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Exclusive Hypothesis Testing for Cox's Proportional Hazards Model

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Journal of Systems Science & Complexity 2024年第5期37卷 2157-2172页

作者： WU Qiang TONG Xingwei DUAN Xiaogang School of statistics Beijing Normal University

Exclusive hypothesis testing is a new and special class of hypothesis testing. This kind of testing can be applied in survival analysis to understand the association between genomics information and clinical information about the survival time. Besides, it is well known that Cox's proportional hazards model is the most commonly used model for regression analysis of failure time. In this paper,the authors consider doing the exclusive hypothesis testing for Cox's proportional hazards model with right-censored data. The authors propose the comprehensive test statistics to make decision, and show that the corresponding decision rule can control the asymptotic Type Ⅰ errors and have good powers in theory. The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Rotterdam Breast Cancer Data study that motivated this study.

关键词： Comprehensive test statistics Cox’s proportional hazards model exclusive hypothesis testing right-censored data Type I error

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

Sound event localization and detection based on deep learning

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Journal of Systems Engineering and Electronics 2024年第2期35卷 294-301页

作者： ZHAO Dada DING Kai QI Xiaogang CHEN Yu FENG Hailin School of Mathematics and statistics Xidian UniversityXi’an 710071China Science and Technology on Near-Surface Detection Laboratory Wuxi 214035China

Acoustic source localization(ASL)and sound event detection(SED)are two widely pursued independent research *** recent years,in order to achieve a more complete spatial and temporal representation of sound field,sound event localization and detection(SELD)has become a very active research *** paper presents a deep learning-based multioverlapping sound event localization and detection algorithm in three-dimensional ***-Mel spectrum and generalized cross-correlation spectrum are joined together in channel dimension as input *** features are classified and regressed in parallel after training by a neural network to obtain sound recognition and localization results *** channel attention mechanism is also introduced in the network to selectively enhance the features containing essential information and suppress the useless ***,a thourough comparison confirms the efficiency and effectiveness of the proposed SELD *** experiments show that the proposed algorithm is robust to reverberation and environment and can achieve higher recognition and localization accuracy compared with the baseline method.

关键词： sound event localization and detection(SELD) deep learning convolutional recursive neural network(CRNN) channel attention mechanism

Bifurcation and optimal control for an infectious disease model with the impact of information

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International Journal of Biomathematics 2024年第1期17卷 113-149页

作者： Zhihui Ma Shenghua Li Shuyan Han School of Mathematics and statistics Lanzhou University Lanzhou Gansu 730000P.R.China

A nonlinear infectious disease model with information-influenced vaccination behavior and contact patterns is proposed in this paper,and the impact of information related to disease prevalence on increasing vaccination coverage and reducing disease incidence during the outbreak is ***,we perform the analysis for the existence of equilibria and the stability properties of the proposed *** particular,the geometric approach is used to obtain the sufficient condition which guarantees the global asymptotic stability of the unique endemic equilibrium Ee when the basic reproduction number Ro>***,mathematical derivation combined with numerical simulation shows the existence of the double Hopf bifurcation around ***,based on the numerical results,it is shown that the information coverage and the average information delay may lead to more complex dynamical ***,the optimal control problem is established with information-infuenced vaccination and treatment as control *** corresponding optimal paths are obtained analytically by using Pontryagin's maximum principle,and the applicability and validity of virous intervention strategies for the proposed controls are presented by numerical experiments.

关键词： Infectious disease model information index stability double Hopf bifurcation optimal control Pontryagin's maximum principle

Block Basis for Modular Coinvariants of Pseudo-Reflection Groups

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Algebra Colloquium 2024年第1期31卷 41-48页

作者： Ke Ou School of statistics and Mathematics Yunnan University of Finance and Economics Kunming 650221China

We investigate the block basis for modular coinvariants of finite pseudo-reflection *** are particularly interested in the case of a subgroup G of the parabolic subgroups of GLn(q)which generalizes the Weyl groups of ... 详细信息

关键词： modular invariant theory pseudo-reflection group block basis coinvariant

Effects of asymmetric coupling and boundary on the dynamic behaviors of a random nearest neighbor coupled system

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Chinese Physics B 2024年第6期33卷 309-322页

作者：徐玲姜磊 School of Mathematical Sciences Sichuan Normal UniversityChengdu 610066China School of Mathematics and statistics Linyi UniversityLinyi 276000China

This study investigates the dynamical behaviors of nearest neighbor asymmetric coupled systems in a confined ***, the study derivative analytical stability and synchronization conditions for the asymmetrically coupled system in an unconfined space, which are then validated through numerical simulations. Simulation results show that asymmetric coupling has a significant impact on synchronization conditions. Moreover, it is observed that irrespective of whether the system is confined, an increase in coupling asymmetry leads to a hastened synchronization pace. Additionally, the study examines the effects of boundaries on the system's collective behaviors via numerical experiments. The presence of boundaries ensures the system's stability and synchronization, and reducing these boundaries can expedite the synchronization process and amplify its effects. Finally, the study reveals that the system's output amplitude exhibits stochastic resonance as the confined boundary size increases.

关键词： asymmetric coupled confined space synchronization stochastic resonance stability

Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

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IEEE/CAA Journal of Automatica Sinica 2024年第4期11卷 1057-1059页

作者： Taixiang Zhang Jinde Cao Xiaodi Li the School of Mathematics Southeast UniversityNanjing 210096China the School of Mathematics and statistics Shandong Normal UniversityJinan 250014Chi

Dear Editor,This letter studies finite-time input-to-state stability(FTISS)for impulsive switched systems.A set of Lyapunov-based conditions are established for guaranteeing FTISS *** constituent modes governing continuous dynamics are FTISS and discrete dynamics involving impulses are destabilizing,the FTISS can be retained if impulsive-switching signals satisfy an average dwell-time(ADT)condition.

关键词： property impulsive satisfy

Kaiser criterion in factor models

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Acta Mathematica Sinica,English Series 2024年

作者： Changhu WANG Jianhua GUO Yanyuan MA Shurong ZHENG School of Mathematical Sciences Peking University KLAS and School of Mathematics and statistics Northeast Normal University School of Mathematics and statistics Beijing Technology and Business University Department of statistics Pennsylvania State University University Park

Despite of the wide use of the factor models, the issue of determining the number of factors has not been resolved in the statistics literature. An ad hoc approach is to set the number of factors to be the number of eigenvalues of the data correlation matrix that are larger than one, and subsequent statistical analysis proceeds assuming the resulting factor number is correct. In this work, we study the relation between the number of such eigenvalues and the number of factors, and provide the if and only if conditions under which the two numbers are equal. We show that the equality only relies on the properties of the loading matrix of the factor model. Guided by the newly discovered condition,we further reveal how the model error affects the estimation of the number of factors.

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Semi-Varying Coefficient Panel Data Model with Technical Indicators Predicts Stock Returns in Financial Market

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Journal of Systems Science & Complexity 2024年第4期37卷 1638-1652页

作者： HU Xuemei PAN Ying LI Xiang School of Mathematics and statistics Chongqing Technology and Business UniversityChongqing 400067China Chongqing Key Laboratory of Social Economy and Applied statistics Chongqing 400067China Research Center for Economy of Upper Reaches of the Yangtse River Chongqing Technology and Business UniversityChongqing 400067China

Accurately predicting stock returns is a conundrum in financial *** this conundrum can bring huge economic benefits for investors and also attract the attention of all circles of *** this paper the authors combine semi-varying coefficient model with technical analysis and statistical learning,and propose semi-varying coefficient panel data model with individual effects to explore the dynamic relations between the stock returns from five companies:CVX,DFS,EMN,LYB,and MET and five technical indicators:CCI,EMV,MOM,ln ATR,ln RSI as well as closing price(ln CP),combine semi-parametric fixed effects estimator,semi-parametric random effects estimator with the testing procedure to distinguish fixed effects(FE) from random effects(RE),and finally apply the estimated dynamic relations and the testing set to predict stock returns in December 2020 for the five *** proposed method can accommodate the varying relationship and the interactive relationship between the different technical indicators,and further enhance the prediction accuracy to stock returns.

关键词： Fixed effects random effects semi-varying coefficient panel data model stock returns technical indicators