Functional relations for elliptic polylogarithms

Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of functional relations are available, but only very few relations are identified. Starting from an approach of Zagier and Gangl, which in turn is based on considerations about an elliptic version of the Bloch group, we explore functional relations between elliptic polylogarithms and link them to the relations which can be derived using the elliptic symbol formalism. The elliptic symbol formalism in turn allows for an alternative proof of the validity of the elliptic Bloch relation. While the five-term identity is the prime example of a functional identity for multiple polylogarithms and implies many dilogarithm identities, the situation in the elliptic setup is more involved: there is no simple elliptic analogue, but rather a whole class of elliptic identities

Amplitude recursions with an extra marked point

The recursive calculation of Selberg integrals by Aomoto and Terasoma using the Knizhnik-Zamolodchikov equation and the Drinfeld associator makes use of an auxiliary point and facilitates the recursive evaluation of string amplitudes at genus zero: open-string N-point amplitudes can be obtained from those at N-1 points. We establish a similar formalism at genus one, which allows the recursive calculation of genus-one Selberg integrals using an extra marked point in a differential equation of Knizhnik-Zamolodchikov-Bernard type. Hereby genus-one Selberg integrals are related to genus-zero Selberg integrals. Accordingly, N-point open-string amplitudes at genus one can be obtained from (N+2)-point open-string amplitudes at tree level. The construction is related to and in accordance with various recent results in intersection theory and string theory

A note on the Drinfeld associator for genus-zero superstring amplitudes in twisted de Rham theory

The string corrections of tree-level open-string amplitudes can be described by Selberg integrals satisfying a Knizhnik-Zamolodchikov (KZ) equation. This allows for a recursion of the $\alpha'$-expansion of tree-level string corrections in the number of external states using the Drinfeld associator. While the feasibility of this recursion is well-known, we provide a mathematical description in terms of twisted de Rham theory and intersection numbers of twisted forms. In particular, this leads to purely combinatorial expressions for the matrix representation of the Lie algebra generators appearing in the KZ equation in terms of directed graphs. This, in turn, admits efficient algorithms for symbolic and numerical computations using adjacency matrices of directed graphs and is a crucial step towards analogous recursions and algorithms at higher genera

Aortic distensibility and coronary artery bypass graft patency

<p>Abstract</p> <p>Background</p> <p>Aortic distensibility is an elasticity index of the aorta, and reflects aortic stiffness. Coronary artery disease has been found to be substantially associated with increased aortic stiffness. In this study we aimed to retrospectively analyze the association of angiographically determined aortic distensibility with the patency rates of coronary bypass grafts</p> <p>Methods</p> <p>The study was conducted in the Cardiology department of the Applied Research Centre for Health of Uludağ University. The coronary angiograms of 53 consecutive coronary bypass patients were analysed retrospectively. Aortic distensibility was calculated using the formula: 2 × (change in aortic diameter)/(diastolic aortic diameter) × (change in aortic pressure). The number of stenosed and patent bypass grafts and the patient characteristics like age, risk factors were noted.</p> <p>Results</p> <p>There were 44 male (83%) and 9 female (17%) cases. Eighteen cases had only one saphenous vein grafting. The number of cases with two, three and four saphenous grafting were 18, 11 and 1; respectively. In the control angiograms the number of cases with one, two, three and four saphenous vein graft obstruction were 15 (31.3%), 7 (14.6%), 1 (2.1%) and 1 (2.1%) respectively. The aortic distensibility did not differ in cases with and without saphenous graft occlusion (p > 0.05). Also left internal mammary artery (LIMA) graft patency was not related to the distensibility of the aorta (p > 0.05). We also evaluated the data for cut-off values of 50 and 70 mmHg of pulse pressure and did not see any significant difference between the groups in terms of saphenous or LIMA grafts.</p> <p>Conclusion</p> <p>In this study we failed to show association of angiographically determined aortic distensibility with coronary bypass graft patency in consecutive 53 patients with coronary artery bypass graft surgery (CABG).</p

Effect of the COVID-19 pandemic on surgery for indeterminate thyroid nodules (THYCOVID): a retrospective, international, multicentre, cross-sectional study

Background Since its outbreak in early 2020, the COVID-19 pandemic has diverted resources from non-urgent and elective procedures, leading to diagnosis and treatment delays, with an increased number of neoplasms at advanced stages worldwide. The aims of this study were to quantify the reduction in surgical activity for indeterminate thyroid nodules during the COVID-19 pandemic; and to evaluate whether delays in surgery led to an increased occurrence of aggressive tumours.Methods In this retrospective, international, cross-sectional study, centres were invited to participate in June 22, 2022; each centre joining the study was asked to provide data from medical records on all surgical thyroidectomies consecutively performed from Jan 1, 2019, to Dec 31, 2021. Patients with indeterminate thyroid nodules were divided into three groups according to when they underwent surgery: from Jan 1, 2019, to Feb 29, 2020 (global prepandemic phase), from March 1, 2020, to May 31, 2021 (pandemic escalation phase), and from June 1 to Dec 31, 2021 (pandemic decrease phase). The main outcomes were, for each phase, the number of surgeries for indeterminate thyroid nodules, and in patients with a postoperative diagnosis of thyroid cancers, the occurrence of tumours larger than 10 mm, extrathyroidal extension, lymph node metastases, vascular invasion, distant metastases, and tumours at high risk of structural disease recurrence. Univariate analysis was used to compare the probability of aggressive thyroid features between the first and third study phases. The study was registered on ClinicalTrials.gov, NCT05178186.Findings Data from 157 centres (n=49 countries) on 87 467 patients who underwent surgery for benign and malignant thyroid disease were collected, of whom 22 974 patients (18 052 [78 center dot 6%] female patients and 4922 [21 center dot 4%] male patients) received surgery for indeterminate thyroid nodules. We observed a significant reduction in surgery for indeterminate thyroid nodules during the pandemic escalation phase (median monthly surgeries per centre, 1 center dot 4 [IQR 0 center dot 6-3 center dot 4]) compared with the prepandemic phase (2 center dot 0 [0 center dot 9-3 center dot 7]; p&lt;0 center dot 0001) and pandemic decrease phase (2 center dot 3 [1 center dot 0-5 center dot 0]; p&lt;0 center dot 0001). Compared with the prepandemic phase, in the pandemic decrease phase we observed an increased occurrence of thyroid tumours larger than 10 mm (2554 [69 center dot 0%] of 3704 vs 1515 [71 center dot 5%] of 2119; OR 1 center dot 1 [95% CI 1 center dot 0-1 center dot 3]; p=0 center dot 042), lymph node metastases (343 [9 center dot 3%] vs 264 [12 center dot 5%]; OR 1 center dot 4 [1 center dot 2-1 center dot 7]; p=0 center dot 0001), and tumours at high risk of structural disease recurrence (203 [5 center dot 7%] of 3584 vs 155 [7 center dot 7%] of 2006; OR 1 center dot 4 [1 center dot 1-1 center dot 7]; p=0 center dot 0039).Interpretation Our study suggests that the reduction in surgical activity for indeterminate thyroid nodules during the COVID-19 pandemic period could have led to an increased occurrence of aggressive thyroid tumours. However, other compelling hypotheses, including increased selection of patients with aggressive malignancies during this period, should be considered. We suggest that surgery for indeterminate thyroid nodules should no longer be postponed even in future instances of pandemic escalation.Funding None.Copyright (c) 2023 Published by Elsevier Ltd. All rights reserved

Penrose quasi-local energy and Kerr-Schild metrics

© 2018 IOP Publishing Ltd. Specialising in the case of Kerr-Schild spacetimes, which include the Kerr black hole and gravitational wave solutions, we propose a modification of the Penrose quasi-local energy. The modification relies on the existence of a natural Minkowski background for Kerr-Schild spacetimes. We find that the modified surface integral reduces to a volume integral of the Einstein tensor, which has been proposed previously as an appropriate definition for quasi-local energy for Kerr-Schild backgrounds. Furthermore, in the special case that the Kerr-Schild null vector is normal to the surface of interest, we construct a 1-1 map between the 2-surface twistors in the Kerr-Schild background and Minkowski twistors projected onto the surface

Morbidity in surgery: impact of the 50-hour work-week limitation in Switzerland

Work-hour regulations for residency programmes in Switzerland, including a 50-hour weekly limit, were set in on 1 January 2005. Patient safety was one of the major arguments for the implementation. As the effect of the restriction of residency work hours on patient care in Switzerland has not yet been evaluated on objective data, the aim of the present study was to assess its impact by comparing the patients' morbidity and mortality before (2001-2004) and after (2005-2008) the implementation