Serre's "formule de masse" in prime degree

For a local field F with finite residue field of characteristic p, we describe completely the structure of the filtered F_p[G]-module K^*/K^*p in characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's mass formula in degree p. We also determine the compositum C of all degree p separable extensions with solvable galoisian closure over an arbitrary base field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in the case of the local field F. Our method allows us to compute the contribution of each character G\to\F_p^* to the degree p mass formula, and, for any given group \Gamma, the contribution of those degree p separable extensions of F whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section

A Comparison of the Ovulation Method With the CUE Ovulation Predictor in Determining the Fertile Period

The purpose of this study was to compare the CUE Ovulation Predictor with the ovulation method in determining the fertile period. Eleven regularly ovulating women measured their salivary and vaginal electrical resistance (ER) with the CUE, observed their cervical-vaginal mucus, and measured their urine for a luteinizing hormone (LH) surge on a daily basis. Data from 21 menstrual cycles showed no statistical difference (T= 0.33, p= 0.63) between the CUE fertile period, which ranged from 5 to 10 days (mean = 6.7 days, SD = 1.6), and the fertile period of the ovulation method, which ranged from 4 to 9 days (mean = 6.5 days, SD = 2.0). The CUE has potential as an adjunctive device in the learning and use of natural family planning methods

Two-divisibility of the coefficients of certain weakly holomorphic modular forms

We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly divisible by 2.Comment: Corrected typos. To appear in the Ramanujan Journa

Defecting or not defecting: how to "read" human behavior during cooperative games by EEG measurements

Understanding the neural mechanisms responsible for human social interactions is difficult, since the brain activities of two or more individuals have to be examined simultaneously and correlated with the observed social patterns. We introduce the concept of hyper-brain network, a connectivity pattern representing at once the information flow among the cortical regions of a single brain as well as the relations among the areas of two distinct brains. Graph analysis of hyper-brain networks constructed from the EEG scanning of 26 couples of individuals playing the Iterated Prisoner's Dilemma reveals the possibility to predict non-cooperative interactions during the decision-making phase. The hyper-brain networks of two-defector couples have significantly less inter-brain links and overall higher modularity - i.e. the tendency to form two separate subgraphs - than couples playing cooperative or tit-for-tat strategies. The decision to defect can be "read" in advance by evaluating the changes of connectivity pattern in the hyper-brain network

Disrupted in Schizophrenia 1 Regulates Neuronal Progenitor Proliferation via Modulation of GSK3β/β-Catenin Signaling

The Disrupted in Schizophrenia 1 (DISC1) gene is disrupted by a balanced chromosomal translocation (1; 11) (q42; q14.3) in a Scottish family with a high incidence of major depression, schizophrenia, and bipolar disorder. Subsequent studies provided indications that DISC1 plays a role in brain development. Here, we demonstrate that suppression of DISC1 expression reduces neural progenitor proliferation, leading to premature cell cycle exit and differentiation. Several lines of evidence suggest that DISC1 mediates this function by regulating GSK3β. First, DISC1 inhibits GSK3β activity through direct physical interaction, which reduces β-catenin phosphorylation and stabilizes β-catenin. Importantly, expression of stabilized β-catenin overrides the impairment of progenitor proliferation caused by DISC1 loss of function. Furthermore, GSK3 inhibitors normalize progenitor proliferation and behavioral defects caused by DISC1 loss of function. Together, these results implicate DISC1 in GSK3β/β-catenin signaling pathways and provide a framework for understanding how alterations in this pathway may contribute to the etiology of psychiatric disorders.National Alliance for Research on Schizophrenia and Depression (U.S.) (Young Investigator Award)Natural Sciences and Engineering Research Council of Canada (Postdoctoral Award)Human Frontier Science Program (Strasbourg, France) (Fellowship)Singleton FellowshipNational Institutes of Health (U.S.) (Grant NS37007

Number Fields Ramified at One Prime

Abstract. For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q) ∼ = G and disc(K) = ±pa for some a. We study the existence of G-p fields for fixed G and varying p. For G a finite group and p a prime, we define a G-p field to be a Galois number field K ⊂ C satisfying Gal(K/Q) ∼ = G and disc(K) = ±pa for some a. Let KG,p denote the finite, and often empty, set of G-p fields. The sets KG,p have been studied mainly from the point of view of fixing p and varying G; see [Har94], for example. We take the opposite point of view, as we fix G and let p vary. Given a finite group G, we let PG be the sequence of primes where each prime p is listed |KG,p | times. We determine, for various groups G, the first few primes in PG and their corresponding fields. Only the primes p dividing |G | can be wildly ramified in a G-p field, and so the sequences PG which are infinite are dominated by tamely ramified fields. In Sections 1, 2, and 3, we consider the cases when G is solvable with length 1, 2, and ≥ 3 respectively, using mainly class field theory. Section 4 deals wit

The disruption of GDP-fucose de novo biosynthesis suggests the presence of a novel fucose-containing glycoconjugate in <i>Plasmodium</i> asexual blood stages

Glycosylation is an important posttranslational protein modification in all eukaryotes. Besides glycosylphosphatidylinositol (GPI) anchors and N-glycosylation, O-fucosylation has been recently reported in key sporozoite proteins of the malaria parasite. Previous analyses showed the presence of GDP-fucose (GDP-Fuc), the precursor for all fucosylation reactions, in the blood stages of Plasmodium falciparum. The GDP-Fuc de novo pathway, which requires the action of GDP-mannose 4,6-dehydratase (GMD) and GDP-L-fucose synthase (FS), is conserved in the parasite genome, but the importance of fucose metabolism for the parasite is unknown. To functionally characterize the pathway we generated a PfGMD mutant and analyzed its phenotype. Although the labelling by the fucose-binding Ulex europaeus agglutinin I (UEA-I) was completely abrogated, GDP-Fuc was still detected in the mutant. This unexpected result suggests the presence of an alternative mechanism for maintaining GDP-Fuc in the parasite. Furthermore, PfGMD null mutant exhibited normal growth and invasion rates, revealing that the GDP-Fuc de novo metabolic pathway is not essential for the development in culture of the malaria parasite during the asexual blood stages. Nonetheless, the function of this metabolic route and the GDP-Fuc pool that is generated during this stage may be important for gametocytogenesis and sporogonic development in the mosquito

Continuous Three-Dimensional Control of a Virtual Helicopter Using a Motor Imagery Based Brain-Computer Interface

Brain-computer interfaces (BCIs) allow a user to interact with a computer system using thought. However, only recently have devices capable of providing sophisticated multi-dimensional control been achieved non-invasively. A major goal for non-invasive BCI systems has been to provide continuous, intuitive, and accurate control, while retaining a high level of user autonomy. By employing electroencephalography (EEG) to record and decode sensorimotor rhythms (SMRs) induced from motor imaginations, a consistent, user-specific control signal may be characterized. Utilizing a novel method of interactive and continuous control, we trained three normal subjects to modulate their SMRs to achieve three-dimensional movement of a virtual helicopter that is fast, accurate, and continuous. In this system, the virtual helicopter's forward-backward translation and elevation controls were actuated through the modulation of sensorimotor rhythms that were converted to forces applied to the virtual helicopter at every simulation time step, and the helicopter's angle of left or right rotation was linearly mapped, with higher resolution, from sensorimotor rhythms associated with other motor imaginations. These different resolutions of control allow for interplay between general intent actuation and fine control as is seen in the gross and fine movements of the arm and hand. Subjects controlled the helicopter with the goal of flying through rings (targets) randomly positioned and oriented in a three-dimensional space. The subjects flew through rings continuously, acquiring as many as 11 consecutive rings within a five-minute period. In total, the study group successfully acquired over 85% of presented targets. These results affirm the effective, three-dimensional control of our motor imagery based BCI system, and suggest its potential applications in biological navigation, neuroprosthetics, and other applications

IgG2 Antibodies against a Clinical Grade Plasmodium falciparum CSP Vaccine Antigen Associate with Protection against Transgenic Sporozoite Challenge in Mice

The availability of a highly purified and well characterized circumsporozoite protein (CSP) is essential to improve upon the partial success of recombinant CSP-based malaria vaccine candidates. Soluble, near full-length, Plasmodium falciparum CSP vaccine antigen (CS/D) was produced in E. coli under bio-production conditions that comply with current Good Manufacturing Practices (cGMP). A mouse immunogenicity study was conducted using a stable oil-in-water emulsion (SE) of CS/D in combination with the Toll-Like Receptor 4 (TLR4) agonist Glucopyranosyl Lipid A (GLA/SE), or one of two TLR7/8 agonists: R848 (un-conjugated) or 3M-051 (covalently conjugated). Compared to Alum and SE, GLA/SE induced higher CS/D specific antibody response in Balb/c mice. Subclass analysis showed higher IgG2:IgG1 ratio of GLA/SE induced antibodies as compared to Alum and SE. TLR synergy was not observed when soluble R848 was mixed with GLA/SE. Antibody response of 3M051 formulations in Balb/c was similar to GLA/SE, except for the higher IgG2:IgG1 ratio and a trend towards higher T cell responses in 3M051 containing groups. However, no synergistic enhancement of antibody and T cell response was evident when 3M051 conjugate was mixed with GLA/SE. In C57Bl/6 mice, CS/D adjuvanted with 3M051/SE or GLA/SE induced higher CSP repeat specific titers compared to SE. While, 3M051 induced antibodies had high IgG2c:IgG1 ratio, GLA/SE promoted high levels of both IgG1 and IgG2c. GLA/SE also induced more potent T-cell responses compared to SE in two independent C57/BL6 vaccination studies, suggesting a balanced and productive TH1/TH2 response. GLA and 3M-051 similarly enhanced the protective efficacy of CS/D against challenge with a transgenic P. berghei parasite and most importantly, high levels of cytophilic IgG2 antibodies were associated with protection in this model. Our data indicated that the cGMP-grade, soluble CS/D antigen combined with the TLR4-containing adjuvant GLA/SE warrants further evaluation for protective responses in humans