Coulomb effects in semiconductor quantum dots

This paper presents a new model for the Internet graph (AS graph) based on the concept of heuristic trade-off optimization, introduced by Fabrikant, Koutsoupias and Papadimitriou in [5] to grow a random tree with a heavily tailed degree distribution. We propose here a generalization of this approach to generate a general graph, as a candidate for modeling the Internet. We present the results of our simulations and an analysis of the standard parameters measured in our model, compared with measurements from the physical Internet graph.Received: 9 February 2004, Published online: 14 May 2004PACS: 89.75.-k Complex systems - 89.75.Hc Networks and genealogical trees - 89.75.Da Systems obeying scaling laws - 89.75.Fb Structures and organization in complex systems - 89.65.Gh Economics; econophysics, financial markets, business and managementLRI: http: //www.lri.fr/~ihameli; CNRS, LIP, ENS Lyon : http: //www.ens-lyon.fr/~nschaban     

一种基于文本互信息的金融复杂网络模型

复杂网络能够解决许多金融问题,能够发现金融市场的拓扑结构特征,反映不同金融主体之间的相互依赖关系.相关性度量在金融复杂网络构建中至关重要.通过将多元金融时间序列符号化,借鉴文本特征提取以及信息论的方法,定义了一种基于文本互信息的相关系数.为检验方法的有效性,分别构建了基于不同相关系数(Pearson和文本互信息)和不同网络缩减方法(阈值和最小生成树)的4个金融复杂网络模型.在阈值网络中提出了使用分位数来确定阈值的方法,将相关系数6等分,取第4部分的中点作为阈值,此时基于Pearson和文本互信息的阈值模型将会有相近的边数,有利于这两种模型的对比.数据使用了沪深两地证券市场地区指数收盘价,时间从2006年1月4日至2016年12月30日,共计2673个交易日.从网络节点相关性看,基于文本互信息的方法能够体现出大约20%的非线性相关关系;在网络整体拓扑指标上,本文计算了4种指标,结果显示能够使所保留的节点联系更为紧密,有效提高保留节点的重要性以及挖掘出更好的社区结构;最后,计算了阈值网络的动态指标,将数据按年分别构建网络,缩减方法只用了阈值方法,结果显示本文提出的方法在小世界动态和网络度中心性等指标上能够成功捕捉到样本区间内存在的两次异常波动.此外,本文构建的地区金融网络具有服从幂律分布、动态稳定性、一些经济欠发达地区在金融地区网络中占据重要地位等特性.     

Finding communities in linear time: a physics approach

We present a method that allows for the discovery of communities within graphs of arbitrary size in times that scale linearly with their size. This method avoids edge cutting and is based on notions of voltage drops across networks that are both intuitive and easy to solve regardless of the complexity of the graph involved. We additionally show how this algorithm allows for the swift discovery of the community surrounding a given node without having to extract all the communities out of a graph.Received: 29 October 2003, Published online: 14 May 2004PACS: 89.75.Fb Structures and organization in complex systems - 89.75.Hc Networks and genealogical trees     

Community analysis in social networks

We present an empirical study of different social networks obtained from digital repositories. Our analysis reveals the community structure and provides a useful visualising technique. We investigate the scaling properties of the community size distribution, and find that all the networks exhibit power law scaling in the community size distributions with exponent either -0.5 or -1. Finally we find that the networks community structure is topologically self-similar using the Horton-Strahler index.Received: 3 November 2003, Published online: 14 May 2004PACS: 89.75.Fb Structures and organization in complex systems - 89.75.Da Systems obeying scaling laws - 89.75.Hc Networks and genealogical trees     

Modelling one-dimensional driven diffusive systems by the Zero-Range Process

In order to characterize networks in the scale-free network class we study the frequency of cycles of length h that indicate the ordering of network structure and the multiplicity of paths connecting two nodes. In particular we focus on the scaling of the number of cycles with the system size in off-equilibrium scale-free networks. We observe that each off-equilibrium network model is characterized by a particular scaling in general not equal to the scaling found in equilibrium scale-free networks. We claim that this anomalous scaling can occur in real systems and we report the case of the Internet at the Autonomous System Level.Received: 15 January 2004, Published online: 14 May 2004PACS: 89.75.-k Complex systems - 89.75.Hc Networks and genealogical trees     

Equity trees and graphs via information theory

We investigate the similarities and differences between two measures of the relationship between equities traded in financial markets. Our measures are the correlation coefficients and the mutual information. In the context of financial markets correlation coefficients are well established whereas mutual information has not previously been as well studied despite its theoretically appealing properties. We show that asset trees which are derived from either the correlation coefficients or the mutual information have a mixture of both similarities and differences at the individual equity level and at the macroscopic level. We then extend our consideration from trees to graphs using the “genus 0” condition recently introduced in order to study the networks of equities.     

Structure of cycles and local ordering in complex networks

We study the properties of quantities aimed at the characterization of grid-like ordering in complex networks. These quantities are based on the global and local behavior of cycles of order four, which are the minimal structures able to identify rectangular clustering. The analysis of data from real networks reveals the ubiquitous presence of a statistically high level of grid-like ordering that is non-trivially correlated with the local degree properties. These observations provide new insights on the hierarchical structure of complex networks.Received: 6 November 2003, Published online: 17 February 2004PACS: 89.75.-k Complex systems - 89.75.Fb Structures and organization in complex systems     

Modeling the world-wide airport network

Recently, we have presented the first exhaustive analysis of the world-wide airport network. Two important results of that study are that: (i) the world-wide airport network is a small-world network with power-law decaying degree and betweenness centrality distributions; (ii) the most connected cities (largest degree) are typically not the most central cities (largest betweenness centrality). This second finding is particularly significant because of results demonstrating that nodes with high betweenness tend to play a more important role in keeping networks connected than those with high degree. Here, we investigate if current network models can explain this finding and we show that they cannot. Thus, we propose a new model that explains this behavior in terms of the geo-political constraints that affect the growth of the airport network. We further hypothesize that in other infrastructures, affected by similar geo-political constraints, critical locations might not coincide with highly-connected hubs.Received: 14 January 2004, Published online: 14 May 2004PACS: 89.75.Fb Structures and organization in complex systems - 89.75.Da Systems obeying scaling laws - 89.40.Dd Air transporation     

Activity autocorrelation in financial markets

We study the activity of financial markets, i.e., the number of transactions per unit of time. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power-law which ultimately recovers an exponential behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.Received: 15 March 2004, Published online: 8 June 2004PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 05.45.Tp Time series analysis - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion     

Efficiency and robustness in ant networks of galleries

Recent theoretical and empirical studies have focused on the topology of large networks of communication/interactions in biological, social and technological systems. Most of them have been studied in the scope of the small-world and scale-free networks theory. Here we analyze the characteristics of ant networks of galleries produced in a 2-D experimental setup. These networks are neither small-worlds nor scale-free networks and belong to a particular class of network, i.e. embedded planar graphs emerging from a distributed growth mechanism. We compare the networks of galleries with both minimal spanning trees and greedy triangulations. We show that the networks of galleries have a path system efficiency and robustness to disconnections closer to the one observed in triangulated networks though their cost is closer to the one of a tree. These networks may have been prevented to evolve toward the classes of small-world and scale-free networks because of the strong spatial constraints under which they grow, but they may share with many real networks a similar trend to result from a balance of constraints leading them to achieve both path system efficiency and robustness at low cost.Received: 16 July 2004, Published online: 26 November 2004PACS: 89.75.Fb Structures and organization in complex systems - 89.75.Hc Networks and genealogical trees - 87.23.Ge Dynamics of social systems     

Thermodynamic properties of an alternating-spin (1/2,1) two-leg ladder

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding evidence of orders of magnitude differences in the fluxes of individual nodes. This dynamical inhomogeneity reflects the emergence of localized high flux regions or hot spots, carrying an overwhelming fraction of the networks activity. We find that each system is characterized by a unique scaling law, coupling the flux fluctuations with the total flux on individual nodes, a result of the competition between the systems internal collective dynamics and changes in the external environment. We propose a method to separate these two components, allowing us to predict the relevant scaling exponents. As high fluctuations can lead to dynamical bottlenecks and jamming, these findings have a strong impact on the predictability and failure prevention of complex transportation networks.Received: 25 October 2003, Published online: 17 February 2004PACS: 89.75.-k Complex systems - 89.75.Da Systems obeying scaling laws - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion     

The structure and resilience of financial market networks

Financial markets can be viewed as a highly complex evolving system that is very sensitive to economic instabilities. The complex organization of the market can be represented in a suitable fashion in terms of complex networks, which can be constructed from stock prices such that each pair of stocks is connected by a weighted edge that encodes the distance between them. In this work, we propose an approach to analyze the topological and dynamic evolution of financial networks based on the stock correlation matrices. An entropy-related measurement is adopted to quantify the robustness of the evolving financial market organization. It is verified that the network topological organization suffers strong variation during financial instabilities and the networks in such periods become less robust. A statistical robust regression model is proposed to quantity the relationship between the network structure and resilience. The obtained coefficients of such model indicate that the average shortest path length is the measurement most related to network resilience coefficient. This result indicates that a collective behavior is observed between stocks during financial crisis. More specifically, stocks tend to synchronize their price evolution, leading to a high correlation between pair of stock prices, which contributes to the increase in distance between them and, consequently, decrease the network resilience.     

Cut-offs and finite size effects in scale-free networks

We analyze the degree distributions cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices N is ruled by the topological constraints induced by the connectivity structure of the network. Even in the simple case of uncorrelated networks, we obtain an expression of the structural cut-off that is smaller than the natural cut-off obtained by means of extremal theory arguments. The obtained results are explicitly applied in the case of the configuration model to recover the size scaling of tadpoles and multiple edges.Received: 18 November 2003, Published online: 24 February 2004PACS: 89.75.-k Complex systems - 87.23.Ge Dynamics of social systems - 05.70.Ln Nonequilibrium and irreversible thermodynamics     

Distribution of the Japanese posted land price and the generalized entropy

The land price can be considered as the economic data which reflects the interactive activity of markets (land market). Since the cumulative distributions often exhibit power law behavior in a number of complex systems, we attempted to investigate the posted land prices available in Japan for the most recent six years of the recession period after the bubble economy. They also seem to be in this category within a certain range. We observe that the generalized exponential function with one parameter which has been frequently used in generalized thermostatistics serving to track the annual change of the distributions.Received: 20 November 2003, Published online: 8 June 2004PACS: 05.90. + m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems - 89.90. + n Other topics in areas of applied and interdisciplinary physics - 89.75.Da Systems obeying scaling laws     

Large deviations in spin-glass ground-state energies

Many crystalline networks can be viewed as decorations of triply periodic minimal surfaces. Such surfaces are covered by the hyperbolic plane in the same way that the Euclidean plane covers a cylinder. Thus, a symmetric hyperbolic network can be wrapped onto an appropriate minimal surface to obtain a 3d periodic net. This requires symmetries of the hyperbolic net to match the symmetries of the minimal surface. We describe a systematic algorithm to find all the hyperbolic symmetries that are commensurate with a given minimal surface, and the generation of simple 3d nets from these symmetry groups.PACS: 61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling - 89.75.Hc Networks and genealogical trees - 02.20.-a Group theory - 02.40.-k Geometry, differential geometry, and topologyThis revised version was published online in July 2004. It contains colour changes to Figure 6.     

Associative memory on a small-world neural network

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered networks are unable to recover the patterns, and are always attracted to non-symmetric mixture states. Besides, for a range of the number of stored patterns, the efficacy has a maximum at an intermediate value of the disorder. We also give a statistical characterization of the spurious attractors for all values of the disorder of the network.Received: 12 January 2004, Published online: 28 May 2004PACS: 84.35. + i Neural networks - 89.75.Hc Networks and genealogical trees - 87.18.Sn Neural networks     

Parametric and nonparametric Granger causality testing: Linkages between international stock markets

This study investigates long-term linear and nonlinear causal linkages among eleven stock markets, six industrialized markets and five emerging markets of South-East Asia. We cover the period 1987-2006, taking into account the on-set of the Asian financial crisis of 1997. We first apply a test for the presence of general nonlinearity in vector time series. Substantial differences exist between the pre- and post-crisis period in terms of the total number of significant nonlinear relationships. We then examine both periods, using a new nonparametric test for Granger noncausality and the conventional parametric Granger noncausality test. One major finding is that the Asian stock markets have become more internationally integrated after the Asian financial crisis. An exception is the Sri Lankan market with almost no significant long-term linear and nonlinear causal linkages with other markets. To ensure that any causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VAR filtered residuals and VAR filtered squared residuals for the post-crisis sample. We find quite a few remaining significant bi- and uni-directional causal nonlinear relationships in these series. Finally, after filtering the VAR-residuals with GARCH-BEKK models, we show that the nonparametric test statistics are substantially smaller in both magnitude and statistical significance than those before filtering. This indicates that nonlinear causality can, to a large extent, be explained by simple volatility effects.     

Statistical properties of agent-based models in markets with continuous double auction mechanism

Real world markets display power-law features in variables such as price fluctuations in stocks. To further understand market behavior, we have conducted a series of market experiments on our web-based prediction market platform which allows us to reconstruct transaction networks among traders. From these networks, we are able to record the degree of a trader, the size of a community of traders, the transaction time interval among traders and other variables that are of interest. The distributions of all these variables show power-law behavior. On the other hand, agent-based models have been proposed to study the properties of real financial markets. We here study the statistical properties of these agent-based models and compare them with the results from our web-based market experiments. In this work, three agent-based models are studied, namely, zero-intelligence (ZI), zero-intelligence-plus (ZIP) and Gjerstad-Dickhaut (GD). Computer simulations of variables based on these three agent-based models were carried out. We found that although being the most naive agent-based model, ZI indeed best describes the properties observed in real markets. Our study suggests that the basic ingredient to produce the observed properties from real world markets could in fact be the result of a continuously evolving dynamical system with basic features similar to the ZI model.     

Comparing the structure of an emerging market with a mature one under global perturbation

In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection.     

Effects of saving and spending patterns on holding time distribution

The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly, and a power law when the saving factor is set diversely. The power distribution can also be obtained by proposing a new model where the preferential spending behavior is considered. The association of the distribution with the probability of money to be exchanged has also been discussed.Received: 4 September 2003, Published online: 19 November 2003PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 87.23.Ge Dynamics of social systems - 05.10.-a Computational methods in statistical physics and nonlinear dynamics - 02.50.-r Probability theory, stochastic processes, and statistics