101 research outputs found
Models and average properties of scale-free directed networks
We extend the merging model for undirected networks by Kim et al. [Eur. Phys.
J. B 43, 369 (2004)] to directed networks and investigate the emerging
scale-free networks. Two versions of the directed merging model, friendly and
hostile merging, give rise to two distinct network types. We uncover that some
non-trivial features of these two network types resemble two levels of a
certain randomization/non-specificity in the link reshuffling during network
evolution. Furthermore the same features show up, respectively, in metabolic
networks and transcriptional networks. We introduce measures that single out
the distinguishing features between the two prototype networks, as well as
point out features which are beyond the prototypes.Comment: 7 pages, 8 figure
Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings
The word-frequency distribution of a text written by an author is well
accounted for by a maximum entropy distribution, the RGF (random group
formation)-prediction. The RGF-distribution is completely determined by the a
priori values of the total number of words in the text (M), the number of
distinct words (N) and the number of repetitions of the most common word
(k_max). It is here shown that this maximum entropy prediction also describes a
text written in Chinese characters. In particular it is shown that although the
same Chinese text written in words and Chinese characters have quite
differently shaped distributions, they are nevertheless both well predicted by
their respective three a priori characteristic values. It is pointed out that
this is analogous to the change in the shape of the distribution when
translating a given text to another language. Another consequence of the
RGF-prediction is that taking a part of a long text will change the input
parameters (M, N, k_max) and consequently also the shape of the frequency
distribution. This is explicitly confirmed for texts written in Chinese
characters. Since the RGF-prediction has no system-specific information beyond
the three a priori values (M, N, k_max), any specific language characteristic
has to be sought in systematic deviations from the RGF-prediction and the
measured frequencies. One such systematic deviation is identified and, through
a statistical information theoretical argument and an extended RGF-model, it is
proposed that this deviation is caused by multiple meanings of Chinese
characters. The effect is stronger for Chinese characters than for Chinese
words. The relation between Zipf's law, the Simon-model for texts and the
present results are discussed.Comment: 15 pages, 10 figures, 2 table
The likely determines the unlikely
We point out that the functional form describing the frequency of sizes of
events in complex systems (e.g. earthquakes, forest fires, bursts of neuronal
activity) can be obtained from maximal likelihood inference, which, remarkably,
only involve a few available observed measures such as number of events, total
event size and extremes. Most importantly, the method is able to predict with
high accuracy the frequency of the rare extreme events. To be able to predict
the few, often big impact events, from the frequent small events is of course
of great general importance. For a data set of wind speed we are able to
predict the frequency of gales with good precision. We analyse several examples
ranging from the shortest length of a recruit to the number of Chinese
characters which occur only once in a text.Comment: 7 pages, 5 figures, 2 table
Dynamic critical behaviors of three-dimensional XY models related to superconductors/superfluids
The dynamic critical exponent z is determined from numerical simulations for
the three-dimensional XY model subject to two types of dynamics, i.e.
relaxational dynamics and resistively shunted junction (RSJ) dynamics, as well
as for two different treatments of the boundary, i.e., periodic boundary
condition (PBC) and fluctuating twist boundary condition (FTBC). In case of
relaxational dynamics, finite size scaling at the critical temperature gives
for PBC and 1.5 for FTBC, while for RSJ dynamics is
obtained in both cases. The results are discussed in the context of
superfluid/superconductors and vortex dynamics, and are compared with what have
been found for other related models.Comment: 7 pages, 5 figures with europhys.sty, to appear in Europhys. Let
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