The nil Hecke ring and singularity of Schubert varieties

We give a criterion for smoothness of a point in any Schubert variety in any G/B in terms of the nil Hecke ring.Comment: AMSTE

Derivatives for smooth representations of GL(n,R) and GL(n,C)

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations by S. Sahi and called the "adduced" representation. In this paper we define derivatives of all order for smooth admissible Frechet representations (of moderate growth). The archimedean case is more problematic than the p-adic case; for example arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation. In [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS12].Comment: First version of this preprint was split into 2. The proofs of two theorems which are technically involved in analytic difficulties were separated into "Twisted homology for the mirabolic nilradical" preprint. All the rest stayed in v2 of this preprint. v3: version to appear in the Israel Journal of Mathematic

Finding Apparent Horizons in Dynamic 3D Numerical Spacetimes

We have developed a general method for finding apparent horizons in 3D numerical relativity. Instead of solving for the partial differential equation describing the location of the apparent horizons, we expand the closed 2D surfaces in terms of symmetric trace--free tensors and solve for the expansion coefficients using a minimization procedure. Our method is applied to a number of different spacetimes, including numerically constructed spacetimes containing highly distorted axisymmetric black holes in spherical coordinates, and 3D rotating, and colliding black holes in Cartesian coordinates.Comment: 19 pages, 13 figures, LaTex, to appear in Phys. Rev. D. Minor changes mad

Transduction of the Geomagnetic Field as Evidenced from Alpha-band Activity in the Human Brain

Magnetoreception, the perception of the geomagnetic field, is a sensory modality well-established across all major groups of vertebrates and some invertebrates, but its presence in humans has been tested rarely, yielding inconclusive results. We report here a strong, specific human brain response to ecologically-relevant rotations of Earth-strength magnetic fields. Following geomagnetic stimulation, a drop in amplitude of EEG alpha oscillations (8-13 Hz) occurred in a repeatable manner. Termed alpha event-related desynchronization (alpha-ERD), such a response has been associated previously with sensory and cognitive processing of external stimuli including vision, auditory and somatosensory cues. Alpha-ERD in response to the geomagnetic field was triggered only by horizontal rotations when the static vertical magnetic field was directed downwards, as it is in the Northern Hemisphere; no brain responses were elicited by the same horizontal rotations when the static vertical component was directed upwards. This implicates a biological response tuned to the ecology of the local human population, rather than a generic physical effect. Biophysical tests showed that the neural response was sensitive to static components of the magnetic field. This rules out all forms of electrical induction (including artifacts from the electrodes) which are determined solely on dynamic components of the field. The neural response was also sensitive to the polarity of the magnetic field. This rules out free-radical 'quantum compass' mechanisms like the cryptochrome hypothesis, which can detect only axial alignment. Ferromagnetism remains a viable biophysical mechanism for sensory transduction and provides a basis to start the behavioral exploration of human magnetoreception

A New Microlensing Event in the Doubly-Imaged Quasar Q0957+561

We present evidence for ultraviolet/optical microlensing in the gravitationally lensed quasar Q0957+561. We combine new measurements from our optical monitoring campaign at the United States Naval Observatory, Flagstaff (USNO) with measurements from the literature and find that the time-delay-corrected r-band flux ratio m_A - m_B has increased by ~0.1 magnitudes over a period of five years beginning in the fall of 2005. We apply our Monte Carlo microlensing analysis procedure to the composite light curves, obtaining a measurement of the optical accretion disk size, log {(r_s/cm)[cos(i)/0.5]^{1/2}} = 16.2^{+0.5}_{-0.6}, that is consistent with the quasar accretion disk size - black hole mass relation.Comment: Replaced with accepted version. Minor adjustments to text but conclusions unchanged. Data in Table 2 have been updated and table now includes additional observation

The Central Component of Gravitational Lens Q0957+561

In 1981, a faint radio source (G') was detected near the center of the lensing galaxy of the famous "twin quasar" Q0957+561. It is still unknown whether this central radio source is a third quasar image or an active nucleus of the lensing galaxy, or a combination of both. In an attempt to resolve this ambiguity, we observed Q0957+561 at radio wavelengths of 13cm, 18cm, and 21cm, using the Very Long Baseline Array in combination with the phased Very Large Array and the Green Bank Telescope. We measured the spectrum of G' for the first time and found it to be significantly different from the spectra of the two bright quasar images. This finding suggests that the central component is primarily or entirely emission from the foreground lens galaxy, but the spectrum is also consistent with the hypothesis of a central quasar image suffering free-free absorption. In addition, we confirm the previously-reported VLBI position of G' just north of the optical center of the lens galaxy. The position slightly favors the hypothesis that G' originates in the lens, but is not conclusive. We discuss the prospects for further clarification of this issue.Comment: 18 pages, accepted for publication in A

Social determinants of health in prognostic machine learning models for orthopaedic outcomes: A systematic review

Rational: Social determinants of health (SDOH) are being considered more frequently when providing orthopaedic care due to their impact on treatment outcomes. Simultaneously, prognostic machine learning (ML) models that facilitate clinical decision making have become popular tools in the field of orthopaedic surgery. When ML-driven tools are developed, it is important that the perpetuation of potential disparities is minimized. One approach is to consider SDOH during model development. To date, it remains unclear whether and how existing prognostic ML models for orthopaedic outcomes consider SDOH variables. Objective: To investigate whether prognostic ML models for orthopaedic surgery outcomes account for SDOH, and to what extent SDOH variables are included in the final models. Methods: A systematic search was conducted in PubMed, Embase and Cochrane for studies published up to 17 November 2020. Two reviewers independently extracted SDOH features using the PROGRESS+ framework (place of residence, race/ethnicity, Occupation, gender/sex, religion, education, social capital, socioeconomic status, ‘Plus+’ age, disability, and sexual orientation). Results: The search yielded 7138 studies, of which 59 met the inclusion criteria. Across all studies, 96% (57/59) considered at least one PROGRESS+ factor during development. The most common factors were age (95%; 56/59) and gender/sex (96%; 57/59). Differential effect analyses, such as subgroup analysis, covariate adjustment, and baseline comparison, were rarely reported (10%; 6/59). The majority of models included age (92%; 54/59) and gender/sex (69%; 41/59) as final input variables. However, factors such as insurance status (7%; 4/59), marital status (7%; 4/59) and income (3%; 2/59) were seldom included. Conclusion: The current level of reporting and consideration of SDOH during the development of prognostic ML models for orthopaedic outcomes is limited. Healthcare providers should be critical of the models they consider using and knowledgeable regarding the quality of model development, such as adherence to recognized methodological standards. Future efforts should aim to avoid bias and disparities when developing ML-driven applications for orthopaedics

Identification of sex hormone-binding globulin in the human hypothalamus

Gonadal steroids are known to influence hypothalamic functions through both genomic and non-genomic pathways. Sex hormone-binding globulin ( SHBG) may act by a non-genomic mechanism independent of classical steroid receptors. Here we describe the immunocytochemical mapping of SHBG-containing neurons and nerve fibers in the human hypothalamus and infundibulum. Mass spectrometry and Western blot analysis were also used to characterize the biochemical characteristics of SHBG in the hypothalamus and cerebrospinal fluid (CSF) of humans. SHBG-immunoreactive neurons were observed in the supraoptic nucleus, the suprachiasmatic nucleus, the bed nucleus of the stria terminalis, paraventricular nucleus, arcuate nucleus, the perifornical region and the medial preoptic area in human brains. There were SHBG-immunoreactive axons in the median eminence and the infundibulum. A partial colocalization with oxytocin could be observed in the posterior pituitary lobe in consecutive semithin sections. We also found strong immunoreactivity for SHBG in epithelial cells of the choroid plexus and in a portion of the ependymal cells lining the third ventricle. Mass spectrometry showed that affinity-purified SHBG from the hypothalamus and choroid plexus is structurally similar to the SHBG identified in the CSF. The multiple localizations of SHBG suggest neurohypophyseal and neuroendocrine functions. The biochemical data suggest that CSF SHBG is of brain rather than blood origin. Copyright (c) 2005 S. Karger AG, Base

S-CAP extends pathogenicity prediction to genetic variants that affect RNA splicing

Exome analysis of patients with a likely monogenic disease does not identify a causal variant in over half of cases. Splice-disrupting mutations make up the second largest class of known disease-causing mutations. Each individual (singleton) exome harbors over 500 rare variants of unknown significance (VUS) in the splicing region. The existing relevant pathogenicity prediction tools tackle all non-coding variants as one amorphic class and/or are not calibrated for the high sensitivity required for clinical use. Here we calibrate seven such tools and devise a novel tool called Splicing Clinically Applicable Pathogenicity prediction (S-CAP) that is over twice as powerful as all previous tools, removing 41% of patient VUS at 95% sensitivity. We show that S-CAP does this by using its own features and not via meta-prediction over previous tools, and that splicing pathogenicity prediction is distinct from predicting molecular splicing changes. S-CAP is an important step on the path to deriving non-coding causal diagnoses

Crystallographic Education in the 21st Century

There are many methods that can be used to incorporate concepts of crystallography into the learning experiences of students, whether they are in elementary school, at university or part of the public at large. It is not always critical that those who teach crystallography have immediate access to diffraction equipment to be able to introduce the concepts of symmetry, packing or molecular structure in an age- and audience-appropriate manner. Crystallography can be used as a tool for teaching general chemistry concepts as well as general research techniques without ever having a student determine a crystal structure. Thus, methods for younger students to perform crystal growth experiments of simple inorganic salts, organic compounds and even metals are presented. For settings where crystallographic instrumentation is accessible (proximally or remotely), students can be involved in all steps of the process, from crystal growth, to data collection, through structure solution and refinement, to final publication. Several approaches based on the presentations in the MS92 Microsymposium at the IUCr 23rd Congress and General Assembly are reported. The topics cover methods for introducing crystallography to undergraduate students as part of a core chemistry curriculum; a successful short-course workshop intended to bootstrap researchers who rely on crystallography for their work; and efforts to bring crystallography to secondary school children and non-science majors. In addition to these workshops, demonstrations and long-format courses, open-format crystallographic databases and three-dimensional printed models as tools that can be used to excite target audiences and inspire them to pursue a deeper understanding of crystallography are described