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Berry-Esseen bounds for self-normalized sums of locally dependent random variables

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science China Mathematics 2024年第11期67卷 2629-2652页

作者： Zhuo-Song Zhang department of statistics and Data science Southern University of Science and Technology

The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal *** this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment *** proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other *** main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.

关键词： Berry-Esseen bounds self-normalized sums localdependence $m$-dependence graph dependency

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The joint Laplace transforms for killed diffusion occupation times

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Applied Mathematics:A Journal of Chinese Universities 2024年第3期39卷 398-415页

作者： LI Ying-qiu CHEN Ye School of Mathematics and statistics Changsha University of Science and Technology College of Mathematics and computational science Hunan University of Arts and Science

The approach of Li and Zhou(2014) is adopted to find the Laplace transform of occupation time over interval(0, a) and joint occupation times over semi-infinite intervals(-∞, a) and(b, ∞) for a time-homogeneous diffusion process up to an independent exponential time eq for 0 < a < b. The results are expressed in terms of solutions to the differential equations associated with the diffusion generator. Applying these results, we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift.

关键词： time-homogeneous diffusion process occupation time joint occupation time Laplace transform Brownian motion with drift

Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

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Communications on Applied Mathematics and Computation 2024年第1期6卷 3-29页

作者： Zachary M.Miksis Yong-Tao Zhang department of Applied and computational Mathematics and statistics University of Notre DameNotre DameIN46556USA

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping *** resulting iterative schemes have a fast convergence rate to steady-state ***,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local ***,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the *** multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational *** this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational ***,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)*** experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

关键词： Fixed-point fast sweeping methods Weighted essentially non-oscillatory(WENO)schemes Sparse grids Static Hamilton-Jacobi(H-J)equations Eikonal equations

Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance

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science China Mathematics 2024年第1期67卷 163-186页

作者： Yang Yang Shaoying Chen Kam Chuen Yuen School of statistics and Data science Nanjing Audit UniversityNanjing 211815China department of statistics and Actuarial science The University of Hong KongHong Kong 999077China

This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually *** two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence *** applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.

关键词： asymptotic joint tail behavior randomly weighted sum heavy-tailed distribution dependence insurance risk model

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Fuzzy Quasi-Pseudo-b-Metrics on Algebraic Structures

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Journal of Mathematical Research with Applications 2024年第3期44卷 397-407页

作者： Jiancai WEI Yeqing SHENG Lihong XIE Piyu LI School of Mathematics and computational science Wuyi University School of Mathematics and statistics Xuzhou Institute of Technology

In this paper, we mainly study fuzzy (quasi-)pseudo-b-metrics on algebraic *** mainly establish the following results:(1) If a group G with a topologyτ, which is induced by a left invariant fuzzy quasi-pseudo-b-metric (resp., pseudo-b-metric) on the G, is a right topological group, then G with the topologyτis a paratopological group (resp., a topological group) and (2) If a semigroup S with a topologyτis induced by an invariant fuzzy quasi-pseudob-metric, then S with the topologyτis a topological semigroup.

关键词： left topological group right topological group semitopological group paratopological group topological group topological semigroup fuzzy quasi-pseudo-b-metric invariant fuzzy (quasi-)pseudo-b-metric

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

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Acta Mathematica Scientia 2024年第4期44卷 1301-1326页

作者： Xuejun ZHANG Yuting GUO Hongxin CHEN Pengcheng TANG College of Mathematics and statistics Hunan Normal University.Changsha 410081China School of Mathematics Hunan UniversityChangsha 410082China School of Mathematics and computational science Hunan University of Science and TechnologyXiangtan 411201China

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type *** order to prov... 详细信息

关键词： Forelli-Rudin type operator L^(p,q,s,k)(B_(n))space boundedness unit ball

Ambarzumyan's Theorem for the Dirac Operator on Equilateral Tree Graphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 568-576页

作者： Dong-Jie WU Xin-Jian XU Chuan-Fu YANG department of Mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China

The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree *** prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.

关键词： dirac operator quantum graph Ambarzumyan’s theorem inverse spectral problem

Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation

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Communications on Applied Mathematics and Computation 2024年第1期6卷 501-532页

作者： Juntao Huang Wei Guo Yingda Cheng department of Mathematics and statistics Texas Tech UniversityLubbockTX79409USA department of computational Mathematics Science and EngineeringMichigan State UniversityEast LansingMI48824USA department of Mathematics Michigan State UniversityEast LansingMI48824USA

This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software *** C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://***/JuntaoHuang/*** package is capable of treating a large class of high dimensional linear and nonlinear *** review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical *** further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.

关键词： Adaptive sparse grid Discontinuous Galerkin High dimensional partial differential equation Software development

Explainable Conformer Network for Detection of COVID-19 Pneumonia from Chest CT Scan: From Concepts toward Clinical Explainability

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Computers, Materials & Continua 2024年第1期78卷 1171-1187页

作者： Mohamed Abdel-Basset Hossam Hawash Mohamed Abouhawwash S.S.Askar Alshaimaa A.Tantawy Faculty of Computers and Informatics Zagazig UniversityZagazig44519Egypt department of computational Mathematics Scienceand Engineering(CMSE)Michigan State UniversityEast LansingMI48824USA department of Mathematics Faculty of ScienceMansoura UniversityMansoura35516Egypt department of statistics and Operations Research College of ScienceKing Saud UniversityP.O.Box 2455Riyadh11451Saudi Arabia

The early implementation of treatment therapies necessitates the swift and precise identification of COVID-19 pneumonia by the analysis of chest CT *** study aims to investigate the indispensable need for precise and interpretable diagnostic tools for improving clinical decision-making for COVID-19 *** paper proposes a novel deep learning approach,called Conformer Network,for explainable discrimination of viral pneumonia depending on the lung Region of Infections(ROI)within a single modality radiographic CT ***,an efficient U-shaped transformer network is integrated for lung image ***,a robust transfer learning technique is introduced to design a robust feature extractor based on pre-trained lightweight Big Transfer(BiT-L)and finetuned on medical data to effectively learn the patterns of infection in the input ***,this work presents a visual explanation method to guarantee clinical explainability for decisions made by Conformer *** evaluation of real-world CT data demonstrated that the diagnostic accuracy of ourmodel outperforms cutting-edge studies with statistical *** Conformer Network achieves 97.40% of detection accuracy under cross-validation *** model not only achieves high sensitivity and specificity but also affords visualizations of salient features contributing to each classification decision,enhancing the overall transparency and trustworthiness of our *** findings provide obvious implications for the ability of our model to empower clinical staff by generating transparent intuitions about the features driving diagnostic decisions.

关键词： Deep learning COVID-19 multi-modal medical image fusion diagnostic image fusion