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Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants

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arXiv 2017年

作者： Chen, Xiao-Min Hu, Xing-Biao Müller-Hoissen, Folkert College of Applied Sciences Beijing University of Technology Beijing100124 China Max Planck Institute for Dynamics and Self-Organization Göttingen Germany LSEC Institute of Computational Mathematics and Scientific Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Institute for Nonlinear Dynamics Georg August University Friedrich-Hund-Platz 1 Göttingen37077 Germany

For the first two equations of the Volterra lattice hierarchy and the first two equations of its non-autonomous (non-isospectral) extension, we present Riccati systems for functions cj(t), j = 0,1,..., such that an expression in terms of Hankel determinants built from them solves these equations on the right half of the lattice. This actually achieves a complete linearization of these equations of the extended Volterra lattice hierarchy.37K10, 37K15, 42C05, 70H06 Copyright © 2017, The Authors. All rights reserved.

关键词： Riccati equations

Liouville integrability of conservative peakons for amodified CH equation

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arXiv 2017年

作者： Chang, Xiangke Szmigielski, Jacek LSEC Institute of Computational Mathematics and Scientific Engineering Computing AMSS Chinese Academy of Sciences P.O.Box 2719 Beijing100190 China Department of Mathematics and Statistics University of Saskatchewan 106 Wiggins Road Saskatoon SaskatchewanS7N5E6 Canada Department OfMathematics and Statistics University of Saskatchewan 106Wiggins Road Saskatoon SaskatchewanS7N5E6 Canada

The modified Camassa-Holm equation (also called FORQ) is one of numerous cousins of the Camassa-Holm equation possessing non-smoth solitons ( peakons) as special solutions. The peakon sector of solutions is not uniquely defined: In one peakon sector (dissapative) the Sobolev H1 norm is not preserved, in the other sector (conservative), introduced in [2], the time evolution of peakons leaves the H1 norm invariant. In this Letter, it is shown that the conservative peakon equations of themodified Camassa-Holmcan be given an appropriate Poisson structure relative to which the equations are Hamiltonian and, in fact, Liouville integrable. The latter is proved directly by exploiting the inverse spectral techniques, especially asymptotic analysis of solutions, developed elsewhere [3]. Copyright © 2017, The Authors. All rights reserved.

关键词： Asymptotic analysis

Lax integrability and the peakon problem for the modified camassa-holm equation

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arXiv 2017年

作者： CHANG, XIANGKE SZMIGIELSKI, JACEK LSEC INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING AMSS CHINESE ACADEMY OF SCIENCES P.O.BOX 2719 BEIJING100190 China THE DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF SASKATCHEWAN 106 WIGGINS ROAD SASKATOONSKS7N 5E6 Canada DEPARTMENT OFMATHEMATICS AND STATISTICS UNIVERSITY OF SASKATCHEWAN 106WIGGINS ROAD SASKATOONSKS7N 5E6 Canada

Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holmequation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfying the modified Camassa-Holmequation in the sense of distributions;our approach is based on solving certain inverse boundary value problem the solution of which hinges on a combination of classical techniques of analysis involving Stieltjes' continued fractions and multi-point Padé approximations. We propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons which share asymptotic speeds, as well as Toda-like sorting *** Codes 35D30, 35Q51, 34K29, 37J35, 35Q53, 34B05, 41A21 Copyright © 2017, The Authors. All rights reserved.

关键词： Nonlinear equations

An inexact Newton-Krylov method for stochastic eigenvalue problems

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arXiv 2017年

作者： Benner, Peter Onwunta, Akwum Stoll, Martin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstrasse 1 Magdeburg39106 Germany Numerical Linear Algebra for Dynamical Systems Group Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstrasse 1 Magdeburg39106 Germany Technische Universität Chemnitz Faculty of Mathematics Professorship Scientific Computing Chemnitz09107 Germany

This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochastic Galerkin method. Here, we exploit this inherent tensor product structure to develop a globalized low-rank inexact Newton method with which we tackle the stochastic eigenproblem. We illustrate the effectiveness of our solver with numerical experiments. Copyright © 2017, The Authors. All rights reserved.

关键词： Galerkin methods

Track 1-A Study of Nanodroplet Diffusion on Smooth Surfaces

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Track 1-A Study of Nanodroplet Diffusion on Smooth Surfaces

2016年大连国际微流控和芯片实验室大会

作者： Chu Li Jizu Huang Zhigang Li Department of Mechanical and Aerospace Engineering The Hong Kong University of Science and Technology Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of Sciences

In this study,we investigate how nanodroplets diffuse on smooth surfaces through molecular dynamics(MD) simulations and theoretical *** dynamics simulations show that nanodroplet surface diffusion is different from that of single molecules and solid *** dependence of nanodroplet diffusion coefficient on temperature undergoes a transition from linear to nonlinear as the surface wettability is weakened due to the coupling of temperature and surface *** also develop a simple relation for the diffusion coefficient by using the contact angle and contact radius of the *** works well for a wide range of surface wettabilities and different sized nanodroplets,as confirmed by MD simulations.

关键词： Track 1-A Study of Nanodroplet Diffusion on Smooth Surfaces

Open Data from the Third Observing Run of LIGO, Virgo, KAGRA, and GEO

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Astrophysical Journal, Supplement Series 2023年第2期267卷 29-29页

作者： Abbott, R. Abe, H. Acernese, F. Ackley, K. Adhicary, S. Adhikari, N. Adhikari, R.X. Adkins, V.K. Adya, V.B. Affeldt, C. Agarwal, D. Agathos, M. Aguiar, O.D. Aiello, L. Ain, A. Ajith, P. Akutsu, T. Albanesi, S. Alfaidi, R.A. Al-Jodah, A. Alléné, C. Allocca, A. Almualla, M. Altin, P.A. Amato, A. Amez-Droz, L. Amorosi, A. Anand, S. Ananyeva, A. Andersen, R. Anderson, S.B. Anderson, W.G. Andia, M. Ando, M. Andrade, T. Andres, N. Andrés-Carcasona, M. Andrić, T. Ansoldi, S. Antelis, J.M. Antier, S. Aoumi, M. Apostolatos, T. Appavuravther, E.Z. Appert, S. Apple, S.K. Arai, K. Araya, A. Araya, M.C. Areeda, J.S. Arène, M. Aritomi, N. Arnaud, N. Arogeti, M. Aronson, S.M. Arun, K.G. Asada, H. Ashton, G. Aso, Y. Assiduo, M. Assis de Souza Melo, S. Aston, S.M. Astone, P. Aubin, F. AultONeal, K. Babak, S. Badalyan, A. Badaracco, F. Badger, C. Bae, S. Bagnasco, S. Bai, Y. Baier, J.G. Baiotti, L. Baird, J. Bajpai, R. Baka, T. Ball, M. Ballardin, G. Ballmer, S.W. Baltus, G. Banagiri, S. Banerjee, B. Bankar, D. Baral, P. Barayoga, J.C. Barber, J. Barish, B.C. Barker, D. Barneo, P. Barone, F. Barr, B. Barsotti, L. Barsuglia, M. Barta, D. Barthelmy, S.D. Barton, M.A. Bartos, I. Basak, S. Basalaev, A. Bassiri, R. Basti, A. Bawaj, M. Bayley, J.C. Baylor, A.C. Bazzan, M. Bécsy, B. Bedakihale, V.M. Beirnaert, F. Bejger, M. Bell, A.S. Benedetto, V. Beniwal, D. Benoit, W. Bentley, J.D. Ben Yaala, M. Bera, S. Berbel, M. Bergamin, F. Berger, B.K. Bernuzzi, S. Beroiz, M. Berry, C.P.L. Bersanetti, D. Bertolini, A. Betzwieser, J. Beveridge, D. Bevins, N. Bhandare, R. Bhandari, A.V. Bhardwaj, U. Bhatt, R. Bhattacharjee, D. Bhaumik, S. Bianchi, A. Bilenko, I.A. Bilicki, M. Billingsley, G. Bini, S. Birnholtz, O. Biscans, S. Bischi, M. Biscoveanu, S. Bisht, A. Biswas, B. Bitossi, M. Bizouard, M.-A. Blackburn, J.K. Blair, C.D. Blair, D.G. Blair, R.M. Bobba, F. Bode, N. Boër, M. Bogaert, G. Boileau, G. Boldrini, M. Bolingbroke, G.N. Bonavena, L.D. Bondarescu, R. Bondu, F. Bonilla, E. Bonilla, G.S. Bonnand, R. Booker, P. Bork, R. Boschi, V. Bose, N. LIGO Laboratory California Institute of Technology Pasadena 91125 CA United States Graduate School of Science Tokyo Institute of Technology 2-12-1 Ookayama Meguro-ku Tokyo 152-8551 Japan Dipartimento di Farmacia Università di Salerno Salerno Fisciano I-84084 Italy INFN Sezione di Napoli Napoli I-80126 Italy OzGrav School of Physics & Astronomy Monash University Clayton 3800 VIC Australia The Pennsylvania State University University Park 16802 PA United States University of Wisconsin-Milwaukee Milwaukee 53201 WI United States Louisiana State University Baton Rouge 70803 LA United States OzGrav Australian National University Canberra 0200 ACT Australia Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Hannover D-30167 Germany Leibniz Universität Hannover Hannover D-30167 Germany Inter-University Centre for Astronomy and Astrophysics Pune 411007 India University of Cambridge Cambridge CB2 1TN United Kingdom Instituto Nacional de Pesquisas Espaciais São Paulo São José dos Campos 12227-010 Brazil Cardiff University Cardiff CF24 3AA United Kingdom INFN Sezione di Pisa Pisa I-56127 Italy International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bengaluru 560089 India Gravitational Wave Science Project National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka City Tokyo 181-8588 Japan Advanced Technology Center National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka City Tokyo 181-8588 Japan Dipartimento di Fisica Università degli Studi di Torino Torino I-10125 Italy INFN Sezione di Torino Torino I-10125 Italy SUPA University of Glasgow Glasgow G12 8QQ United Kingdom OzGrav University of Western Australia Crawley 6009 WA Australia Univ. Savoie Mont Blanc CNRS Laboratoire d'Annecy de Physique des Particules - IN2P3 Annecy F-74000 France Università di Napoli “Federico II” Napoli I-80126 Italy University of Minnesota Minneapolis 55455 MN United States M

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://***. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages. © 2023. The Author(s). Published by the American Astronomical Society.

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SciPy 1.0—Fundamental algorithms for scientific computing in python

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arXiv 2019年

作者： Virtanen, Pauli Gommers, Ralf Oliphant, Travis E. Haberland, Matt Reddy, Tyler Cournapeau, David Burovski, Evgeni Peterson, Pearu Weckesser, Warren Bright, Jonathan van der Walt, Stéfan J. Brett, Matthew Wilson, Joshua Millman, K. Jarrod Mayorov, Nikolay Nelson, Andrew R.J. Jones, Eric Kern, Robert Larson, Eric Carey, C.J. Polat, Ilhan Feng, Yu Moore, Eric W. VanderPlas, Jake Laxalde, Denis Perktold, Josef Cimrman, Robert Henriksen, Ian Quintero, E.A. Harris, Charles R. Archibald, Anne M. Ribeiro, Antônio H. Pedregosa, Fabian van Mulbregt, Paul University of Jyväskylä University of Jyväskylä FI-40014 Finland Quansight LLC AustinTX United States Ultrasound Imaging Mayo Clinic RochesterMN55902 United States Electrical Engineering Brigham Young University ProvoUT84604 United States Enthought Inc. AustinTX78701 United States Anaconda Inc AustinTX78701 United States BioResource and Agricultural Engineering Department California Polytechnic State University San Luis ObispoCA93407 United States Department of Mathematics University of California Los AngelesCA90025 United States Los Alamos National Laboratory Los AlamosNM87544 United States Independent Researcher Higher School of Economics Myasnitskaya 20 Moscow101000 Russia Independent Researcher Saue Estonia Department of Mechanics and Applied Mathematics Institute of Cybernetics Tallinn Technical University Akadeemia Rd 21 Tallinn Estonia Independent Researcher NY United States Berkeley Institute for Data Science University of California BerkeleyCA94720 United States School of Psychology University of Birmingham Edgbaston BirmighamB15 2TT United Kingdom Division of Biostatistics University of California BerkeleyCA94720 United States WayRay LLC Skolkovo Innovation Center Moscow143026 Russia Australian Nuclear Science and Technology Organisation Locked Bag 2001 Kirrawee DCNSW2232 Australia Institute for Learning and Brain Sciences University of Washington SeattleWA98195 United States College of Information and Computing Sciences University of Massachusetts Amherst AmherstMA01002 United States Berkeley Center for Cosmological Physics University of California BerkeleyCA94720 United States Bruker Biospin Corp. 15 Fortune Drive BillericaMA01821 United States University of Washington SeattleWA98195 United States New Technologies - Research Centre University of West Bohemia Univerzitní 8 Plzeň306 14 Czech Republic Oden Institute for Computational Engineering and Sciences University of Texas at Austin AustinTX7

SciPy is an open source scientific computing library for the Python programming language. SciPy 1.0 was released in late 2017, about 16 years after the original version 0.1 release. SciPy has become a de facto standard for leveraging scientific algorithms in the Python programming language, with more than 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories, and millions of downloads per year. This includes usage of SciPy in almost half of all machine learning projects on GitHub, and usage by high profile projects including LIGO gravitational wave analysis and creation of the first-ever image of a black hole (M87). The library includes functionality spanning clustering, Fourier transforms, integration, interpolation, file I/O, linear algebra, image processing, orthogonal distance regression, minimization algorithms, signal processing, sparse matrix handling, computational geometry, and statistics. In this work, we provide an overview of the capabilities and development practices of the SciPy library and highlight some recent technical developments. Copyright © 2019, The Authors. All rights reserved.

关键词： Open source software

Search for anisotropic gravitational-wave backgrounds using data from Advanced LIGO and Advanced Virgo’s first three observing runs

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Physical Review D 2021年第2期104卷 022005-022005页

作者： R. Abbott T. D. Abbott S. Abraham F. Acernese K. Ackley A. Adams C. Adams R. X. Adhikari V. B. Adya C. Affeldt D. Agarwal M. Agathos K. Agatsuma N. Aggarwal O. D. Aguiar L. Aiello A. Ain P. Ajith T. Akutsu K. M. Aleman G. Allen A. Allocca P. A. Altin A. Amato S. Anand A. Ananyeva S. B. Anderson W. G. Anderson M. Ando S. V. Angelova S. Ansoldi J. M. Antelis S. Antier S. Appert Koya Arai Koji Arai Y. Arai S. Araki A. Araya M. C. Araya J. S. Areeda M. Arène N. Aritomi N. Arnaud S. M. Aronson H. Asada Y. Asali G. Ashton Y. Aso S. M. Aston P. Astone F. Aubin P. Aufmuth K. AultONeal C. Austin S. Babak F. Badaracco M. K. M. Bader S. Bae Y. Bae A. M. Baer S. Bagnasco Y. Bai L. Baiotti J. Baird R. Bajpai M. Ball G. Ballardin S. W. Ballmer M. Bals A. Balsamo G. Baltus S. Banagiri D. Bankar R. S. Bankar J. C. Barayoga C. Barbieri B. C. Barish D. Barker P. Barneo F. Barone B. Barr L. Barsotti M. Barsuglia D. Barta J. Bartlett M. A. Barton I. Bartos R. Bassiri A. Basti M. Bawaj J. C. Bayley A. C. Baylor M. Bazzan B. Bécsy V. M. Bedakihale M. Bejger I. Belahcene V. Benedetto D. Beniwal M. G. Benjamin T. F. Bennett J. D. Bentley M. BenYaala F. Bergamin B. K. Berger S. Bernuzzi D. Bersanetti A. Bertolini J. Betzwieser R. Bhandare A. V. Bhandari D. Bhattacharjee S. Bhaumik J. Bidler I. A. Bilenko G. Billingsley R. Birney O. Birnholtz S. Biscans M. Bischi S. Biscoveanu A. Bisht B. Biswas M. Bitossi M.-A. Bizouard J. K. Blackburn J. Blackman C. D. Blair D. G. Blair R. M. Blair F. Bobba N. Bode M. Boer G. Bogaert M. Boldrini F. Bondu E. Bonilla R. Bonnand P. Booker B. A. Boom R. Bork V. Boschi N. Bose S. Bose V. Bossilkov V. Boudart Y. Bouffanais A. Bozzi C. Bradaschia P. R. Brady A. Bramley A. Branch M. Branchesi J. E. Brau M. Breschi T. Briant J. H. Briggs A. Brillet M. Brinkmann P. Brockill A. F. Brooks J. Brooks D. D. Brown S. Brunett G. Bruno R. Bruntz J. Bryant A. Buikema T. Bulik H. J. Bulten A. Buonanno R. Buscicchio D. Buskulic R. L. Byer L. Cadonati M. Caesar G. Cagnoli C. Cahillane H. W. Cain, III J. Calderón Bustillo J. LIGO Laboratory California Institute of Technology Pasadena California 91125 USA Louisiana State University Baton Rouge Louisiana 70803 USA Inter-University Centre for Astronomy and Astrophysics Pune 411007 India Dipartimento di Farmacia Università di Salerno I-84084 Fisciano Salerno Italy INFN Sezione di Napoli Complesso Universitario di Monte S.Angelo I-80126 Napoli Italy OzGrav School of Physics & Astronomy Monash University Clayton 3800 Victoria Australia Christopher Newport University Newport News Virginia 23606 USA LIGO Livingston Observatory Livingston Louisiana 70754 USA OzGrav Australian National University Canberra Australian Capital Territory 0200 Australia Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-30167 Hannover Germany Leibniz Universität Hannover D-30167 Hannover Germany University of Cambridge Cambridge CB2 1TN United Kingdom Theoretisch-Physikalisches Institut Friedrich-Schiller-Universität Jena D-07743 Jena Germany University of Birmingham Birmingham B15 2TT United Kingdom Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA) Northwestern University Evanston Illinois 60208 USA Instituto Nacional de Pesquisas Espaciais 12227-010 São José dos Campos São Paulo Brazil Gravity Exploration Institute Cardiff University Cardiff CF24 3AA United Kingdom Gran Sasso Science Institute (GSSI) I-67100 L’Aquila Italy INFN Laboratori Nazionali del Gran Sasso I-67100 Assergi Italy INFN Sezione di Pisa I-56127 Pisa Italy Università di Pisa I-56127 Pisa Italy International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bengaluru 560089 India Gravitational Wave Science Project National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan Advanced Technology Center National Astronomical Observatory of Japan (NAOJ) Mitaka City Tokyo 181-8588 Japan California State University Fullerton Fullerton California 92831 USA NCSA University of Illinois

We report results from searches for anisotropic stochastic gravitational-wave backgrounds using data from the first three observing runs of the Advanced LIGO and Advanced Virgo detectors. For the first time, we include Virgo data in our analysis and run our search with a new efficient pipeline called pystoch on data folded over one sidereal day. We use gravitational-wave radiometry (broadband and narrow band) to produce sky maps of stochastic gravitational-wave backgrounds and to search for gravitational waves from point sources. A spherical harmonic decomposition method is employed to look for gravitational-wave emission from spatially-extended sources. Neither technique found evidence of gravitational-wave signals. Hence we derive 95% confidence-level upper limit sky maps on the gravitational-wave energy flux from broadband point sources, ranging from Fα,Θ<(0.013–7.6)×10−8 erg cm−2 s−1 Hz−1, and on the (normalized) gravitational-wave energy density spectrum from extended sources, ranging from Ωα,Θ<(0.57–9.3)×10−9 sr−1, depending on direction (Θ) and spectral index (α). These limits improve upon previous limits by factors of 2.9–3.5. We also set 95% confidence level upper limits on the frequency-dependent strain amplitudes of quasimonochromatic gravitational waves coming from three interesting targets, Scorpius X-1, SN 1987A and the Galactic Center, with best upper limits range from h0<(1.7–2.1)×10−25, a factor of ≥2.0 improvement compared to previous stochastic radiometer searches.

关键词： Experimental studies of gravity General relativity Gravitational waves

Causes of blindness and vision impairment in 2020 and trends over 30 years, and prevalence of avoidable blindness in relation to VISION 2020: the Right to Sight: an analysis for the Global Burden of Disease Study (vol 2, pg 144, 2021)

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LANCET GLOBAL HEALTH 2021年第4期9卷 E408-E408页

作者： Steinmetz, Jaimie D. Vision and Eye Research Institute Anglia Ruskin University Cambridge United Kingdom Biomedical Informatics Seoul National University Hospital Seoul South Korea Institute for Health Metrics and Evaluation University of Washington Seattle WA United States Department of Health Metrics Sciences School of Medicine University of Washington Seattle WA United States Institute of Health Services Research Yonsei University Seoul South Korea Department of Ophthalmology University of Washington Seattle WA United States Department of Mathematics Imperial College London London United Kingdom WHO Collaborating Centre for Public Health Education and Training Imperial College London London United Kingdom Department of Primary Care and Public Health Imperial College London London United Kingdom School of Population and Global Health University of Melbourne Carlton VIC Australia School of Optometry and Vision Science UNSW Sydney NSW Australia Brien Holden Vision Institute Sydney Australia Department of Ophthalmology University of Adelaide Adelaide SA Australia Department of Parasitology and Mycology Jahrom University of Medical Sciences Jahrom Iran Department of Clinical Sciences University of Sharjah Sharjah United Arab Emirates Ophthalmic Research Center Shahid Beheshti University of Medical Sciences Tehran Iran Department of Ophthalmology Shahid Beheshti University of Medical Sciences Tehran Iran Research Institute for Endocrine Sciences Shahid Beheshti University of Medical Sciences Tehran Iran Ophthalmic Epidemiology Research Center Shahid Beheshti University of Medical Sciences Tehran Iran Health Services Management Department Qazvin University of Medical Sciences Qazvin Iran Department of Systems Populations and Leadership University of Michigan Ann Arbor MI United States Department of Medicine Sofia Ismail Memorial Medical Centre Bogura Bangladesh The Fred Hollows Foundation Sydney NSW Australia Berhan Public Health & Eye Care Consultancy Addis A

Hospital El Salvador: a novel paradigm of intensive care in response to COVID-19 in central America. Lancet Glob Health 2021;9: e241?42?In this Comment, the conflict of interest statement should have included the following: ?By virtue of their roles within a public hospital or the Ministry of Health, MB, LC, WH, and XS are government employees. The findings and conclusions in the Comment are only those of the authors.? This correction has been made as of Feb 26, 2021.

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