On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3: corrections in the table with unipotent discrete series of G

Motion corrected 3D reconstruction of the fetal thorax from prenatal MRI

In this paper we present a semi-automatic method for analysis of the fetal thorax in genuine three-dimensional volumes. After one initial click we localize the spine and accurately determine the volume of the fetal lung from high resolution volumetric images reconstructed from motion corrupted prenatal Magnetic Resonance Imaging (MRI). We compare the current state-of-the-art method of segmenting the lung in a slice-by-slice manner with the most recent multi-scan reconstruction methods. We use fast rotation invariant spherical harmonics image descriptors with Classification Forest ensemble learning methods to extract the spinal cord and show an efficient way to generate a segmentation prior for the fetal lung from this information for two different MRI field strengths. The spinal cord can be segmented with a DICE coefficient of 0.89 and the automatic lung segmentation has been evaluated with a DICE coefficient of 0.87. We evaluate our method on 29 fetuses with a gestational age (GA) between 20 and 38 weeks and show that our computed segmentations and the manual ground truth correlate well with the recorded values in literature

The subconvexity problem for \GL_{2}

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of \GL_{1} and \GL_{2} automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda.Comment: Almost final version to appear in Publ. Math IHES. References updated

Eisenstein series for infinite-dimensional U-duality groups

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E_n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E9, E10 and E11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D<3 space-time dimensions.Comment: 69 pages. v2: Added references and small additions, to be published in JHE

Sur les paquets d'Arthur des groupes classiques et unitaires non quasi-d\'eploy\'es

15 pages, in FrenchNous \'etendons aux groupes orthogonaux et unitaires non quasi-d\'eploy\'es sur un corps local des r\'esultats de J. Arthur et de la premi\`ere auteure \'etablis dans le cas quasi-d\'eploy\'e. En particulier, nous obtenons une classification de Langlands compl\`ete pour les repr\'esentations temp\'er\'ees dans le cas $p$-adique. Nous en d\'eduisons en utilisant l'involution d'Aubert-Schneider-Stuhler un r\'esultat de multiplicit\'e un dans les paquets unipotents, et par des m\'ethodes globales, le m\^eme r\'esultat pour les paquets unipotents dans le cas archim\'edien. We extend to non quasi-split orthogonal and unitary groups over a local field some results of J. Arthur and the first author established in the quasi-split case. In particular, we obtain a full Langlands classification for tempered representations in the $p$-adic case. Using Aubert-Schneider-Stuhler involution, we deduce from this a multiplicity one result for unipotent packets, and by global methods, the same result for unipotent packets in the archimedean case

Petrology, geochemistry, and geochronology of Proterozoic granitoid and related rocks of the northern Mummy Range, north-central Colorado

Detailed geologic mapping in the northern Mummy Range, north-central Colorado, reveals seven distinguishable igneous granitoid rock units intruded into a sequence of high-grade metamorphic host rocks. U-Pb dating of zircons from twelve samples indicates that these granitoids were emplaced during two separate periods of magmatism about 300 m.y. apart, one in the Paleoproterozoic and another in the Mesoproterozoic. Zircon dating confirms that all of this magmatic activity post-dated the peak of Paleoproterozoic metamorphism in this area. Based on field, geochemical and mineralogical analyses, four distinct Paleoproterozoic granitoid rock units are interpreted to represent three separate, but geochronologically indistinguishable, magmatic events at ∼1.7 Ga. The earliest igneous event is recorded by a body of leucocratic tonalite which yields a zircon age of 1702 ± 6 Ma. The second event is recorded by small bodies of granodiorite which are mineralogically and geochemically very similar to the approximately contemporaneous Boulder Creek Granodiorite exposed to the south. The third Paleoproterozoic igneous event produced foliated granitoid rocks that yield a composite zircon age of 1695 ± 20 Ma and which comprise two distinct lithologies: a melanocratic roof facies and a strongly foliated monzogranite. This foliated Paleoproterozoic monzogranite, which is geochemically and mineralogically indistinguishable from the approximately contemporaneous Rawah batholith exposed to the northwest, is the most widespread rock unit exposed in the northern Mummy Range, accounting for over 65% of the area of the Comanche Peak quadrangle north of the Skin Gulch shear zone. The earliest Mesoproterozoic igneous event in the northern Mummy Range is represented by small bodies of coarse-grained quartz diorite. The second Mesoproterozoic event is represented by the strongly porphyritic granodiorite of the Hagues Peak pluton. The third and final Mesoproterozoic igneous event in the area produced widespread bodies of equigranular “Silver-Plume-type” peraluminous monzogranite that yields a zircon age of 1393 ± 25 Ma. Most of our zircon ages for the Mummy Range granitoids are consistent with the most recent synthesis of models for the tectonic evolution of the Proterozoic Colorado province. Our dates for certain individual samples of the Paleoproterozoic granodiorite and foliated Paleoproterozoic monzogranite suggest that Paleoproterozoic syntectonic plutonism may have continued slightly longer in this area than previously recognized. The mineralogy and geochemistry of most of the Mummy Range granitoids are consistent with current tectonic syntheses of the region. The composition of the foliated Paleoproterozoic monzogranite in the Mummy Range suggests a source that included pre-existing continental crustal material, consistent with recent suggestions of \u3c1.8-Ga crustal basement beneath parts of the Colorado province

Predominant polarity in bipolar disorder patients: The COPE bipolar sample

Background: The concept of predominant polarity (PP) is defined as presenting more symptoms of one polarity. Previous studies have defined PP as one polarity (either a depression or mania episode) occurring during at least two-thirds of the lifetime. Methods: We conducted an observational study with the COPE-BD (Clinical Outcome and Psycho-Education for Bipolar Disorder, Clinical Outcome Measures Section) dataset to identify the diagnostic and treatment differences between bipolar disorder (BD) patients with and without PP. Results: The final sample included 210 BD-I (59.0%) and 146 BD-II (41.0%) patients. Of these, 28.9% patients presented predominant polarity (PP): 62 (17.4%) of those patients were depressed polarity predominant (DPP), 41 (11.5%) were manic polarity predominant (MPP), and 253 (71.1%) met criteria for bipolar disorders but did not present with PP. In comparison to this group of BD patients with undetermined polarity, the group of BD patients with PP presented more rapid cycling. Furthermore, in the undetermined polarity group, the onset of illness occurred earlier, and the duration of the illness was longer, with more hypomanic/manic and depressive episodes than patients who met the PP criteria. Limitations: This study has a naturalistic and retrospective design and does not allow a specific follow-up of polarity over time. Conclusions: These different clinical characteristics underline the importance of considering PP in patients with BD, and justify the need for differential treatment approach which could have an impact on patients' prognosis. Yet, more independent and prospective research is needed to confirm these findings, especially with the new classification of DSM-5 concerning mixed states