Characterizations and algorithms for generalized Cops and Robbers games

We propose a definition of generalized Cops and Robbers games where there are two players, the Pursuer and the Evader, who each move via prescribed rules. If the Pursuer can ensure that the game enters into a fixed set of final positions, then the Pursuer wins; otherwise, the Evader wins. A relational characterization of the games where the Pursuer wins is provided. A precise formula is given for the length of the game, along with an algorithm for computing if the Pursuer has a winning strategy whose complexity is a function of the parameters of the game. For games where the position of one player does not affect the available moves of he other, a vertex elimination ordering characterization, analogous to a cop-win ordering, is given for when the Pursuer has a winning strategy

A Study of kk-dipath Colourings of Oriented Graphs

We examine $t$-colourings of oriented graphs in which, for a fixed integer $k \geq 1$, vertices joined by a directed path of length at most $k$ must be assigned different colours. A homomorphism model that extends the ideas of Sherk for the case $k=2$ is described. Dichotomy theorems for the complexity of the problem of deciding, for fixed $k$ and $t$, whether there exists such a $t$-colouring are proved.Comment: 14 page

Interrupting the social amplification of risk process: a case study in collective emissions reduction

One of the main approaches we have for studying the progressive divergence of understandings around a risk issue is that of social risk amplification. This article describes a case study of a particular environmental contaminant, a chemical flame retardant that could be interpreted as having produced a risk amplifying process. It describes in particular how a group of industrial organizations acted collectively to reduce emissions of this contaminant, in an apparent attempt to avert regulation and boycotts—that is, to intercept the social amplification process and avoid its secondary effects. The aim of the study was to investigate the constitutive qualities of this collective action: the qualities that defined it and made it effective in the eyes of those involved. These include institutionalisation and independence, the ability to confer individual as well as collective benefit, the capacity to attract (rather than avoid) criticism, and the ‘branding’ that helps communicate what otherwise appear to be a set of unconnected, local actions. Although the risk amplification framework has been criticised for implying that there is some externally given risk level that is subsequently amplified, it does appear to capture the mentality of actors involved in issues of this kind. They talk and act as though they believe they are participants in a risk amplification process

Reducing the volume, exposure and negative impacts of advertising for foods high in fat, sugar and salt to children: a systematic review of the evidence from statutory and self-regulatory actions and educational measures

Purpose: To identify and review evidence on 1) the effectiveness of statutory and self-regulatory actions to reduce the volume, exposure or wider impact of advertising for foods high in fat, sugar and salt (HFSS) to children, and 2) the role of educational measures. Design/methodology/approach: A systematic review of three databases (Medline, CINAHL and PsycINFO) and grey literature was carried out. Relevant evidence included studies evaluating advertising bans and restrictions, advertising literacy programmes and parental communication styles. Relevant media included TV, internet, radio, magazines and newspaper advertising. No studies were excluded based on language or publication date. Findings: Forty-seven publications were included: 19 provided evidence for the results of statutory regulation, 25 for self-regulation, and six for educational approaches. Outcome measures varied in approach, quality and results. Findings suggested statutory regulation could reduce the volume of and children's exposure to advertising for foods HFSS, and had potential to impact more widely. Self-regulatory approaches showed varied results in reducing children's exposure. There was some limited support for educational measures. Discussion: Consistency in measures from evaluations over time would assist the development and interpretation of the evidence base on successful actions and measures to reduce the volume, exposure and impact of advertising for foods HFSS to children

Characterising bias in regulatory risk and decision analysis: An analysis of heuristics applied in health technology appraisal, chemicals regulation, and climate change governance

In many environmental and public health domains, heuristic methods of risk and decision analysis must be relied upon, either because problem structures are ambiguous, reliable data is lacking, or decisions are urgent. This introduces an additional source of uncertainty beyond model and measurement error – uncertainty stemming from relying on inexact inference rules. Here we identify and analyse heuristics used to prioritise risk objects, to discriminate between signal and noise, to weight evidence, to construct models, to extrapolate beyond datasets, and to make policy. Some of these heuristics are based on causal generalisations, yet can misfire when these relationships are presumed rather than tested (e.g. surrogates in clinical trials). Others are conventions designed to confer stability to decision analysis, yet which may introduce serious error when applied ritualistically (e.g. significance testing). Some heuristics can be traced back to formal justifications, but only subject to strong assumptions that are often violated in practical applications. Heuristic decision rules (e.g. feasibility rules) in principle act as surrogates for utility maximisation or distributional concerns, yet in practice may neglect costs and benefits, be based on arbitrary thresholds, and be prone to gaming. We highlight the problem of rule-entrenchment, where analytical choices that are in principle contestable are arbitrarily fixed in practice, masking uncertainty and potentially introducing bias. Strategies for making risk and decision analysis more rigorous include: formalising the assumptions and scope conditions under which heuristics should be applied; testing rather than presuming their underlying empirical or theoretical justifications; using sensitivity analysis, simulations, multiple bias analysis, and deductive systems of inference (e.g. directed acyclic graphs) to characterise rule uncertainty and refine heuristics; adopting “recovery schemes” to correct for known biases; and basing decision rules on clearly articulated values and evidence, rather than convention

Graph homomorphisms with infinite targets

AbstractLet H be a fixed graph whose vertices are called colours. Informally, an H-colouring of a graph G is an assignment of these colours to the vertices of G such that adjacent vertices receive adjacent colours. We introduce a new tool for proving NP-completeness of H-colouring problems, which unifies all methods used previously. As an application we extend, to infinite graphs of bounded degree, the theorem of Hell and Nešetřil that classifies finite H-colouring problems by complexity