Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

Maintenance of Undifferentiated State and Self-Renewal of Embryonic Neural Stem Cells by Polycomb Protein Ring1B

12 pages, 7 figures.-- PMID: 19544461 [PubMed].-- Printed version published Jul 2009.Supporting information (Suppl. figures S1-S9, tables S1-S2) available at: http://www3.interscience.wiley.com/journal/122302104/suppinfoCell lineages generated during development and tissue maintenance are derived from self-renewing stem cells by differentiation of their committed progeny. Recent studies suggest that epigenetic mechanisms, and in particular the Polycomb group (PcG) of genes, play important roles in controlling stem cell self-renewal. Here, we address PcG regulation of stem cell self-renewal and differentiation through inactivation of Ring1B, a histone H2A E3 monoubiquitin ligase, in embryonic neural stem cells (NSCs) from the olfactory bulb of a conditional mouse mutant line. We show that neural stem/progenitor cell proliferation in vivo and in neurosphere assays is impaired, lacking Ring1B, and their self-renewal and multipotential abilities, assessed as sphere formation and differentiation from single cells, are severely affected. We also observed unscheduled neuronal, but not glial, differentiation of mutant stem/progenitor cells under proliferating conditions, an alteration enhanced in cells also lacking Ring1A, the Ring1B paralog, some of which turned into morphologically identifiable neurons. mRNA analysis of mutant cells showed upregulation of some neuronal differentiation-related transcription factors and the cell proliferation inhibitor Cdkn1a/p21, as well as downregulation of effectors of the Notch signaling pathway, a known inhibitor of neuronal differentiation of stem/progenitor cells. In addition, differentiation studies of Ring1B-deficient progenitors showed decreased oligodendrocyte formation in vitro and enhanced neurogenesis and reduced gliogenesis in vivo. These data suggest a role for Ring1B in maintenance of the undifferentiated state of embryonic neural stem/progenitor cells. They also suggest that Ring1B may modulate the differentiation potential of NSCs to neurons and glia.M.R-T. and H. M-G. were recipients of FPU and FPI fellowships, from the Ministerio de Educacion y Ciencia and Comunidad de Madrid, respectively. This work was supported by grants SAF2007-65957-C02-01 (M.V.), the Onco-Cycle program from the Comunidad de Madrid (M.V.), SAF2004-05798, and CIBERNED CB06/05/0065 from Instituto de Salud Carlos III (C.V-A.).Peer reviewe

Distinct cellular pathways select germline-encoded and somatically mutated antibodies into immunological memory

One component of memory in the antibody system is long-lived memory B cells selected for the expression of somatically mutated, high-affinity antibodies in the T cell-dependent germinal center (GC) reaction. A puzzling observation has been that the memory B cell compartment also contains cells expressing unmutated, low-affinity antibodies. Using conditional Bcl6 ablation, we demonstrate that these cells are generated through proliferative expansion early after immunization in a T cell-dependent but GC-independent manner. They soon become resting and long-lived and display a novel distinct gene expression signature which distinguishes memory B cells from other classes of B cells. GC-independent memory B cells are later joined by somatically mutated GC descendants at roughly equal proportions and these two types of memory cells efficiently generate adoptive secondary antibody responses. Deletion of T follicular helper (Tfh) cells significantly reduces the generation of mutated, but not unmutated, memory cells early on in the response. Thus, B cell memory is generated along two fundamentally distinct cellular differentiation pathways. One pathway is dedicated to the generation of high-affinity somatic antibody mutants, whereas the other preserves germ line antibody specificities and may prepare the organism for rapid responses to antigenic variants of the invading pathogen

Crystal structure, site selectivity, and electronic structure of layered chalcogenide LaOBiPbS3

We have investigated the crystal structure of LaOBiPbS3 using neutron diffraction and synchrotron X-ray diffraction. From structural refinements, we found that the two metal sites, occupied by Bi and Pb, were differently surrounded by the sulfur atoms. Calculated bond valence sum suggested that one metal site was nearly trivalent and the other was nearly divalent. Neutron diffraction also revealed site selectivity of Bi and Pb in the LaOBiPbS3 structure. These results suggested that the crystal structure of LaOBiPbS3 can be regarded as alternate stacks of the rock-salt-type Pb-rich sulfide layers and the LaOBiS2-type Bi-rich layers. From band calculations for an ideal (LaOBiS2)(PbS) system, we found that the S bands of the PbS layer were hybridized with the Bi bands of the BiS plane at around the Fermi energy, which resulted in the electronic characteristics different from that of LaOBiS2. Stacking the rock-salt type sulfide (chalcogenide) layers and the BiS2-based layered structure could be a new strategy to exploration of new BiS2-based layered compounds, exotic two-dimensional electronic states, or novel functionality.Comment: 11 pages, 5 figure

Novel Parvovirus and Related Variant in Human Plasma

We report a novel parvovirus (PARV4) and related variants in pooled human plasma used in the manufacture of plasma-derived medical products. Viral DNA was detected by using highly selective polymerase chain reaction assays; 5% of pools tested positive, and amounts of DNA ranged from <500 copies/mL to >106 copies/mL plasma

Sturmian bases for two-electron systems in hyperspherical coordinates

We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron-electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb sturmian functions of half integer angular momentum. We show that, in the case of H$^-$, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for $S\rightarrow P$ transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method.Comment: 28 pages, 4 figure

Structural studies of Helicase NS3 variants from Hepatitis C virus genotype 3 in virological sustained responder and non-responder patients

<p>Abstract</p> <p>Background</p> <p>About 130 million people are infected with the hepatitis C virus (HCV) worldwide, but effective treatment options are not yet available. One of the most promising targets for antiviral therapy is nonstructural protein 3 (NS3). To identify possible changes in the structure of NS3 associated with virological sustained response or non-response of patients, a model was constructed for each helicase NS3 protein coding sequence. From this, the goal was to verify the interaction between helicases variants and their ligands.</p> <p>Findings</p> <p>Evidence was found that the NS3 helicase portion of non-responder patients contained substitutions in its ATP and RNA binding sites. K210E substitution can cause an imbalance in the distribution of loads, leading to a decrease in the number of ligations between the essential amino acids required for the hydrolysis of ATP. W501R substitution causes an imbalance in the distribution of loads, leading and forcing the RNA to interact with the amino acid Thr269, but not preventing binding of ribavirin inhibitor.</p> <p>Conclusions</p> <p>Useful information is provided on the genetic profiling of the HCV genotype 3, specifically the coding region of the NS3 protein, improving our understanding of the viral genome and the regions of its protein catalytic site.</p

Extramuscular myofascial force transmission within the rat anterior tibial compartment: Proximo-distal differences in muscle force

Intramuscular connective tissues are continuous to extramuscular connective tissues. If force is transmitted there, differences should be present between force at proximal and distal attachments of muscles. Extensor digitorum longus (EDL), tibialis anterior (TA), and extensor hallucis longus muscles (EHL) were excited simultaneously and maximally. Only EDL length was changed, exclusively by moving the position of its proximal tendon. Distal force exerted by TA + EHL complex was not affected significantly. Proximal and distal EDL isometric force were not equal for most EDL lengths:

Genetic Heterogeneity of Hepatitis C Virus in Association with Antiviral Therapy Determined by Ultra-Deep Sequencing

The hepatitis C virus (HCV) invariably shows wide heterogeneity in infected patients, referred to as a quasispecies population. Massive amounts of genetic information due to the abundance of HCV variants could be an obstacle to evaluate the viral genetic heterogeneity in detail.Using a newly developed massive-parallel ultra-deep sequencing technique, we investigated the viral genetic heterogeneity in 27 chronic hepatitis C patients receiving peg-interferon (IFN) α2b plus ribavirin therapy.Ultra-deep sequencing determined a total of more than 10 million nucleotides of the HCV genome, corresponding to a mean of more than 1000 clones in each specimen, and unveiled extremely high genetic heterogeneity in the genotype 1b HCV population. There was no significant difference in the level of viral complexity between immediate virologic responders and non-responders at baseline (p = 0.39). Immediate virologic responders (n = 8) showed a significant reduction in the genetic complexity spanning all the viral genetic regions at the early phase of IFN administration (p = 0.037). In contrast, non-virologic responders (n = 8) showed no significant changes in the level of viral quasispecies (p = 0.12), indicating that very few viral clones are sensitive to IFN treatment. We also demonstrated that clones resistant to direct-acting antivirals for HCV, such as viral protease and polymerase inhibitors, preexist with various abundances in all 27 treatment-naïve patients, suggesting the risk of the development of drug resistance against these agents.Use of the ultra-deep sequencing technology revealed massive genetic heterogeneity of HCV, which has important implications regarding the treatment response and outcome of antiviral therapy