120 research outputs found
Zipf Law in Firms Bankruptcy
Using an exhaustive list of Japanese bankruptcy in 1997, we discover a Zipf
law for the distribution of total liabilities of bankrupted firms in high debt
range. The life-time of these bankrupted firms has exponential distribution in
correlation with entry rate of new firms. We also show that the debt and size
are highly correlated, so the Zipf law holds consistently with that for size
distribution. In attempt to understand ``physics'' of bankruptcy, we show that
a model of debtor-creditor dynamics of firms and a bank, recently proposed by
economists, can reproduce these phenomenological findings
Tail universalities in rank distributions as an algebraic problem: the beta-like function
Although power laws of the Zipf type have been used by many workers to fit
rank distributions in different fields like in economy, geophysics, genetics,
soft-matter, networks etc., these fits usually fail at the tails. Some
distributions have been proposed to solve the problem, but unfortunately they
do not fit at the same time both ending tails. We show that many different data
in rank laws, like in granular materials, codons, author impact in scientific
journal, etc. are very well fitted by a beta-like function. Then we propose
that such universality is due to the fact that a system made from many
subsystems or choices, imply stretched exponential frequency-rank functions
which qualitatively and quantitatively can be fitted with the proposed
beta-like function distribution in the limit of many random variables. We prove
this by transforming the problem into an algebraic one: finding the rank of
successive products of a given set of numbers
Directed Accelerated Growth: Application in Citation Network
In many real world networks, the number of links increases nonlinearly with
the number of nodes. Models of such accelerated growth have been considered
earlier with deterministic and stochastic number of links. Here we consider
stochastic accelerated growth in a network where links are directed. With the
number of out-going links following a power law distribution, the results are
similar to the undirected case. As the accelerated growth is enhanced, the
degree distribution becomes independent of the ``initial attractiveness'', a
parameter which plays a key role in directed networks. As an example of a
directed model with accelerated growth, the citation network is considered, in
which the distribution of the number of outgoing link has an exponential tail.
The role of accelerated growth is examined here with two different growth laws.Comment: To be published in the proceedings of Statphys Kolkata V (Physica A
Scale-free download network for publications
The scale-free power-law behavior of the statistics of the download frequency
of publications has been, for the first time, reported. The data of the
download frequency of publications are taken from a well-constructed web page
in the field of economic physics (http://www.unifr.ch/econophysics/). The
Zipf-law analysis and the Tsallis entropy method were used to fit the download
frequency. It was found that the power-law exponent of rank-ordered frequency
distribution is which is consistent with the
power-law exponent for the cumulated frequency
distributions. Preferential attachment model of Barabasi and Albert network has
been used to explain the download network.Comment: 3 pages, 2 figure
Citation Networks in High Energy Physics
The citation network constituted by the SPIRES data base is investigated
empirically. The probability that a given paper in the SPIRES data base has
citations is well described by simple power laws, ,
with for less than 50 citations and for 50 or more citations. Two models are presented that both represent the
data well, one which generates power laws and one which generates a stretched
exponential. It is not possible to discriminate between these models on the
present empirical basis. A consideration of citation distribution by subfield
shows that the citation patterns of high energy physics form a remarkably
homogeneous network. Further, we utilize the knowledge of the citation
distributions to demonstrate the extreme improbability that the citation
records of selected individuals and institutions have been obtained by a random
draw on the resulting distribution.Comment: 9 pages, 6 figures, 2 table
Multifractality of Inverse Statistics of Exit Distances in 3D Fully Developed Turbulence
The inverse structure functions of exit distances have been introduced as a
novel diagnostic of turbulence which emphasizes the more laminar regions [1-4].
Using Taylor's frozen field hypothesis, we investigate the statistical
properties of the exit distances of empirical 3D fully developed turbulence. We
find that the probability density functions of exit distances at different
velocity thresholds can be approximated by stretched exponentials with
exponents varying with the velocity thresholds below a critical threshold. We
show that the inverse structure functions exhibit clear extended
self-similarity (ESS). The ESS exponents \xi(p,2) for small p (p<3.5) are well
captured by the prediction of \xi(p,2)= p/2 obtained by assuming a universal
distribution of the exit distances, while the observed deviations for large p's
characterize the dependence of these distributions on the velocity thresholds.
By applying a box-counting multifractal analysis of the natural measure
constructed on the time series of exit distances, we demonstrate the existence
of a genuine multifractality, endowed in addition with negative dimensions.
Performing the same analysis of reshuffled time series with otherwise identical
statistical properties for which multifractality is absent, we show that
multifractality can be traced back to non-trivial dependence in the time series
of exit times, suggesting a non-trivial organization of weakly-turbulent
regions.Comment: 16 RevTex pages including 7 eps figure
Beyond the Power Law: Uncovering Stylized Facts in Interbank Networks
We use daily data on bilateral interbank exposures and monthly bank balance
sheets to study network characteristics of the Russian interbank market over
Aug 1998 - Oct 2004. Specifically, we examine the distributions of (un)directed
(un)weighted degree, nodal attributes (bank assets, capital and
capital-to-assets ratio) and edge weights (loan size and counterparty
exposure). We search for the theoretical distribution that fits the data best
and report the "best" fit parameters. We observe that all studied distributions
are heavy tailed. The fat tail typically contains 20% of the data and can be
mostly described well by a truncated power law. Also the power law, stretched
exponential and log-normal provide reasonably good fits to the tails of the
data. In most cases, however, separating the bulk and tail parts of the data is
hard, so we proceed to study the full range of the events. We find that the
stretched exponential and the log-normal distributions fit the full range of
the data best. These conclusions are robust to 1) whether we aggregate the data
over a week, month, quarter or year; 2) whether we look at the "growth" versus
"maturity" phases of interbank market development; and 3) with minor
exceptions, whether we look at the "normal" versus "crisis" operation periods.
In line with prior research, we find that the network topology changes greatly
as the interbank market moves from a "normal" to a "crisis" operation period.Comment: 17 pages, 9 figure
q-exponential, Weibull, and q-Weibull distributions: an empirical analysis
In a comparative study, the q-exponential and Weibull distributions are
employed to investigate frequency distributions of basketball baskets, cyclone
victims, brand-name drugs by retail sales, and highway length. In order to
analyze the intermediate cases, a distribution, the q-Weibull one, which
interpolates the q-exponential and Weibull ones, is introduced. It is verified
that the basketball baskets distribution is well described by a q-exponential,
whereas the cyclone victims and brand-name drugs by retail sales ones are
better adjusted by a Weibull distribution. On the other hand, for highway
length the q-exponential and Weibull distributions do not give satisfactory
adjustment, being necessary to employ the q-Weibull distribution. Furthermore,
the introduction of this interpolating distribution gives an illumination from
the point of view of the stretched exponential against inverse power law
(q-exponential with q > 1) controversy.Comment: 6 pages, Latex. To appear in Physica
Complex Network Properties of Chinese Natural Science Basic Research
In this paper, we studied the research areas of Chinese natural science basic
research from a point view of complex network. Two research areas are
considered to be connected if they appear in one fund proposal. The explicit
network of such connections using data from 1999 to 2004 is constructed. The
analysis of the real data shows that the degree distribution of the {\bf
research areas network} (RAN) may be better fitted by the exponential
distribution. It displays small world effect in which randomly chosen pairs of
research areas are typically separated by only a short path of intermediate
research areas. The average distance of RAN decreases with time, while the
average clustering coefficient increases with time, which indicates that the
scientific study would like to be integrated together in terms of the studied
areas. The relationship between the clustering coefficient and the
degree indicates that there is no hierarchical organization in RAN.Comment: 12 pages, 8 figures, accepted by Physica
Internal avalanches in a pile of superconducting vortices
Using an array of miniature Hall probes, we monitored the spatiotemporal
variation of the internal magnetic induction in a superconducting niobium
sample during a slow sweep of external magnetic field. We found that a sizable
fraction of the increase in the local vortex population occurs in abrupt jumps.
The size distribution of these avalanches presents a power-law collapse on a
limited range. In contrast, at low temperatures and low fields, huge avalanches
with a typical size occur and the system does not display a well-defined
macroscopic critical current.Comment: 5 pages including 5 figure
- …