This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking...This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking capacity for systems with uncertainties and disturbances. First, SMC discrete equivalent control law is designed on the basis of the nominal model of the system and the adaptive exponential reaching law, and subsequently, stability of the algorithm is analyzed. Second, RBF network is used to f...展开更多
Based on the assumptions of ＂information transfer＂ and ＂information creation＂, this paper educes the multiplied growth mechanism of network information： that the gross quantity of network information （Im） is ab...Based on the assumptions of ＂information transfer＂ and ＂information creation＂, this paper educes the multiplied growth mechanism of network information： that the gross quantity of network information （Im） is about n times as much as the quantity of real network information （Ir）. According to this theoretical model, we give a uniform explanation to all kinds of information growth models in existence, and put forward some proposals, such as ＂forbidding information transfer＂ and ＂building up the central information base＂, to control the repeated information flooding on the network and facilitate the full use of network information.展开更多
A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the ...A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS （Kolmogorov-Smirnov） test statistics for 10 CNN （Connecting Nearest-Neighbor） networks.展开更多
This paper,using pseudo-conservation laws in cyclic-service systems, derives some expressions for the weighted sum of the mean waiting time token ring networks with exhaustive limitedservice policies on condition that...This paper,using pseudo-conservation laws in cyclic-service systems, derives some expressions for the weighted sum of the mean waiting time token ring networks with exhaustive limitedservice policies on condition that messages arrived with batch Poisson, and discusses boundary conditions. At the same time, the results of the token ring network with exhaustive and non-exhaustiveservice strategy are obtained. Finally the exact expression of mean waiting time in symmetric ringnetwork with same service strategy is given.展开更多
It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One exampl...It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One example is the scale-freeness which is described by the degree distribution in the power law shape. In this paper, within an analytical approach, we investigate the analytical conditions under which the distribution is reduced to the power law. We show that power law distributions are obtained without introducing conditions specific to each system or variable. Conversely, if we demand no special condition to a distribution, it is imposed to follow the power law. This result explains the universality and the ubiquitous presence of the power law distributions in complex networks.展开更多
This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolut...This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.展开更多
为准确求解双曲守恒律,得到高分辨率数值结果,将数据驱动与三阶CCWENO(Compact Central Weighted Essentially Non-Oscillatory)格式相结合,提出了一种基于数据驱动的CCWENO-ANN高分辨率格式求解双曲守恒律。通过构建人工神经网络的归...为准确求解双曲守恒律,得到高分辨率数值结果,将数据驱动与三阶CCWENO(Compact Central Weighted Essentially Non-Oscillatory)格式相结合,提出了一种基于数据驱动的CCWENO-ANN高分辨率格式求解双曲守恒律。通过构建人工神经网络的归一化校准层和稀疏化层,引入适当的先验知识,加快收敛速度;同时,损失函数动态地调整神经网络输出与理想权重之间的偏差,并在合适的数据集上采用监督学习策略进行离线训练,以提高神经网络性能。通过一维无粘Burgers方程、一维Euler方程、二维无粘Burgers方程以及二维Euler方程验证算法性能,结果表明本文提出的CCWENO-ANN继承了传统CCWENO格式的收敛性,能够准确捕捉激波和接触间断,具有鲁棒性强、低耗散和高分辨率的优点。展开更多
In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new...In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new local-world evolving network model is proposed in this paper. In the model, not all the nodes obtain local network information, which is different from the local world network model proposed by Li and Chen （LC model）. In the LC model, each node has only the local connections therefore owns only local information about the entire networks. Theoretical analysis and numerical simulation show that adjusting the ratio of the number of nodes obtaining the global information of the network to the total number of nodes can effectively control the valuing range for the power-law exponent of the new network. Therefore, if the topological structure of a complex network, especially its exponent of power-law degree distribution, needs controlling, we just add or take away a few nodes which own the global information of the network.展开更多
A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, N, as the only parameter, two ...A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, N, as the only parameter, two parameters including N and a second parameter α are included in our formula. The parameter α is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.展开更多
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol ...In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.展开更多
Air traffic is a typical complex system, in which movements of traffic components （pilots, controllers, equipment, and environment）, especially airport arrival and departure traffic, form complicated spatial and tem...Air traffic is a typical complex system, in which movements of traffic components （pilots, controllers, equipment, and environment）, especially airport arrival and departure traffic, form complicated spatial and temporal dynamics. The fluctuations of airport arrival and departure traffic are studied from the point of view of networks as the special correlation between different airports. Our collected flow volume data on the time-dependent activity of US airport arrival and departure traffic indicate that the coupling between the average flux and the fluctuation of an individual airport obeys a certain scaling law with a wide variety of scaling exponents between 1/2 and 1. These scaling phenomena can explain the interaction between the airport internal dynamics （e.g. queuing at airports, a ground delay program and following flying traffic） and a change in the external （network-wide） traffic demand （e.g. an increase in traffic during peak hours every day）, allowing us to further understand the mechanisms governing the collective behaviour of the transportation system. We separate internal dynamics from external fluctuations using a scaling law which is helpful for us to systematically determine the origin of fluctuations in airport arrival and departure traffic, uncovering the collective dynamics. Hot spot features are observed in airport traffic data as the dynamical inhomogeneity in the fluxes of individual airports. The intrinsic characteristics of airport arrival and departure traffic under severe weather is discussed as well.展开更多
In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide...In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.展开更多
We study the phenomena of preferential linking in a large-scale evolving online social network and find that the linear preference holds for preferential creation, preferential acceptance, and preferential attachment....We study the phenomena of preferential linking in a large-scale evolving online social network and find that the linear preference holds for preferential creation, preferential acceptance, and preferential attachment. Based on the linear preference, we propose an analyzable model, which illustrates the mechanism of network growth and reproduces the process of network evolution. Our simulations demonstrate that the degree distribution of the network produced by the model is in good agreement with that of the real network. This work provides a possible bridge between the micro=mechanisms of network growth and the macrostructures of online social networks.展开更多
In this paper we propose a simple evolving network with link additions as well as removals. The preferential attachment of link additions is similar to BA model’s, while the removal rule is newly added. From the pers...In this paper we propose a simple evolving network with link additions as well as removals. The preferential attachment of link additions is similar to BA model’s, while the removal rule is newly added. From the perspective of Markov chain, we give the exact solution of the degree distribution and show that whether the network is scale-free or not depends on the parameter m, and the degree exponent varying in （3, 5] is also depend on m if scale-free.展开更多
In this paper,we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads.On individual roads,we consider the standard Lighthill-Whitham-Richards model which is discretiz...In this paper,we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads.On individual roads,we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters.To solve traffic flows on networks,we construct suitable numerical fluxes at junctions based on preferences of the drivers.We prove basic properties of the constructed numerical flux and the resulting scheme and present numerical experiments,including a junction with complicated traffic light patterns with multiple phases.Differences with the approach to numerical fluxes at junctions fromČanićet al.(J Sci Comput 63:233-255,2015)are discussed and demonstrated numerically on a simple network.展开更多
To forecast exactly the key components＇ quantities needed for the mass customization in complex machine manufac-turing,a weighted acyclic networks directed model is constructed,and the power-law distribution of the t...To forecast exactly the key components＇ quantities needed for the mass customization in complex machine manufac-turing,a weighted acyclic networks directed model is constructed,and the power-law distribution of the topological properties for the networks is mined,which makes the relationship between the sum quantities of products and components as well as the relationship between the sum quantities of products and key components clear. The conclusion is that it is an equilibrium network if the time-scale is short and it is a non-equilibrium network if the time-scale is long. As for the evolution law for the components in the mass customiza-tion process,the exponent for equilibrium networks is 0.99 and the exponent for non-equilibrium networks is 1.36.展开更多
文摘This article proposes a novel approach combining exponential-reaching-law-based equivalent control law with radial basis function (RBF) network-based switching law to strengthen the sliding mode control (SMC) tracking capacity for systems with uncertainties and disturbances. First, SMC discrete equivalent control law is designed on the basis of the nominal model of the system and the adaptive exponential reaching law, and subsequently, stability of the algorithm is analyzed. Second, RBF network is used to f...
基金This work was supported by the National Natural Science Foundation of China （Grant No. 70273032）.
文摘Based on the assumptions of ＂information transfer＂ and ＂information creation＂, this paper educes the multiplied growth mechanism of network information： that the gross quantity of network information （Im） is about n times as much as the quantity of real network information （Ir）. According to this theoretical model, we give a uniform explanation to all kinds of information growth models in existence, and put forward some proposals, such as ＂forbidding information transfer＂ and ＂building up the central information base＂, to control the repeated information flooding on the network and facilitate the full use of network information.
基金Project supported by the National Natural Science Foundation of China (Nos.70431002, 70401019)
文摘A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS （Kolmogorov-Smirnov） test statistics for 10 CNN （Connecting Nearest-Neighbor） networks.
文摘This paper,using pseudo-conservation laws in cyclic-service systems, derives some expressions for the weighted sum of the mean waiting time token ring networks with exhaustive limitedservice policies on condition that messages arrived with batch Poisson, and discusses boundary conditions. At the same time, the results of the token ring network with exhaustive and non-exhaustiveservice strategy are obtained. Finally the exact expression of mean waiting time in symmetric ringnetwork with same service strategy is given.
文摘It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One example is the scale-freeness which is described by the degree distribution in the power law shape. In this paper, within an analytical approach, we investigate the analytical conditions under which the distribution is reduced to the power law. We show that power law distributions are obtained without introducing conditions specific to each system or variable. Conversely, if we demand no special condition to a distribution, it is imposed to follow the power law. This result explains the universality and the ubiquitous presence of the power law distributions in complex networks.
基金supported by the National Natural Science Foundation of China(Grant No.70871082)the Shanghai Leading Academic Discipline Project,China(Grant No.S30504)
文摘This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.
文摘为准确求解双曲守恒律,得到高分辨率数值结果,将数据驱动与三阶CCWENO(Compact Central Weighted Essentially Non-Oscillatory)格式相结合,提出了一种基于数据驱动的CCWENO-ANN高分辨率格式求解双曲守恒律。通过构建人工神经网络的归一化校准层和稀疏化层,引入适当的先验知识,加快收敛速度;同时,损失函数动态地调整神经网络输出与理想权重之间的偏差,并在合适的数据集上采用监督学习策略进行离线训练,以提高神经网络性能。通过一维无粘Burgers方程、一维Euler方程、二维无粘Burgers方程以及二维Euler方程验证算法性能,结果表明本文提出的CCWENO-ANN继承了传统CCWENO格式的收敛性,能够准确捕捉激波和接触间断,具有鲁棒性强、低耗散和高分辨率的优点。
基金supported by the Scientific Research Starting Foundation of Hangzhou Dianzi University (Grant No KYS091507073)partly by the National High Technology Research and Development Program of China (Grant No 2005AA147030)
文摘In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new local-world evolving network model is proposed in this paper. In the model, not all the nodes obtain local network information, which is different from the local world network model proposed by Li and Chen （LC model）. In the LC model, each node has only the local connections therefore owns only local information about the entire networks. Theoretical analysis and numerical simulation show that adjusting the ratio of the number of nodes obtaining the global information of the network to the total number of nodes can effectively control the valuing range for the power-law exponent of the new network. Therefore, if the topological structure of a complex network, especially its exponent of power-law degree distribution, needs controlling, we just add or take away a few nodes which own the global information of the network.
基金supported by the National Natural Science Foundation of China (Grant Nos 60672142, 60772053 and 90304005)
文摘A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, N, as the only parameter, two parameters including N and a second parameter α are included in our formula. The parameter α is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70871082)the Shanghai Leading Academic Discipline Project (Grant No. S30504)
文摘In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61039001)
文摘Air traffic is a typical complex system, in which movements of traffic components （pilots, controllers, equipment, and environment）, especially airport arrival and departure traffic, form complicated spatial and temporal dynamics. The fluctuations of airport arrival and departure traffic are studied from the point of view of networks as the special correlation between different airports. Our collected flow volume data on the time-dependent activity of US airport arrival and departure traffic indicate that the coupling between the average flux and the fluctuation of an individual airport obeys a certain scaling law with a wide variety of scaling exponents between 1/2 and 1. These scaling phenomena can explain the interaction between the airport internal dynamics （e.g. queuing at airports, a ground delay program and following flying traffic） and a change in the external （network-wide） traffic demand （e.g. an increase in traffic during peak hours every day）, allowing us to further understand the mechanisms governing the collective behaviour of the transportation system. We separate internal dynamics from external fluctuations using a scaling law which is helpful for us to systematically determine the origin of fluctuations in airport arrival and departure traffic, uncovering the collective dynamics. Hot spot features are observed in airport traffic data as the dynamical inhomogeneity in the fluxes of individual airports. The intrinsic characteristics of airport arrival and departure traffic under severe weather is discussed as well.
基金supported by the National Natural Science Foundation (11071258, 60874083, 10872119, 10901164)
文摘In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61104139,70871082,and 71101053)the ECUST for Excellent Young Scientists,China
文摘We study the phenomena of preferential linking in a large-scale evolving online social network and find that the linear preference holds for preferential creation, preferential acceptance, and preferential attachment. Based on the linear preference, we propose an analyzable model, which illustrates the mechanism of network growth and reproduces the process of network evolution. Our simulations demonstrate that the degree distribution of the network produced by the model is in good agreement with that of the real network. This work provides a possible bridge between the micro=mechanisms of network growth and the macrostructures of online social networks.
基金supported by the National Natural Science Foundation of China (10671212)Research Fund for the Doctoral Program of Higher Education of China (20050533036)
文摘In this paper we propose a simple evolving network with link additions as well as removals. The preferential attachment of link additions is similar to BA model’s, while the removal rule is newly added. From the perspective of Markov chain, we give the exact solution of the degree distribution and show that whether the network is scale-free or not depends on the parameter m, and the degree exponent varying in （3, 5] is also depend on m if scale-free.
基金The work of L.Vacek is supported by the Charles University,project GA UK No.1114119The work of V.Kučera is supported by the Czech Science Foundation,project No.20-01074S.
文摘In this paper,we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads.On individual roads,we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters.To solve traffic flows on networks,we construct suitable numerical fluxes at junctions based on preferences of the drivers.We prove basic properties of the constructed numerical flux and the resulting scheme and present numerical experiments,including a junction with complicated traffic light patterns with multiple phases.Differences with the approach to numerical fluxes at junctions fromČanićet al.(J Sci Comput 63:233-255,2015)are discussed and demonstrated numerically on a simple network.
文摘To forecast exactly the key components＇ quantities needed for the mass customization in complex machine manufac-turing,a weighted acyclic networks directed model is constructed,and the power-law distribution of the topological properties for the networks is mined,which makes the relationship between the sum quantities of products and components as well as the relationship between the sum quantities of products and key components clear. The conclusion is that it is an equilibrium network if the time-scale is short and it is a non-equilibrium network if the time-scale is long. As for the evolution law for the components in the mass customiza-tion process,the exponent for equilibrium networks is 0.99 and the exponent for non-equilibrium networks is 1.36.
