共查询到20条相似文献,搜索用时 109 毫秒
1.
BA无标度网络中的SIR模型 总被引:1,自引:0,他引:1
网络化是现代世界的一个重要特征,不仅包括互联网,还包括航空网,人际关系网,而它们都是很典型的无标度网络.在BA无标度网中,结合经典的SIR模型,建立了新的SIR模型,并对模型进行了研究,得到了BA无标度网络对传染病与计算机病毒传播具有脆弱性的结论. 相似文献
2.
当遭遇突发的公共社会安全事件时,具有负面影响的应激行为可能迅速在社会范围内传播扩散,形成群体行为.虽然一些复杂网络的传染模型能够对此进行刻画,但更为符合实际的是行为群体根据一些特性可能划分为不同的亚群体,为此将建立异质节点SIS复杂网络模型.此后,依据亚群体的有效传播率与度分布无关、正相关和负相关三种情形,分别研究了群体行为在异质节点的小世界网络传播特性,及异质节点的无标度网络传播特性.无论是异质节点的小世界网络模型还是异质节点的无标度网络模型,平均场动力学分析和计算机模拟结果显示,当亚群体的传播率与度分布呈正相关时,群体行为的传播会出现放大相应;反之,当亚群体的传播率与度分布成负相关时,群体行为的传播会出现抑制效应.但以上的两种效应在离散性更强的无标度网络上更为明显. 相似文献
3.
该文基于马氏链的概念和技巧, 给出了BA无标度网络模型稳态度分布存在性的严格证明, 并且从数学上重新推导了度分布的精确解析表达式. 此处所用的方法具有一定的普适性, 适用于更一般的无标度型复杂网络模型. 相似文献
4.
《数学物理学报(A辑)》2010,(5)
该文基于马氏链的概念和技巧,给出了BA无标度网络模型稳态度分布存在性的严格证明,并且从数学上重新推导了度分布的精确解析表达式.此处所用的方法具有一定的普适性,适用于更一般的无标度型复杂网络模型. 相似文献
5.
基于二项分布随机增长的无标度网络 总被引:1,自引:0,他引:1
提出—个具有随机增长的无标度网络模型.该模型的演化规则仍然是BA模型的增长和择优连接,但是每一时间间隔添加到网络中的边数是—个具有二项分布的随机变量.通过率方程方法,本文证明了该网络的度分布具有幂律尾部,该模型生成了—个无标度网络. 相似文献
6.
7.
顾华路 《数学的实践与认识》2018,(6)
复杂网络是一种介于规则网络和随机网络之间的网络模型,受生物进化的启发,结合无标度网络的优先连接特性,将进化过程中资源竞争和基因遗传引入到网络的增长过程中,提出一种新的增长模型.仿真实验发现,竞争增长网络模型度分布不再是幂律的,而是服从指数分布.完全遗传竞争增长网络则呈负偏态,且平均度与网络规模取对数后呈线性关系,从数学推导上也证明了这一关系.新模型具有优越的抗恶意攻击能力,且遗传系数越高这种能力越强.另外,网络的平均聚集系数随遗传系数增大而减小,平均路径长度随遗传系数增大而增大.整个模型是拓扑可调的,不同的参数组合可产生具有不同性质的网络模型. 相似文献
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9.
基于金融时间序列的多重分形特征及衡量市场风险的VaR模型,建立我国沪深股市的股票关联网络,实证研究三种网络拓扑结构特征,并使用协整检验方法分析网络稳定性和宏观经济变量间的长期均衡关系。结果表明:股票价格网络不具有无标度性,多标度网络和风险网络都具有无标度性;在三种网络中,风险网络具有更强的鲁棒性。此外,股市波动率和网络稳定系数间互为格兰杰因果关系,股市波动的前期变化能有效解释网络稳定性系数的变化;网络稳定性与宏观经济变量间具有长期的均衡关系,GDP增长率、消费者物价水平CPI对网络稳定性具有正向效应,利率对网络稳定性具有负向效应。风险网络的提出有助于分析我国股市的短期风险及稳定性,并为制定系统风险防御策略提供参考。 相似文献
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11.
We study what happens if, in the Krull-Schmidt Theorem, instead of considering modules whose endomorphism rings have one maximal
ideal, we consider modules whose endomorphism rings have two maximal ideals. If a ring has exactly two maximal right ideals,
then the two maximal right ideals are necessarily two-sided. We call such a ring of type 2. The behavior of direct sums of finitely many modules whose endomorphism rings have type 2 is completely described by a
graph whose connected components are either complete graphs or complete bipartite graphs. The vertices of the graphs are ideals
in a suitable full subcategory of Mod-R. The edges are isomorphism classes of modules. The complete bipartite graphs give rise to a behavior described by a Weak
Krull-Schmidt Theorem. Such a behavior had been previously studied for the classes of uniserial modules, biuniform modules,
cyclically presented modules over a local ring, kernels of morphisms between indecomposable injective modules, and couniformly
presented modules. All these modules have endomorphism rings that are either local or of type 2. Here we present a general
theory that includes all these cases. 相似文献
12.
We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic measures, Green?s functions and Poisson kernels to their continuous counterparts. Among other applications, the results can be used to establish universality of the critical Ising and other lattice models. 相似文献
13.
A. D. Sankey 《Journal of Algebraic Combinatorics》2010,32(1):133-153
Type-II matrices are nonzero complex matrices that were introduced in connection with spin models for link invariants. Type-II
matrices have been found in connection with symmetric designs, sets of equiangular lines, strongly regular graphs, and some
distance regular graphs. We investigate weighted complete and strongly regular graphs, and show that type-II matrices arise
in this setting as well. 相似文献
14.
I. A. Shakirov 《Russian Mathematics (Iz VUZ)》2011,55(10):70-77
Explicit forms of Lebesgue functions are not described in the mathematical literature by now. This issue is related to the
problem of reducing sums of modules of fundamental polynomials or the corresponding Dirichlet kernels. That is why the complete
study of graphs of Lebesgue functions remains a complicated topical problem in the theory of approximation. In this paper
we solve the mentioned problems both for odd and even numbers of interpolation nodes. We find explicit forms of Lebesgue functions
and study them by means of the differential calculus. All mentioned forms are new. 相似文献
15.
We show that the problem to decide whether a graph can be made triangle-free with at most k edge deletions remains NP-complete even when restricted to planar graphs of maximum degree seven. In addition, we provide polynomial-time data reduction rules for this problem and obtain problem kernels consisting of 6k vertices for general graphs and 11k/3 vertices for planar graphs. 相似文献
16.
Nick Dungey 《Semigroup Forum》2006,72(3):404-410
We offer a new, simple method of deriving time regularity estimates
for discrete time "heat kernels". Our method applies, for example, to suitable Markov chains
and to random walks on weighted graphs, and provides Gaussian estimates or Lp off-diagonal estimates for time differences of the iterated kernels. 相似文献
17.
Isidoro Gitler 《Discrete Mathematics》2010,310(3):430-441
We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideals are minimally generated by Gröbner bases. We prove that any graph can be oriented such that its toric ideal is a complete intersection with a universal Gröbner basis determined by the cycles. It turns out that bipartite ring graphs are exactly the bipartite graphs that have complete intersection toric ideals for any orientation. 相似文献
18.
Strongly Regular Decompositions of the Complete Graph 总被引:3,自引:0,他引:3
Edwin R. van Dam 《Journal of Algebraic Combinatorics》2003,17(2):181-201
We study several questions about amorphic association schemes and other strongly regular decompositions of the complete graph. We investigate how two commuting edge-disjoint strongly regular graphs interact. We show that any decomposition of the complete graph into three strongly regular graphs must be an amorphic association scheme. Likewise we show that any decomposition of the complete graph into strongly regular graphs of (negative) Latin square type is an amorphic association scheme. We study strongly regular decompositions of the complete graph consisting of four graphs, and find a primitive counterexample to A.V. Ivanov's conjecture which states that any association scheme consisting of strongly regular graphs only must be amorphic. 相似文献
19.
We consider a class of Boolean networks called and-nets, and we address the question of whether the absence of negative cycle in local interaction graphs implies the existence of a fixed point. By defining correspondences with the notion of kernel in directed graphs, we prove a particular case of this question, and at the same time, we prove new theorems in kernel theory, on the existence and unicity of kernels. 相似文献
20.
Recently Alon and Friedland have shown that graphs which are the union of complete regular bipartite graphs have the maximum number of 1-factors over all graphs with the same degree sequence. We identify two families of graphs that have the maximum number of 1-factors over all graphs with the same number of vertices and edges: the almost regular graphs which are unions of complete regular bipartite graphs, and complete graphs with a matching removed. The first family is determined using the Alon and Friedland bound. For the second family, we show that a graph transformation which is known to increase network reliability also increases the number of 1-factors. In fact, more is true: this graph transformation increases the number of k-factors for all k≥1, and “in reverse” also shows that in general, threshold graphs have the fewest k-factors. We are then able to determine precisely which threshold graphs have the fewest 1-factors. We conjecture that the same graphs have the fewest k-factors for all k≥2 as well. 相似文献