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

Emotional dysfunction in schizophrenia spectrum psychosis: the role of illness perceptions

Background. Assessing illness perceptions has been useful in a range of medical disorders. This study of people with a recent relapse of their psychosis examines the relationship between illness perception, their emotional responses and their attitudes to medication.Method. One hundred patients diagnosed with a non-affective psychotic disorder were assessed within 3 months of relapse. Measures included insight, self-reported. illness perceptions, medication adherence, depression, self-esteem and anxiety.Results. Illness perceptions about psychosis explained 46, 36 and 34% of the variance in depression, anxiety and self-esteem respectively. However, self-reported medication adherence was more strongly associated with a measure of insight.Conclusions. Negative illness perceptions in psychosis are clearly related to depression, anxiety and self-esteem. These in turn have been linked to symptom maintenance and recurrence. Clinical interventions that foster appraisals of recovery rather than of chronicity and severity may therefore improve emotional well-being in people with psychosis. It might be better to address adherence to medication through direct attempts at helping them understand their need for treatment

Planning with Information-Processing Constraints and Model Uncertainty in Markov Decision Processes

Information-theoretic principles for learning and acting have been proposed to solve particular classes of Markov Decision Problems. Mathematically, such approaches are governed by a variational free energy principle and allow solving MDP planning problems with information-processing constraints expressed in terms of a Kullback-Leibler divergence with respect to a reference distribution. Here we consider a generalization of such MDP planners by taking model uncertainty into account. As model uncertainty can also be formalized as an information-processing constraint, we can derive a unified solution from a single generalized variational principle. We provide a generalized value iteration scheme together with a convergence proof. As limit cases, this generalized scheme includes standard value iteration with a known model, Bayesian MDP planning, and robust planning. We demonstrate the benefits of this approach in a grid world simulation.Comment: 16 pages, 3 figure

Bolometric light curves and explosion parameters of 38 stripped-envelope core-collapse supernovae

Literature data are collated for 38 stripped-envelope core-collapse supernovae (SE SNe; i.e. SNe IIb, Ib, Ic and Ic-BL) that have good light curve coverage in more than one optical band. Using bolometric corrections derived in previous work, the bolometric light curve of each SN is recovered and template bolometric light curves provided. Peak light distributions and decay rates are investigated; SNe subtypes are not cleanly distinguished in this parameter space, although some grouping of types does occur and there is a suggestion of a Phillips-like relation for most SNe Ic-BL. The bolometric light curves are modelled with a simple analytical prescription and compared to results from more detailed modelling. Distributions of the explosion parameters shows the extreme nature of SNe Ic-BL in terms of their 56Ni mass and the kinetic energy, however ejected masses are similar to other subtypes. SNe Ib and Ic have very similar distributions of explosion parameters, indicating a similarity in progenitors. SNe~IIb are the most homogeneous subtype and have the lowest average values for 56Ni mass, ejected mass, and kinetic energy. Ejecta masses for each subtype and SE SNe as a whole are inconsistent with those expected from very massive stars. The majority of the ejecta mass distribution is well described by more moderately massive progenitors in binaries, indicating these are the dominant progenitor channel for SE SNe

Fe-rich pentlandite in Allende bulk samples and separates: Mössbauer spectroscopy analysis.

Published versio

QAA subject benchmark statement architecture : version for consultation December 2019

The Statement is intended to guide lecturers and course leaders in the design of academic courses leading to qualifications in architecture, it will also be useful to those developing other related courses. Higher education providers may need to consider other reference points in addition to this Statement in designing, delivering and reviewing courses. These may include requirements set out by the Architects Registration Board (ARB), the Royal Institute of British Architects (RIBA) and the Institute for Apprenticeships and Technical Education (IfATE). Providers may also need to consider industry or employer expectations. Individual higher education providers will decide how they use this information. The broad subject of architecture is both academic and vocational. The bachelor's award for architecture is the first stage of the typical education of an architect. This is typically either a BSc or a BA degree. The second stage of academic qualification is a master's level degree, typically in the form of a two-year MArch, which is defined as an undergraduate master's award. Architecture qualifications typically require a total of 360 (Credit Accumulation and Transfer Scheme, or CATS) credits at bachelor's level and 240 (CATS) credits within a master's level degree. While this may equate to five years of 120 (CATS) credits each, higher education providers may construct alternatives to enable flexibility in student learning. This Statement seeks to encapsulate the nature of a rich and diverse academic discipline. It is not intended to prescribe a curriculum, but rather describes the broad intellectual territory within which individual higher education providers will locate their courses of study in architecture

Ferric ion phases in Mössbauer spectra of “oxidized” and “reduced” CV3 chondrites.

Accepted versio

Buckling Instabilities of a Confined Colloid Crystal Layer

A model predicting the structure of repulsive, spherically symmetric, monodisperse particles confined between two walls is presented. We study the buckling transition of a single flat layer as the double layer state develops. Experimental realizations of this model are suspensions of stabilized colloidal particles squeezed between glass plates. By expanding the thermodynamic potential about a flat state of $N$ confined colloidal particles, we derive a free energy as a functional of in-plane and out-of-plane displacements. The wavevectors of these first buckling instabilities correspond to three different ordered structures. Landau theory predicts that the symmetry of these phases allows for second order phase transitions. This possibility exists even in the presence of gravity or plate asymmetry. These transitions lead to critical behavior and phases with the symmetry of the three-state and four-state Potts models, the X-Y model with 6-fold anisotropy, and the Heisenberg model with cubic interactions. Experimental detection of these structures is discussed.Comment: 24 pages, 8 figures on request. EF508

Large-Scale Structures Behind the Milky Way from Near-IR Surveys

About 25% of the optical extragalactic sky is obscured by the dust and stars of our Milky Way. Dynamically important structures might still lie hidden in this zone. Various approaches are presently being employed to uncover the galaxy distribution in the Zone of Avoidance (ZOA) but all suffer from (different) limitations and selection effects. We investigated the potential of using the DENIS NIR survey for studies of galaxies behind the obscuration layer of our Milky Way and for mapping the Galactic extinction. As a pilot study, we recovered DENIS I, J and K band images of heavily obscured but optically still visible galaxies. We determined the I, J and K band luminosity functions of galaxies on three DENIS strips that cross the center of the nearby, low-latitude, rich cluster Abell 3627. The extinction-corrected I-J and J-K colours of these cluster galaxies compare well with that of an unobscured cluster. We searched for and identified galaxies at latitudes where the Milky Way remains fully opaque (|b| 4-5mag) - in a systematic search as well as around positions of galaxies detected with the blind HI survey of the ZOA currently conducted with the Multibeam Receiver of the Parkes Radiotelescope.Comment: 12 pages, including 5 PS figures, LaTeX, uses crckapb.sty and epsf.tex. Better resolved figures available upon request. To appear in proceedings of the 3rd Euroconference (Meudon, France, June 1997) on ``The Impact of Near IR Surveys'', Kluwer 199

HLA Class-II Associated HIV Polymorphisms Predict Escape from CD4+ T Cell Responses.

Antiretroviral therapy, antibody and CD8+ T cell-mediated responses targeting human immunodeficiency virus-1 (HIV-1) exert selection pressure on the virus necessitating escape; however, the ability of CD4+ T cells to exert selective pressure remains unclear. Using a computational approach on HIV gag/pol/nef sequences and HLA-II allelic data, we identified 29 HLA-II associated HIV sequence polymorphisms or adaptations (HLA-AP) in an African cohort of chronically HIV-infected individuals. Epitopes encompassing the predicted adaptation (AE) or its non-adapted (NAE) version were evaluated for immunogenicity. Using a CD8-depleted IFN-γ ELISpot assay, we determined that the magnitude of CD4+ T cell responses to the predicted epitopes in controllers was higher compared to non-controllers (p<0.0001). However, regardless of the group, the magnitude of responses to AE was lower as compared to NAE (p<0.0001). CD4+ T cell responses in patients with acute HIV infection (AHI) demonstrated poor immunogenicity towards AE as compared to NAE encoded by their transmitted founder virus. Longitudinal data in AHI off antiretroviral therapy demonstrated sequence changes that were biologically confirmed to represent CD4+ escape mutations. These data demonstrate an innovative application of HLA-associated polymorphisms to identify biologically relevant CD4+ epitopes and suggests CD4+ T cells are active participants in driving HIV evolution