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101.
M. Gligor M. Ausloos 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(4):533-539
GDP/capita correlations are investigated in various time windows (TW), for the time interval 1990–2005. The target group of
countries is the set of 25 EU members, 15 till 2004 plus the 10 countries which joined EU later on. The TW-means of the statistical
correlation coefficients are taken as the weights (links) of a fully connected network having the countries as nodes. Thereafter
we define and introduce the overlapping index of weighted network nodes. A cluster structure of EU countries is derived from the statistically relevant eigenvalues and
eigenvectors of the adjacency matrix. This may be considered to yield some information about the structure, stability and
evolution of the EU country clusters in a macroeconomic sense. 相似文献
102.
Zhongzhi Zhang Shuigeng Zhou Lichao Chen Jihong Guan 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,64(2):277-283
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying
model for the two types of networks. Our model network is governed by a parameter q. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal
dimensions, and betweenness centrality distribution, which are controlled by parameter q. Interestingly, we show that by adjusting q, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from ‘large’ to small worlds
at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal
networks. 相似文献
103.
Zhongzhi Zhang Shuigeng Zhou Yi Qi Jihong Guan 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(4):507-513
The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here
we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform
recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the
main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential
degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations.
Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph.
Interestingly, all the Laplacian eigenvalues are distinct. 相似文献
104.
Zhongzhi Zhang Shuigeng Zhou Zhan Su Tao Zou Jihong Guan 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,65(1):141-147
In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski
network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained results reveal
that the properties of RSN is particularly rich, it is simultaneously scale-free, small-world, uncorrelated, modular, and
maximal planar. All obtained analytical predictions are successfully contrasted with extensive numerical simulations. Our
network representation method could be applied to study the complexity of some real systems in biological and information
fields. 相似文献
105.
106.
Kinkar Ch. Das 《Graphs and Combinatorics》2007,23(6):625-632
Let G = (V,E) be a simple graph with n vertices, e edges and d1 be the highest degree. Further let λi, i = 1,2,...,n be the non-increasing eigenvalues of the Laplacian matrix of the graph G. In this paper, we obtain the following result: For connected graph G, λ2 = λ3 = ... = λn-1 if and only if G is a complete graph or a star graph or a (d1,d1) complete bipartite graph.
Also we establish the following upper bound for the number of spanning trees of G on n, e and d1 only:
The equality holds if and only if G is a star graph or a complete graph. Earlier bounds by Grimmett [5], Grone and Merris [6], Nosal [11], and Kelmans [2] were
sharp for complete graphs only. Also our bound depends on n, e and d1 only.
This work was done while the author was doing postdoctoral research in LRI, Université Paris-XI, Orsay, France. 相似文献
107.
Rü diger Gö bel Saharon Shelah 《Proceedings of the American Mathematical Society》2007,135(6):1641-1649
A module is called absolutely indecomposable if it is directly indecomposable in every generic extension of the universe. We want to show the existence of large abelian groups that are absolutely indecomposable. This will follow from a more general result about -modules over a large class of commutative rings with endomorphism ring which remains the same when passing to a generic extension of the universe. It turns out that `large' in this context has a precise meaning, namely being smaller than the first -Erdos cardinal defined below. We will first apply a result on large rigid valuated trees with a similar property established by Shelah in 1982, and will prove the existence of related `-modules' (-modules with countably many distinguished submodules) and finally pass to -modules. The passage through -modules has the great advantage that the proofs become very transparent essentially using a few `linear algebra' arguments also accessible for graduate students. The result closes a gap of Eklof and Shelah (1999) and Eklof and Mekler (2002), provides a good starting point for Fuchs and Göbel, and gives a new construction of indecomposable modules in general using a counting argument.
108.
109.
可能性概念与可靠性分析 总被引:1,自引:0,他引:1
本文讨论了可能性概念在大系统特别是人-机混合系统的可靠性分析的应用,依据Zadeh的原始思想,人为差错率应该用可能性分析与概率分析来描述,前者描述差错的潜在可能性而后者描述差错发生的实际可能性。这一点,在大型灾害性事故的分析中具有特殊重要意义。 相似文献
110.