Phase synchronization from noisy univariate signals

We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft, another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Karman vortex flow meters.Comment: 4 pages, 4 figure

Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood

A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least squares approach is fundamentally flawed in that it assumes independent, normally distributed (IND) forecast errors: nonlinear models will not yield IND errors even if the noise is IND. A new cost function is obtained via the maximum likelihood principle; superior results are illustrated both for small data sets and infinitely long data streams.Comment: RevTex, 11 pages, 4 figure

X-ray Fluctuation Power Spectral Densities of Seyfert 1 Galaxies

By combining complementary monitoring observations spanning long, medium and short time scales, we have constructed power spectral densities (PSDs) of six Seyfert~1 galaxies. These PSDs span $\gtrsim$4 orders of magnitude in temporal frequency, sampling variations on time scales ranging from tens of minutes to over a year. In at least four cases, the PSD shows a "break," a significant departure from a power law, typically on time scales of order a few days. This is similar to the behavior of Galactic X-ray binaries (XRBs), lower mass compact systems with breaks on time scales of seconds. NGC 3783 shows tentative evidence for a doubly-broken power law, a feature that until now has only been seen in the (much better-defined) PSDs of low-state XRBs. It is also interesting that (when one previously-observed object is added to make a small sample of seven), an apparently significant correlation is seen between the break time scale $T$ and the putative black hole mass $M_{\rm BH}$, while none is seen between break time scale and luminosity. The data are consistent with the linear relation T = M_{\rm BH}/10^{6.5} \Msun; extrapolation over 6--7 orders of magnitude is in reasonable agreement with XRBs. All of this strengthens the case for a physical similarity between Seyfert~1s and XRBs.Comment: 27 pages, 13 figures. Accepted for publication in ApJ. Typo correcte

A near-IR variability study of the Galactic black hole: a red noise source with no detected periodicity

We present the results of near-infrared (2 and 3 microns) monitoring of Sgr A*-IR with 1 min time sampling using the natural and laser guide star adaptive optics (LGS AO) system at the Keck II telescope. Sgr A*-IR was observed continuously for up to three hours on each of seven nights, between 2005 July and 2007 August. Sgr A*-IR is detected at all times and is continuously variable, with a median observed 2 micron flux density of 0.192 mJy, corresponding to 16.3 magnitude at K'. These observations allow us to investigate Nyquist sampled periods ranging from about 2 minutes to an hour. Using Monte Carlo simulations, we find that the variability of Sgr A* in this data set is consistent with models based on correlated noise with power spectra having frequency dependent power law slopes between 2.0 to 3.0, consistent with those reported for AGN light curves. Of particular interest are periods of ~20 min, corresponding to a quasi-periodic signal claimed based upon previous near-infrared observations and interpreted as the orbit of a 'hot spot' at or near the last stable orbit of a spinning black hole. We find no significant periodicity at any time scale probed in these new observations for periodic signals. This study is sensitive to periodic signals with amplitudes greater than 20% of the maximum amplitude of the underlying red noise component for light curves with duration greater than ~2 hours at a 98% confidence limit.Comment: 37 pages, 2 tables, 17 figures, accepted by Ap

Explicit Model Checking of Very Large MDP using Partitioning and Secondary Storage

The applicability of model checking is hindered by the state space explosion problem in combination with limited amounts of main memory. To extend its reach, the large available capacities of secondary storage such as hard disks can be exploited. Due to the specific performance characteristics of secondary storage technologies, specialised algorithms are required. In this paper, we present a technique to use secondary storage for probabilistic model checking of Markov decision processes. It combines state space exploration based on partitioning with a block-iterative variant of value iteration over the same partitions for the analysis of probabilistic reachability and expected-reward properties. A sparse matrix-like representation is used to store partitions on secondary storage in a compact format. All file accesses are sequential, and compression can be used without affecting runtime. The technique has been implemented within the Modest Toolset. We evaluate its performance on several benchmark models of up to 3.5 billion states. In the analysis of time-bounded properties on real-time models, our method neutralises the state space explosion induced by the time bound in its entirety.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-24953-7_1

Comparative Compositions of Grain of Bread Wheat, Emmer and Spelt Grown with Different Levels of Nitrogen Fertilisation

Five cultivars of bread wheat and spelt and three of emmer were grown in replicate randomised field trials on two sites for two years with 100 and 200 kg nitrogen fertiliser per hectare, reflecting low input and intensive farming systems. Wholemeal flours were analysed for components that are suggested to contribute to a healthy diet. The ranges of all components overlapped between the three cereal types, reflecting the effects of both genotype and environment. Nevertheless, statistically significant differences in the contents of some components were observed. Notably, emmer and spelt had higher contents of protein, iron, zinc, magnesium, choline and glycine betaine, but also of asparagine (the precursor of acrylamide) and raffinose. By contrast, bread wheat had higher contents of the two major types of fibre, arabinoxylan (AX) and _-glucan, than emmer and a higher AX content than spelt. Although such differences in composition may be suggested to result in effects on metabolic parameters and health when studied in isolation, the final effects will depend on the quantity consumed and the composition of the overall diet

An Extreme Ultraviolet Explorer Atlas of Seyfert Galaxy Light Curves: Search for Periodicity

The Deep Survey instrument on the Extreme Ultraviolet Explorer satellite (EUVE) obtained long, nearly continuous soft X-ray light curves of 5-33 days duration for 14 Seyfert galaxies and QSOs. We present a uniform reduction of these data, which account for a total of 231 days of observation. Several of these light curves are well suited to a search for periodicity or QPOs in the range of hours to days that might be expected from dynamical processes in the inner accretion disk around ~10^8 M_sun black holes. Light curves and periodograms of the three longest observations show features that could be transient periods: 0.89 days in RX J0437.4-4711, 2.08 days in Ton S180, and 5.8 days in 1H 0419-577. The statistical significance of these signals is estimated using the method of Timmer & Konig (1995), which carefully takes into account the red-noise properties of Seyfert light curves. The result is that the signals in RX J0437.4-4711 and Ton S180 exceed 95% confidence with respect to red noise, while 1H 0419-577 is only 64% significant. These period values appear unrelated to the length of the observation, which is similar in the three cases, but they do scale roughly as the luminosity of the object, which would be expected in a dynamical scenario if luminosity scales with black hole mass.Comment: 26 pages, 9 figures, accepted by Ap

Critical temperature of non-interacting Bose gases on disordered lattices

For a non-interacting Bose gas on a lattice we compute the shift of the critical temperature for condensation when random-bond and onsite disorder are present. We evidence that the shift depends on the space dimensionality D and the filling fraction f. For D -> infinity (infinite-range model), using results from the theory of random matrices, we show that the shift of the critical temperature is negative, depends on f, and vanishes only for large f. The connections with analogous results obtained for the spherical model are discussed. For D=3 we find that, for large f, the critical temperature Tc is enhanced by disorder and that the relative shift does not sensibly depend on f; at variance, for small f, Tc decreases in agreement with the results obtained for a Bose gas in the continuum. We also provide numerical estimates for the shift of the critical temperature due to disorder induced on a non-interacting Bose gas by a bichromatic incommensurate potential.Comment: 18 pages, 8 figures; Fig. 8 improved adding results for another value of q (q=830/1076

Point process model of 1/f noise versus a sum of Lorentzians

We present a simple point process model of $1/f^{\beta}$ noise, covering different values of the exponent $\beta$. The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interval resulting in the power-law distribution. Our model is free from the requirement of a wide distribution of relaxation times and from the power-law forms of the pulses. It contains only one relaxation rate and yields $1/f^ {\beta}$ spectra in a wide range of frequency. We obtain explicit expressions for the power spectra and present numerical illustrations of the model. Further we analyze the relation of the point process model of $1/f$ noise with the Bernamont-Surdin-McWhorter model, representing the signals as a sum of the uncorrelated components. We show that the point process model is complementary to the model based on the sum of signals with a wide-range distribution of the relaxation times. In contrast to the Gaussian distribution of the signal intensity of the sum of the uncorrelated components, the point process exhibits asymptotically a power-law distribution of the signal intensity. The developed multiplicative point process model of $1/f^{\beta}$ noise may be used for modeling and analysis of stochastic processes in different systems with the power-law distribution of the intensity of pulsing signals.Comment: 23 pages, 10 figures, to be published in Phys. Rev.