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Joint 87th Annual Meeting on the International Association of Applied Mathematics and Mechanics, GAMM 2016 and Deutsche Mathematiker‐Vereinigung, DMV 2016

作者： Köhler, Martin Lang, Norman Saak, Jens Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Computational Methods in Systems and Control Theory Germany Technische Universität Chemnitz Faculty of Mathematics Germany

Differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time-varying systems and many more. Here, we will focus on differential Riccati equations (DRE). Solving such matrix-valued ordinary differential equations (ODE) is a highly time consuming process. We present a Parareal based algorithm applied to Rosenbrock methods for the solution of the matrix-valued differential Riccati equations. Considering problems of moderate size, direct matrix equation solvers for the solution of the algebraic Lyapunov equations arising inside the time intgration methods are used. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

关键词： Ordinary differential equations

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AFast Solver for an H_(1) Regularized PDE-Constrained Optimization Problem

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Communications in computational Physics 2016年第1期19卷 143-167页

作者： Andrew T.Barker Tyrone Rees Martin Stoll Center for Applied Scientific Computing Lawrence Livermore National LaboratoryMail Stop L-561LivermoreCA 94551USA Numerical Analysis Group Scientific Computing DepartmentRutherford Appleton LaboratoryChiltonDidcotOxfordshireOX110QXUnited Kingdom Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical SystemsSandtorstr.139106MagdeburgGermany

In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control *** focus on a time-dependent PDE,and consider both distributed and boundary *** problems we consider include bound constraints on the state,and we use a Moreau-Yosida penalty function to handle *** propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

关键词： Preconditioning Krylov methods PDE-constrained optimization optimal control of PDEs

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Model reduction of controlled fokker-planck and liouville-von neumann equations

arXiv

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arXiv 2017年

作者： BENNER, PETER BREITEN, TOBIAS HARTMANN, CARSTEN SCHMIDT, BURKHARD Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 MagdeburgD-39106 Germany Institut fur Mathematik Karl-Franzens-Universitat Heinrichstr. 36/III GrazA-8010 Austria Institut fur Mathematik Brandenburgische Technische Universitat Konrad-Wachsmann-Allee 1 CottbusD-03046 Germany Institut fur Mathematik Freie Universitat Berlin Arnimallee 6 BerlinD-14195 Germany

Model reduction methods for bilinear control systems are compared by means of practical examples of Liouville-von Neumann and Fokker-Planck type. methods based on balancing generalized system Gramians and on minimizing an H2-type cost functional are considered. The focus is on the numerical implementation and a thorough comparison of the methods. Structure and stability preservation are investigated, and the competitiveness of the approaches is shown for practically relevant, large-scale examples. Copyright © 2017, The Authors. All rights reserved.

关键词： Lyapunov functions

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Reduced-Order Modeling of Index-1 Vibrational systems Using Interpolatory Projections

Reduced-Order Modeling of Index-1 Vibrational Systems Using ...

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International Conference on Computer and Information Technology

作者： Peter Benner Jens Saak M. Monir Uddin Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstra?e 1 D-39106 Magdeburg Germany Department of Mathematics and Physics North South University 15/B Bashundhara Dhaka-1239 Bangladesh

ISBN: (纸本)9781509040919

Large sparse second order index-1 descriptor systems arise in various disciplines of science and engineering, such as constraint mechanics or multibody dynamics, mechatronics (where mechanical and electrical elements are coupled), but also RLC circuit design. Simulation, controller design and design optimization are only some applications of such models. Either of these tasks, just like any other many-query situation becomes unfeasible when the system is high dimensional. This paper discusses an algorithm to obtain a reduced state space model of a large sparse second order index-1 system using an interpolatory projection method based on the iterative rational Krylov algorithm (IRKA). In each iteration of this algorithm, we need to solve a number of linear systems. The main contribution of this paper is to solve these linear systems by exploiting the sparsity of the original model, which reduces the computational cost drastically. The algorithm is applied to a micro-mechanical piezo-actuated structural FEM model of a certain building block of a machine tool. Numerical experiments with a complex 3d model of an adaptive spindle support (a piezo-mechanical multiphysics system) show the effectivity and efficiency of the techniques.

关键词： second order index-1 systems sparsity model reduction interpolatory projections

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Adjoint-Based Optimal Boundary control of a Stefan Problem System Fully Coupled with Navier-Stokes Equations

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PAMM 2016年第1期16卷

作者： Björn Baran Jan Heiland Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg

Free boundary and moving boundary problems, that can be used to model crystal growth or the solidification and melting of pure materials, receive growing attention in science and technology. The optimal control of these problems appear even more interesting since certain desired shapes of the boundaries improve, e.g., the material quality in the case of crystal growth. We consider the so called two-phase Stefan problem that models a solid and a liquid phase separated by a moving interface. In the work presented, we take a sharp interface model approach and define a quadratic tracking-type cost functional that penalizes the deviation of the interface from the desired state at a final time as well as the control costs. Following the “optimize-then-discretize” paradigm, we formulate a first order optimality system using the formal Lagrange approach and derive the adjoint PDE system that provides the needed gradient of the cost functional. By means of an example setup of a container with an in- and outflow of water and a cooling unit at the bottom, we illustrate how the derived formulations can be used to achieve a desired interface between the solid and the fluid phase by controlling the flow at the inlet. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Numerical solution to low rank perturbed Lyapunov equations by the sign function method

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PAMM 2016年第1期16卷

作者： Peter Benner Jonas Denißen Max Planck Institute for Dynamics of Complex Technical Systems Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg Germany

We investigate the numerical solution to a low rank perturbed Lyapunov equation A T X + XA = W via the sign function method (SFM). The sign function method has been proposed to solve Lyapunov equations, see e.g. [1], but here we focus on a framework where the matrix A has a special structure, i. e. A = B + UCV T , where B is a blockdiagonal matrix and UCV T is a low rank perturbation. We show that this structure can be kept throughout the sign function iteration but the rank of the perturbation doubles per iteration. Therefore, we apply a low rank approximation to the perturbation in order to keep its numerical rank small. We compare the standard SFM with its structure preserving variant presented in this paper by means of numerical examples from viscously damped mechanical systems. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Solving Differential Matrix Equations using Parareal

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PAMM 2016年第1期16卷

作者： Martin Köhler Norman Lang Jens Saak Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Computational Methods in Systems and Control Theory Technische Universität Chemnitz Faculty of Mathematics

Differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time varying systems and many more. Here, we will focus on differential Riccati equations (DRE). Solving such matrix-valued ordinary differential equations (ODE) is a highly time consuming process. We present a Parareal based algorithm applied to Rosenbrock methods for the solution of the matrix-valued differential Riccati equations. Considering problems of moderate size, direct matrix equation solvers for the solution of the algebraic Lyapunov equations arising inside the time intgration methods are used. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Distributed optimal control problems governed by coupled convection dominated PDEs with control constraints

Lecture Notes in Computational Science and Engineering

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Lecture Notes in computational Science and Engineering 2015年 103卷 469-478页

作者： Yücel, Hamdullah Benner, Peter Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

We study the numerical solution of control constrained optimal control problems governed by a system of convection diffusion equations with nonlinear reaction terms, arising from chemical processes. control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a posteriori error estimates is applied for both approaches. © Springer International Publishing Switzerland 2015.

关键词： Optimal control systems

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Genetic drivers of heterogeneity in type 2 diabetes pathophysiology

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Nature 2024年第8003期627卷 347-357页

作者： Ken Suzuki Konstantinos Hatzikotoulas Lorraine Southam Henry J Taylor Xianyong Yin Kim M Lorenz Ravi Mandla Alicia Huerta-Chagoya Giorgio E M Melloni Stavroula Kanoni Nigel W Rayner Ozvan Bocher Ana Luiza Arruda Kyuto Sonehara Shinichi Namba Simon S K Lee Michael H Preuss Lauren E Petty Philip Schroeder Brett Vanderwerff Mart Kals Fiona Bragg Kuang Lin Xiuqing Guo Weihua Zhang Jie Yao Young Jin Kim Mariaelisa Graff Fumihiko Takeuchi Jana Nano Amel Lamri Masahiro Nakatochi Sanghoon Moon Robert A Scott James P Cook Jung-Jin Lee Ian Pan Daniel Taliun Esteban J Parra Jin-Fang Chai Lawrence F Bielak Yasuharu Tabara Yang Hai Gudmar Thorleifsson Niels Grarup Tamar Sofer Matthias Wuttke Chloé Sarnowski Christian Gieger Darryl Nousome Stella Trompet Soo-Heon Kwak Jirong Long Meng Sun Lin Tong Wei-Min Chen Suraj S Nongmaithem Raymond Noordam Victor J Y Lim Claudia H T Tam Yoonjung Yoonie Joo Chien-Hsiun Chen Laura M Raffield Bram Peter Prins Aude Nicolas Lisa R Yanek Guanjie Chen Jennifer A Brody Edmond Kabagambe Ping An Anny H Xiang Hyeok Sun Choi Brian E Cade Jingyi Tan K Alaine Broadaway Alice Williamson Zoha Kamali Jinrui Cui Manonanthini Thangam Linda S Adair Adebowale Adeyemo Carlos A Aguilar-Salinas Tarunveer S Ahluwalia Sonia S Anand Alain Bertoni Jette Bork-Jensen Ivan Brandslund Thomas A Buchanan Charles F Burant Adam S Butterworth Mickaël Canouil Juliana C N Chan Li-Ching Chang Miao-Li Chee Ji Chen Shyh-Huei Chen Yuan-Tsong Chen Zhengming Chen Lee-Ming Chuang Mary Cushman John Danesh Swapan K Das H Janaka de Silva George Dedoussis Latchezar Dimitrov Ayo P Doumatey Shufa Du Qing Duan Kai-Uwe Eckardt Leslie S Emery Daniel S Evans Michele K Evans Krista Fischer James S Floyd Ian Ford Oscar H Franco Timothy M Frayling Barry I Freedman Pauline Genter Hertzel C Gerstein Vilmantas Giedraitis Clicerio González-Villalpando Maria Elena González-Villalpando Penny Gordon-Larsen Myron Gross Lindsay A Guare Sophie Hackinger Liisa Hakaste Sohee Han Andrew T Hattersley Christian Herder Momoko Horikoshi Annie-Green Howard Willa Centre for Genetics and Genomics Versus Arthritis Centre for Musculoskeletal Research Division of Musculoskeletal and Dermatological Sciences University of Manchester Manchester UK. Department of Diabetes and Metabolic Diseases Graduate School of Medicine University of Tokyo Tokyo Japan. Department of Statistical Genetics Osaka University Graduate School of Medicine Suita Japan. Institute of Translational Genomics Helmholtz Zentrum München German Research Center for Environmental Health Neuherberg Germany. konstantinos.hatzikotoulas@helmholtz-munich.de. Institute of Translational Genomics Helmholtz Zentrum München German Research Center for Environmental Health Neuherberg Germany. Center for Precision Health Research National Human Genome Research Institute National Institutes of Health Bethesda MD USA. British Heart Foundation Cardiovascular Epidemiology Unit Department of Public Health and Primary Care University of Cambridge Cambridge UK. Heart and Lung Research Institute University of Cambridge Cambridge UK. Department of Epidemiology School of Public Health Nanjing Medical University Nanjing China. Department of Biostatistics and Center for Statistical Genetics University of Michigan Ann Arbor MI USA. Corporal Michael J. Crescenz VA Medical Center Philadelphia PA USA. Department of Systems Pharmacology and Translational Therapeutics University of Pennsylvania Perelman School of Medicine Philadelphia PA USA. Department of Genetics University of Pennsylvania Perelman School of Medicine Philadelphia PA USA. Programs in Metabolism and Medical and Population Genetics Broad Institute of Harvard and MIT Cambridge MA USA. Diabetes Unit and Center for Genomic Medicine Massachusetts General Hospital Boston MA USA. TIMI Study Group Division of Cardiovascular Medicine Brigham and Women's Hospital Harvard Medical School Boston MA USA. William Harvey Research Institute Barts and the London School of Medicine and Dentistry Queen Mary University of London L

Type 2 diabetes (T2D) is a heterogeneous disease that develops through diverse pathophysiological processes and molecular mechanisms that are often specific to cell type. Here, to characterize the genetic contribution to these processes across ancestry groups, we aggregate genome-wide association study data from 2,535,601 individuals (39.7% not of European ancestry), including 428,452 cases of T2D. We identify 1,289 independent association signals at genome-wide significance (P < 5 × 10) that map to 611 loci, of which 145 loci are, to our knowledge, previously unreported. We define eight non-overlapping clusters of T2D signals that are characterized by distinct profiles of cardiometabolic trait associations. These clusters are differentially enriched for cell-type-specific regions of open chromatin, including pancreatic islets, adipocytes, endothelial cells and enteroendocrine cells. We build cluster-specific partitioned polygenic scores in a further 279,552 individuals of diverse ancestry, including 30,288 cases of T2D, and test their association with T2D-related vascular outcomes. Cluster-specific partitioned polygenic scores are associated with coronary artery disease, peripheral artery disease and end-stage diabetic nephropathy across ancestry groups, highlighting the importance of obesity-related processes in the development of vascular outcomes. Our findings show the value of integrating multi-ancestry genome-wide association study data with single-cell epigenomics to disentangle the aetiological heterogeneity that drives the development and progression of T2D. This might offer a route to optimize global access to genetically informed diabetes care.

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The overlapping burden of the three leading causes of disability and death in sub-Saharan African children

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Nature Communications 2022年第1期13卷 1-14页

作者： Reiner, Robert C. Welgan, Catherine A. Troeger, Christopher E. Baumann, Mathew M. Weiss, Daniel J. Deshpande, Aniruddha Blacker, Brigette F. Miller-Petrie, Molly K. Earl, Lucas Bhatt, Samir Abolhassani, Hassan Abosetugn, Akine Eshete Abu-Gharbieh, Eman Adekanmbi, Victor Adetokunboh, Olatunji O. Aghaali, Mohammad Aji, Budi Alahdab, Fares Al-Aly, Ziyad Alhassan, Robert Kaba Ali, Saqib Alizade, Hesam Aljunid, Syed Mohamed Almasi-Hashiani, Amir Al-Mekhlafi, Hesham M. Altirkawi, Khalid A. Alvis-Guzman, Nelson Amare, Azmeraw T. Amini, Saeed Amugsi, Dickson A. Ancuceanu, Robert Andrei, Catalina Liliana Ansari, Fereshteh Anvari, Davood Appiah, Seth Christopher Yaw Arabloo, Jalal Aremu, Olatunde Atout, Maha Moh’d Wahbi Ausloos, Marcel Ausloos, Floriane Ayanore, Martin Amogre Aynalem, Yared Asmare Azene, Zelalem Nigussie Badawi, Alaa Baig, Atif Amin Banach, Maciej Bedi, Neeraj Bhagavathula, Akshaya Srikanth Bhandari, Dinesh Bhardwaj, Nikha Bhardwaj, Pankaj Bhattacharyya, Krittika Bhutta, Zulfiqar A. Bijani, Ali Birhanu, Tesega Tesega Mengistu Bitew, Zebenay Workneh Boloor, Archith Brady, Oliver J. Butt, Zahid A. Car, Josip Carvalho, Felix Casey, Daniel C. Chattu, Vijay Kumar Chowdhury, Mohiuddin Ahsanul Kabir Chu, Dinh-Toi Coelho, Camila H. Cook, Aubrey J. Damiani, Giovanni Daoud, Farah Gela, Jiregna Darega Darwish, Amira Hamed Daryani, Ahmad Das, Jai K. Davis Weaver, Nicole Deribe, Kebede Desalew, Assefa Dharmaratne, Samath Dhamminda Dianatinasab, Mostafa Diaz, Daniel Djalalinia, Shirin Dorostkar, Fariba Dubljanin, Eleonora Duko, Bereket Dwyer-Lindgren, Laura Effiong, Andem El Sayed Zaki, Maysaa El Tantawi, Maha Enany, Shymaa Fattahi, Nazir Feigin, Valery L. Fernandes, Eduarda Ferrara, Pietro Fischer, Florian Foigt, Nataliya A. Folayan, Morenike Oluwatoyin Foroutan, Masoud Frostad, Joseph Jon Fukumoto, Takeshi Gaidhane, Abhay Motiramji Gebrekrstos, Hailemikael Gebrekidan G. K. Gebremeskel, Leake Gebreslassie, Assefa Ayalew Gething, Peter W. Gezae, Kebede Embaye Ghadiri, Keyghobad Ghashghaee, Ahmad Golechha, Mahaveer Gubar 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 Malaria Atlas Project University of Oxford Oxford United Kingdom Imperial College London London United Kingdom Department of Laboratory Medicine Karolinska University Hospital Huddinge Sweden Research Center for Immunodeficiencies Tehran University of Medical Sciences Tehran Iran Department of Public Health Debre Berhan University Debre Berhan Ethiopia Department of Clinical Sciences University of Sharjah Sharjah United Arab Emirates Population Health Sciences King’s College London London United Kingdom Centre of Excellence for Epidemiological Modelling and Analysis Stellenbosch University Stellenbosch South Africa Department of Global Health Stellenbosch University Cape Town South Africa Department of Epidemiology and Biostatistics Qom University of Medical Sciences Qom Iran Faculty of Medicine and Public Health Jenderal Soedirman University Purwokerto Indonesia Mayo Evidence-based Practice Center Mayo Clinic Foundation for Medical Education and Research Rochester MN United States John T. Milliken Department of Internal Medicine Washington University in St. Louis St. Louis MO United States Clinical Epidemiology Center Department of Veterans Affairs St Louis MO United States Institute of Health Research University of Health and Allied Sciences Ho Ghana Department of Information Systems College of Economics and Political Science Sultan Qaboos University Muscat Oman Infectious and Tropical Disease Research Center Hormozgan University of Medical Sciences Bandar Abbas Iran Department of Health Policy and Management Kuwait University Safat Kuwait International Centre for Casemix and Clinical Coding National University of Malaysia Bandar Tun Razak Malaysia Department of Epidemiology Arak University of Medical Sciences Arak Iran Medical Research Center

Despite substantial declines since 2000, lower respiratory infections (LRIs), diarrhoeal diseases, and malaria remain among the leading causes of nonfatal and fatal disease burden for children under 5 years of age (under 5), primarily in sub-Saharan Africa (SSA). The spatial burden of each of these diseases has been estimated subnationally across SSA, yet no prior analyses have examined the pattern of their combined burden. Here we synthesise subnational estimates of the burden of LRIs, diarrhoea, and malaria in children under-5 from 2000 to 2017 for 43 sub-Saharan countries. Some units faced a relatively equal burden from each of the three diseases, while others had one or two dominant sources of unit-level burden, with no consistent pattern geographically across the entire subcontinent. Using a subnational counterfactual analysis, we show that nearly 300 million DALYs could have been averted since 2000 by raising all units to their national average. Our findings are directly relevant for decision-makers in determining which and targeting where the most appropriate interventions are for increasing child survival. © 2022, The Author(s).

关键词： Biogeography Epidemiology Infectious diseases Malaria

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