Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

The Valentiner group as Galois group

We obtain the complete set of solutions to the Galois embedding problem given by the Valentiner group as a triple cover of the alternatinggroup A6.

Synorogenic extension: Quantitative constraints on the age and displacement of the Zanskar shear zone (northwest Himalaya)

subsequent extension-induced exhumation. Geochronological dating of various Structural, thermobarometric, and geochronological data place limits on the age and tectonic displacement along the Zanskar shear zone, a major north-dipping synorogenic extensional structure separating the high-grade metamorphic sequence of the High Himalayan Crystalline Sequence from the overlying low-grade sedimentary rocks of the Tethyan Himalaya, A complete Barrovian metamorphic succession, from kyanite to biotite zone mineral assemblages, occurs within the I-km-thick Zanskar shear zone. Thermobarometric data indicate a difference In equilibration depths of 12 +/- 3 km between the lower kyanite zone and the garnet zone, which is Interpreted as a minimum estimate for the finite vertical displacement accommodated by the Zanskar shear zone. For the present-day dip of the structure (20 degrees), a simple geometrical model shows that a net slip of 35 +/- 9 km is required to regroup these samples to the same structural level. Because the kyanite to garnet zone rocks represent only part of the Zanskar shear zone, and because its original dip may have been less than the present-day dip, these estimates fur the finite displacement represent minimum values. Field relations and petrographic data suggest that migmatization and associated leucogranite intrusion in the footwall of the Zanskar shear zone occurred as a continuous profess starting at the Barrovian metamorphic peak and lasting throughout the subsequent extension-induced exhumation. Geochronological dataing of various leucogranitic plutons and dikes in the Zanskar shear zone footwall indicates that the main ductile shearing along the structure ended by 19.8 Ma and that extension most likely initiated shortly before 22.2 Ma.

Characterization of lower-limbs inter-segment coordination during the take-off extension in ski jumping.

Take-off, the most important phase in ski jumping, has been primarily studied in terms of spatio-temporal parameters; little is known about its motor control aspects. This study aims to assess the inter-segment coordination of the shank-thigh and thigh-sacrum pairs using the continuous relative phase (CRP). In total 87 jumps were recorded from 33 athletes with an inertial sensor-based system. The CRP curves indicated that the thighs lead the shanks during the first part of take-off extension and that the shanks rotated faster at the take-off extension end. The thighs and sacrum first rotated synchronously, with the sacrum then taking lead, with finally the thighs rotating faster. Five characteristic features were extracted from the CRP and their relationship with jump length was tested. Three features of the shank-thigh pair and one of the thigh-sacrum pair reported a significant association with jump length. It was observed that athletes who achieved longer jumps had their thighs leading their shanks during a longer time, with these athletes also having a more symmetric movement between thighs and sacrum. This study shows that inter-segment coordination during the take-off extension is related to performance and further studies are necessary to contrast its importance with other ski jumping aspects.

Squamous cell carcinoma of the larynx with subglottic extension: is larynx preservation possible?. Plattenepithelkarzinom des Larynx mit subglottischer Ausdehnung: ist ein Larynxerhalt möglich ?

PURPOSE: Squamous cell carcinoma of larynx with subglottic extension (sSCC) is a rare location described to carry a poor prognosis. The aim of this study was to analyze outcomes and feasibility of larynx preservation in sSCC patients. PATIENTS AND METHODS: Between 1996 and 2012, 197 patients with sSCC were treated at our institution and included in the analysis. Stage III-IV tumors accounted for 76 %. Patients received surgery (62 %), radiotherapy (RT) (18 %), or induction chemotherapy (CT) (20 %) as front-line therapy. RESULTS: The 5-year actuarial overall survival (OS), locoregional control (LRC), and distant control rate were 59 % (95 % CI 51-68), 83 % (95 % CI 77-89), and 88 % (95 % CI 83-93), respectively, with a median follow-up of 54.4 months. There was no difference in OS and LRC according to front-line treatments or between primary subglottic cancer and glottosupraglottic cancers with subglottic extension. In the multivariate analysis, age > 60 years and positive N stage were the only predictors for OS (HR 2, 95 % CI 1.2-3.6; HR1.9, 95 % CI 1-3.5, respectively). A lower LRC was observed for T3 patients receiving a larynx preservation protocol as compared with those receiving a front-line surgery (HR 14.1, 95 % CI 2.5-136.7; p = 0.02); however, no difference of ultimate LRC was observed according to the first therapy when including T3 patients who underwent salvage laryngectomy (p = 0.6). In patients receiving a larynx preservation protocol, the 5-year larynx-preservation rate was 55 % (95 % CI 43-68), with 36 % in T3 patients. The 5-year larynx preservation rate was 81 % (95 % CI 65-96) and 35 % (95 % CI 20-51) for patients who received RT or induction CT as a front-line treatment, respectively. CONCLUSION: Outcomes of sSCC are comparable with other laryngeal cancers when managed with modern therapeutic options. Larynx-preservation protocols could be a suitable option in T1-T2 (RT or chemo-RT) and selected T3 sSCC patients (induction CT).

Bailey Avenue extension, dedication, September 4, 1986

Program from the dedication ceremony of the Bailey Avenue Extension from the RISE Program : "Revitalize Iowa's Sound Economy" program for the construction and improvement of Iowa's roads.

Instrumental leadership: An extension of the Full-Range Leadership Theory

From a theoretical perspective, an extension to the Full Range leadership Theory (FRLT) seems needed. In this paper, we explain why instrumental leadership--a class of leadership includes leader behaviors focusing on task and strategic aspects that are neither values nor exchange oriented--can fulfill this extension. Instrument leadership is composed of four factors: environmental monitoring, strategy formulation and implementation, path-goal facilitation and outcome monitoring; these aspects of leadership are currently not included in any of the FRLT's nine leadership scales (as measured by the MLQ--Multifactor Leadership Questionnaire). We present results from two empirical studies using very large samples from a wide array of countries (N > 3,000) to examine the factorial, discriminant and criterion-related validity of the instrumental leadership scales. We find support for a four-factor instrumental leadership model, which explains incremental variance in leader outcomes in over and above transactional and transformational leadership.

The Iowa State Capitol Grounds 1913 Extension and Reconstruction Project, October 2012

The Capitol grounds have been evolving through planned and unplanned actions for more than 150 years. The 1857 Constitutio established Des Moines as the capital. The commissioners appointed to choose a site decided on land donated by Wilson Alexander Scott and Harrison Lyon. Located on the east side of the Des Moines River, on a gently rising hill, the site for the Iowa State Capitol began with fewer than 10 acres. The Old Brick Capitol was built in the center of that 10-acre plot, and the area to the north was used as a public park until work began on the present day Capitol. In 1884, the two-year process of moving from the Old Brick Capitol to the new Capitol began. The state commissioned John Weidenman to design the first formal decoration of the grounds. Weidenman’s plans for the west approach to the Capitol included planting statues, and walkways. The State held some additional land but not necessarily land adjacent to the Capitol. In 1909, legislation was passed, and in 1913, the Thirty-Fifth General Assembly enacted controversial legislation to acquire additional land. A commission was formed to locate a purposed monument honoring the long-serving U.S. Senator William B. Allison. E.L. Masqueray was hired as the architect expert focusing on the selection of a proper site for the proposed Allison Memorial. Masqueray’s plan detailed the placement of buildings and potential monuments. Growth of the Capitol Complex, as known today, began.