Power-law Properties Research Articles

Power-law correlations in finance-related Google searches, and their cross-correlations with volatility and traded volume: Evidence from the Dow Jones Industrial components

We study power-law correlations properties of the Google search queries for Dow Jones Industrial Average (DJIA) component stocks. Examining the daily data of the searched terms with a combination of the rescaled range and rescaled variance tests together with the detrended fluctuation analysis, we show that the searches are in fact power-law correlated with Hurst exponents between 0.8 and 1.1. The general interest in the DJIA stocks is thus strongly persistent. We further reinvestigate the cross-correlation structure between the searches, traded volume and volatility of the component stocks using the detrended cross-correlation and detrending moving-average cross-correlation coefficients. Contrary to the universal power-law correlations structure of the related Google searches, the results suggest that there is no universal relationship between the online search queries and the analyzed financial measures. Even though we confirm positive correlation for a majority of pairs, there are several pairs with insignificant or even negative correlations. In addition, the correlations vary quite strongly across scales.

Pfaffian orientations and perfect matchings of scale-free networks

Counting perfect matchings is of great interest in theoretical computer science, mathematics, among other disciplines. However, explicitly determining the number of perfect matchings of general graphs is a challenge. In this paper, we present a first analytical study of the enumeration problem of perfect matchings on scale-free networks, which are ubiquitous in real-life systems. We focus on two iteratively growing scale-free networks: one is fractal, while the other is non-fractal. For each network, we construct an orientation and prove that it is Pfaffian. Then, based on the connection between the number of perfect matchings and determinant of the skew adjacency matrix corresponding to a Pfaffian orientation, we derive the recursive expressions for the number of perfect matchings of the networks at two successive iterations. Furthermore, using the recursive relations, we show that for both scale-free networks, their entropy is zero, which is in sharp contrast to the previously obtained results for other networks without scale-free behavior, but having the same average degree as the studied networks, such as square lattice and honeycomb lattice, whose entropies are larger than zero. Our results indicate from another angle that scale-free networks have a distinct architecture in comparison with those lattices lacking the power-law property.

QUASI-PERIODIC PULSATIONS IN SOLAR AND STELLAR FLARES: RE-EVALUATING THEIR NATURE IN THE CONTEXT OF POWER-LAW FLARE FOURIER SPECTRA

The nature of quasi-periodic pulsations in solar and stellar flares remains debated. Recent work has shown that power-law-like Fourier power spectra, also referred to as 'red' noise processes, are an intrinsic property of solar and stellar flare signals, a property that many previous studies of this phenomenon have not accounted for. Hence a re-evaluation of the existing interpretations and assumptions regarding QPP is needed. Here we adopt a Bayesian method for investigating this phenomenon, fully considering the Fourier power law properties of flare signals. Using data from the PROBA2/LYRA, Fermi/GBM, Nobeyama Radioheliograph and Yohkoh/HXT instruments, we study a selection of flares from the literature identified as QPP events. Additionally we examine optical data from a recent stellar flare that appears to exhibit oscillatory properties. We find that, for all but one event tested, an explicit oscillation is not required in order to explain the observations. Instead, the flare signals are adequately described as a manifestation of a power law in the Fourier power spectrum, rather than a direct signature of oscillating components or structures. However, for the flare of 1998 May 8, strong evidence for the existence of an explicit oscillation with P ~ 14-16 s is found in the 17 GHz radio data and the 13-23 keV Yohkoh HXT data. We conclude that, most likely, many previously analysed events in the literature may be similarly described in terms of power laws in the flare Fourier power spectrum, without the need to invoke a narrowband, oscillatory component. As a result the prevalence of oscillatory signatures in solar and stellar flares may be less than previously believed. The physical mechanism behind the appearance of the observed power laws is discussed.

The Effect of Heterogeneous Interactions Among Traders in an Artificial Stock Market

In financial market, one of complex systems, there is highly nonlinear interaction between heterogeneous traders. Due to this nonlinear interaction, emergent behavior, which is so called ‘stylized facts’ occurs in financial market. To understand impact of interaction between heterogeneous traders in financial market, we propose an agent based model, consisting of heterogeneous agents such as fundamentalist, optimist, and pessimist and interaction between them. Fundamentalist who uses the fundamental value of market play a role of stabilizing market, whereas optimist and pessimist they are called by chartist having an investment strategy dominated by the trend of past price has a role of destabilizing market. Optimist (pessimist) forecasts future price will be larger (smaller) than current price. These three type agents change their own types into other types using herding and relative payoff strategy. We consider the topology of interaction between traders using complex network that are constructed by the regular, random, small world and scale-free network. We find that there were observed ‘stylized facts’ such as power-law tails and long memory property of volatility in scale free network. These results support that the heterogeneous and power-law scaling of interaction between traders would be the source of ‘stylized facts’ in financial market.

Modeling and dynamical topology properties of VANET based on complex networks theory

Vehicular Ad hoc Network (VANET) is a special subset of multi-hop Mobile Ad hoc Networks in which vehicles can not only communicate with each other but also with the fixed equipments along the roads through wireless interfaces. Recently, it has been discovered that essential systems in real world share similar properties. When they are regarded as networks, among which the dynamic topology structure of VANET system is an important issue. Many real world networks are actually growing with preferential attachment like Internet, transportation system and telephone network. Those phenomena have brought great possibility in finding a strategy to calibrate and control the topology parameters which can help find VANET topology change regulation to relieve traffic jam, prevent traffic accident and improve traffic safety. VANET is a typical complex network which has its basic characteristics. In this paper, we focus on the macroscopic Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V) inter-vehicle communication network with complex network theory. In particular, this paper is the first one to propose a method analyzing the topological structure and performance of VANET and present the communications in VANET from a new perspective. Accordingly, we propose degree distribution, clustering coefficient and the short path length of complex network to implement our strategy by numerical example and simulation. All the results demonstrate that VANET shows small world network features and is characterized by a truncated scale-free degree distribution with power-law degree distribution. The average path length of the network is simulated numerically, which indicates that the network shows small-world property and is rarely affected by the randomness. What’s more, we carry out extensive simulations of information propagation and mathematically prove the power law property when γ > 2. The results of this study provide useful information for VANET optimization from a macroscopic perspective.

Power-Law Property of High Clustering Network Induced by Deactivation Mechanism

We study the high clustering model of K. Klemm and V.M. Eguiliuz [1]. The basic idea is the growing networks based on a finite memory of the nodes. Our main contributions are as follows: based on the high clustering model, we investigate analytically that it does generate a power-law degree distribution and give the exact solution from the perspective of Markov chain. And the degree exponent varying is depend on the parameters α and m.

Strategies for network security

Security of networks has become an increasingly important issue in the highly connected world. Security depends on attacks. Typical attacks include both cascading failure of virus spreading and of information propagation and physical attacks of removal of nodes or edges. Numerous experiments have shown that none of the existing models construct secure networks, and that the universal properties of power law and small world phenomenon of networks seem unavoidable obstacles for security of networks against attacks. Here, we propose a new strategy of attacks, the attack of rules of evolution of networks. By using the strategy, we proposed a new model of networks which generates provably secure networks. It was shown both analytically and numerically that the best strategy is to attack on the rules of the evolution of networks, that the second best strategy is the attack by cascading failure models, that the third best strategy is the physical attack of removal of nodes or edges, and that the least desirable strategy is the physical attack of deleting structures of the networks. The results characterize and classify the strategies for network security, providing a foundation for a security theory of networks. Equally important, our results demonstrate that security can be achieved provably by structures of networks, that there is a tradeoff between the roles of structures and of thresholds in security engineering, and that power law and small world property are never obstacles of security of networks. Our model explores a number of new principles of networks, including some topological principles, probabilistic principles, and combinatorial principles. The new principles build the foundation for new strategies for enhancing security of networks, and for new protocols of communications and security of the Internet and computer networks etc. We anticipate that our theory can be used in analyzing security of real systems in economy, society and technology.

Multifractal detrended fluctuation analysis to characterize phase couplings in seahorse (Hippocampus kuda) feeding clicks

Nonlinear phenomena in animal vocalizations fundamentally includes known features, namely, frequency jump, subharmonics, biphonation, and deterministic chaos. In the present study, the multifractal detrended fluctuation analysis (MFDFA) has been employed to characterize the phase couplings revealed in the feeding clicks of Hippocampus kuda yellow seahorse. The fluctuation function Fq(s), generalized Hurst exponent h(q), multifractal scaling exponent τ(q), and the multifractal spectrum f(α) calculated in the procedure followed were analyzed to comprehend the underlying nonlinearities in the seahorse clicks. The analyses carried out reveal long-range power-law correlation properties in the data, substantiating the multifractal behavior. The resulting h(q) spectrum exhibits a distinct characteristic pattern in relation to the seahorse sex and size, and reveals a spectral blind spot in the data that was not possible to detect by conventional spectral analyses. The corresponding multifractal spectrum related width parameter Δh(q) is well clustered, defining the individual seahorse clicks. The highest degree of multifractality is evident in the 18 cm male seahorse, signifying greater heterogeneity. A further comparison between the seahorse body size and weight (wet) with respect to the width parameter Δh(q) and the second-order Hurst exponent h(q=2) underscores the versatility of MFDFA as a robust statistical tool to analyze bioacoustic observations.

A novel opinion dynamics model based on expanded observation ranges and individuals’ social influences in social networks

In this paper, we propose an opinion dynamics model in order to investigate opinion evolution and interactions and the behavior of individuals. By introducing social influence and its feedback mechanism, the proposed model can highlight the heterogeneity of individuals and reproduce realistic online opinion interactions. It can also expand the observation range of affected individuals. Combining psychological studies on the social impact of majorities and minorities, affected individuals update their opinions by balancing social impact from both supporters and opponents. It can be seen that complete consensus is not always obtained. When the initial density of either side is greater than 0.8, the enormous imbalance leads to complete consensus. Otherwise, opinion clusters consisting of a set of tightly connected individuals who hold similar opinions appear. Moreover, a tradeoff is discovered between high interaction intensity and low stability with regard to observation ranges. The intensity of each interaction is negatively correlated with observation range, while the stability of each individual’s opinion positively affects the correlation. Furthermore, the proposed model presents the power-law properties in the distribution of individuals’ social influences, which is in agreement with people’s daily cognition. Additionally, it is proven that the initial distribution of individuals’ social influences has little effect on the evolution.

Long memory in Indian exchange rates: an application of power-law scaling analysis

This article studies the power-law scaling properties of Indian exchange rates relative to US dollar, British pound, Euro and Japanese yen and measures the evolution of their long-memory phenomenon. We apply the generalized Hurst exponent (GHE) approach for the computation of the scaling exponent. This article also tests the accuracy of the GHE approach by means of Monte Carlo experiments. The Monte Carlo experiments indicate that the GHE approach provides good estimates of the Hurst exponent. We also find that the efficiency characteristics of Indian exchange rates and their stages of development are dynamic in nature.

Measurement and Analysis Topological Characteristics of Video-Sharing Network

Recently the fast-growing business of the Internet are Online Social networking services, Online Social networking sites also become the most popular sites. In order to establish future social network which is optimized, and to eventually exploit the user base for commercial purposes, in-depth understanding the social characteristic of these networks is important. In this paper, we present a large-scale measurement study and analysis on the social structure of YouKu. Our results validate the power-law, small-world and clustering coefficient properties, present the correlation and difference among four centrality properties. Finally we discuss the utilization of these structural properties for the commercial purposes.

Some Properties of Random Apollonian Networks

AbstractIn this work, we analyze fundamental properties of random Apollonian networks [Zhang et al. 06, Zhou et al. 05], a popular random graph model that generates planar graphs with power-law properties. Specifically, we analyze the degree distribution, the k largest degrees, the k largest eigenvalues, and the diameter, where k is a constant.

Transfer Entropy Expressions for a Class of Non-Gaussian Distributions

Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I – IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

Nonlinear analysis of an imperfect radially graded annular plate with a heated edge

The present work deals with a geometrically nonlinear finite element analysis of an imperfect radially graded annular plate with a heated edge. The geometrical imperfection of the graded annular plate is assumed in aspect of its little intrinsic transverse deflection. The analysis is mainly for investigating the effects of intrinsic geometrical imperfection and temperature in the graded annular plate on its nonlinear flexural behaviour under a transverse mechanical load. The temperature is uniformly distributed across the thickness of the plate and it varies along the radial direction only. The temperature-dependent material properties are radially graded according to a simple power-law that is formed by power-law exponent and material properties of constituent materials (ceramic and metal). Based on the Von Karman nonlinear strain–displacement relations for imperfect annular plates, the nonlinear finite element equations of equilibrium are derived employing the principle of minimum potential energy. A single nodal displacement-control solution strategy is described for numerical solutions of nonlinear finite element equations of equilibrium. The numerical illustrations show a significant role of geometrical imperfection of the annular plate for its unstable equilibrium and alteration of structural behaviour under thermo-mechanical load. The analysis reveals the usefulness of radially graded annular plate in order to mitigate the unstable equilibrium of imperfect monolithic annular plate under thermo-mechanical load. It is found that the radial location for maximum value of a stress component insignificantly depends on the magnitudes of power-law exponent and applied temperature. The effects of material properties and applied temperature on the critical mechanical load corresponding to the unstable equilibrium of the imperfect radially graded annular plate are also presented.

Temporal organization of rest defined by actigraphy data in healthy and childhood chronic fatigue syndrome children

BackgroundAccumulating evidence has shown a universality in the temporal organization of activity and rest among animals ranging from mammals to insects. Previous reports in both humans and mice showed that rest bout durations followed long-tailed (i.e., power-law) distributions, whereas activity bouts followed exponential distributions. We confirmed similar results in the fruit fly, Drosophila melanogaster. Conversely, another report showed that the awakening bout durations, which were defined by polysomnography in bed, followed power-law distributions, while sleeping periods, which may correspond to rest, followed exponential distributions. This apparent discrepancy has been left to be resolved.MethodsActigraphy data from healthy and disordered children were analyzed separately for two periods: time out of bed (UP period) and time in bed (DOWN period).ResultsWhen data over a period of 24 h were analyzed as a whole, rest bouts showed a power law distribution as previously reported. However, when UP and DOWN period data were analyzed separately, neither showed power law properties. Using a newly developed strict method, only 30% of individuals satisfied the power law criteria, even when the 24 h data were analyzed. The human results were in contrast to the Drosophila results, which revealed clear power-law distributions for both day time and night time rest through the use of a strict method. In addition, we analyzed the actigraphy data from patients with childhood type chronic fatigue syndrome (CCFS), and found that they showed differences from healthy controls when their UP and DOWN data were analyzed separately.ConclusionsThese results suggested that the DOWN sleep, the bout distribution of which showed exponential properties, contributes to the production of long-tail distributions in human rest periods. We propose that separate analysis of UP and DOWN period data is important for understanding the temporal organization of activity.

A near-optimal adaptive algorithm for maximizing modularity in dynamic scale-free networks

We introduce A$$^3$$3CS, an adaptive framework with approximation guarantees for quickly identifying community structure in dynamic networks via maximizing Modularity Q. Our framework explores the advantages of the power-law distribution property found in many real-world complex systems. The framework is scalable for very large networks, and more excitingly, possesses approximation factors to ensure the quality of its detected community structure. To the best of our knowledge, this is the first framework that achieves approximation guarantees for the NP-hard Modularity maximization problem, especially on dynamic scale-free networks. To certify our approach, we conduct extensive experiments in comparison with other adaptive methods on both synthesized networks with known community structures and real-world traces including ArXiv e-print citation and Facebook social networks. Excellent empirical results not only confirm our theoretical results but also promise the practical applicability of A$$^3$$3CS in a wide range of dynamic networks.

On the relationships between hardness and the elastic and plastic properties of isotropic power-law hardening materials

A comprehensive understanding of the relationship between the hardness and the elastic and plastic properties for a wide range of materials is obtained by analysing the hardness characteristics (that are predicted by experimentally verified indentation analyses) of over 9000 distinct combinations of material properties that represent isotropic, homogeneous, power-law hardening metallic materials. Finite element analysis has been used to develop the indentation algorithms that provide the relationships between the elastic and plastic properties of the indented material and its indentation hardness. Based on computational analysis and virtual testing, the following observations are made. The hardness (H) of a material tends to increase with an increase in the elastic modulus (E), yield strength (σy) and the strain-hardening exponent (n). Several materials with different combinations of elastic and plastic properties can exhibit identical true hardness (for a particular indenter geometry/apex angle). In general, combinations of materials that exhibit relatively low elastic modulus and high yield strength or strain-hardening exponents and those that exhibit relatively high elastic modulus and low yield strength or strain-hardening exponents exhibit similar hardness properties. Depending on the strain-hardening characteristics of the indented material, (i.e. n = 0 or ), the ratio H/σy ranges, respectively, from 2.2 to 2.6 or 2 to 20 (for indentations with a cone angle of 70.3°). The materials that have lower σy/E and higher n exhibit higher H/σy ratios. The commonly invoked relationship between hardness and the yield strength, i.e. H ≈ 3σy, is not generally valid or applicable for all power-law hardening materials. The indentation hardness of a power law hardening material can be taken as following the relationship H ≈ (2.1–2.8)σr where σr is the representative stress based on Tabor’s representative strain for a wide range of materials.

Scale-Free Networks Based on the Value of Interest

Assigning the value of interest to each node in the network, we give a scale-free network model. The value of interest is related to the fitness and the degree of the node. Experimental results show that the interest model not only has the characteristics of the BA scale-free model but also has the characteristics of fitness model, and the network has a power-law distribution property.

Mining and generating large-scaled social networks via MapReduce

The computational efficiency is usually a concern when dealing with large-scale social network mining tasks containing billions of entities. Cloud computing is widely regarded as a feasible solution to this problem. In this work, we present an open-source graph mining library called the MapReduce Graph Mining Framework (MGMF) to be a robust and efficient MapReduce-based graph mining tool. We start from dividing graph mining algorithms into several categories and design a MapReduce framework for algorithms in each category. The experimental results show that MGMF is 3–20 times more efficient than PEGASUS, a state-of-the-art library for graph mining on MapReduce. Moreover, it provides broader coverage of a variety of graph mining algorithms. Furthermore, we designed a model to generate large-scale social networks capturing the power-law degree distribution property by parallelizing the mechanism of preferential attachment so that it is possible to produce billion-sized scale-free network in minutes. Our implemented open-source library can be downloaded from http://mslab.csie.ntu.edu.tw/~noahsark/MGMF/.

Preferential Migration and Random Mobility in Population Size Distribution of Municipalities

Some approaches in statistical physics have been applied to analyzing economic and social events. Recently, Kobayashi, Kuninaka et al. reviewed the statistical properties of several social and biological phenomena as ‘‘complex systems’’ from the viewpoint of stochastic processes. In their review, the population size distribution of municipalities in Japan was treated as one example. They stated that the log-normal distribution is basic for complex systems, which are generally described as a multiplicative random growth given by the equation xðt þ 1Þ xðtÞ 1⁄4 ðtÞxðtÞ. Here, xðtÞ is the population size at time t for example, and ðtÞ is the growth rate, which is a random variable. This property is well known as Gibrat’s law. For the population size distribution, the following feature has been recognized: the major part of the distribution obeys the log-normality, but the tail part corresponding to a large size exhibits the power law. Sasaki, Kuninaka et al. classified Japanese municipalities into three types (i.e., village, town, and city) and found that villages and cities are fitted with the log-normal and power-law distributions, respectively. Their conclusion was that the difference in these distributions is due to the existence of a lower population threshold in cities, but not in villages. The power-law distribution is reproducible by an additional effect to the above multiplicative random growth. Particularly, the following models have been applied to the Japanese case: (i) Random growth model: This model treats multiplicative random growth with an additive random noise, namely, the Kesten process, which possesses a powerlaw property. (ii) Migration model: There are two approaches focusing on population migration. (ii-a) Tomita and Hayashi adopted an urn model where preferential attachment in complex networks was applied. (ii-b) Sasaki and coworkers proposed another model and took population thresholds into account. Depending on the existence of such thresholds, the size distributions of villages, towns, and cities have been separately reproduced. It is noted that the emergence of the power law due to a threshold has already been reported in fragmentation process. In this short note, we review model (ii-b) with modification by focusing on the preferential migration effect, which is a different viewpoint from those in Refs. 9 and 15. Now, N sites representing each municipality are prepared. The time evolution of xjðtÞ, the size of the j-th site, is described by xjðt þ 1Þ xjðtÞ 1⁄4 XN