A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds

The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative method computing a coordinate independent property of a function (such as a zero or a local minimum). All possible Newton methods on manifolds are believed to come under this framework. Changes of coordinates, and not any Riemannian structure, are shown to play a natural role in lifting the Newton method to a manifold. The framework also gives new insight into the design of Newton methods in general.Comment: 36 page

Dilemmas in doing insider research in professional education

This article explores the dilemmas I encountered when researching social work education in England as an insider researcher who was simultaneously employed as an educator in the host institution. This was an ethnographic project deploying multiple methods and generating rich case study material which informed the student textbook Becoming a Social Worker the four-year period of the project. First, ethical dilemmas emerged around informed consent and confidentiality when conducting surveys of students and reading their portfolios. Second, professional dilemmas stemmed from the ways in which my roles as a researcher, academic tutor, social worker and former practice educator converged and collided. Third, political dilemmas pertained to the potential for the project to crystallize and convey conflicts among stakeholders in the university and community. Since the majority of research in social work education is conducted by insiders, we have a vital interest in making sense of such complexity

Ethnographic research on crime and control: Editors’ introduction

Jennifer Fleetwood and Gary R. Potter introduce a special section on ethnographic research on crime and control

On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions

The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A general framework based on the notion of tree projection of hypergraphs is considered, which generalizes all known decomposition methods. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. These results are shown to be tight, by exhibiting dichotomies for classes of structures having bounded arity and where the tree decomposition method is considered

Priority for the Worse Off and the Social Cost of Carbon

The social cost of carbon (SCC) is a monetary measure of the harms from carbon emission. Specifically, it is the reduction in current consumption that produces a loss in social welfare equivalent to that caused by the emission of a ton of CO2. The standard approach is to calculate the SCC using a discounted-utilitarian social welfare function (SWF)—one that simply adds up the well-being numbers (utilities) of individuals, as discounted by a weighting factor that decreases with time. The discounted-utilitarian SWF has been criticized both for ignoring the distribution of well-being, and for including an arbitrary preference for earlier generations. Here, we use a prioritarian SWF, with no time-discount factor, to calculate the SCC in the integrated assessment model RICE. Prioritarianism is a well-developed concept in ethics and theoretical welfare economics, but has been, thus far, little used in climate scholarship. The core idea is to give greater weight to well-being changes affecting worse off individuals. We find substantial differences between the discounted-utilitarian and non-discounted prioritarian SCC

Linear MIM-Width of Trees

We provide an $O(n \log n)$ algorithm computing the linear maximum induced matching width of a tree and an optimal layout.Comment: 19 pages, 7 figures, full version of WG19 paper of same nam

What two models may teach us about duality violations in QCD

Though the operator product expansion is applicable in the calculation of current correlation functions in the Euclidean region, when approaching the Minkowskian domain, violations of quark-hadron duality are expected to occur, due to the presence of bound-state or resonance poles. In QCD finite-energy sum rules, contour integrals in the complex energy plane down to the Minkowskian axis have to be performed, and thus the question arises what the impact of duality violations may be. The structure and possible relevance of duality violations is investigated on the basis of two models: the Coulomb system and a model for light-quark correlators which has already been studied previously. As might yet be naively expected, duality violations are in some sense "maximal" for zero-width bound states and they become weaker for broader resonances whose poles lie further away from the physical axis. Furthermore, to a certain extent, they can be suppressed by choosing appropriate weight functions in the finite-energy sum rules. A simplified Ansatz for including effects of duality violations in phenomenological QCD sum rule analyses is discussed as well.Comment: 17 pages, 6 figures; version to appear in JHE

Issues potentially affecting quality of life arising from long-term medicines use: a qualitative study

Background Polypharmacy is increasing and managing large number of medicines may create a burden for patients. Many patients have negative views of medicines and their use can adversely affect quality of life. No studies have specifically explored the impact of general long-term medicines use on quality of life. Objective To determine the issues which patients taking long-term medicines consider affect their day-to-day lives, including quality of life. Setting Four primary care general practices in North West England Methods Face-to-face interviews with adults living at home, prescribed four or more regular medicines for at least 1 year. Interviewees were identified from primary care medical records and purposively selected to ensure different types of medicines use. Interviews were recorded, transcribed and analysed thematically. Results Twenty-one interviews were conducted and analysed. Patients used an average of 7.8 medicines, 51 % were preventive, 40 % for symptom relief and 9 % treatment. Eight themes emerged: relationships with health professionals, practicalities, information, efficacy, side effects, attitudes, impact and control. Ability to discuss medicines with health professionals varied and many views were coloured by negative experiences, mainly with doctors. All interviewees had developed routines for using multiple medicines, some requiring considerable effort. Few felt able to exert control over medicines routines specified by health professionals. Over half sought additional information about medicines whereas others avoided this, trusting in doctors to guide their medicines use. Patients recognised their inability to assess efficacy for many medicines, notably those used for prophylaxis. All were concerned about possible side effects and some had poor experiences of discussing concerns with doctors. Medicines led to restrictions on social activities and personal life to the extent that, for some, life can revolve around medicines. Conclusion There is a multiplicity and complexity of issues surrounding medicines use, which impact on day-to-day lives for patients with long-term conditions. While most patients adapt to long-term medicines use, others did so at some cost to their quality of life

Case report 220

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46818/1/256_2004_Article_BF00352557.pd

Child and adolescent psychiatric patients and later criminality

<p>Abstract</p> <p>Background</p> <p>Sweden has an extensive child and adolescent psychiatric (CAP) research tradition in which longitudinal methods are used to study juvenile delinquency. Up to the 1980s, results from descriptions and follow-ups of cohorts of CAP patients showed that children's behavioural disturbances or disorders and school problems, together with dysfunctional family situations, were the main reasons for families, children, and youth to seek help from CAP units. Such factors were also related to registered criminality and registered alcohol and drug abuse in former CAP patients as adults. This study investigated the risk for patients treated 1975–1990 to be registered as criminals until the end of 2003.</p> <p>Methods</p> <p>A regional sample of 1,400 former CAP patients, whose treatment occurred between 1975 and 1990, was followed to 2003, using database-record links to the Register of Persons Convicted of Offences at the National Council for Crime Prevention (NCCP).</p> <p>Results</p> <p>Every third CAP patient treated between 1975 and 1990 (every second man and every fifth woman) had entered the Register of Persons Convicted of Offences during the observation period, which is a significantly higher rate than the general population.</p> <p>Conclusion</p> <p>Results were compared to published results for CAP patients who were treated between 1953 and 1955 and followed over 20 years. Compared to the group of CAP patients from the 1950s, the results indicate that the risk for boys to enter the register for criminality has doubled and for girls, the risk seems to have increased sevenfold. The reasons for this change are discussed. Although hypothetical and perhaps speculative this higher risk of later criminality may be the result of lack of social control due to (1) rising consumption of alcohol, (2) changes in organisation of child social welfare work, (3) the school system, and (4) CAP methods that were implemented since 1970.</p