Perfect quantum excitation energy transport via single edge perturbation in a complete network

We consider quantum excitation energy transport (EET) in a network of two-state nodes in the Markovian approximation by employing the Lindblad formulation. We find that EET from an initial site, where the excitation is inserted to the sink, is generally inefficient due to the inhibition of transport by localization of the excitation wave packet in a symmetric, fully-connected network. We demonstrate that the EET efficiency can be significantly increased up to ≈100% by perturbing hopping transport between the initial node and the one connected directly to the sink, while the rate of energy transport is highest at a finite value of the hopping parameter. We also show that prohibiting hopping between the other nodes which are not directly linked to the sink does not improve the efficiency. We show that external dephasing noise in the network plays a constructive role for EET in the presence of localization in the network, while in the absence of localization it reduces the efficiency of EET. We also consider the influence of off-diagonal disorder in the hopping parameters of the network.     

A non-linear analysis of the interactions between parametric and external excitations

Solutions of a non-linear equation having a form often encountered in the study of structural dynamics and in which both parametric and external excitation is present have been obtained analytically and numerically. All the asymptotic (analytical) results can be verified by numerical integration for small values of ϵ. Some other solutions, obtained numerically, cannot be approximated by conventional asymptotic methods. Both types of solutions can exist simultaneously; in these situations the initial conditions determine which solution describes the actual response of the system. The solutions that can be predicted only by numerical means exhibit period multiplications (i.e., the response has a period that is an integral multiple of the period of the excitation) and chaos. In fact, in a certain range of ϵ, one set of initial conditions can lead to period doubling in the response while another set can lead to a response very close to the asymptotic prediction. Very flexible structures can exhibit non-linear characteristics in their response at very small amplitudes of the excitation. The present results serve to illustrate some of the extraordinary behavior that such structures can exhibit and suggest that it may be extremely difficult to develop control systems for them.     

基于在线社交网络的信息传播模型

本文构造了一个基于在线社交网络的信息传播模型.该模型考虑了节点度和传播机理的影响,结合复杂网络和传染病动力学理论,进一步建立了动力学演化方程组.该方程组刻画了不同类型节点随着时间的演化关系,反映了传播动力学过程受到网络拓扑结构和传播机理的影响.本文模拟了在线社交网络中的信息传播过程,并分析了不同类型节点在网络中的行为规律.仿真结果表明:由于在线社交网络的高度连通性,信息在网络中传播的门槛几乎为零;初始传播节点的度越大,信息越容易在网络中迅速传播;中心节点具有较大的社会影响力;具有不同度数的节点在网络中的变 关键词： 在线社交网络 信息传播 微分方程 传染病动力学     

Dynamics of opinion formation in hierarchical social networks: Network structure and initial bias

The dynamics of opinion formation based on a majority rule model is studied in a network with the social hierarchical structure as one of its limits. The exit probability is found to change sensitively with the number of nodes in the system, but not with the parameter of homophyly characterizing the network structure. The consensus time is found to be a result of non-trivial interplay between the network structure characterized by the parameter of homophyly and the initial bias in opinion. For unbiased initial opinion, a common consensus is easier to be reached in a random network than a highly structured hierarchical network and it follows the behavior of the length of shortest paths. For biased initial opinion, a common consensus is easier to be reached in a hierarchical network, as the local majority opinion of the groups may take on the biased opinions and hence be the same.     

Synchronization and information transmission in spatio-temporal networks of deformable units

We study the relationship between synchronization and the rate with which information is exchanged between nodes in a spatio-temporal network that describes the dynamics of classical particles under a substrate Remoissenet-Peyrard potential. We also show how phase and complete synchronization can be detected in this network. The difficulty in detecting phase synchronization in such a network appears due to the highly non-coherent character of the particle dynamics which unables a proper definition of the phase dynamics. The difficulty in detecting complete synchronization appears due to the spatio character of the potential which results in an asymptotic state highly dependent on the initial state.      

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen; (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes.     

Solution of the unanimity rule on exponential, uniform and scalefree networks: A simple model for biodiversity collapse in foodwebs

We solve the Unanimity Rule on networks with exponential, uniform and scalefree degree distributions. In particular we arrive at equations relating the asymptotic number of nodes in one of two states to the initial fraction of nodes in this state. The solutions for exponential and uniform networks are exact, the analytical approximation for the scalefree case is in perfect agreement with simulation results. We use these solutions to provide a theoretical understanding for biodiversity loss in experimental data of foodwebs, which is available for the three network types discussed. The model allows in principle to estimate the critical value of species that have to be removed from the system to induce a complete diversity collapse.     

Asymptotic support of localized solutions of the linearized system of magnetohydrodynamics

The asymptotic behavior of solutions of the Cauchy problem for the linearized system of magnetohydrodynamic equations with initial conditions localized near a two-dimensional surface was obtained by the authors earlier. Here, this asymptotic behavior is refined.     

基于节点拓扑特征的中国基金公司共持网络持股行为波动相关性

选取2003—2012年期间半年度中国基金公司持上市公司股票份额面板数据为样本数据,以基金公司为节点,以同一时刻共持同一家上市公司股票关系为边,以同一时刻共持的上市公司数量为权重,构建中国基金公司共持关系结构等价加权网络(简称共持网络).结合统计物理学等方法,分析了共持网络的拓扑结构稳定性及具有不同拓扑特征值的节点随时间演变过程中与共持网络中三类节点集合持股行为波动相关性.三类节点集合分别为t-1时刻基于某一股票形成的共持关系完全连通子图节点集合(第一类节点集合)、t-1时刻共持网络中非完全连通子图的节点集合(第二类节点集合)、t时刻新进入共持网络的节点集合(第三类节点集合).分析结果显示:1)节点与第二类节点集合持股行为波动呈正相关,且相关系数随着节点集聚系数的增强而增大;2)只有当节点的度和点强度值较高时,节点与第一类和第二类节点集合的持股行为呈正相关;3)不同拓扑特征条件下的节点与第三类节点集合的持股行为均不存在波动相关性.本文提供了一个研究持股行为相关性的新思路,并为进一步研究股票市场结构等价网络及节点重要性差异提供了基础.     

推荐重要节点部署防御策略的优化模型

当前网络安全防御策略集中部署于高连接度节点主要有2个方面的不足: 一是高连接度节点在很多场合中并不是网络通信的骨干节点; 二是该类节点对信息的转发和传播并非总是最有效的.针对以上传统部署策略的不足, 改进了恶意病毒程序传播的离散扩散模型并采用中间路径跳数来衡量网络节点的重要程度, 提出了基于介数中心控制力和接近中心控制力模型的重要节点优先推荐部署技术.实验结果显示具有高介数中心控制力和低接近中心控制力的节点相对于传统的高连接度节点无论在无标度网络还是小世界网络均能够对恶意病毒程序的疫情扩散和早期传播速度起到更加有效的抑制作用, 同时验证了网络分簇聚类行为产生的簇团特性也将对恶意程序的传播起到一定的负面影响.     

中国城市航空网络的实证研究与分析

以城市为节点，城市间直航线路为边，实证地研究了中国城市航空网络的拓扑性质.研究表明，中国城市航空网络是一个小世界网络，具有短的平均路径长度和大的簇系数，且其度分布服从双段幂律分布.它的度度相关性质与世界航空网络和北美航空网络都不相同.当度较小时，世界航空网络和北美航空网络都是正相关的，但中国城市航空网络未表现出度度相关性；而对于度较大的节点，世界航空网络中其邻点平均度几乎是一个常值，但中国城市航空网络却呈现出负相关性.以往的实证研究暗示，节点具有明确几何位置的网络，如计算机互联网、电力网络等，不表现层次性.但是中国城市航空网络展现出明显的层次性，表明地理因素对其结构演化的影响并不强烈.进一步地，以城市间直航计划每周提供的座位数为边权，研究了网络的含权性质，发现该网络节点度权之间是幂律相关的，相关指数为1.37.     

Random solution of the Burgers equation in the inviscid case

The structure of solutions of the Burgers equation in the inviscid case is investigated numerically by computing the space-time behavior of the asymptotic solutions expressed as sequences of triangular shock waves. They are sensitively dependent on initial conditions and can display intrinsic randomness, depending on the number of zeros of the initial velocity fields.     

节点结构互异的复杂网络的时空混沌反同步

研究了节点结构互异的离散型时空混沌系统构成复杂网络的反同步问题. 通过构造合适的Lyapunov函数, 确定了复杂网络中连接节点之间的耦合函数的结构以及控制增益的取值范围. 以物理中具有时空混沌行为的激光相位共轭波空间扩展系统、Gibbs电光时空混沌 模型、Bragg声光时空混沌模型以及一维对流方程的离散形式作为 网络节点构成的复杂网络为例进行了仿真模拟, 发现整个网络存在稳定的混沌反同步现象.     

Symmetry induced compression of discrete phase space

A compressed representation is described of the state space of discrete systems with some kind of symmetry of its states. An initial state space is represented as a network of states. Two states are linked if some single process leads from one state to another. The network can be compressed by a grouping of states into classes. States in the same class are represented by nodes of equal degree. Further, subclasses are defined: states belong to the same subclass if their neighbouring states belong to the same subclasses. The goal is that the equilibrium probability distribution of states in the initial network can be found from the probability of subclasses in the compressed network. The approach is applied to three exemplary systems: two pieces of a triangular lattice (25 and 36 nodes) with Ising spins at the lattice nodes, and a roundabout with three access roads and three exit roads. The compression is from 3630 ground states to 12 subclasses, from 263 640 ground states to 409 subclasses, and from 729 states to 55 subclasses, respectively.     

Detecting overlapping communities based on vital nodes in complex networks

Detection of community structures in the complex networks is significant to understand the network structures and analyze the network properties. However, it is still a problem on how to select initial seeds as well as to determine the number of communities. In this paper, we proposed the detecting overlapping communities based on vital nodes algorithm(DOCBVA), an algorithm based on vital nodes and initial seeds to detect overlapping communities. First, through some screening method, we find the vital nodes and then the seed communities through the pretreatment of vital nodes. This process differs from most existing methods, and the speed is faster. Then the seeds will be extended. We also adopt a new parameter of attribution degree to extend the seeds and find the overlapping communities. Finally, the remaining nodes that have not been processed in the first two steps will be reprocessed. The number of communities is likely to change until the end of algorithm. The experimental results using some real-world network data and artificial network data are satisfactory and can prove the superiority of the DOCBVA algorithm.     

复Ginzburg-Landau方程时空混沌的网络同步与参量辨识

研究了参量未知的时空混沌系统构成复杂网络的同步与参量辨识问题. 设计的参量辨识律可以有效地辨识复杂网络中所有节点时空混沌系统中的未知参量. 基于稳定性定理, 通过构造适当的Lyapunov函数, 确定了网络完全同步的条件. 以参量未知的一维复Ginzburg-Landau方程作为网络节点为例, 通过仿真模拟检验了参量辨识律以及同步方法的有效性.     

Effects of Inhibitory Signal on Criticality in Excitatory-Inhibitory Networks

We study the criticality in excitatory-inhibitory networks consisting of excitable elements. We investigate the effects of the inhibitory strength using both numerical simulations and theoretical analysis. We show that the inhibitory strength cannot affect the critical point. The dynamic range is decreased as the inhibitory strength increases.To simulate of decreasing the efficacy of excitation and inhibition which was studied in experiments, we remove excitatory or inhibitory nodes, delete excitatory or inhibitory links, and weaken excitatory or inhibitory coupling strength in critical excitatory-inhibitory network. Decreasing the excitation, the change of the dynamic range is most dramatic as the same as previous experimental results. However, decreasing inhibition has no effect on the criticality in excitatory-inhibitory network.     

Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations

We study the behavior of the wave part of asymptotic solutions to the Cauchy problem for linearized shallow water equations with initial perturbations localized near the origin. The global representation for these solutions based on the generalized Maslov canonical operator was given earlier. The asymptotic solutions are also localized in the neighborhood of certain curves (fronts). The simplification of general formulas and the behavior of asymptotic solutions in a neighborhood of the regular part of fronts was also given earlier. Here the behavior of asymptotic solutions in a neighborhood of the focal point of the fronts is discussed in detail and the proof of formulas announced earlier for the wave equation is given. This paper can be regarded as a continuation of the paper in Russiian Journal of Mathematical Physics 15 (2), 192–221 (2008). In memoriam V.A. Borovikov     

Chaotic switching in a two-person game

We study robust long-term complex behaviour in the Rock-Scissors-Paper game with two players, played using reinforcement learning. The complex behaviour is connected to the existence of a heteroclinic network for the dynamics. This network is made of three heteroclinic cycles consisting of nine equilibria and the trajectories connecting them. We provide analytical proof both for the existence of chaotic switching near the heteroclinic network and for the relative asymptotic stability of at least one cycle in the network, leading to some trajectories paying alternate visits to only two nodes while others follow a complicated sequence of visits to all nodes in the network. Our results are obtained by making use of the symmetry of the original problem, a new approach in the context of learning, and they provide an explanation of numerical results previously obtained by other authors.