Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understand...Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understanding of friendship paradox is very limited.Only few works provide theoretical evidence of single-step and multi-step friendship paradoxes,given that the neighbors of interest are onehop and multi-hop away from the target node.However,they consider non-evolving networks,as opposed to the topology of real social networks that are constantly growing over time.We are thus motivated to present a first look into friendship paradox in evolving networks,where newly added nodes preferentially attach themselves to those with higher degrees.Our analytical verification of both single-step and multistep friendship paradoxes in evolving networks,along with comparison to the non-evolving counterparts,discloses that“friendship paradox is even more paradoxical in evolving networks”,primarily from three aspects:1)we demonstrate a strengthened effect of single-step friendship paradox in evolving networks,with a larger probability(more than 0.8)of a random node’s neighbors having higher average degree than the random node itself;2)we unravel higher effectiveness of multi-step friendship paradox in seeking for influential nodes in evolving networks,as the rate of reaching the max degree node can be improved by a factor of at least Θ(t^(2/3))with t being the network size;3)we empirically verify our findings through both synthetic and real datasets,which suggest high agreements of results and consolidate the reasonability of evolving model for real social networks.展开更多
A cooperative system of a fuzzy logic model and a fuzzy neural network(CSFLMFNN)is proposed,in which a fuzzy logic model is acquired from domain experts and a fuzzy neural network is generated and prewired according t...A cooperative system of a fuzzy logic model and a fuzzy neural network(CSFLMFNN)is proposed,in which a fuzzy logic model is acquired from domain experts and a fuzzy neural network is generated and prewired according to the model.Then PSO-CSFLMFNN is constructed by introducing particle swarm optimization(PSO)into the cooperative system instead of the commonly used evolutionary algorithms to evolve the prewired fuzzy neural network.The evolutionary fuzzy neural network implements accuracy fuzzy inference without rule matching.PSO-CSFLMFNN is applied to the intelligent fault diagnosis for a petrochemical engineering equipment,in which the cooperative system is proved to be effective.It is shown by the applied results that the performance of the evolutionary fuzzy neural network outperforms remarkably that of the one evolved by genetic algorithm in the convergence rate and the generalization precision.展开更多
With the arrival of the 4G and 5G,the telecommunications networks have experienced a large expansion of these networks.That enabled the integration of many services and adequate flow,thus enabling the operators to res...With the arrival of the 4G and 5G,the telecommunications networks have experienced a large expansion of these networks.That enabled the integration of many services and adequate flow,thus enabling the operators to respond to the growing demand of users.This rapid evolution has given the operators to adapt,their methods to the new technologies that increase.This complexity becomes more important,when these networks include several technologies to access different from the heterogeneous network like in the 4G network.The dimensional new challenges tell the application and the considerable increase in demand for services and the compatibility with existing networks,the management of mobility intercellular of users and it offers a better quality of services.Thus,the proposed solution to meet these new requirements is the sizing of the EPC(Evolved Packet Core)core network to support the 5G access network.For the case of Orange Guinea,this involves setting up an architecture for interconnecting the core networks of Sonfonia and Camayenne.The objectives of our work are of two orders:(1)to propose these solutions and recommendations for the heart network EPC sizing and the deployment to be adopted;(2)supply and architectural interconnection in the heart network EPC and an existing heart network.In our work,the model of traffic in communication that we use to calculate the traffic generated with each technology has link in the network of the heart.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 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 multi-local-world model is introduced to describe the evolving networks that have a localization property such as the Internet. Based on this model, we show that the traffic load defined by 'betweenness centrali...A multi-local-world model is introduced to describe the evolving networks that have a localization property such as the Internet. Based on this model, we show that the traffic load defined by 'betweenness centrality' on the multi-local-world scale-free networks' model also follows a power law form. In this kind of network, a few vertices have heavier loads and so play more important roles than the others in the network.展开更多
Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolvi...Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are difficult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges（CNFNOEs） is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion relationship and hierarchy relationship. According to the property difference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is transformed to interlacing layered complex networks（ILCN）. Secondly,the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method.Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distribution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE＇s evolving process and law. Also, the model has good application prospects in structure and dynamics research of transportation network, communication network, social contact network,etc.展开更多
In this paper, we propose an evolving network model growing fast in units of module, according to the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing...In this paper, we propose an evolving network model growing fast in units of module, according to the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected nodes and the nodes between the modules are linked by preferential attachment on degree of nodes. We study the modularity measure of the proposed model, which can be adjusted by changing the ratio of the number of inner- module edges and the number of inter-module edges. In view of the mean-field theory, we develop an analytical function of the degree distribution, which is verified by a numerical example and indicates that the degree distribution shows characteristics of the small-world network and the scale-free network distinctly at different segments. The clustering coefficient and the average path length of the network are simulated numerically, indicating that the network shows the small-world property and is affected little by the randomness of the new module.展开更多
基金supported by NSF China(No.61960206002,62020106005,42050105,62061146002)Shanghai Pilot Program for Basic Research–Shanghai Jiao Tong University.
文摘Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understanding of friendship paradox is very limited.Only few works provide theoretical evidence of single-step and multi-step friendship paradoxes,given that the neighbors of interest are onehop and multi-hop away from the target node.However,they consider non-evolving networks,as opposed to the topology of real social networks that are constantly growing over time.We are thus motivated to present a first look into friendship paradox in evolving networks,where newly added nodes preferentially attach themselves to those with higher degrees.Our analytical verification of both single-step and multistep friendship paradoxes in evolving networks,along with comparison to the non-evolving counterparts,discloses that“friendship paradox is even more paradoxical in evolving networks”,primarily from three aspects:1)we demonstrate a strengthened effect of single-step friendship paradox in evolving networks,with a larger probability(more than 0.8)of a random node’s neighbors having higher average degree than the random node itself;2)we unravel higher effectiveness of multi-step friendship paradox in seeking for influential nodes in evolving networks,as the rate of reaching the max degree node can be improved by a factor of at least Θ(t^(2/3))with t being the network size;3)we empirically verify our findings through both synthetic and real datasets,which suggest high agreements of results and consolidate the reasonability of evolving model for real social networks.
基金Sponsored by the Natural Science Foundation of Guangdong Province of China(Grant No.06029281 and 05011905).
文摘A cooperative system of a fuzzy logic model and a fuzzy neural network(CSFLMFNN)is proposed,in which a fuzzy logic model is acquired from domain experts and a fuzzy neural network is generated and prewired according to the model.Then PSO-CSFLMFNN is constructed by introducing particle swarm optimization(PSO)into the cooperative system instead of the commonly used evolutionary algorithms to evolve the prewired fuzzy neural network.The evolutionary fuzzy neural network implements accuracy fuzzy inference without rule matching.PSO-CSFLMFNN is applied to the intelligent fault diagnosis for a petrochemical engineering equipment,in which the cooperative system is proved to be effective.It is shown by the applied results that the performance of the evolutionary fuzzy neural network outperforms remarkably that of the one evolved by genetic algorithm in the convergence rate and the generalization precision.
文摘With the arrival of the 4G and 5G,the telecommunications networks have experienced a large expansion of these networks.That enabled the integration of many services and adequate flow,thus enabling the operators to respond to the growing demand of users.This rapid evolution has given the operators to adapt,their methods to the new technologies that increase.This complexity becomes more important,when these networks include several technologies to access different from the heterogeneous network like in the 4G network.The dimensional new challenges tell the application and the considerable increase in demand for services and the compatibility with existing networks,the management of mobility intercellular of users and it offers a better quality of services.Thus,the proposed solution to meet these new requirements is the sizing of the EPC(Evolved Packet Core)core network to support the 5G access network.For the case of Orange Guinea,this involves setting up an architecture for interconnecting the core networks of Sonfonia and Camayenne.The objectives of our work are of two orders:(1)to propose these solutions and recommendations for the heart network EPC sizing and the deployment to be adopted;(2)supply and architectural interconnection in the heart network EPC and an existing heart network.In our work,the model of traffic in communication that we use to calculate the traffic generated with each technology has link in the network of the heart.
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This work was supported by the Hong Kong Research Grants Council under the CERG Grants CityU 1031/01E and 1115/03E.
文摘A multi-local-world model is introduced to describe the evolving networks that have a localization property such as the Internet. Based on this model, we show that the traffic load defined by 'betweenness centrality' on the multi-local-world scale-free networks' model also follows a power law form. In this kind of network, a few vertices have heavier loads and so play more important roles than the others in the network.
基金supported by the National Natural Science Foundation of China(615730176140149961174162)
文摘Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are difficult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges（CNFNOEs） is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion relationship and hierarchy relationship. According to the property difference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is transformed to interlacing layered complex networks（ILCN）. Secondly,the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method.Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distribution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE＇s evolving process and law. Also, the model has good application prospects in structure and dynamics research of transportation network, communication network, social contact network,etc.
基金supported by the National Natural Science Foundation of China (Grant No.51078165)the Fundamental Research Funds for Central Universities,China (Grant No.HUST 2010MS030)
文摘In this paper, we propose an evolving network model growing fast in units of module, according to the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected nodes and the nodes between the modules are linked by preferential attachment on degree of nodes. We study the modularity measure of the proposed model, which can be adjusted by changing the ratio of the number of inner- module edges and the number of inter-module edges. In view of the mean-field theory, we develop an analytical function of the degree distribution, which is verified by a numerical example and indicates that the degree distribution shows characteristics of the small-world network and the scale-free network distinctly at different segments. The clustering coefficient and the average path length of the network are simulated numerically, indicating that the network shows the small-world property and is affected little by the randomness of the new module.
