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Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment

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Journal of Mathematical Research with Applications 2023年第6期43卷 737-753页

作者： Hao WU xiequan fan Zhiqiang GAO Yinna YE Center for Applied Mathematics Tianjin University School of Mathematics and Statistics Northeastern University at Qinhuangdao Laboratory of Mathematics and Complex Systems School of Mathematical SciencesBeijing Normal University Department of Applied Mathematics School of Mathematics and PhysicsXi'an Jiaotong-Liverpool University

Let(Zn)n≥0be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process(Zn)n≥0, which completes a result of Grama et al. [Stochastic ***., 2017, 127(4): 1255–1281]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Znare discussed.

关键词： Branching processes Random environment Wasserstein-1 distance Nonuniform Berry-Esseen bounds

Sharp large deviations for sums of bounded from above random variables

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Science China Mathematics 2017年第12期60卷 2465-2480页

作者： fan xiequan Center for Applied Mathematics Tianjin University Tianjin 300072 China Regularity Team INRIA Saclay Palaiseau 91120 France

We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.

关键词： sharp large deviations Cram′er large deviations Talagrand’s inequality Hoeffding’s inequality sums of independent random variables

Uniform Cramer moderate deviations and Berry-Esseen bounds for a supercritical branching process in a random environment

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Frontiers of Mathematics in China 2020年第5期15卷 891-914页

作者： xiequan fan Haijuan HU Quansheng LIU Center for Applied Mathematics Tianjin UniversityTianjin 300072China School of Mathematics and Statistics Northeastern University at QinhuangdaoQinhuangdao 066004China Universite de Bretagne-Sud LMBAUMR CNRS 6205Campus de Tohannic56017 VannesFrance School of Statistics and Mathematics Zhongnan University of Economics and LawWuhan 430073China

Let{Zn,n≥0}be a supercritical branching process in an independent and identically distributed random *** prove Cramer moderate deviations and Berry-Esseen bounds for log(Zn+n0/Zn0)uniformly in n0∈N,which extend the corresponding results by ***,***,and ***[Stochastic ***.,2017,127:1255-1281]established for n0=*** extension is interesting in theory,and is motivated by applications.A new method is developed for the proofs;some conditions of Grama et *** relaxed in our present *** example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log(Zn+n0/Zn0)and n.

关键词： Branching processes random environment Cramer moderatedeviations Berry-Esseen bounds

Sharp large deviation results for sums of independent random variables

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Science China Mathematics 2015年第9期58卷 1939-1958页

作者： fan xiequan GRAMA Ion LIU QuanSheng Regularity Team Institut National de Recherche en Informatique et en Automatique Laboratoire de Mathmatiques Appliques aux Systèmes Ecole Centrale Paris-Grande Voie des Vignes Laboratoire de Mathmatiques de Bretagne Atlantique UMR 6205 University Bretagne-Sud School of Mathematics and Computing Science Changsha University of Science and Technology

We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand(1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram′er(1938),Bahadur-Rao(1960) and Sakhanenko(1991). We also show that our bound can be used to improve a recent inequality of Pinelis(2014).

关键词：独立随机变量和大偏差不等式伯恩斯坦高斯法概率类似

Berry-Esseen Bounds for Self-Normalized Martingales

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Communications in Mathematics and Statistics 2018年第1期6卷 13-27页

作者： xiequan fan Qi-Man Shao Center for Applied Mathematics Tianjin UniversityTianjin 300072China Department of Statistics Chinese University of Hong KongShatinNTHong Kong

A Berry–Esseen bound is obtained for self-normalized martingales under the assumption of finite *** bound coincides with the classical Berry–*** of the *** to Student’s statistic and autoregressive process are also... 详细信息

关键词： Self-normalized process Berry-Esseen bounds Martingales Student’s statistic Autoregressive process

A progressive framework for rotary motion deblurring

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Defence Technology（防务技术） 2024年第2期32卷 159-172页

作者： Jinhui Qin Yong Ma Jun Huang fan fan You Du School of Electronic Information Wuhan UniversityWuhan430072China

The rotary motion deblurring is an inevitable procedure when the imaging seeker is mounted in the rotating *** rotary motion deblurring methods suffer from ringing artifacts and noise,especially for large blur *** solve the above problems,we propose a progressive rotary motion deblurring framework consisting of a coarse deblurring stage and a refinement *** the first stage,we design an adaptive blur extents factor(BE factor)to balance noise suppression and details *** a novel deconvolution model is proposed based on BE *** the second stage,a triplescale deformable module CNN(TDM-CNN)is designed to reduce the ringing artifacts,which can exploit the 2D information of an image and adaptively adjust spatial sampling *** establish a standard evaluation benchmark,a real-world rotary motion blur dataset is proposed and released,which includes rotary blurred images and corresponding ground truth images with different blur *** results demonstrate that the proposed method outperforms the state-of-the-art models on synthetic and real-world rotary motion blur *** code and dataset are available at https://***/JinhuiQin/RotaryDeblurring.

关键词： Rotary motion deblurring Progressive framework Blur extents factor TDM-CNN

Optimization of microstructure design for enhanced sensing performance in flexible piezoresistive sensors

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Journal of Advanced Ceramics 2024年第6期13卷 711-728页

作者： Xinghao fan Hailong Hu Bin Liao Yaqi Zhang fan Zhang School of Minerals Processing and Bioengineering Central South UniversityChangsha 410083China Research Institute of Aerospace Technology Central South UniversityChangsha 410083China

Flexible piezoresistive strain sensors have received significant attention due to their diverse applications in monitoring human activities and health,as well as in robotics,prosthetics,and human–computer interaction *** the various flexible sensor types,those with microstructure designs are considered promising for strain sensing due to their simple structure,high sensitivity,extensive operational range,rapid response time,and robust *** review provides a concise overview of recent advancements in flexible piezoresistive sensors based on microstructure design for enhanced strain sensing performance,including the impact of microstructure on sensing mechanisms,classification of microstructure designs,fabrication methods,and practical ***,this review delves into the analysis of piezoresistive sensor sensing mechanisms and performance parameters,exploring the relationship between microstructure design and performance ***,an in-depth discussion is presented,focusing on the primary themes of microstructure design classification,process selection,performance characteristics,and specific *** review employs mathematical modeling and hierarchical analysis to emphasize the directionality of different microstructures on performance enhancement and to highlight the performance advantages and applicable features of various microstructure *** conclusion,this review examines the multifunctionality of flexible piezoresistive sensors based on microstructure design and addresses the challenges that still need to be overcome and improved,such as achieving a wide range of stretchability,high sensitivity,and robust *** review summarizes the research directions for enhancing sensing performance through microstructure design,aiming to assist in the advancement of flexible piezoresistive sensors.

关键词： microstructure design sensing performance flexible piezoresistive strain sensors microsensing mechanism

Impact of non-ideal UE hardware on cell-free massive MIMO network with centralized operation

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Science China(Information Sciences) 2024年第4期67卷 255-271页

作者： Ning LI Pingzhi fan Institute of Mobile Communications Southwest Jiaotong University

This paper investigates the impact of non-ideal user equipment(UE) hardware on a cell-free(CF) massive MIMO(mMIMO) network with centralized operation under spatially correlated channels. The minimum mean-squared error(MMSE) estimator can be derived with the help of the generic non-ideal UE hardware model. It is demonstrated that even if the effective signal-to-noise ratio approaches infinity, pilot contamination and imperfect hardware can cause a non-zero estimation error floor. After that, a lower bound is determined for the ergodic uplink capacity of the centralized CF mMIMO network under non-ideal UE hardware. Moreover, the optimal receive combining vector is obtained to maximize the uplink spectral efficiency(SE). The maximum ratio(MR) and regularized zero-forcing(RZF) combining schemes are offered as alternatives in light of the computational complexity of the MMSE receiver. Comparing the RZF to the MMSE scheme under different levels of hardware impairments, our findings indicate that the RZF receiver suffers a negligible loss in total SE. For MR combining, a novel closed-form uplink achievable SE expression is obtained based on the MMSE estimator and the use-and-then-forget bounding technique. This expression gives vital insights into the achievable uplink performance with UE hardware impairments. Besides, for various hardware impairment factors, the impact of pilot sequence length on average sum SE is disclosed for different receive combining schemes. To increase the overall SE of the max-min fairness scheme, a heuristic fractional power control scheme with UE hardware impairments is developed, which can essentially avoid sacrificing the SE of other UEs while maximizing the SE of the unluckiest UE in the whole network. Finally,our theoretical performance analysis and power control algorithm are validated by simulation results, and fundamental design guidelines are provided for selecting hardware satisfying the practical UE requirements.

关键词： cell-free massive MIMO centralized operation spatially correlated channels hardware impairments channel estimation uplink spectral efficiency optimal receive combining pilot length design fractional power control

Semi-analytical Solutions for Wellbores with Graded Skin Zones in Poroelastic Media

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Acta Mechanica Solida Sinica 2024年第3期37卷 385-395页

作者： Zhiqiang fan Zhihe Jin School of Mechanics Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’an710072China Department of Mechanical Engineering University of MaineOronoME04469USA

In analyzing the complex interaction between the wellbore and the reservoir formation,the hydromechanical properties of the region proximal to the wellbore,referred to as the“wellbore skin zone”,play a pivotal role in determining flow dynamics and the resulting formation *** models of the wellbore skin zone generally assume a constant permeability throughout,resulting in a sharp permeability discontinuity at the skin-reservoir *** paper introduces a model for a wellbore with a continuously graded skin zone of finite thickness within a poroelastic *** solutions are derived using the Laplace transform method,addressing both positive and negative skin *** results are presented to illustrate the effects of graded permeability/skin zone thickness on pore pressures and stresses around a *** results highlight a distinct divergence in stress and pore pressure fields when comparing wellbores with negative skin zones to those with positive skin zones or no skin at all.

关键词： Poroelastic Graded permeability Analytical solution Wellbore Skin zone