Automorphism groupoids in noncommutative projective geometry

We address a natural question in noncommutative geometry, namely the rigidity observed in many examples, whereby noncommutative spaces (or equivalently their coordinate algebras) have very few automorphisms by comparison with their commutative counterparts. In the framework of noncommutative projective geometry, we define a groupoid whose objects are noncommutative projective spaces of a given dimension and whose morphisms correspond to isomorphisms of these. This groupoid is then a natural generalization of an automorphism group. Using work of Zhang, we may translate this structure to the algebraic side, wherein we consider homogeneous coordinate algebras of noncommutative projective spaces. The morphisms in our groupoid precisely correspond to the existence of a Zhang twist relating the two coordinate algebras. We analyse this automorphism groupoid, showing that in dimension 1 it is connected, so that every noncommutative $\mathbb{P}^{1}$ is isomorphic to commutative $\mathbb{P}^{1}$. For dimension 2 and above, we use the geometry of the point scheme, as introduced by Artin-Tate-Van den Bergh, to relate morphisms in our groupoid to certain automorphisms of the point scheme. We apply our results to two important examples, quantum projective spaces and Sklyanin algebras. In both cases, we are able to use the geometry of the point schemes to fully describe the corresponding component of the automorphism groupoid. This provides a concrete description of the collection of Zhang twists of these algebras.Comment: 27 pages; v2: minor corrections and additional reference

Automorphism groupoids in noncommutative projective geometry

We address a natural question in noncommutative geometry, namely the rigidity observed in many examples, whereby noncommutative spaces (or equivalently their coordinate algebras) have very few automorphisms by comparison with their commutative counterparts. In the framework of noncommutative projective geometry, we define a groupoid whose objects are noncommutative projective spaces of a given dimension and whose morphisms correspond to isomorphisms of these. This groupoid is then a natural generalization of an automorphism group. Using work of Zhang, we may translate this structure to the algebraic side, wherein we consider homogeneous coordinate algebras of noncommutative projective spaces. The morphisms in our groupoid precisely correspond to the existence of a Zhang twist relating the two coordinate algebras. We analyse this automorphism groupoid, showing that in dimension 1 it is connected, so that every noncommutative ℙ1 is isomorphic to commutative ℙ1. For dimension 2 and above, we use the geometry of the point scheme, as introduced by Artin-Tate-Van den Bergh, to relate morphisms in our groupoid to certain automorphisms of the point scheme. We apply our results to two important examples, quantum projective spaces and Sklyanin algebras. In both cases, we are able to use the geometry of the point schemes to fully describe the corresponding component of the automorphism groupoid. This provides a concrete description of the collection of Zhang twists of these algebras

PATH-38. ROSETTE-FORMING GLIONEURONAL TUMOR IS DEFINED BY FGFR1 ACTIVATING ALTERATIONS WITH FREQUENT ACCOMPANYING PI3K AND MAPK PATHWAY MUTATIONS

Abstract BACKGROUND Rosette-forming glioneuronal tumor (RGNT) is an uncommon CNS tumor originally described in the fourth ventricle characterized by a low-grade glial neoplasm admixed with a rosette-forming neurocytic component. METHODS We reviewed clinicopathologic features of 42 patients with RGNT. Targeted next-generation sequencing was performed, and genome-wide methylation profiling is underway. RESULTS The 20 male and 22 female patients had a mean age of 25 years (range 3–47) at time of diagnosis. Tumors were located within or adjacent to the lateral ventricle (n=16), fourth ventricle (15), third ventricle (9), and spinal cord (2). All 31 tumors assessed to date contained FGFR1 activating alterations, either in-frame gene fusion, kinase domain tandem duplication, or hotspot missense mutation in the kinase domain (p.N546 or p.K656). While 7 of these 31 tumors harbored FGFR1 alterations as the solitary pathogenic event, 24 contained additional pathogenic alterations within PI3-kinase or MAP kinase pathway genes: 5 with additional PIK3CA and NF1 mutations, 4 with PIK3CA mutation, 3 with PIK3R1 mutation (one of which also contained focal RAF1 amplification), 5 with PTPN11 mutation (one with additional PIK3R1 mutation), and 2 with NF1 deletion. The other 5 cases demonstrated anaplastic features including hypercellularity and increased mitotic activity. Among these anaplastic cases, 3 harbored inactivating ATRX mutations and two harbored CDKN2A homozygous deletion, in addition to the FGFR1 alterations plus other PI3-kinase and MAP kinase gene mutations seen in those RGNT without anaplasia. CONCLUSION Independent of ventricular location, RGNT is defined by FGFR1 activating mutations or rearrangements, which are frequently accompanied by mutations involving PIK3CA, PIK3R1, PTPN11, NF1, and KRAS. Whereas pilocytic astrocytoma and ganglioglioma are characterized by solitary activating MAP kinase pathway alterations (e.g. BRAF fusion or mutation), RGNT are genetically more complex with dual PI3K-Akt-mTOR and Ras-Raf-MAPK pathway activation. Rare anaplastic examples may show additional ATRX and/or CDKN2A inactivation

Chemohormonal Therapy in Metastatic Hormone-Sensitive Prostate Cancer: Long-Term Survival Analysis of the Randomized Phase III E3805 CHAARTED Trial

Purpose Docetaxel added to androgen-deprivation therapy (ADT) significantly increases the longevity of some patients with metastatic hormone-sensitive prostate cancer. Herein, we present the outcomes of the CHAARTED (Chemohormonal Therapy Versus Androgen Ablation Randomized Trial for Extensive Disease in Prostate Cancer) trial with more mature follow-up and focus on tumor volume. Patients and Methods In this phase III study, 790 patients with metastatic hormone-sensitive prostate cancer were equally randomly assigned to receive either ADT in combination with docetaxel 75 mg/mm2 for up to six cycles or ADT alone. The primary end point of the study was overall survival (OS). Additional analyses of the prospectively defined low- and high-volume disease subgroups were performed. High-volume disease was defined as presence of visceral metastases and/or ≥ four bone metastases with at least one outside of the vertebral column and pelvis. Results At a median follow-up of 53.7 months, the median OS was 57.6 months for the chemohormonal therapy arm versus 47.2months for ADT alone (hazard ratio [HR], 0.72; 95% CI, 0.59 to 0.89; P = .0018). For patients with high-volume disease (n = 513), the median OS was 51.2 months with chemohormonal therapy versus 34.4 months with ADT alone (HR, 0.63; 95% CI, 0.50 to 0.79; P \u3c .001). For those with low-volume disease (n = 277), no OS benefit was observed (HR, 1.04; 95% CI, 0.70 to 1.55; P = .86). Conclusion The clinical benefit from chemohormonal therapy in prolonging OS was confirmed for patients with high-volume disease; however, for patients with low-volume disease, no OS benefit was discerned

Post hoc Analysis for Detecting Individual Rare Variant Risk Associations Using Probit Regression Bayesian Variable Selection Methods in Case-Control Sequencing Studies

Rare variants (RVs) have been shown to be significant contributors to complex disease risk. By definition, these variants have very low minor allele frequencies and traditional single-marker methods for statistical analysis are underpowered for typical sequencing study sample sizes. Multimarker burden-type approaches attempt to identify aggregation of RVs across case-control status by analyzing relatively small partitions of the genome, such as genes. However, it is generally the case that the aggregative measure would be a mixture of causal and neutral variants, and these omnibus tests do not directly provide any indication of which RVs may be driving a given association. Recently, Bayesian variable selection approaches have been proposed to identify RV associations from a large set of RVs under consideration. Although these approaches have been shown to be powerful at detecting associations at the RV level, there are often computational limitations on the total quantity of RVs under consideration and compromises are necessary for large-scale application. Here, we propose a computationally efficient alternative formulation of this method using a probit regression approach specifically capable of simultaneously analyzing hundreds to thousands of RVs. We evaluate our approach to detect causal variation on simulated data and examine sensitivity and specificity in instances of high RV dimensionality as well as apply it to pathway-level RV analysis results from a prostate cancer (PC) risk case-control sequencing study. Finally, we discuss potential extensions and future directions of this work

British Society of Gastroenterology guidance for management of inflammatory bowel disease during the COVID-19 pandemic.

The COVID-19 pandemic is putting unprecedented pressures on healthcare systems globally. Early insights have been made possible by rapid sharing of data from China and Italy. In the UK, we have rapidly mobilised inflammatory bowel disease (IBD) centres in order that preparations can be made to protect our patients and the clinical services they rely on. This is a novel coronavirus; much is unknown as to how it will affect people with IBD. We also lack information about the impact of different immunosuppressive medications. To address this uncertainty, the British Society of Gastroenterology (BSG) COVID-19 IBD Working Group has used the best available data and expert opinion to generate a risk grid that groups patients into highest, moderate and lowest risk categories. This grid allows patients to be instructed to follow the UK government's advice for shielding, stringent and standard advice regarding social distancing, respectively. Further considerations are given to service provision, medical and surgical therapy, endoscopy, imaging and clinical trials

AVONET: Morphological, ecological and geographical data for all birds

Functional traits offer a rich quantitative framework for developing and testing theories in evolutionary biology, ecology and ecosystem science. However, the potential of functional traits to drive theoretical advances and refine models of global change can only be fully realised when species-level information is complete. Here we present the AVONET dataset containing comprehensive functional trait data for all birds, including six ecological variables, 11 continuous morphological traits, and information on range size and location. Raw morphological measurements are presented from 90,020 individuals of 11,009 extant bird species sampled from 181 countries. These data are also summarised as species averages in three taxonomic formats, allowing integration with a global phylogeny, geographical range maps, IUCN Red List data and the eBird citizen science database. The AVONET dataset provides the most detailed picture of continuous trait variation for any major radiation of organisms, offering a global template for testing hypotheses and exploring the evolutionary origins, structure and functioning of biodiversity.Fil: Tobias, Joseph A.. Imperial College London; Reino Unido. University of Oxford; Reino UnidoFil: Sheard, Catherine. University of Oxford; Reino Unido. University of Bristol; Reino UnidoFil: Pigot, Alex L.. University of Oxford; Reino Unido. University College London; Estados UnidosFil: Devenish, Adam J. M.. Imperial College London; Reino UnidoFil: Yang, Jingyi. Imperial College London; Reino UnidoFil: Sayol, Ferran. University College London; Estados UnidosFil: Neate Clegg, Montague H. C.. University of Oxford; Reino Unido. University of Utah; Estados UnidosFil: Alioravainen, Nico. University of Oxford; Reino Unido. Natural Resources Institute Finland; FinlandiaFil: Weeks, Thomas L.. Imperial College London; Reino Unido. Natural History Museum; Reino UnidoFil: Barber, Robert A.. Imperial College London; Reino UnidoFil: Walkden, Patrick A.. Imperial College London; Reino Unido. Natural History Museum; Reino UnidoFil: MacGregor, Hannah E. A.. University of Oxford; Reino Unido. University of Bristol; Reino UnidoFil: Jones, Samuel E. I.. University of Oxford; Reino Unido. University of London; Reino UnidoFil: Vincent, Claire. Organización de Las Naciones Unidas; ArgentinaFil: Phillips, Anna G.. Senckenberg Biodiversity And Climate Research Centre; AlemaniaFil: Marples, Nicola M.. Trinity College; Estados UnidosFil: Montaño Centellas, Flavia A.. Universidad Mayor de San Andrés; Bolivia. University of Florida; Estados UnidosFil: Leandro Silva, Victor. Universidade Federal de Pernambuco; BrasilFil: Claramunt, Santiago. University of Toronto; Canadá. Royal Ontario Museum; CanadáFil: Darski, Bianca. Universidade Federal do Rio Grande do Sul; BrasilFil: Freeman, Benjamin G.. University of British Columbia; CanadáFil: Bregman, Tom P.. University of Oxford; Reino Unido. Future-Fit Foundation; Reino UnidoFil: Cooney, Christopher R.. University Of Sheffield; Reino UnidoFil: Hughes, Emma C.. University Of Sheffield; Reino UnidoFil: Capp, Elliot J. R.. University Of Sheffield; Reino UnidoFil: Varley, Zoë K.. University Of Sheffield; Reino Unido. Natural History Museum; Reino UnidoFil: Friedman, Nicholas R.. Okinawa Institute of Science and Technology Graduate University; JapónFil: Korntheuer, Heiko. Johannes Gutenberg Universitat Mainz; AlemaniaFil: Corrales Vargas, Andrea. Universidad Nacional de Costa Rica; Costa RicaFil: García, Natalia Cristina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; Argentin