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

Gaussian processes for switching regimes

It has been shown that Gaussian processes are a competitive tool for nonparametric regression and classification. Furthermore they are equivalent to neural networks in the limit of an infinite number of neurons. Here we show that the versatility of Gaussian processes at defining different textural characteristics can be used to recognise different regimes in a signal switching between different sources

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

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

Quantum chemistry calculations for molecules coupled to reservoirs: Formalism, implementation, and application to benzenedithiol

Modern quantum chemistry calculations are usually implemented for isolated systems—big molecules or atom clusters; total energy and particle number are fixed. However, in many situations, like quantum transport calculations or molecules in a electrochemical environment, the molecule can exchange particles (and energy) with a reservoir. Calculations for such cases require to switch from the canonical to a grand canonical description, where one fixes the chemical potential rather than particle number. To achieve this goal, the authors propose an implementation in standard quantum chemistry packages. An application to the nonlinear charge transport through 1,4-benzenedithiol will be presented. They explain the leading finite bias effect on the transmission as a consequence of a nonequilibrium Stark effect and discuss the relation to earlier work

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

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

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.

High-density genotyping reveals candidate genomic regions for chicken body size in breeds of Asian origin

Body size is one of the main selection indices in chicken breeding. Although often investigated, knowledge of the underlying genetic mechanisms is incomplete. The aim of the current study was to identify genomic regions associated with body size differences between Asian Game and Asian Bantam type chickens. In this study, 94 and 107 chickens from four Asian Game and five Asian Bantam type breeds, respectively, were genotyped using the chicken 580K single nucleotide polymorphism (SNP) array. A genome-wide association study (GWAS) and principal component analyses (PCA) were performed to identify genomic regions associated with body size related-traits such as wing length, shank length, shank thickness, keel length, and body weight. Hierarchical clustering of genotype data showed a clear genetic difference between the investigated Asian Game and Asian Bantam chicken types. GWAS identified 16 genomic regions associated with wing length (2, FDR ≤ 0.018), shank thickness (6, FDR ≤ 0.008), keel length (5, FDR ≤ 0.023), and body weight (3, FDR ≤ 0.041). PCA showed that the first principal component (PC1) separated the two chicken types and significantly correlated with the measured body size related-traits (p ≤ 2.24e-40). SNPs contributing significantly to PC1 were subjected to a more detailed investigation. This analysis identified 11 regions potentially associated with differences in body size related-traits. A region on chromosome 4 (GGA4) (17.3 - 21.3 Mb) was detected in both analyses GWAS and PCA. This region harbors 60 genes. Among them are myotubularin 1 (MTM1) and secreted frizzled-related protein 2 (SFPR2) which can be considered as potential candidate genes for body size related-traits. Our results clearly show that the investigated Asian Game type chicken breeds are genetically different from the Asian Bantam breeds. A region on GGA4 between 17.3 and 21.3 Mb was identified which contributes to the phenotypic difference, though further validation of candidate genes is necessary