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A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems

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Communications in Computational Physics 2015年第6期18卷 203-229页

作者： Guoqiao You shingyu leung The School of Science Nanjing Audit UniversityNanjingJiangsu ProvinceChina Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayHong Kong

We propose a new semi-implicit level set approach to a class of curvature dependent *** method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi(ROF)model for image *** proposal is general enough so that one can easily extend and apply the method to other curvature dependent *** the derivation is based on a semi-implicit time discretization,this suggests that the numerical scheme is stable even using a time-step significantly larger than that of the corresponding explicit *** an interesting application of the numerical approach,we propose a new variational approach for extracting limit cycles in dynamical *** resulting algorithm can automatically detect multiple limit cycles staying inside the initial guess with no condition imposed on the number nor the location of the limit ***,we also propose in this work an Eulerian approach based on the level set method to test if the limit cycles are stable or unstable.

关键词： Numerical methods for PDEs level set method dynamical systems flow visualization

A Simple Embedding Method for the Laplace-Beltrami Eigenvalue Problem onImplicit Surfaces

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Communications on Applied Mathematics and Computation 2024年第2期6卷 1189-1216页

作者： Young Kyu Lee shingyu leung Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayHong KongChina

We propose a simple embedding method for computing the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on implicit *** approach follows an embedding approach for solving the surface eikonal *** replace the differential operator on the interface with a typical Cartesian differential operator in the surface *** proposed algorithm is easy to implement and *** will give some two-and three-dimensional numerical examples to demonstrate the effectiveness of our proposed approach.

关键词： Laplace-Beltrami operator Level set method Implicit representation Eigenvalues Numerical PDEs

Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems

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Communications in Computational Physics 2023年第3期33卷 824-848页

作者： Wai Ming Chau shingyu leung Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayHong Kong

We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then cluster these data from differentinitial locations into groups. The method then uses the normalized standarddeviation or mean absolute deviation to quantify the deformation. Unlike the usualfinite-time Lyapunov exponent (FTLE), the proposed algorithm considers the completetraveling history of the particles. We also suggest two extensions of the method. To improvethe computational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite time interval. Tostart the computation in parallel to the flow trajectory data collection, we also developan on-the-fly approach to improve the solution as we continue to provide more measurementsfor the algorithm. The method can efficiently compute the WCVE over adifferent time interval by modifying the available data points.

关键词： Dynamical system visualization finite time Lyapunov exponent numerical methods for differential equations k-means clustering

An Adjoint StateMethod for Numerical Approximation of Continuous Traffic Congestion Equilibria

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Communications in Computational Physics 2011年第10期10卷 1113-1131页

作者： Songting Luo shingyu leung Jianliang Qian Department of Mathematics Michigan State UniversityEast LansingMI 48824USA Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayHong Kong

The equilibriummetric forminimizing a continuous congested trafficmodel is the solution of a variational problem involving geodesic *** continuous equilibrium metric and its associated variational problem are closely related to the classical discrete Wardrop’s *** propose an adjoint state method to numerically approximate continuous traffic congestion equilibria through the continuous *** method formally derives an adjoint state equation to compute the gradient descent direction so as to minimize a nonlinear functional involving the equilibrium metric and the resulting geodesic *** geodesic distance needed for the state equation is computed by solving a factored eikonal equation,and the adjoint state equation is solved by a fast sweeping *** examples demonstrate that the proposed adjoint state method produces desired equilibrium metrics and outperforms the subgradient marching method for computing such equilibrium metrics.

关键词： Traffic congestion adjoint state method gradient descent fast sweeping method factored eikonal equation

A Fast Local Level Set Method for Inverse Gravimetry

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Communications in Computational Physics 2011年第9期10卷 1044-1070页

作者： Victor Isakov shingyu leung Jianliang Qian Department of Mathematics and Statistics Wichita State UniversityWichitaKansasUSA Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayHong Kong SAR Department of Mathematics Michigan State UniversityEast LansingMI 48824USA

We propose a fast local level set method for the inverse problem of *** theoretical foundation for our approach is based on the following uniqueness result:if an open set D is star-shaped or x3-convex with respect to its center of gravity,then its exterior potential uniquely determines the open set *** achieve this purpose constructively,the first challenge is how to parametrize this open set D as its boundary may have a variety of possible *** describe those different shapes we propose to use a level-set function to parametrize the unknown boundary of this open *** second challenge is how to deal with the issue of partial data as gravimetric measurements are only made on a part of a given reference domainΩ.To overcome this difficulty,we propose a linear numerical continuation approach based on the single layer representation to find potentials on the boundary of some artificial domain containing the unknown set *** third challenge is how to speed up the level set inversion *** on some features of the underlying inverse gravimetry problem such as the potential density being constant inside the unknown domain,we propose a novel numerical approach which is able to take advantage of these features so that the computational speed is accelerated by an order of *** carry out numerical experiments for both two-and three-dimensional cases to demonstrate the effectiveness of the new algorithm.

关键词： Level set methods inverse gravimetry fast algorithms numerical continuation

Asymptotic false discovery control of the Benjamini-Hochberg procedure for pairwise comparisons

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Science China Mathematics 2025年第1期 223-252页

作者： Weidong Liu Dennis leung Qi-Man Shao School of Mathematical Sciences Shanghai Jiao Tong University School of Mathematics and Statistics University of Melbourne Department of Statistics and Data Science SICMSouthern University of Science and Technology

In a one-way analysis-of-variance(ANOVA) model,the number of pairwise comparisons can become large even with a moderate number of *** by this,we consider a regime with a growing number of groups and prove that,when testing pairwise comparisons,the Benjamini-Hochberg(BH) procedure can asymptotically control false discoveries,despite the fact that the involved t-statistics do not exhibit the wellknown positive dependence structure required for exact false discovery rate(FDR) *** Tukey's perspective that the difference between the means of any two groups cannot be exactly zero,our main result provides control over the directional false discovery rate and directional false discovery proportion.A key technical contribution of our work is demonstrating that the dependence among the t-statistics is sufficiently weak to establish the convergence result typically required for asymptotic FDR *** analysis does not rely on conventional assumptions such as normality,variance homogeneity,or a balanced design,thereby offering a theoretical foundation for applications in more general settings.

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Polyethylene glycol fusion repair of severed sciatic nerves accelerates recovery of nociceptive sensory perceptions in male and female rats of different strains

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Neural Regeneration Research 2025年第9期20卷 2667-2681页

作者： Liwen Zhou Karthik Venkudusamy Emily A.Hibbard Yessenia Montoya Alexa Olivarez Cathy Z.Yang Adelaide leung Varun Gokhale Guhan Periyasamy Zeal Pathak Dale R.Sengelaub George D.Bittner Department of Neuroscience University of TexasAustinTXUSA Program in Neuroscience Indiana UniversityBloomingtonINUSA Department of Molecular Biosciences University of TexasAustinTXUSA

Successful polyethylene glycol fusion(PEG-fusion)of severed axons following peripheral nerve injuries for PEG-fused axons has been reported to:(1)rapidly restore electrophysiological continuity;(2)prevent distal Wallerian Degeneration and maintain their myelin sheaths;(3)promote primarily motor,voluntary behavioral recoveries as assessed by the Sciatic Functional Index;and,(4)rapidly produce correct and incorrect connections in many possible combinations that produce rapid and extensive recovery of functional peripheral nervous system/central nervous system connections and reflex(e.g.,toe twitch)or voluntary *** preceding companion paper describes sensory terminal field reo rganization following PEG-fusion repair of sciatic nerve transections or ablations;howeve r,sensory behavioral recovery has not been explicitly explored following PEG-fusion *** the current study,we confirmed the success of PEG-fusion surgeries according to criteria(1-3)above and more extensively investigated whether PEG-fusion enhanced mechanical nociceptive recovery following sciatic transection in male and female outbred Sprague-Dawley and inbred Lewis *** nociceptive responses were assessed by measuring withdrawal thresholds using von Frey filaments on the dorsal and midplantar regions of the *** von Frey filament tests were a more reliable method than plantar von Frey filament tests to assess mechanical nociceptive sensitivity following sciatic nerve *** withdrawal thresholds of the sciatic-mediated lateral dorsal region differed significantly across strain but not *** thresholds did not change significantly from baseline in chronic Unoperated and Sham-operated *** sciatic transection,all rats exhibited severe hyposensitivity to stimuli at the lateral dorsal region of the hindpaw ipsilateral to the ***,PEG-fused rats exhibited significantly earlier return to baseline withdrawal thresholds than Negative

关键词： autophagia axotomy collateral sprouting neuropathic pain peripheral nerve repair polyethylene glycol fusion(PEG-fusion) saphenous nerve sensory neurons sex and strain Wallerian degeneration

Message from Deputy Editor-in-Chief Gabriel M leung—International Trade and Global Health Protection

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China CDC weekly 2019年第4期1卷 45-46页

作者： Gabriel M leung China CDC Weekly Dean of Medicine The University of Hong KongHong Kong SARChina

It was external trade that first prompted the collection and reporting of surveillance data at the foreign ports from which the US imported *** established Bulletin of the Public Health—the first precursor to the US ... 详细信息

关键词： Trade prompt Health

Modelling for registration of remotely sensed imagery when reference control points contain error

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Science China Earth Sciences 2006年第7期49卷 739-746页

作者： leung Yee The Department of Geography and Resource Management The Chinese University of Hong Kong Shatin Hong Kong China

Reference control points (RCPs) used in establishing the regression model in the regis-tration or geometric correction of remote sensing images are generally assumed to be “perfect”. That is, the RCPs, as explanatory variables in the regression equation, are accurate and the coordinates of their locations have no errors. Thus ordinary least squares (OLS) estimator has been applied exten-sively to the registration or geometric correction of remotely sensed data. However, this assumption is often invalid in practice because RCPs always contain errors. Moreover, the errors are actually one of the main sources which lower the accuracy of geometric correction of an uncorrected image. Under this situation, the OLS estimator is biased. It cannot handle explanatory variables with errors and cannot propagate appropriately errors from the RCPs to the corrected image. Therefore, it is essential to develop new feasible methods to overcome such a problem. This paper introduces a consistent adjusted least squares (CALS) estimator and proposes relaxed consistent adjusted least squares (RCALS) estimator, with the latter being more general and flexible, for geometric correction or regis-tration. These estimators have good capability in correcting errors contained in the RCPs, and in propagating appropriately errors of the RCPs to the corrected image with and without prior information. The objective of the CALS and proposed RCALS estimators is to improve the accuracy of measure-ment value by weakening the measurement errors. The conceptual arguments are substantiated by a real remotely sensed data. Compared to the OLS estimator, the CALS and RCALS estimators give a superior overall performance in estimating the regression coefficients and variance of measurement errors.

关键词： error modelling, registration, ordinary least squares, relaxed consistent adjusted least squares, remote sensing images.