Power-law Properties Research Articles

Heterogeneous game resource distributions promote cooperation in spatial prisoner’s dilemma game

In social networks, individual abilities to establish interactions are always heterogeneous and independent of the number of topological neighbors. We here study the influence of heterogeneous distributions of abilities on the evolution of individual cooperation in the spatial prisoner’s dilemma game. First, we introduced a prisoner’s dilemma game, taking into account individual heterogeneous abilities to establish games, which are determined by the owned game resources. Second, we studied three types of game resource distributions that follow the power-law property. Simulation results show that the heterogeneous distribution of individual game resources can promote cooperation effectively, and the heterogeneous level of resource distributions has a positive influence on the maintenance of cooperation. Extensive analysis shows that cooperators with large resource capacities can foster cooperator clusters around themselves. Furthermore, when the temptation to defect is high, cooperator clusters in which the central pure cooperators have larger game resource capacities are more stable than other cooperator clusters.

Maximum matchings and minimum dominating sets in Apollonian networks and extended Tower of Hanoi graphs

The Apollonian networks display the remarkable power-law and small-world properties as observed in most realistic networked systems. Their dual graphs are extended Tower of Hanoi graphs, which are obtained from the Tower of Hanoi graphs by adding a special vertex linked to all its three extreme vertices. In this paper, we study analytically maximum matchings and minimum dominating sets in Apollonian networks and their dual graphs, both of which have found vast applications in various fields, e.g. structural controllability of complex networks. For both networks, we determine their matching number, domination number, the number of maximum matchings, as well as the number of minimum dominating sets.

Protein lipograms

Linguistic analysis of protein sequences is an underexploited technique. Here, we capitalize on the concept of the lipogram to characterize sequences at the proteome levels. A lipogram is a literary composition which omits one or more letters. A protein lipogram likewise omits one or more types of amino acid. In this article, we establish a usable terminology for the decomposition of a sequence collection in terms of the lipogram. Next, we characterize Uniref50 using a lipogram decomposition. At the global level, protein lipograms exhibit power-law properties. A clear correlation with metabolic cost is seen. Finally, we use the lipogram construction to assign proteomes to the four branches of the tree-of-life: archaea, bacteria, eukaryotes and viruses. We conclude from this pilot study that the lipogram demonstrates considerable potential as an additional tool for sequence analysis and proteome classification.

On flame height of circulation-controlled firewhirls with variable physical properties and in power-law vortices: A mass-diffusivity-ratio model correction

This paper presents a theory on the flame height of circulation-controlled firewhirls, approximately combining variable physical properties, a power-law vortex model, and a mass-diffusivity-ratio model. The theoretical results show that the dimensionless flame height can be expressed as a multiplication of four dimensionless factors. The first factor is the stoichiometric-mixture-fraction-scaled Peclet number that was first identified by Chuah et al. (2011) in their theory based on the assumptions of Burgers vortex and constant physical properties. The second factor characterizes the axial flame-stretching effect found by Klimenko and Williams (2013) in their theory based on the assumptions of power-law strong vortex and constant physical properties. The third factor quantifies the effect of variable density, which was recently unveiled in Yu and Zhang's (2017) theory. The last factor describes the effect of distinct mass diffusivities of fuel and oxidizer, which has not been considered in the previous studies. Although integrating the first three factors in the theory would lead to an over-prediction to the flame height, accounting for the distinct mass diffusivities of fuel and oxidizer, leading to a mass-diffusivity-ratio model correction, results in the finding of a “reduction” mechanism for the flame height, which is comparable in order of magnitude with the other “enhancement” mechanisms obtained from considering either the power-law strong vortex or variable density.

Degree-degree distribution in a power law random intersection graph with clustering

The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree distribution of a sparse inhomogeneous random intersection graph and discuss its relation to the clustering and power law properties of the graph.

Examining the efficiency and interdependence of US credit and stock markets through MF-DFA and MF-DXA approaches

This study examines the power law properties of 11 US credit and stock markets at the industry level. We use multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrended cross-correlation analysis (MF-DXA) to first investigate the relative efficiency of credit and stock markets and then evaluate the mutual interdependence between CDS-equity market pairs. The scaling exponents of the MF-DFA approach suggest that CDS markets are relatively more inefficient than their equity counterparts. However, Banks and Financial credit markets are relatively more efficient. Basic Materials (both CDS and equity indices) is the most inefficient sector of the US economy. The cross-correlation exponents obtained through MF-DXA also suggest that the relationship of the CDS and equity sectors within and across markets is multifractal for all pairs. Within the CDS market, Basic Materials is the most dependent sector, whereas equity market sectors can be divided into two distinct groups based on interdependence. The pair-wise dependence between Basic Materials sector CDSs and the equity index is also the highest. The degree of cross-correlation shows that the sectoral pairs of CDS and equity markets belong to a persistent cross-correlated series within selected time intervals.

Parameter estimation method for blurred cell images from fluorescence microscope

Microscopic cell image analysis is indispensable to cell biology. Images of cells can easily degrade due to optical diffraction or focus shift, as this results in low signal-to-noise ratio (SNR) and poor image quality, hence affecting the accuracy of cell analysis and identification. For a quantitative analysis of cell images, restoring blurred images to improve the SNR is the first step. A parameter estimation method for defocused microscopic cell images based on the power law properties of the power spectrum of cell images is proposed. The circular radon transform (CRT) is used to identify the zero-mode of the power spectrum. The parameter of the CRT curve is initially estimated by an improved differential evolution algorithm. Following this, the parameters are optimized through the gradient descent method. Using synthetic experiments, it was confirmed that the proposed method effectively increased the peak SNR (PSNR) of the recovered images with high accuracy. Furthermore, experimental results involving actual microscopic cell images verified that the superiority of the proposed parameter estimation method for blurred microscopic cell images other method in terms of qualitative visual sense as well as quantitative gradient and PSNR.

Spatial patterns of landslide dimension: A tool for magnitude mapping

The magnitude of mass movements, which may be expressed by their dimension in terms of area or volume, is an important component of intensity together with velocity. In the case of slow-moving deep-seated landslides, the expected magnitude is the prevalent parameter for defining intensity when assessed as a spatially distributed variable in a given area. In particular, the frequency–volume statistics of past landslides may be used to understand and predict the magnitude of new landslides and reactivations. In this paper we study the spatial properties of volume frequency distributions in the Arno river basin (Central Italy, about 9100km2). The overall landslide inventory taken into account (around 27,500 events) shows a power-law scaling of volumes for values greater than a cutoff value of about 2×104m3. We explore the variability of the power-law exponent in the geographic space by setting up local subsets of the inventory based on neighbourhoods with radii between 5 and 50km. We found that the power-law exponent α varies according to geographic position and that the exponent itself can be treated as a random space variable with autocorrelation properties both at local and regional scale. We use this finding to devise a simple method to map the magnitude frequency distribution in space and to create maps of exceeding probability of landslide volume for risk analysis. We also study the causes of spatial variation of α by analysing the dependence of power-law properties on geological and geomorphological factors, and we find that structural settings and valley density exert a strong influence on mass movement dimensions.

Stochastic model of financial markets reproducing scaling and memory in volatility return intervals

We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce various stylized facts of different markets and different assets with the same set of model parameters. We show that the power-law properties and the scaling of return intervals and other financial variables have a similar origin and could be a result of a general class of non-linear stochastic differential equations derived from a master equation of an agent system that is coupled by herding interactions. Specifically, we find that this approach enables us to recover the volatility return interval statistics as well as volatility probability and spectral densities for the NYSE and FOREX markets, for different assets, and for different time-scales. We find also that the historical S\&P500 monthly series exhibits the same volatility return interval properties recovered by our proposed model. Our statistical results suggest that human herding is so strong that it persists even when other evolving fluctuations perturbate the financial system.

Protein complexes predictions within protein interaction networks using genetic algorithms.

BackgroundProtein–protein interaction networks are receiving increased attention due to their importance in understanding life at the cellular level. A major challenge in systems biology is to understand the modular structure of such biological networks. Although clustering techniques have been proposed for clustering protein–protein interaction networks, those techniques suffer from some drawbacks. The application of earlier clustering techniques to protein–protein interaction networks in order to predict protein complexes within the networks does not yield good results due to the small-world and power-law properties of these networks.ResultsIn this paper, we construct a new clustering algorithm for predicting protein complexes through the use of genetic algorithms. We design an objective function for exclusive clustering and overlapping clustering. We assess the quality of our proposed clustering algorithm using two gold-standard data sets.ConclusionsOur algorithm can identify protein complexes that are significantly enriched in the gold-standard data sets. Furthermore, our method surpasses three competing methods: MCL, ClusterOne, and MCODE in terms of the quality of the predicted complexes. The source code and accompanying examples are freely available at http://faculty.kfupm.edu.sa/ics/eramadan/GACluster.zip.

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

In this study, nonlocal elasticity theory in conjunction with Gurtin–Murdoch elasticity theory is employed to investigate biaxial buckling and free vibration behavior of nanoplate made of functionally graded material (FGM) and resting on a visco-Pasternak standard linear solid-type of the foundation. The material characteristics of simply supported FGM nanoplates are assumed to be varied continuously as a power law function of the plate thickness. Hamilton’s principle is implemented to derive the non-classical governing equations of motion and related boundary conditions, which analytically solved to obtain the explicit closed-form expression for complex natural frequencies and buckling loads. Finally, attention is focused on considering the influences of various parameters on variation of damped natural frequency and buckling load ratio such as nonlocal parameter, surface effects, geometric parameters, power law index and properties of visco-Pasternak foundation and it is clearly demonstrated that these factors highly affect on vibration and buckling behavior.

Buckling design of conical shells based on palm trunks: Survey of power-law distributed thin-walled conical

This paper aims at the elastic buckling of multilayered thin-walled conical shells with power-law distributed material properties under the axial load and lateral pressure based on the experimental study of palm trunks. The material properties of the shells are assumed to vary continuously in the radial direction. Relations and analytical approaches for linear buckling response are presented by using the layer-wise shell theory. The buckling behaviors of the conical shells subjected to axial and transverse loads are investigated. Parametric study in geometry (relative thickness, relative stiffness and cone angle) is performed to enhance the overall buckling resistance and minimize the weight. Numerical results show the possibility to achieve larger load-carrying capacity by simultaneously optimizing the material and geometric parameters based on the structure of palm trunks.

Time-varying Volatility and the Power Law Distribution of Stock Returns

While many studies find that the tail distribution of high frequency stock returns follow a power law, there are only a few explanations for this finding. This study presents evidence that time-varying volatility can account for the power law property of high frequency stock returns. The power law coefficients obtained by estimating a conditional normal model with nonparametric volatility show a striking correspondence to the power law coefficients estimated from returns data for stocks in the Dow Jones index. A cross-sectional regression of the data coefficients on the model-implied coefficients yields a slope close to one, supportive of the hypothesis that the two sets of power law coefficients are identical. Further, for most of the stocks in the sample taken individually, the model-implied coefficient falls within the 95 percent confidence interval for the coefficient estimated from returns data.

Model predictions of features in microsaccade-related neural responses in a feedforward network with short-term synaptic depression.

Recently, the significant microsaccade-induced neural responses have been extensively observed in experiments. To explore the underlying mechanisms of the observed neural responses, a feedforward network model with short-term synaptic depression has been proposed [Yuan, W.-J., Dimigen, O., Sommer, W. and Zhou, C. Front. Comput. Neurosci. 7, 47 (2013)]. The depression model not only gave an explanation for microsaccades in counteracting visual fading, but also successfully reproduced several microsaccade-related features in experimental findings. These results strongly suggest that, the depression model is very useful to investigate microsaccade-related neural responses. In this paper, by using the model, we extensively study and predict the dependance of microsaccade-related neural responses on several key parameters, which could be tuned in experiments. Particularly, we provide a significant prediction that microsaccade-related neural response also complies with the property “sharper is better” observed in many contexts in neuroscience. Importantly, the property exhibits a power-law relationship between the width of input signal and the responsive effectiveness, which is robust against many parameters in the model. By using mean field theory, we analytically investigate the robust power-law property. Our predictions would give theoretical guidance for further experimental investigations of the functional role of microsaccades in visual information processing.

Power law analysis of the human microbiome.

Taylor's (1961, Nature, 189:732) power law, a power function (V=am(b) ) describing the scaling relationship between the mean and variance of population abundances of organisms, has been found to govern the population abundance distributions of single species in both space and time in macroecology. It is regarded as one of few generalities in ecology, and its parameter b has been widely applied to characterize spatial aggregation (i.e. heterogeneity) and temporal stability of single-species populations. Here, we test its applicability to bacterial populations in the human microbiome using extensive data sets generated by the US-NIH Human Microbiome Project (HMP). We further propose extending Taylor's power law from the population to the community level, and accordingly introduce four types of power-law extensions (PLEs): type I PLE for community spatial aggregation (heterogeneity), type II PLE for community temporal aggregation (stability), type III PLE for mixed-species population spatial aggregation (heterogeneity) and type IV PLE for mixed-species population temporal aggregation (stability). Our results show that fittings to the four PLEs with HMP data were statistically extremely significant and their parameters are ecologically sound, hence confirming the validity of the power law at both the population and community levels. These findings not only provide a powerful tool to characterize the aggregations of population and community in both time and space, offering important insights into community heterogeneity in space and/or stability in time, but also underscore the three general properties of power laws (scale invariance, no average and universality) and their specific manifestations in our four PLEs.

Thermomechanical Vibration Behavior of FG Nanobeams Subjected to Linear and Non-Linear Temperature Distributions

In this study, thermomechanical vibration analysis of functionally graded (FG) nanobeams subjected to in-plane thermal loads are carried out by presenting a Navier-type solution and employing a semi-analytical differential transform method (DTM) for the first time. Two types of thermal loading, namely, linear and non-linear temperature rises through the thickness direction are considered. Thermomechanical properties of FG nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model and material properties are assumed to be temperature-dependent. Eringen non-local elasticity theory is exploited to describe the size dependency of FG nanobeam. Using Hamilton's principle, the non-local equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of FG nanobeams including size effect and they are solved applying DTM. According to numerical results, it was revealed that the proposed modeling and semi-analytical approach can provide accurate frequency results of the FG nanobeams as compared to analytical results and also some cases in the literature. A parametric study is included to examine the effects of several parameters, such as temperature rise, gradient index, small-scale parameter and boundary conditions on the normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the vibration behaviour of a FG nanobeams is significantly influenced by these effects. The new results can be used as benchmark solutions for analyses of FG nanobeams.

Truncated lognormals as a power-law mimic in operational risk

Real operational loss data in some cases exhibits power laws on a wide part of the tail distributions, with sharp deviations far to the right, suggesting they decrease to zero faster at infinity. Taking into account such deviations when modeling operational risk leads to large differences in value-at-risk estimates, stemming from different asymptotic distributions of extreme events. We make use of the power-law mimicry properties of the truncated lognormal distribution and show how they fit operational risk data considerably well in these cases. For the few exceptions we show how a mixture of truncated lognormals can pass the goodness-of-fit test.

In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams

In the present study, the effect of in-plane thermal loading on vibrational behaviour of functionally graded (FG) nanobeams are carried out by presenting both Navier type solution and differential transform method. Classical and first order shear deformation beam theories are adopted to count for the effect of shear deformations. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly throughout the thickness based on power-law model and material properties are assumed to be temperature-dependent. Eringen’s nonlocal elasticity theory is exploited to describe the size dependency of FG nanobeam. Using Hamilton’s principle, the nonlocal equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of FG nanobeams based on Euler–Bernoulli and Timoshenko beam theories. According to the numerical results, it is revealed that the proposed modeling and semi analytical approach can provide accurate frequency results of the FG nanobeams as compared to analytical results and also some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as temperature change, gradient indexes, small scale parameter, mode number and boundary conditions on the natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the vibration behaviour of a FG nanobeam are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

Mapping Power Law Distributions in Digital Health Social Networks: Methods, Interpretations, and Practical Implications.

BackgroundSocial networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena.ObjectivesThe objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison.MethodsData from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described.ResultsAll four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R 2 values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001).ConclusionsThis is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

A new discrete economic model involving generalized fractal derivative

The current article is mainly concerned with applying generalized fractal derivatives in a macroeconomic model. We propose a discrete model involving four macroeconomic variables, the gross domestic production, exchange rate, money supply and exports/imports by using the generalized fractal derivative. The fractal derivative can describe the power-law phenomenon and memory property of economic variables more accurately. Based on the concrete macroeconomic data of Canada, the coefficients of this nonlinear system are estimated by the method of least squares. The statistical test results show that the four variables we have selected have an apparent causal connection, and the sum of squared residuals of the fitting equations is also acceptable. In simulation, the actual data of Canada from 1990 to 2008 are considered, and the effectiveness of our model is verified. The empirical study shows that in the coming few years, the money supply will grow quickly and hence it may lead to proper inflation.