Herbrand's theorem and non-Euclidean geometry

We use Herbrand's theorem to give a new proof that Euclid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.Comment: 12 pages, 5 figure

Vol. 31, No. 5, pp 323-350

Philippe Boutry et Pierre-Antoine Fabre, directeurs d’études avec Dominique Julia, directeur de recherche au CNRS et Claude Langlois, directeur d’études à l’EPHE-Ve section L’histoire religieuse au XXe siècle Compte rendu non communiqué. André Mary, directeur de recherche au CNRS Anthropologie des formes contemporaines du religieux. Les anthropologues et la religion Le séminaire a poursuivi sa réflexion sur le rapport problématique des anthropologues, et de la tradition anthropologique, à la ..

Construction of 12 EST libraries and characterization of a 12,226 EST dataset for chicory (Cichorium intybus) root, leaves and nodules in the context of carbohydrate metabolism investigation

<p>Abstract</p> <p>Background</p> <p>The industrial chicory, <it>Cichorium intybus</it>, is a member of the <it>Asteraceae </it>family that accumulates fructan of the inulin type in its root. Inulin is a low calories sweetener, a texture agent and a health promoting ingredient due to its prebiotic properties. Average inulin chain length is a critical parameter that is genotype and temperature dependent. In the context of the study of carbohydrate metabolism and to get insight into the transcriptome of chicory root and to visualize temporal changes of gene expression during the growing season, we obtained and characterized 10 cDNA libraries from chicory roots regularly sampled in field during a growing season. A leaf and a nodule libraries were also obtained for comparison.</p> <p>Results</p> <p>Approximately 1,000 Expressed Sequence Tags (EST) were obtained from each of twelve cDNA libraries resulting in a 12,226 EST dataset. Clustering of these ESTs returned 1,922 contigs and 4,869 singlets for a total of 6,791 putative unigenes. All ESTs were compared to public sequence databases and functionally classified. Data were specifically searched for sequences related to carbohydrate metabolism. Season wide evolution of functional classes was evaluated by comparing libraries at the level of functional categories and unigenes distribution.</p> <p>Conclusion</p> <p>This chicory EST dataset provides a season wide outlook of the genes expressed in the root and to a minor extent in leaves and nodules. The dataset contains more than 200 sequences related to carbohydrate metabolism and 3,500 new ESTs when compared to other recently released chicory EST datasets, probably because of the season wide coverage of the root samples. We believe that these sequences will contribute to accelerate research and breeding of the industrial chicory as well as of closely related species.</p

Challenges for molecular neuroimaging with MRI

Magnetic resonance (MRI)-based molecular imaging methods are beginning to have impact in neuroscience. A growing number of molecular imaging agents have been synthesized and tested in vitro, but so far relatively few have been validated in the brains of live animals. Here, we discuss key challenges associated with expanding the repertoire of successful molecular neuroimaging approaches. The difficulty of delivering agents past the blood-brain barrier (BBB) is a particular obstacle to molecular imaging in the central nervous system. We review established and emerging techniques for trans-BBB delivery, including intracranial infusion, BBB disruption, and transporter-related methods. Improving the sensitivity with which MRI-based molecular agents can be detected is a second major challenge. Better sensitivity would in turn reduce the requirements for delivery and alleviate potential side effects. We discuss recent efforts to enhance relaxivity of conventional longitudinal relaxation time (T1) and transverse relaxation time (T2) MRI contrast agents, as well as strategies that involve amplifying molecular signals or reducing endogenous background influences. With ongoing refinement of imaging approaches and brain delivery methods, MRI-based techniques for molecular-level neuroscientific investigation will fall increasingly within reach.Raymond and Beverley Sackler FoundationNational Institutes of Health (U.S.) (R01-DA28299)National Institutes of Health (U.S.) (DP2-OD2441

Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus

A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P=9.2 × 10-20), ER-negative BC (P=1.1 × 10-13), BRCA1-associated BC (P=7.7 × 10-16) and triple negative BC (P-diff=2 × 10-5). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P=2 × 10-3) and ABHD8 (P<2 × 10-3). Chromosome conformation capture identifies interactions between four candidate SNPs and ABHD8, and luciferase assays indicate six risk alleles increased transactivation of the ADHD8 promoter. Targeted deletion of a region containing risk SNP rs56069439 in a putative enhancer induces ANKLE1 downregulation; and mRNA stability assays indicate functional effects for an ANKLE1 3′-UTR SNP. Altogether, these data suggest that multiple SNPs at 19p13 regulate ABHD8 and perhaps ANKLE1 expression, and indicate common mechanisms underlying breast and ovarian cancer risk

A case-only study to identify genetic modifiers of breast cancer risk for BRCA1/BRCA2 mutation carriers

Breast cancer (BC) risk for BRCA1 and BRCA2 mutation carriers varies by genetic and familial factors. About 50 common variants have been shown to modify BC risk for mutation carriers. All but three, were identified in general population studies. Other mutation carrier-specific susceptibility variants may exist but studies of mutation carriers have so far been underpowered. We conduct a novel case-only genome-wide association study comparing genotype frequencies between 60,212 general population BC cases and 13,007 cases with BRCA1 or BRCA2 mutations. We identify robust novel associations for 2 variants with BC for BRCA1 and 3 for BRCA2 mutation carriers, P &lt; 10−8, at 5 loci, which are not associated with risk in the general population. They include rs60882887 at 11p11.2 where MADD, SP11 and EIF1, genes previously implicated in BC biology, are predicted as potential targets. These findings will contribute towards customising BC polygenic risk scores for BRCA1 and BRCA2 mutation carriers

Common breast cancer susceptibility alleles are associated with tumor subtypes in BRCA1 and BRCA2 mutation carriers : results from the Consortium of Investigators of Modifiers of BRCA1/2.

Abstract Introduction Previous studies have demonstrated that common breast cancer susceptibility alleles are differentially associated with breast cancer risk for BRCA1 and/or BRCA2 mutation carriers. It is currently unknown how these alleles are associated with different breast cancer subtypes in BRCA1 and BRCA2 mutation carriers defined by estrogen (ER) or progesterone receptor (PR) status of the tumour. Methods We used genotype data on up to 11,421 BRCA1 and 7,080 BRCA2 carriers, of whom 4,310 had been affected with breast cancer and had information on either ER or PR status of the tumour, to assess the associations of 12 loci with breast cancer tumour characteristics. Associations were evaluated using a retrospective cohort approach. Results The results suggested stronger associations with ER-positive breast cancer than ER-negative for 11 loci in both BRCA1 and BRCA2 carriers. Among BRCA1 carriers, single nucleotide polymorphism (SNP) rs2981582 (FGFR2) exhibited the biggest difference based on ER status (per-allele hazard ratio (HR) for ER-positive = 1.35, 95% CI: 1.17 to 1.56 vs HR = 0.91, 95% CI: 0.85 to 0.98 for ER-negative, P-heterogeneity = 6.5 &#215; 10-6). In contrast, SNP rs2046210 at 6q25.1 near ESR1 was primarily associated with ER-negative breast cancer risk for both BRCA1 and BRCA2 carriers. In BRCA2 carriers, SNPs in FGFR2, TOX3, LSP1, SLC4A7/NEK10, 5p12, 2q35, and 1p11.2 were significantly associated with ER-positive but not ER-negative disease. Similar results were observed when differentiating breast cancer cases by PR status. Conclusions The associations of the 12 SNPs with risk for BRCA1 and BRCA2 carriers differ by ER-positive or ER-negative breast cancer status. The apparent differences in SNP associations between BRCA1 and BRCA2 carriers, and non-carriers, may be explicable by differences in the prevalence of tumour subtypes. As more risk modifying variants are identified, incorporating these associations into breast cancer subtype-specific risk models may improve clinical management for mutation carriers

Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus

A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P = 9.2 x 10(-20)), ER-negative BC (P = 1.1 x 10(-13)), BRCA1-associated BC (P = 7.7 x 10(-16)) and triple negative BC (P-diff = 2 x 10(-5)). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P = 2 x 10(-3)) and ABHD8 (PPeer reviewe

A case-only study to identify genetic modifiers of breast cancer risk for BRCA1/BRCA2 mutation carriers

Abstract: Breast cancer (BC) risk for BRCA1 and BRCA2 mutation carriers varies by genetic and familial factors. About 50 common variants have been shown to modify BC risk for mutation carriers. All but three, were identified in general population studies. Other mutation carrier-specific susceptibility variants may exist but studies of mutation carriers have so far been underpowered. We conduct a novel case-only genome-wide association study comparing genotype frequencies between 60,212 general population BC cases and 13,007 cases with BRCA1 or BRCA2 mutations. We identify robust novel associations for 2 variants with BC for BRCA1 and 3 for BRCA2 mutation carriers, P < 10−8, at 5 loci, which are not associated with risk in the general population. They include rs60882887 at 11p11.2 where MADD, SP11 and EIF1, genes previously implicated in BC biology, are predicted as potential targets. These findings will contribute towards customising BC polygenic risk scores for BRCA1 and BRCA2 mutation carriers