Integral cohomology of finite postnikov towers

Depuis le séminaire H. Cartan de 1954-55, il est bien connu que l'on peut trouver des éléments de torsion arbitrairement grande dans l'homologie entière des espaces d'Eilenberg-MacLane K(G,n) où G est un groupe abélien non trivial et n>1. L'objectif majeur de ce travail est d'étendre ce résultat à des H-espaces possédant plus d'un groupe d'homotopie non trivial. Dans le but de contrôler précisément le résultat de H. Cartan, on commence par étudier la dualité entre l'homologie et la cohomologie des espaces d'Eilenberg-MacLane 2-locaux de type fini. On parvient ainsi à raffiner quelques résultats qui découlent des calculs de H. Cartan. Le résultat principal de ce travail peut être formulé comme suit. Soit X un H-espace ne possédant que deux groupes d'homotopie non triviaux, tous deux finis et de 2-torsion. Alors X n'admet pas d'exposant pour son groupe gradué d'homologie entière réduite. On construit une large classe d'espaces pour laquelle ce résultat n'est qu'une conséquence d'une caractéristique topologique, à savoir l'existence d'un rétract faible X K(G,n) pour un certain groupe abélien G et n>1. On généralise également notre résultat principal à des espaces plus compliqués en utilisant la suite spectrale d'Eilenberg-Moore ainsi que des méthodes analytiques faisant apparaître les nombres de Betti et leur comportement asymptotique. Finalement, on conjecture que les espaces qui ne possédent qu'un nombre fini de groupes d'homotopie non triviaux n'admettent pas d'exposant homologique. Ce travail contient par ailleurs la présentation de la « machine d'Eilenberg-MacLane », un programme C++ conçu pour calculer explicitement les groupes d'homologie entière des espaces d'Eilenberg-MacLane. <br/><br/>By the work of H. Cartan, it is well known that one can find elements of arbitrarilly high torsion in the integral (co)homology groups of an Eilenberg-MacLane space K(G,n), where G is a non-trivial abelian group and n>1. The main goal of this work is to extend this result to H-spaces having more than one non-trivial homotopy groups. In order to have an accurate hold on H. Cartan's result, we start by studying the duality between homology and cohomology of 2-local Eilenberg-MacLane spaces of finite type. This leads us to some improvements of H. Cartan's methods in this particular case. Our main result can be stated as follows. Let X be an H-space with two non-vanishing finite 2-torsion homotopy groups. Then X does not admit any exponent for its reduced integral graded (co)homology group. We construct a wide class of examples for which this result is a simple consequence of a topological feature, namely the existence of a weak retract X K(G,n) for some abelian group G and n>1. We also generalize our main result to more complicated stable two stage Postnikov systems, using the Eilenberg-Moore spectral sequence and analytic methods involving Betti numbers and their asymptotic behaviour. Finally, we investigate some guesses on the non-existence of homology exponents for finite Postnikov towers. We conjecture that Postnikov pieces do not admit any (co)homology exponent. This work also includes the presentation of the "Eilenberg-MacLane machine", a C++ program designed to compute explicitely all integral homology groups of Eilenberg-MacLane spaces. <br/><br/>Il est toujours difficile pour un mathématicien de parler de son travail. La difficulté réside dans le fait que les objets qu'il étudie sont abstraits. On rencontre assez rarement un espace vectoriel, une catégorie abélienne ou une transformée de Laplace au coin de la rue ! Cependant, même si les objets mathématiques sont difficiles à cerner pour un non-mathématicien, les méthodes pour les étudier sont essentiellement les mêmes que celles utilisées dans les autres disciplines scientifiques. On décortique les objets complexes en composantes plus simples à étudier. On dresse la liste des propriétés des objets mathématiques, puis on les classe en formant des familles d'objets partageant un caractère commun. On cherche des façons différentes, mais équivalentes, de formuler un problème. Etc. Mon travail concerne le domaine mathématique de la topologie algébrique. Le but ultime de cette discipline est de parvenir à classifier tous les espaces topologiques en faisant usage de l'algèbre. Cette activité est comparable à celle d'un ornithologue (topologue) qui étudierait les oiseaux (les espaces topologiques) par exemple à l'aide de jumelles (l'algèbre). S'il voit un oiseau de petite taille, arboricole, chanteur et bâtisseur de nids, pourvu de pattes à quatre doigts, dont trois en avant et un, muni d'une forte griffe, en arrière, alors il en déduira à coup sûr que c'est un passereau. Il lui restera encore à déterminer si c'est un moineau, un merle ou un rossignol. Considérons ci-dessous quelques exemples d'espaces topologiques: a) un cube creux, b) une sphère et c) un tore creux (c.-à-d. une chambre à air). a) b) c) Si toute personne normalement constituée perçoit ici trois figures différentes, le topologue, lui, n'en voit que deux ! De son point de vue, le cube et la sphère ne sont pas différents puisque ils sont homéomorphes: on peut transformer l'un en l'autre de façon continue (il suffirait de souffler dans le cube pour obtenir la sphère). Par contre, la sphère et le tore ne sont pas homéomorphes: triturez la sphère de toutes les façons (sans la déchirer), jamais vous n'obtiendrez le tore. Il existe un infinité d'espaces topologiques et, contrairement à ce que l'on serait naïvement tenté de croire, déterminer si deux d'entre eux sont homéomorphes est très difficile en général. Pour essayer de résoudre ce problème, les topologues ont eu l'idée de faire intervenir l'algèbre dans leurs raisonnements. Ce fut la naissance de la théorie de l'homotopie. Il s'agit, suivant une recette bien particulière, d'associer à tout espace topologique une infinité de ce que les algébristes appellent des groupes. Les groupes ainsi obtenus sont appelés groupes d'homotopie de l'espace topologique. Les mathématiciens ont commencé par montrer que deux espaces topologiques qui sont homéomorphes (par exemple le cube et la sphère) ont les même groupes d'homotopie. On parle alors d'invariants (les groupes d'homotopie sont bien invariants relativement à des espaces topologiques qui sont homéomorphes). Par conséquent, deux espaces topologiques qui n'ont pas les mêmes groupes d'homotopie ne peuvent en aucun cas être homéomorphes. C'est là un excellent moyen de classer les espaces topologiques (pensez à l'ornithologue qui observe les pattes des oiseaux pour déterminer s'il a affaire à un passereau ou non). Mon travail porte sur les espaces topologiques qui n'ont qu'un nombre fini de groupes d'homotopie non nuls. De tels espaces sont appelés des tours de Postnikov finies. On y étudie leurs groupes de cohomologie entière, une autre famille d'invariants, à l'instar des groupes d'homotopie. On mesure d'une certaine manière la taille d'un groupe de cohomologie à l'aide de la notion d'exposant; ainsi, un groupe de cohomologie possédant un exposant est relativement petit. L'un des résultats principaux de ce travail porte sur une étude de la taille des groupes de cohomologie des tours de Postnikov finies. Il s'agit du théorème suivant: un H-espace topologique 1-connexe 2-local et de type fini qui ne possède qu'un ou deux groupes d'homotopie non nuls n'a pas d'exposant pour son groupe gradué de cohomologie entière réduite. S'il fallait interpréter qualitativement ce résultat, on pourrait dire que plus un espace est petit du point de vue de la cohomologie (c.-à-d. s'il possède un exposant cohomologique), plus il est intéressant du point de vue de l'homotopie (c.-à-d. il aura plus de deux groupes d'homotopie non nuls). Il ressort de mon travail que de tels espaces sont très intéressants dans le sens où ils peuvent avoir une infinité de groupes d'homotopie non nuls. Jean-Pierre Serre, médaillé Fields en 1954, a montré que toutes les sphères de dimension >1 ont une infinité de groupes d'homotopie non nuls. Des espaces avec un exposant cohomologique aux sphères, il n'y a qu'un pas à franchir...

Implementing statistical learning methods through Bayesian networks (Part 2): bayesian evaluations for results of black toner analyses in forensic document examination

This paper presents and discusses the use of Bayesian procedures - introduced through the use of Bayesian networks in Part I of this series of papers - for 'learning' probabilities from data. The discussion will relate to a set of real data on characteristics of black toners commonly used in printing and copying devices. Particular attention is drawn to the incorporation of the proposed procedures as an integral part in probabilistic inference schemes (notably in the form of Bayesian networks) that are intended to address uncertainties related to particular propositions of interest (e.g., whether or not a sample originates from a particular source). The conceptual tenets of the proposed methodologies are presented along with aspects of their practical implementation using currently available Bayesian network software.

The Discrimination of Colored Acrylic, Cotton, and Wool Textile Fibers Using Micro-Raman Spectroscopy. Part 1 : In Situ Detection and Characterization of Dyes

Raman spectroscopy has been applied to characterize fiber dyes and determine the discriminating ability of the method. Black, blue, and red acrylic, cotton, and wool samples were analyzed. Four excitation sources were used to obtain complementary responses in the case of fluorescent samples. Fibers that did not provide informative spectra using a given laser were usually detected using another wavelength. For any colored acrylic, the 633-nm laser did not provide Raman information. The 514-nm laser provided the highest discrimination for blue and black cotton, but half of the blue cottons produced noninformative spectra. The 830-nm laser exhibited the highest discrimination for red cotton. Both visible lasers provided the highest discrimination for black and blue wool, and NIR lasers produced remarkable separation for red and black wool. This study shows that the discriminating ability of Raman spectroscopy depends on the fiber type, color, and the laser wavelength.

Exploration of the visual system : Part 2. In vivo analysis methods : virtual-reality optomotor system, fundus examination and fluorescent angiography

The mouse has emerged as an animal model for many diseases. At IRO, we have used this animal to understand the development of many eye diseases and treatment of some of them. Precise evaluation of vision is a prerequisite for both these approaches. In this unit we describe three ways to measure vision: testing the optokinetic response, and evaluating the fundus by direct observation and by fluorescent angiography.

Substance use among sportive adolescents in the French-speaking part of Switzerland

[Contents] Introduction. Objectives. Methodology. Results. Characteristics of the sample. Substance use (Psychoactive substances, Performance-enhancing substances). Profile of sportive adolescents using substances. Mixed substance use. Other factors related to substance use. Inactivity. Conclusions. References. Annexes. Annex 1. Questionnaire. Annex 2. Sample weighting procedure. Annex 3. Sports type.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Use of DNA profiles for investigation using a simulated national DNA database: Part I. Partial SGM Plus profiles.

In traditional criminal investigation, uncertainties are often dealt with using a combination of common sense, practical considerations and experience, but rarely with tailored statistical models. For example, in some countries, in order to search for a given profile in the national DNA database, it must have allelic information for six or more of the ten SGM Plus loci for a simple trace. If the profile does not have this amount of information then it cannot be searched in the national DNA database (NDNAD). This requirement (of a result at six or more loci) is not based on a statistical approach, but rather on the feeling that six or more would be sufficient. A statistical approach, however, could be more rigorous and objective and would take into consideration factors such as the probability of adventitious matches relative to the actual database size and/or investigator's requirements in a sensible way. Therefore, this research was undertaken to establish scientific foundations pertaining to the use of partial SGM Plus loci profiles (or similar) for investigation.

An alteration in the levels of populations of CD4+ Treg is in part responsible for altered cytokine production by cells of aged mice which follows injection with a fetal liver extract.

We have shown previously that a fetal sheep liver extract (FSLE) containing significant quantities of fetal ovine gamma globin chain (Hbgamma) and LPS injected into aged (>20 months) mice could reverse the altered polarization (increased IL-4 and IL-10 with decreased IL-2 and IFNgamma) in cytokine production seen from ConA stimulated lymphoid cells of those mice. The mechanism(s) behind this change in cytokine production were not previously investigated. We report below that aged mice show a >60% decline in numbers and suppressive function of both CD4(+)CD25(+)Foxp3(+) Treg and so-called Tr3 (CD4(+)TGFbeta(+)), and that their number/function is restored to levels seen in control (8-week-old) mice by FSLE. In addition, on a per cell basis, CD4(+)CD25(-)Treg from aged mice were >4-fold more effective in suppression of proliferation and IL-2 production from ConA-activated lymphoid cells of a pool of CD4(+)CD25(-)T cells from 8-week-old mice than similar cells from young animals, and this suppression by CD25(-)T cells was also ameliorated following FSLE treatment. Infusion of anti-TGFbeta and anti-IL-10 antibodies in vivo altered Treg development following FSLE treatment, and attenuated FSLE-induced alterations in cytokine production profiles.

Subcellular fractionation of stored red blood cells reveals a compartment-based protein carbonylation evolution.

During blood banking, erythrocytes undergo storage lesions, altering or degrading their metabolism, rheological properties, and protein content. Carbonylation is a hallmark of protein oxidative lesions, thus of red blood cell oxidative stress. In order to improve global erythrocyte protein carbonylation assessment, subcellular fractionation has been established, allowing us to work on four different protein populations, namely soluble hemoglobin, hemoglobin-depleted soluble fraction, integral membrane and cytoskeleton membrane protein fractions. Carbonylation in erythrocyte-derived microparticles has also been investigated. Carbonylated proteins were derivatized with 2,4-dinitrophenylhydrazine (2,4-DNPH) and quantified by western blot analyses. In particular, carbonylation in the cytoskeletal membrane fraction increased remarkably between day 29 and day 43 (P<0.01). Moreover, protein carbonylation within microparticles released during storage showed a two-fold increase along the storage period (P<0.01). As a result, carbonylation of cytoplasmic and membrane protein fractions differs along storage, and the present study allows explaining two distinct steps in global erythrocyte protein carbonylation evolution during blood banking. This article is part of a Special Issue entitled: Integrated omics.

New perspectives in the use of ink evidence in forensic science: Part I. Development of a quality assurance process for forensic ink analysis by HPTLC

The level of information provided by ink evidence to the criminal and civil justice system is limited. The limitations arise from the weakness of the interpretative framework currently used, as proposed in the ASTM 1422-05 and 1789-04 on ink analysis. It is proposed to use the likelihood ratio from the Bayes theorem to interpret ink evidence. Unfortunately, when considering the analytical practices, as defined in the ASTM standards on ink analysis, it appears that current ink analytical practices do not allow for the level of reproducibility and accuracy required by a probabilistic framework. Such framework relies on the evaluation of the statistics of the ink characteristics using an ink reference database and the objective measurement of similarities between ink samples. A complete research programme was designed to (a) develop a standard methodology for analysing ink samples in a more reproducible way, (b) comparing automatically and objectively ink samples and (c) evaluate the proposed methodology in a forensic context. This report focuses on the first of the three stages. A calibration process, based on a standard dye ladder, is proposed to improve the reproducibility of ink analysis by HPTLC, when these inks are analysed at different times and/or by different examiners. The impact of this process on the variability between the repetitive analyses of ink samples in various conditions is studied. The results show significant improvements in the reproducibility of ink analysis compared to traditional calibration methods.

Dirigent domain-containing protein is part of the machinery required for formation of the lignin-based Casparian strip in the root.

The endodermis acts as a "second skin" in plant roots by providing the cellular control necessary for the selective entry of water and solutes into the vascular system. To enable such control, Casparian strips span the cell wall of adjacent endodermal cells to form a tight junction that blocks extracellular diffusion across the endodermis. This junction is composed of lignin that is polymerized by oxidative coupling of monolignols through the action of a NADPH oxidase and peroxidases. Casparian strip domain proteins (CASPs) correctly position this biosynthetic machinery by forming a protein scaffold in the plasma membrane at the site where the Casparian strip forms. Here, we show that the dirigent-domain containing protein, enhanced suberin1 (ESB1), is part of this machinery, playing an essential role in the correct formation of Casparian strips. ESB1 is localized to Casparian strips in a CASP-dependent manner, and in the absence of ESB1, disordered and defective Casparian strips are formed. In addition, loss of ESB1 disrupts the localization of the CASP1 protein at the casparian strip domain, suggesting a reciprocal requirement for both ESB1 and CASPs in forming the casparian strip domain.

Purification and activity standardisation of a (166m)Ho solution.

As part of a project to use the long-lived (T(1/2)=1200a) (166m)Ho as reference source in its reference ionisation chamber, IRA standardised a commercially acquired solution of this nuclide using the 4pibeta-gamma coincidence and 4pigamma (NaI) methods. The (166m)Ho solution supplied by Isotope Product Laboratories was measured to have about 5% Europium impurities (3% (154)Eu, 0.94% (152)Eu and 0.9% (155)Eu). Holmium had therefore to be separated from europium, and this was carried out by means of ion-exchange chromatography. The holmium fractions were collected without europium contamination: 162h long HPGe gamma measurements indicated no europium impurity (detection limits of 0.01% for (152)Eu and (154)Eu, and 0.03% for (155)Eu). The primary measurement of the purified (166m)Ho solution with the 4pi (PC) beta-gamma coincidence technique was carried out at three gamma energy settings: a window around the 184.4keV peak and gamma thresholds at 121.8 and 637.3keV. The results show very good self-consistency, and the activity concentration of the solution was evaluated to be 45.640+/-0.098kBq/g (0.21% with k=1). The activity concentration of this solution was also measured by integral counting with a well-type 5''x5'' NaI(Tl) detector and efficiencies computed by Monte Carlo simulations using the GEANT code. These measurements were mutually consistent, while the resulting weighted average of the 4pi NaI(Tl) method was found to agree within 0.15% with the result of the 4pibeta-gamma coincidence technique. An ampoule of this solution and the measured value of the concentration were submitted to the BIPM as a contribution to the Système International de Référence.

Review of therapeutic drug monitoring of anticancer drugs part one - Cytotoxics.

Most anticancer drugs are characterised by a steep dose-response relationship and narrow therapeutic window. Inter-individual pharmacokinetic (PK) variability is often substantial. The most relevant PK parameter for cytotoxic drugs is the area under the plasma concentration versus time curve (AUC). Thus it is somewhat surprising that therapeutic drug monitoring (TDM) is still uncommon for the majority of agents. Goals of the review were to assess the rationale for more widely used TDM of cytotoxics in oncology. There are several reasons why TDM has never been fully implemented into daily oncology practice. These include difficulties in establishing appropriate concentration target ranges, common use of combination chemotherapies for many tumour types, analytical challenges with prodrugs, intracellular compounds, the paucity of published data from pharmacological trials and 'Day1=Day21' administration schedules. There are some specific situations for which these limitations are overcome, including high dose methotrexate, 5-fluorouracil infusion, mitotane and some high dose chemotherapy regimens. TDM in paediatric oncology represents an important challenge. Established TDM approaches includes the widely used anticancer agents carboplatin, busulfan and methotrexate, with 13-cis-retinoic acid also recently of interest. Considerable effort should be made to better define concentration-effect relationships and to utilise tools such as population PK/PD models and comparative randomised trials of classic dosing versus pharmacokinetically guided adaptive dosing. There is an important heterogeneity among clinical practices and a strong need to promote TDM guidelines among the oncological community.

Prevalence and risk factors for gastro-esophageal reflux disease in the North-Eastern part of Bangladesh.

Despite a common disorder population-based data on gastro-esophageal reflux disease (GERD) in Bangladesh is lacking. This epidemiological study was designed to determine the prevalence of GERD and its association with lifestyle factors. This population-based cross-sectional study was done by door to door interview of randomly selected persons in both urban and rural areas of North Eastern part of Bangladesh by using a validated questionnaire. A cutoff point 3 was chosen as a valid and reliable scale to confirm GERD. Statistical analysis was done by SPSS-12 version and the level of significance was set at P < or = 0.05. A total of 2000 persons with an age range of 15 to 85 years were interviewed; 1000 subjects from urban area and 1000 from rural area. Among the study subjects 1064 were male and 936 were female. A total of 110 persons (5.5%) were found to have GERD symptoms and among them 47 were men and 67 were women. The monthly, weekly and daily prevalence of heart-burn and or acid regurgitation was 5.5%, 5.25% and 2.5% respectively. Female sex, increased age and lower level of education were significantly associated with GERD symptoms. Prevalence was found more among city dwellers (approximately 6.0% versus 4.8%), married (6.23%, n = 86), widowed/widowers (16.83%, n = 17) and day labourer (8.78%). Level of education inversely influenced the prevalence. No significant association of GERD was found with body mass index (BMI) and smoking. Prevalence of GERD in North-Eastern part of Bangladesh was lower than that of western world. Prevalence was found higher in urban population, women, married, widowed/widowers and in poor an dilliterate persons. BMI and smoking had no significant association with GERD.