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.

Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality

We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In particular, we give bounds on the first negative Lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time. We then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum and relate the scaling exponent to the scaling of quantities like avalanche size, duration, density of active sites, etc ...Comment: 33 pages, 6 figures, 1 table (to appear

A hyperchaotic system without equilibrium

Abstract: This article introduces a new chaotic system of 4-D autonomous ordinary differential equations, which has no equilibrium. This system shows a hyper-chaotic attractor. There is no sink in this system as there is no equilibrium. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincaré maps. There is little difference between this chaotic system and other chaotic systems with one or several equilibria shown by phase portraits, Lyapunov exponents and time series methods, but the Poincaré maps show this system is a chaotic system with more complicated dynamics. Moreover, the circuit realization is also presented

Nonlinear time-series analysis of Hyperion's lightcurves

Hyperion is a satellite of Saturn that was predicted to remain in a chaotic rotational state. This was confirmed to some extent by Voyager 2 and Cassini series of images and some ground-based photometric observations. The aim of this aticle is to explore conditions for potential observations to meet in order to estimate a maximal Lyapunov Exponent (mLE), which being positive is an indicator of chaos and allows to characterise it quantitatively. Lightcurves existing in literature as well as numerical simulations are examined using standard tools of theory of chaos. It is found that existing datasets are too short and undersampled to detect a positive mLE, although its presence is not rejected. Analysis of simulated lightcurves leads to an assertion that observations from one site should be performed over a year-long period to detect a positive mLE, if present, in a reliable way. Another approach would be to use 2---3 telescopes spread over the world to have observations distributed more uniformly. This may be achieved without disrupting other observational projects being conducted. The necessity of time-series to be stationary is highly stressed.Comment: 34 pages, 12 figures, 4 tables; v2 after referee report; matches the version accepted in Astrophysics and Space Scienc

Role of anatomical sites and correlated risk factors on the survival of orthodontic miniscrew implants:a systematic review and meta-analysis

Abstract Objectives The aim of this review was to systematically evaluate the failure rates of miniscrews related to their specific insertion site and explore the insertion site dependent risk factors contributing to their failure. Search methods An electronic search was conducted in the Cochrane Central Register of Controlled Trials (CENTRAL), Web of Knowledge, Scopus, MEDLINE and PubMed up to October 2017. A comprehensive manual search was also performed. Eligibility criteria Randomised clinical trials and prospective non-randomised studies, reporting a minimum of 20 inserted miniscrews in a specific insertion site and reporting the miniscrews’ failure rate in that insertion site, were included. Data collection and analysis Study selection, data extraction and quality assessment were performed independently by two reviewers. Studies were sub-grouped according to the insertion site, and the failure rates for every individual insertion site were analysed using a random-effects model with corresponding 95% confidence interval. Sensitivity analyses were performed in order to test the robustness of the reported results. Results Overall, 61 studies were included in the quantitative synthesis. Palatal sites had failure rates of 1.3% (95% CI 0.3–6), 4.8% (95% CI 1.6–13.4) and 5.5% (95% CI 2.8–10.7) for the midpalatal, paramedian and parapalatal insertion sites, respectively. The failure rates for the maxillary buccal sites were 9.2% (95% CI 7.4–11.4), 9.7% (95% CI 5.1–17.6) and 16.4% (95% CI 4.9–42.5) for the interradicular miniscrews inserted between maxillary first molars and second premolars and between maxillary canines and lateral incisors, and those inserted in the zygomatic buttress respectively. The failure rates for the mandibular buccal insertion sites were 13.5% (95% CI 7.3–23.6) and 9.9% (95% CI 4.9–19.1) for the interradicular miniscrews inserted between mandibular first molars and second premolars and between mandibular canines and first premolars, respectively. The risk of failure increased when the miniscrews contacted the roots, with a risk ratio of 8.7 (95% CI 5.1–14.7). Conclusions Orthodontic miniscrew implants provide acceptable success rates that vary among the explored insertion sites. Very low to low quality of evidence suggests that miniscrews inserted in midpalatal locations have a failure rate of 1.3% and those inserted in the zygomatic buttress have a failure rate of 16.4%. Moderate quality of evidence indicates that root contact significantly contributes to the failure of interradicular miniscrews placed between the first molars and second premolars. Results should be interpreted with caution due to methodological drawbacks in some of the included studies