Torsion in Graph Homology

Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsions. When the underlying algebra is $\mathbb{Z}[x]/(x^2)$, we determine precisely those graphs whose cohomology contains torsion. For a larger class of algebras, we show that torsion often occurs. Our investigation of torsion led to other related general results. The ideas of this paper could potentially be used to predict the Khovanov-Rozansky $sl(m)$ homology of knots (in particular $(2,n)$ torus knots). We also predict that our work is connected with Hochschild and Connes cyclic homology of algebras.Comment: 45 pages, 20 figures, Fundamenta Mathematicae, 190, 2006, to appea

La contamination perçue des produits : vers une meilleure compréhension de ses antécédents et de ses effets

CAHIER DE RECHERCHES n° 2012-05 E3L'avènement des produits en libre-service conduit les consommateurs à exercer davantage leur sens tactile. Si les recherches en marketing sensoriel ont montré l'intérêt de laisser les consommateurs manipuler librement les produits, il convient de nuancer ce constat. De récentes recherches se sont intéressées aux aspects négatifs du toucher et plus spécifiquement à la perception de contamination des produits. L'objectif de ce papier est de mieux cerner le phénomène de contamination. Des entretiens semi-directifs permettent de mettre en évidence les réponses d'ordre émotionnel, cognitif et comportemental suscitées lorsqu'un consommateur se retrouve confronté à un produit déjà manipulé

The chromatic polynomial of fatgraphs and its categorification

Motivated by Khovanov homology and relations between the Jones polynomial and graph polynomials, we construct a homology theory for embedded graphs from which the chromatic polynomial can be recovered as the Euler characteristic. For plane graphs, we show that our chromatic homology can be recovered from the Khovanov homology of an associated link. We apply this connection with Khovanov homology to show that the torsion-free part of our chromatic homology is independent of the choice of planar embedding of a graph. We extend our construction and categorify the Bollobas-Riordan polynomial (a generalisation of the Tutte polynomial to embedded graphs). We prove that both our chromatic homology and the Khovanov homology of an associated link can be recovered from this categorification.Comment: A substantial revision. To appear in Advances in Mathematic

A mixed-methods approach to understanding barriers and facilitators to healthy eating and exercise from five European countries: highlighting the roles of enjoyment, emotion and social engagement

Healthy adults are consistently falling below national and international recommendations for physical activity and dietary intake across Europe. This study took a co-creative approach with adult samples from five European countries to qualitatively and quantitatively establish motivators, barriers and sustaining factors for positive health behaviour change. Stage 1 delivered a newly-designed online programme, creating a community who identified challenges, motivators and solutions to sustaining positive healthy eating and physical activity behaviours. Stage 2 administered an online survey (developed from Stage 1 findings) to a larger sample to quantify the relative importance of these motivators and barriers. Results from both stages indicated enjoyment, positive emotions, and reward as key motivators for both behaviours across all five countries. Barriers included habit-breaking difficulties, temptation and negative affective states. Those with a high BMI placed more importance on social pressure than those with healthy BMI. Participants’ reports of motivators and barriers reflected relevant approaches from consumer science, behavioural economics, and psychology. Interventions supporting adults who are not chronically ill but would benefit from improved diet and/or physical activity should not focus exclusively on health as a motivating factor. Emphasis on enjoyable behaviours, social engagement and reward will likely improve engagement and sustained behaviour change

Picture, mental imagery and persuasive communication effects : the case of an advertisment including a work of art

Ce cahier est le résumé d'une recherche doctorale (soutenue en 1997) dont l'objectif principal était l'étude du rôle médiateur de l'imagerie mentale (visuelle, auditive, gustative et olfactive) dans la formation des réponses attitudinales et comportementales à une annonce publicitaire contenant une oeuvre d'art. Les fondements théoriques, le cadre conceptuel et les choix méthodologiques de ladite recherche sont synthétisés. Puis, les principaux résultats sont présentés et discutés. Enfin, les limites sont mentionnées et des voies de recherches futures sont esquissées.This working paper summarises a PhD research (attended in 1997). Its main purpose was to study whether mental imagery (visual, audivite, gustative and olfactive) mediates attitudes and behavior in response to an advertisement in which a congruent work of art is included. Its theoretical baseline, its conceptual framework, its methodology are synthetized. Then its main results are presented and discussed. Finally its limits and resarch avenues are sketched.ou

Le comportement du consommateur sur un site marchand est-il fondamentalement différent de son comportement en magasin ? Proposition d'un cadre d'appréhension de ses spécificités

International audienceUn cadre d'appréhension des spécificités du comportement du consommateur sur un site marchand est proposé. Sa construction, guidée par l'impact de la technologie et notamment de l'interactivité, s'appuie sur la mise en regard des connaissances actuelles sur le comportement du consommateur en ligne avec la littérature classique sur le magasinage (faire des courses ou shopping)