Unite and conquer: univariate and multivariate approaches for finding differentially expressed gene sets

Motivation: Recently, many univariate and several multivariate approaches have been suggested for testing differential expression of gene sets between different phenotypes. However, despite a wealth of literature studying their performance on simulated and real biological data, still there is a need to quantify their relative performance when they are testing different null hypotheses.

Results: In this article, we compare the performance of univariate and multivariate tests on both simulated and biological data. In the simulation study we demonstrate that high correlations equally affect the power of both, univariate as well as multivariate tests. In addition, for most of them the power is similarly affected by the dimensionality of the gene set and by the percentage of genes in the set, for which expression is changing between two phenotypes. The application of different test statistics to biological data reveals that three statistics (sum of squared t-tests, Hotelling's T2, N-statistic), testing different null hypotheses, find some common but also some complementing differentially expressed gene sets under specific settings. This demonstrates that due to complementing null hypotheses each test projects on different aspects of the data and for the analysis of biological data it is beneficial to use all three tests simultaneously instead of focusing exclusively on just one.

Prising open the black box: Critical realism, action research and social work

There is a growing interest in critical realism and its application to social work. This article makes a case for adopting this philosophical position in qualitative social work research. More specifically, it suggests that there is a concordance between critical realist premises and action research with its cyclical inquiry and advancement of social change. This combination of philosophy and method, it is argued, promotes anti-oppressive social work research and illuminates the processes shaping outcomes in programme evaluations. Overall, the article underscores the importance of 'depth' in qualitative inquiry by conceiving the social world in terms of five interlacing, social domains.

A general framework for measuring inconsistency through minimal inconsistent sets

Hunter and Konieczny explored the relationships between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base in several of their papers. In particular, an inconsistency value termed MIVC, defined from minimal inconsistent subsets, can be considered as a Shapley Inconsistency Value. Moreover, it can be axiomatized completely in terms of five simple axioms. MinInc, one of the five axioms, states that each minimal inconsistent set has the same amount of conflict. However, it conflicts with the intuition illustrated by the lottery paradox, which states that as the size of a minimal inconsistent belief base increases, the degree of inconsistency of that belief base becomes smaller. To address this, we present two kinds of revised inconsistency measures for a belief base from its minimal inconsistent subsets. Each of these measures considers the size of each minimal inconsistent subset as well as the number of minimal inconsistent subsets of a belief base. More specifically, we first present a vectorial measure to capture the inconsistency for a belief base, which is more discriminative than MIVC. Then we present a family of weighted inconsistency measures based on the vectorial inconsistency measure, which allow us to capture the inconsistency for a belief base in terms of a single numerical value as usual. We also show that each of the two kinds of revised inconsistency measures can be considered as a particular Shapley Inconsistency Value, and can be axiomatically characterized by the corresponding revised axioms presented in this paper.

Action research and reflective practice: towards a holistic view

Two concepts that have captured the imagination of the educational community in the last 60 years have been those of ‘reflective practice’ and ‘action research’. Both, in their various forms, are considered to be critical dimensions of the professional development of teachers. However, whilst both were receiving academic attention during the 1930s and 1940s (Lewin, 1934, cited in Adelman, 1993; Lewin, 1946; Dewey, 1933), it was not until Stenhouse’s (1975) notion of the teacher-as-researcher that the two came most compellingly into relationship and educational action research as a process, which held at its centre different kinds of reflection, began to be reformulated in Britain (Carr, 1993). This article considers the important part played in teachers’ development by different kinds of action research. Its central thesis is that, although action research has a critical role to play not least as a means of building the capacity of teachers as researchers of their own practice, there has been insufficient attention given to both the nature of reflection in the action research process, and its relationship to the purposes, processes and outcomes. The article challenges the rational, cognitive models of reflection that are implicit in much of the action research literature. It suggests that more attention needs to be given to the importance of the role of emotion in understanding and developing the capacities for reflection which facilitates personal, professional and ultimately system change.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.