Berezovsky number

Berezovsky number is defined analogously to Erdos number. Berezovsky network is investigated

Bernoulli effect in superconductors and Cooper-pair mass spectroscopy

Recently Mishonov (Phys. Rev. B {\bf 50}, 4009 (1994)) suggested to measure the Cooper-pair effective mass using current-induced contact potential difference in superconductors. In this Comment it is shown that actual experiments can be substantially simplified

Abstract art grandmasters score like class D amateurs

Hawley-Dolan and Winner had asked the art students to compare paintings by abstract artists with paintings made by a child or by an animal. In 67% of the cases, art students said that the painting by a renowned artist is better. I compare this with the winning probability of the chessplayers of different ratings. I conclude that the great artists score on the level of class D amateurs

Statistics against irritations: a response to Dickens's apologists

In a recent article (arXiv:0909.2479) I reported the results of the test, where the takers had to tell the prose of Charles Dickens from the prose of Edward Bulwer-Lytton. The former is a required reading in school, and the latter has a bad writing contest named after him. Nevertheless, the test-takers performed on the level of random guessing. This research has met much criticism, which I refute the in the present article

Mathematical proof of fraud in Russian elections unsound

The Washigton Post had published allegations, that results of Russian elections "violate Gauss's groundbreaking work on statistics." I show that these allegations lack scientific basis

Stochastic modeling of citation slips

We present empirical data on frequency and pattern of misprints in citations to twelve high-profile papers. We find that the distribution of misprints, ranked by frequency of their repetition, follows Zipf's law. We propose a stochastic model of citation process, which explains these findings, and leads to the conclusion that 70-90% of scientific citations are copied from the lists of references used in other papers.Comment: Some corrections and additions. To appear in Scientometric

A mathematical theory of fame

We study empirically how the fame of WWI fighter-pilot aces, measured in numbers of web pages mentioning them, is related to their achievement, measured in numbers of opponent aircraft destroyed. We find that on the average fame grows exponentially with achievement; the correlation coefficient between achievement and the logarithm of fame is 0.72. The number of people with a particular level of achievement decreases exponentially with the level, leading to a power-law distribution of fame. We propose a stochastic model that can explain the exponential growth of fame with achievement. Next, we hypothesize that the same functional relation between achievement and fame that we found for the aces holds for other professions. This allows us to estimate achievement for professions where an unquestionable and universally accepted measure of achievement does not exist. We apply the method to Nobel Prize winners in Physics. For example, we obtain that Paul Dirac, who is a hundred times less famous than Einstein contributed to physics only two times less. We compare our results with Landau's ranking.Comment: Journal of Statistical Physics, Published on line 12 January 2013. arXiv admin note: substantial text overlap with arXiv:0906.3558, arXiv:cond-mat/031004

Statistical study of time intervals between murders for serial killers

We study the distribution of 2,837 inter-murder intervals (cooling off periods) for 1,012 American serial killers. The distribution is smooth, following a power law in the region of 10-10,000 days. The power law cuts off where inter-murder intervals become comparable with the length of human life. Otherwise there is no other characteristic scale in the distribution. In particular, we do not see any characteristic spree-killer interval or serial-killer interval, but only a monotonous smooth distribution lacking any features. This suggests that there is only a quantitative difference between serial killers and spree-killers, representing different samples generated by the same underlying phenomenon. The over decade long inter-murder intervals are not anomalies, but rare events described by the same power-law distribution and therefore should not necessarily be looked upon with suspicion, as has been done in a recent case involving a serial killer dubbed as the "Grim Sleeper." This large-scale study supports the conclusions of a previous study, involving three prolific serial killers, and the associated neural net model, which can explain the observed power law distribution

Theory of aces: high score by skill or luck?

We studied the distribution of World War I fighter pilots by the number of victories they were credited with, along with casualty reports. Using the maximum entropy method we obtained the underlying distribution of pilots by their skill. We find that the variance of this skill distribution is not very large, and that the top aces achieved their victory scores mostly by luck. For example, the ace of aces, Manfred von Richthofen, most likely had a skill in the top quarter of the active WWI German fighter pilots and was no more special than that. When combined with our recent study (cond-mat/0310049), showing that fame grows exponentially with victory scores, these results (derived from real data) show that both outstanding achievement records and resulting fame are mostly due to chance

Theory of Aces: Fame by chance or merit?

We study empirically how fame of WWI fighter-pilot aces, measured in numbers of web pages mentioning them, is related to their achievement or merit, measured in numbers of opponent aircraft destroyed. We find that on the average fame grows exponentially with achievement; to be precise, there is a strong correlation (~0.7) between achievement and the logarithm of fame. At the same time, the number of individuals achieving a particular level of merit decreases exponentially with the magnitude of the level, leading to a power-law distribution of fame. A stochastic model that can explain the exponential growth of fame with merit is also proposed