A new deterministic complex network model with hierarchical structure

We introduce a new simple pseudo tree-like network model, deterministic complex network (DCN). The proposed DCN model may simulate the hierarchical structure nature of real networks appropriately and have the unique property of ‘skipping the levels’, which is ubiquitous in social networks. Our results indicate that the DCN model has a rather small average path length and large clustering coefficient, leading to the small-world effect. Strikingly, our DCN model obeys a discrete power-law degree distribution P(k)∝k^−γ, with exponent γ approaching 1.0. We also discover that the relationship between the clustering coefficient and degree follows the scaling law C(k)∼k⁻¹, which quantitatively determines the DCN's hierarchical structure.     

A tree-like complex network model

We propose a new tree-like network model. Our results indicate that the tree-like model has a small-world effect with a small average path length and large clustering coefficient. Strikingly, our tree-like model is scale-free. We also add weight to the links following the network structure. With this adding-weight method, the weight of the nodes shows exponential growth, which is ubiquitous in social networks.     

Symbolic dynamics and computation in model gene networks

We analyze a class of ordinary differential equations representing a simplified model of a genetic network. In this network, the model genes control the production rates of other genes by a logical function. The dynamics in these equations are represented by a directed graph on an n-dimensional hypercube (n-cube) in which each edge is directed in a unique orientation. The vertices of the n-cube correspond to orthants of state space, and the edges correspond to boundaries between adjacent orthants. The dynamics in these equations can be represented symbolically. Starting from a point on the boundary between neighboring orthants, the equation is integrated until the boundary is crossed for a second time. Each different cycle, corresponding to a different sequence of orthants that are traversed during the integration of the equation always starting on a boundary and ending the first time that same boundary is reached, generates a different letter of the alphabet. A word consists of a sequence of letters corresponding to a possible sequence of orthants that arise from integration of the equation starting and ending on the same boundary. The union of the words defines the language. Letters and words correspond to analytically computable Poincare maps of the equation. This formalism allows us to define bifurcations of chaotic dynamics of the differential equation that correspond to changes in the associated language. Qualitative knowledge about the dynamics found by integrating the equation can be used to help solve the inverse problem of determining the underlying network generating the dynamics. This work places the study of dynamics in genetic networks in a context comprising both nonlinear dynamics and the theory of computation. (c) 2001 American Institute of Physics.     

A new collision avoidance model for pedestrian dynamics

The pedestrians can only avoid collisions passively under the action of forces during simulations using the social force model, which may lead to unnatural behaviors. This paper proposes an optimization-based model for the avoidance of collisions, where the social repulsive force is removed in favor of a search for the quickest path to destination in the pedestrian's vision field. In this way, the behaviors of pedestrians are governed by changing their desired walking direction and desired speed. By combining the critical factors of pedestrian movement, such as positions of the exit and obstacles and velocities of the neighbors, the choice of desired velocity has been rendered to a discrete optimization problem. Therefore,it is the self-driven force that leads pedestrians to a free path rather than the repulsive force, which means the pedestrians can actively avoid collisions. The new model is verified by comparing with the fundamental diagram and actual data. The simulation results of individual avoidance trajectories and crowd avoidance behaviors demonstrate the reasonability of the proposed model.     

一种信息传播促进网络增长的网络演化模型

为了研究信息传播过程对复杂网络结构演化的影响,提出了一种信息传播促进网络增长的网络演化模型,模型包括信息传播促进网内增边、新节点通过局域世界建立第一条边和信息传播促进新节点连边三个阶段,通过多次自回避随机游走模拟信息传播过程,节点根据路径节点的节点度和距离与其选择性建立连接。理论分析和仿真实验表明,模型不仅具有小世界和无标度特性,而且不同参数下具有漂移幂律分布、广延指数分布等分布特性,呈现小变量饱和、指数截断等非幂律现象,同时,模型可在不改变度分布的情况下调节集聚系数,并能够产生从同配到异配具有不同匹配模式的网络.     

A two-level complex network model and its application

This paper investigates the competitive relationship and rivalry of industrial markets, using Chinese household electrical appliance firms as a platform for the study. The common complex network models belong to one-level networks in layered classification, while this paper formulates and evaluates a new two-level network model, in which the first level is the whole unweighted-undirected network useful for macro-analyzing the industrial market structure while the second level is a local weighted-directed network capable of micro-analyzing the inter-firm rivalry in the market. It is believed that the relationship is determined by objective factors whereas the action is rather subjective, and the idea in this paper lies in that the objective relationship and the subjective action subjected to this relationship are being simultaneously considered but at deferent levels of the model which may be applicable to many real applications.     

A linear two-state model with complex dynamics

We study the dynamics of a stochastic two-state model in which all forces are linear. While conceptually simple, we show that the behavior of this system is surprisingly complex. The moments of the system undergo a series of bifurcations as either the overall fluctuation rate or the ratio between the two transition rates is varied. The system displays the very counterintuitive behavior in which all its spatial moments diverge in time, and yet the mean time to escape from a region that includes the origin is infinite. Finally, the system displays resonant activation in a particularly transparent way.     

A complex network model for seismicity based on mutual information

Seismicity is the product of the interaction between the different parts of the lithosphere. Here, we model each part of the Earth as a cell that is constantly communicating its state to its environment. As a neuron is stimulated and produces an output, the different parts of the lithosphere are constantly stimulated by both other cells and the ductile part of the lithosphere, and produce an output in the form of a stress transfer or an earthquake. This output depends on the properties of each part of the Earth’s crust and the magnitude of the inputs. In this study, we propose an approach to the quantification of this communication, with the aid of the Information Theory, and model seismicity as a Complex Network. We have used data from California, and this new approach gives a better understanding of the processes involved in the formation of seismic patterns in that region.     

A new local-world evolving network model

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.     

A new electromagnetic particle-in-cell model with adaptive mesh refinement for high-performance parallel computation

A new electromagnetic particle-in-cell (EMPIC) model with adaptive mesh refinement (AMR) has been developed to achieve high-performance parallel computation in distributed memory system. For minimizing the amount and frequency of inter-processor communications, the present study uses the staggering grid scheme with the charge conservation method, which consists only of the local operations. However, the scheme provides no numerical damping for electromagnetic waves regardless of the wavenumber, which results in significant noise in the refinement region that eventually covers over physical signals. In order to suppress the electromagnetic noise, the present study introduces a smoothing method which gives numerical damping preferentially for short wavelength modes. The test simulations show that only a weak smoothing results in drastic reduction in the noise, so that the implementation of the AMR is possible in the staggering grid scheme. The computational load balance among the processors is maintained by a new method termed the adaptive block technique for the domain decomposition parallelization. The adaptive block technique controls the subdomain (block) structure dynamically associated with the system evolution, such that all the blocks have almost the same number of particles. The performance of the present code is evaluated for the simulations of the current sheet evolution. The test simulations demonstrate that the usage of the adaptive block technique as well as the staggering grid scheme enhances significantly the parallel efficiency of the AMR-EMPIC model.     

A generation-attraction model for renewable energy flows in Italy: A complex network approach

In recent years, in Italy, the trend of the electricity demand and the need to connect a large number of renewable energy power generators to the power-grid, developed a novel type of energy transmission/distribution infrastructure. The Italian Transmission System Operator (TSO) and the Distribution System Operator (DSO), worked on a new infrastructural model, based on electronic meters and information technology. In pursuing this objective it is crucial importance to understand how even more larger shares of renewable energy can be fully integrated, providing a constant and reliable energy background over space and time. This is particularly true for intermittent sources as photovoltaic installations due to the fine-grained distribution of them across the Country. In this work we use an over-simplified model to characterize the Italian power grid as a graph whose nodes are Italian municipalities and the edges cross the administrative boundaries between a selected municipality and its first neighbours, following a Delaunay triangulation. Our aim is to describe the power flow as a diffusion process over a network, and using open data on the solar irradiation at the ground level, we estimate the production of photovoltaic energy in each node. An attraction index was also defined using demographic data, in accordance with average per capita energy consumption data. The available energy on each node was calculated by finding the stationary state of a generation-attraction model.     

A new network model for the integer quantum Hall effect

A Landauer–Büttiker-type formulation of backscattering between pairs of opposite directed channels is used to describe the coupling at the nodes of a network. Physically, these nodes correspond to saddle points of a slowly varying lateral potential modulation in a 2D electron system in the high magnetic field regime. We show that the network can be solved without needing a transfer matrix as used by Chalker and Coddington. We use an exponential dependence of the coupling on the filling factor of the associated Landau level. We demonstrate that our network representation allows a quantitative modeling of almost every realistic sample geometry in the quantum Hall regime, including the effect of gate electrodes across a Hall bar.     

在可扩展机群系统上二维分子动力学问题的并行计算

用分子动力学方法可以有效地研究凝聚介质的激波压缩,并在许多领域得到了广泛应用。由于此方法计算量太大,所以研究并行算法和优化计算就显得特别重要。现在,在可扩展机群系统上,实现了分子动力学程序的并行计算。     

Two-population dynamics in a growing network model

We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own population versus between the populations. The model is able to generate all stable triads observed in real social systems. In the framework of rate equations theory, we employ the mean-field approximation to derive analytical expressions of the degree distribution and the local clustering coefficient for each type of nodes. Analytical derivations agree well with numerical simulation results. The assortativity of the potentially violent network qualitatively resembles the connectivity pattern in terrorist networks that was recently reported. The assortativity of the network driven by aggression shows clearly different behavior than the assortativity of the networks with connections of non-aggressive nature in agreement with recent empirical results of an online social system.     

交通流驱动的含权网络

文章对含权复杂网络研究的最近进展给予了评述，特别报道了文章作者最近提出的一个交通流驱动的含权技术网络模型。这一模型能够同时给出网络连接度分布的幂函数律、网络强度分布的幂函数律、网络权重分布的幂函数律，以及高聚集性和非相称混合性等五大特征，因此成功地刻画了真实技术网络的无尺度性质和小世界效应     

A complex network model based on the Gnutella protocol

Gnutella is one of the basic protocols for P2P software. In this paper, a novel network model based on Gnutella is introduced. The mechanism of this network is based on resource occupancy and search activities of peers. As for the structure, the power-law exponent of in-degree γ_in≈4.2, the length of the average shortest path 〈l〉=57.74, and the diameter of the network is 156; these topological properties of the proposed structure differ from known results.     

交通流驱动的含权网络

文章对含权复杂网络研究的最近进展给予了评述,特别报道了文章作者最近提出的一个交通流驱动的含权技术网络模型.这一模型能够同时给出网络连接度分布的幂函数律、网络强度分布的幂函数律、网络权重分布的幂函数律,以及高聚集性和非相称混合性等五大特征,因此成功地刻画了真实技术网络的无尺度性质和小世界效应.     

A new approximation for the dynamics of the transverse ising model

An improved mean field theory, the Reaction Field Approximation, which was previously used to obtain the static properties of model systems of localized spins (Heisenberg, XY, Ising and also more complicated interaction Hamiltonians) is extendend so that dynamical properties of the Ising model in presence of a transverse field can also be calculated. Theq- and -dependent susceptibility is obtained as function of field and temperature, from which the dynamic correlation functions can also be obtained. The dependence of the critical temperature on the transverse field is calculated and a phase diagram is presented.Work partly supported by Conselho Nacional de Desenvolvimento Cientifico e Tecnológico, CNPq, Brazil and by Alexander von Humboldt Stiftung, FRG     

A new approximation for the dynamics of the transverse ising model

An improved mean field theory, the Reaction Field Approximation, which was previously used to obtain the static properties of model systems of localized spins (Heisenberg, XY, Ising and also more complicated interaction Hamiltonians) is extendend so that dynamical properties of the Ising model in presence of a transverse field can also be calculated. Theq- and ω-dependent susceptibility is obtained as function of field and temperature, from which the dynamic correlation functions can also be obtained. The dependence of the critical temperature on the transverse field is calculated and a phase diagram is presented.