1,564 research outputs found
Google matrix of the world trade network
Using the United Nations Commodity Trade Statistics Database
[http://comtrade.un.org/db/] we construct the Google matrix of the world trade
network and analyze its properties for various trade commodities for all
countries and all available years from 1962 to 2009. The trade flows on this
network are classified with the help of PageRank and CheiRank algorithms
developed for the World Wide Web and other large scale directed networks. For
the world trade this ranking treats all countries on equal democratic grounds
independent of country richness. Still this method puts at the top a group of
industrially developed countries for trade in {\it all commodities}. Our study
establishes the existence of two solid state like domains of rich and poor
countries which remain stable in time, while the majority of countries are
shown to be in a gas like phase with strong rank fluctuations. A simple random
matrix model provides a good description of statistical distribution of
countries in two-dimensional rank plane. The comparison with usual ranking by
export and import highlights new features and possibilities of our approach.Comment: 14 pages, 13 figures. More detailed data and high definition figures
are available on the website:
http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank/index.htm
Google matrix analysis of DNA sequences
For DNA sequences of various species we construct the Google matrix G of
Markov transitions between nearby words composed of several letters. The
statistical distribution of matrix elements of this matrix is shown to be
described by a power law with the exponent being close to those of outgoing
links in such scale-free networks as the World Wide Web (WWW). At the same time
the sum of ingoing matrix elements is characterized by the exponent being
significantly larger than those typical for WWW networks. This results in a
slow algebraic decay of the PageRank probability determined by the distribution
of ingoing elements. The spectrum of G is characterized by a large gap leading
to a rapid relaxation process on the DNA sequence networks. We introduce the
PageRank proximity correlator between different species which determines their
statistical similarity from the view point of Markov chains. The properties of
other eigenstates of the Google matrix are also discussed. Our results
establish scale-free features of DNA sequence networks showing their
similarities and distinctions with the WWW and linguistic networks.Comment: latex, 11 fig
Enhancement of localization length for two interacting kicked rotators
We study the effect of coherent propagation of two interacting particles in a
disordered potential. The dependence of the enhancement factor for coherent
localization length due to interaction is investigated numerically in the model
of quantum chaos. The effect of interaction for two particles in many
dimensions is also discussed.Comment: 17 pages in revtex, 9 figures (postscript obtained upon request via
e-mail at [email protected]) submitted to Nonlinearit
Disorder and superconductivity : a new phase of bi-particle localized states
We study the two-dimensional, disordered, attractive Hubbard model by the
projector quantum Monte Carlo method and Bogoliubov - de Gennes mean-field
theory. Our results for the ground state show the appearance of a new phase
with charge localization in the metallic regime of the non-interacting model.
Contrary to the common lore, we demonstrate that mean-field theory fails to
predict this phase and is unable to describe the correct physical picture in
this regime.Comment: revtex, 4 pages, 3 figure
Google matrix analysis of the multiproduct world trade network
Using the United Nations COMTRADE database \cite{comtrade} we construct the
Google matrix of multiproduct world trade between the UN countries and
analyze the properties of trade flows on this network for years 1962 - 2010.
This construction, based on Markov chains, treats all countries on equal
democratic grounds independently of their richness and at the same time it
considers the contributions of trade products proportionally to their trade
volume. We consider the trade with 61 products for up to 227 countries. The
obtained results show that the trade contribution of products is asymmetric:
some of them are export oriented while others are import oriented even if the
ranking by their trade volume is symmetric in respect to export and import
after averaging over all world countries. The construction of the Google matrix
allows to investigate the sensitivity of trade balance in respect to price
variations of products, e.g. petroleum and gas, taking into account the world
connectivity of trade links. The trade balance based on PageRank and CheiRank
probabilities highlights the leading role of China and other BRICS countries in
the world trade in recent years. We also show that the eigenstates of with
large eigenvalues select specific trade communities.Comment: 19 pages, 25 figure
Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions
We study numerically the frequency modulated kicked nonlinear rotator with
effective dimension . We follow the time evolution of the model up
to kicks and determine the exponent of subdiffusive spreading
which changes from to when the dimension changes from to
. All results are obtained in a regime of relatively strong Anderson
localization well below the Anderson transition point existing for . We
explain that this variation of the exponent is different from the usual
dimensional Anderson models with local nonlinearity where drops
with increasing . We also argue that the renormalization arguments proposed
by Cherroret N et al. arXiv:1401.1038 are not valid.Comment: 8 pages, 3 figure
Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
We study numerically time evolution in classical lattices with weak or
moderate nonlinearity which leads to interactions between linear modes. Our
results show that in a certain strength range a moderate nonlinearity generates
a dynamical thermalization process which drives the system to the quantum Gibbs
distribution of probabilities, or average oscillation amplitudes. The effective
dynamical temperature of the lattice varies from large positive to large
negative values depending on energy of initially excited modes. This quantum
Gibbs distribution is drastically different from usually expected energy
equipartition over linear modes corresponding to a regime of classical
thermalization. Possible experimental observations of this dynamical
thermalization are discussed for cold atoms in optical lattices, nonlinear
photonic lattices and optical fiber arrays.Comment: 15 pages, 12 figures. Small modifs., video abstract 107MB at
http://www.quantware.ups-tlse.fr/dima/video/gibbs2013.mp
Opinion formation driven by PageRank node influence on directed networks
We study a two states opinion formation model driven by PageRank node
influence and report an extensive numerical study on how PageRank affects
collective opinion formations in large-scale empirical directed networks. In
our model the opinion of a node can be updated by the sum of its neighbor
nodes' opinions weighted by the node influence of the neighbor nodes at each
step. We consider PageRank probability and its sublinear power as node
influence measures and investigate evolution of opinion under various
conditions. First, we observe that all networks reach steady state opinion
after a certain relaxation time. This time scale is decreasing with the
heterogeneity of node influence in the networks. Second, we find that our model
shows consensus and non-consensus behavior in steady state depending on types
of networks: Web graph, citation network of physics articles, and LiveJournal
social network show non-consensus behavior while Wikipedia article network
shows consensus behavior. Third, we find that a more heterogeneous influence
distribution leads to a more uniform opinion state in the cases of Web graph,
Wikipedia, and Livejournal. However, the opposite behavior is observed in the
citation network. Finally we identify that a small number of influential nodes
can impose their own opinion on significant fraction of other nodes in all
considered networks. Our study shows that the effects of heterogeneity of node
influence on opinion formation can be significant and suggests further
investigations on the interplay between node influence and collective opinion
in networks.Comment: 10 pages, 6 figures. Published in Physica A 436, 707-715 (2015
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