Polynomial functors and combinatorial Dyson-Schwinger equations

We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally equivalences of groupoids. Key features of combinatorial Dyson-Schwinger equations are revealed to follow from general categorical constructions and universal properties. Rather than beginning with an equation inside a given Hopf algebra and referring to given Hochschild $1$-cocycles, our starting point is an abstract fixpoint equation in groupoids, shown canonically to generate all the algebraic structure. Precisely, for any finitary polynomial endofunctor $P$ defined over groupoids, the system of combinatorial Dyson-Schwinger equations $X=1+P(X)$ has a universal solution, namely the groupoid of $P$-trees. The isoclasses of $P$-trees generate naturally a Connes-Kreimer-like bialgebra, in which the abstract Dyson-Schwinger equation can be internalised in terms of canonical $B_+$-operators. The solution to this equation is a series (the Green function) which always enjoys a Fa\`a di Bruno formula, and hence generates a sub-bialgebra isomorphic to the Fa\`a di Bruno bialgebra. Varying $P$ yields different bialgebras, and cartesian natural transformations between various $P$ yield bialgebra homomorphisms and sub-bialgebras, corresponding for example to truncation of Dyson-Schwinger equations. Finally, all constructions can be pushed inside the classical Connes-Kreimer Hopf algebra of trees by the operation of taking core of $P$-trees. A byproduct of the theory is an interpretation of combinatorial Green functions as inductive data types in the sense of Martin-L\"of Type Theory (expounded elsewhere).Comment: v4: minor adjustments, 49pp, final version to appear in J. Math. Phy

Profile of menthol cigarette smokers in the months following the removal of these products from the market: a cross-sectional population survey in England

Introduction: In May 2020, the EU Tobacco Products Directive ban on the sale of menthol cigarettes was implemented in England. This study examined the prevalence of menthol cigarette smoking after the ban, according to sociodemographic and smoking characteristics. / Methods: Cross-sectional data came from a representative survey of current smokers (18+) in England (unweighted n=2681) between July 2020 and June 2021. The weighted prevalence of menthol cigarette smoking as a proportion of total cigarette smoking was calculated, log-binomial regression explored trends over time, and χ2 statistics assessed the relationship between menthol smoking, sociodemographic and smoking characteristics. Sources of purchase of menthol cigarettes were explored. / Results: Between July 2020 and June 2021, 15.7% (95% CI 14.5 to 17.1) of smokers reported smoking menthol cigarettes. The fitted non-linear trend supported no initial change followed by a possible reduction across April–June 2021 and fit the data better than linear and null (no change) models (χ2(2)=2519.7, p=0.06; χ2(3)=2519.7, p=0.006). Menthol cigarette smoking was more common among younger groups (16–24=25.2%; 25–34=19.9%) and women (19.4%). Menthol cigarette smokers showed lower cigarette dependence compared with other smokers. Past-6-month purchases of menthol cigarettes from any illicit or cross-border source declined from 30.1% in the last 6 months of 2020 to 17.5% in the first 6 months of 2021. / Conclusions: A substantial minority of current smokers in England reported menthol cigarette smoking between July 2020 and June 2021, despite the ban, possibly reflecting mitigation of restrictions by a variety of licit means, such as legal menthol accessories. The reduction in menthol smoking across April–June 2021 warrants further monitoring

Involutive Categories and Monoids, with a GNS-correspondence

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories

EUREGIO MRSA-net Twente/Munsterland - a Dutch-German cross-border network for the prevention and control of infections caused by methicillin-resistant Staphylococcus aureus

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Poisson algebras for non-linear field theories in the Cahiers topos

We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisson algebra, which are sufficient to guarantee existence, and analytical aspects that are crucial to analyze its properties

Family farmers as agents of resilience in the Western Region of Santa Catarina (Brazil)

This article analyses how the resilience of family farmers has contributed to the development of the western region of Santa Catarina, Brazil. Despite having largest agro-industrial complex in Latin America, the region has faced cyclical crisis and challenges in recent decades. In fact, the quality of life of the rural population - the region is the main strongholds of family farming in Brazil - has not improved. Rural exodus, an aging population and the impairment of environmental quality are some of the evidences that point to the limits of the adopted agribusiness model. Family farmers and their organizations have responded to this socioeconomic environment of uncertainty with adaptive strategies based on local resilience, such as pluriactivity, productive diversification, transformation of raw materials in the property and production for own consumption. These strategies have served not only for the social reproduction of the group but also have contributed to a renewed regional dynamismEste artículo analiza cómo la resiliencia de las explotaciones agrarias familiares contribuye al desarrollo de la región occidental del Estado de Santa Catarina en Brasil. A pesar de acoger un complejo agroindustrial con larga tradición en America Latina, la región ha sufrido crisis cíclicas en las recientes décadas. De hecho, la calidad de vida de la población rural no ha mejorado en esta región, que es la más importante del Brasil en agricultura familiar. La emigración rural, el envejecimiento de la población y la no consideración de la calidad ambiental son algunas de las evidencias que fijan los límites del modelo de los "agro-negocios". Los agricultores familiares y sus organizaciones han respondido a esta situación de incertidumbre socioeconómica adoptando estrategias que se basan en la resiliencia local, tales como la pluriactividad, la diversificación productiva, la transformación de materias primas en la explotación y produciendo para el autoconsumo. Estas estrategias han servido, no únicamente para la reproducción social del grupo, sino también para revitalizar el dinamismo en esta región

Non-persistente virusoverdracht door bladluizen in bloembollen

Dit driejarig onderzoeksproject naar non-persistente virusoverdracht door bladluizen in bloembollen heeft direct toepasbare kennis en gewasbeschermingsadviezen opgeleverd, maar ook heldere adviezen voor zowel de chemische als biologische bestrijding van virusoverdracht door bladluizen. Deze adviezen vormen de basis voor verder onderzoek om uiteindelijk de non-persistente virusverspreiding door bladluizen nog effectiever te kunnen bestrijden