Frequently cocited publications: Features and kinetics

Content Propagation in Online Social Networks

We often find skewed distributions such as the power law distribution and the lognormal distribution in studies of complex systems. Emergence of lognormal distribution is explained based on multiplicative stochastic processes, while power-law distribution can be explained by the multiplicative stochastic process with a modification. Thus, multiplicative process and lognormal distribution can serve as a starting point to discuss the statistical aspect of complex systems. In this paper, we show some economic and social phenomena in which lognormal and its related distributions can be observed to discuss their origins in terms of multiplicative growth.

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

Empirical analysis of Zipf’s law, power law, and lognormal distributions in medical discharge reports

Long-tailed distributions in biological systems have been studied. First, we found that lognormal distributions show excellent fit with various data for the duration distribution of disability in aged people, irrespective of their severity and gender. The robust lognormal distribution of disability implies that the incidence of diseases can be completed by many independent subprocesses in succession. Next, we studied food fragmentation by human mastication. A lognormal distribution well fits to the entire region for masticated food fragments for a small number of chewing strokes. Furthermore, the tail of the fragmentsize distribution changes from the lognormal distribution to a power-law one as the chewing stroke number increases. The good data fitting by the lognormal and power-law distribution implies that two functions of mastication, a sequential fragmentation with cascade and randomness and a lower threshold for fragment size, may affect the size distribution of masticated food fragments.

Is the cross-sectional distribution of house prices close to a (log) normal distribution, as is often assumed in empirical studies on house price indexes? How does the distribution evolve over time? To address these questions, we investigate the cross-sectional distribution of house prices in the Greater Tokyo Area for the period 1986 to 2009. We find that size-adjusted house prices follow a lognormal distribution except for the period of the housing bubble and its collapse in Tokyo, for which the price distribution has a substantially heavier right tail than that of a lognormal distribution. In addition, we find that, during the bubble era, the sharp price movements were concentrated in particular areas, and this spatial heterogeneity is the source of the fat upper tail. These findings suggest that the shape of the size-adjusted price distribution, especially the shape of the tail part, may contain information useful for the detection of housing bubbles. Specifically, the presence of a bubble can be safely ruled out if recent price observations are found to follow a lognormal distribution. On the other hand, if there are many outliers, especially near the upper tail, this may indicate the presence of a bubble, since such price observations are unlikely to occur if they follow a lognormal distribution. This method of identifying bubbles is quite different from conventional ones based on aggregate measures of housing prices, and therefore should be a useful tool to supplement existing methods.

Power Laws in Real Estate Prices? Some Evidence

Power Laws in Real Estate Prices? Some Evidence

The Galactic center black hole Sagittarius A* is a variable near-infrared (NIR) source that exhibits bright flux excursions called flares. When flux from Sgr A* is detected, the light curve has been shown to exhibit red noise characteristics and the distribution of flux densities is non-linear, non-Gaussian, and skewed to higher flux densities. However, the low-flux density turnover of the flux distribution is below the sensitivity of current single-aperture telescopes. For this reason, the median NIR flux has only been inferred indirectly from model fitting, but it has not been directly measured. In order to explore the lowest flux ranges, to measure the median flux density, and to test if the previously proposed flux distributions fit the data, we use the unprecedented resolution of the GRAVITY instrument at the VLTI. We obtain light curves using interferometric model fitting and coherent flux measurements. Our light curves are unconfused, overcoming the confusion limit of previous photometric studies. We analyze the light curves using standard statistical methods and obtain the flux distribution. We find that the flux distribution of Sgr A* turns over at a median flux density of (1.1 ± 0.3) mJy. We measure the percentiles of the flux distribution and use them to constrain the NIR K-band spectral energy distribution. Furthermore, we find that the flux distribution is intrinsically right-skewed to higher flux density in log space. Flux densities below 0.1 mJy are hardly ever observed. In consequence, a single powerlaw or lognormal distribution does not suffice to describe the observed flux distribution in its entirety. However, if one takes into account a power law component at high flux densities, a lognormal distribution can describe the lower end of the observed flux distribution. We confirm the rms–flux relation for Sgr A* and find it to be linear for all flux densities in our observation. We conclude that Sgr A* has two states: the bulk of the emission is generated in a lognormal process with a well-defined median flux density and this quiescent emission is supplemented by sporadic flares that create the observed power law extension of the flux distribution.

Distributions for cited articles from individual subjects and years

Abstract. We present the combined power law and log-normal distribution (PL+LN) model, a computationally efficient model to be used in simulations where the particle size distribution cannot be accurately represented by log-normal distributions, such as in simulations involving the initial steps of aerosol formation, where new particle formation and growth occur simultaneously, or in the case of inverse modeling. The model was evaluated against highly accurate sectional models using input parameter values that reflect conditions typical to particle formation occurring in the atmosphere and in vehicle exhaust. The model was tested in the simulation of a particle formation event performed in a mobile aerosol chamber at Mäkelänkatu street canyon measurement site in Helsinki, Finland. The number, surface area, and mass concentrations in the chamber simulation were conserved with the relative errors lower than 2 % using the PL+LN model, whereas a moment-based log-normal model and sectional models with the same computing time as with the PL+LN model caused relative errors up to 17 and 79 %, respectively.

A high-resolution data set of kinematic aperture (opening displacement) of opening-mode fractures, from large (up to 2 m long) quartz-cemented sandstone samples, shows that microfractures are ubiquitous and that most natural-fracture sets are better fit by power-law size distributions than by exponential, normal, or log-normal distributions. The data set includes 3822 fractures within 68 scanlines from eight formations on three continents. Kinematic apertures were measured along scanlines using scanning electron microscope–based cathodoluminescence (SEM-CL) and, for field data, using a hand lens. Microtextural evidence from SEM-CL shows that power law–distributed fractures typically have crack-seal texture and are composed of opening increments having a narrow (characteristic) aperture size range. In contrast, rare non-power-law–distributed fracture populations lack crack-seal texture. Power-law exponents, as measured in one dimension, have values of −0.8 ± 0.1. Most variation among fracture sets results from power-law coefficients, which constitute a scale-invariant measure of fracture intensity. We show how observed scaling patterns can be used to improve estimations of large-fracture spacing in cases where fracture sampling is limited, as by the width of cores. The low (

In the study of oceanic bubbles based on empirical acoustics, the distributions among the sizes are typically represented by power laws with negative slopes as convenient descriptors of data in log/log format. However, power laws do not address the fact that as bubble sizes approach zero their numbers must approach zero. Multiple power laws, including a horizontal segment preceded by a positive power-law segment and followed by the expected negative power-law segment, have been used to recognize and mitigate this problem. Although not universally adopted as yet, several acoustic researchers have suggested that at least some oceanic bubble distributions are more appropriately represented by lognormal distributions. In 1941, A. N. Kolmogorov used the 1922 work of L. R. Richardson concerning a stochastic downward cascade of random sizes of turbulent vortices that asymptotically result in lognormal distributions of vortices. This current paper uses such a cascade of vortices to begin a downward cascade of bubbles sizes causing cascading shear forces on large bubbles that were created by breaking waves. In combination with this decreasing effect of turbulent shear on these fragmenting bubbles, the downward cascade of bubbles sizes overlaps and continues with a strengthened partial-pressure effect on ever increasing surface tension caused by their diminishing sizes. Issues associated with this approach, such as summing lognormal generators and intermittency, will be discussed.

Particle size strongly influences particle behavior. To summarize the distribution of particle sizes, a distribution function can be used. The characteristics of the particle size distributions chosen are important for two specification documents currently under revision: (1) FED-STD-209D, concerning air-cleanliness in manufacturing, which uses cumulative particle size distributions that are linear when plotted on log-log axes; these are power law distributions. (2) MIL-STD-1246B, "Product Cleanliness Levels and Contamination Control Programs," primarily concerning surface cleanliness, which uses cumulative particle size distributions that are linear when plotted as the logarithm of the cumulative distribution versus the square of the logarithm of the particle size, log2x, A third distribution, the lognormal, is commonly found in aerosol science, especially where there is a single particle source. The distributions are compared and discussed. The FED-STD-209D power law distribution can approximate a lognormal distribution over only a limited size range. The MIL-STD-1246B distribution is an asymptotic approximation to the lognormal distribution.

Flow characteristics of slug flow for air-water mixtures upward flowing, including gas slug velocity, gas slug length, liquid slug length and void fraction profile, are discussed experimentally and/or analytically in present report. The experiments were carried out in three sizes of pipe that were used in the previous work (2nd Report) and the analysis were done using the equations presented in the previous paper (3rd Report). The results are summarized as follows.(1) The gas slug velocity was represented by Eq.(10), however it was shown that the coefficient C1 is influenced slightly by the void fraction in the liquid slug region.(2) The distribution of lengths of the gas and liquid slugs was described by a logarithmic normal distribution.(3) The mean value and the standard deviation of gas slug length were expressed by empirical equations (11) and (12) respectively.(4) The liquid slug length was insensitive to the gas and liquid flow rates and almost constant for a given tube diameter.(5) The void fraction profile in the overall slug was denoted by the power law distribution as Eq.(15).(6) It was suggested from the analysis of liquid-phase velocity profile that the presence of small bubble in the liquid slug region brings a flattening effect on the velocity profile.(7) It was found that the void fraction profile in the gas slug is denoted by Eq.(44) in general.