2,754 research outputs found
Using Topological Statistics to Detect Determinism in Time Series
Statistical differentiability of the measure along the reconstructed
trajectory is a good candidate to quantify determinism in time series. The
procedure is based upon a formula that explicitly shows the sensitivity of the
measure to stochasticity. Numerical results for partially surrogated time
series and series derived from several stochastic models, illustrate the
usefulness of the method proposed here. The method is shown to work also for
high--dimensional systems and experimental time seriesComment: 23 RevTeX pages, 14 eps figures. To appear in Physical Review
A quasi-diagonal approach to the estimation of Lyapunov spectra for spatio-temporal systems from multivariate time series
We describe methods of estimating the entire Lyapunov spectrum of a spatially
extended system from multivariate time-series observations. Provided that the
coupling in the system is short range, the Jacobian has a banded structure and
can be estimated using spatially localised reconstructions in low embedding
dimensions. This circumvents the ``curse of dimensionality'' that prevents the
accurate reconstruction of high-dimensional dynamics from observed time series.
The technique is illustrated using coupled map lattices as prototype models for
spatio-temporal chaos and is found to work even when the coupling is not
strictly local but only exponentially decaying.Comment: 13 pages, LaTeX (RevTeX), 13 Postscript figs, to be submitted to
Phys.Rev.
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
Exploring helical dynamos with machine learning
We use ensemble machine learning algorithms to study the evolution of
magnetic fields in magnetohydrodynamic (MHD) turbulence that is helically
forced. We perform direct numerical simulations of helically forced turbulence
using mean field formalism, with electromotive force (EMF) modeled both as a
linear and non-linear function of the mean magnetic field and current density.
The form of the EMF is determined using regularized linear regression and
random forests. We also compare various analytical models to the data using
Bayesian inference with Markov Chain Monte Carlo (MCMC) sampling. Our results
demonstrate that linear regression is largely successful at predicting the EMF
and the use of more sophisticated algorithms (random forests, MCMC) do not lead
to significant improvement in the fits. We conclude that the data we are
looking at is effectively low dimensional and essentially linear. Finally, to
encourage further exploration by the community, we provide all of our
simulation data and analysis scripts as open source IPython notebooks.Comment: accepted by A&A, 11 pages, 6 figures, 3 tables, data + IPython
notebooks: https://github.com/fnauman/ML_alpha
Bose-Einstein correlations for Levy stable source distributions
The peak of the two-particle Bose-Einstein correlation functions has a very
interesting structure. It is often believed to have a multivariate Gaussian
form. We show here that for the class of stable distributions, characterized by
the index of stability , the peak has a stretched exponential
shape. The Gaussian form corresponds then to the special case of .
We give examples for the Bose-Einstein correlation functions for univariate as
well as multivariate stable distributions, and check the model against
two-particle correlation data.Comment: 30 pages, 1 figure, an important misprint in former eqs. (37-38) and
other minor misprints are corrected, citations update
Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection
Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness.

Methods: This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices.

Results: On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8% plus or minus 2.0%. The true positive classification performance is 95.4% plus or minus 3.2%, and the true negative performance is 91.5% plus or minus 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools.

Conclusions: Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.

Top Quark Physics at the Tevatron
We review the field of top-quark physics with an emphasis on experimental
techniques. The role of the top quark in the Standard Model of particle physics
is summarized and the basic phenomenology of top-quark production and decay is
introduced. We discuss how contributions from physics beyond the Standard Model
could affect top-quark properties or event samples. The many measurements made
at the Fermilab Tevatron, which test the Standard Model predictions or probe
for direct evidence of new physics using the top-quark event samples, are
reviewed here.Comment: 50 pages, 17 figures, 2 tables; version accepted by Review of Modern
Physic
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