Runaway Events Dominate the Heavy Tail of Citation Distributions

Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of the best-known heavy tail distributions. Even in this case there is a considerable debate whether citation distribution follows the log-normal or power-law fit. The goal of our study is to solve this debate by measuring citation distribution for a very large and homogeneous data. We measured citation distribution for 418,438 Physics papers published in 1980-1989 and cited by 2008. While the log-normal fit deviates too strong from the data, the discrete power-law function with the exponent $\gamma=3.15$ does better and fits 99.955% of the data. However, the extreme tail of the distribution deviates upward even from the power-law fit and exhibits a dramatic "runaway" behavior. The onset of the runaway regime is revealed macroscopically as the paper garners 1000-1500 citations, however the microscopic measurements of autocorrelation in citation rates are able to predict this behavior in advance.Comment: 6 pages, 5 Figure

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

A Biased Review of Sociophysics

Various aspects of recent sociophysics research are shortly reviewed: Schelling model as an example for lack of interdisciplinary cooperation, opinion dynamics, combat, and citation statistics as an example for strong interdisciplinarity.Comment: 16 pages for J. Stat. Phys. including 2 figures and numerous reference

An Analysis of the Dismal Theorem

In a series of papers, Martin Weitzman has proposed a Dismal Theorem. The general idea is that, under limited conditions concerning the structure of uncertainty and preferences, society has an indefinitely large expected loss from high-consequence, low-probability events. Under such conditions, standard economic analysis cannot be applied. The present study is intended to put the Dismal Theorem in context and examine the range of its applicability, with an application to catastrophic climate change. I conclude that Weitzman makes an important point about selection of distributions in the analysis of decision-making under uncertainty. However, the conditions necessary for the Dismal Theorem to hold are limited and do not apply to a wide range of potential uncertain scenarios

Distribution of Citations in one Volume of a Journal

Citations to published scientific articles are regularly collected and processed, bringing about the impact factor and a large number of other bibliometric indicators. We interpret the set of citations collected during fixed period as a characteristic statistical distribution of citations, argue about its properties and conjecture what statistical measures represent reliably such distributions. In that way we try to contribute to determining precisely the scope and level of suitability of impact factor if accompanied with a small set of additional indicators, all derived solely from the distribution function