Strong invariance principles for sequential Bahadur-Kiefer and Vervaat error processes of long-range dependent sequences

In this paper we study strong approximations (invariance principles) of the sequential uniform and general Bahadur-Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, i.e., the integrated sequential Bahadur-Kiefer process, properly normalized, as well as that of its deviation from its limiting process, the so-called Vervaat error process. It is well known that the Bahadur-Kiefer and the Vervaat error processes cannot converge weakly in the i.i.d. case. In contrast to this we conclude that the Bahadur-Kiefer and Vervaat error processes, as well as their sequential versions, do converge weakly to a Dehling-Taqqu type limit process for certain long-range dependent sequences.Long-range dependence; Sequential empirical and quantile processes; Sequential Bahadur-Kiefer process; Sequential Vervaat and Vervaat error processes; Strong invariance principles.

Decoding sequential vs non-sequential two-photon double ionization of helium using nuclear recoil

Above 54.4 eV, two-photon double ionization of helium is dominated by a sequential absorption process, producing characteristic behavior in the single and triple differential cross sections. We show that the signature of this process is visible in the nuclear recoil cross section, integrated over all energy sharings of the ejected electrons, even below the threshold for the sequential process. Since nuclear recoil momentum imaging does not require coincident photoelectron measurement, the predicted images present a viable target for future experiments with new short-pulse VUV and soft X-ray sources.Comment: 4 pages, 3 figure

Multi-Species Asymmetric Exclusion Process in Ordered Sequential Update

A multi-species generalization of the asymmetric simple exclusion process (ASEP) is studied in ordered sequential and sub-lattice parallel updating schemes. In this model particles hop with their own specific probabilities to their rightmost empty site and fast particles overtake slow ones with a definite probability. Using Matrix Product Ansatz (MPA), we obtain the relevant algebra, and study the uncorrelated stationary state of the model both for an open system and on a ring. A complete comparison between the physical results in these updates and those of random sequential introduced in [20,21] is made.Comment: Latex file 36 pages with 10 EPS figure

Physical activity in England: Who is meeting the recommended level of participation through sports and exercise?

This article is available through the Brunel Open Access Publishing Fund. Copyright © 2012 Anokye et al.Background: Little is known about the correlates of meeting recommended levels of participation in physical activity (PA) and how this understanding informs public health policies on behaviour change. Objective: To analyse who meets the recommended level of participation in PA in males and females separately by applying ‘process’ modelling frameworks (single vs. sequential 2-step process). Methods: Using the Health Survey for England 2006, (n = 14 142; ≥16 years), gender-specific regression models were estimated using bivariate probit with selectivity correction and single probit models. A ‘sequential, 2-step process’ modelled participation and meeting the recommended level separately, whereas the ‘single process’ considered both participation and level together. Results: In females, meeting the recommended level was associated with degree holders [Marginal effect (ME) = 0.013] and age (ME = −0.001), whereas in males, age was a significant correlate (ME = −0.003 to −0.004). The order of importance of correlates was similar across genders, with ethnicity being the most important correlate in both males (ME = −0.060) and females (ME = −0.133). In females, the ‘sequential, 2-step process’ performed better (ρ = −0.364, P < 0.001) than that in males (ρ = 0.154). Conclusion: The degree to which people undertake the recommended level of PA through vigorous activity varies between males and females, and the process that best predicts such decisions, i.e. whether it is a sequential, 2-step process or a single-step choice, is also different for males and females. Understanding this should help to identify subgroups that are less likely to meet the recommended level of PA (and hence more likely to benefit from any PA promotion intervention).This study was funded by the Department of Health’s Policy Research Programme

Two-photon double ionization of neon using an intense attosecond pulse train

We present the first demonstration of two-photon double ionization of neon using an intense extreme ultraviolet (XUV) attosecond pulse train (APT) in a photon energy regime where both direct and sequential mechanisms are allowed. For an APT generated through high-order harmonic generation (HHG) in argon we achieve a total pulse energy close to 1 $\mu$J, a central energy of 35 eV and a total bandwidth of $\sim30$ eV. The APT is focused by broadband optics in a neon gas target to an intensity of $3\cdot10^{12}$W$\cdot$cm$^{-2}$. By tuning the photon energy across the threshold for the sequential process the double ionization signal can be turned on and off, indicating that the two-photon double ionization predominantly occurs through a sequential process. The demonstrated performance opens up possibilities for future XUV-XUV pump-probe experiments with attosecond temporal resolution in a photon energy range where it is possible to unravel the dynamics behind direct vs. sequential double ionization and the associated electron correlation effects

Process tomography via sequential measurements on a single quantum system

We utilize a discrete (sequential) measurement protocol to investigate quantum process tomography of a single two-level quantum system, with an unknown initial state, undergoing Rabi oscillations. The ignorance of the dynamical parameters is encoded into a continuous-variable classical system which is coupled to the two-level quantum system via a generalized Hamiltonian. This combined estimate of the quantum state and dynamical parameters is updated by using the information obtained from sequential measurements on the quantum system and, after a sufficient waiting period, faithful state monitoring and parameter determination is obtained. Numerical evidence is used to demonstrate the convergence of the state estimate to the true state of the hybrid system.Comment: 7 pages, 2 figure

Asymptotic properties of the sequential empirical ROC, PPV and NPV curves under case-control sampling

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough understanding of the asymptotic properties of the sequential empirical ROC, PPV and NPV curves will provide more flexibility when designing group sequential diagnostic biomarker studies. In this paper, we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves under case-control sampling using sequential empirical process theory. We show that the sequential empirical ROC, PPV and NPV curves converge to the sum of independent Kiefer processes and show how these results can be used to derive asymptotic results for summaries of the sequential empirical ROC, PPV and NPV curves.Comment: Published in at http://dx.doi.org/10.1214/11-AOS937 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org