Previous work puts forward a random edge rewiring method which is capable of improving the network robustness noticeably, while it lacks further discussions about how to improve the robustness faster. In this study, t...Previous work puts forward a random edge rewiring method which is capable of improving the network robustness noticeably, while it lacks further discussions about how to improve the robustness faster. In this study, the detailed analysis of the structures of improved networks show that regenerating the edges between high-degree nodes can enhance the robustness against a targeted attack. Therefore, we propose a novel rewiring strategy based on regenerating more edges between high-degree nodes, called smart rewiring, which could speed up the increase of the robustness index effectively. The smart rewiring method also explains why positive degree-degree correlation could enhance network robustness.展开更多
As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structur...As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored.From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.展开更多
The world airport network（WAN） is one of the networked infrastructures that shape today＇s economic and social activity, so its resilience against incidents affecting the WAN is an important problem. In this paper, ...The world airport network（WAN） is one of the networked infrastructures that shape today＇s economic and social activity, so its resilience against incidents affecting the WAN is an important problem. In this paper, the robustness of air route networks is extended by defining and testing several heuristics to define selection criteria to detect the critical nodes of the WAN.In addition to heuristics based on genetic algorithms and simulated annealing, custom heuristics based on node damage and node betweenness are defined. The most effective heuristic is a multiattack heuristic combining both custom heuristics. Results obtained are of importance not only for advance in the understanding of the structure of complex networks, but also for critical node detection.展开更多
Transportation network vulnerability analysis has developed increasingly in the last decade with the goal to identify the most critical locations against incidences.In this domain,many of the previous researches have ...Transportation network vulnerability analysis has developed increasingly in the last decade with the goal to identify the most critical locations against incidences.In this domain,many of the previous researches have focused on congested urban networks;however,there is still a need to consider regional and interurban sparse rail networks,specifically those networks in developing countries.In such sparse rail networks,there are limited possibilities to redirect trains if a link is disrupted,there might be less possibility of finding redundant alternative routes,and network failures are usually accompanied by a phenomenon called‘unsatisfied demand.’The study reported in this paper stemmed from research aimed to design precautionary actions for a developing country’s sparse railway system.Our study framework deemed to find the most vulnerable part of an inter-urban sparse rail network using a network scan approach,which found the consequences of network disruptions.A number of criteria were defined to determine the total cost including unsatisfied demand and additional transportation costs due to disruptions.The results showed that how well the process of the vulnerability analysis,considering the features of both supply and demand sides,can be a guide for railway authorities in applying system safety measures.展开更多
Network robustness is one of the core contents of complex network security research.This paper focuses on the robustness of community networks with respect to cascading failures,considering the nodes influence and com...Network robustness is one of the core contents of complex network security research.This paper focuses on the robustness of community networks with respect to cascading failures,considering the nodes influence and community heterogeneity.A novel node influence ranking method,community-based Clustering-LeaderRank(CCL)algorithm,is first proposed to identify influential nodes in community networks.Simulation results show that the CCL method can effectively identify the influence of nodes.Based on node influence,a new cascading failure model with heterogeneous redistribution strategy is proposed to describe and analyze node fault propagation in community networks.Analytical and numerical simulation results on cascading failure show that the community attribute has an important influence on the cascading failure process.The network robustness against cascading failures increases when the load is more distributed to neighbors of the same community instead of different communities.When the initial load distribution and the load redistribution strategy based on the node influence are the same,the network shows better robustness against node failure.展开更多
Networked control systems are subject to adversary conditions that affect their network topologies.To ensure reliable system operations,network topologies need to be characterized and managed for their impact on the o...Networked control systems are subject to adversary conditions that affect their network topologies.To ensure reliable system operations,network topologies need to be characterized and managed for their impact on the overall system performance.This paper introduces the concept of network robustness depth for this pursuit.Discrete event systems are used as a foundation to model dynamic behavior of network topologies,support their analysis,and carry out their management.Stochastic analysis relates the link reliability probabilities to a probabilistic characterization of network robustness depth.Several topology management strategies are discussed,including passive methods,random strategies,and optimization methodologies.Their respective benefits and limitations are quantified.By using platoon control as a platform of hybrid(continuous and discrete event) systems and packet erasure channels as a communication protocol,the results are demonstrated with case studies.展开更多
Despite the large size of most communication and transportation systems, there are short paths between nodes in these networks which guarantee the efficient information, data and passenger delivery; furthermore these ...Despite the large size of most communication and transportation systems, there are short paths between nodes in these networks which guarantee the efficient information, data and passenger delivery; furthermore these networks have a surprising tolerance under random errors thanks to their inherent scale-free topology. However, their scale-free topology also makes them fragile under intentional attacks, leaving us a challenge on how to improve the network robustness against intentional attacks without losing their strong tolerance under random errors and high message and passenger delivering capacity. Here We propose two methods （SL method and SH method） to enhance scale-free network＇s tolerance under attack in different conditions.展开更多
In order to overcome the system non-linearity and uncertainty inherent in magnetic bearing systems, a GA（genetic algnrithm）-based PID neural network controller is designed and trained tO emulate the operation of a c...In order to overcome the system non-linearity and uncertainty inherent in magnetic bearing systems, a GA（genetic algnrithm）-based PID neural network controller is designed and trained tO emulate the operation of a complete system （magnetic bearing, controller, and power amplifiers）. The feasibility of using a neural network to control nonlinear magnetic bearing systems with unknown dynamics is demonstrated. The key concept of the control scheme is to use GA to evaluate the candidate solutions （chromosomes）, increase the generalization ability of PID neural network and avoid suffering from the local minima problem in network learning due to the use of gradient descent learning method. The simulation results show that the proposed architecture provides well robust performance and better reinforcement learning capability in controlling magnetic bearing systems.展开更多
A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as mea...A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.展开更多
One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that ...One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that Boolean networks,which are a promising model of biological networks,do not always represent the conservation law.This paper thus addresses a kind of conservation law as a generic property of Boolean networks.In particular,we consider the problem of finding network structures on which,for any Boolean operation on nodes,the number of active nodes,i.ev nodes whose state is one,is constant over time.As a solution to the problem,we focus on the strongly-connected network structures and present a necessary and sufficient condition.展开更多
In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential s...In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential stability. Finally, we use one numerical simulation example to illustrate the correctness and effectiveness of our results.展开更多
It is known that both excitatory and inhibitory neuronal networks can achieve robust synchronization only under certain conditions, such as long synaptic delay or low level of heterogeneity. In this work, robust synch...It is known that both excitatory and inhibitory neuronal networks can achieve robust synchronization only under certain conditions, such as long synaptic delay or low level of heterogeneity. In this work, robust synchronization can be found in an excitatory/inhibitory （E/I） neuronal network with medium synaptie delay and high level of heterogeneity, which often occurs in real neuronal networks. Two effects of post-synaptic potentials （PSP） to network synchronization are presented, and the synaptic contribution of excitatory and inhibitory neurons to robust synchronization in this E/I network is investigated. It is found that both excitatory and inhibitory neurons may contribute to robust synchronization in E/I networks, especially the excitatory PSP has a more positive effect on synchronization in E/I networks than that in excitatory networks. This may explain the strong robustness of synchronization in Eli neuronal networks.展开更多
In the context of accelerated globalization,intercity factor flows are becoming in-creasingly dependent on a reasonable and orderly spatial structure.Therefore,an indepth study of the optimization and adjustment of sp...In the context of accelerated globalization,intercity factor flows are becoming in-creasingly dependent on a reasonable and orderly spatial structure.Therefore,an indepth study of the optimization and adjustment of spatial structure is essential for coordinated development.This study quantitatively evaluated urban development levels and introduced network analysis methods to analyse the spatial structure and robustness of development.The results indicated the following:(1)The urban development level in the Beijing-Tianjin-Hebei(BTH)region increased in all dimensions,and the transmission efficiency significantly improved.(2)The spatial structure of the BTH region has been relatively stable,as illustrated by the main pattern of the spatial distribution of central cities,with a trend towards contiguous development.(3)The ranking of network robustness is environment>society>economy,and the core network and key nodes are primarily located within the radiation of the three central cities of Beijing,Tianjin,and Shijiazhuang.(4)The coordinated development of the BTH region is effective but still needs to be optimized and adjusted,and the strategic significance of edge cities has not been completely exploited.This study aims to provide an emerging ana-lytical perspective for optimizing regional spatial structure and promoting regional coordinated development.展开更多
Robustness of deep neural networks(DNNs)has caused great concerns in the academic and industrial communities,especially in safety-critical domains.Instead of verifying whether the robustness property holds or not in c...Robustness of deep neural networks(DNNs)has caused great concerns in the academic and industrial communities,especially in safety-critical domains.Instead of verifying whether the robustness property holds or not in certain neural networks,this paper focuses on training robust neural networks with respect to given perturbations.State-of-the-art training methods,interval bound propagation(IBP)and CROWN-IBP,perform well with respect to small perturbations,but their performance declines significantly in large perturbation cases,which is termed“drawdown risk”in this paper.Specifically,drawdown risk refers to the phenomenon that IBPfamily training methods cannot provide expected robust neural networks in larger perturbation cases,as in smaller perturbation cases.To alleviate the unexpected drawdown risk,we propose a global and monotonically decreasing robustness training strategy that takes multiple perturbations into account during each training epoch(global robustness training),and the corresponding robustness losses are combined with monotonically decreasing weights(monotonically decreasing robustness training).With experimental demonstrations,our presented strategy maintains performance on small perturbations and the drawdown risk on large perturbations is alleviated to a great extent.It is also noteworthy that our training method achieves higher model accuracy than the original training methods,which means that our presented training strategy gives more balanced consideration to robustness and accuracy.展开更多
A new parameter coordination and robust optimization approach for multidisciplinary design is presented. Firstly, the constraints network model is established to support engineering change, coordination and optimizati...A new parameter coordination and robust optimization approach for multidisciplinary design is presented. Firstly, the constraints network model is established to support engineering change, coordination and optimization. In this model, interval boxes are adopted to describe the uncertainty of design parameters quantitatively to enhance the design robustness. Secondly, the parameter coordination method is presented to solve the constraints network model, monitor the potential conflicts due to engineering changes, and obtain the consistency solution space corresponding to the given product specifications. Finally, the robust parameter optimization model is established, and genetic arithmetic is used to obtain the robust optimization parameter. An example of bogie design is analyzed to show the scheme to be effective.展开更多
Finding out the key node sets that affect network robustness has great practical significance for network protection and network disintegration.In this paper,the problem of finding key node sets in complex networks is...Finding out the key node sets that affect network robustness has great practical significance for network protection and network disintegration.In this paper,the problem of finding key node sets in complex networks is defined firstly.Because it is an NP-hard combinatorial optimization problem,discrete fireworks algorithm is introduced to search the optimal solution,which is a swarm intelligence algorithm and is improved by the prior information of networks.To verify the effect of improved discrete fireworks algorithm(IDFA),experiments are carried out on various model networks and real power grid.Results show that the proposed IDFA is obviously superior to the benchmark algorithms,and networks suffer more damage when the key node sets obtained by IDFA are removed from the networks.The key node sets found by IDFA contain a large number of non-central nodes,which provides the authors a new perspective that the seemingly insignificant nodes may also have an important impact on the robustness of the network.展开更多
Analyzing network robustness under various circumstances is generally regarded as a challenging problem.Robustness against failure is one of the essential properties of large-scale dynamic network systems such as powe...Analyzing network robustness under various circumstances is generally regarded as a challenging problem.Robustness against failure is one of the essential properties of large-scale dynamic network systems such as power grids,transportation systems,communication systems,and computer networks.Due to the network diversity and complexity,many topological features have been proposed to capture specific system properties.For power grids,a popular process for improving a network’s structural robustness is via the topology design.However,most of existing methods focus on localized network metrics,such as node connectivity and edge connectivity,which do not encompass a global perspective of cascading propagation in a power grid.In this paper,we use an informative global metric algebraic connectivity because it is sensitive to the connectedness in a broader spectrum of graphs.Our process involves decreasing the average propagation in a power grid by minimizing the increase in its algebraic connectivity.We propose a topology-based greedy strategy to optimize the robustness of the power grid.To evaluate the network robustness,we calculate the average propagation using MATCASC to simulate cascading line outages in power grids.Experimental results illustrate that our proposed method outperforms existing techniques.展开更多
In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D3 dominates D3 ＋ λ（D2 - D1） for any λ ≥0 if D1 dominat...In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D3 dominates D3 ＋ λ（D2 - D1） for any λ ≥0 if D1 dominates D2. Let u（D） be the set of all the traffic matrices that are dominated by the traffic matrix D. It is shown that u （ D∞） and u （D ∈） are isomorphic. Besides, similar results are obtained on multi-commodity flow problems. Fhrthermore, the results are the generalized to integral flows.展开更多
基金Supported by the Open Cooperation Research in National University of Defense Technology(NUDT)under Grant No 2014021the Graduate Innovation Fund of NUDT under Grant No B150501
文摘Previous work puts forward a random edge rewiring method which is capable of improving the network robustness noticeably, while it lacks further discussions about how to improve the robustness faster. In this study, the detailed analysis of the structures of improved networks show that regenerating the edges between high-degree nodes can enhance the robustness against a targeted attack. Therefore, we propose a novel rewiring strategy based on regenerating more edges between high-degree nodes, called smart rewiring, which could speed up the increase of the robustness index effectively. The smart rewiring method also explains why positive degree-degree correlation could enhance network robustness.
基金Project supported by the National Natural Science Foundation of China (Grant No. 62006169)the Youth Natural Science Foundation of Shanxi Province, China (Grant No. 201901D211304)+1 种基金the China Postdoctoral Science Foundation (Grant No. 2021M692400)the Science and Technology Innovation Projects of Universities in Shanxi Province, China (Grant No. 2020L0021)。
文摘As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored.From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.
文摘The world airport network（WAN） is one of the networked infrastructures that shape today＇s economic and social activity, so its resilience against incidents affecting the WAN is an important problem. In this paper, the robustness of air route networks is extended by defining and testing several heuristics to define selection criteria to detect the critical nodes of the WAN.In addition to heuristics based on genetic algorithms and simulated annealing, custom heuristics based on node damage and node betweenness are defined. The most effective heuristic is a multiattack heuristic combining both custom heuristics. Results obtained are of importance not only for advance in the understanding of the structure of complex networks, but also for critical node detection.
文摘Transportation network vulnerability analysis has developed increasingly in the last decade with the goal to identify the most critical locations against incidences.In this domain,many of the previous researches have focused on congested urban networks;however,there is still a need to consider regional and interurban sparse rail networks,specifically those networks in developing countries.In such sparse rail networks,there are limited possibilities to redirect trains if a link is disrupted,there might be less possibility of finding redundant alternative routes,and network failures are usually accompanied by a phenomenon called‘unsatisfied demand.’The study reported in this paper stemmed from research aimed to design precautionary actions for a developing country’s sparse railway system.Our study framework deemed to find the most vulnerable part of an inter-urban sparse rail network using a network scan approach,which found the consequences of network disruptions.A number of criteria were defined to determine the total cost including unsatisfied demand and additional transportation costs due to disruptions.The results showed that how well the process of the vulnerability analysis,considering the features of both supply and demand sides,can be a guide for railway authorities in applying system safety measures.
基金the National Natural Science Foundation of China(Grant Nos.62203229,61672298,61873326,and 61802155)the Philosophy and Social Sciences Research of Universities in Jiangsu Province(Grant No.2018SJZDI142)+2 种基金the Natural Science Research Projects of Universities in Jiangsu Province(Grant No.20KJB120007)the Jiangsu Natural Science Foundation Youth Fund Project(Grant No.BK20200758)Qing Lan Project and the Science and Technology Project of Market Supervision Administration of Jiangsu Province(Grant No.KJ21125027)。
文摘Network robustness is one of the core contents of complex network security research.This paper focuses on the robustness of community networks with respect to cascading failures,considering the nodes influence and community heterogeneity.A novel node influence ranking method,community-based Clustering-LeaderRank(CCL)algorithm,is first proposed to identify influential nodes in community networks.Simulation results show that the CCL method can effectively identify the influence of nodes.Based on node influence,a new cascading failure model with heterogeneous redistribution strategy is proposed to describe and analyze node fault propagation in community networks.Analytical and numerical simulation results on cascading failure show that the community attribute has an important influence on the cascading failure process.The network robustness against cascading failures increases when the load is more distributed to neighbors of the same community instead of different communities.When the initial load distribution and the load redistribution strategy based on the node influence are the same,the network shows better robustness against node failure.
基金supported in part by the National Science Foundation under Grant No.CPS-1136007
文摘Networked control systems are subject to adversary conditions that affect their network topologies.To ensure reliable system operations,network topologies need to be characterized and managed for their impact on the overall system performance.This paper introduces the concept of network robustness depth for this pursuit.Discrete event systems are used as a foundation to model dynamic behavior of network topologies,support their analysis,and carry out their management.Stochastic analysis relates the link reliability probabilities to a probabilistic characterization of network robustness depth.Several topology management strategies are discussed,including passive methods,random strategies,and optimization methodologies.Their respective benefits and limitations are quantified.By using platoon control as a platform of hybrid(continuous and discrete event) systems and packet erasure channels as a communication protocol,the results are demonstrated with case studies.
基金Project supported in part by the China Scholarships Council (Grant No. 2007103794)the Defence Threat Reduction Agency Award HDTRA1-08-1-0027+5 种基金the James S. McDonnell Foundation 21st Century Initiative in Studying Complex Systems,the National Science Foundation within the DDDAS (CNS-0540348)ITR (DMR-0426737)IIS-0513650 programsthe US Office of Naval Research Award N00014-07-Cthe National Natural Science Foundation of China (Grant Nos. 80678605 and 60903157)the National High Technology Research and Development Program of China (Grant No. 2009AA01Z422)
文摘Despite the large size of most communication and transportation systems, there are short paths between nodes in these networks which guarantee the efficient information, data and passenger delivery; furthermore these networks have a surprising tolerance under random errors thanks to their inherent scale-free topology. However, their scale-free topology also makes them fragile under intentional attacks, leaving us a challenge on how to improve the network robustness against intentional attacks without losing their strong tolerance under random errors and high message and passenger delivering capacity. Here We propose two methods （SL method and SH method） to enhance scale-free network＇s tolerance under attack in different conditions.
基金This project is supported by National Natural Science Foundation of China (No. 5880203).
文摘In order to overcome the system non-linearity and uncertainty inherent in magnetic bearing systems, a GA（genetic algnrithm）-based PID neural network controller is designed and trained tO emulate the operation of a complete system （magnetic bearing, controller, and power amplifiers）. The feasibility of using a neural network to control nonlinear magnetic bearing systems with unknown dynamics is demonstrated. The key concept of the control scheme is to use GA to evaluate the candidate solutions （chromosomes）, increase the generalization ability of PID neural network and avoid suffering from the local minima problem in network learning due to the use of gradient descent learning method. The simulation results show that the proposed architecture provides well robust performance and better reinforcement learning capability in controlling magnetic bearing systems.
基金Project(71001079)supported by the National Natural Science Foundation of China
文摘A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.
基金supported by Grant-in-Aid for Scientific Research(B)#17H03280 from the Ministry of Education,Culture,Sports,Science and Technology of Japan.
文摘One of the typical properties of biological systems is the law o f conservation o f mass,that is,the property that the mass must remain constant over time in a closed chemical reaction system.However,it is known that Boolean networks,which are a promising model of biological networks,do not always represent the conservation law.This paper thus addresses a kind of conservation law as a generic property of Boolean networks.In particular,we consider the problem of finding network structures on which,for any Boolean operation on nodes,the number of active nodes,i.ev nodes whose state is one,is constant over time.As a solution to the problem,we focus on the strongly-connected network structures and present a necessary and sufficient condition.
基金Supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2011FQ002)
文摘In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential stability. Finally, we use one numerical simulation example to illustrate the correctness and effectiveness of our results.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11102038,11472061,70971021,71371046and 61203325the Shanghai Natural Science Foundation under Grant No 13ZR1400200+1 种基金the Undergraduate Education Key Reform Project of Shanghai Universities under Grant No X12071306the Fundamental Research Funds for the Central Universities at Donghua University under Grant Nos 14D110402,2232013D3-39 and 14D110417
文摘It is known that both excitatory and inhibitory neuronal networks can achieve robust synchronization only under certain conditions, such as long synaptic delay or low level of heterogeneity. In this work, robust synchronization can be found in an excitatory/inhibitory （E/I） neuronal network with medium synaptie delay and high level of heterogeneity, which often occurs in real neuronal networks. Two effects of post-synaptic potentials （PSP） to network synchronization are presented, and the synaptic contribution of excitatory and inhibitory neurons to robust synchronization in this E/I network is investigated. It is found that both excitatory and inhibitory neurons may contribute to robust synchronization in E/I networks, especially the excitatory PSP has a more positive effect on synchronization in E/I networks than that in excitatory networks. This may explain the strong robustness of synchronization in Eli neuronal networks.
基金National Key Research and Development Program,No.2023YFC3804001Natural Resources Planning and Management Project,No.A2417,No.A2418。
文摘In the context of accelerated globalization,intercity factor flows are becoming in-creasingly dependent on a reasonable and orderly spatial structure.Therefore,an indepth study of the optimization and adjustment of spatial structure is essential for coordinated development.This study quantitatively evaluated urban development levels and introduced network analysis methods to analyse the spatial structure and robustness of development.The results indicated the following:(1)The urban development level in the Beijing-Tianjin-Hebei(BTH)region increased in all dimensions,and the transmission efficiency significantly improved.(2)The spatial structure of the BTH region has been relatively stable,as illustrated by the main pattern of the spatial distribution of central cities,with a trend towards contiguous development.(3)The ranking of network robustness is environment>society>economy,and the core network and key nodes are primarily located within the radiation of the three central cities of Beijing,Tianjin,and Shijiazhuang.(4)The coordinated development of the BTH region is effective but still needs to be optimized and adjusted,and the strategic significance of edge cities has not been completely exploited.This study aims to provide an emerging ana-lytical perspective for optimizing regional spatial structure and promoting regional coordinated development.
基金supported by the National Key R&D Program of China(No.2022YFA1005101)the National Natural Science Foundation of China(Nos.61872371,62032024,and U19A2062)the CAS Pioneer Hundred Talents Program,China。
文摘Robustness of deep neural networks(DNNs)has caused great concerns in the academic and industrial communities,especially in safety-critical domains.Instead of verifying whether the robustness property holds or not in certain neural networks,this paper focuses on training robust neural networks with respect to given perturbations.State-of-the-art training methods,interval bound propagation(IBP)and CROWN-IBP,perform well with respect to small perturbations,but their performance declines significantly in large perturbation cases,which is termed“drawdown risk”in this paper.Specifically,drawdown risk refers to the phenomenon that IBPfamily training methods cannot provide expected robust neural networks in larger perturbation cases,as in smaller perturbation cases.To alleviate the unexpected drawdown risk,we propose a global and monotonically decreasing robustness training strategy that takes multiple perturbations into account during each training epoch(global robustness training),and the corresponding robustness losses are combined with monotonically decreasing weights(monotonically decreasing robustness training).With experimental demonstrations,our presented strategy maintains performance on small perturbations and the drawdown risk on large perturbations is alleviated to a great extent.It is also noteworthy that our training method achieves higher model accuracy than the original training methods,which means that our presented training strategy gives more balanced consideration to robustness and accuracy.
基金This project is supported by National Natural Science Foundation of China (No.60304015, No.50575142).
文摘A new parameter coordination and robust optimization approach for multidisciplinary design is presented. Firstly, the constraints network model is established to support engineering change, coordination and optimization. In this model, interval boxes are adopted to describe the uncertainty of design parameters quantitatively to enhance the design robustness. Secondly, the parameter coordination method is presented to solve the constraints network model, monitor the potential conflicts due to engineering changes, and obtain the consistency solution space corresponding to the given product specifications. Finally, the robust parameter optimization model is established, and genetic arithmetic is used to obtain the robust optimization parameter. An example of bogie design is analyzed to show the scheme to be effective.
基金supported by the National Natural Science Foundation of China under Grant No.61502522。
文摘Finding out the key node sets that affect network robustness has great practical significance for network protection and network disintegration.In this paper,the problem of finding key node sets in complex networks is defined firstly.Because it is an NP-hard combinatorial optimization problem,discrete fireworks algorithm is introduced to search the optimal solution,which is a swarm intelligence algorithm and is improved by the prior information of networks.To verify the effect of improved discrete fireworks algorithm(IDFA),experiments are carried out on various model networks and real power grid.Results show that the proposed IDFA is obviously superior to the benchmark algorithms,and networks suffer more damage when the key node sets obtained by IDFA are removed from the networks.The key node sets found by IDFA contain a large number of non-central nodes,which provides the authors a new perspective that the seemingly insignificant nodes may also have an important impact on the robustness of the network.
基金supported by the National Natural Science Foundation of China(No.U1866602)the National Key R&D Program of China(Nos.2019YFB1600700 and 2018AAA0101505)。
文摘Analyzing network robustness under various circumstances is generally regarded as a challenging problem.Robustness against failure is one of the essential properties of large-scale dynamic network systems such as power grids,transportation systems,communication systems,and computer networks.Due to the network diversity and complexity,many topological features have been proposed to capture specific system properties.For power grids,a popular process for improving a network’s structural robustness is via the topology design.However,most of existing methods focus on localized network metrics,such as node connectivity and edge connectivity,which do not encompass a global perspective of cascading propagation in a power grid.In this paper,we use an informative global metric algebraic connectivity because it is sensitive to the connectedness in a broader spectrum of graphs.Our process involves decreasing the average propagation in a power grid by minimizing the increase in its algebraic connectivity.We propose a topology-based greedy strategy to optimize the robustness of the power grid.To evaluate the network robustness,we calculate the average propagation using MATCASC to simulate cascading line outages in power grids.Experimental results illustrate that our proposed method outperforms existing techniques.
基金Supported by National Natural Science Foundation of China under Grant No.(1157101511331012)the Open Project of Key Laboratory of Big Data Mining and Knowledge ManagementKnowledge Innovation Program of the Chinese Academy of Sciences under Grant No.(KGCX2-RW-329)
文摘In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D3 dominates D3 ＋ λ（D2 - D1） for any λ ≥0 if D1 dominates D2. Let u（D） be the set of all the traffic matrices that are dominated by the traffic matrix D. It is shown that u （ D∞） and u （D ∈） are isomorphic. Besides, similar results are obtained on multi-commodity flow problems. Fhrthermore, the results are the generalized to integral flows.
