Towards a Continuous Record of the Sky

It is currently feasible to start a continuous digital record of the entire sky sensitive to any visual magnitude brighter than 15 each night. Such a record could be created with a modest array of small telescopes, which collectively generate no more than a few Gigabytes of data daily. Alternatively, a few small telescopes could continually re-point to scan and reco rd the entire sky down to any visual magnitude brighter than 15 with a recurrence epoch of at most a few weeks, again always generating less than one Gigabyte of data each night. These estimates derive from CCD ability and budgets typical of university research projects. As a prototype, we have developed and are utilizing an inexpensive single-telescope system that obtains optical data from about 1500 square degrees. We discuss the general case of creating and storing data from a both an epochal survey, where a small number of telescopes continually scan the sky, and a continuous survey, composed of a constellation of telescopes dedicated each continually inspect a designated section of the sky. We compute specific limitations of canonical surveys in visible light, and estimate that all-sky continuous visual light surveys could be sensitive to magnitude 20 in a single night by about 2010. Possible scientific returns of continuous and epochal sky surveys include continued monitoring of most known variable stars, establishing case histories for variables of future interest, uncovering new forms of stellar variability, discovering the brightest cases of microlensing, discovering new novae and supernovae, discovering new counterparts to gamma-ray bursts, monitoring known Solar System objects, discovering new Solar System objects, and discovering objects that might strike the Earth.Comment: 38 pages, 9 postscript figures, 2 gif images. Revised and new section added. Accepted to PASP. Source code submitted to ASCL.ne

Three routes to the exact asymptotics for the one-dimensional quantum walk

We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly easier to use than the Darboux method. It also provides a single integral representation for the wavefunction that works over the full range of positions, $n,$ including throughout the transitional range where the behaviour changes from oscillatory to exponential. Previous analyses of this system have run into difficulties in the transitional range, because the approximations on which they were based break down here. The fact that there are two different kinds of approach to this problem (Path Integral vs. Schr\"{o}dinger wave mechanics) is ultimately a manifestation of the equivalence between the path-integral formulation of quantum mechanics and the original formulation developed in the 1920s. We discuss how and why our approach is related to the two methods that have already been used to analyse these systems.Comment: 25 pages, AMS preprint format, 4 figures as encapsulated postscript. Replaced because there were sign errors in equations (80) & (85) and Lemma 2 of the journal version (v3

Development of an exercise intervention for the prevention of musculoskeletal shoulder problems after breast cancer treatment : the prevention of shoulder problems trial (UK PROSPER)

Background Musculoskeletal shoulder problems are common after breast cancer treatment. There is some evidence to suggest that early postoperative exercise is safe and may improve shoulder function. We describe the development and delivery of a complex intervention for evaluation within a randomised controlled trial (RCT), designed to target prevention of musculoskeletal shoulder problems after breast cancer surgery (The Prevention of Shoulder Problems Trial; PROSPER). Methods A pragmatic, multicentre RCT to compare the clinical and cost-effectiveness of best practice usual care versus a physiotherapy-led exercise and behavioural support intervention in women at high risk of shoulder problems after breast cancer treatment. PROSPER will recruit 350 women from approximately 15 UK centres, with follow-up at 6 and 12 months. The primary outcome is shoulder function at 12 months; secondary outcomes include postoperative pain, health related quality of life, adverse events and healthcare resource use. A multi-phased approach was used to develop the PROSPER intervention which was underpinned by existing evidence and modified for implementation after input from clinical experts and women with breast cancer. The intervention was tested and refined further after qualitative interviews with patients newly diagnosed with breast cancer; a pilot RCT was then conducted at three UK clinical centres. Discussion The PROSPER intervention incorporates three main components: shoulder-specific exercises targeting range of movement and strength; general physical activity; and behavioural strategies to encourage adherence and support exercise behaviour. The final PROSPER intervention is fully manualised with clear, documented pathways for clinical assessment, exercise prescription, use of behavioural strategies, and with guidance for treatment of postoperative complications. This paper adheres to TIDieR and CERT recommendations for the transparent, comprehensive and explicit reporting of complex interventions. Trial registration: International Standard Randomised Controlled Trial Number: ISRCTN 35358984

Asymptotics of Some Convolutional Recurrences

Research supported by NSERC Research supported by NSERC and Canada Research Chair Program We study the asymptotic behavior of the terms in sequences satisfying recurrences of the form an = an−1 + ∑n−d k=d f(n,k)akan−k where, very roughly speaking, f(n,k) behaves like a product of reciprocals of binomial coefficients. Some examples of such sequences from map enumerations, Airy constants, and Painlevé I equations are discussed in detail. 1 Main results There are many examples in the literature of sequences defined recursively using a convolution. It often seems difficult to determine the asymptotic behavior of such sequences. In this note we study the asymptotics of a general class of such sequences. We prove subexponential growth by using an iterative method that may be useful for other recurrences. By subexponential growth we mean that, for every constant D> 1, an = o(D n

Evanescence in Coined Quantum Walks

In this paper we complete the analysis begun by two of the authors in a previous work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795 (2003) quant-ph/0303105 ]. We obtain uniformly convergent asymptotics for the "exponential decay'' regions at the leading edges of the main peaks in the Schr{\"o}dinger (or wave-mechanics) picture. This calculation required us to generalise the method of stationary phase and we describe this extension in some detail, including self-contained proofs of all the technical lemmas required. We also rigorously establish the exact Feynman equivalence between the path-integral and wave-mechanics representations for this system using some techniques from the theory of special functions. Taken together with the previous work, we can now prove every theorem by both routes.Comment: 32 pages AMS LaTeX, 5 figures in .eps format. Rewritten in response to referee comments, including some additional references. v3: typos fixed in equations (131), (133) and (134). v5: published versio

A Large, Uniform Sample of X-ray Emitting AGN from the ROSAT All-Sky and Sloan Digital Sky Surveys: the Data Release 5 Sample

We describe further results of a program aimed to yield ~10^4 fully characterized optical identifications of ROSAT X-ray sources. Our program employs X-ray data from the ROSAT All-Sky Survey (RASS), and both optical imaging and spectroscopic data from the Sloan Digital Sky Survey (SDSS). RASS/SDSS data from 5740 deg^2 of sky spectroscopically covered in SDSS Data Release 5 (DR5) provide an expanded catalog of 7000 confirmed quasars and other AGN that are probable RASS identifications. Again in our expanded catalog, the identifications as X-ray sources are statistically secure, with only a few percent of the SDSS AGN likely to be randomly superposed on unrelated RASS X-ray sources. Most identifications continue to be quasars and Seyfert 1s with 15<m<21 and 0.01<z<4; but the total sample size has grown to include very substantial numbers of even quite rare AGN, e.g., now including several hundreds of candidate X-ray emitting BL Lacs and narrow-line Seyfert 1 galaxies. In addition to exploring rare subpopulations, such a large total sample may be useful when considering correlations between the X-ray and the optical, and may also serve as a resource list from which to select the "best" object (e.g., X-ray brightest AGN of a certain subclass, at a preferred redshift or luminosity) for follow-on X-ray spectral or alternate detailed studies.Comment: Accepted for publication in AJ; 32 pages, including 11 figures, and 6 example table