Determination of the Joint Confidence Region of Optimal Operating Conditions in Robust Design by Bootstrap Technique

Robust design has been widely recognized as a leading method in reducing variability and improving quality. Most of the engineering statistics literature mainly focuses on finding "point estimates" of the optimum operating conditions for robust design. Various procedures for calculating point estimates of the optimum operating conditions are considered. Although this point estimation procedure is important for continuous quality improvement, the immediate question is "how accurate are these optimum operating conditions?" The answer for this is to consider interval estimation for a single variable or joint confidence regions for multiple variables. In this paper, with the help of the bootstrap technique, we develop procedures for obtaining joint "confidence regions" for the optimum operating conditions. Two different procedures using Bonferroni and multivariate normal approximation are introduced. The proposed methods are illustrated and substantiated using a numerical example.Comment: Two tables, Three figure

Analyzing the House Fly's Exploratory Behavior with Autoregression Methods

This paper presents a detailed characterization of the trajectory of a single housefly with free range of a square cage. The trajectory of the fly was recorded and transformed into a time series, which was fully analyzed using an autoregressive model, which describes a stationary time series by a linear regression of prior state values with the white noise. The main discovery was that the fly switched styles of motion from a low dimensional regular pattern to a higher dimensional disordered pattern. This discovered exploratory behavior is, irrespective of the presence of food, characterized by anomalous diffusion.Comment: 20 pages, 9 figures, 1 table, full pape

Implications of Compressed Supersymmetry for Collider and Dark Matter Searches

Martin has proposed a scenario dubbed ``compressed supersymmetry'' (SUSY) where the MSSM is the effective field theory between energy scales M_{\rm weak} and M_{\rm GUT}, but with the GUT scale SU(3) gaugino mass M_3<< M_1 or M_2. As a result, squark and gluino masses are suppressed relative to slepton, chargino and neutralino masses, leading to a compressed sparticle mass spectrum, and where the dark matter relic density in the early universe may be dominantly governed by neutralino annihilation into ttbar pairs via exchange of a light top squark. We explore the dark matter and collider signals expected from compressed SUSY for two distinct model lines with differing assumptions about GUT scale gaugino mass parameters. For dark matter signals, the compressed squark spectrum leads to an enhancement in direct detection rates compared to models with unified gaugino masses. Meanwhile, neutralino halo annihilation rates to gamma rays and anti-matter are also enhanced relative to related scenarios with unified gaugino masses but, depending on the halo dark matter distribution, may yet be below the sensitivity of indirect searches underway. In the case of collider signals, we compare the rates for the potentially dominant decay modes of the stop_1 which may be expected to be produced in cascade decay chains at the LHC: \tst_1\to c\tz_1 and \tst_1\to bW\tz_1. We examine the extent to which multilepton signal rates are reduced when the two-body decay mode dominates. For the model lines that we examine here, the multi-lepton signals, though reduced, still remain observable at the LHC.Comment: 22 pages including 24 eps figure

Stochastic simulations of conditional states of partially observed systems, quantum and classical

In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional state will be given by a state matrix $\rho_r(t)$ and if classical the conditional state will be given by a probability distribution $P_r(x,t)$ where $r$ is the result of the measurement. Thus to determine the evolution of this conditional state under continuous-in-time monitoring requires an expensive numerical calculation. In this paper we demonstrating a numerical technique based on linear measurement theory that allows us to determine the conditional state using only pure states. That is, our technique reduces the problem size by a factor of $N$, the number of basis states for the system. Furthermore we show that our method can be applied to joint classical and quantum systems as arises in modeling realistic measurement.Comment: 16 pages, 11 figure

The Distribution of Redshifts in New Samples of Quasi-stellar Objects

Two new samples of QSOs have been constructed from recent surveys to test the hypothesis that the redshift distribution of bright QSOs is periodic in $\log(1+z)$. The first of these comprises 57 different redshifts among all known close pairs or multiple QSOs, with image separations $\leq$ 10\arcsec, and the second consists of 39 QSOs selected through their X-ray emission and their proximity to bright comparatively nearby active galaxies. The redshift distributions of the samples are found to exhibit distinct peaks with a periodic separation of $\sim 0.089$ in $\log(1+z)$ identical to that claimed in earlier samples but now extended out to higher redshift peaks $z = 2.63, 3.45$ and 4.47, predicted by the formula but never seen before. The periodicity is also seen in a third sample, the 78 QSOs of the 3C and 3CR catalogues. It is present in these three datasets at an overall significance level $10^{-5}$ - $10^{-6}$, and appears not to be explicable by spectroscopic or similar selection effects. Possible interpretations are briefly discussed.Comment: submitted for publication in the Astronomical Journal, 15 figure

State and dynamical parameter estimation for open quantum systems

Following the evolution of an open quantum system requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is ``uncertain''. In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency $\Omega$ (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge acquisition (quantified by the posterior distribution for $\Omega$, and the conditional purity of the system, respectively) are quite distinct processes, which are not strongly correlated. Also, the quality and quantity of knowledge gain depend strongly on the type of monitoring scheme. We compare five different detection schemes (direct, adaptive, homodyne of the $x$ quadrature, homodyne of the $y$ quadrature, and heterodyne) using four different measures of the knowledge gain (Shannon information about $\Omega$, variance in $\Omega$, long-time system purity, and short-time system purity).Comment: 14 pages, 18 figure

Temporal variability and statistics of the Strehl ratio in adaptive-optics images

We have investigated the temporal variability and statistics of the "instantaneous" Strehl ratio. The observations were carried out with the 3.63-m AEOS telescope equipped with a high-order adaptive optics system. In this paper Strehl ratio is defined as the peak intensity of a single short exposure. We have also studied the behaviour of the phase variance computed on the reconstructed wavefronts. We tested the Marechal approximation and used it to explain the observed negative skewness of the Strehl ratio distribution. The estimate of the phase variance is shown to fit a three-parameter Gamma distribution model. We show that simple scaling of the reconstructed wavefronts has a large impact on the shape of the Strehl ratio distribution.Comment: submitted to PAS

Quantum trajectories for the realistic measurement of a solid-state charge qubit

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman and H. Mabuchi, Phys. Rev. A_65_ 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the ``realistic quantum trajectories'' of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.Comment: 7 pages, 2 figures. Shorter, significantly modified, updated versio

Impact of Scottish smoke-free legislation on smoking quit attempts and prevalence

&lt;p&gt;&lt;b&gt;Objectives:&lt;/b&gt; In Scotland, legislation was implemented in March 2006 prohibiting smoking in all wholly or partially enclosed public spaces. We investigated the impact on attempts to quit smoking and smoking prevalence.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods:&lt;/b&gt; We performed time series models using Box-Jenkins autoregressive integrated moving averages (ARIMA) on monthly data on the gross ingredient cost of all nicotine replacement therapy (NRT) prescribed in Scotland in 2003–2009, and quarterly data on self-reported smoking prevalence between January 1999 and September 2010 from the Scottish Household Survey.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Results:&lt;/b&gt; NRT prescription costs were significantly higher than expected over the three months prior to implementation of the legislation. Prescription costs peaked at £1.3 million in March 2006; £292,005.9 (95% CI £260,402.3, £323,609, p&#60;0.001) higher than the monthly norm. Following implementation of the legislation, costs fell exponentially by around 26% per month (95% CI 17%, 35%, p&#60;0.001). Twelve months following implementation, the costs were not significantly different to monthly norms. Smoking prevalence fell by 8.0% overall, from 31.3% in January 1999 to 23.7% in July–September 2010. In the quarter prior to implementation of the legislation, smoking prevalence fell by 1.7% (95% CI 2.4%, 1.0%, p&#60;0.001) more than expected from the underlying trend.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusions:&lt;/b&gt; Quit attempts increased in the three months leading up to Scotland's smoke-free legislation, resulting in a fall in smoking prevalence. However, neither has been sustained suggesting the need for additional tobacco control measures and ongoing support.&lt;/p&gt