3,214 research outputs found
Characterization of laser propagation through turbulent media by quantifiers based on the wavelet transform: dynamic study
We analyze, within the wavelet theory framework, the wandering over a screen
of the centroid of a laser beam after it has propagated through a time-changing
laboratory-generated turbulence. Following a previous work (Fractals 12 (2004)
223) two quantifiers are used, the Hurst parameter, , and the Normalized
Total Wavelet Entropy, . The temporal evolution of both
quantifiers, obtained from the laser spot data stream is studied and compared.
This allows us to extract information of the stochastic process associated to
the turbulence dynamics.Comment: 11 pages, 3 figures, accepted to be published in Physica
Distinguishing noise from chaos: objective versus subjective criteria using Horizontal Visibility Graph
A recently proposed methodology called the Horizontal Visibility Graph (HVG)
[Luque {\it et al.}, Phys. Rev. E., 80, 046103 (2009)] that constitutes a
geometrical simplification of the well known Visibility Graph algorithm [Lacasa
{\it et al.\/}, Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to
study the distinction between deterministic and stochastic components in time
series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)].
Specifically, the authors propose that the node degree distribution of these
processes follows an exponential functional of the form , in which is the node degree and is a
positive parameter able to distinguish between deterministic (chaotic) and
stochastic (uncorrelated and correlated) dynamics. In this work, we investigate
the characteristics of the node degree distributions constructed by using HVG,
for time series corresponding to chaotic maps and different stochastic
processes. We thoroughly study the methodology proposed by Lacasa and Toral
finding several cases for which their hypothesis is not valid. We propose a
methodology that uses the HVG together with Information Theory quantifiers. An
extensive and careful analysis of the node degree distributions obtained by
applying HVG allow us to conclude that the Fisher-Shannon information plane is
a remarkable tool able to graphically represent the different nature,
deterministic or stochastic, of the systems under study.Comment: Submitted to PLOS On
Connection Matrices and the Definability of Graph Parameters
In this paper we extend and prove in detail the Finite Rank Theorem for
connection matrices of graph parameters definable in Monadic Second Order Logic
with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and
J.A. Makowsky (2009). We demonstrate its vast applicability in simplifying
known and new non-definability results of graph properties and finding new
non-definability results for graph parameters. We also prove a Feferman-Vaught
Theorem for the logic CFOL, First Order Logic with the modular counting
quantifiers
The first order convergence law fails for random perfect graphs
We consider first order expressible properties of random perfect graphs. That
is, we pick a graph uniformly at random from all (labelled) perfect
graphs on vertices and consider the probability that it satisfies some
graph property that can be expressed in the first order language of graphs. We
show that there exists such a first order expressible property for which the
probability that satisfies it does not converge as .Comment: 11 pages. Minor corrections since last versio
- âŠ