Grover's search with faults on some marked elements

Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the algorithm, however, is very sensitive to errors in queries. It is known that if query may fail (report all marked elements as unmarked) the algorithm needs $\Omega(N)$ queries to find a marked element \cite{RS08}. \cite{AB+13} have proved the same result for the model where each marked element has its own probability to be reported as unmarked. We study the behavior of Grover's algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of non-faulty marked items in $O(\sqrt{N})$ queries. We also analyze the limiting behavior of the algorithm for a large number of steps and show the existence and the structure of limiting state $\rho_{lim}$.Comment: 17 pages, 6 figure

Scattering of non-uniform incident fields by long cylinders

Copyright University of BremenWe investigate experimentally far-field scattering from cylinders with illumination non-uniform along the axis of the cylinder. Scattered intensity as a function of angle in two orthogonal directions is examined. Variation along the scattering angle is found to be little affected by the illumination profile. However, variation in the transverse direction follows closely the Fourier transform of the illumination pattern and reproduces the angular distribution of the incident wave. These finding apply to circular as well as hexagonal cross-section cylinders

Risk of Tooth Loss After Cigarette Smoking Cessation

INTRODUCTION. Little is known about the effect of cigarette smoking cessation on risk of tooth loss. We examined how risk of tooth loss changed with longer periods of smoking abstinence in a prospective study of oral health in men. METHODS. Research subjects were 789 men who participated in the Veterans Administration Dental Longitudinal Study from 1968 to 2004. Tooth status and smoking status were determined at examinations performed every 3 years, for a maximum follow-up time of 35 years. Risk of tooth loss subsequent to smoking cessation was assessed sequentially at 1-year intervals with multivariate proportional hazards regression models. Men who never smoked cigarettes, cigars, or pipes formed the reference group. Hazard ratios were adjusted for age, education, total pack-years of cigarette exposure, frequency of brushing, and use of floss. RESULTS. The hazard ratio for tooth loss was 2.1 (95% confidence interval [CI], 1.5-3.1) among men who smoked cigarettes during all or part of follow-up. Risk of tooth loss among men who quit smoking declined as time after smoking cessation increased, from 2.0 (95% CI, 1.4-2.9) after 1 year of abstinence to 1.0 (95% CI, 0.5-2.2) after 15 years of abstinence. The risk remained significantly elevated for the first 9 years of abstinence but eventually dropped to the level of men who never smoked after 13 or more years. CONCLUSION. These results indicate that smoking cessation is beneficial for tooth retention, but long-term abstinence is required to reduce the risk to the level of people who have never smoked.U.S. Department of Veterans Affairs Epidemiology (Merit Review grant); Massachusetts Veterans Epidemiology Research and Information Center; National Institutes of Health (R01 DA10073, R03 DE016357, R15 DE12644, K24 DE00419

International Commercial Arbitration Coming to a Courthouse Near You

Some people view international commercial arbitration as an exotic, private dispute resolution mechanism that is entirely separate from U.S. state and federal courts. However, the truth of the matter is that judges from around the country increasingly are being asked to handle disputes that are somehow related to international commercial arbitration

Design of a high efficiency cyclone for collection of rare and low concentration airborne pathogens

Recent serious outbreaks of pathogens such as Chalara Fraxinea, (Ash Dieback) demonstrate the vulnerability of UK’s forests, woods, and trees. Early detection of threats is critical in the fight against such tree pests and pathogens. This requires a process for collecting and analysing the spores which is robust, flexible and can be deployed rapidly, but which also has sufficient sensitivity to detect the earliest precursors. The work presented here describes a newly-developed high-efficiency detection apparatus and is part of an ongoing BBRSC project to improve the UK’s biosecurity. Our automatic spore system is capable of collecting and analysing Chalara Fraxinea using a novel cyclonic pathogen collector. Cyclones are an effective way to separate small particles (spores) from large quantities of surrounding air and store them for analysis. Our system incorporates a purpose-designed high efficiency cyclone directly integrated with a low power custom impeller to maximise volumetric air sampling while minimising the power requirement. 3D printing was used extensively to validate theoretical models and the particle collection and retention capability of this series of prototypes was evaluated experimentally within our Aerosol test chamber. We found that we could collect greater than 90% of particulate in the target size range, thus providing a front-end to a detection platform. Our system is capable of operating autonomously and at low power, with a high sensitivity to ambient particles. The final system design incorporates the use of multiple cyclone storage vessels ensuring complete isolation of each sample, eradicating cross-contamination, and facilitating automated handling of the sample inside the same apparatus. COTS – commercial off the shelf components were incorporated into the cyclone to make a series of cost effective collection vessels. Early collection and detection of pathogens in-situ represents a considerable advance in surveillance and monitoring of pathogens strengthening UK biosecurity for the future

Development of an automated smart trap for wheat pathogens

National surveys show fungicide use on wheat continues to increase despite fluctuations in disease pressure, reaching a 30 year high in 2012 (Defra). Septoria tritici is the most significant foliar disease in UK wheat causing between £43M to £53M in yield losses annually; Yellow and brown rust are more sporadic but have caused significant losses during high disease years. In all cases control is by fungicide application costing £82M annually (GFK Kynetec 2013). Effective disease management relies on either prophylactic pesticide use or significant manual intervention and time consuming assessment of crop disease indicators by farmers and agronomists. Furthermore indications are that current levels of pesticide use could lead to increased risk of pesticide resistance, if this should occur it is estimated that wheat yields could reduce by up to 20%. To address this we have developed a prototype integrated and automated spore detection system, designed for unattended field application, to monitor and identify the presence of Septoria, brown and yellow rust. The prototype system incorporates novel cyclonic pathogen collection, on-board sample processing and isothermal DNA amplification chemistry (LAMP). We present the engineering design, optimisation and evaluation of our prototype system reporting on successfully completed laboratory testing and initial field trial results. This prototype will be the basis for the development of a commercially available system which, in addition to inoculum detection, will be capable of providing growers/agronomists with real-time information on inoculum moving into a crop enabling more effective timing and selection of fungicide application, and thus better control, increased yield, and improved environmental stewardship

Light scattering and phase behavior of Lysozyme-PEG mixtures

Measurements of liquid-liquid phase transition temperatures (cloud points) of mixtures of a protein (lysozyme) and a polymer, poly(ethylene glycol) (PEG) show that the addition of low molecular weight PEG stabilizes the mixture whereas high molecular weight PEG was destabilizing. We demonstrate that this behavior is inconsistent with an entropic depletion interaction between lysozyme and PEG and suggest that an energetic attraction between lysozyme and PEG is responsible. In order to independently characterize the lysozyme/PEG interactions, light scattering experiments on the same mixtures were performed to measure second and third virial coefficients. These measurements indicate that PEG induces repulsion between lysozyme molecules, contrary to the depletion prediction. Furthermore, it is shown that third virial terms must be included in the mixture's free energy in order to qualitatively capture our cloud point and light scattering data. The light scattering results were consistent with the cloud point measurements and indicate that attractions do exist between lysozyme and PEG.Comment: 5 pages, 2 figures, 1 tabl