Modules d'endo-permutation

Dans la th´eorie des repr´esentations modulaires des groupes finis, les modules d?endo-permutation occupent une place importante. En e_et, c?est le r?ole jou´e par ces modules dans l?analyse de la structure de certains modules simples pour des groupes finis p-nilpotents, qui a amen´e E. Dade `a en introduire le concept, en 1978. Quelques ann´ees plus tard, L. Puig a d´emontr´e que la source de n?importe quel module simple pour un groupe fini p-r´esoluble quelconque est un module d?endo-permutation. Plus r´ecemment, on s?est rendu compte que ces modules interviennent aussi dans l?analyse locale des cat´egories d´eriv´ees et dans l?´etude des syst`emes de fusion. La situation que l?on consid`ere est la suivante. On se donne un nombre premier p, un p-groupe fini P, un corps alg´ebriquement clos k de caract´eristique p et on veut d´eterminer tous les kP-modules d?endo-permutation couverts ind´ecomposables de type fini, c?est-`a-dire tous les kP-modules ind´ecomposables de type fini, tels que leur alg`ebre d?endomorphismes est un kP-module de permutation ayant un facteur direct trivial. On d´efinit une relation d?´equivalence sur l?ensemble de ces kP-modules et le produit tensoriel des modules induit une structure de groupe ab´elien sur l?ensemble des classes d?´equivalence. On appelle ce groupe, le groupe de Dade de P. Ainsi, classifier les modules d?endo-permutation couverts revient `a d´eterminer le groupe de Dade de P. Le groupe de Dade d?un p-groupe fini arbitraire est encore inconnu, bien qu?E. Dade, en 1978, ´etait d´ej`a parvenu `a la classification dans le cas o`u P est ab´elien. La premi`ere partie de ce travail de th`ese est consacr´ee au probl`eme de la classification dans le cas g´en´eral et r´esoud la question dans le cas de deux familles de p-groupes finis, `a savoir celle des p-groupes m´etacycliques, pour un nombre premier p impair, et celle des 2-groupes extrasp´eciaux, de la forme D8 _ · · · _ D8. Ces deux choix ont ´et´e motiv´es par le fait que ces groupes sont "presque" ab´eliens. De plus, certains r´esultats sur la structure du groupe de Dade d?un p-groupe fini quelconque rendent le groupe de Dade des groupes de ces deux familles plus simple `a ´etudier. Dans un deuxi`eme temps, nous nous sommes int´eress´es `a deux occurrences de ces modules dans la th´eorie de la repr´esentation des groupes finis, c?est-`a-dire `a deux raisons qui motivent leur ´etude. Ainsi, nous avons r´ealis´e des modules d?endo-permutation comme sources de modules simples. En particulier, il s?av`ere que, dans le cas d?un nombre premier p impair, tout module d?endo-permutation ind´ecomposable dont la classe est un ´el´ement de torsion dans le groupe de Dade est la source d?un module simple. Finalement, nous avons d´etermin´e, parmi tous les modules d?endo-permutation connus actuellement, lesquels poss`edent une r´esolution de permutation endo-scind´ee. Nous sommes arriv´es `a la conclusion que les seuls modules d?endo-permutation qui n?ont pas de r´esolution de permutation endo-scind´ee sont les modules "exceptionnels" apparaissant pour un 2-groupe de quaternions g´en´eralis´es.<br/><br/>In modular representation theory, endo-permutation modules occupy an important position. Indeed, the role that these modules play, in the analysis of the structure of some particular simple modules for finite p-nilpotent groups, induced E. Dade, in 1978, to give them their current name. A few years later, L. Puig proved that the source of any simple module for any finite psolvable group is an endo-permutation module. More recently, the occurrence of endo-permutation modules has also been noticed in the local analysis of splendid equivalences between derived categories and in the study of fusion systems. We consider the following situation. Given a prime number p, a finite pgroup P and an algebraically closed field k of characteristic p, we are looking for all finitely generated indecomposable capped endo-permutation kP-modules. That is, all finitely generated indecomposable kP-modules such that their endomorphism algebra is a permutation kP-module having a trivial direct summand. Then, we define an equivalence relation on the set of all isomorphism classes of such modules, and it turns out that the tensor product (over k) induces a structure of abelian group on this set. We call this group the Dade group of P. Hence, classifying all indecomposable finitely generated capped endo-permutation kPmodules is equivalent to determining the Dade group of P. At present, the Dade group of an arbitrary finite p-group is still unknown. However, E. Dade computed the Dade group of all finite abelian p-groups, in 1978 already. The first part of this doctoral thesis is concerned with the problem of the classification in the general case and solve it in the case of two families of finite p-groups, namely the metacyclic p-groups, for an odd prime number p, and the extraspecial 2-groups of the shape D8 _· · ·_D8. These two choices have been motivated by the fact that these groups are not far from being abelian. Moreover, some general results concerning the Dade group of arbitrary finite p-groups suggest that the Dade group of the groups belonging to these two families is easier to study. In the second part of this thesis, we have been looking at two particular occurrences of these modules in representation theory of finite groups which motivate the interest of their classification. Thus, we realised endo-permutation modules as sources of simple modules. In particular, it turns out that, in case p is an odd prime, any indecomposable module whose class in the Dade group is a torsion element is the source of some simple module. Finally, we considered all the modules we know at present and determined which ones have an endo-split permutation resolution. We could then conclude that all but the "exceptionnal" modules occurring in the generalized quaternion case have an endo-split permutation resolution.<br/><br/>"Module d?endo-permutation" n?est pas le nom d?une maladie exotique contagieuse (du moins pas `a ma connaissance), comme vous pourriez peut-?etre l?imaginer si vous faites partie des personnes qui croient que le titre de docteur n?est destin´e qu?aux m´edecins. Dans ce cas, il se peut que le sujet dont il est question ici vous cause quelques naus´ees et r´eveille de douloureux souvenirs d?´ecole, car un module d?endo-permutation est un objet math´ematique, alg´ebrique, plus pr´ecis´ement. Ce concept a ´et´e introduit il y a un quart de si`ecle, de l?autre c?ot´e de l?Atlantique, et il s?est r´ev´el´e su_samment int´eressant pour qu?aujourd?hui il ait franchi bien des fronti`eres, celles de l?alg`ebre y compris. Mais de quoi s?agit-il ? Si vous entendez le terme "endo-permutation" probablement pour la premi`ere fois, ce n?est certainement pas le cas pour celui de "module". Cependant, sa d´efinition dans le pr´esent contexte ne co¨ýncide avec aucune de celles figurant dans les dictionnaires ordinaires. Les personnes qui ont d´ej`a entendu parler de Frobenius, Burnside, Schur, ou encore Brauer, pourront vous dire qu?un module est une repr´esentation. "De quoi ?" vous demanderezvous. "Un spectacle de marionnettes, peut-?etre ?" Bien s?ur que non ! Un module d?endo-permutation est une repr´esentation particuli`ere de certains groupes finis, o`u un groupe n?est pas un groupe de rock, comme vous pouvez vous en douter, mais d´esigne un objet math´ematique connu par tous les ´etudiants en sciences au terme de leur premi`ere ann´ee universitaire (en th´eorie, du moins). La "popularit´e" de la notion de groupe, fini ou non, est due au fait que les groupes sont fr´equemment utilis´es, aussi bien dans le domaine abstrait des math´ematiques, que dans le monde r´eel des physiciens, chimistes et autres biologistes (pour ne citer qu?eux). "Mais comment peut-on utiliser concr`etement ces objets invisibles ?" vous demanderez-vous alors. Et bien, justement, en les consid´erant par l?interm´ediaire de leurs repr´esentations, c?est-`a-dire en leur associant des matrices, de fa¸con plus ou moins naturelle. Or, comme il y a "beaucoup trop" de matrices pour un groupe donn´e, elles sont classifi´ees selon certaines de leurs propri´et´es, ce qui permet de les r´epertorier dans diverses familles (celle des modules d?endo-permutation, par exemple). Un groupe est ainsi rendu "concret", car les donn´ees matricielles sont manipulables par tous les scienti- fiques (et leurs ordinateurs), qui peuvent alors les utiliser dans leurs recherches, afin de contribuer au progr`es de la science. En toute franchise, c?est bien loin de ces soucis terre-`a-terre que ce travail de th`ese sur la classification des modules d?endo-permutation a ´et´e accompli. En fait, quitte `a choquer certaines ?ames sensibles, sa r´ealisation est surtout due au caract`ere ´epicure de son auteur, qui, avouons-le, en a ´et´e pleinement satisfait !

Use of GRADE for assessment of evidence about prognosis : rating confidence in estimates of event rates in broad categories of patients.

Main concepts : The Grades of Recommendation, Assessment, Development, and Evaluation (GRADE) approach defines quality of evidence as confidence in effect estimates; this conceptualization can readily be applied to bodies of evidence estimating the risk of future of events (that is, prognosis) in broadly defined populations In the field of prognosis, a body of observational evidence (including single arms of randomized controlled trials) begins as high quality evidence. The five domains GRADE considers in rating down confidence in estimates of treatment effect-that is, risk of bias, imprecision, inconsistency, indirectness, and publication bias-as well as the GRADE criteria for rating up quality, also apply to estimates of the risk of future of events from a body of prognostic studies Applying these concepts to systematic reviews of prognostic studies provides a ful approach to determine confidence in estimates of overall prognosis in broad populations.

Anàlisi del bloc de fonaments individuals per demarcació (fid) corresponent a la defensa de l'espai per la posició dels laterals en el futbol: comparació entre categories amateur i semi-professional

L’objectiu d’aquest estudi va ser analitzar un element del component tàctic com a factor determinant en el rendiment del futbol, és a dir, comprovar si hi ha diferències en l’execució del bloc de Fonaments Individuals per Demarcació (FID) corresponent a la defensa de l’espai per la posició dels laterals en el futbol, entre les categories amateur i semi-professional. Es van enregistrar un total de 18 partits, on 9 dels quals feien referència a l’equip de l’Arbúcies Club de Futbol i la resta a l’equip de la Unió Esportiva Llagostera. Les variables estudiades van ser les següents: cobertures al central que defensa al possessor de la pilota, evitar passades interiors que guanyin l’esquena, defensa individual dels jugadors que intenten passar per l’esquena del segon central (entrar-sortir) i eliminar l’espai de desmarcada en profunditat, mantenint la línia amb el central. Per analitzar-les es va utilitzar el programa Longomatch i el Excel on hi vam configurar un instrument d’avaluació. Els principals resultats del treball van ser que l’equip de la Unió Esportiva Llagostera va fer menys errors en l’execució dels FID, tot i que va seguir tenint errors en el compliment d’aquests fonaments.

Positive predictive values of Breast Imaging Reporting and Data System (BI-RADS®) categories 3, 4 and 5 in breast lesions submitted to percutaneous biopsy

Objective To evaluate the BI-RADS as a predictive factor of suspicion for malignancy in breast lesions by correlating radiological with histological results and calculating the positive predictive value for categories 3, 4 and 5 in a breast cancer reference center in the city of São Paulo. Materials and Methods Retrospective, analytical and cross-sectional study including 725 patients with mammographic and/or sonographic findings classified as BI-RADS categories 3, 4 and 5 who were referred to the authors' institution to undergo percutaneous biopsy. The tests results were reviewed and the positive predictive value was calculated by means of a specific mathematical equation. Results Positive predictive values found for categories 3, 4 and 5 were respectively the following: 0.74%, 33.08% and 92.95%, for cases submitted to ultrasound-guided biopsy, and 0.00%, 14.90% and 100% for cases submitted to stereotactic biopsy. Conclusion The present study demonstrated high suspicion for malignancy in lesions classified as category 5 and low risk for category 3. As regards category 4, the need for systematic biopsies was observed.

A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence of categories between its localisation with respect to weak equivalences and the relative localisation of the subcategory of cofibrant objects with respect to strong equivalences. This equivalence of categories allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latter case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theorem.

Foodstuffs and medicines as legal categories in the EU and China. Functional foods as a borderline case

The thesis discusses the regulation of foodstuffs and medicines, and particularly the regulation of functional foods. Legal systems investigated are the EU and China. Both are members of the WTO and Codex Alimentarius, which binds European and Chinese rules together. The study uses three Chinese berries as case examples of how product development faces regulation in practice. The berries have traditional uses as herbal medicines. Europe and China have similar nutrition problems to be resolved, such as obesity, cardiovascular disease, and diabetes. The three berries might be suitable raw materials for functional foods. Consumer products with health-enhancing functions, such as lowering blood pressure, might legally be classifi ed either as foodstuffs or medicines. The classifi cation will depend on functions and presentation of the product. In our opinion, food and medicine regulation should come closer together so the classifi cation issue would no longer be an issue. Safety of both foodstuffs and medicines is strictly regulated. With medicines, safety is a more relative concept, where benefi ts of the product are compared to side-effects in thorough scientifi c tests and trials. Foods, on the other hand, are not allowed to have side-effects. Hygiene rules and rules on the use of chemicals apply. In China, food safety is currently at focus as China has had several severe food scandals. Newly developed foods are called novel foods, and are specifi cally regulated. The current European novel food regulation from 1997 treats traditional third country products as novel. The Chinese regulation of 2007 also defi nes novel foods as something unfamiliar to a Chinese consumer. The concepts of novel food thus serve a protectionist purpose. As regards marketing, foods are allowed to bear health claims, whereas medicines bear medicinal claims. The separation is legally strict: foods are not to be presented as having medicinal functions. European nutrition and health claim regulation exists since 2006. China also has its regulation on health foods, listing the permitted claims and how to substantiate them. Health claims are allowed only on health foods. The European rules on medicines include separate categories for herbal medicines, traditional herbal medicines, and homeopathic medicines, where there are differing requirements for scientifi c substantiation. The scientifi c and political grounds for the separate categories provoke criticism. At surface, the Chinese legal system seems similar to the European one. To facilitate trade, China has enacted modern laws. Laws are needed as the country moves from planned economy to market economy: ‘rule of law’ needs to replace ‘rule of man’. Instead of being citizens, Chinese people long were subordinates to the Emperor. Confucius himself advised to avoid confl ict. Still, Chinese people do not and cannot always trust the legal system, as laws are enforced in an inconsistent manner, and courts are weak. In China, there have been problems with confl icting national and local laws. In Europe, the competence of the EU vs. the competence of the Member States is still not resolved, even though the European Commission often states that free trade requires harmonisation. Food and medicine regulation is created by international organisations, food and medicine control agencies, standards agencies, companies and their organisations. Regulation can be divided in ‘hard law’ and ‘soft law’. One might claim that hard law is in crisis, as soft law is gaining importance. If law is out of fashion, regulation certainly isn’t. In the future, ‘law’ might mean a process where rules and incentives are created by states, NGOs, companies, consumers, and other stakeholders. ‘Law’ might thus refer to a constant negotiation between public and private actors. Legal principles such as transparency, equal treatment, and the right to be heard would still be important.

Distribution of HCV genotypes among different exposure categories in Brazil

Hepatitis C virus (HCV) infection is widespread and responsible for more than 60% of chronic hepatitis cases. HCV presents a genetic variability which has led to viral classification into at least 6 genotypes and a series of subtypes. These variants present characteristic geographical distribution, but their association with different responses to treatment with interferon and severity of disease still remains controversial. The aim of this study was to investigate the patterns of distribution of HCV genotypes among different exposure categories in Brazil. Two hundred and fifty anti-HCV positive samples were submitted to HCV-RNA detection by RT-PCR and their genotype was determined by restriction fragment length polymorphism (RFLP) analysis. In addition, the genotype/subtype of 60 samples was also determined by a reverse hybridization assay. HCV 1 was the most prevalent (72.0%), followed by type 3 (25.3%), HCV 2 (2.0%) and HCV 4 (0.7%). The HCV genotype distribution varied among the different exposure categories, with HCV 1 being more frequent among blood donors, hemophiliacs and hemodialysis patients. A high frequency of HCV 3 was observed in cirrhotic patients, blood donors from the South of Brazil and injecting drug users (IDUs). The general distribution of the HCV genotype in Brazil is similar to that in other regions of the world.

On some systems of aesthetic categories

UANL

Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

Image classification for a large number of object categories

L'increment de bases de dades que cada vegada contenen imatges més difícils i amb un nombre més elevat de categories, està forçant el desenvolupament de tècniques de representació d'imatges que siguin discriminatives quan es vol treballar amb múltiples classes i d'algorismes que siguin eficients en l'aprenentatge i classificació. Aquesta tesi explora el problema de classificar les imatges segons l'objecte que contenen quan es disposa d'un gran nombre de categories. Primerament s'investiga com un sistema híbrid format per un model generatiu i un model discriminatiu pot beneficiar la tasca de classificació d'imatges on el nivell d'anotació humà sigui mínim. Per aquesta tasca introduïm un nou vocabulari utilitzant una representació densa de descriptors color-SIFT, i desprès s'investiga com els diferents paràmetres afecten la classificació final. Tot seguit es proposa un mètode par tal d'incorporar informació espacial amb el sistema híbrid, mostrant que la informació de context es de gran ajuda per la classificació d'imatges. Desprès introduïm un nou descriptor de forma que representa la imatge segons la seva forma local i la seva forma espacial, tot junt amb un kernel que incorpora aquesta informació espacial en forma piramidal. La forma es representada per un vector compacte obtenint un descriptor molt adequat per ésser utilitzat amb algorismes d'aprenentatge amb kernels. Els experiments realitzats postren que aquesta informació de forma te uns resultats semblants (i a vegades millors) als descriptors basats en aparença. També s'investiga com diferents característiques es poden combinar per ésser utilitzades en la classificació d'imatges i es mostra com el descriptor de forma proposat juntament amb un descriptor d'aparença millora substancialment la classificació. Finalment es descriu un algoritme que detecta les regions d'interès automàticament durant l'entrenament i la classificació. Això proporciona un mètode per inhibir el fons de la imatge i afegeix invariança a la posició dels objectes dins les imatges. S'ensenya que la forma i l'aparença sobre aquesta regió d'interès i utilitzant els classificadors random forests millora la classificació i el temps computacional. Es comparen els postres resultats amb resultats de la literatura utilitzant les mateixes bases de dades que els autors Aixa com els mateixos protocols d'aprenentatge i classificació. Es veu com totes les innovacions introduïdes incrementen la classificació final de les imatges.

Categories of GM risk-benefit perceptions and their antecedents

The stated benefits and perceived risks of genetic modification (GM) cover very diverse issues, such as food safety, world food security, and the environment, that may differentially affect consumer acceptance. In this research, we hypothesize that consumers perceive up to eight dimensions: risks to business (farmers, agribusiness, etc.), benefits to business, risks and benefits to the environment, risks and benefits to the developing world, and risks and benefits to self and family. Moral concerns are also recognized. Using data collected in 2002 in the United States, France, and the UK, we investigate these different dimensions. Second, we analyze the extent to which the dimensions of risk-benefit perceptions can be explained by general attitudes widely used to explain food purchase behavior (such as general attitude to the environment, to technology, etc.), as well as by perceived knowledge of GM, level of education, and trust in various sources of information. In all locations, the majority of consumers only perceive a medium level of risk from GM products. Attitude to technology is the most important attitude variable—those with a positive attitude to technology in general also have a positive attitude to GM technology. More Americans than Europeans fall into this category. Those who trust government and the food industry tend to think GM technology is less risky, whereas those who trust activists believe the opposite. Americans are more trusting of the former, Europeans of the latter. Level of education is positively associated with benefit perceptions and negatively associated with moral concerns. Location continues to play a limited independent role in explaining perceptions even after these factors have been taken into account.

Proposing a way forward: a review of standardisation in the use of age categories and ageing techniques in osteological analysis (2004 to 2009)

This study assesses the current state of adult skeletal age-at-death estimation in biological anthropology through analysis of data published in recent research articles from three major anthropological and archaeological journals (2004–2009). The most commonly used adult ageing methods, age of ‘adulthood’, age ranges and the maximum age reported for ‘mature’ adults were compared. The results showed a wide range of variability in the age at which individuals were determined to be adult (from 14 to 25 years), uneven age ranges, a lack of standardisation in the use of descriptive age categories and the inappropriate application of some ageing methods for the sample being examined. Such discrepancies make comparisons between skeletal samples difficult, while the inappropriate use of some techniques make the resultant age estimations unreliable. At a time when national and even global comparisons of past health are becoming prominent, standardisation in the terminology and age categories used to define adults within each sample is fundamental. It is hoped that this research will prompt discussions in the osteological community (both nationally and internationally) about what defines an ‘adult’, how to standardise the age ranges that we use and how individuals should be assigned to each age category. Skeletal markers have been proposed to help physically identify ‘adult’ individuals.