Quotients d'une variété algébrique par un groupe algébrique linéairement réductif et ses sous-groupes maximaux unipotents

La construction d'un quotient, en topologie, est relativement simple; si $G$ est un groupe topologique agissant sur un espace topologique $X$, on peut considérer l'application naturelle de $X$ dans $X/G$, l'espace d'orbites muni de la topologie quotient. En géométrie algébrique, malheureusement, il n'est généralement pas possible de munir l'espace d'orbites d'une structure de variété. Dans le cas de l'action d'un groupe linéairement réductif $G$ sur une variété projective $X$, la théorie géométrique des invariants nous permet toutefois de construire un morphisme de variété d'un ouvert $U$ de $X$ vers une variété projective $X//U$, se rapprochant autant que possible d'une application quotient, au sens topologique du terme. Considérons par exemple $X\subseteq P^{n}$, une $k$-variété projective sur laquelle agit un groupe linéairement réductif $G$ et supposons que cette action soit induite par une action linéaire de $G$ sur $A^{n+1}$. Soit $\widehat{X}\subseteq A^{n+1}$, le cône affine au dessus de $\X$. Par un théorème de la théorie classique des invariants, il existe alors des invariants homogènes $f_{1},...,f_{r}\in C[\widehat{X}]^{G}$ tels que $$C[\widehat{X}]^{G}= C[f_{1},...,f_{r}].$$ On appellera le nilcone, que l'on notera $N$, la sous-variété de $\X$ définie par le locus des invariants $f_{1},...,f_{r}$. Soit $Proj(C[\widehat{X}]^{G})$, le spectre projectif de l'anneau des invariants. L'application rationnelle $$\pi:X\dashrightarrow Proj(C[f_{1},...,f_{r}])$$ induite par l'inclusion de $C[\widehat{X}]^{G}$ dans $C[\widehat{X}]$ est alors surjective, constante sur les orbites et sépare les orbites autant qu'il est possible de le faire; plus précisément, chaque fibre contient exactement une orbite fermée. Pour obtenir une application régulière satisfaisant les mêmes propriétés, il est nécessaire de jeter les points du nilcone. On obtient alors l'application quotient $$\pi:X\backslash N\rightarrow Proj(C[f_{1},...,f_{r}]).$$ Le critère de Hilbert-Mumford, dû à Hilbert et repris par Mumford près d'un demi-siècle plus tard, permet de décrire $N$ sans connaître les $f_{1},...,f_{r}$. Ce critère est d'autant plus utile que les générateurs de l'anneau des invariants ne sont connus que dans certains cas particuliers. Malgré les applications concrètes de ce théorème en géométrie algébrique classique, les démonstrations que l'on en trouve dans la littérature sont généralement données dans le cadre peu accessible des schémas. L'objectif de ce mémoire sera, entre autres, de donner une démonstration de ce critère en utilisant autant que possible les outils de la géométrie algébrique classique et de l'algèbre commutative. La version que nous démontrerons est un peu plus générale que la version originale de Hilbert \cite{hilbert} et se retrouve, par exemple, dans \cite{kempf}. Notre preuve est valide sur $C$ mais pourrait être généralisée à un corps $k$ de caractéristique nulle, pas nécessairement algébriquement clos. Dans la seconde partie de ce mémoire, nous étudierons la relation entre la construction précédente et celle obtenue en incluant les covariants en plus des invariants. Nous démontrerons dans ce cas un critère analogue au critère de Hilbert-Mumford (Théorème 6.3.2). C'est un théorème de Brion pour lequel nous donnerons une version un peu plus générale. Cette version, de même qu'une preuve simplifiée d'un théorème de Grosshans (Théorème 6.1.7), sont les éléments de ce mémoire que l'on ne retrouve pas dans la littérature.

Prevalence of DEA 1 canine blood group system in dogs (Canis familiaris, Linnaeus, 1758) reared in Brazil

Os cães possuem cinco grupos sangüíneos bem estabelecidos, compostos por sete determinantes antigênicos eritrocitários, os quais são denominados de dog erythrocyte antigen (DEA). O grupo DEA 1 (subgrupos 1.1, 1.2 e 1.3) tem sido considerado o mais importante no que se refere às transfusões de sangue. Isto ocorre porque esse grupo possui um alto potencial para estimulação antigênica e, dessa forma, pode estimular a produção de anticorpos se um receptor DEA 1 negativo receber uma transfusão de sangue DEA 1 positivo, levando a uma reação transfusional hemolítica em uma segunda transfusão com hemácias do tipo DEA 1. A freqüência de aparecimento do grupo DEA 1 é bem conhecida em outros países, porém, até então, não havia informações disponíveis sobre o referido grupo no Brasil. No presente estudo, objetivou-se avaliar a prevalência do grupo sangüíneo DEA 1 (subgrupos 1.1 e 1.2) em cães criados no Brasil. Para tanto, 150 cães de raças, sexos e idades diferentes, triados junto ao Hospital Veterinário da FCAV/UNESP, Campus de Jaboticabal, foram submetidos a tipagem sangüínea para o grupo DEA 1 (subgrupos 1.1 e 1.2) canino, utilizando-se reagentes adquiridos comercialmente junto ao Laboratório de Imunoematologia e Sorologia da Universidade de Michigan (EUA). Os resultados obtidos neste ensaio revelaram que a prevalência geral para o grupo DEA 1 é de 91,3%, consideradas as condições e características da população estudada, compreendendo 51,3% de cães do tipo DEA 1.1, 40% de cães do tipo DEA 1.2, e os 8,7% restantes sendo negativos para o referido grupo. A partir das prevalências encontradas, calculou-se que a probabilidade de um cão DEA 1 negativo receber sangue DEA 1.1, em uma primeira transfusão feita ao acaso, é de aproximadamente 4,5%. Sendo assim, este índice reflete um risco potencial para a sensibilização de um receptor DEA 1 negativo, o que deflagraria a produção de anticorpos. Posteriormente, se este mesmo paciente recebesse uma segunda transfusão de sangue, feita ao acaso, a probabilidade de receber hemácias do tipo DEA 1.1 seria de aproximadamente 2,3%, o que representaria o risco potencial de ocorrência de uma reação transfusional hemolítica aguda. Por outro lado, a probabilidade de este cão receber sangue do tipo DEA 1.2 seria cerca de 1,8%, o que levaria a uma reação transfusional menos grave, porém potencialmente prejudicial. No presente estudo, observou-se que o risco potencial para uma reação transfusional é mínimo, quando se trata de um cão mestiço.

The Novel Tubulin-Targeting Agent Pyrrolo-1,5-Benzoxazepine-15 Induces Apoptosis in Poor Prognostic Subgroups of Chronic Lymphocytic Leukemia

Pyrrolo-1,5-benzoxazepine-15 (PBOX-15) is a novel microtubule depolymerization agent that induces cell cycle arrest and subsequent apoptosis in a number of cancer cell lines. Chronic lymphocytic leukemia (CLL) is characterized by clonal expansion of predominately nonproliferating mature B cells. Here, we present data suggesting PBOX-15 is a potential therapeutic agent for CLL. We show activity of PBOX-15 in samples taken from a cohort of CLL patients (n = 55) representing both high-risk and low-risk disease. PBOX-15 exhibited cytotoxicity in CLL cells (n = 19) in a dose-dependent manner, with mean IC(50) of 0.55 mu mol/L. PBOX-15 significantly induced apoptosis in CLL cells (n = 46) including cells with poor prognostic markers: unmutated IgV(II) genes, CD38 and zeta-associated protein 70 (ZAP-70) expression, and fludarabine-resistant cells with chromosomal deletions in 17p. In addition, PBOX-15 was more potent than fludarabine in inducing apoptosis in fludarabine-sensitive cells. Pharmacologic inhibition and small interfering RNA knockdown of caspase-8 significantly inhibited PBOX-15-induced apoptosis. Pharmacologic inhibition of c-jun NH(2)-terminal kinase inhibited PBOX-15-induced apoptosis in mutated IgV(II) and ZAP-70(-) CLL cells but not in unmutated IgV(II) and ZAP-70(+) cells. PBOX-15 exhibited selective cytotoxicity in CLL cells compared with normal hematopoietic cells. Our data suggest that PBOX-15 represents a novel class of agents that are toxic toward both high-risk and low-risk CLL cells. The need for novel treatments is acute in CLL, especially for the subgroup of patients with poor clinical outcome and drug-resistant disease. This study identifies a novel agent with significant clinical potential.

Latent class analysis reveals distinct subgroups of patients based on symptom occurrence and demographic and clinical characteristics

Context Cancer patients experience a broad range of physical and psychological symptoms as a result of their disease and its treatment. On average, these patients report ten unrelieved and co-occurring symptoms. Objectives To determine if subgroups of oncology outpatients receiving active treatment (n=582) could be identified based on their distinct experience with thirteen commonly occurring symptoms; to determine whether these subgroups differed on select demographic, and clinical characteristics; and to determine if these subgroups differed on quality of life (QOL) outcomes. Methods Demographic, clinical, and symptom data from one Australian and two U.S. studies were combined. Latent class analysis (LCA) was used to identify patient subgroups with distinct symptom experiences based on self-report data on symptom occurrence using the Memorial Symptom Assessment Scale (MSAS). Results Four distinct latent classes were identified (i.e., All Low (28.0%), Moderate Physical and Lower Psych (26.3%), Moderate Physical and Higher Psych (25.4%), All High (20.3%)). Age, gender, education, cancer diagnosis, and presence of metastatic disease differentiated among the latent classes. Patients in the All High class had the worst QOL scores. Conclusion Findings from this study confirm the large amount of interindividual variability in the symptom experience of oncology patients. The identification of demographic and clinical characteristics that place patients are risk for a higher symptom burden can be used to guide more aggressive and individualized symptom management interventions.

Concordance of genetic risk across migraine subgroups: Impact on current and future genetic association studies

BACKGROUND There has been intensive debate whether migraine with aura (MA) and migraine without aura (MO) should be considered distinct subtypes or part of the same disease spectrum. There is also discussion to what extent migraine cases collected in specialised headache clinics differ from cases from population cohorts, and how female cases differ from male cases with respect to their migraine. To assess the genetic overlap between these migraine subgroups, we examined genome-wide association (GWA) results from analysis of 23,285 migraine cases and 95,425 population-matched controls. METHODS Detailed heterogeneity analysis of single-nucleotide polymorphism (SNP) effects (odds ratios) between migraine subgroups was performed for the 12 independent SNP loci significantly associated (p < 5 x 10(-8); thus surpassing the threshold for genome-wide significance) with migraine susceptibility. Overall genetic overlap was assessed using SNP effect concordance analysis (SECA) at over 23,000 independent SNPs. RESULTS: Significant heterogeneity of SNP effects (p het < 1.4 x 10(-3)) was observed between the MA and MO subgroups (for SNP rs9349379), and between the clinic- and population-based subgroups (for SNPs rs10915437, rs6790925 and rs6478241). However, for all 12 SNPs the risk-increasing allele was the same, and SECA found the majority of genome-wide SNP effects to be in the same direction across the subgroups. CONCLUSIONS Any differences in common genetic risk across these subgroups are outweighed by the similarities. Meta-analysis of additional migraine GWA datasets, regardless of their major subgroup composition, will identify new susceptibility loci for migraine.

Lens shape and refractive index distribution in type 1 diabetes

Purpose: To compare lens dimensions and refractive index distributions in type 1 diabetes and age-matched control groups. Methods: There were 17 participants with type 1 diabetes, consisting of two subgroups (7 young [23 ± 4 years] and 10 older [54 ± 4 years] participants), with 23 controls (13 young, 24 ± 4 years; 10 older, 55 ± 4 years). For each participant, one eye was tested with relaxed accommodation. A 3T clinical magnetic resonance imaging scanner was used to image the eye, employing a multiple spin echo (MSE) sequence to determine lens dimensions and refractive index profiles along the equatorial and axial directions. Results: The diabetes group had significantly smaller lens equatorial diameters and larger lens axial thicknesses than the control group (diameter mean ± 95% confidence interval [CI]: diabetes group 8.65 ± 0.26 mm, control group 9.42 ± 0.18 mm; axial thickness: diabetes group 4.33 ± 0.30 mm, control group 3.80 ± 0.14 mm). These differences were also significant within each age group. The older group had significantly greater axial thickness than the young group (older group 4.35 ± 0.26 mm, young group 3.70 ± 0.25 mm). Center refractive indices of diabetes and control groups were not significantly different. There were some statistically significant differences between the refractive index fitting parameters of young and older groups, but not between diabetes and control groups of the same age. Conclusions: Smaller lens diameters occurred in the diabetes groups than in the age-matched control groups. Differences in refractive index distribution between persons with and without diabetes are too small to have important effects on instruments measuring axial thickness.

Genome-wide methylation profiling identifies an essential role of reactive oxygen species in pediatric glioblastoma multiforme and validates a methylome specific for H3 histone family 3A with absence of G-CIMP/isocitrate dehydrogenase 1 mutation

Background. Pediatric glioblastoma multiforme (GBM) is rare, and there is a single study, a seminal discovery showing association of histone H3.3 and isocitrate dehydrogenase (IDH) 1 mutation with a DNA methylation signature. The present study aims to validate these findings in an independent cohort of pediatric GBM, compare it with adult GBM, and evaluate the involvement of important functionally altered pathways. Methods. Genome-wide methylation profiling of 21 pediatric GBM cases was done and compared with adult GBM data (GSE22867). We performed gene mutation analysis of IDH1 and H3 histone family 3A (H3F3A), status evaluation of glioma cytosine-phosphate-guanine island methylator phenotype (G-CIMP), and Gene Ontology analysis. Experimental evaluation of reactive oxygen species (ROS) association was also done. Results. Distinct differences were noted between methylomes of pediatric and adult GBM. Pediatric GBM was characterized by 94 hypermethylated and 1206 hypomethylated cytosine-phosphate-guanine (CpG) islands, with 3 distinct clusters, having a trend to prognostic correlation. Interestingly, none of the pediatric GBM cases showed G-CIMP/IDH1 mutation. Gene Ontology analysis identified ROS association in pediatric GBM, which was experimentally validated. H3F3A mutants (36.4%; all K27M) harbored distinct methylomes and showed enrichment of processes related to neuronal development, differentiation, and cell-fate commitment. Conclusions. Our study confirms that pediatric GBM has a distinct methylome compared with that of adults. Presence of distinct clusters and an H3F3A mutation-specific methylome indicate existence of epigenetic subgroups within pediatric GBM. Absence of IDH1/G-CIMP status further indicates that findings in adult GBM cannot be simply extrapolated to pediatric GBM and that there is a strong need for identification of separate prognostic markers. A possible role of ROS in pediatric GBM pathogenesis is demonstrated for the first time and needs further evaluation.

On an embedding property of generalized Carter subgroups

If E and F are saturated formations, we say that E is strongly contained in F if for any solvable group G with E-subgroup, E, and F-subgroup, F, some conjugate of E is contained in F. In this paper, we investigate the problem of finding the formations which strongly contain a fixed saturated formation E.

Our main results are restricted to formations, E, such that E = {G|G/F(G) ϵT}, where T is a non-empty formation of solvable groups, and F(G) is the Fitting subgroup of G. If T consists only of the identity, then E=N, the class of nilpotent groups, and for any solvable group, G, the N-subgroups of G are the Carter subgroups of G.

We give a characterization of strong containment which depends only on the formations E, and F. From this characterization, we prove:

If T is a non-empty formation of solvable groups, E = {G|G/F(G) ϵT}, and E is strongly contained in F, then

(1) there is a formation V such that F = {G|G/F(G) ϵV}.

(2) If for each prime p, we assume that T does not contain the class, S_p’, of all solvable p’-groups, then either E = F, or F contains all solvable groups.

This solves the problem for the Carter subgroups.

We prove the following result to show that the hypothesis of (2) is not redundant:

If R = {G|G/F(G) ϵS_r’}, then there are infinitely many formations which strongly contain R.

Estimating the magnitude of trastuzumab effects within patient subgroups in the HERA trial.

BACKGROUND: Trastuzumab (Herceptin(R)) improves disease-free survival (DFS) and overall survival for patients with human epidermal growth factor receptor 2 (HER2)-positive early breast cancer. We aimed to assess the magnitude of its clinical benefit for subpopulations defined by nodal and steroid hormone receptor status using data from the Herceptin Adjuvant (HERA) study. PATIENTS AND METHODS: HERA is an international multicenter randomized trial comparing 1 or 2 years of trastuzumab treatment with observation after standard chemotherapy in women with HER2-positive breast cancer. In total, 1703 women randomized to 1-year trastuzumab and 1698 women randomized to observation were included in these analyses. Median follow-up was 23.5 months. The primary endpoint was DFS. RESULTS: The overall hazard ratio (HR) for trastuzumab versus observation was 0.64 [95% confidence interval (CI) 0.54-0.76; P < 0.0001], ranging from 0.46 to 0.82 for subgroups. Estimated improvement in 3-year DFS in subgroups ranged from +11.3% to +0.6%. Patients with the best prognosis (those with node-negative disease and tumors 1.1-2.0 cm) had benefit similar to the overall cohort (HR 0.53, 95% CI 0.26-1.07; 3-year DFS improvement +4.6%, 95% CI -4.0% to 13.2%). CONCLUSIONS: Adjuvant trastuzumab therapy reduces the risk of relapse similarly across subgroups defined by nodal status and steroid hormone receptor status, even those at relatively low risk for relapse.

Behavioural and histopathological analyses of ibuprofen treatment on the effect of aggregated AB (1-42) injections in the rat

It has been suggested that inflammatory processes may play a role in the development of Alzheimerâ??s disease (AD), and that nonsteroidal anti-inflammatory drug treatments may provide protection against the onset of AD. In the current study male Wistar rats were trained in two-lever operant chambers under an alternating lever cyclic-ratio ratio (ALCR) schedule. When responding showed no trends, subjects were divided into groups. One group was bilaterally injected into the CA3 area of the hippocampus with 5 μl of aggregated β-amyloid (Aβ) suspension, and one group was bilaterally injected into the CA3 area of the hippocampus with 5 μl of sterile saline. Subgroups were treated twice daily with 0.1 ml (40 mg/kg) ibuprofen administered orally. The results indicated that chronic administration of ibuprofen protected against detrimental behavioural effects following aggregated Aβ injections. Withdrawal of ibuprofen treatment from aggregated Aβ-injected subjects produced a decline in behavioural performance to the level of the non-treated aggregated Aβ-injected group. Ibuprofen treatment reduced the numbers of reactive astrocytes following aggregated Aβ injection, and withdrawal of ibuprofen resulted in an increase of reactive astrocytes. These results suggest that induced inflammatory processes may play a role in AD, and that ibuprofen treatment may protect against some of the symptoms seen in AD.

Evaluation of an algorithm to guide patients with type 1 diabetes treated with continuous subcutaneous insulin infusion on how to respond to real-time continuous glucose levels:A randomized controlled trial

OBJECTIVE - To evaluate an algorithm guiding responses of continuous subcutaneous insulin infusion (CSII)-treated type 1 diabetic patients using real-time continuous glucose monitoring (RT-CGM). RESEARCH DESIGN AND METHODS - Sixty CSII-treated type 1 diabetic participants (aged 13-70 years, including adult and adolescent subgroups, with A1C =9.5%) were randomized in age-, sex-, and A1C-matched pairs. Phase 1 was an open 16-week multicenter randomized controlled trial. Group A was treated with CSII/RT-CGM with the algorithm, and group B was treated with CSII/RT-CGM without the algorithm. The primary outcome was the difference in time in target (4-10 mmol/l) glucose range on 6-day masked CGM. Secondary outcomes were differences in A1C, low (=3.9 mmol/l) glucose CGM time, and glycemic variability. Phase 2 was the week 16-32 follow-up. Group A was returned to usual care, and group B was provided with the algorithm. Glycemia parameters were as above. Comparisons were made between baseline and 16 weeks and 32 weeks. RESULTS - In phase 1, after withdrawals 29 of 30 subjects were left in group A and 28 of 30 subjects were left in group B. The change in target glucose time did not differ between groups. A1C fell (mean 7.9% [95% CI 7.7-8.2to 7.6% [7.2-8.0]; P <0.03) in group A but not in group B (7.8% [7.5-8.1] to 7.7 [7.3-8.0]; NS) with no difference between groups. More subjects in group A achieved A1C =7% than those in group B (2 of 29 to 14 of 29 vs. 4 of 28 to 7 of 28; P = 0.015). In phase 2, one participant was lost from each group. In group A, A1C returned to baseline with RT-CGM discontinuation but did not change in group B, who continued RT-CGM with addition of the algorithm. CONCLUSIONS - Early but not late algorithm provision to type 1 diabetic patients using CSII/RT-CGM did not increase the target glucose time but increased achievement of A1C =7%. Upon RT-CGM cessation, A1C returned to baseline. © 2010 by the American Diabetes Association.

DNA methylation subgroups and the CpG island methylator phenotype in gastric cancer: a comprehensive profiling approach

BACKGROUND: Methylation-induced silencing of promoter CpG islands in tumor suppressor genes plays an important role in human carcinogenesis. In colorectal cancer, the CpG island methylator phenotype (CIMP) is defined as widespread and elevated levels of DNA methylation and CIMP+ tumors have distinctive clinicopathological and molecular features. In contrast, the existence of a comparable CIMP subtype in gastric cancer (GC) has not been clearly established. To further investigate this issue, in the present study we performed comprehensive DNA methylation profiling of a well-characterised series of primary GC.

METHODS: The methylation status of 1,421 autosomal CpG sites located within 768 cancer-related genes was investigated using the Illumina GoldenGate Methylation Panel I assay on DNA extracted from 60 gastric tumors and matched tumor-adjacent gastric tissue pairs. Methylation data was analysed using a recursively partitioned mixture model and investigated for associations with clinicopathological and molecular features including age, Helicobacter pylori status, tumor site, patient survival, microsatellite instability and BRAF and KRAS mutations.

RESULTS: A total of 147 genes were differentially methylated between tumor and matched tumor-adjacent gastric tissue, with HOXA5 and hedgehog signalling being the top-ranked gene and signalling pathway, respectively. Unsupervised clustering of methylation data revealed the existence of 6 subgroups under two main clusters, referred to as L (low methylation; 28% of cases) and H (high methylation; 72%). Female patients were over-represented in the H tumor group compared to L group (36% vs 6%; P = 0.024), however no other significant differences in clinicopathological or molecular features were apparent. CpG sites that were hypermethylated in group H were more frequently located in CpG islands and marked for polycomb occupancy.

CONCLUSIONS: High-throughput methylation analysis implicates genes involved in embryonic development and hedgehog signaling in gastric tumorigenesis. GC is comprised of two major methylation subtypes, with the highly methylated group showing some features consistent with a CpG island methylator phenotype.

Intake of total and subgroups of fat minimally affect the associations between selected single nucleotide polymorphisms in the PPARγ pathway and changes in anthropometry among European adults from cohorts of the DiOGenes study

BACKGROUND: Although the peroxisome proliferator-activated receptor γ (PPARγ) pathway is central in adipogenesis, it remains unknown whether it influences change in body weight (BW) and whether dietary fat has a modifying effect on the association. OBJECTIVES: We examined whether 27 single nucleotide polymorphisms (SNPs) within 4 genes in the PPARγ pathway are associated with the OR of being a BW gainer or with annual changes in anthropometry and whether intake of total fat, monounsaturated fat, polyunsaturated fat, or saturated fat has a modifying effect on these associations. METHODS: A case-noncase study included 11,048 men and women from cohorts in the European Diet, Obesity and Genes study; 5552 were cases, defined as individuals with the greatest BW gain during follow-up, and 6548 were randomly selected, including 5496 noncases. We selected 4 genes [CCAAT/enhancer binding protein β (CEBPB), phosphoenolpyruvate carboxykinase 2, PPARγ gene (PPARG), and sterol regulatory element binding transcription factor 1] according to evidence about biologic plausibility for interactions with dietary fat in weight regulation. Diet was assessed at baseline, and anthropometry was followed for 7 y. RESULTS: The ORs for being a BW gainer for the 27 genetic variants ranged from 0.87 (95% CI: 0.79, 1.03) to 1.12 (95% CI: 0.96, 1.22) per additional minor allele. Uncorrected, CEBPB rs4253449 had a significant interaction with the intake of total fat and subgroups of fat. The OR for being a BW gainer for each additional rs4253449 minor allele per 100 kcal higher total fat intake was 1.07 (95% CI: 1.02, 1.12; P = 0.008), and similar associations were found for subgroups of fat. CONCLUSIONS: Among European men and women, the influence of dietary fat on associations between SNPs in the PPARγ pathway and anthropometry is likely to be absent or marginal. The observed interaction between rs4253449 and dietary fat needs confirmation.