919 research outputs found
Neuropsychological constraints to human data production on a global scale
Which are the factors underlying human information production on a global
level? In order to gain an insight into this question we study a corpus of
252-633 Million publicly available data files on the Internet corresponding to
an overall storage volume of 284-675 Terabytes. Analyzing the file size
distribution for several distinct data types we find indications that the
neuropsychological capacity of the human brain to process and record
information may constitute the dominant limiting factor for the overall growth
of globally stored information, with real-world economic constraints having
only a negligible influence. This supposition draws support from the
observation that the files size distributions follow a power law for data
without a time component, like images, and a log-normal distribution for
multimedia files, for which time is a defining qualia.Comment: to be published in: European Physical Journal
Two Universality Properties Associated with the Monkey Model of Zipf's Law
The distribution of word probabilities in the monkey model of Zipf's law is
associated with two universality properties: (1) the power law exponent
converges strongly to as the alphabet size increases and the letter
probabilities are specified as the spacings from a random division of the unit
interval for any distribution with a bounded density function on ; and
(2), on a logarithmic scale the version of the model with a finite word length
cutoff and unequal letter probabilities is approximately normally distributed
in the part of the distribution away from the tails. The first property is
proved using a remarkably general limit theorem for the logarithm of sample
spacings from Shao and Hahn, and the second property follows from Anscombe's
central limit theorem for a random number of i.i.d. random variables. The
finite word length model leads to a hybrid Zipf-lognormal mixture distribution
closely related to work in other areas.Comment: 14 pages, 3 figure
Sales Distribution of Consumer Electronics
Using the uniform most powerful unbiased test, we observed the sales
distribution of consumer electronics in Japan on a daily basis and report that
it follows both a lognormal distribution and a power-law distribution and
depends on the state of the market. We show that these switches occur quite
often. The underlying sales dynamics found between both periods nicely matched
a multiplicative process. However, even though the multiplicative term in the
process displays a size-dependent relationship when a steady lognormal
distribution holds, it shows a size-independent relationship when the power-law
distribution holds. This difference in the underlying dynamics is responsible
for the difference in the two observed distributions
Innovation and corporate dynamics: a theoretical framework
We provide a detailed analysis of a generalized proportional growth model (GPGM) of innovation and corporate dynamics that encompasses the Gibrat’s Law of Proportionate Effect and the Simon growth process as particular instances. The predictions of the model are derived in terms of (i) firm size distribution, (ii) the distribution of firm growth rates, and (iii-iv) the relationships between firm size and the mean and variance of firm growth rates. We test the model against data from the worldwide pharmaceutical industry and find its predictions to be in good agreement with empirical evidence on all four dimensions
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