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Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 320-346页

作者： En-wen ZHU Zi-wei DENG Han-jun ZHANG Jun CAO Xiao-hui LIU Department of Mathematics and Statistics Changsha University of Science and TechnologyChangsha 410114China School of Mathematics and computational science Xiangtan UniversityXiangtan 411105China School of Statistics and data science and Key Laboratory of Data Science in Finance and EconomicsJiangxi University of Finance and EconomicsNanchang 330013China

This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV *** first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant *** semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.

关键词： random coefficient autoregressive model time-functional variance conditional least squares semiparametric least squares

A Tutorial on Federated Learning from Theory to Practice:Foundations,Software Frameworks,Exemplary Use Cases,and Selected Trends

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IEEE/CAA Journal of Automatica Sinica 2024年第4期11卷 824-850页

作者： M.Victoria Luzón Nuria Rodríguez-Barroso Alberto Argente-Garrido Daniel Jiménez-López Jose M.Moyano Javier Del Ser Weiping Ding Francisco Herrera Department of Software Engineering Andalusian Research Institute in Data Science and Computational Intelligence(DaSCI)University of GranadaGranada 18071Spain Department of Computer science and Artificial Intelligence Andalusian Research Institute in Data Science and Computational Intelligence(DaSCI)University of GranadaGranada 18071Spain Department of Communications Engineering University of the Basque Country(UPV/EHU)and also with TECNALIABasque Research&Technology Alliance(BRTA)Spain School of Information science and Technology Nantong UniversityNantong 226019China

When data privacy is imposed as a necessity,Federated learning(FL)emerges as a relevant artificial intelligence field for developing machine learning(ML)models in a distributed and decentralized *** allows ML models to be trained on local devices without any need for centralized data transfer,thereby reducing both the exposure of sensitive data and the possibility of data interception by malicious third *** paradigm has gained momentum in the last few years,spurred by the plethora of real-world applications that have leveraged its ability to improve the efficiency of distributed learning and to accommodate numerous participants with their data *** virtue of FL,models can be learned from all such distributed data sources while preserving data *** aim of this paper is to provide a practical tutorial on FL,including a short methodology and a systematic analysis of existing software ***,our tutorial provides exemplary cases of study from three complementary perspectives:i)Foundations of FL,describing the main components of FL,from key elements to FL categories;ii)Implementation guidelines and exemplary cases of study,by systematically examining the functionalities provided by existing software frameworks for FL deployment,devising a methodology to design a FL scenario,and providing exemplary cases of study with source code for different ML approaches;and iii)Trends,shortly reviewing a non-exhaustive list of research directions that are under active investigation in the current FL *** ultimate purpose of this work is to establish itself as a referential work for researchers,developers,and data scientists willing to explore the capabilities of FL in practical applications.

关键词： data privacy distributed machine learning federated learning software frameworks

Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems

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science China Mathematics 2024年第7期67卷 1641-1664页

作者： Jinye Shen Fanhai Zeng Martin Stynes School of Mathematics Southwestern University of Finance and EconomicsChengdu611130China School of Mathematics Shandong UniversityJinan250100China Applied and computational Mathematics division Beijing Computational Science Research CenterBeijing100193China

Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关键词： time-fractional subdiffusion averaged L1 scheme

Construction of Optimal Mixed-Level Uniform Designs

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Journal of Systems science & Complexity 2024年第2期37卷 841-862页

作者： CHATTERJEE Kashinath LIU Min-Qian QIN Hong YANG Liuqing Department of Population Health sciences Division of Biostatistics and Data ScienceAugusta UniversityGA 30912USA NITFID LPMC&KLMDASRSchool of Statistics and Data ScienceNankai UniversityTianjin 300071China School of Statistics and Mathematics Zhongnan University of Economics and LawWuhan 430073China

The theory of uniform design has received increasing interest because of its wide application in the field of computer *** generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial *** this paper,the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower *** methods are all deterministic construction methods which can avoid the complexity of stochastic *** saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these ***,the resulting designs are also χ^(2)-optimal and minimum moment aberration designs.

关键词： Generalized discrete discrepancy Hadamard matrix mixed-level design orthogonal array supersaturated design

Asymptotic Inferences in the Random Coefficient Autoregressive Model with Time-functional Variance Noises

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Acta Mathematicae Applicatae Sinica 2024年

作者： En-wen ZHU Zi-wei DENG Han-jun ZHANG Jun CAO Xiao-hui LIU Department of Mathematics and Statistics Changsha University of Science and Technology School of Statistics and data science and Key Laboratory of Data Science in Finance and Economics Jiangxi University of Finance and Economics School of Mathematics and computational science Xiangtan University

This paper considers the random coefficient autoregressive model with time-functional variance noises, hereafter the RCA-TFV model. We first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant coefficient. The semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported. A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.

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Influences of Co-Flow and Counter-Flow Modes of Reactant Flow Arrangement on a PEMFC at Start-Up

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Computer Modeling in Engineering & sciences 2024年第5期139卷 1337-1356页

作者： Qianqian Shao Min Wang Nuo Xu School of Petroleum Engineering Guangdong University of Petrochemical TechnologyMaoming525000China Mechanics division Beijing Computational Science Research CenterBeijing100193China

To investigate the influences of co-flowand counter-flowmodes of reactant flowarrangement on a proton exchange membrane fuel cell(PEMFC)during start-up,unsteady physical and mathematical models fully coupling the flow,heat,and electrochemical reactions in a PEMFC are *** continuity equation and momentum equation are solved by handling pressure-velocity coupling using the SIMPLE *** electrochemical reaction rates in the catalyst layers(CLs)of the cathode and anode are calculated using the Butler-Volmer *** multiphase mixture model describes the multiphase transport process of gas mixtures and liquid water in the fuel *** validation,the influences of co-flow and counter-flow modes on the PEMFC performance are investigated,including the evolution of the current density,flow field,temperature field,and reactant concentration field during start-up,as well as the steady distribution of the current density,reactant concentration,andmembrane water content when the start-up ***-flow and counter-flow modes influence the current density distribution and temperature *** the one hand,the co-flow mode accelerates the start-up process of the PEMFC and leads to a more evenly distributed current density than the counter-flow *** the other hand,the temperature difference between the inlet and outlet sections of the cell is up to 10.1℃ under the co-flow mode,much larger than the 5.0℃ observed in the counter-flow ***,the counter-flowmode results in a more evenly distributed temperature and a lower maximum temperature than the co-flow ***,in the flow field design of a PEMFC,the reactant flow arrangements can be considered to weigh between better heat management and higher current density distribution of the cell.

关键词： PEMFC full coupling model Butler-Volmer equation multiphase mixture model co-flow mode counter-flow mode

Spectroscopy and molecule opacity investigation on excited states of SiS

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Chinese Physics B 2024年第5期33卷 381-387页

作者：李瑞吕浩男桑纪群刘晓华梁桂颖吴勇 College of Teacher Education Qiqihar UniversityQiqihar 161006China National Key Laboratory of computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Department of Physics College of ScienceQiqihar UniversityQiqihar 161006China School of data science and Artificial Intelligence Jilin Engineering Normal UniversityChangchun 130052China HEDPS Center for Applied Physics and TechnologyPeking UniversityBeijing 100084China

The SiS molecule,which plays a significant role in space,has attracted a great deal of attention for many *** to complex interactions among its low-lying electronic states,precise information regarding the molecular structure of SiS is *** obtain accurate information about the structure of its excited states,the high-precision multireference configuration interaction(MRCI)method has been *** method is used to calculate the potential energy curves(PECs)of the 18Λ–S states corresponding to the lowest dissociation limit of *** core–valence correlation effect,Davidson’s correction and the scalar relativistic effect are also included to guarantee the precision of the MRCI *** on the calculated PECs,the spectroscopic constants of quasi-bound and bound electronic states are calculated and they are in accordance with previous experimental *** transition dipole moments(TDMs)and dipole moments(DMs)are determined by the MRCI *** addition,the abrupt variations of the DMs for the 1^(5)Σ^(+)and 2^(5)Σ^(+)states at the avoided crossing point are attributed to the variation of the electronic *** opacity of SiS at a pressure of 100 atms is presented across a series of *** increasing temperature,the expanding population of excited states blurs the band boundaries.

关键词： SiS opacity excited state spectroscopic constant configuration interaction

On convergence of covariance matrix of empirical Bayes hyper-parameter estimator

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Control Theory and Technology 2024年第2期22卷 149-162页

作者： Yue Ju Biqiang Mu Tianshi Chen School of data science and Shenzhen Research Institute of Big data The Chinese University of Hong KongShenzhenShenzhen518172GuangdongChina division of Decision and Control Systems School of Electrical Engineering and Computer ScienceKTH Royal Institute of Technology10044StockholmSweden Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and System ScienceChinese Academy of SciencesBeijing100190China

Regularized system identification has become the research frontier of system identification in the past *** related core subject is to study the convergence properties of various hyper-parameter estimators as the sample size goes to *** this paper,we consider one commonly used hyper-parameter estimator,the empirical Bayes(EB).Its convergence in distribution has been studied,and the explicit expression of the covariance matrix of its limiting distribution has been ***,what we are truly interested in are factors contained in the covariance matrix of the EB hyper-parameter estimator,and then,the convergence of its covariance matrix to that of its limiting distribution is *** general,the convergence in distribution of a sequence of random variables does not necessarily guarantee the convergence of its covariance ***,the derivation of such convergence is a necessary complement to our theoretical analysis about factors that influence the convergence properties of the EB hyper-parameter *** this paper,we consider the regularized finite impulse response(FIR)model estimation with deterministic inputs,and show that the covariance matrix of the EB hyper-parameter estimator converges to that of its limiting ***,we run numerical simulations to demonstrate the efficacy of ourtheoretical results.

关键词： Regularized system identification Hyper-parameter estimator Empirical Bayes Convergence of covariance matrix

SPARSE RECOVERY BASED ON THE GENERALIZED ERROR FUNCTION

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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 *** introduced penalty function involves both the shape and the scale parameters,making it extremely *** 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 *** practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are *** experiments are carried out to demonstrate the benefits of the suggested approach in a variety of *** 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