Probability Distribution of China Aviation Network Average Degree of Edge Vertices and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of average degree of edge vertices of China aviation network were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the average degrees of edge vertices in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the average degree of edge vertices had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.

Nonlinear Relationship and Its Evolutionary Trace between Node Degree and Average Path Length of China Aviation Network Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the node degree and the average path length of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the node average path length of China aviation network in 1988,1994,2001,2008 and 2015 was calculated.Through regression analysis,it was found that the node degree had a logarithmic relationship with the average length of node path,and the two parameters of the logarithmic relationship had linear evolutionary trace.Key word:China aviation network,complex network,node degree,average length of node path,logarithmic relationship,evolutionary trace.

Probability Distribution of Ratio of China Aviation Network Edge Vertices Degree and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.

Nonlinear Relationship and Its Evolutionary Trace between Node Degree and Nearest Neighbor Average Degree of China Aviation Network Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network, the relationship between the node degree and the nearest neighbor average degree and its evolution trace of China aviation network in 1988, 1994, 2001, 2008 and 2015 were studied. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network. According to the statistical data, the node nearest neighbor average degree of China aviation network in 1988, 1994, 2001, 2008 and 2015 was calculated. Through regression analysis, it was found that the node degree had a negative exponential relationship with the nearest neighbor average degree, and the two parameters of the negative exponential relationship had linear evolution trace.

Probability Distribution of China Aviation Network Nearest Neighbor Average Degree and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of node nearest neighbor average degree of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the nearest neighbor average degrees of nodes in China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the nearest neighbor average degree had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.

THE STUDY ON DEGREE DISTRIBUTION PROPERTY OF COMPLEX NETWORK BASED ON COOPERATIVE COMMUNICATION

Complex networks have been widely studied. Recently,many results show that the degree distributions of some large networks follow the form of power-law and these networks possess better robustness against random nodes failure. As an effective technology on combating the channel fading,wireless cooperative communication is becoming one of the most important methods to improve the wireless communication performances. In this paper,the complex network models based on cooperative communication and non-cooperative communication are established; and the degree distribution properties for them are studied. The simulation results show that the degree distributions of these networks also follow the form of power-law,which means that the addition of cooperative communi-cation links will not change the property of degree distribution and then these networks will possess better robustness against random nodes failure as well.

Evolvement of the System Complexity Degree under Different Time Scalings:an Illustration of the Traffic Flow System

It is investigable how the system scaling affects the system complexity degree. The traffic flow system is taken in this paper as an illustration to study this question. First, the Lempel-Ziv algorithm is introduced for accurate depiction of the complexity degree of the traffic flow system. We gain 3 actual sequences and 20s period traffic flow sequences on the basis of the measure of the traffic flow data; we gain 5 traffic flow sequences whose periods are between 1-5min by simulating the traffic flow system. By calculating the complicacy of the 11 sequences, we obtain two hypothesis: the complicacies of the same system are different under different time scalings; negative correlation exists between the complicacy and the time scaling of the system.

NEW METHOD TO ESTIMATE SCALING EXPONENTS OF POWER-LAW DEGREE DISTRIBUTION AND HIERARCHICAL CLUSTERING FUNCTION FOR COMPLEX NETWORKS

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.

Study on Complex System Evaluation Method Based on PCA and Grey Relative Degree

The complexity and limited data samples in evaluation of complex system are obstacles for traditional evaluation method. Based on Grey relative degree theory and principal components analysis (PCA) method, a novel systemic evaluation method is put forward in this paper. Firstly, standardization method is modified for evaluation objective, and the method includes expression (2) and (3). Secondly, for few schemes of complex system, grey relative degree, expression (5), is substituted for relation coefficient. At last, validity of the method is verified by evaluating 3 schemes of a type of UUV.

EFFECT OF Si CONTENT ON ORDERING DEGREE AND ELECTROMAGNETIC CHARACTERISTICS IN FeSiAl ALLOYS

FeSiAl alloys ribbons synthesized by melt-quench were annealed in vacuum at 873 K for 60 rain. The flaky powders were prepared by milling the annealed ribbons for 70 h. After milling, the powders were heat treated at 573 K for 90 rain. The ordering degree of the powders lattice structure was analyzed by X-ray diffraction （XRD）. The measurement of specific saturation magnetization was carried out by vibrating samples magnetometer （VSM）. Complex permittivity and complex permeability in the frequency band of 0.5-18 GHz were measured with the vector network analyzer. The ordering degree of the superlattice structure increased from 0.2＇7 to 0.49. Complex permittivity and complex permeability decreased with increasing Si content. After ordering, the specific saturation magnetization decreased from 134.2 to 85.0 A.m2.kg-1. For use in anti-EMI material, the total contents of Si and Al in FeSiAl alloys should be controlled at a low level.

Degree distribution and robustness of cooperative communication network with scale-free model

With the requirements of users enhanced for wireless communication, the cooperative communication will become a development trend in future. In this paper, a model based on complex networks with both preferential attachment is researched to solve an actual network CCN （Cooperative Communication Network）. Firstly, the evolution of CCN is given by four steps with different probabilities. At the same time, the rate equations of nodes degree are presented to analyze the evolution of CCN. Secondly, the degree distribution is analyzed by calculating the rate equation and numerical simulation. Finally, the robustness of CCN is studied by numerical simulation with random attack and intentional attack to analyze the effects of degree distribution and average path length. The results of this paper are more significant for building CCN to programme the resource of communication.

The effects of degree correlations on network topologies and robustness

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence （set of degrees） is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.

An optimized framework for degree distribution in LT codes based on power law

LT codes are practical realization of digital fountain codes, which provides the concept of rateless coding. In this scheme, encoded symbols are generated infinitely from k information symbols. Decoder uses only(1+α)k number of encoded symbols to recover the original information. The degree distribution function in the LT codes helps to generate a random graph also referred as tanner graph. The artifact of tanner graph is responsible for computational complexity and overhead in the LT codes. Intuitively, a well designed degree distribution can be used for an efficient implementation of LT codes. The degree distribution function is studied as a function of power law, and LT codes are classified into two different categories: SFLT and RLT codes. Also, two different degree distributions are proposed and analyzed for SFLT codes which guarantee optimal performance in terms of computational complexity and overhead.

Low-degree toroidal modes from the Sumatra-Andaman event observed by superconducting gravimeters

The complex frequencies of the low-degree toroidal modes are helpful in constraining the mantle structure.In the early years,the traditional method to detect the low-degree toroidal modes is seismic approach,which is primarily limited by the horizontal noise of seismometers.Recently,it has been proved that gravity method is competitive.Therefore,we re-estimated or newly estimated the complex frequencies of the toroidal modes below 1.5 mHz excited by the 2004 Sumatra-Andaman event using gravity method in this paper.The results show that(1)The quality factors of0 T5-0 T9 and1 T2-1 T3 are estimated from superconducting gravity data for the first time;(2)The estimated frequencies and quality factors for0 T2-0 T9 and1 T2-1 T3 are consistent with those provided by previous publications,which verifies the correctness and effectiveness of our estimations;(3)The maximum difference of frequencies between our results and those from CPREM is on the order of 0.01 mHz and the maximum difference of quality factors is at the level of 10.

Effect of degree correlation on edge controllability of real networks

We use the controllability limit theory to study impact of correlation between in- and out-degrees (degree correlation) on edge controllability of real networks. Simulation results and analytic calculations show that the degree correlation plays an important role in the edge controllability of real networks, especially dense real networks. The upper and lower controllability limits hold for all kinds of real networks. Any edge controllability in between the limits is achievable by properly adjusting the degree correlation. In addition, we find that the edge dynamics in some real networks with positive degree correlation may be difficult to control, and explain the rationality of this anomaly based on the controllability limit theory.

CVBEM and FVM Computational Model Comparison for Solving Ideal Fluid Flow in a 90-Degree Bend

While finite volume methodologies (FVM) have predominated in fluid flow computations, many flow problems, including groundwater models, would benefit from the use of boundary methods, such as the Complex Variable Boundary Element Method (CVBEM). However, to date, there has been no reporting of a comparison of computational results between the FVM and the CVBEM in the assessment of flow field characteristics. In this work, the CVBEM is used to develop a flow field vector outcome of ideal fluid flow in a 90-degree bend which is then compared to the computational results from a finite volume model of the same situation. The focus of the modelling comparison in the current work is flow field trajectory vectors of the fluid flow, with respect to vector magnitude and direction. Such a comparison is necessary to validate the development of flow field vectors from the CVBEM and is of interest to many engineering flow problems, specifically groundwater modelling. Comparison of the CVBEM and FVM flow field trajectory vectors for the target problem of ideal flow in a 90-degree bend shows good agreement between the considered methodologies.

考虑节点度紧致化的最优主动解列模型

为解决主动解列模型的连通性和解列模型趋于复杂化导致计算效率下降的问题,本文提出了考虑节点度紧致化的主动解列模型。首先基于单商品流的思想,提出保证孤岛连通性的解析约束;再结合主动解列自身特点和复杂网络中度的概念,提出一种模型紧致化方法以压缩混合整数规划模型的可行域;最后以切负荷与最小潮流中断之和最小为目标求取最优的解列断面。所提模型能保证孤岛内的连通性并且能够较快地求解大型系统的解列问题。3个测试系统的仿真实验表明了该模型的有效性和快速性。

中国省会航空节点城市复杂时空系统协调度变化及空间特征分析

航空运输业提升了城市系统的吸引力并激发新的交通需求,引导城市经济和空间结构快速演进。本文构建了包含经济、规模、外贸、科技、社会、环境、航空等要素在内的城市复杂时空系统指标体系,对中国省会航空节点城市及其构成的7个空管区的复杂时空系统发展的协调程度变化情况及时空聚类特征、空间溢出效应进行了分析。研究发现:2001—2019年,中国31个省会(首府、直辖市)航空节点城市在复杂时空系统发展过程中呈现了或分散、或集中的趋势特征,南方城市在研究末期的协调程度表现更好。7个空管区中,华北区协调度最高,新疆区、西北区、华东区、中南区的协调度水平发展增速较快,航空系统的平均协调度最高。各航空节点城市复杂时空系统协调度的时空聚类模式存在空间分异特征与聚类特征,航空系统在空管区的聚类优势最为突出,经济系统在空管区聚类辐射范围最大。航空、规模、科技与环境系统均表现了正向直接空间溢出效应,经济与科技系统表现了正向间接空间溢出效应。通过全面分析航空节点城市及空管区的复杂时空系统协调度变化,精准判定了航空节点城市多指标系统在区域发展过程中的影响程度及时空分布异质性,对拓展航空地理研究及促进航空节点城市高质量综合发展提供理论依据。

Probability Distribution of Arithmetic Average of China Aviation Network Edge Vertices Nearest Neighbor Average Degree Value and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.