Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits

For zero energy, $E=0$, we derive exact, classical solutions for {\em all} power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions lead to the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv \nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of $\th(t)$ and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We describe a procedure to connect different analytic solutions for successive orbits at the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. Also, we explain why they all must violate the virial theorem. The unbound orbits are also discussed in detail. This includes the unusual orbits which have finite travel times to infinity and also the special $\nu = 2$ case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be generated from Mathematica instructions at end of the fil

Spread of Infectious Diseases with a Latent Period

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node represents a population (group) which has many individuals. In this paper, we propose a modified metapopulation SIR model in which a latent period is taken into account. We call it SIIR model. We divide the infection period into two stages: an infected stage, which is the same as the previous model, and a seriously ill stage, in which individuals are infected and cannot move to the other populations. The two infectious stages in our modified metapopulation SIR model produce a discontinuous final size distribution. Individuals in the infected stage spread the disease like individuals in the seriously ill stage and never recover directly, which makes an effective recovery rate smaller than the given recovery rate.Comment: 6 pages, 3 figure

Leprosy in England and Wales 1953-2012: surveillance and challenges in low incidence countries

OBJECTIVE: To review all notified cases of leprosy in England and Wales between 1953 and 2012. DESIGN: National surveillance study of all reported cases. SETTING: England and Wales. OUTCOME: Number and characteristics of reported cases. RESULTS: During this period, a total of 1449 leprosy cases were notified. The incidence fell from 356 new cases notified between 1953 and 1962 to 139 new cases between 2003 and 2012. Where data were available, leprosy was more common in men, 15-45 year olds and those from the Indian subcontinent. There was considerable undernotification in 2001-2012. CONCLUSIONS: The high level of under-reporting indicates a need for improved surveillance in the UK. Public Health England, in collaboration with the UK Panel of Leprosy opinion, has revised the UK Memorandum on Leprosy in order to provide updated guidance on diagnostic procedures, treatment, case management, contact tracing and notification

Relative proximity of chromosome territories influences chromosome exchange partners in radiation-induced chromosome rearrangements in primary human bronchial epithelial cells

Copyright © 2013 The Authors. This article is made available through the Brunel Open Access Publishing Fund. This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial-No Derivative Works License, which permits non-commercial use, distribution, and reproduction in any medium, provided the original author and source are credited.Copyright © 2013 The Authors. It is well established that chromosomes exist in discrete territories (CTs) in interphase and are positioned in a cell-type specific probabilistic manner. The relative localisation of individual CTs within cell nuclei remains poorly understood, yet many cancers are associated with specific chromosome rearrangements and there is good evidence that relative territorial position influences their frequency of exchange. To examine this further, we characterised the complexity of radiation-induced chromosome exchanges in normal human bronchial epithelial (NHBE) cells by M-FISH analysis of PCC spreads and correlated the exchanges induced with their preferred interphase position, as determined by 1/2-colour 2D-FISH analysis, at the time of irradiation. We found that the frequency and complexity of aberrations induced were reduced in ellipsoid NHBE cells in comparison to previous observations in spherical cells, consistent with aberration complexity being dependent upon the number and proximity of damaged CTs, i.e. lesion proximity. To ask if particular chromosome neighbourhoods could be identified we analysed all radiation-induced pair-wise exchanges using SCHIP (statistics for chromosome interphase positioning) and found that exchanges between chromosomes (1;13), (9;17), (9;18), (12;18) and (16;21) all occurred more often than expected assuming randomness. All of these pairs were also found to be either sharing similar preferred positions in interphase and/or sharing neighbouring territory boundaries. We also analysed a human small cell lung cancer cell line, DMS53, by M-FISH observing the genome to be highly rearranged, yet possessing rearrangements also involving chromosomes (1;13) and (9;17). Our findings show evidence for the occurrence of non-random exchanges that may reflect the territorial organisation of chromosomes in interphase at time of damage and highlight the importance of cellular geometry for the induction of aberrations of varying complexity after exposure to both low and high-LET radiation.Department of Healt

Optimised configuration of sensors for fault tolerant control of an electro-magnetic suspension system

For any given system the number and location of sensors can affect the closed-loop performance as well as the reliability of the system. Hence, one problem in control system design is the selection of the sensors in some optimum sense that considers both the system performance and reliability. Although some methods have been proposed that deal with some of the aforementioned aspects, in this work, a design framework dealing with both control and reliability aspects is presented. The proposed framework is able to identify the best sensor set for which optimum performance is achieved even under single or multiple sensor failures with minimum sensor redundancy. The proposed systematic framework combines linear quadratic Gaussian control, fault tolerant control and multiobjective optimisation. The efficacy of the proposed framework is shown via appropriate simulations on an electro-magnetic suspension system

Observations of ozone and related species in the northeast Pacific during the PHOBEA campaigns 2. Airborne observations

During late March and April of 1999 the University of Wyoming's King Air research aircraft measured atmospheric concentrations of NO, O3, peroxyacetyl nitrate (PAN), CO, CH4, VOCs, aerosols, and J(NO2) off the west coast of the United States. During 14 flights, measurements were made between 39°-48° N latitude, 125°-129° W longitude, and at altitudes from 0-8 km. These flights were part of the Photochemical Ozone Budget of the Eastern North Pacific Atmosphere (PHOBEA) experiment, which included both ground-based and airborne measurements. Flights were scheduled when meteorological conditions minimized the impact of local pollution sources. The resulting measurements were segregated by air mass source region as indicated by back isentropic trajectory analysis. The chemical composition of marine air masses whose 5-day back isentropic trajectories originated north of 40° N latitude or west of 180° W longitude (WNW) differed significantly from marine air masses whose 5-day back isentropic trajectories originated south of 40° N latitude and east of 180° W longitude (SW). Trajectory and chemical analyses indicated that the majority of all encountered air masses, both WNW and SW, likely originated from the northwestern Pacific and have characteristics of emissions from the East Asian continental region. However, air masses with WNW back trajectories contained higher mixing ratios of NO, NOx, O3, PAN, CO, CH4, various VOC pollution tracers, and aerosol number concentration, compared to those air masses with SW back trajectories. Calculations of air mass age using two separate methods, photochemical and back trajectory, are consistent with transport from the northwestern Pacific in 8-10 days for air masses with WNW back trajectories and 16-20 days for air masses with SW back trajectories. Correlations, trajectory analysis, and comparisons with measurements made in the northwestern Pacific during NASA's Pacific Exploritory Mission-West Phase B (PEM-West B) experiment in 1994 are used to investigate the data. These analyses provide evidence that anthropogenically influenced air masses from the northwestern Pacific affect the overall chemical composition of the northeastern Pacific troposphere. Copyright 2001 by the American Geophysical Union

Impacts of Unattended Train Operations (UTO) on Productivity and Efficiency in Metropolitan Railways

Urban metro subway systems (metros) around the world are choosing increasing levels of automation for new and existing lines: the global length of metro lines capable of unattended train operation (UTO) is predicted to triple in the next 10 years. Despite significant investment in this technology, empirical evidence for the financial and service quality impacts of UTO in metros remains scarce. This study used questionnaires and semistructured interviews with the Community of Metros and Nova Group benchmarking groups to assemble emerging evidence of how automation affected costs, staffing, service capacity, and reliability. The results from an analysis of data from 23 lines suggested that UTO could reduce staff numbers by 30% to 70%, with the amount of wage cost reduction depending on whether staff on UTO lines were paid more. On the basis of the experience of seven metros, the capital costs of lines capable of UTO were higher, but the internal rate of return had been estimated by two metros at 10% to 15%. Automated lines were capable of operating at the highest service frequencies of up to 42 trains per hour, and the limited available data suggested that automated lines were more reliable. The findings indicated that UTO was a means to a more flexible and reliable operating model that could increase metro productivity and efficiency. The study identified important work needed to understand the impacts of UTO and identify where statistical analyses would add value once sufficiently large data sets became available

The relationship between quality of life (EORTC QLQ-C30) and survival in patients with gastro-oesopohageal cancer

It remains unclear whether any aspect of quality of life has a role in predicting survival in an unselected cohort of patients with gastro-oesophageal cancer. Therefore the aim of the present study was to examine the relationship between quality of life (EORTC QLQ-C30), clinico-pathological characteristics and survival in patients with gastro-oesophageal cancer. Patients presenting with gastric or oesophageal cancer, staged using the UICC tumour node metastasis (TNM) classification and who received either potentially curative surgery or palliative treatment between November 1997 and December 2002 (n=152) participated in a quality of life study, using the EORTC QLQ-C30 core questionnaire. On univariate analysis, age (P &#60; 0.01), tumour length (P &#60; 0.0001), TNM stage (P&#60;0.0001), weight loss (P&#60;0.0001), dysphagia score (P&#60;0.001), performance status (P&#60;0.1) and treatment (P&#60;0.0001) were significantly associated with cancer-specific survival. EORTC QLQ-C30, physical functioning (P&#60;0.0001), role functioning (P&#60;0.001), cognitive functioning (P&#60;0.01), social functioning (P&#60;0.0001), global quality of life (P&#60;0.0001), fatigue (P&#60;0.0001), nausea/vomiting (P&#60;0.01), pain (P&#60;0.001), dyspnoea (P&#60;0.0001), appetite loss (P&#60;0.0001) and constipation (P&#60;0.05) were also significantly associated with cancer-specific survival. On multivariate survival analysis, tumour stage (P&#60;0.0001), treatment (P&#60;0.001) and appetite loss (P&#60;0.0001) were significant independent predictors of cancer-specific survival. The present study highlights the importance of quality of life (EORTC QLQ-C30) measures, in particular appetite loss, as a prognostic factor in these patients

Probing the Neutron Star Interior with Glitches

With the aim of constraining the structural properties of neutron stars and the equation of state of dense matter, we study sudden spin-ups, glitches, occurring in the Vela pulsar and in six other pulsars. We present evidence that glitches represent a self-regulating instability for which the star prepares over a waiting time. The angular momentum requirements of glitches in Vela indicate that at least 1.4% of the star's moment of inertia drives these events. If glitches originate in the liquid of the inner crust, Vela's `radiation radius' $R_\infty$ must exceed ~12 km for a mass of 1.4 solar masses. The isolated neutron star RX J18563-3754 is a promising candidate for a definitive radius measurement, and offers to further our understanding of dense matter and the origin of glitches.Comment: Invited talk at the Pacific Rim Conference on Stellar Astrophysics, Hong Kong, Aug. 1999. 9 pages, 5 figure