Modular Invariant of Quantum Tori II: The Golden Mean

In our first article in this series ("Modular Invariant of Quantum Tori I: Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of quantum tori was defined. In this paper, we consider the case of the quantum torus associated to the golden mean. We show that the modular invariant is approximately 9538.249655644 by producing an explicit formula for it involving weighted versions of the Rogers-Ramanujan functions

On Petersson's partition limit formula

For each prime $p\equiv 1\pmod{4}$ consider the Legendre character $\chi=(\frac{\cdot}{p})$. Let $p_\pm(n)$ be the number of partitions of $n$ into parts $\lambda>0$ such that $\chi(\lambda)=\pm 1$. Petersson proved a beautiful limit formula for the ratio of $p_+(n)$ to $p_-(n)$ as $n\to\infty$ expressed in terms of important invariants of the real quadratic field $\mathbb{Q}(\sqrt{p})$. But his proof is not illuminating and Grosswald conjectured a more natural proof using a Tauberian converse of the Stolz-Ces\`aro theorem. In this paper we suggest an approach to address Grosswald's conjecture. We discuss a monotonicity conjecture which looks quite natural in the context of the monotonicity theorems of Bateman-Erd\H{o}s

SYZ mirror symmetry for hypertoric varieties

We construct a Lagrangian torus fibration on a smooth hypertoric variety and a corresponding SYZ mirror variety using $T$-duality and generating functions of open Gromov-Witten invariants. The variety is singular in general. We construct a resolution using the wall and chamber structure of the SYZ base.Comment: v_2: 31 pages, 5 figures, minor revision. To appear in Communications in Mathematical Physic

Traces of past activity in the Galactic Centre

The Milky Way centre hosts a supermassive Black Hole (BH) with a mass of ~4*10^6 M_Sun. Sgr A*, its electromagnetic counterpart, currently appears as an extremely weak source with a luminosity L~10^-9 L_Edd. The lowest known Eddington ratio BH. However, it was not always so; traces of "glorious" active periods can be found in the surrounding medium. We review here our current view of the X-ray emission from the Galactic Center (GC) and its environment, and the expected signatures (e.g. X-ray reflection) of a past flare. We discuss the history of Sgr A*'s past activity and its impact on the surrounding medium. The structure of the Central Molecular Zone (CMZ) has not changed significantly since the last active phase of Sgr A*. This relic torus provides us with the opportunity to image the structure of an AGN torus in exquisite detail.Comment: Invited refereed review. Chapter of the book: "Cosmic ray induced phenomenology in star forming environments" (eds. Olaf Reimer and Diego F. Torres

Consistent patterns of common species across tropical tree communities

D.L.M.C. was supported by the London Natural Environmental Research Council Doctoral Training Partnership grant (grant no. NE/L002485/1). This paper developed from analysing data from the African Tropical Rainforest Observatory Network (AfriTRON), curated at ForestPlots.net. AfriTRON has been supported by numerous people and grants since its inception. We sincerely thank the people of the many villages and local communities who welcomed our field teams and without whose support this work would not have been possible. Grants that have funded the AfriTRON network, including data in this paper, are a European Research Council Advanced Grant (T-FORCES; 291585; Tropical Forests in the Changing Earth System), a NERC standard grant (NER/A/S/2000/01002), a Royal Society University Research Fellowship to S.L.L., a NERC New Investigators Grant to S.L.L., a Philip Leverhulme Award to S.L.L., a European Union FP7 grant (GEOCARBON; 283080), Leverhulme Program grant (Valuing the Arc); a NERC Consortium Grant (TROBIT; NE/D005590/), NERC Large Grant (CongoPeat; NE/R016860/1) the Gordon and Betty Moore Foundation the David and Lucile Packard Foundation, the Centre for International Forestry Research (CIFOR), and Gabon’s National Parks Agency (ANPN). This paper was supported by ForestPlots.net approved Research Project 81, ‘Comparative Ecology of African Tropical Forests’. The development of ForestPlots.net and data curation has been funded by several grants, including NE/B503384/1, NE/N012542/1, ERC Advanced Grant 291585—‘T-FORCES’, NE/F005806/1, NERC New Investigators Awards, the Gordon and Betty Moore Foundation, a Royal Society University Research Fellowship and a Leverhulme Trust Research Fellowship. Fieldwork in the Democratic Republic of the Congo (Yangambi and Yoko sites) was funded by the Belgian Science Policy Office BELSPO (SD/AR/01A/COBIMFO, BR/132/A1/AFRIFORD, BR/143/A3/HERBAXYLAREDD, FED-tWIN2019-prf-075/CongoFORCE, EF/211/TREE4FLUX); by the Flemish Interuniversity Council VLIR-UOS (CD2018TEA459A103, FORMONCO II); by L’Académie de recherche et d’enseignement supérieur ARES (AFORCO project) and by the European Union through the FORETS project (Formation, Recherche, Environnement dans la TShopo) supported by the XIth European Development Fund. EMV was supported by fellowship from the CNPq (Grant 308543/2021-1). RAPELD plots in Brazil were supported by the Program for Biodiversity Research (PPBio) and the National Institute for Amazonian Biodiversity (INCT-CENBAM). BGL post-doc grant no. 2019/03379-4, São Paulo Research Foundation (FAPESP). D.A.C. was supported by the CCI Collaborative fund. Plots in Mato Grosso, Brazil, were supported by the National Council for Scientific and Technological Development (CNPq), PELD-TRAN 441244/2016-5 and 441572/2020-0, and Mato Grosso State Research Support Foundation (FAPEMAT)—0346321/2021. We thank E. Chezeaux, R. Condit, W. J. Eggeling, R. M. Ewers, O. J. Hardy, P. Jeanmart, K. L. Khoon, J. L. Lloyd, A. Marjokorpi, W. Marthy, H. Ntahobavuka, D. Paget, J. T. A. Proctor, R. P. Salomão, P. Saner, S. Tan, C. O. Webb, H. Woell and N. Zweifel for contributing forest inventory data. We thank numerous field assistants for their invaluable contributions to the collection of forest inventory data, including A. Nkwasibwe, ITFC field assistant.Peer reviewe

THE CONCISE GUIDE TO PHARMACOLOGY 2021/22: G protein-coupled receptors

The Concise Guide to PHARMACOLOGY 2021/22 is the fifth in this series of biennial publications. The Concise Guide provides concise overviews, mostly in tabular format, of the key properties of nearly 1900 human drug targets with an emphasis on selective pharmacology (where available), plus links to the open access knowledgebase source of drug targets and their ligands (www.guidetopharmacology.org), which provides more detailed views of target and ligand properties. Although the Concise Guide constitutes over 500 pages, the material presented is substantially reduced compared to information and links presented on the website. It provides a permanent, citable, point-in-time record that will survive database updates. The full contents of this section can be found at http://onlinelibrary.wiley.com/doi/bph.15538. G protein-coupled receptors are one of the six major pharmacological targets into which the Guide is divided, with the others being: ion channels, nuclear hormone receptors, catalytic receptors, enzymes and transporters. These are presented with nomenclature guidance and summary information on the best available pharmacological tools, alongside key references and suggestions for further reading. The landscape format of the Concise Guide is designed to facilitate comparison of related targets from material contemporary to mid-2021, and supersedes data presented in the 2019/20, 2017/18, 2015/16 and 2013/14 Concise Guides and previous Guides to Receptors and Channels. It is produced in close conjunction with the Nomenclature and Standards Committee of the International Union of Basic and Clinical Pharmacology (NC-IUPHAR), therefore, providing official IUPHAR classification and nomenclature for human drug targets, where appropriate

Consistent patterns of common species across tropical tree communities

Trees structure the Earth’s most biodiverse ecosystem, tropical forests. The vast number of tree species presents a formidable challenge to understanding these forests, including their response to environmental change, as very little is known about most tropical tree species. A focus on the common species may circumvent this challenge. Here we investigate abundance patterns of common tree species using inventory data on 1,003,805 trees with trunk diameters of at least 10 cm across 1,568 locations1,2,3,4,5,6 in closed-canopy, structurally intact old-growth tropical forests in Africa, Amazonia and Southeast Asia. We estimate that 2.2%, 2.2% and 2.3% of species comprise 50% of the tropical trees in these regions, respectively. Extrapolating across all closed-canopy tropical forests, we estimate that just 1,053 species comprise half of Earth’s 800 billion tropical trees with trunk diameters of at least 10 cm. Despite differing biogeographic, climatic and anthropogenic histories7, we find notably consistent patterns of common species and species abundance distributions across the continents. This suggests that fundamental mechanisms of tree community assembly may apply to all tropical forests. Resampling analyses show that the most common species are likely to belong to a manageable list of known species, enabling targeted efforts to understand their ecology. Although they do not detract from the importance of rare species, our results open new opportunities to understand the world’s most diverse forests, including modelling their response to environmental change, by focusing on the common species that constitute the majority of their trees.Publisher PDFPeer reviewe

Peri-operative red blood cell transfusion in neonates and infants: NEonate and Children audiT of Anaesthesia pRactice IN Europe: A prospective European multicentre observational study

BACKGROUND: Little is known about current clinical practice concerning peri-operative red blood cell transfusion in neonates and small infants. Guidelines suggest transfusions based on haemoglobin thresholds ranging from 8.5 to 12 g dl-1, distinguishing between children from birth to day 7 (week 1), from day 8 to day 14 (week 2) or from day 15 (≥week 3) onwards. OBJECTIVE: To observe peri-operative red blood cell transfusion practice according to guidelines in relation to patient outcome. DESIGN: A multicentre observational study. SETTING: The NEonate-Children sTudy of Anaesthesia pRactice IN Europe (NECTARINE) trial recruited patients up to 60 weeks' postmenstrual age undergoing anaesthesia for surgical or diagnostic procedures from 165 centres in 31 European countries between March 2016 and January 2017. PATIENTS: The data included 5609 patients undergoing 6542 procedures. Inclusion criteria was a peri-operative red blood cell transfusion. MAIN OUTCOME MEASURES: The primary endpoint was the haemoglobin level triggering a transfusion for neonates in week 1, week 2 and week 3. Secondary endpoints were transfusion volumes, 'delta haemoglobin' (preprocedure - transfusion-triggering) and 30-day and 90-day morbidity and mortality. RESULTS: Peri-operative red blood cell transfusions were recorded during 447 procedures (6.9%). The median haemoglobin levels triggering a transfusion were 9.6 [IQR 8.7 to 10.9] g dl-1 for neonates in week 1, 9.6 [7.7 to 10.4] g dl-1 in week 2 and 8.0 [7.3 to 9.0] g dl-1 in week 3. The median transfusion volume was 17.1 [11.1 to 26.4] ml kg-1 with a median delta haemoglobin of 1.8 [0.0 to 3.6] g dl-1. Thirty-day morbidity was 47.8% with an overall mortality of 11.3%. CONCLUSIONS: Results indicate lower transfusion-triggering haemoglobin thresholds in clinical practice than suggested by current guidelines. The high morbidity and mortality of this NECTARINE sub-cohort calls for investigative action and evidence-based guidelines addressing peri-operative red blood cell transfusions strategies. TRIAL REGISTRATION: ClinicalTrials.gov, identifier: NCT02350348