检索结果-南通市图书馆

Character Sheaves for Classical Graded Lie Algebras

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2024年第3期40卷 870-884页

作者： Ting XUE School of Mathematics and statistics University of MelbourneVIC 3010Australia department of Mathematics and statistics University of HelsinkiHelsinki 00014Finland

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type Ⅱ classical graded Lie algebras.

关键词： Graded Lie algebras character sheaves Fourier transform nilpotent orbits

Double Moving Extremes Ranked Set Sampling Design

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2024年第1期40卷 75-90页

作者： Meng Chen Wang-xue Chen Rui Yang department of Mathematics and statistics Jishou UniversityJishou416000China

The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are considered.It turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population mean.Also,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.

关键词： double moving extremes ranked set sampling symmetric distribution efficiency

Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2024年第8期67卷 1735-1760页

作者： Ji Lin Liangang Peng department of Mathematics and statistics Fuyang Normal University School of Mathematics Sichuan University

Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions. We define the semi-derived Ringel-Hall algebra of A from the category CZ/t（A） of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra. Moreover, we describe the semiderived Ringel-Hall algebra by the generators and defining relations. In particular, if t is an odd integer, we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.

关键词： hereditary abelian categories the categories of $\mathbb{Z}/t$-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras

Flexible, efficient, and accurate tests for epidemics

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Science China Mathematics 2024年第8期67卷 1881-1898页

作者： Linjiajie Fang Bing-Yi Jing Shen Ling Qiyue Wang Qing Yang Data Science and Analytics Thrust The Hong Kong University of Science and Technology department of statistics and Data Science Southern University of Science and Technology department of Mathematics and statistics Dalhousie University department of Mathematics The Hong Kong University of Science and Technology

Group testing involves discovering a small subset of distinguished subjects from a large population while efficiently reducing the total number of tests. It has been widely used for industrial testing, information technology, and biology, especially epidemic screening. Tests, in reality, are noisy for the presence of false outcomes. Some tests are accurate but time-consuming, while others are cheaper but less accurate. Exactly which test to use is constrained by various considerations, such as availability, cost, accuracy, and efficiency.In this paper, we propose flexible, efficient, and accurate tests(FEATs). FEATs are based on group testing with simple but careful designs by incorporating ideas such as close contact cliques and repeated tests. FEATs could dramatically improve the efficiency or accuracy of existing tests. For example, for accurate but slow tests, the FEAT can improve efficiency multiple times without compromising accuracy. On the other hand,for fast but inaccurate tests, the FEAT can sharply reduce the false-negative rate(FNR) and significantly increase efficiency. Theoretical justifications are provided. We point out some scenarios where the FEAT can be effectively employed.

关键词： epidemiology control blood testing testing efficiency testing accuracy

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

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

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 independent.Under 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 structures.As 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

Automated Machine Learning Algorithm Using Recurrent Neural Network to Perform Long-Term Time Series Forecasting

在线全文

学校读者我要写书评

暂无评论

Computers, Materials & Continua 2024年第3期78卷 3529-3549页

作者： Ying Su Morgan C.Wang Shuai Liu department of statistics and Data Science University of Central FloridaOrlandoFL32816-2370USA School of Mathematics and statistics Beijing Technology and Business UniversityBeijing100048China

Long-term time series forecasting stands as a crucial research domain within the realm of automated machine learning(AutoML).At present,forecasting,whether rooted in machine learning or statistical learning,typically relies on expert input and necessitates substantial manual involvement.This manual effort spans model development,feature engineering,hyper-parameter tuning,and the intricate construction of time series models.The complexity of these tasks renders complete automation unfeasible,as they inherently demand human intervention at multiple junctures.To surmount these challenges,this article proposes leveraging Long Short-Term Memory,which is the variant of Recurrent Neural Networks,harnessing memory cells and gating mechanisms to facilitate long-term time series prediction.However,forecasting accuracy by particular neural network and traditional models can degrade significantly,when addressing long-term time-series tasks.Therefore,our research demonstrates that this innovative approach outperforms the traditional Autoregressive Integrated Moving Average(ARIMA)method in forecasting long-term univariate time series.ARIMA is a high-quality and competitive model in time series prediction,and yet it requires significant preprocessing efforts.Using multiple accuracy metrics,we have evaluated both ARIMA and proposed method on the simulated time-series data and real data in both short and long term.Furthermore,our findings indicate its superiority over alternative network architectures,including Fully Connected Neural Networks,Convolutional Neural Networks,and Nonpooling Convolutional Neural Networks.Our AutoML approach enables non-professional to attain highly accurate and effective time series forecasting,and can be widely applied to various domains,particularly in business and finance.

关键词： Automated machine learning autoregressive integrated moving average neural networks time series analysis

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

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

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 order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,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 system.Hence,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 literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In 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 costs.Here,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)equations.Numerical 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

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

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

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 graphs.We 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

SPARSE RECOVERY BASED ON THE GENERALIZED ERROR FUNCTION

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2024年第3期42卷 679-704页

作者： Zhiyong Zhou department of statistics and Data Science and Institute of Digital FinanceHangzhou City UniversityHangzhou 310015China

In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.

关键词： Sparse recovery Generalized error function Nonconvex regularization Itera-tive reweighted Li Difference of convex functions algorithms