Some Weyl modules of the algebraic groups of type E6E_6

Let $G$ be a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic $p>0$. We determine the submodule structure of the Weyl modul es with highest weight $r\omega_1$ for $0\leq r\leq p-1$, where $\omega_1$ is the fundamental weight of the standard $27$-dimensional module. In the process, the structures of other Weyl modules with highest weights linked to $r\omega_1$ are also found. %We also give some computations for the Weyl modules with highest weights %of the form $r(\omega_1+\omega_6)$, which arise in the study of %the graph automorphism and associated twisted finite groups.Comment: 25 page

Local Projections of Low-Momentum Potentials

Nuclear interactions evolved via renormalization group methods to lower resolution become increasingly non-local (off-diagonal in coordinate space) as they are softened. This inhibits both the development of intuition about the interactions and their use with some methods for solving the quantum many-body problem. By applying "local projections", a softened interaction can be reduced to a local effective interaction plus a non-local residual interaction. At the two-body level, a local projection after similarity renormalization group (SRG) evolution manifests the elimination of short-range repulsive cores and the flow toward universal low-momentum interactions. The SRG residual interaction is found to be relatively weak at low energy, which motivates a perturbative treatment

Frobenius Splittings

We give a gentle introduction to Frobenius splittings. Then we recall a few results that have been obtained with the method.Comment: 21 pages, typos correcte

Multi-view Face Detection Using Deep Convolutional Neural Networks

In this paper we consider the problem of multi-view face detection. While there has been significant research on this problem, current state-of-the-art approaches for this task require annotation of facial landmarks, e.g. TSM [25], or annotation of face poses [28, 22]. They also require training dozens of models to fully capture faces in all orientations, e.g. 22 models in HeadHunter method [22]. In this paper we propose Deep Dense Face Detector (DDFD), a method that does not require pose/landmark annotation and is able to detect faces in a wide range of orientations using a single model based on deep convolutional neural networks. The proposed method has minimal complexity; unlike other recent deep learning object detection methods [9], it does not require additional components such as segmentation, bounding-box regression, or SVM classifiers. Furthermore, we analyzed scores of the proposed face detector for faces in different orientations and found that 1) the proposed method is able to detect faces from different angles and can handle occlusion to some extent, 2) there seems to be a correlation between dis- tribution of positive examples in the training set and scores of the proposed face detector. The latter suggests that the proposed methods performance can be further improved by using better sampling strategies and more sophisticated data augmentation techniques. Evaluations on popular face detection benchmark datasets show that our single-model face detector algorithm has similar or better performance compared to the previous methods, which are more complex and require annotations of either different poses or facial landmarks.Comment: in International Conference on Multimedia Retrieval 2015 (ICMR

Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems

We investigate the scalar K pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t=0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher order ChPT corrections at the second Callan-Treiman point.Comment: 5 pages latex, uses EPJ style files, 3 figures, replaced with version accepted by EPJ

Improvement in medication education in a pediatric subspecialty practice

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to measure the impact of an educational intervention on parents of children taking methotrexate (MTX) for juvenile idiopathic arthritis (JIA).</p> <p>Methods</p> <p>This study was conducted using a pre- and postsurvey design. The parents of 100 children with JIA taking MTX for at least 2 months were surveyed during a routine office visit. The parents completed an initial questionnaire regarding the safe use, adverse effects, and guidelines for monitoring the toxicity of MTX. An educational intervention was then administered, and an identical follow-up questionnaire was given during the next office visit. Statistical analysis using a paired <it>t</it>-test (critical <it>P </it>value < 0.05) was performed on individuals who answered both questionnaires.</p> <p>Results</p> <p>There were 100 responses to the initial questionnaire and 67 responses to the follow-up questionnaire. The mean length of time between surveys was 2.9 ± 0.9 months. In those who completed both questionnaires, the overall correct score increased significantly from 75.8% to 93.4%, respectively (<it>P </it>< 0.0001). Individuals scored the lowest (49%) on the question that addressed MTX's impact on pregnancy and fertility.</p> <p>Conclusions</p> <p>MTX knowledge may be less than expected in the parents of children with JIA. Brief educational interventions in the pediatric subspecialty practice can significantly affect a family's understanding of their child's medications.</p

Stability of homogeneous bundles on P^3

We study the stability of some homogeneous bundles on P^3 by using their representations of the quiver associated to the homgeneous bundles on P^3. In particular we show that homogeneous bundles on P^3 whose support of the quiver representation is a parallelepiped are stable, for instance the bundles E whose minimal free resolution is of the kind 0 --> S^{l_1, l_2, l_3} V (t) --> S^{l_1 +s, l_2, l_3} V (t+s) --> E --> 0 are stable.Comment: to appear in Geometriae Dedicata http://www.springer.com/mathematics/geometry/journal/1071