Author
Lexing Ying
Other affiliations: California Institute of Technology, Facebook, China University of Mining and Technology ...read more
Bio: Lexing Ying is an academic researcher from Stanford University. The author has contributed to research in topics: Preconditioner & Discretization. The author has an hindex of 45, co-authored 250 publications receiving 9213 citations. Previous affiliations of Lexing Ying include California Institute of Technology & Facebook.
Papers published on a yearly basis
Papers
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TL;DR: This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform in two and three dimensions, based on unequally spaced fast Fourier transforms, while the second is based on the wrapping of specially selected Fourier samples.
Abstract: This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform in two and three dimensions. The first digital transformation is based on unequally spaced fast Fourier transforms, while the second is based on the wrapping of specially selected Fourier samples. The two implementations essentially differ by the choice of spatial grid used to translate curvelets at each scale and angle. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. And both implementations are fast in the sense that they run in O(n^2 log n) flops for n by n Cartesian arrays; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity. Our digital transformations improve upon earlier implementations—based upon the first generation of curvelets—in the sense that they are conceptually simpler, faster, and far less redundant. The software CurveLab, which implements both transforms presented in this paper, is available at http://www.curvelet.org.
2,603 citations
TL;DR: A new fast multipole method for particle simulations that does not require the implementation of multipole expansions of the underlying kernel, and it is based only on kernel evaluations that matches its potential to the potential of the original sources at a surface, in the far field.
501 citations
TL;DR: It is proved that warped oscillatory functions, a toy model for texture, have a signicantly sparser expansion in wave atoms than in other xed standard representations like wavelets, Gabor atoms, or curvelets.
302 citations
TL;DR: In this paper, a low-rank approximation of the space-wavenumber wave propagation matrix is proposed for wave propagation in 3D heterogeneous isotropic or anisotropic media.
Abstract: We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space‐wavenumber wave‐propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse‐time migration in 3D heterogeneous isotropic or anisotropic media.
223 citations
TL;DR: The sweeping preconditioner is introduced, which is highly efficient for iterative solutions of the variable‐coefficient Helmholtz equation including very‐high‐frequency problems and is extended to the three‐dimensional case with some success.
Abstract: The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable-coefficient Helmholtz equation including very-high-frequency problems. The first central idea of this novel approach is to construct an approximate factorization of the discretized Helmholtz equation by sweeping the domain layer by layer, starting from an absorbing layer or boundary condition. Given this specific order of factorization, the second central idea is to represent the intermediate matrices in the hierarchical matrix framework. In two dimensions, both the construction and the application of the preconditioners are of linear complexity. The generalized minimal residual method (GMRES) solver with the resulting preconditioner converges in an amazingly small number of iterations, which is essentially independent of the number of unknowns. This approach is also extended to the three-dimensional case with some success. Numerical results are provided in both two and three dimensions to demonstrate the efficiency of this new approach.
185 citations
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28 Jul 2005
TL;DR: PfPMP1）与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作�ly.
Abstract: 抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。
18,940 citations
TL;DR: A first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure can achieve O(1/N2) convergence on problems, where the primal or the dual objective is uniformly convex, and it can show linear convergence, i.e. O(ωN) for some ω∈(0,1), on smooth problems.
Abstract: In this paper we study a first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N) in finite dimensions for the complete class of problems. We further show accelerations of the proposed algorithm to yield improved rates on problems with some degree of smoothness. In particular we show that we can achieve O(1/N 2) convergence on problems, where the primal or the dual objective is uniformly convex, and we can show linear convergence, i.e. O(? N ) for some ??(0,1), on smooth problems. The wide applicability of the proposed algorithm is demonstrated on several imaging problems such as image denoising, image deconvolution, image inpainting, motion estimation and multi-label image segmentation.
4,487 citations
University of Udine1, École Polytechnique Fédérale de Lausanne2, University of Lugano3, Leipzig University4, University of Paris5, University of North Texas6, Princeton University7, National Research Council8, International School for Advanced Studies9, Cornell University10, University of Lincoln11, University of Milan12, École Polytechnique13, International Centre for Theoretical Physics14, University of Paderborn15, University of Oxford16, Jožef Stefan Institute17, University of Padua18, Sapienza University of Rome19, Vietnam Academy of Science and Technology20, University of British Columbia21, Centre national de la recherche scientifique22, University of Lorraine23, University of Zurich24, École Normale Supérieure25, Université Paris-Saclay26, Wake Forest University27, Temple University28
TL;DR: Recent extensions and improvements are described, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.
Abstract: Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software
3,638 citations
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.
3,015 citations