16,646 research outputs found
Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding
The vicinity of phase transitions selectively amplifies weak stimuli,
yielding optimal sensitivity to distinguish external input. Along with this
enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the
specificity of the response. Given that the specificity of the response is
largely compromised when the sensitivity is maximal, the overall benefit of
criticality for signal processing remains questionable. Here it is shown that
this impasse can be solved by heterogeneous systems incorporating functional
diversity, in which critical and subcritical components coexist. The subnetwork
of critical elements has optimal sensitivity, and the subnetwork of subcritical
elements has enhanced specificity. Combining segregated features extracted from
the different subgroups, the resulting collective response can maximise the
tradeoff between sensitivity and specificity measured by the
dynamic-range-to-noise-ratio. Although numerous benefits can be observed when
the entire system is critical, our results highlight that optimal performance
is obtained when only a small subset of the system is at criticality.Comment: 7 pages, 4 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
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
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
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