检索结果-内蒙古大学图书馆

On optimal finite element schemes for biharmonic equation

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

In this paper, two nonconforming finite element schemes that use piecewise cubic and piecewise quartic polynomials respectively are constructed for the planar biharmonic equation with optimal convergence rates on general shape-regular triangulations. Therefore, it is proved that optimal finite element schemes of arbitrary order for planar biharmonic equation can be constructed on general shape-regular triangulations. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite element method

Automated Detection and Forecasting of COVID-19 using Deep Learning Techniques: A Review

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Shoeibi, Afshin Khodatars, Marjane Jafari, Mahboobeh Ghassemi, Navid Sadeghi, Delaram Moridian, Parisa Khadem, Ali Alizadehsani, Roohallah Hussain, Sadiq Zare, Assef Sani, Zahra Alizadeh Khozeimeh, Fahime Nahavandi, Saeid Rajendra Acharya, U. Gorriz, Juan M. The Data Science and Computational Intelligence Institute University of Granada Spain The Computer Engineering Department Ferdowsi University of Mashhad Mashhad Iran Deakin University VIC3217 Australia The Faculty of Electrical Engineering K. N. Toosi University of Technology Tehran Iran System Administrator at Dibrugarh University Assam786004 India Faculty of Electrical Engineering Gonabad Branch Islamic Azad University Gonabad Iran Rajaie Cardiovascular Medical and Research Center Iran University of Medical Sciences Tehran Iran The School of Mathematics Physics and Computing University of Southern Queensland Springfield Australia Dept. of Psychiatry University of Cambridge United Kingdom

Coronavirus, or COVID-19, is a hazardous disease that has endangered the health of many people around the world by directly affecting the lungs. COVID-19 is a medium-sized, coated virus with a single-stranded RNA, and also has one of the largest RNA genomes and is approximately 120 nm. The X-Ray and computed tomography (CT) imaging modalities are widely used to obtain a fast and accurate medical diagnosis. Identifying COVID-19 from these medical images is extremely challenging as it is time-consuming and prone to human errors. Hence, artificial intelligence (AI) methodologies can be used to obtain consistent high performance. Among the AI methods, deep learning (DL) networks have gained popularity recently compared to conventional machine learning (ML). Unlike ML, all stages of feature extraction, feature selection, and classification are accomplished automatically in DL models. In this paper, a complete survey of studies on the application of DL techniques for COVID-19 diagnostic and segmentation of lungs is discussed, concentrating on works that used X-Ray and CT images. Additionally, a review of papers on the forecasting of coronavirus prevalence in different parts of the world with DL is presented. Lastly, the challenges faced in the detection of COVID-19 using DL techniques and directions for future research are discussed. © 2020, CC BY-NC-ND.

关键词： COVID-19

Stochastic conformal multi-symplectic method for damped stochastic nonlinear Schrödinger equation

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Chen, Chuchu Hong, Jialin Ji, Lihai Department of Mathematics Michigan State University Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Institute of Applied Physics and Computational Mathematics Beijing100094 China

In this paper, we propose a stochastic conformal multi-symplectic method for a class of damped stochastic Hamiltonian partial differential equations in order to inherit the intrinsic properties, and apply the numerical method to solve a kind of damped stochastic nonlinear Schrödinger equation with multiplicative noise. It is shown that the stochastic conformal multi-symplectic method preserves the discrete stochastic conformal multi-symplectic conservation law, the discrete charge exponential dissipation law almost surely, and we also deduce the recurrence relation of the discrete global energy. Numerical experiments are preformed to verify the good performance of the proposed stochastic conformal multi-symplectic method, compared with a Crank-Nicolson type method. Finally, we present the mean square convergence result of the proposed numerical method in temporal direction numerically.60H15, 37K05, 65P10 Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

Metrics Reloaded: Recommendations for image analysis validation

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Maier-Hein, Lena Reinke, Annika Godau, Patrick Tizabi, Minu D. Buettner, Florian Christodoulou, Evangelia Glocker, Ben Isensee, Fabian Kleesiek, Jens Kozubek, Michal Reyes, Mauricio Riegler, Michael A. Wiesenfarth, Manuel Emre Kavur, A. Sudre, Carole H. Baumgartner, Michael Eisenmann, Matthias Heckmann-Nötzel, Doreen Rädsch, Tim Acion, Laura Antonelli, Michela Arbel, Tal Bakas, Spyridon Benis, Arriel Blaschko, Matthew B. Jorge Cardoso, M. Cheplygina, Veronika Cimini, Beth A. Collins, Gary S. Farahani, Keyvan Ferrer, Luciana Galdran, Adrian Ginneken, Bram Van Haase, Robert Hashimoto, Daniel A. Hoffman, Michael M. Huisman, Merel Jannin, Pierre Kahn, Charles E. Kainmueller, Dagmar Kainz, Bernhard Karargyris, Alexandros Karthikesalingam, Alan Kenngott, Hannes Kofler, Florian Kopp-Schneider, Annette Kreshuk, Anna Kurc, Tahsin Landman, Bennett A. Litjens, Geert Madani, Amin Maier-Hein, Klaus Martel, Anne L. Mattson, Peter Meijering, Erik Menze, Bjoern Moons, Karel G.M. Müller, Henning Nichyporuk, Brennan Nickel, Felix Petersen, Jens Rajpoot, Nasir Rieke, Nicola Saez-Rodriguez, Julio Sánchez, Clara I. Shetty, Shravya Smeden, Maarten Van Summers, Ronald M. Taha, Abdel A. Tiulpin, Aleksei Tsaftaris, Sotirios A. Calster, Ben Van Varoquaux, Gaël Jäger, Paul F. Heidelberg Division of Intelligent Medical Systems and HI Helmholtz Imaging Germany Faculty of Mathematics and Computer Science and Medical Faculty Heidelberg University Heidelberg Germany NCT Heidelberg a partnership between DKFZ University Medical Center Heidelberg Germany Faculty of Mathematics and Computer Science Heidelberg University Heidelberg Germany Heidelberg Division of Intelligent Medical Systems Germany partner site Frankfurt/Mainz a partnership between DKFZ and UCT Frankfurt-Marburg Germany Heidelberg Goethe University Frankfurt Germany Department of Medicine Goethe University Frankfurt Germany Department of Informatics Frankfurt Cancer Insititute Germany Department of Computing Imperial College London London United Kingdom Heidelberg Division of Medical Image Computing and HI Applied Computer Vision Lab Germany Institute for AI in Medicine University Medicine Essen Essen Germany Centre for Biomedical Image Analysis Faculty of Informatics Masaryk University Brno Czech Republic ARTORG Center for Biomedical Engineering Research University of Bern Bern Switzerland Department of Radiation Oncology University Hospital Bern University of Bern Bern Switzerland Simula Metropolitan Center for Digital Engineering Oslo Norway UiT The Arctic University of Norway Romsø Norway Heidelberg Division of Biostatistics Germany Heidelberg Division of Intelligent Medical Systems Division of Medical Image Computing HI Applied Computer Vision Lab Germany MRC Unit for Lifelong Health and Ageing UCL Centre for Medical Image Computing Department of Computer Science University College London London United Kingdom School of Biomedical Engineering and Imaging Science King’s College London London United Kingdom Heidelberg Division of Medical Image Computing Germany Instituto de Cálculo CONICET – Universidad de Buenos Aires Buenos Aires Argentina Centre for Medical Image Computing University College London London United Kingdom McGill University Montréal

Increasing evidence shows that flaws in machine learning (ML) algorithm validation are an underestimated global problem. Particularly in automatic biomedical image analysis, chosen performance metrics often do not reflect the domain interest, thus failing to adequately measure scientific progress and hindering translation of ML techniques into practice. To overcome this, we created Metrics Reloaded, a comprehensive framework guiding researchers in the problem-aware selection of metrics. It was developed by a large international consortium in a multi-stage Delphi process and is based on the novel concept of a problem fingerprint – a structured representation of the given problem that captures all aspects that are relevant for metric selection, from the domain interest to the properties of the target structure(s), data set and algorithm output. Based on the problem fingerprint, users are guided through the process of choosing and applying appropriate validation metrics while being made aware of potential pitfalls. Metrics Reloaded targets image analysis problems that can be interpreted as a classification task at image, object or pixel level, namely image-level classification, object detection, semantic segmentation, and instance segmentation tasks. To improve the user experience, we implemented the framework in the Metrics Reloaded online tool. Following the convergence of ML methodology across application domains, Metrics Reloaded fosters the convergence of validation methodology. Its applicability is demonstrated for various biomedical use cases. © 2022, CC BY.

关键词： Semantic Segmentation

Energy stable second order linear schemes for the allen-cahn phase-field equation

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Wang, Lin Yu, Haijun LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS and LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China

Phase-field model is a powerful mathematical tool to study the dynamics of interface and morphol- ogy changes in fluid mechanics and material sciences. However, numerically solving a phase field model for a real problem is a challenge task due to the non-convexity of the bulk energy and the small interface thickness parameter in the equation. In this paper, we propose two stabilized second order semi-implicit linear schemes for the Allen-Cahn phase-field equation based on backward differentiation formula and Crank-Nicolson method, respectively. In both schemes, the nonlinear bulk force is treated explicitly with two second-order stabilization terms, which make the schemes unconditional energy stable and numerically efficient. By using a known result of the spectrum estimate of the linearized Allen-Cahn operator and some regularity estimates of the exact solution, we obtain an optimal second order con- vergence in time with a prefactor depending on the inverse of the characteristic interface thickness only in some lower polynomial order. Both 2-dimensional and 3-dimensional numerical results are presented to verify the accuracy and efficiency of proposed *** Codes 65M12, 65M15, 65P40 Copyright © 2018, The Authors. All rights reserved.

关键词： Fluid mechanics

Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections

学校读者我要写书评

暂无评论

Physical Review Letters 2019年第3期123卷 036601-036601页

作者： J. Vučičević J. Kokalj R. Žitko N. Wentzell D. Tanasković J. Mravlje Scientific Computing Laboratory Center for the Study of Complex Systems Institute of Physics Belgrade University of Belgrade Pregrevica 118 11080 Belgrade Serbia University of Ljubljana Faculty of Civil and Geodetic Engineering Jamova 2 Ljubljana Slovenia Jozef Stefan Institute Jamova 39 SI-1000 Ljubljana Slovenia University of Ljubljana Faculty of Mathematics and Physics Jadranska 19 Ljubljana Slovenia Center for Computational Quantum Physics Simons Foundation Flatiron Institute New York New York 10010 USA

Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results, and the question of the exact solution for the conductivity in the Hubbard model remained open. In this Letter, we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity and identify the best available result to be compared to experiment. We find that, at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size 4×4, and the corresponding Lanczos diagonalization result is, therefore, close to the exact result in the thermodynamic limit.

关键词： Electrical conductivity 2-dimensional systems Mott insulators Strongly correlated systems Dynamical mean field theory Exact diagonalization Hubbard model Lattice models in condensed matter Monte Carlo methods Numerical Renormalization Group

Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Perlmutter, Michael Gao, Feng Wolf, Guy Hirn, Matthew Michigan State University Department of Computational Mathematics Science & Engineering East LansingMI United States Yale University Department of Genetics New HavenCT United States Université de Montréal Department of Mathematics and Statistics Mila Quebec Artificial Intelligence Institute MontréalQC Canada Center for Quantum Computing Science & Engineering East LansingMI United States

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data. Copyright © 2019, The Authors. All rights reserved.

关键词： Geometry

Convergence Analysis of an Unconditionally Energy Stable Linear Crank-Nicolson Scheme for the Cahn-Hilliard Equation

学校读者我要写书评

暂无评论

数学研究 2018年第1期51卷 89-114页

作者： Lin Wang Haijun Yu School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing 100190 China

Efficient and unconditionally stable high order time marching schemes are very important but not easy to construct for nonlinear phase dynamics. In this paper, we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for the Cahn-Hilliard equation with provable unconditional stability. In this scheme the non-linear bulk force are treated explicitly with two second-order linear stabilization terms. The semi-discretized equation is a linear elliptic system with constant coefficients, thus robust and efficient solution procedures are guaranteed. Rigorous error analysis show that, when the time step-size is small enough, the scheme is second order accurate in time with a prefactor controlled by some lower degree polynomial of 1/ε. Here ε is the interface thickness parameter. Numerical results are presented to verify the accuracy and efficiency of the scheme.

关键词： phase field model Cahn-Hilliard equation unconditionally stable stabilized semi-implicit scheme high order time marching

Application of bounded total variation denoising in urban traffic analysis

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Tang, Shanshan Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China NCMIS LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences

While it is believed that denoising is not always necessary in many big data applications, we show in this paper that denoising is helpful in urban traffic analysis by applying the method of bounded total variation denoising to the urban road traffic prediction and clustering problem. We propose two easy-to-implement methods to estimate the parameter noise strength in the denoising algorithm, and apply the denoising algorithm to GPS-based traffic data from Beijing taxi system. For the traffic prediction problem, numerical experiments show that the predicting accuracy is improved by applying the proposed bounded total variation denoising algorithm. For the clustering problem, we apply a recently developed parameter-free clustering analysis method for more than one hundred urban road segments in Beijing based on their velocity profiles. Much better clustering results are obtained after denoising. Copyright © 2018, The Authors. All rights reserved.

关键词： Cluster analysis