An adjunction formula for the Emerton-Jacquet functor

The Emerton–Jacquet functor is a tool for studying locally analytic representations of p-adic Lie groups. It provides a way to access the theory of p-adic automorphic forms. Here we give an adjunction formula for the Emerton–Jacquet functor, relating it directly to locally analytic inductions, under a strict hypothesis that we call non-critical. We also further study the relationship to socles of principal series in the non-critical setting

Universal deformation rings for the symmetric group S_4

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Let S_4 denote the symmetric group on 4 letters. We determine the universal deformation ring R(S_4,V) for every kS_4-module V which has stable endomorphism ring k and show that R(S_4,V) is isomorphic to either k, or W[t]/(t^2,2t), or the group ring W[Z/2]. This gives a positive answer in this case to a question raised by the first author and Chinburg whether the universal deformation ring of a representation of a finite group with stable endomorphism ring k is always isomorphic to a subquotient ring of the group ring over W of a defect group of the modular block associated to the representation.Comment: 12 pages, 2 figure

Color improves edge classification in human vision

Data Availability Statement: All relevant data are within the manuscript and its Supporting Information files.© 2019 Breuil et al. Despite the complexity of the visual world, humans rarely confuse variations in illumination, for example shadows, from variations in material properties, such as paint or stain. This ability to distinguish illumination from material edges is crucial for determining the spatial layout of objects and surfaces in natural scenes. In this study, we explore the role that color (chromatic) cues play in edge classification. We conducted a psychophysical experiment that required subjects to classify edges into illumination and material, in patches taken from images of natural scenes that either contained or did not contain color information. The edge images were of various sizes and were pre-classified into illumination and material, based on inspection of the edge in the context of the whole image from which the edge was extracted. Edge classification performance was found to be superior for the color compared to grayscale images, in keeping with color acting as a cue for edge classification. We defined machine observers sensitive to simple image properties and found that they too classified the edges better with color information, although they failed to capture the effect of image size observed in the psychophysical experiment. Our findings are consistent with previous work suggesting that color information facilitates the identification of material properties, transparency, shadows and the perception of shape-from-shading.IDEX; Canadian Institute of Health. The study was supported by a travel grant from IDEX given to CB and a Canadian Institute of Health Research grant #MOP 123349 given to FK. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Urinary peptidome analyses for the diagnosis of chronic kidney disease in dogs

Chronic kidney disease (CKD) is clinically important in canine medicine. Current diagnostic tools lack sensitivity for detection of subclinical CKD. The aim of the present study was to evaluate urinary peptidome analysis for diagnosis of CKD in dogs. Capillary electrophoresis coupled to mass spectrometry analysis demonstrated presence of approximately 5400 peptides in dog urine. Comparison of urinary peptide abundance of dogs with and without CKD led to the identification of 133 differentially excreted peptides (adjusted P for each peptide <0.05). Sequence information was obtained for 35 of these peptides. This 35 peptide subset and the total group of 133 peptides were used to construct two predictive models of CKD which were subsequently validated by researchers masked to results in an independent cohort of 20 dogs. Both models diagnosed CKD with an area under the receiver operating characteristic (ROC) curve of 0.88 (95% confidence intervals [CI], 0.72–1.0). Most differentially excreted peptides represented fragments of collagen I, indicating possible association with fibrotic processes in CKD (similar to the equivalent human urinary peptide CKD model, CKD273). This first study of the urinary peptidome in dogs identified peptides that were associated with presence of CKD. Future studies are needed to validate the utility of this model for diagnosis and prediction of progression of canine CKD in a clinical setting

Elliptic curves of large rank and small conductor

For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabulate, for each r=5,6,...,11, the five curves of lowest conductor, and (except for r=11) also the five of lowest absolute discriminant, that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after comments by J.Silverman on the previous draft, and again to get the correct page break

Elliptic Curves over Real Quadratic Fields are Modular

We prove that all elliptic curves defined over real quadratic fields are modular.Comment: 38 pages. Magma scripts available as ancillary files with this arXiv versio

2012 update of French guidelines for the pharmacological treatment of postmenopausal osteoporosis

OBJECTIVES: To update the evidence-based position statement published by the French National Authority for Health (HAS) in 2006 regarding the pharmacological treatment of postmenopausal osteoporosis, under the auspices of the French Society for Rheumatology and Groupe de Recherche et d\u27Information sur les Ostéoporoses (GRIO), and with the participation of several learned societies (Collège National des Gynécologues et Obstétriciens Français, Groupe d\u27Étude de la Ménopause et du Vieillissement hormonal, Société Française de Chirurgie Orthopédique, Société Française d\u27Endocrinologie, and Société Française de Gériatrie et de Gérontologie). METHODS: A multidisciplinary panel representing the spectrum of clinical specialties involved in managing patients with postmenopausal osteoporosis developed updated recommendations based on a systematic literature review conducted according to the method advocated by the HAS. RESULTS: The updated recommendations underline the need for osteoporosis pharmacotherapy in women with a history of severe osteoporotic fracture. In these patients, any osteoporosis medication can be used; however, zoledronic acid is the preferred first-line medication after a hip fracture. In patients with non-severe fractures or no fractures, the appropriateness of osteoporosis pharmacotherapy depends on the bone mineral density and FRAX(®) values; any osteoporosis medication can be used, but raloxifene and ibandronate should be reserved for patients at low risk for peripheral fractures. Initially, osteoporosis pharmacotherapy should be prescribed for 5 years. The results of the evaluation done at the end of the 5-year period determine whether further treatment is in order. CONCLUSIONS: These updated recommendations are intended to provide clinicians with clarifications about the pharmacological treatment of osteoporosis

Eisenstein Series of Weight One, q-Averages of the 0-Logarithm and Periods of Elliptic Curves

For any elliptic curve E over k ⊂ R with E(C) = C^×/q^Z, q = e^(2πiz),Im(z) >, we study the q-average D_(0,q), defined on E(C), of the function D_0(z) = Im(z/(1−z)). Let Ω+(E) denote the real period of E. We show that there is a rational function R ∈ Q(X_1(N)) such that for any non-cuspidal real point s ∈ X_1(N) (which defines an elliptic curve E(s) over R together with a point P(s) of order N), πD_(0,q)(P(s)) equals Ω+(E(s))R(s). In particular, if s is Q-rational point of X_1(N), a rare occurrence according to Mazur, R(s) is a rational number

Actions infinit\'esimales dans la correspondance de Langlands locale p-adique

Let V be a two-dimensional absolutely irreducible p-adic Galois representation and let Pi be the p-adic Banach space representation associated to V via Colmez's p-adic Langlands correspondence. We establish a link between the infinitesimal action of GL_2(Q_p) on the locally analytic vectors of Pi, the differential equation associated to V via the theory of Fontaine and Berger, and the Sen polynomial of V. This answers a question of Harris and gives a new proof of a theorem of Colmez: Pi has nonzero locally algebraic vectors if and only if V is potentially semi-stable with distinct Hodge-Tate weights.Comment: Completely revised version, to appear in Math. Annale