Power-law Hypothesis Research Articles

The ‘Power’ of Tourism in Portugal

The author analyses the upper tail of the distribution of tourism supply in Portugal from 2002 to 2009, using data from the Instituto Nacional de Estatística database. Tourism supply is defined in terms of the lodging capacity of hotel establishments in about 250 tourist destinations. The paper shows that the empirical distribution of tourism supply in Portugal is heavy-tailed and consistent with a power law behaviour in its upper tail. Such behaviour seems to be stable over the years, provided that, for the time horizon covered by the data sets, the scaling parameter is always close to the value of two. The power law hypothesis is tested positively through the use of graphical and analytical methods. Cooperation among stakeholders and the enlargement of the base for tourism supply are the main policy implications drawn from the power law analysis to avoid the threat of a fall in tourist arrivals in Portugal.

Power law distribution in high frequency financial data? An econometric analysis

Power law distributions are very common in natural sciences. We analyze high frequency financial data from XETRA and the NYSE using maximum likelihood estimation and the Kolmogorov–Smirnov statistic to test whether the power law hypothesis holds also for these data. We find that the universality and scale invariance properties of the power law are violated. Furthermore, the returns of Daimler Chrysler and SAP traded simultaneously on both exchanges follow a power law at one exchange, but not at the other. These results raise some questions about the no-arbitrage condition. Finally, we find that an exponential function provides a better fit for the tails of the sample distributions than a power law function.

Noncharacteristic half-lives in radioactive decay

Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that we explore a method for fitting power laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation.

Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to −1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling (“finite size” effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to −1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.

Generalizing unweighted network measures to capture the focus in interactions

Several important complex network measures that helped discovering common patterns across real-world networks ignore edge weights, an important information in real-world networks. We propose a new methodology for generalizing measures of unweighted networks through a generalization of the cardinality concept of a set of weights. The key observation here is that many measures of unweighted networks use the cardinality (the size) of some subset of edges in their computation. For example, the node degree is the number of edges incident to a node. We define the effective cardinality, a new metric that quantifies how many edges are effectively being used, assuming that an edge's weight reflects the amount of interaction across that edge. We prove that a generalized measure, using our method, reduces to the original unweighted measure if there is no disparity between weights, which ensures that the laws that govern the original unweighted measure will also govern the generalized measure when the weights are equal. We also prove that our generalization ensures a partial ordering (among sets of weighted edges) that is consistent with the original unweighted measure, unlike previously developed generalizations. We illustrate the applicability of our method by generalizing four unweighted network measures. As a case study, we analyze four real-world weighted networks using our generalized degree and clustering coefficient. The analysis shows that the generalized degree distribution is consistent with the power-law hypothesis but with steeper decline and that there is a common pattern governing the ratio between the generalized degree and the traditional degree. The analysis also shows that nodes with more uniform weights tend to cluster with nodes that also have more uniform weights among themselves.

Assessing the power law hypothesis for the size–frequency distribution of terrestrial and martian dust devils

Competing hypotheses for the diameter dependence of terrestrial and martian dust devil frequency are assessed using new field observations from two sites in the southwestern United States. We show that at diameters less than 12 m, our observed dust devil size–frequency distributions are better fit by an exponential function than by a power law formulation, and discuss the implications for larger dust devils on Earth and Mars.

On the upper tail of Italian firms’ size distribution

Abstract In this paper we analyze the upper tail of the size distribution of Italian companies with limited liability belonging to the CEBI database. Size is defined in terms of net worth. In particular, we show that the largest firms follow a power law distribution, according to the well-known Pareto law, for which we give estimates of the shape parameter. Such a behavior seems to be quite persistent over time, view that for almost 20 years of observations, the shape parameter is always in the vicinity of 1.8. The power law hypothesis is also positively tested using graphical and analytical methods.

Simulations of the probability structure of a dispersing, passive scalar

AbstractIt is established that there is a time asymptotic dependency of the higher order moments of concentration on the lowest three moments through statistical analysis of field plume releases [Mole and Clarke, 1995]. A microscale model of a diffusion layer randomly buffeted by supercloud size eddies and a model of advection and diffusion in a deterministic helical eddy both demonstrated that this slaving of the higher moments to lower moments obtains time‐asymptotically and collapses with all intermittency factors onto a universal curve for kurtosis against skewness. In this article, this universality with residence time and intermittency factor obtains in two distinct plume models for transverse dispersion – diffusion within a 1‐D lamellae structure and during advection by a 2‐D random streamfunction. In the latter case, some evidence for Chatwin's closure hypothesis relating the expectation of the norm square of the gradient of the concentration, conditional at a given concentration, and the pdf of concentration, is presented. At early residence times in the plume, the power law hypothesis is consistent with simulations to a good degree. At intermediate residence times, however, there are apparently two branches to the proposed relationship, one matching Chatwin's hypothesis. Although not tested here, at long residence times the hypothesis should hold under the simulation scheme as it asymptotes to the assumptions of Chatwin's theory. Copyright © 2001 John Wiley & Sons, Ltd.

Generalized treatment of thermal conductivity enhancement in the critical region

The power-law hypothesis and National Bureau of Standards (NBS) equation of state were adopted to express thermodynamic behavior in the critical region. This predictive procedure requires only critical constants of pure fluids. Values calculated with this generalized model when compared with corresponding thermal conductivity enhancement data yield for 16 fluids an approximate overall average absolute deviation of 12 % within the critical region bounded by 1<T R <1.03 and 0.7<ρ R <1.3

Monotonicity, convexity, and other qualitative psychophysical laws

General methods are described for directly testing qualitative psychophysical laws, such as monotonicity and convexity. These methods consist of estimating lower and higher orders of derivatives and procedures for verifying qualitative laws involving these derivatives. The quantitative power law hypothesis is compared for goodness of fit with the qualitative hypothesis that the psychophysical function is monotone and convex, in application to bisection brightness data. Other topics include discussion of a possible topological formulation of the distinction between qualitative and quantitative laws; the search for psychophysical invariants; and the failure of qualitative laws such as convexity to conform to Luce's invariance-theoretic principles of theory construction.

Power law hypothesis in the thermodynamics-like theory of annoyance.

The thermodynamics-like theory (an analogue theory of the ideal gas) of annoyance coupled with a power law hypothesis is studied, particularly on the behavior of the constant γ in the theory. It is found that magnitude of the constant γ should depend on the energy of the external stimulus of noise under the power law hypothesis. Further, numerical values of the parameters of the power law are discussed.

Individual half-judgment brightness functions

Nine Ss made half-judgments of each of nine brightness standards. Individual half-judgment brightness functions were constructed, one for each of the two threshold forms of the power law. The ω-Law (translation on the psychological axis) provided a better fit to the half-judgment data than did the ϕ-Law (translation on the intensity axis). A test of scale consistency for the fractionation method was confounded with the power law hypothesis, but the data are interpreted as providing fair support for the method independent of the form of the power law. The effect of Standard on exponent estimates was significant for both forms of the law, and the effect of Standard on threshold estimates was significant for the ϕ-Law but not for the ω-Law. Both forms of the law contain a so-called threshold parameter, but the interpretation of this parameter as a threshold was rejected for the ϕ-Law and accepted for the ω-Law.