170,073 research outputs found
Power laws, Pareto distributions and Zipf's law
When the probability of measuring a particular value of some quantity varies
inversely as a power of that value, the quantity is said to follow a power law,
also known variously as Zipf's law or the Pareto distribution. Power laws
appear widely in physics, biology, earth and planetary sciences, economics and
finance, computer science, demography and the social sciences. For instance,
the distributions of the sizes of cities, earthquakes, solar flares, moon
craters, wars and people's personal fortunes all appear to follow power laws.
The origin of power-law behaviour has been a topic of debate in the scientific
community for more than a century. Here we review some of the empirical
evidence for the existence of power-law forms and the theories proposed to
explain them.Comment: 28 pages, 16 figures, minor corrections and additions in this versio
Cognitive modelling of language acquisition with complex networks
ABSTRACT Cognitive modelling is a well-established computational intelligence tool, which is very useful for studying cognitive phenomena, such as young children's first language acquisition. Specifically, linguistic modelling has recently benefited greatly from complex network theory by modelling large sets of empirical linguistic data as complex networks, thereby illuminating interesting new patterns and trends. In this chapter, we show how simple network analysis techniques can be applied to the study of language acquisition, and we argue that they reveal otherwise hidden information. We also note that a key network parameter -the ranked frequency distribution of the links -provides useful knowledge about the data, even though it had been previously neglected in this domain
The quantum Loschmidt echo on flat tori
The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum
system to perturbations of the Hamiltonian. In the case of the standard
2-torus, we derive some explicit formulae for this quantity in the transition
regime where it is expected to decay in the semiclassical limit. The expression
involves both a two-microlocal defect measure of the initial data and the form
of the perturbation. As an application, we exhibit a non-concentration
criterium on the sequence of initial data under which one does not observe a
macroscopic decay of the Quantum Loschmidt Echo. We also apply our results to
several examples of physically relevant initial data such as coherent states
and plane waves.Comment: 34 page
Nuclear forward scattering in particulate matter: dependence of lineshape on particle size distribution
In synchrotron Moessbauer spectroscopy, the nuclear exciton polariton
manifests itself in the lineshape of the spectra of nuclear forward scattering
(NFS) Fourier-transformed from time domain to frequency domain. This lineshape
is generally described by the convolution of two intensity factors. One of them
is Lorentzian related to free decay. We derived the expressions for the second
factor related to Frenkel exciton polariton effects at propagation of
synchrotron radiation in Moessbauer media. Parameters of this Frenkelian shape
depend on the spatial configuration of Moessbauer media. In a layer of uniform
thickness, this factor is found to be a simple hypergeometric function. Next,
we consider the particles spread over a 2D surface or diluted in non-Moessbauer
media to exclude an overlap of ray shadows by different particles. Deconvolving
the purely polaritonic component of linewidths is suggested as a simple
procedure sharpening the experimental NFS spectra in frequency domain. The
lineshapes in these sharpened spectra are theoretically expressed via the
parameters of the particle size distributions (PSD). Then, these parameters are
determined through least-squares fitting of the line shapes.Comment: 13 pages, 12 figure
Adaptive Filtering Enhances Information Transmission in Visual Cortex
Sensory neuroscience seeks to understand how the brain encodes natural
environments. However, neural coding has largely been studied using simplified
stimuli. In order to assess whether the brain's coding strategy depend on the
stimulus ensemble, we apply a new information-theoretic method that allows
unbiased calculation of neural filters (receptive fields) from responses to
natural scenes or other complex signals with strong multipoint correlations. In
the cat primary visual cortex we compare responses to natural inputs with those
to noise inputs matched for luminance and contrast. We find that neural filters
adaptively change with the input ensemble so as to increase the information
carried by the neural response about the filtered stimulus. Adaptation affects
the spatial frequency composition of the filter, enhancing sensitivity to
under-represented frequencies in agreement with optimal encoding arguments.
Adaptation occurs over 40 s to many minutes, longer than most previously
reported forms of adaptation.Comment: 20 pages, 11 figures, includes supplementary informatio
Tsallis Distribution Decorated With Log-Periodic Oscillation
In many situations, in all branches of physics, one encounters power-like
behavior of some variables which are best described by a Tsallis distribution
characterized by a nonextensivity parameter and scale parameter .
However, there exist experimental results which can be described only by a
Tsallis distributions which are additionally decorated by some log-periodic
oscillating factor. We argue that such a factor can originate from allowing for
a complex nonextensivity parameter . The possible information conveyed by
such an approach (like the occurrence of complex heat capacity, the notion of
complex probability or complex multiplicative noise) will also be discussed.Comment: 17 pages, 1 figure. The content of this article was presented by Z.
Wlodarczyk at the SigmaPhi2014 conference at Rhodes, Greece, 7-11 July 2014.
To be published in Entropy (2015
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