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Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

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Science China Mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao tao Tang Tao Zhou School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for Mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators.More precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

Management of hepatocellular carcinoma patients with portal vein tumor thrombosis:A narrative review

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Hepatobiliary & Pancreatic Diseases International 2022年第2期21卷 134-144页

作者： Zi-Wen tao Bao-Quan Cheng Tao Zhou Yan-Jing Gao Department of Gastroenterology Qilu HospitalCheeloo College of MedicineShandong UniversityJinan 250012China

Background: Hepatocellular carcinoma(HCC) is one of the main reasons for malignancy-related death. Portal vein tumor thrombosis(PVTT) is the most common form of macrovascular invasion related to HCC occurring in 10%-60% of patients. HCC with PVTT is usually characterized by worsening liver function, vulnerability to blood metastasis, higher incidence of complications associated with portal hypertension, and intolerance to treatment when compared with that without PVTT. If only treated with supportive care, the median survival of HCC with PVTT is about 2.7 months. In the past, sorafenib was the only recommended therapy by guidelines with limited effectiveness. This narrative review aimed to describe the current management options for HCC with PVTT. Data sources: We have reviewed literature from Pub Med on the treatment of HCC with PVTT and compiled evidence-based facts on effective therapies available for different types of PVTT. Results: Sorafenib monotherapy is not much effective, but combining it with other methods can improve survival. Each type of PVTT can beneft from the combination of transarterial chemoembolization and sorafenib than sorafenib monotherapy. The tumor downstaging can be realized possibly after transarterial chemoembolization, but tumor invasion into the main trunk of the portal vein greatly impairs efficacy. Although surgery is a curative approach, it is often not recommended for Vp4 PVTT. Some new methods can broaden the indication, but further explorations are needed. Radiotherapy can decrease the possibility of Vp3 progression to Vp4, but building a forecast model of best radiation dose and response is necessary. Systemic chemotherapy, hepatic arterial infusion chemotherapy, radiofrequency ablation, portal stenting, and traditional Chinese medicine are also benefcial in Vp3-4 PVTT. The accurate diagnosis of PVTT can be made by radiomics, and prognostic classifcation models can be used to design personalized treatments. The application of new treatment methods such as the atezolizumab plus

关键词： Hepatocellular carcinoma Portal vein tumor thrombosis Transarterial chemoembolization Radiotherapy Surgery Sorafenib

Specificity-preserving RGB-D saliency detection

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Computational Visual Media 2023年第2期9卷 297-317页

作者： Tao Zhou Deng-Ping Fan Geng Chen Yi zhou Huazhu Fu School of Computer Science and Engineering Nanjing University of Science and TechnologyNanjing 210094China Key Laboratory of System Control and Information Processing Ministry of EducationShanghaiChina Computer Vision Lab ETH Z¨urichZ¨urichSwitzerland School of Computer Science and Engineering Northwestern Polytechnical UniversityXi’anChina School of Computer Science and Engineering Southeast UniversityNanjingChina Inception Institute of Artificial Intelligence Abu DhabiUnited Arab Emirates

Salient object detection(SOD)in RGB and depth images has attracted increasing research interest.Existing RGB-D SOD models usually adopt fusion strategies to learn a shared representation from RGB and depth modalities,while few methods explicitly consider how to preserve modality-specific characteristics.In this study,we propose a novel framework,the specificity-preserving network(SPNet),which improves SOD performance by exploring both the shared information and modality-specific properties.Specifically,we use two modality-specific networks and a shared learning network to generate individual and shared saliency prediction maps.To effectively fuse cross-modal features in the shared learning network,we propose a cross-enhanced integration module(CIM)and propagate the fused feature to the next layer to integrate cross-level information.Moreover,to capture rich complementary multi-modal information to boost SOD performance,we use a multi-modal feature aggregation(MFA)module to integrate the modalityspecific features from each individual decoder into the shared decoder.By using skip connections between encoder and decoder layers,hierarchical features can be fully combined.Extensive experiments demonstrate that our SPNet outperforms cutting-edge approaches on six popular RGB-D SOD and three camouflaged object detection benchmarks.The project is publicly available at https://***/taozh2017/SPNet.

关键词： salient object detection(SOD) RGB-D cross-enhanced integration module(CIM) multi-modal feature aggregation(MFA)

AN ACCELERATION STRATEGY FOR RANDOMIZE-THEN-OPTIMIZE SAMPLING VIA DEEP NEURAL NETWORKS

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Journal of Computational Mathematics 2021年第6期39卷 848-864页

作者： Liang Yan Tao Zhou School of Mathematics Southeast UniversityNanjing210096China Nanjing Center for Applied Mathematics Nanjing211135China LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO can be computationally intensive forcomplexity problems due to repetitive evaluations of the expensive forward model and itsgradient. In this work, we present a novel goal-oriented deep neural networks (DNN) surrogate approach to substantially reduce the computation burden of RTO. In particular,we propose to drawn the training points for the DNN-surrogate from a local approximatedposterior distribution – yielding a flexible and efficient sampling algorithm that convergesto the direct RTO approach. We present a Bayesian inverse problem governed by ellipticPDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO approach, which shows that DNN-RTO can significantly outperform the traditional RTO.

关键词： Bayesian inverse problems Deep neural network Markov chain Monte Carlo

AN EXPLICIT MULTISTEP SCHEME FOR MEAN-FIELD FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2022年第4期40卷 517-540页

作者： Yabing Sun Jie Yang Weidong Zhao Tao Zhou School of Mathematics Shandong UniversityJinan 250100ChinaCollege of ScienceNational University of Defense TechnologyChangsha 410073China School of Mathematics and Statistics Shandong UniversityWeihai 264209China School of Mathematics and Finance Institute Shandong UniversityJinan 250100China LSEC Institute of Computational MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

This is one of our series works on numerical methods for mean-field forward backward stochastic differential equations(MFBSDEs).In this work,we propose an explicit multistep scheme for MFBSDEs which is easy to implement,and is of high order rate of convergence.Rigorous error estimates of the proposed multistep scheme are presented.Numerical experiments are carried out to show the efficiency and accuracy of the proposed scheme.

关键词： Mean-field forward backward stochastic differential equations Explicit multistep scheme Error estimates

MSWNet:A visual deep machine learning method adopting transfer learning based upon ResNet 50 for municipal solid waste sorting

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Frontiers of Environmental Science & Engineering 2023年第6期17卷 165-176页

作者： Kunsen Lin Youcai Zhao Lina Wang Wenjie Shi Feifei Cui Tao Zhou The State Key Laboratory of Pollution Control and Resource Reuse College of Environmental Science and EngineeringTongji UniversityShanghai 200092China Shanghai Institute of Pollution Control and Ecological Security Shanghai 200092China Shanghai Key Laboratory of Atmospheric Particle Pollution and Prevention(LAP3) Department of Environmental Science and EngineeringFudan UniversityShanghai 200433China Institute of Eco-Chongming(IEC) Shanghai 202150China Institute of Fundamental and Frontier Sciences University of Electronic Science and Technology of ChinaChengdu 610054China

An intelligent and efficient methodology is needed owning to the continuous increase of global municipal solid waste(MSW).This is because the common methods of manual and semi-mechanical screenings not only consume large amount of manpower and material resources but also accelerate virus community transmission.As the categories of MSW are diverse considering their compositions,chemical reactions,and processing procedures,etc.,resulting in low efficiencies in MSW sorting using the traditional methods.Deep machine learning can help MSW sorting becoming into a smarter and more efficient mode.This study for the first time applied MSWNet in MSW sorting,a ResNet-50 with transfer learning.The method of cyclical learning rate was taken to avoid blind finding,and tests were repeated until accidentally encountering a good value.Measures of visualization were also considered to make the MSWNet model more transparent and accountable.Results showed transfer learning enhanced the efficiency of training time(from 741 s to 598.5 s),and improved the accuracy of recognition performance(from 88.50%to 93.50%);MSWNet showed a better performance in MSW classsification in terms of sensitivity(93.50%),precision(93.40%),F1-score(93.40%),accuracy(93.50%)and AUC(92.00%).The findings of this study can be taken as a reference for building the model MSW classification by deep learning,quantifying a suitable learning rate,and changing the data from high dimensions to two dimensions.

关键词： Municipal solid waste sorting Deep residual network Transfer learning Cyclic learning rate Visualization

Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

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Science China Mathematics 2021年第5期64卷 887-902页

作者： Hong-Lin Liao Xuehua Song tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211101China Department of Mathematics and International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China NCMIS&LSEC Institute of Computational Mathematics and Scientific Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula(BDF2)with variable steps for the molecular beam epitaxial model without slope selection.We first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step constraint.Then we show that it preserves an energy dissipation law if the adjacent time-step ratios satisfy r_(k):=τ_(k)/τ_(k-1)<3.561.Moreover,with a novel discrete orthogonal convolution kernels argument and some new estimates on the corresponding positive definite quadratic forms,the L^(2)norm stability and rigorous error estimates are established,under the same step-ratio constraint that ensures the energy stability,i.e.,0

关键词： molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis

A Stochastic Collocation Method for Delay Differential Equations with Random Input

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Advances in Applied Mathematics and Mechanics 2014年第4期6卷 403-418页

作者： Tao Zhou Institute of Computational Mathematics Academy of Mathematics and Systems SciencesThe Chinese Academy of SciencesBeijing 100190China

In this work,we concern with the numerical approach for delay differential equations with random coefficients.We first show that the exact solution of the problem considered admits good regularity in the random space,provided that the given data satisfy some reasonable assumptions.A stochastic collocation method is proposed to approximate the solution in the random space,and we use the Legendre spectral collocation method to solve the resulting deterministic delay differential equations.Convergence property of the proposed method is analyzed.It is shown that the numerical method yields the familiar exponential order of convergence in both the random space and the time space.Numerical examples are given to illustrate the theoretical results.

关键词： Delay differential equations stochastic collocation sparse grid legendre spectral method

Multistage oscillators for ultra-low frequency vibration isolation and energy harvesting

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Science China(Technological Sciences) 2022年第3期65卷 631-645页

作者： YANG tao ZHANG YongQi zhou ShengXi Department of Engineering Mechanics Northwestern Polytechnical UniversityXi’an 710072China School of Aeronautics Northwestern Polytechnical UniversityXi’an 710072China

Limited by the mass,stiffness,barrier height and natural frequency of the oscillator,the existing structure or mechanism is still difficult to achieve vibration suppression and effective utilization under ultra-low frequency excitation.In particular,it is difficult to break through the technical bottleneck of the integration and intelligence of vibration isolation and energy harvesting(VIEH).The introduction of nonlinearity is usually used to solve the problem of ultra-low frequency,and the integration problem can be overcome through electromechanical coupling.Therefore,the purpose of this article is to reveal and deeply explore the geometric nonlinearity and electromechanical coupling of multistage oscillators for ultra-low frequency VIEH.This kind of multifunctional oscillators can be realized by combining mechanical multistage coupling and electromechanical conversion technologies.The experimental results confirm the development of multistage theory,and the results show that,especially in the case of multicoupling structures,the multistage oscillators with high-order quasi-zero stiffness can effectively reduce the initial frequencies of vibration isolation and the frequencies corresponding to the maximum output power.The theoretical and experimental results in this paper show that the multistage oscillators are suitable for VIEH of ultra-low frequency sources.

关键词： multistage geometric nonlinearity vibration isolation energy harvesting