What can be inferred from surrogate data testing?

Surrogate data testing for linearity is frequently applied to confirm the results of nonlinear time series analysis. We argue that this, in general, is not possible.Comment: 1 pag

Cross-spectral analysis of physiological tremor and muscle activity. I. Theory and application to unsynchronized EMG

We investigate the relationship between the extensor electromyogram (EMG) and tremor time series in physiological hand tremor by cross-spectral analysis. Special attention is directed to the phase spectrum and the effects of observational noise. We calculate the theoretical phase spectrum for a second order linear stochastic process and compare the results to measured tremor data recorded from subjects who did not show a synchronized EMG activity in the corresponding extensor muscle. The results show that physiological tremor is well described by the proposed model and that the measured EMG represents a Newtonian force by which the muscle acts on the hand.Comment: 9 pages, 6 figures, to appear in Biological Cybernetic

Artifacts with uneven sampling of red noise

The vast majority of sampling systems operate in a standard way: at each tick of a fixed-frequency master clock a digitizer reads out a voltage that corresponds to the value of some physical quantity and translates it into a bit pattern that is either transmitted, stored, or processed right away. Thus signal sampling at evenly spaced time intervals is the rule: however this is not always the case, and uneven sampling is sometimes unavoidable. While periodic or quasi-periodic uneven sampling of a deterministic signal can reasonably be expected to produce artifacts, it is much less obvious that the same happens with noise: here I show that this is indeed the case only for long-memory noise processes, i.e., power-law noises $1/f^\alpha$ with $\alpha > 2$. The resulting artifacts are usually a nuisance although they can be eliminated with a proper processing of the signal samples, but they could also be turned to advantage and used to encode information.Comment: 5 figure

Cessation of X-ray Pulsation of GX 1+4

We report results from our weekly monitoring campaign on the X-ray pulsar GX 1+4 with the {\em Rossi X-ray Timing Explorer} satellite. The spin-down trend of GX 1+4 was continuing, with the pulsar being at its longest period ever measured (about 138.7 s). At the late stage of the campaign, the source entered an extended faint state, when its X-ray (2-60 keV) flux decreased significantly to an average level of $\sim 3 \times 10^{-10} ergs cm^{-2} s^{-1}$. It was highly variable in the faint state; the flux dropped to as low as $\sim 3 \times 10^{-11} ergs cm^{-2} s^{-1}$. In several observations during this period, the X-ray pulsation became undetectable. We can, therefore, conclude conservatively that the pulsed fraction, which is normally $\gtrsim$ 70% (peak-to-peak), must have decreased drastically in those cases. This is very similar to what was observed of GX 1+4 in 1996 when it became similarly faint in X-ray. In fact, the flux at which the cessation of X-ray pulsation first occurred is nearly the same as it was in 1996. We suggest that we have, once again, observed the propeller effect in GX 1+4, a phenomenon that is predicted by theoretical models of accreting X-ray pulsars.Comment: 13 pages, 9 figures (available at http://www.physics.purdue.edu/~cui/ftp/cuifigs.tar.gz). To appear in Ap

Non-cooperative queueing games on a Jackson network

In this paper we introduce non-cooperative games on a Jackson network. A player has a set of routes available and has to decide which routes to use for its customers. Each player's goal is to minimize the expected sojourn time of its customers. We consider two cases. First, each player is allowed to divide his customers over multiple routes. This results in a game for which it can be shown that a unique pure-strategy Nash equilibrium exists. This Nash equilibrium can be found by using a best-response algorithm. Second, each player may only select a single route for its customers. This results in a game with finite strategy spaces. In general, such games need not have a pure-strategy Nash equilibrium, as shown by an example. We show the existence of pure-strategy Nash equilibria for four subclasses of games on a Jackson network: (i) N-player games with equal arrival rates for the players, (ii) 2-player games with identical service rates for all nodes, (iii) 2-player games on a 2 x 2-grid, and (iv) 2-player games on an A x B-grid with small differences in the service rates

Linear and nonlinear time series analysis of the black hole candidate Cygnus X-1

We analyze the variability in the X-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the over-all second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear andnonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.Comment: 15 pages, to appear in Phys. Rev.

X-ray Variability Characteristics of the Seyfert 1 Galaxy NGC 3783

We have characterized the energy-dependent X-ray variability properties of the Seyfert~1 galaxy NGC 3783 using archival XMM-Newton and Rossi X-ray Timing Explorer data. The high-frequency fluctuation power spectral density function (PSD) slope is consistent with flattening towards higher energies. Light curve cross correlation functions yield no significant lags, but peak coefficients generally decrease as energy separation of the bands increases on both short and long timescales. We have measured the coherence between various X-ray bands over the temporal frequency range of 6e-8 to 1e-4 Hz; this range includes the temporal frequency of the low-frequency power spectral density function (PSD) break tentatively detected by Markowitz et al. and includes the lowest temporal frequency over which coherence has been measured in any AGN to date. Coherence is generally near unity at these temporal frequencies, though it decreases slightly as energy separation of the bands increases. Temporal frequency-dependent phase lags are detected on short time scales; phase lags are consistent with increasing as energy separation increases or as temporal frequency decreases. All of these results are similar to those obtained previously for several Seyfert galaxies and stellar-mass black hole systems. Qualitatively, these results are consistent with the variability models of Kotov et al. and Lyubarskii, wherein the X-ray variability is due to inwardly propagating variations in the local mass accretion rate.Comment: Accepted for publication in The Astrophysical Journal, 2005, vol. 635, p. 180; version 2 has minor grammatical changes; 23 pages; uses emulateapj

Talking quiescence: a rigorous theory that supports parallel composition, action hiding and determinisation

The notion of quiescence - the absence of outputs - is vital in both behavioural modelling and testing theory. Although the need for quiescence was already recognised in the 90s, it has only been treated as a second-class citizen thus far. This paper moves quiescence into the foreground and introduces the notion of quiescent transition systems (QTSs): an extension of regular input-output transition systems (IOTSs) in which quiescence is represented explicitly, via quiescent transitions. Four carefully crafted rules on the use of quiescent transitions ensure that our QTSs naturally capture quiescent behaviour. We present the building blocks for a comprehensive theory on QTSs supporting parallel composition, action hiding and determinisation. In particular, we prove that these operations preserve all the aforementioned rules. Additionally, we provide a way to transform existing IOTSs into QTSs, allowing even IOTSs as input that already contain some quiescent transitions. As an important application, we show how our QTS framework simplifies the fundamental model-based testing theory formalised around ioco.Comment: In Proceedings MBT 2012, arXiv:1202.582

Neuron dynamics in the presence of 1/f noise

Interest in understanding the interplay between noise and the response of a non-linear device cuts across disciplinary boundaries. It is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors. Most studies of noise in non-linear devices are limited to either time-correlated noise with a Lorentzian spectrum (of which the white noise is a limiting case) or just white noise. We use analytical theory and numerical simulations to study the impact of the more ubiquitous "natural" noise with a 1/f frequency spectrum. Specifically, we study the impact of the 1/f noise on a leaky integrate and fire model of a neuron. The impact of noise is considered on two quantities of interest to neuron function: The spike count Fano factor and the speed of neuron response to a small step-like stimulus. For the perfect (non-leaky) integrate and fire model, we show that the Fano factor can be expressed as an integral over noise spectrum weighted by a (low pass) filter function. This result elucidates the connection between low frequency noise and disorder in neuron dynamics. We compare our results to experimental data of single neurons in vivo, and show how the 1/f noise model provides much better agreement than the usual approximations based on Lorentzian noise. The low frequency noise, however, complicates the case for information coding scheme based on interspike intervals by introducing variability in the neuron response time. On a positive note, the neuron response time to a step stimulus is, remarkably, nearly optimal in the presence of 1/f noise. An explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli.Comment: Phys. Rev. E in pres