90 research outputs found
Universal patterns in sound amplitudes of songs and music genres
We report a statistical analysis over more than eight thousand songs.
Specifically, we investigate the probability distribution of the normalized
sound amplitudes. Our findings seems to suggest a universal form of
distribution which presents a good agreement with a one-parameter stretched
Gaussian. We also argue that this parameter can give information on music
complexity, and consequently it goes towards classifying songs as well as music
genres. Additionally, we present statistical evidences that correlation aspects
of the songs are directly related with the non-Gaussian nature of their sound
amplitude distributions.Comment: Accepted for publication as a Brief Report in Physical Review
Anomalous diffusion in a symbolic model
We address this work to investigate some statistical properties of symbolic
sequences generated by a numerical procedure in which the symbols are repeated
following a power law probability density. In this analysis, we consider that
the sum of n symbols represents the position of a particle in erratic movement.
This approach revealed a rich diffusive scenario characterized by non-Gaussian
distributions and, depending on the power law exponent and also on the
procedure used to build the walker, we may have superdiffusion, subdiffusion or
usual diffusion. Additionally, we use the continuous-time random walk framework
to compare with the numerical data, finding a good agreement. Because of its
simplicity and flexibility, this model can be a candidate to describe real
systems governed by power laws probabilities densities.Comment: Accepted for publication in Physica Script
Renormalization: the observable-state model
The usual mathematical formalism of quantum field theory is non-rigorous
because it contains divergences that can only be renormalized by non-rigorous
mathematical methods. The purpose of this paper is to present a method of
subtraction of this divergences using the formalism of decoherence. This is
achieved by replacing the standard renormalization method by a projector on a
well defined Hilbert subspace. In this way a list of problems of the standard
formalism disappears while the physical results of QFT remains valid. From it
own nature, this formalism can be used in non-renormalizable theories.Comment: 23 page
Dynamics of tournaments: the soccer case
A random walk-like model is considered to discuss statistical aspects of
tournaments. The model is applied to soccer leagues with emphasis on the
scores. This competitive system was computationally simulated and the results
are compared with empirical data from the English, the German and the Spanish
leagues and showed a good agreement with them. The present approach enabled us
to characterize a diffusion where the scores are not normally distributed,
having a short and asymmetric tail extending towards more positive values. We
argue that this non-Gaussian behavior is related with the difference between
the teams and with the asymmetry of the scores system. In addition, we compared
two tournament systems: the all-play-all and the elimination tournaments.Comment: To appear in EPJ
`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories
Based on the algebraico-categorical (:sheaf-theoretic and sheaf
cohomological) conceptual and technical machinery of Abstract Differential
Geometry, a new, genuinely background spacetime manifold independent, field
quantization scenario for vacuum Einstein gravity and free Yang-Mills theories
is introduced. The scheme is coined `third quantization' and, although it
formally appears to follow a canonical route, it is fully covariant, because it
is an expressly functorial `procedure'. Various current and future Quantum
Gravity research issues are discussed under the light of 3rd-quantization. A
postscript gives a brief account of this author's personal encounters with
Rafael Sorkin and his work.Comment: 43 pages; latest version contributed to a fest-volume celebrating
Rafael Sorkin's 60th birthday (Erratum: in earlier versions I had wrongly
written that the Editor for this volume is Daniele Oriti, with CUP as
publisher. I apologize for the mistake.
Complexity-entropy causality plane: a useful approach for distinguishing songs
Nowadays we are often faced with huge databases resulting from the rapid
growth of data storage technologies. This is particularly true when dealing
with music databases. In this context, it is essential to have techniques and
tools able to discriminate properties from these massive sets. In this work, we
report on a statistical analysis of more than ten thousand songs aiming to
obtain a complexity hierarchy. Our approach is based on the estimation of the
permutation entropy combined with an intensive complexity measure, building up
the complexity-entropy causality plane. The results obtained indicate that this
representation space is very promising to discriminate songs as well as to
allow a relative quantitative comparison among songs. Additionally, we believe
that the here-reported method may be applied in practical situations since it
is simple, robust and has a fast numerical implementation.Comment: Accepted for publication in Physica
The Possibilist Transactional Interpretation and Relativity
A recent ontological variant of Cramer's Transactional Interpretation, called
"Possibilist Transactional Interpretation" or PTI, is extended to the
relativistic domain. The present interpretation clarifies the concept of
'absorption,' which plays a crucial role in TI (and in PTI). In particular, in
the relativistic domain, coupling amplitudes between fields are interpreted as
amplitudes for the generation of confirmation waves (CW) by a potential
absorber in response to offer waves (OW), whereas in the nonrelativistic
context CW are taken as generated with certainty. It is pointed out that
solving the measurement problem requires venturing into the relativistic domain
in which emissions and absorptions take place; nonrelativistic quantum
mechanics only applies to quanta considered as 'already in existence' (i.e.,
'free quanta'), and therefore cannot fully account for the phenomenon of
measurement, in which quanta are tied to sources and sinks.Comment: Final version with some minor corrections as published in Foundations
of Physics. This paper has significant overlap with Chapter 6 of my book on
the Transactional Interpretation, forthcoming from Cambridge University
Press:
http://www.cambridge.org/us/knowledge/isbn/item6860644/?site_locale=en_US
(Additional preview material is available at rekastner.wordpress.com)
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