Mean Curvature Flow on Ricci Solitons

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds \cite{a_14}.Comment: 19 page

Irreversibility of World-sheet Renormalization Group Flow

We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in $\alpha'$ in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target manifolds. In the case of somewhere-negative scalar curvature (of the target space), we give a proof by constructing an entropy that increases monotonically along the flow, based on Perelman's Ricci flow entropy. One consequence is the absence of periodic solutions, and we are able to give a second, direct proof of this. If the scalar curvature is everywhere positive, we instead construct a regularized volume to provide an entropy for the flow. Our results are, in a sense, the analogue of Zamolodchikov's $c$-theorem for world-sheet RG flows on noncompact spacetimes (though our entropy is not the Zamolodchikov $C$-function).Comment: Minor changes, added one citation, version accepted for publicatio

Retrotransposon mapping in spider monkey genomes of the family Atelidae (Platyrrhini, Primates) shows a high level of LINE-1 amplification

To investigate the distribution of LINE-1 repeat sequences, a LINE-1 probe was Fluorescence In Situ Hybridized (FISH) on the chromosomes of Ateles geoffroyi and Ateles fusciceps (Atelidae); a LINE-1 probe was also mapped on Cebuella pygmaea (Cebidae) and used as an outgroup for phylogenetic comparison. Ateles spider monkeys have a highly rearranged genome and are an ideal model for testing whether LINE-1 is involved in genome evolution. The LINE-1 probe has been mapped in the two Atelidae species for the first time, revealing a high accumulation of LINE-1 sequences along chromosomal arms, including telomeres, and a scarcity of LINE-1 signals at centromere positions. LINE-1 mapping in C. pygmaea (Cebidae) revealed signals at centromere positions and along chromosome arms, which was consistent with previous published data from other Cebidae species. In a broader sense, the results were analyzed in light of published data on whole-chromosomal human probes mapped in these genomes. This analysis allows us to speculate about the presence of LINE-1 sequences at the junction of human chromosomal syntenies, as well as a possible link between these sequences and chromosomal rearrangements

A simple proof of Perelman's collapsing theorem for 3-manifolds

We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theorem is almost self-contained, accessible to non-experts and advanced graduate students. Perelman's collapsing theorem for 3-manifolds can be viewed as an extension of implicit function theoremComment: v1: 9 Figures. In this version, we improve the exposition of our arguments in the earlier arXiv version. v2: added one more grap

Investigating Off-shell Stability of Anti-de Sitter Space in String Theory

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow, and then show this implies its geometric stability with respect to Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.Comment: 29 pages, references added in this version to appear in Classical and Quantum Gravit

Biosecurity assessment of Argentinian pig farms

The pig industry is growing very fast in Argentina with an increasing need for replacement animals, feedstuff and transportation of animals. One of the main competitive advantages of the Argentinian pig industry is its being free of most major pig diseases. Within this context, applying measures aimed to reduce the risk of introduction and spread of pathogens is critical. The aim of the present study was to assess the biosecurity of Argentinian pig farms. Two types of farms were assessed: firstly, all official suppliers of high-genetic-value (n = 110) and secondly, a sample from commercial farms (n = 192). Data on the external and internal biosecurity practices applied on the farms was collected with a questionnaire. Data was analysed using a correspondence analysis and a hierarchical clustering analysis, which allowed identification of types of farms with regard to the biosecurity measures applied. Key variables characterizing the clusters were identified through an indicator value analysis. In addition, the external biosecurity of the farms was evaluated by using risk assessment tools with respect to the potential introduction of porcine epidemic diarrhoea virus. Results made evident three clusters: the first one which, amongst other measures, applied several barriers to prevent the entry of people, trucks and other vehicles, and could be considered as a group of high biosecurity, and the two other groups which applied a lower number of external and internal biosecurity measures. The results of the risk assessment showed that the routes with the highest risk of disease introduction were: replacement animals, vehicles transporting feed or animals, and visitors. The assessment of the external biosecurity showed that most Argentinian farms were not prepared for the contingency of a pathogen such as porcine epidemic diarrhoea virus. Special efforts should be made in official suppliers of high-genetic-value farms with poor biosecurity scores since they are at the top of the pig production chain and can be key for the spread of diseases.info:eu-repo/semantics/acceptedVersio

Ricci flow and black holes

Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the canonical ensemble for gravity in a box. At high temperature the action has three saddle points: hot flat space and a large and small black hole. Adding a time direction, these also give static 5-dimensional Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action. The small black hole has a Gross-Perry-Yaffe-type negative mode, and is therefore unstable under Ricci flow. We numerically simulate the two flows seeded by this mode, finding that they lead to the large black hole and to hot flat space respectively, in the latter case via a topology-changing singularity. In the context of string theory these flows are world-sheet renormalization group trajectories. We also use them to construct a novel free energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space of metrics corrected and expanded, references adde

a cross-sectional study in six European cities

Background: The relationship between socioeconomic position (SEP) and adolescent physical activity is uncertain, as most evidence is limited to specific settings and a restricted number of SEP indicators. This study aimed to assess the magnitude of socioeconomic differences in adolescent vigorous physical activity (VPA) across various European countries using a wide range of SEP indicators, including family-based (education, family affluence, perceived social standing, parents’ employment, housing tenure) and adolescent-based (academic performance and pocket money) ones. Methods: We used data from a survey among 10,510 students aged 14–17 from 50 schools in six European cities: Namur (BE), Tampere (FI), Hannover (DE), Latina (IT), Amersfoort (NL), Coimbra (PT). The questionnaire included socio-demographic characteristics and the amount of time spent in VPA. Results: The mean time spent practicing VPA was 60.4 min per day, with lower values for Namur (BE) and Latina (IT), and higher values for Amersfoort (NL). In the multivariable analysis, both categories of SEP indicators (family-based and adolescent based indicators) were independently associated with VPA. For each SEP indicator, lower levels of VPA were recorded in lower socioeconomic groups. In the total sample, each additional category of low SEP was associated with a decrease in mean VPA of about 4 min per day. Conclusions: This study showed that across European cities adolescent VPA is positively related to both family-based SEP and adolescents’ own SEP. When analysing socioeconomic differences in adolescent VPA, one should consider the use of multiple indicators of SEP.publishersversionpublishe

A Gradient Flow for Worldsheet Nonlinear Sigma Models

We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinear sigma models with closed target manifolds supporting a Riemannian metric, dilaton, and 2-form B-field. By generalizing recent mathematical results to incorporate the B-field and by decoupling the dilaton, we are able to describe the 1-loop beta-functions of the metric and B-field as the components of the gradient of a potential functional on the space of coupling constants. We emphasize a special choice of diffeomorphism gauge generated by the lowest eigenfunction of a certain Schrodinger operator whose potential and kinetic terms evolve along the flow. With this choice, the potential functional is the corresponding lowest eigenvalue, and gives the order alpha' correction to the Weyl anomaly at fixed points of (g(t),B(t)). Since the lowest eigenvalue is monotonic along the flow and reproduces the Weyl anomaly at fixed points, it accords with the c-theorem for flows that remain always in the first-order regime. We compute the Hessian of the lowest eigenvalue functional and use it to discuss the linear stability of points where the 1-loop beta-functions vanish, such as flat tori and K3 manifolds.Comment: Accepted version for publication. Citations added to Friedan and to Fateev, Onofri, and Zamolodchikov. Introduction modified slightly to discuss these citations. 25 pages, LaTe

a cross-section analysis on 36 European countries

Background: Schools have a crucial role to play in preventing youth smoking. However, the well-known long-term health consequences of youth smoking may be insufficient to convince education stakeholders to devote efforts to implement school-based programmes. However, if youth smoking were to have short-term consequences, this evidence could prompt education stakeholders' action. In this article, we investigate the link between smoking and school absenteeism. Methods: We used data from the 2011 wave of the European School Survey Project on Alcohol and Other Drugs, on adolescents aged 15-16. We applied logistic models to assess the risk of more than 3 missed school days, by cause, as function of smoking intensity, adjusting for age, sex, socioeconomic status, academic performance, parental involvement and other risk behaviours (alcohol and cannabis consumption). Consistency was assessed by replicating the analyses for each sex and age group and further adjusting for depression and self-esteem. Results: Smoking more than five cigarettes per day was significantly linked to school absenteeism, with a 55% excess risk of missing more than 3 school days per month due to illness (OR = 1.55, 95% CI 1.46-1.64), and a more than two times excess risk due to skipping (OR = 2.29; 95% CI 2.16-2.43). These findings were consistent across age and sex groups. Conclusion: We observed an association between smoking intensity and absenteeism among youth in Europe. This implies that, to the extent that this association is causal, school tobacco control policies may reduce the short-term consequences of smoking on adolescents' education and health.publishersversionpublishe