Canonical tree-decompositions of finite graphs I. Existence and algorithms

We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject to the requirement that they commute with graph isomorphisms. In particular, all the decompositions constructed are invariant under the automorphisms of the graph.Comment: 23 pages, 5 figure

kk-Blocks: a connectivity invariant for graphs

A $k$-block in a graph $G$ is a maximal set of at least $k$ vertices no two of which can be separated in $G$ by fewer than $k$ other vertices. The block number $\beta(G)$ of $G$ is the largest integer $k$ such that $G$ has a $k$-block. We investigate how $\beta$ interacts with density invariants of graphs, such as their minimum or average degree. We further present algorithms that decide whether a graph has a $k$-block, or which find all its $k$-blocks. The connectivity invariant $\beta(G)$ has a dual width invariant, the block-width ${\rm bw}(G)$ of $G$. Our algorithms imply the duality theorem $\beta = {\rm bw}$: a graph has a block-decomposition of width and adhesion $< k$ if and only if it contains no $k$-block.Comment: 22 pages, 5 figures. This is an extended version the journal article, which has by now appeared. The version here contains an improved version of Theorem 5.3 (which is now best possible) and an additional section with examples at the en

The celebrity logics of the academic field. The unequal distribution of citation visibility of Applied Linguistics professors in Germany, France, and the United Kingdom.

This article investigates the distribution of citation visibility of Applied Linguistics professors in France, Germany and the United Kingdom. By comparing citation counts from Google Scholar, we reveal hyperinequalities between more and less visible professors. We register strong inequalities between English-, German- and French-language scholars as well within languages, especially within the English-language community. These inequalities bear witness to the celebrity logics in academia, i.e. the hyperunequal distribution of visibility between a few >starsdiscursive capitalism<, which designates the institutional transfer of value from the many citing to the few cited members in disciplinary communities

Attitudes towards shared decision making in mental health: A qualitative synthesis

Purpose: Shared decision making (SDM) prioritises joint deliberation between practitioner and service user, and a respect for service-users’ experiential knowledge, values and preferences. The purpose of this paper is to review the existing literature pertaining to key stakeholders’ attitudes towards SDM in mental health. It examines whether perceived barriers and facilitators differ by group (e.g. service user, psychiatrist, nurse and social worker) and includes views of what facilitates and hinders the process for service users and practitioners. Design/methodology/approach: This review adopts the principles of a qualitative research synthesis. A key word search of research published between 1990 and 2016 was undertaken. Qualitative, quantitative and mixed methods studies were included. Findings: In total, 43 papers were included and several themes identified for service user and practitioner perspectives. Both practitioners and service users see SDM as an ethical imperative, and both groups highlight the need to be flexible in implementing SDM, suggesting it is context dependent. A range of challenges and barriers are presented by both practitioners and service users reflecting complex contextual and cultural features within which interactions in mental health take place. There were qualitative differences in what service users and practitioners describe as preventing or enabling SDM. The differences highlighted point towards different challenges and priorities in SDM for service users and practitioners. Originality/value: The presentation of nuanced views and attitudes that practitioners and service users hold represent an important and under reported area and offer insight into the reasons for the gap between idealised policy and actual practice of SDM in mental health settings