Multidimensional continued fractions, dynamical renormalization and KAM theory

The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. We explicitely construct renormalization schemes for (a) the linearization of vector fields on tori of arbitrary dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page

The changing of the guard: groupwork with people who have intellectual disabilities

This paper considers the impact of service systems on group activities. It describes an inter-professional groupwork project facilitated by a social worker and a community nurse. The project provided an emancipatory experience for a group of adults who had intellectual disabilities. The group was charged with the task of reviewing and updating the recruitment and interview processes used by a 'Learning Disability Partnership Board', when employing new support workers. The paper begins with a brief history of intellectual disability and provides a context to the underpinning philosophical belief that people should be encouraged and supported to inhabit valued social roles no matter what disability they may have. It then identifies the ways in which the sponsoring health, education and social care services impacted on the creation and development of a groupwork project. It might have been expected that the nature of the intellectual disability would have been the major influence on group process. However the paper reveals that organisational constraints had a significant impact on group functioning. Issues including, staffing budgets and transport contracts impacted on group process and function. The results of the project show how, with adequate support, people with intellectual disability can make important decisions that have long-reaching impacts on the services

Physics of Solar Prominences: I - Spectral Diagnostics and Non-LTE Modelling

This review paper outlines background information and covers recent advances made via the analysis of spectra and images of prominence plasma and the increased sophistication of non-LTE (ie when there is a departure from Local Thermodynamic Equilibrium) radiative transfer models. We first describe the spectral inversion techniques that have been used to infer the plasma parameters important for the general properties of the prominence plasma in both its cool core and the hotter prominence-corona transition region. We also review studies devoted to the observation of bulk motions of the prominence plasma and to the determination of prominence mass. However, a simple inversion of spectroscopic data usually fails when the lines become optically thick at certain wavelengths. Therefore, complex non-LTE models become necessary. We thus present the basics of non-LTE radiative transfer theory and the associated multi-level radiative transfer problems. The main results of one- and two-dimensional models of the prominences and their fine-structures are presented. We then discuss the energy balance in various prominence models. Finally, we outline the outstanding observational and theoretical questions, and the directions for future progress in our understanding of solar prominences.Comment: 96 pages, 37 figures, Space Science Reviews. Some figures may have a better resolution in the published version. New version reflects minor changes brought after proof editin

A Markov chain Monte Carlo analysis of the CMSSM

We perform a comprehensive exploration of the Constrained MSSM parameter space employing a Markov Chain Monte Carlo technique and a Bayesian analysis. We compute superpartner masses and other collider observables, as well as a cold dark matter abundance, and compare them with experimental data. We include uncertainties arising from theoretical approximations as well as from residual experimental errors of relevant Standard Model parameters. We delineate probability distributions of the CMSSM parameters, the collider and cosmological observables as well as a dark matter direct detection cross section. The 68% probability intervals of the CMSSM parameters are: 0.52 TeV < m1/2 < 1.26 TeV, m0 < 2.10 TeV, -0.34 TeV < A0 < 2.41 TeV and 38.5 < tan \u3b2 < 54.6. Generally, large fractions of high probability ranges of the superpartner masses will be probed at the LHC. For example, we find that the probability of mg < 2.7TeV is 78%, of mqR < 2.5TeV is 85% and of m\u3c7\ub11 < 0.8TeV is 65%. As regards the other observables, for example at 68% probability we find 3.5 710-9 < BR(Bs \u2192 \u3bc+\u3bc-) < 1.7 710-8, 1.9 710-10 < \u3b4a SUSY \u3bc < 9.9 710-10 and 1 7 10 -10 pb < \u3c3SIp < 1 7 10 -8 pb for direct WIMP detection. We highlight a complementarity between LHC and WIMP dark matter searches in exploring the CMSSM parameter space. We further expose a number of correlations among the observables, in particular between BR(Bs \u2192 \u3bc+\u3bc-) and BR(B \u2192 X s\u3b3) or \u3c3SIp. Once SUSY is discovered, this and other correlations may prove helpful in distinguishing the CMSSM from other supersymmetric models. We investigate the robustness of our results in terms of the assumed ranges of CMSSM parameters and the effect of the (g - 2)\u3bc anomaly which shows some tension with the other observables. We find that the results for m0, and the observables which strongly depend on it, are sensitive to our assumptions, while our conclusions for the other variables are robust

Measurement of the CP-Violating Asymmetry Amplitude sin2β\beta

We present results on time-dependent CP-violating asymmetries in neutral B decays to several CP eigenstates. The measurements use a data sample of about 88 million Y(4S) --> B Bbar decays collected between 1999 and 2002 with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We study events in which one neutral B meson is fully reconstructed in a final state containing a charmonium meson and the other B meson is determined to be either a B0 or B0bar from its decay products. The amplitude of the CP-violating asymmetry, which in the Standard Model is proportional to sin2beta, is derived from the decay-time distributions in such events. We measure sin2beta = 0.741 +/- 0.067 (stat) +/- 0.033 (syst) and |lambda| = 0.948 +/- 0.051 (stat) +/- 0.017 (syst). The magnitude of lambda is consistent with unity, in agreement with the Standard Model expectation of no direct CP violation in these modes

Measurement of the electron energy spectrum and its moments in inclusive B -> Xe nu decays

We report a measurement of the inclusive electron energy spectrum for semileptonic decays of B mesons in a data sample of 52 million Y(4S)-->B(B) over bar decays collected with the BABAR detector at the PEP-II asymmetric-energy B-meson factory at SLAC. We determine the branching fraction, first, second, and third moments of the spectrum for lower cutoffs on the electron energy between 0.6 and 1.5 GeV. We measure the partial branching fraction to be B(B-->Xenu,E-e>0.6 GeV)=[10.36+/-0.06(stat.)+/-0.23(sys.)]%

Global, regional, and national life expectancy, all-cause mortality, and cause-specific mortality for 249 causes of death, 1980�2015: a systematic analysis for the Global Burden of Disease Study 2015

Background Improving survival and extending the longevity of life for all populations requires timely, robust evidence on local mortality levels and trends. The Global Burden of Disease 2015 Study (GBD 2015) provides a comprehensive assessment of all-cause and cause-specific mortality for 249 causes in 195 countries and territories from 1980 to 2015. These results informed an in-depth investigation of observed and expected mortality patterns based on sociodemographic measures. Methods We estimated all-cause mortality by age, sex, geography, and year using an improved analytical approach originally developed for GBD 2013 and GBD 2010. Improvements included refinements to the estimation of child and adult mortality and corresponding uncertainty, parameter selection for under-5 mortality synthesis by spatiotemporal Gaussian process regression, and sibling history data processing. We also expanded the database of vital registration, survey, and census data to 14�294 geography�year datapoints. For GBD 2015, eight causes, including Ebola virus disease, were added to the previous GBD cause list for mortality. We used six modelling approaches to assess cause-specific mortality, with the Cause of Death Ensemble Model (CODEm) generating estimates for most causes. We used a series of novel analyses to systematically quantify the drivers of trends in mortality across geographies. First, we assessed observed and expected levels and trends of cause-specific mortality as they relate to the Socio-demographic Index (SDI), a summary indicator derived from measures of income per capita, educational attainment, and fertility. Second, we examined factors affecting total mortality patterns through a series of counterfactual scenarios, testing the magnitude by which population growth, population age structures, and epidemiological changes contributed to shifts in mortality. Finally, we attributed changes in life expectancy to changes in cause of death. We documented each step of the GBD 2015 estimation processes, as well as data sources, in accordance with Guidelines for Accurate and Transparent Health Estimates Reporting (GATHER). Findings Globally, life expectancy from birth increased from 61·7 years (95 uncertainty interval 61·4�61·9) in 1980 to 71·8 years (71·5�72·2) in 2015. Several countries in sub-Saharan Africa had very large gains in life expectancy from 2005 to 2015, rebounding from an era of exceedingly high loss of life due to HIV/AIDS. At the same time, many geographies saw life expectancy stagnate or decline, particularly for men and in countries with rising mortality from war or interpersonal violence. From 2005 to 2015, male life expectancy in Syria dropped by 11·3 years (3·7�17·4), to 62·6 years (56·5�70·2). Total deaths increased by 4·1 (2·6�5·6) from 2005 to 2015, rising to 55·8 million (54·9 million to 56·6 million) in 2015, but age-standardised death rates fell by 17·0 (15·8�18·1) during this time, underscoring changes in population growth and shifts in global age structures. The result was similar for non-communicable diseases (NCDs), with total deaths from these causes increasing by 14·1 (12·6�16·0) to 39·8 million (39·2 million to 40·5 million) in 2015, whereas age-standardised rates decreased by 13·1 (11·9�14·3). Globally, this mortality pattern emerged for several NCDs, including several types of cancer, ischaemic heart disease, cirrhosis, and Alzheimer's disease and other dementias. By contrast, both total deaths and age-standardised death rates due to communicable, maternal, neonatal, and nutritional conditions significantly declined from 2005 to 2015, gains largely attributable to decreases in mortality rates due to HIV/AIDS (42·1, 39·1�44·6), malaria (43·1, 34·7�51·8), neonatal preterm birth complications (29·8, 24·8�34·9), and maternal disorders (29·1, 19·3�37·1). Progress was slower for several causes, such as lower respiratory infections and nutritional deficiencies, whereas deaths increased for others, including dengue and drug use disorders. Age-standardised death rates due to injuries significantly declined from 2005 to 2015, yet interpersonal violence and war claimed increasingly more lives in some regions, particularly in the Middle East. In 2015, rotaviral enteritis (rotavirus) was the leading cause of under-5 deaths due to diarrhoea (146�000 deaths, 118�000�183�000) and pneumococcal pneumonia was the leading cause of under-5 deaths due to lower respiratory infections (393�000 deaths, 228�000�532�000), although pathogen-specific mortality varied by region. Globally, the effects of population growth, ageing, and changes in age-standardised death rates substantially differed by cause. Our analyses on the expected associations between cause-specific mortality and SDI show the regular shifts in cause of death composition and population age structure with rising SDI. Country patterns of premature mortality (measured as years of life lost YLLs) and how they differ from the level expected on the basis of SDI alone revealed distinct but highly heterogeneous patterns by region and country or territory. Ischaemic heart disease, stroke, and diabetes were among the leading causes of YLLs in most regions, but in many cases, intraregional results sharply diverged for ratios of observed and expected YLLs based on SDI. Communicable, maternal, neonatal, and nutritional diseases caused the most YLLs throughout sub-Saharan Africa, with observed YLLs far exceeding expected YLLs for countries in which malaria or HIV/AIDS remained the leading causes of early death. Interpretation At the global scale, age-specific mortality has steadily improved over the past 35 years; this pattern of general progress continued in the past decade. Progress has been faster in most countries than expected on the basis of development measured by the SDI. Against this background of progress, some countries have seen falls in life expectancy, and age-standardised death rates for some causes are increasing. Despite progress in reducing age-standardised death rates, population growth and ageing mean that the number of deaths from most non-communicable causes are increasing in most countries, putting increased demands on health systems. Funding Bill & Melinda Gates Foundation. © 2016 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY licens