Class Number Two for Real Quadratic Fields of Richaud-Degert Type

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.

Sociology, Gender and Educational Aspirations: Girls and their Ambitions

This study helps develop an overall understanding as to why some students achieve where others don't. Debate on the effects of class on educational attainment is well documented and typically centres on the reproductive nature of class whilst studies of the effect of class on educational aspirations also predict outcomes that see education reinforcing and reproducing a student's class background.Despite a number of government initiatives to help raise higher education participation to 50 per cent by 2010, for the working class numbers have altered little. Using data from an ethnographic case study of a low-achieving girls school, the author explores aspirations and argues that whilst class is very powerful in explaining educational attainment, understanding educational aspirations is somewhat more complex. The purpose of this book, therefore, is to question and challenge popular assumptions surrounding class-based theory in making sense of girls' aspirations and to question the usefulness of the continued over reliance of such broad categorisations by both academics and policy makers

On a Class of Vertex Folkman Numbers

Let a1 , . . . , ar, be positive integers, i=1 ... r, m = ∑(ai − 1) + 1 and p = max{a1 , . . . , ar }. For a graph G the symbol G → (a1 , . . . , ar ) means that in every r-coloring of the vertices of G there exists a monochromatic ai -clique of color i for some i ∈ {1, . . . , r}. In this paper we consider the vertex Folkman numbers F (a1 , . . . , ar ; m − 1) = min |V (G)| : G → (a1 , . . . , ar ) and Km−1 ⊂ G} We prove that F (a1 , . . . , ar ; m − 1) = m + 6, if p = 3 and m ≧ 6 (Theorem 3) and F (a1 , . . . , ar ; m − 1) = m + 7, if p = 4 and m ≧ 6 (Theorem 4).

Immunolocalization and pathological alterations following Strongyloides venezuelensis infection in the lungs and the intestine of MHC class I or II deficient mice

The present study, investigated the mechanisms involved in the immune responses of Major Histocompatibility Complex class I or class II knockout mice, following Strongyloides venezuelensis infection. Wild-type C57BL/6 (WT), MHC II(-/-) and MHC I(-/-) mice were individually inoculated with 3000 larvae (U) of S. venezuelensis and sacrificed on days 1, 3, 5, 8, 13 and 21 post-infection (p.i.). Samples of blood, lungs and small intestines were collected. The tissue samples were stained with hematoxylineosin for the pathological analysis. The presence of the parasite was demonstrated by immunoperoxidase analysis. MHC II(-/-) mice presented a significantly higher number of adult worms recovered from the small intestine on day 5 p.i. and presented elevated numbers of eggs in the feces. The infection by S. venezuelensis was completely eliminated 13 days after infection in WT as well as in MHC I(-/-) mice. In MHC II(-/-) mice, eggs and adult worms were still found on day 21 p.i., however, there was a significant reduction in their numbers. In the lung, the parasite was observed in MHC I(-/-) on day 1 p.i. and in MHC II(-/-) mice on days 1 and 5 p.i. In the small intestine of WT mice, a larger number of parasites were observed on day 8 p.i. and their absence was observed after day 13 p.i. Through immunohistochemistry analysis, the parasite was detected in the duodenum of WT on days 5 and 8 p.i., and in knockout mice on days 5, 8 and 13 p.i.; as well as in posterior portions of the small intestine in MHC I(-/-) and MHC II(-/-) on day 13 p.i., a finding which was not observed in WT mice. We concluded that immunohistochemistry analysis contributed to a more adequate understanding of the parasite localization in immunodeficient hosts and that the findings aid in the interpretation of immunopathogenesis in Strongyloides infection. (C) 2008 Elsevier B.V. All rights reserved.

Phase diagrams of binary mixtures of patchy colloids with distinct numbers and types of patches: Theempty fluid regime

We investigate the effect of distinct bonding energies on the onset of criticality of low functionality fluid mixtures. We focus on mixtures ofparticles with two and three patches as this includes the mixture where "empty" fluids were originally reported. In addition to the number of patches, thespecies differ in the type of patches or bonding sites. For simplicity, we consider that the patches on each species are identical: one species has threepatches of type A and the other has two patches of type B. We have found a rich phase behavior with closed miscibility gaps, liquid-liquid demixing, and negative azeotropes. Liquid-liquid demixing was found to pre-empt the "empty" fluid regime, of these mixtures, when the AB bonds are weaker than the AA or BB bonds. By contrast, mixtures in this class exhibit "empty" fluid behavior when the AB bonds are stronger than at least one of the other two. Mixtureswith bonding energies epsilon(BB) = epsilon(AB) and epsilon(AA) < epsilon(BB), were found to exhibit an unusual negative azeotrope. (C) 2011 American Institute of Physics. [doi:10.1063/1.3561396]

A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

TCR-MHC class II interaction is required for peripheral expansion of CD4 cells in a T cell-deficient host.

It is well established that T cell-deficient nude and SCID mice can be reconstituted by i.v. injection of small numbers of purified peripheral CD4+ T cells; however, the requirements for expansion of the transferred T cells in such systems are not clear. We show here that blood and lymphoid organs of MHC class II-deficient mice (which selectively lack mature CD4+ T cells) cannot be reconstituted by transfer of purified splenic CD4+ T cells, whereas TCRalpha-deficient mice (which lack both CD4+ and CD8+ mature T cells) are readily reconstituted. The failure of CD4+ T cell reconstitution in MHC class II-deficient mice was not due to the presence of CD8+ T cells, since similar results were obtained in TCRalpha-MHC class II double-deficient mice. Consistent with most previous studies CD4+ T cells in reconstituted TCRalpha-deficient mice had a diverse TCR Vbeta repertoire and were predominantly of an activated/memory (CD44high) phenotype. Collectively our data demonstrate that the expansion of peripheral CD4+ T cells in a T cell-deficient host is dependent upon interactions of the TCR with MHC class II.

Dissociation of thymic positive and negative selection in transgenic mice expressing major histocompatibility complex class I molecules exclusively on thymic cortical epithelial cells.

Thymic positive and negative selection of developing T lymphocytes confronts us with a paradox: How can a T-cell antigen receptor (TCR)-major histocompatibility complex (MHC)/peptide interaction in the former process lead to transduction of signals allowing for cell survival and in the latter induce programmed cell death or a hyporesponsive state known as anergy? One of the hypotheses put forward states that the outcome of a TCR-MHC/peptide interaction depends on the cell type presenting the selecting ligand to the developing thymocyte. Here we describe the development and lack of self-tolerance of CD8(+) T lymphocytes in transgenic mice expressing MHC class I molecules in the thymus exclusively on cortical epithelial cells. Despite the absence of MHC class I expression on professional antigen-presenting cells, normal numbers of CD8(+) cells were observed in the periphery. Upon specific activation, transgenic CD8(+) T cells efficiently lysed syngeneic MHC class I(+) targets in vitro and in vivo, indicating that thymic cortical epithelium (in contrast to medullary epithelium and antigen-presenting cells of hematopoietic origin) is incapable of tolerance induction. Thus, compartmentalization of the antigen-presenting cells involved in thymic positive selection and tolerance induction can (at least in part) explain the positive/negative selection paradox.

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

Positive impact of inhibitory Ly49 receptor-MHC class I interaction on NK cell development.

NK cells can kill MHC-different or MHC-deficient but not syngeneic MHC-expressing target cells. This MHC class I-specific tolerance is acquired during NK cell development. MHC recognition by murine NK cells largely depends on clonally distributed Ly49 family receptors, which inhibit NK cell function upon ligand engagement. We investigated whether these receptors play a role for the development of NK cells and provide evidence that the expression of a Ly49 receptor transgene on developing NK cells endowed these cells with a significant developmental advantage over NK cells lacking such a receptor, but only if the relevant MHC ligand was present in the environment. The data suggest that the transgenic Ly49 receptor accelerates and/or rescues the development of NK cells which would otherwise fail to acquire sufficient numbers of self-MHC-specific receptors. Interestingly, the positive effect on NK cell development is most prominent when the MHC ligand is simultaneously present on both hemopoietic and nonhemopoietic cells. These findings correlate with functional data showing that MHC class I ligand on all cells is required to generate functionally mature NK cells capable of reacting to cells lacking the respective MHC ligand. We conclude that the engagement of inhibitory MHC receptors during NK cell development provides signals that are important for further NK cell differentiation and/or maturation.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

MHC Class II Transactivator Is an In Vivo Regulator of Osteoclast Differentiation and Bone Homeostasis Co-opted From Adaptive Immunity.

The molecular networks controlling bone homeostasis are not fully understood. The common evolution of bone and adaptive immunity encourages the investigation of shared regulatory circuits. MHC Class II Transactivator (CIITA) is a master transcriptional co-activator believed to be exclusively dedicated for antigen presentation. CIITA is expressed in osteoclast precursors, and its expression is accentuated in osteoporotic mice. We thus asked whether CIITA plays a role in bone biology. To this aim, we fully characterized the bone phenotype of two mouse models of CIITA overexpression, respectively systemic and restricted to the monocyte-osteoclast lineage. Both CIITA-overexpressing mouse models revealed severe spontaneous osteoporosis, as assessed by micro-computed tomography and histomorphometry, associated with increased osteoclast numbers and enhanced in vivo bone resorption, whereas osteoblast numbers and in vivo bone-forming activity were unaffected. To understand the underlying cellular and molecular bases, we investigated ex vivo the differentiation of mutant bone marrow monocytes into osteoclasts and immune effectors, as well as osteoclastogenic signaling pathways. CIITA-overexpressing monocytes differentiated normally into effector macrophages or dendritic cells but showed enhanced osteoclastogenesis, whereas CIITA ablation suppressed osteoclast differentiation. Increased c-fms and receptor activator of NF-κB (RANK) signaling underlay enhanced osteoclast differentiation from CIITA-overexpressing precursors. Moreover, by extending selected phenotypic and cellular analyses to additional genetic mouse models, namely MHC Class II deficient mice and a transgenic mouse line lacking a specific CIITA promoter and re-expressing CIITA in the thymus, we excluded MHC Class II expression and T cells from contributing to the observed skeletal phenotype. Altogether, our study provides compelling genetic evidence that CIITA, the molecular switch of antigen presentation, plays a novel, unexpected function in skeletal homeostasis, independent of MHC Class II expression and T cells, by exerting a selective and intrinsic control of osteoclast differentiation and bone resorption in vivo. © 2014 American Society for Bone and Mineral Research.

Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.