1,457 research outputs found
Dynamic scaling approach to study time series fluctuations
We propose a new approach for properly analyzing stochastic time series by
mapping the dynamics of time series fluctuations onto a suitable nonequilibrium
surface-growth problem. In this framework, the fluctuation sampling time
interval plays the role of time variable, whereas the physical time is treated
as the analog of spatial variable. In this way we found that the fluctuations
of many real-world time series satisfy the analog of the Family-Viscek dynamic
scaling ansatz. This finding permits to use the powerful tools of kinetic
roughening theory to classify, model, and forecast the fluctuations of
real-world time series.Comment: 25 pages, 7 figures, 1 tabl
Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics
We experimentally observe the nonlinear dynamics of an optoelectronic
time-delayed feedback loop designed for chaotic communication using commercial
fiber optic links, and we simulate the system using delay differential
equations. We show that synchronization of a numerical model to experimental
measurements provides a new way to assimilate data and forecast the future of
this time-delayed high-dimensional system. For this system, which has a
feedback time delay of 22 ns, we show that one can predict the time series for
up to several delay periods, when the dynamics is about 15 dimensional.Comment: 10 pages, 4 figure
Local prediction of turning points of oscillating time series
For oscillating time series, the prediction is often focused on the turning
points. In order to predict the turning point magnitudes and times it is
proposed to form the state space reconstruction only from the turning points
and modify the local (nearest neighbor) model accordingly. The model on turning
points gives optimal prediction at a lower dimensional state space than the
optimal local model applied directly on the oscillating time series and is thus
computationally more efficient. Monte Carlo simulations on different
oscillating nonlinear systems showed that it gives better predictions of
turning points and this is confirmed also for the time series of annual
sunspots and total stress in a plastic deformation experiment.Comment: 7 pages, 5 figures, 2 tables, submitted to PR
The prediction of future from the past: an old problem from a modern perspective
The idea of predicting the future from the knowledge of the past is quite
natural when dealing with systems whose equations of motion are not known. Such
a long-standing issue is revisited in the light of modern ergodic theory of
dynamical systems and becomes particularly interesting from a pedagogical
perspective due to its close link with Poincar\'e's recurrence. Using such a
connection, a very general result of ergodic theory - Kac's lemma - can be used
to establish the intrinsic limitations to the possibility of predicting the
future from the past. In spite of a naive expectation, predictability results
to be hindered rather by the effective number of degrees of freedom of a system
than by the presence of chaos. If the effective number of degrees of freedom
becomes large enough, regardless the regular or chaotic nature of the system,
predictions turn out to be practically impossible. The discussion of these
issues is illustrated with the help of the numerical study of simple models.Comment: 9 pages, 4 figure
Many Roads to Synchrony: Natural Time Scales and Their Algorithms
We consider two important time scales---the Markov and cryptic orders---that
monitor how an observer synchronizes to a finitary stochastic process. We show
how to compute these orders exactly and that they are most efficiently
calculated from the epsilon-machine, a process's minimal unifilar model.
Surprisingly, though the Markov order is a basic concept from stochastic
process theory, it is not a probabilistic property of a process. Rather, it is
a topological property and, moreover, it is not computable from any
finite-state model other than the epsilon-machine. Via an exhaustive survey, we
close by demonstrating that infinite Markov and infinite cryptic orders are a
dominant feature in the space of finite-memory processes. We draw out the roles
played in statistical mechanical spin systems by these two complementary length
scales.Comment: 17 pages, 16 figures:
http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm. Santa Fe Institute Working
Paper 10-11-02
Phylogeny, genetic relationships and population structure of five Italian local chicken breeds
Number and population size of local chicken breeds in Italy is considered to be critical. Molecular data can be used to provide reliable insight into the diversity of chicken breeds. The first aim of this study was to investigate the maternal genetic origin of five Italian local chicken breeds (Ancona, Livorno, Modenese, Romagnola and Valdarnese bianca) based on mitochondrial DNA (mtDNA) information. Secondly, the extent of the genetic diversity, population structure and the genetic relationships among these chicken populations, by using 27 microsatellite markers, were assessed. To achieve these targets, a 506 bp fragment of the D-loop region was sequenced in 50 chickens of the five breeds. Eighteen variable sites were observed which defined 12 haplotypes. They were assigned to three clades and two maternal lineages. Results indicated that 90% of the haplotypes are related to clade E, which has been described to originate from the Indian subcontinent. For the microsatellite analysis, 137 individual blood samples from the five Italian breeds were included. A total of 147 alleles were detected at 27 microsatellite loci. The five Italian breeds showed a slightly higher degree of inbreeding (FIS=0.08) than the commercial populations that served as reference. Structure analysis showed a separation of the Italian breeds from the reference populations. A further sub-clustering allowed discriminating among the five different Italian breeds. This research provides insight into population structure, relatedness and variability of the five studied breeds
A pseudo-spectral approach to inverse problems in interface dynamics
An improved scheme for computing coupling parameters of the
Kardar-Parisi-Zhang equation from a collection of successive interface
profiles, is presented. The approach hinges on a spectral representation of
this equation. An appropriate discretization based on a Fourier representation,
is discussed as a by-product of the above scheme. Our method is first tested on
profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it
is shown to reproduce the input parameters very accurately. When applied to
microscopic models of growth, it provides the values of the coupling parameters
associated with the corresponding continuum equations. This technique favorably
compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys.
Rev.
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