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Page 1 of 4

  • Associations of negative affective biases and depressive symptoms in a community-based sample

  • Laura de Nooij, Mark J. Adams, Emma L. Hawkins, Liana Romaniuk, Marcus R. Munafò, Ian S. Penton-Voak, Rebecca Elliott, Amy R. Bland, Gordon D. Waiter, Anca-Larisa Sandu, Tina Habota, J. Douglas Steele, Alison D. Murray, Archie Campbell, David J. Porteous, Generation Scotland, Andrew M. McIntosh, Heather C. Whalley
  • Journal:
    Psychological Medicine / Volume 53 / Issue 12 / September 2023
    Published online by Cambridge University Press:
    21 September 2022, pp. 5518-5527
    • Article
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  • Background

    Major depressive disorder (MDD) was previously associated with negative affective biases. Evidence from larger population-based studies, however, is lacking, including whether biases normalise with remission. We investigated associations between affective bias measures and depressive symptom severity across a large community-based sample, followed by examining differences between remitted individuals and controls.

    Methods

    Participants from Generation Scotland (N = 1109) completed the: (i) Bristol Emotion Recognition Task (BERT), (ii) Face Affective Go/No-go (FAGN), and (iii) Cambridge Gambling Task (CGT). Individuals were classified as MDD-current (n = 43), MDD-remitted (n = 282), or controls (n = 784). Analyses included using affective bias summary measures (primary analyses), followed by detailed emotion/condition analyses of BERT and FAGN (secondary analyses).

    Results

    For summary measures, the only significant finding was an association between greater symptoms and lower risk adjustment for CGT across the sample (individuals with greater symptoms were less likely to bet more, despite increasingly favourable conditions). This was no longer significant when controlling for non-affective cognition. No differences were found for remitted-MDD v. controls. Detailed analysis of BERT and FAGN indicated subtle negative biases across multiple measures of affective cognition with increasing symptom severity, that were independent of non-effective cognition [e.g. greater tendency to rate faces as angry (BERT), and lower accuracy for happy/neutral conditions (FAGN)]. Results for remitted-MDD were inconsistent.

    Conclusions

    This suggests the presence of subtle negative affective biases at the level of emotion/condition in association with depressive symptoms across the sample, over and above those accounted for by non-affective cognition, with no evidence for affective biases in remitted individuals.

Topological Geometry
  • Ian R. Porteous
  • Published online:
    06 January 2010
    Print publication:
    05 February 1981
  • The earlier chapter of this self-contained text provide a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place. In parallel with this is an account, also from first principles, of the elementary theory of topological spaces and of continuous and differentiable maps that leads up to the definitions of smooth manifolds and their tangent spaces and of Lie groups and Lie algebras. The calculus is presented as far as possible in basis free form to emphasize its geometrical flavour and its linear algebra content. In this second edition Dr Porteous has taken the opportunity to add a chapter on triality which extends earlier work on the Spin groups in the chapter on Clifford algebras. The details include a number of important transitive group actions and a description of one of the exceptional Lie groups, the group G2. A number of corrections and improvements have also been made. There are many exercises throughout the book and senior undergraduates in mathematics as well as first-year graduate students will continue to find it stimulating and rewarding.

Clifford Algebras and the Classical Groups
  • Ian R. Porteous
  • Published online:
    22 September 2009
    Print publication:
    05 October 1995
  • The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G2, and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.

  • 1 - Linear spaces

  • Ian R. Porteous, University of Liverpool
  • Book:
    Clifford Algebras and the Classical Groups
    Published online:
    22 September 2009
    Print publication:
    05 October 1995, pp 1-8

  • Summary

    In this chapter we recall briefly some salient facts about linear spaces and linear maps. Proofs for the most part are omitted.

    Maps

    Let X and Y be sets and f : X → Y a map. Then, for each x ∈ X an element f(x) ∈ Y is defined, the subset of Y consisting of all such elements being called the image of f, denoted by im f. More generally f : X ↣ Y will denote a map of an unspecified subset of X to Y, X being called the source of the map and the subset of X consisting of those points x ∈ X for which f(x) is defined being called the domain of f, denoted by dom f. In either case the set Y is the target of f.

    Given a map f : X ↣ Y and a point y ∈ Y, the subset f−1{y} of X consisting of those points x ∈ X such that f(x) = y is called the fibre of f over y, this being non-null if and only if y ∈ im f. The set of non-null fibres of f is called the coimage of f and the map

    dom f → coim f ; x ↦ f−1{f(x)}

    the partition of dom f induced by f. The fibres of a map f are sometimes called the level sets or the contours of f, especially when the target of f is the field of real numbers R.

  • Foreword

  • Ian R. Porteous, University of Liverpool
  • Book:
    Clifford Algebras and the Classical Groups
    Published online:
    22 September 2009
    Print publication:
    05 October 1995, pp ix-x

  • Summary

    This book's parent Topological Geometry (Porteous (1969)), originally written in the 1960's to make propaganda for a basis-free approach to the differential calculus of functions of several variables, contained, almost by accident, a central section on Clifford algebras, a generalisation of quaternions that was at that time little known. This section was strengthened in the second edition (Porteous (1981)) by an additional chapter on the triality outer automorphism of the group Spin(8), a feature which illuminates the structure of several of the other Spin groups and which is related to a property of six-dimensional projective quadrics first noticed almost a hundred years ago by Study in work on the rigid motions of three-dimensional space.

    In recent years Clifford algebras have become a more popular tool in theoretical physics and it seems therefore appropriate to rework the original book, summarising the linear algebra and calculus required but expanding the Clifford algebra material. This seems the more worth while since it is clear that the central result of the old book, the classification of the conjugation anti-involution of the Clifford algebras Rp,q and their complexifications, was dealt with too briefly to be readily understood, and some of the more recent treatments of it elsewhere have been less than complete.

    As in the previous version, the opportunity has been taken to give an exhaustive treatment of all the generalisations of the orthogonal and unitary groups known as the classical groups, since the full set plays a part in the Clifford algebra story.

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