Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy, and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and we obtain expressions for the average search cost both in the presence and the absence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: starlike configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when it is large.     

Correlation structures in short-term variabilities of stock indices and exchange rates

Financial data usually show irregular fluctuations and some trends. We investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) among financial data from the viewpoint of deterministic dynamical systems. Our method is based on the small-shuffle surrogate method. The data we use are daily closing price of Standard & Poor's 500 and the volume, and daily foreign exchange rates, Euro/US Dollar (USD), British Pound/USD and Japanese Yen/USD. We found that these data are not independent.     

Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies

We present a model of complex network generated from Hang Seng index (HSI) of Hong Kong stock market, which encodes stock market relevant both interconnections and interactions between fluctuation patterns of HSI in the network topologies. In the network, the nodes (edges) represent all kinds of patterns of HSI fluctuation (their interconnections). Based on network topological statistic, we present efficient algorithms, measuring betweenness centrality (BC) and inverse participation ratio (IPR) of network adjacency matrix, for detecting topological important nodes. We have at least obtained three uniform nodes of topological importance, and find the three nodes, i.e. 18.7% nodes undertake 71.9% betweenness centrality and closely correlate other nodes. From these topological important nodes, we can extract hidden significant fluctuation patterns of HSI. We also find these patterns are independent the time intervals scales. The results contain important physical implication, i.e. the significant patterns play much more important roles in both information control and transport of stock market, and should be useful for us to more understand fluctuations regularity of stock market index. Moreover, we could conclude that Hong Kong stock market, rather than a random system, is statistically stable, by comparison to random networks.     

Characteristic times in stock market indices

In this study we analyze the Standard and Poor's 500 index data of the New York Stock Exchange for more than 32 years. Using a simple random walk model we demonstrate that the proper variable to look at is the logarithmic return. In the statistical analysis we have done fittings to the Lévy distribution using either the index data as such or pre-processing it with ARCH, GARCH or IGARCH methods, which tend to remove the time-dependent variance. For short times the truncated Lévy distribution is found to fit the data quite well. Since this is not a stable distribution, the scaling behavior observed for short times should brake down for longer times. We demonstrate that the characteristic time where this cross-over starts is of the order of one day.     

Viscoelastic behavior of stock indices

The scattering diagram of a stock index results in a complex network structure, which can be used to analyze the viscoelastic properties of the index. The change along x- or y-direction of the diagram corresponds to purely elastic (or spring like) movement whereas the diagonal change at an angle of 45° corresponds to purely viscous (or dashpot like) movement. The viscous component pushes the price from its current value to any other value, while the elastic component acts like a restoring force. Four indices, namely, DJI, S&P-500, NASDAQ-100, and NASDAQ-composite were studied for the period of 2001-2009. NASDAQ-composite displayed very high elasticity while NASDAQ-100 displayed the highest fluidity in the time period considered. The fluidity of DJI and S&P-500 came out to be close to each other, and they are almost the same in the second half of the period.     

Systemic risk on different interbank network topologies

In this paper we develop an interbank market with heterogeneous financial institutions that enter into lending agreements on different network structures. Credit relationships (links) evolve endogenously via a fitness mechanism based on agents’ performance. By changing the agent’s trust on its neighbor’s performance, interbank linkages self-organize themselves into very different network architectures, ranging from random to scale-free topologies. We study which network architecture can make the financial system more resilient to random attacks and how systemic risk spreads over the network. To perturb the system, we generate a random attack via a liquidity shock. The hit bank is not automatically eliminated, but its failure is endogenously driven by its incapacity to raise liquidity in the interbank network. Our analysis shows that a random financial network can be more resilient than a scale free one in case of agents’ heterogeneity.     

The coevolutionary ultimatum game on different network topologies

In this paper, a model of ultimatum game is discussed from the coevolutionary perspective, where strategy dynamics and structure dynamics coexist. The interplay between structure dynamics and strategy dynamics leads to overwhelmingly interesting evolved topology and fairness behaviors. It is found that fair division emerges for specific ratios of structure updating probability to strategy updating probability. Furthermore, it is shown that the initial structures have no essentially different effect on the coevolutionary results. In particular, the results for strategy are almost similar whenever the initial structure is set to be the nearest-neighbor coupled network, the ER random network or the scale-free network. Besides, the effects of other spatial factors are also investigated, e.g. the population size has a positive influence on the offer, while the average degree has a negative effect. In addition, one extrinsic factor, the background payoff, is also of great importance in promoting fair divisions. Apart from above, we study the properties of the evolved networks, which have the small-world effect and positive assortative behaviors.     

The effects of degree correlations on network topologies and robustness

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence (set of degrees) is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.     

On interrelations of recurrences and connectivity trends between stock indices

Financial data has been extensively studied for correlations using Pearson’s cross-correlation coefficient ρ$\rho$ as the point of departure. We employ an estimator based on recurrence plots — the correlation of probability of recurrence (CPR$CPR$) — to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR$CPR$ approach in order to get more robust results. We examine trends in CPR$CPR$ for an approximately 19-month window moved along the time series and compare them to trends in ρ$\rho$. Binning CPR$CPR$ into three levels of connectedness (strong, moderate, and weak), we extract the trends in number of connections in each bin over time. We also look at the behavior of CPR$CPR$ during the dot-com bubble by shifting the time series to align their peaks. CPR$CPR$ mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonically towards increasing global connectivity. This is in contrast to ρ$\rho$, which gives a picture of ever-increasing correlation. CPR$CPR$ also exhibits that time-shifted markets have high connectivity around the dot-com bubble of 2000. We use significance tests using twin surrogates to interpret all the measures estimated in the study.     

Salient features of dependence in daily US stock market indices

This paper deals with the analysis of long range dependence in the US stock market. We focus first on the log-values of the Dow Jones Industrial Average, Standard and Poors 500 and Nasdaq indices, daily from February, 1971 to February, 2007. The volatility processes are examined based on the squared and the absolute values of the returns series, and the stability of the parameters across time is also investigated in both the level and the volatility processes. A method that permits us to estimate fractional differencing parameters in the context of structural breaks is conducted in this paper. Finally, the “day of the week” effect is examined by looking at the order of integration for each day of the week, providing also a new modeling approach to describe the dependence in this context.     

Long-term memory of the returns in the Chinese stock indices

The modified R/S statistic (MRS) and the local Whittle method (LWM) are used to analyze the long-range dependence on various indices of the Chinese stock markets. The MRS accepts the null hypothesis of no long-range dependence while the LWM rejects it. We also find that the long-range dependence phenomena presented in these markets depend on the time in which they are measured.      

Long-term memory of the returns in the Chinese stock indices

The modified R/S statistic (MRS) and the local Whittle method (LWM) are used to analyze the long-range dependence on various indices of the Chinese stock markets. The MRS accepts the null hypothesis of no long-range dependence while the LWM rejects it. We also find that the long-range dependence phenomena presented in these markets depend on the time in which they are measured.     

Recurrence quantification analysis of global stock markets

This study investigates the presence of deterministic dependencies in international stock markets using recurrence plots and recurrence quantification analysis (RQA). The results are based on a large set of free float-adjusted market capitalization stock indices, covering a period of 15 years. The statistical tests suggest that the dynamics of stock prices in emerging markets is characterized by higher values of RQA measures when compared to their developed counterparts. The behavior of stock markets during critical financial events, such as the burst of the technology bubble, the Asian currency crisis, and the recent subprime mortgage crisis, is analyzed by performing RQA in sliding windows. It is shown that during these events stock markets exhibit a distinctive behavior that is characterized by temporary decreases in the fraction of recurrence points contained in diagonal and vertical structures.     

Statistical properties of stock market indices of different economies

Daily changes in the logarithm of stock market index from 1997 to 2004 are analyzed for countries from three subgroups of economies classified by the International Monetary Fund (IMF): developing Asian countries, newly industrialized Asian economies and major advanced economies. For all markets, the daily changes are well fitted by a non-Gaussian stable probability density. The time evolution of the standard deviation of the daily changes for each market obeys a power law. However, the developing Asian countries have the smallest stable density characteristic parameters α and the largest exponents b of the power law, except China's SSEC and India's SENSEX. The values of α and b for these two markets are closer to those of the newly industrialized Asian economies; in particular, those for China's SSEC are close to those for Hong Kong's HSI. The values of α and b for the newly industrialized Asian economies are in between those for the developing Asian countries and major advanced economies, consistent with the results for generalized Hurst exponent [Physica A 324 (2003) 183]. The daily changes for the developing Asian countries and newly industrialized Asian economies have a weak long-range correlation, whereas the daily changes for the major advanced economies have a weak long-range anti-correlation.     

On local and global currents in mesoscopic conductors

Using linear response theory we show that, in a quasi-stationary state, the local multiprobe conductance of a mesoscopic system of non-interacting electrons with a time reversal invariant Hamiltonian does not depend on the local shape of the driving self-consistent potential and thus is entirely determined by the asymptotic values of the potential in the leads. In the ballistic limit, the local conductance in the lateral direction exhibits oscillations depending on the occupation of channels. Scattering by a point impurity leads to softening of the quantized global conductance steps. In addition to that for an attractive scattering potential, a dip occurs in each plateau regime the shape of which is calculated for different values of the potential strength. We also investigate the local conductance for both a point scatterer and a finite scattering region.     

Finite-time consensus for leader-following multi-agent systems over switching network topologies

Finite-time consensus problem of the leader-following multi-agent system under switching network topologies is studied in this paper.Based on the graph theory,matrix theory,homogeneity with dilation,and LaSalle’s invariance principle,the control protocol of each agent using local information is designed,and the detailed analysis of the leaderfollowing finite-time consensus is provided.Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

Complex stock trading network among investors

We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extract detailed information of each executed order for each trading day and demonstrate that the trade size distributions for different trading days exhibit power-law tails and that most of the estimated power-law exponents are well within the Lévy stable regime. Based on the records of order matching among investors, we can construct a stock trading network for each trading day, in which the investors are mapped into nodes and each transaction is translated as a direct edge from the seller to the buyer with the trade size as its weight. We find that all the trading networks comprise a giant component and have power-law degree distributions and disassortative architectures. In particular, the degrees are correlated with order sizes by a power-law function. By regarding the size of executed order as its fitness, the fitness model can reproduce the empirical power-law degree distribution.     

Peculiar statistical properties of Chinese stock indices in bull and bear market phases

Chinese stock markets have experienced an extraordinary bull market since Jan 2006, which attracted global eyes. We investigate the statistical properties of the indices’ log-return r(t) for the bull market (Jan 2006-Oct 2007) and the previous bear market (Jan 2001-Dec 2005). Here we report three peculiar features of r(t): (i) the cumulative distribution function curve of r(t) in the bull market is similar to that in the bear market; (ii) the autocorrelation function of r(t) in the bull market has a stronger negative correlation and a shorter correlation time than that in the bear market; (iii) the bull market shows stronger long-term correlation than the bear market. This work has relevance to understanding novel statistical properties in economic systems.