Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Rappresentazioni lineari di SL3(C)

Espongo i fatti di base della teoria delle rappresentazioni con lo scopo di indagare i possibili modi in cui un dato gruppo di Lie o algebra di Lie agisce su uno spazio vettoriale di dimensione finita. Tali risultati verranno applicati all'algebra di Lie del gruppo speciale lineare.

Diffusion maps in the Subriemannian motion group and perceptual grouping

Il presente lavoro è motivato dal problema della constituzione di unità percettive a livello della corteccia visiva primaria V1. Si studia dettagliatamente il modello geometrico di Citti-Sarti con particolare attenzione alla modellazione di fenomeni di associazione visiva. Viene studiato nel dettaglio un modello di connettività. Il contributo originale risiede nell'adattamento del metodo delle diffusion maps, recentemente introdotto da Coifman e Lafon, alla geometria subriemanniana della corteccia visiva. Vengono utilizzati strumenti di teoria del potenziale, teoria spettrale, analisi armonica in gruppi di Lie per l'approssimazione delle autofunzioni dell'operatore del calore sul gruppo dei moti rigidi del piano. Le autofunzioni sono utilizzate per l'estrazione di unità percettive nello stimolo visivo. Sono presentate prove sperimentali e originali delle capacità performanti del metodo.

Low-Income Fathers’ Barriers to Participation in Family and Parenting Programs

This exploratory study used semi-structured focus groups to examine: 1) where and from whom fathers obtain information about parenting; 2) the types of parenting services men are aware of, and their attitudes about participating in such services; and 3) fathers’ perceived norms about the acceptability and utility of various parenting practices. Low-income men (N = 17) were recruited from a human services agency in Detroit, Michigan. Four major themes emerged. First was the need for male-focused community resources for fathers. Second was that men were aware of and used positive disciplinary strategies. Third was emphasis on fathers’ positive and effective communication, with male children in particular. Finally, men suggested that constructive and concrete activities, such as engaging with children in activities or mentorship programs with other adult men in the community, were preferable to traditional parenting class such as those offered through Child Protective Services.

All-loop anomalous dimensions in integrable λ-deformed σ-models

We calculate the all-loop anomalous dimensions of current operators in λ-deformed σ-models. For the isotropic integrable deformation and for a semi-simple group G we compute the anomalous dimensions using two different methods. In the first we use the all-loop effective action and in the second we employ perturbation theory along with the Callan–Symanzik equation and in conjunction with a duality-type symmetry shared by these models. Furthermore, using CFT techniques we compute the all-loop anomalous dimension of bilinear currents for the isotropic deformation case and a general G . Finally we work out the anomalous dimension matrix for the cases of anisotropic SU(2) and the two couplings, corresponding to the symmetric coset G/H and a subgroup H, splitting of a group G.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Statnote 10: the two-way analysis of variance

The two-way design has been variously described as a matched-sample F-test, a simple within-subjects ANOVA, a one-way within-groups ANOVA, a simple correlated-groups ANOVA, and a one-factor repeated measures design! This confusion of terminology is likely to lead to problems in correctly identifying this analysis within commercially available software. The essential feature of the design is that each treatment is allocated by randomization to one experimental unit within each group or block. The block may be a plot of land, a single occasion in which the experiment was performed, or a human subject. The ‘blocking’ is designed to remove an aspect of the error variation and increase the ‘power’ of the experiment. If there is no significant source of variation associated with the ‘blocking’ then there is a disadvantage to the two-way design because there is a reduction in the DF of the error term compared with a fully randomised design thus reducing the ‘power’ of the analysis.

Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

How much is '5-a-day'? A qualitative investigation into consumer understanding of fruit and vegetable intake guidelines

BACKGROUND: Despite the known health benefits of fruit and vegetables (FV), population intakes remain low. One potential contributing factor may be a lack of understanding surrounding recommended intakes. The present study aimed to explore the understanding of FV intake guidelines among a sample of low FV consumers.

METHODS: Six semi-structured focus groups were held with low FV consumers (n = 28, age range 19-55 years). Focus groups were recorded digitally, transcribed verbatim and analysed thematically using nvivo (QSR International, Melbourne, Australia) to manage the coded data. Participants also completed a short questionnaire assessing knowledge on FV intake guidelines. Descriptive statistics were used to analyse responses.

RESULTS: The discussions highlighted that, although participants were aware of FV intake guidelines, they lacked clarity with regard to the meaning of the '5-a-day' message, including what foods are included in the guideline, as well as what constitutes a portion of FV. There was also a sense of confusion surrounding the concept of achieving variety with regard to FV intake. The sample highlighted a lack of previous education on FV portion sizes and put forward suggestions for improving knowledge, including increased information on food packaging and through health campaigns. Questionnaire findings were generally congruent with the qualitative findings, showing high awareness of the '5-a-day' message but a lack of knowledge surrounding FV portion sizes.

CONCLUSIONS: Future public health campaigns should consider how best to address the gaps in knowledge identified in the present study, and incorporate evaluations that will allow the impact of future initiatives on knowledge, and ultimately behaviour, to be investigated.

Térmitas como bioindicadores de qualidade de habitat na caatinga, Brasil: há uma sintonia entre as variáveis estruturais dos habitats e as taxocenoses amostradas?

The composition of termite assemblages was analyzed at three Caatinga sites of the Seridó Ecological Station, located in the municipality of Serra Negra do Norte, in the state of Rio Grande do Norte, Brazil. These sites have been subjected to selective logging, and cleared for pasture and farming. A standardized sampling protocol for termite assemblages (30h/person/site) was conducted between September 2007 and February 2009. At each site we measured environmental variables, such as soil granulometry, pH and organic matter, necromass stock, vegetation height, tree density, stem diameter at ankle height (DAH) and the largest and the smallest crown width. Ten species of termites, belonging to eight genera and three families, were found at the three experimental sites. Four feeding-groups were sampled: wood-feeders, soil-feeders, wood-soil interface feeders and leaf-feeders. The wood-feeders were dominant in number of species and number of encounters at all sites. In general, the sites were not significantly different in relation to the environmental variables measured. The same pattern was observed for termite assemblages, where no significant differences in species richness, relative abundance and taxonomic and functional composition were observed between the three sites. The agreement between the composition of assemblages and environmental variables reinforces the potential of termites as biological indicators of habitat quality

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

Efficient simple groups

We prove that the simple group L-3(5) which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million, S-4(4) which has order 979200, whose efficiency or otherwise remains to be determined.

On landslide risk, resilience and vulnerability of mountain communities in Central-Eastern Nepal

Executive SummaryIn Nepal, landslides are one of the major natural hazards after epidemics, killing over 100 persons per year. However, this figure is an underreported reflection of the actual impact that landslides have on livelihoods and food security in rural Nepal. With predictions of more intense rainfall patterns, landslide occurrence in the Himalayas is likely to increase and continue to be one of the major impediments to development. Due to the remoteness of many localities and lack of resources, responsibilities for disaster preparedness and response in mountain areas usually lie with the communities themselves. Everyday life is full of risk in mountains of Nepal. This is why mountain populations, as well as other populations living in harsh conditions have developed a number of coping strategies for dealing with adverse situations. Perhaps due to the dispersed and remote nature of landslides in Nepal, there have been few studies on vulnerability, coping- and mitigation strategies of landslide affected populations. There are also few recommendations available to guide authorities and populations how to reduce losses due to landslides in Nepal, and even less so, how to operationalize resilience and vulnerability.Many policy makers, international donors, NGOs and national authorities are currently asking what investments are needed to increase the so-called 'resilience' of mountain populations to deal with climate risks. However, mountain populations are already quite resilient to seasonal fluctuations, temperature variations, rainfall patterns and market prices. In spite of their resilience, they continue to live in places at risk due to high vulnerability caused by structural inequalities: access to land, resources, markets, education. This interdisciplinary thesis examines the concept of resilience by questioning its usefulness and validity as the current goal of international development and disaster risk reduction policies, its conceptual limitations and its possible scope of action. The goal of this study is two-fold: to better define and distinguish factors and relationships between resilience, vulnerability, capacities and risk; and to test and improve a participatory methodology for evaluating landslide risk that can serve as a guidance tool for improving community-based disaster risk reduction. The objective is to develop a simple methodology that can be used by NGOs, local authorities and communities to reduce losses from landslides.Through its six case studies in Central-Eastern Nepal, this study explores the relation between resilience, vulnerability and landslide risk based on interdisciplinary methods, including geological assessments of landslides, semi-structured interviews, focus groups and participatory risk mapping. For comparison, the study sites were chosen in Tehrathum, Sunsari and Dolakha Districts of Central/Eastern Nepal, to reflect a variety of landslide types, from chronic to acute, and a variety of communities, from very marginalized to very high status. The study uses the Sustainable Livelihoods Approach as its conceptual basis, which is based on the notion that access and rights to resources (natural, human/institutional, economic, environmental, physical) are the basis for coping with adversity, such as landslides. The study is also intended as a contribution to the growing literature and practices on Community Based Disaster Risk Reduction specifically adapted to landslide- prone areas.In addition to the six case studies, results include an indicator based methodology for assessing and measuring vulnerability and resilience, a composite risk assessment methodology, a typology of coping strategies and risk perceptions and a thorough analysis of the relation between risk, vulnerability and resilience. The methodology forassessing vulnerability, resilience and risk is relatively cost-effective and replicable in a low-data environment. Perhaps the major finding is that resilience is a process that defines a community's (or system's) capacity to rebound following adversity but it does not necessarily reduce vulnerability or risk, which requires addressing more structural issues related to poverty. Therefore, conclusions include a critical view of resilience as a main goal of international development and disaster risk reduction policies. It is a useful concept in the context of recovery after a disaster but it needs to be addressed in parallel with vulnerability and risk.This research was funded by an interdisciplinary grant (#26083591) from the Swiss National Science Foundation for the period 2009-2011 and a seed grant from the Faculty of Geosciences and Environment at the University of Lausanne in 2008.Résumé en françaisAu Népal, les glissements de terrain sont un des aléas les plus dévastateurs après les épidémies, causant 100 morts par an. Pourtant, ce chiffre est une sous-estimation de l'impact réel de l'effet des glissements sur les moyens de subsistance et la sécurité alimentaire au Népal. Avec des prévisions de pluies plus intenses, l'occurrence des glissements dans les Himalayas augmente et présente un obstacle au développement. Du fait de l'éloignement et du manque de ressources dans les montagnes au Népal, la responsabilité de la préparation et la réponse aux catastrophes se trouve chez les communautés elles-mêmes. Le risque fait partie de la vie quotidienne dans les montagnes du Népal. C'est pourquoi les populations montagnardes, comme d'autres populations vivant dans des milieux contraignants, ont développé des stratégies pour faire face aux situations défavorables. Peu d'études existent sur la vulnérabilité, ceci étant probablement dû à l'éloignement et pourtant, les stratégies d'adaptation et de mitigation des populations touchées par des glissements au Népal existent.Beaucoup de décideurs politiques, bailleurs de fonds, ONG et autorités nationales se demandent quels investissements sont nécessaires afin d'augmenter la 'resilience' des populations de montagne pour faire face aux changements climatiques. Pourtant, ces populations sont déjà résilientes aux fluctuations des saisons, des variations de température, des pluies et des prix des marchés. En dépit de leur résilience, ils continuent de vivre dans des endroits à fort risque à cause des vulnérabilités créées par les inégalités structurelles : l'accès à la terre, aux ressources, aux marchés et à l'éducation. Cette thèse interdisciplinaire examine le concept de la résilience en mettant en cause son utilité et sa validité en tant que but actuel des politiques internationales de développement et de réduction des risques, ainsi que ses limitations conceptuelles et ses possibles champs d'action. Le but de cette étude est double : mieux définir et distinguer les facteurs et relations entre la résilience, la vulnérabilité, les capacités et le risque ; Et tester et améliorer une méthode participative pour évaluer le risque des glissements qui peut servir en tant qu'outil indicatif pour améliorer la réduction des risques des communautés. Le but est de développer une méthodologie simple qui peut être utilisée par des ONG, autorités locales et communautés pour réduire les pertes dues aux glissements.A travers les études de cas au centre-est du Népal, cette étude explore le rapport entre la résilience, la vulnérabilité et les glissements basée sur des méthodes interdisciplinaires ; Y sont inclus des évaluations géologiques des glissements, des entretiens semi-dirigés, des discussions de groupes et des cartes de risques participatives. Pour la comparaison, les zones d'études ont été sélectionnées dans les districts de Tehrathum, Sunsari et Dolakha dans le centre-est du Népal, afin de refléter différents types de glissements, de chroniques à urgents, ainsi que différentes communautés, variant de très marginalisées à très haut statut. Pour son cadre conceptuel, cette étude s'appuie sur l'approche de moyens de subsistance durable, qui est basée sur les notions d'accès et de droit aux ressources (naturelles, humaines/institutionnelles, économiques, environnementales, physiques) et qui sont le minimum pour faire face à des situations difficiles, comme des glissements. Cette étude se veut aussi une contribution à la littérature et aux pratiques en croissantes sur la réduction des risques communautaires, spécifiquement adaptées aux zones affectées par des glissements.En plus des six études de cas, les résultats incluent une méthodologie basée sur des indicateurs pour évaluer et mesurer la vulnérabilité et la résilience, une méthodologie sur le risque composé, une typologie de stratégies d'adaptation et perceptions des risques ainsi qu'une analyse fondamentale de la relation entre risque, vulnérabilité et résilience. Les méthodologies pour l'évaluation de la vulnérabilité, de la résilience et du risque sont relativement peu coûteuses et reproductibles dans des endroits avec peu de données disponibles. Le résultat probablement le plus pertinent est que la résilience est un processus qui définit la capacité d'une communauté (ou d'un système) à rebondir suite à une situation défavorable, mais qui ne réduit pas forcement la vulnérabilité ou le risque, et qui requiert une approche plus fondamentale s'adressant aux questions de pauvreté. Les conclusions incluent une vue critique de la résilience comme but principal des politiques internationales de développement et de réduction des risques. C'est un concept utile dans le contexte de la récupération après une catastrophe mais il doit être pris en compte au même titre que la vulnérabilité et le risque.Cette recherche a été financée par un fonds interdisciplinaire (#26083591) du Fonds National Suisse pour la période 2009-2011 et un fonds de préparation de recherches par la Faculté des Géosciences et Environnement à l'Université de Lausanne en 2008.