On the power-law distribution of language family sizes

2005 ◽  
Vol 41 (1) ◽  
pp. 117-131 ◽  
Author(s):  
SØREN WICHMANN
Keyword(s):  
Power Law ◽  
Rank Order ◽  
Language Family ◽  
Power Law Distribution ◽  
Stochastic Nature ◽  
Wide Range ◽  
The Family ◽  
Rank 2 ◽  
Physical Phenomena ◽  
Power Law Distributions

When the sizes of language families of the world, measured by the number of languages contained in each family, are plotted in descending order on a diagram where the x-axis represents the place of each family in the rank-order (the largest family having rank 1, the next-largest, rank 2, and so on) and the y-axis represents the number of languages in the family determining the rank-ordering, it is seen that the distribution closely approximates a curve defined by the formula y=ax−b. Such ‘power-law’ distributions are known to characterize a wide range of social, biological, and physical phenomena and are essentially of a stochastic nature. It is suggested that the apparent power-law distribution of language family sizes is of relevance when evaluating overall classifications of the world's languages, for the analysis of taxonomic structures, for developing hypotheses concerning the prehistory of the world's languages, and for modelling the future extinction of language families.

Interpreting erosion frequency and magnitude from luminescence profiles in boulders

2020 ◽  
Author(s):  
Nathan Brown ◽  
Seulgi Moon
Keyword(s):  
Power Law ◽  
Ground Level ◽  
Erosion Rates ◽  
Stochastic Nature ◽  
Wide Range ◽  
Bedrock Erosion ◽  
Instrumental Record ◽  
Simulation Results ◽  
Subcritical Cracking ◽  
Power Law Distributions

<p>Exposed bedrock is ubiquitous on terrestrial and planetary landscapes, yet little is known<br>about the rate of bedrock erosion at a granular scale on timescales longer than the<br>instrumental record. As recently suggested, using the bleaching depth of luminescence<br>signals as a measure of bedrock erosion may fit these scales. Yet this approach assumes<br>constant erosion through time, a condition likely violated by the stochastic nature of erosional<br>events. Here we simulate bleaching in response to power-law distributions of removal<br>lengths and hiatus durations. We compare simulation results with previously measured<br>luminescence profiles from boulder surfaces to illustrate that prolonged hiatuses are unlikely<br>and that typical erosion scales are sub-granular with occasional loss at mm scales,<br>consistent with ideas about microflaws governing bedrock detachment. For a wide range of<br>erosion rates, measurements are integrated over many removal events, producing<br>reasonably accurate estimates despite the stochastic nature of the simulated process. We<br>hypothesize that the greater or equal erosion rates atop large boulders compared to rates at<br>ground level suggest that subcritical cracking may be more influential than aeolian abrasion<br>for boulder degradation in the Eastern Pamirs, China.</p>

A note regarding ‘On the power-law distribution of language family sizes’

2006 ◽  
Vol 42 (2) ◽  
pp. 373-376 ◽  
Author(s):  
RICHARD ARNOLD ◽  
LAURIE BAUER
Keyword(s):  
Family Size ◽  
Power Law ◽  
Language Family ◽  
Power Law Distribution ◽  
Maximum Value ◽  
The Family ◽  
The Relationship

Wichmann (2005) discusses the power-law distribution n=ar−b as a description of the relationship between the number of languages n in a language family, and the rank r of that family in a list ordered by decreasing n. Two datasets are used by Wichmann, one from Ethnologue (Grimes 2000), which lists 130 language families, and one from Ruhlen (1987), listing 21 families. We have reanalysed these data and find that the method of fitting a power-law used in the paper is not optimal because it does not allow for a sensible maximum value for the family size n.

scholarly journals Predicting observational signatures of coronal heating by Alfvén waves and nanoflares

2007 ◽  
Vol 3 (S247) ◽  
pp. 279-287
Author(s):  
Patrick Antolin ◽  
Kazunari Shibata ◽  
Takahiro Kudoh ◽  
Daiko Shiota ◽  
David Brooks
Keyword(s):  
Power Law ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Power Law Distribution ◽  
Longitudinal Modes ◽  
Heating Mechanism ◽  
Set Up ◽  
Power Law Index ◽  
Power Law Distributions ◽  
Release Processes

AbstractAlfvén waves can dissipate their energy by means of nonlinear mechanisms, and constitute good candidates to heat and maintain the solar corona to the observed few million degrees. Another appealing candidate is the nanoflare-reconnection heating, in which energy is released through many small magnetic reconnection events. Distinguishing the observational features of each mechanism is an extremely difficult task. On the other hand, observations have shown that energy release processes in the corona follow a power law distribution in frequency whose index may tell us whether small heating events contribute substantially to the heating or not. In this work we show a link between the power law index and the operating heating mechanism in a loop. We set up two coronal loop models: in the first model Alfvén waves created by footpoint shuffling nonlinearly convert to longitudinal modes which dissipate their energy through shocks; in the second model numerous heating events with nanoflare-like energies are input randomly along the loop, either distributed uniformly or concentrated at the footpoints. Both models are based on a 1.5-D MHD code. The obtained coronae differ in many aspects, for instance, in the simulated intensity profile that Hinode/XRT would observe. The intensity histograms display power law distributions whose indexes differ considerably. This number is found to be related to the distribution of the shocks along the loop. We thus test the observational signatures of the power law index as a diagnostic tool for the above heating mechanisms and the influence of the location of nanoflares.

From the central limit theorem to heavy-tailed distributions

2003 ◽  
Vol 40 (3) ◽  
pp. 803-806 ◽  
Author(s):  
Jinwen Chen
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Power Law ◽  
Power Law Distribution ◽  
The Central Limit Theorem ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Random Indices ◽  
Power Law Distributions

It has been observed that in many practical situations randomly stopped products of random variables have power law distributions. In this note we show that, in order for such a product to have a power law distribution, the only random indices are the exponentially distributed ones. We also consider a more general problem, which is closely related to problems concerning transformation from the central limit theorem to heavy-tailed distributions.

scholarly journals Sliding Blocks Revisited: A Simulational Study

1998 ◽  
Vol 09 (06) ◽  
pp. 875-880 ◽  
Author(s):  
A. R. de Lima ◽  
C. Moukarzel ◽  
T. J. P. Penna
Keyword(s):  
Experimental Data ◽  
Friction Coefficient ◽  
Power Law ◽  
Computational Study ◽  
Recent Experimental Data ◽  
Power Law Distribution ◽  
Inclined Surfaces ◽  
Wide Range

A computational study of sliding blocks on inclined surfaces is presented. Assuming that the friction coefficient μ is a function of position, the probability P(λ) for the block to slide down over a length λ is numerically calculated. Our results are consistent with recent experimental data suggesting a power-law distribution of events over a wide range of displacements when the chute angle is close to the critical one, and suggest that the variation of μ along the surface is responsible for this.

Power Law Distributions and the Size Distribution of Strikes

2017 ◽  
Vol 48 (3) ◽  
pp. 561-587 ◽  
Author(s):  
Michele Campolieti
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Model Fit ◽  
Power Law Distribution ◽  
Policy Perspective ◽  
Methodological Research ◽  
Canadian Data ◽  
Alternative Measures ◽  
Power Law Distributions ◽  
Research And Policy

Using Canadian data from 1976 to 2014, I study the size distribution of strikes with three alternative measures of strike size: the number of workers on strike, strike duration in calendar days, and the number of person calendar days lost to a strike. I use a maximum likelihood framework that provides a way to estimate distributions, evaluate model fit, and also test against alternative distributions. I consider a few theories that can create power law distributions in strike size, such as the joint costs model that posits strike size is inversely proportional to dispute costs. I find that the power law distribution fits the data for the number of lost person calendar days relatively well and is also more appropriate than the lognormal distribution. I also discuss the implications of my findings from a methodological, research, and policy perspective.

An analysis of power law distributions and tipping points during the global financial crisis

2018 ◽  
Vol 13 (1) ◽  
pp. 80-91 ◽  
Author(s):  
Yifei Li ◽  
Lei Shi ◽  
Neil Allan ◽  
John Evans
Keyword(s):  
Financial Crisis ◽  
Power Law ◽  
Global Financial Crisis ◽  
Operational Risk ◽  
Tipping Point ◽  
Power Law Distribution ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
The Global Financial Crisis ◽  
Power Law Distributions

AbstractHeavy-tailed distributions have been observed for various financial risks and papers have observed that these heavy-tailed distributions are power law distributions. The breakdown of a power law distribution is also seen as an indicator of a tipping point being reached and a system then moves from stability through instability to a new equilibrium. In this paper, we analyse the distribution of operational risk losses in US banks, credit defaults in US corporates and market risk events in the US during the global financial crisis (GFC). We conclude that market risk and credit risk do not follow a power law distribution, and even though operational risk follows a power law distribution, there is a better distribution fit for operational risk. We also conclude that whilst there is evidence that credit defaults and market risks did reach a tipping point, operational risk losses did not. We conclude that the government intervention in the banking system during the GFC was a possible cause of banks avoiding a tipping point.

scholarly journals Exploring the Citywide Human Mobility Patterns of Taxi Trips through a Topic-Modeling Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Hui Xiong ◽  
Kaiqiang Xie ◽  
Lu Ma ◽  
Feng Yuan ◽  
Rui Shen
Keyword(s):  
Power Law ◽  
Traffic Management ◽  
Large Scale ◽  
Latent Dirichlet Allocation ◽  
Topic Model ◽  
Human Mobility ◽  
Mobility Patterns ◽  
Power Law Distribution ◽  
Modeling Analysis ◽  
Wide Range

Understanding human mobility patterns is of great importance for a wide range of applications from social networks to transportation planning. Toward this end, the spatial-temporal information of a large-scale dataset of taxi trips was collected via GPS, from March 10 to 23, 2014, in Beijing. The data contain trips generated by a great portion of taxi vehicles citywide. We revealed that the geographic displacement of those trips follows the power law distribution and the corresponding travel time follows a mixture of the exponential and power law distribution. To identify human mobility patterns, a topic model with the latent Dirichlet allocation (LDA) algorithm was proposed to infer the sixty-five key topics. By measuring the variation of trip displacement over time, we find that the travel distance in the morning rush hour is much shorter than that in the other time. As for daily patterns, it shows that taxi mobility presents weekly regularity both on weekdays and on weekends. Among different days in the same week, mobility patterns on Tuesday and Wednesday are quite similar. By quantifying the trip distance along time, we find that Topic 44 exhibits dominant patterns, which means distance less than 10 km is predominant no matter what time in a day. The findings could be references for travelers to arrange trips and policymakers to formulate sound traffic management policies.

Comparing Three Environmental Particle Size Distributions: Power Law (FED-STD-209D), Lognormal, Approximate Lognormal (MIL-STD-1246B)

1991 ◽  
Vol 34 (1) ◽  
pp. 21-24
Author(s):  
Douglas Cooper
Keyword(s):  
Particle Size ◽  
Power Law ◽  
Lognormal Distribution ◽  
Cumulative Distribution ◽  
Size Distributions ◽  
Power Law Distribution ◽  
Particle Size Distributions ◽  
Contamination Control ◽  
Control Programs ◽  
Power Law Distributions

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.

scholarly journals TRANSITION FROM EXPONENTIAL TO POWER LAW INCOME DISTRIBUTIONS IN A CHAOTIC MARKET

2011 ◽  
Vol 22 (01) ◽  
pp. 21-33 ◽  
Author(s):  
CARMEN PELLICER-LOSTAO ◽  
RICARDO LOPEZ-RUIZ
Keyword(s):  
Power Law ◽  
Chaotic Dynamics ◽  
Pairing Symmetry ◽  
Power Law Distribution ◽  
Closed Economies ◽  
Income Distributions ◽  
Chaotic Model ◽  
New Models ◽  
Micro Level ◽  
Power Law Distributions

Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.

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