvement process.Based on the trust relationship among DMs,the preferences are modified,and the corresponding social network is updated to accelerate the consensus.Compared with the previous research,the proposedmodel not only allows the subgroups to be reconstructed and updated during the adjustment process,but also improves the accuracy of the adjustment by the feedbackmechanism.Finally,an example analysis is conducted to verify the effectiveness and flexibility of the proposed method.Moreover,compared with previous studies,the superiority of the proposed method in solving the LGDM problem is highlighted.

Dynamic analysis of major public health emergency transmission considering the dual-layer coupling of community–resident complex networks

We construct a dual-layer coupled complex network of communities and residents to represent the interconnected risk transmission network between communities and the disease transmission network among residents. It characterizes the process of infectious disease transmission among residents between communities through the SE2IHR model considering two types of infectors. By depicting a more fine-grained social structure and combining further simulation experiments, the study validates the crucial role of various prevention and control measures implemented by communities as primary executors in controlling the epidemic. Research shows that the geographical boundaries of communities and the social interaction patterns of residents have a significant impact on the spread of the epidemic, where early detection, isolation and treatment strategies at community level are essential for controlling the spread of the epidemic. In addition, the study explores the collaborative governance model and institutional advantages of communities and residents in epidemic prevention and control.

A Neural-network-based Alternative Scheme to Include Nonhydrostatic Processes in an Atmospheric Dynamical Core

Here,a nonhydrostatic alternative scheme(NAS)is proposed for the grey zone where the nonhydrostatic impact on the atmosphere is evident but not large enough to justify the necessity to include an implicit nonhydrostatic solver in an atmospheric dynamical core.The NAS is designed to replace this solver,which can be incorporated into any hydrostatic models so that existing well-developed hydrostatic models can effectively serve for a longer time.Recent advances in machine learning(ML)provide a potential tool for capturing the main complicated nonlinear-nonhydrostatic relationship.In this study,an ML approach called a neural network(NN)was adopted to select leading input features and develop the NAS.The NNs were trained and evaluated with 12-day simulation results of dry baroclinic-wave tests by the Weather Research and Forecasting(WRF)model.The forward time difference of the nonhydrostatic tendency was used as the target variable,and the five selected features were the nonhydrostatic tendency at the last time step,and four hydrostatic variables at the current step including geopotential height,pressure in two different forms,and potential temperature,respectively.Finally,a practical NAS was developed with these features and trained layer by layer at a 20-km horizontal resolution,which can accurately reproduce the temporal variation and vertical distribution of the nonhydrostatic tendency.Corrected by the NN-based NAS,the improved hydrostatic solver at different horizontal resolutions can run stably for at least one month and effectively reduce most of the nonhydrostatic errors in terms of system bias,anomaly root-mean-square error,and the error of the wave spatial pattern,which proves the feasibility and superiority of this scheme.

Multi-head neural networks for simulating particle breakage dynamics

The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation.In this paper,the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics.Unlike conventional methods,the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size,predicting values on arbitrarily fine grids without the need for model retraining.The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes.The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill.The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.

Set-Membership Filtering Approach to Dynamic Event-Triggered Fault Estimation for a Class of Nonlinear Time-Varying Complex Networks

The present study addresses the problem of fault estimation for a specific class of nonlinear time-varying complex networks,utilizing an unknown-input-observer approach within the framework of dynamic event-triggered mechanism(DETM).In order to optimize communication resource utilization,the DETM is employed to determine whether the current measurement data should be transmitted to the estimator or not.To guarantee a satisfactory estimation performance for the fault signal,an unknown-input-observer-based estimator is constructed to decouple the estimation error dynamics from the influence of fault signals.The aim of this paper is to find the suitable estimator parameters under the effects of DETM such that both the state estimates and fault estimates are confined within two sets of closed ellipsoid domains.The techniques of recursive matrix inequality are applied to derive sufficient conditions for the existence of the desired estimator,ensuring that the specified performance requirements are met under certain conditions.Then,the estimator gains are derived by minimizing the ellipsoid domain in the sense of trace and a recursive estimator parameter design algorithm is then provided.Finally,a numerical example is conducted to demonstrate the effectiveness of the designed estimator.

A Game-Theoretic Perspective on Resource Management for Large-Scale UAV Communication Networks

As a result of rapid development in electronics and communication technology,large-scale unmanned aerial vehicles(UAVs)are harnessed for various promising applications in a coordinated manner.Although it poses numerous advantages,resource management among various domains in large-scale UAV communication networks is the key challenge to be solved urgently.Specifically,due to the inherent requirements and future development trend,distributed resource management is suitable.In this article,we investigate the resource management problem for large-scale UAV communication networks from game-theoretic perspective which are exactly coincident with the distributed and autonomous manner.By exploring the inherent features,the distinctive challenges are discussed.Then,we explore several gametheoretic models that not only combat the challenges but also have broad application prospects.We provide the basics of each game-theoretic model and discuss the potential applications for resource management in large-scale UAV communication networks.Specifically,mean-field game,graphical game,Stackelberg game,coalition game and potential game are included.After that,we propose two innovative case studies to highlight the feasibility of such novel game-theoretic models.Finally,we give some future research directions to shed light on future opportunities and applications.

Topology identification for a class of complex dynamical networks using output variables

A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stability theory. Here the output of the network and the states of the observer are used to construct the updating law of the topology such that the communication resources from the network to its observer are saved. Some convergent criteria of the adaptive observer are derived in the form of linear inequality matrices. Several numerical examples are shown to demonstrate the effectiveness of the proposed observer.

SYNCHRONIZATION OF MASTER-SLAVE MARKOVIAN SWITCHING COMPLEX DYNAMICAL NETWORKS WITH TIME-VARYING DELAYS IN NONLINEAR FUNCTION VIA SLIDING MODE CONTROL

In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Synchronization of complex switched delay dynamical networks with simultaneously diagonalizable coupling matrices

This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.

Disturbance rejection and H_∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.

Successive lag synchronization on dynamical networks with communication delay

In this paper, successive lag synchronization （SLS） on a dynamical network with communication delay is investigated. In order to achieve SLS on the dynamical network with communication delay, we design linear feedback control and adaptive control, respectively. By using the Lyapunov function method, we obtain some sufficient conditions for global stability of SLS. To verify these results, some numerical examples are further presented. This work may find potential applications in consensus of multi-agent systems.

Efficient Routing Protection Algorithm in Large-Scale Networks

With an increasing urgent demand for fast recovery routing mechanisms in large-scale networks,minimizing network disruption caused by network failure has become critical.However,a large number of relevant studies have shown that network failures occur on the Internet inevitably and frequently.The current routing protocols deployed on the Internet adopt the reconvergence mechanism to cope with network failures.During the reconvergence process,the packets may be lost because of inconsistent routing information,which reduces the network’s availability greatly and affects the Internet service provider’s(ISP’s)service quality and reputation seriously.Therefore,improving network availability has become an urgent problem.As such,the Internet Engineering Task Force suggests the use of downstream path criterion(DC)to address all single-link failure scenarios.However,existing methods for implementing DC schemes are time consuming,require a large amount of router CPU resources,and may deteriorate router capability.Thus,the computation overhead introduced by existing DC schemes is significant,especially in large-scale networks.Therefore,this study proposes an efficient intra-domain routing protection algorithm(ERPA)in large-scale networks.Theoretical analysis indicates that the time complexity of ERPA is less than that of constructing a shortest path tree.Experimental results show that ERPA can reduce the computation overhead significantly compared with the existing algorithms while offering the same network availability as DC.

Fault diagnosis of time-delay complex dynamical networks using output signals

This paper proposes a novel approach for fault diagnosis of a time-delay complex dynamical network. Unlike the other methods, assuming that the dynamics of the network can be described by a linear stochastic model, or using the state variables of nodes in the network to design an adaptive observer, it only uses the output variable of the nodes to design an observer and an adaptive law of topology matrix in the observer of a complex network, leading to simple design of the observer and easy realisation of topology monitoring for the complex networks in real engineering. The proposed scheme can monitor any changes of the topology structure of a time-delay complex network. The effectiveness of this method is successfully demonstrated by virtue of a complex networks with Lorenz model.

Stochastic synchronization for time-varying complex dynamical networks

This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.