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Science China Mathematics 2024年第3期67卷 627-646页

作者： Hui Xiao Ion Grama Quansheng Liu Institut fur Mathematik und Angewandte Informatik Universitat HildesheimHildesheim 31141Germany Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China LMBA Universite Bretagne SudCNRS UMR 6205Vannes F-56000France

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_*** suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

关键词： Berry-Esseen bound Cramér-type moderate deviation product of random matrices operator norm entry spectral radius

A new method for removing mixed noises

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Science China(Information Sciences) 2011年第1期54卷 51-59页

作者： LI Bing1,3,LIU QuanSheng1,2,XU JiaWei1 & LUO XiaoJun1 1School of Mathematics and Computation Science,Changsha university of Science&Technology, Changsha 410076,China 2LMAM,université de bretagne-sud,Campus de Tohannic,Vannes 56017.université Européenne de bretagne,France 3department of Mathematics,Zhongshan Polytechnic,Zhongshan 528404,China School of Mathematics and Computation Science Changsha University of Science & Technology Changsha China department of Mathematics Zhongshan Polytechnic Zhongshan China LMAM Université de Bretagne-Sud Vannes France université Européenne de bretagne Bretagne France

We first introduce a similarity assumption to describe the similarity phenomenon in natural images, and establish a similarity principle which supplies a simple mathematical justification for the non-local means filter in removing Gaussian *** the similarity principe in an adapted way,we then propose a new algorithm,called mixed noise filter(MNF)to remove simultaneously a mixture of Gaussian and random impulse *** experiments show that our new filter improves significantly the trilateral filter in removing mixed noises,and that it is as effcient as the non-local means filter in removing Gaussian noises,and as good as the trilateral filter in removing random impulse noises.

关键词： mixed noises Gaussian noises random impulse noises image restoration nonlinear filters trilateral filter non-local means filter denoising similarity principle

BOREL RADIUS AND T-RADIUS OF THE ALGEBROIDAL FUNCTION IN THE UNIT DISC

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Acta Mathematica Scientia 2012年第5期32卷 1805-1812页

作者：孔荫蒙 School of Mathematics and Computational Science Guangdong University of Business Studies LMBAuniversit'e de bretagne-sud Campus de Tohanic universit'e Europ'eenne de bretagne France

Using Ahlfors’ theory of covering surface and a type-function,we confirm the existence theorem of a Borel radius and a T-radius for the algebroidal function dealing with multiple values in the unit disc,which briefly... 详细信息

关键词： algebroidal function Borel radius T-radius type-function

Coupling ground-level panoramas and aerial imagery for change detection

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Geo-Spatial Information Science 2016年第3期19卷 222-232页

作者： Nehla Ghouaiel Sébastien Lefèvre Institute of Research in Computer Science and Random Systems Universitéde Bretagne-SudUMR 6074 IRISAVannesFrance

Geographic landscapes in all over the world may be subject to rapid changes induced,for instance,by urban,forest,and agricultural *** such kind of changes is usually achieved through remote ***,obtaining regular and up-to-date aerial or satellite images is found to be a high costly process,thus preventing regular updating of land cover ***,in this paper,we propose a low-cost solution based on the use of groundlevel geo-located landscape panoramic photos providing high spatial resolution information of the *** photos can be acquired from various sources:digital cameras,smartphone,or even web ***,since the acquisition is performed at the ground level,the users’immediate surroundings,as sensed by a camera device,can provide information at a very high level of precision,enabling to update the land cover type of the geographic *** the described herein method,we propose to use inverse perspective mapping(inverse warping)to transform the geo-tagged ground-level 360◦photo onto a top-down view as if it had been acquired from a nadiral aerial *** re-projected,the warped photo is compared to a previously acquired remotely sensed image using standard techniques such as *** differences in orientation,resolution,and geographical extent between the top-down view and the aerial image are addressed through specific processing steps(***).Experiments on publicly available data-sets made of both ground-level photos and aerial images show promising results for updating land cover maps with mobile ***,the proposed approach contributes to the crowdsourcing efforts in geo-information processing and mapping,providing hints on the evolution of a landscape.

关键词： Image analysis remote sensing change detection crowdsourcing mobile mapping panoramic photos

Limit theorems for a supercritical branching process with immigration in a random environment

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Science China Mathematics 2017年第12期60卷 2481-2502页

作者： WANG YanQing LIU QuanSheng School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan 430073 China Laboratoire de Mathematiques de bretagne-Atlantique Universitd de Bretagne-Sud Vannes F-56017 France

Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normalized population size W_n converges almost surely to a finite random variable W. Secondly, we show criterions for the non-degeneracy and for the existence of moments of the limit random variable W. Finally, we establish a central limit theorem, a large deviation principle and a moderate deviation principle about log Z_n.

关键词： branching process with immigration random environment almost sure convergence nondegeneration Lpconvergence and moments large and moderate deviations central limit theorem

ON GLOBAL MEROMORPHIC SOLUTIONS OF SECOND-ORdeR LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS

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Acta Mathematica Scientia 2013年第2期33卷 423-429页

作者：孔荫莹孙道椿 School of Mathematics and Computational Science Guangdong University of Business Studies LMBA Universit de Bretagne-Sud School of Mathematics Science of South China Normal university

The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory ... 详细信息

关键词： Second-order linear differential equations global meromorphic solutions mero-morphic continuation

Tail estimates for one-dimensional non-nearest-neighbor random walk in random environment

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Science China Mathematics 2010年第9期53卷 475-484页

作者： GAO ZhiQiang 1,2 1 School of Mathematical Sciences, Beijing Normal university, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China 2 Laboratoire de Mathatiques et Applications des Mathmatiques, universit de bretagne-sud, BP 573, Vannes 56017, France School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing China Laboratoire de Mathéatiques et Applications des Mathématiques Université de Bretagne-Sud Vannes France

Suppose that the integers are assigned i.i.d. random variables {(β gx , . . . , β 1x , α x )} (each taking values in the unit interval and the sum of them being 1), which serve as an environment. This environment defines a random walk {X n } (called RWRE) which, when at x, moves one step of length 1 to the right with probability α x and one step of length k to the left with probability β kx for 1≤ k≤ g. For certain environment distributions, we determine the almost-sure asymptotic speed of the RWRE and show that the chance of the RWRE deviating below this speed has a polynomial rate of decay. This is the generalization of the results by dembo, Peres and Zeitouni in 1996. In the proof we use a large deviation result for the product of random matrices and some tail estimates and moment estimates for the total population size in a multi-type branching process with random environment.

关键词： random walks in random environment large deviations

Age-dependent branching processes in random environments

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Science China Mathematics 2008年第10期51卷 1807-1830页

作者： LI YingQiu LIU QuanSheng College of Mathematics and Computing Science Changsha University of Science and TechnologyChangsha 410076China LMAM Universit′e de Bretagne SudCampus de TohannicBP57356017 VannesFrance

We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R+, and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.

关键词： age-dependent branching processes random environments probability generating function integral equation extinction probability exponential growth rates of expectation and conditional expectation random walks and renewal equation in random environments renewal theorem

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

Modeling Abstraction Hierarchy Levels of the Cyber Attacks Using Random Process

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Open Journal of Statistics 2017年第3期7卷 500-520页

作者： Gilles Durrieu Emmanuel Frenod Thierry Morineau Thong Quoc Nguyen université de bretagne sud Laboratoire de Mathématiques de Bretagne Atlantique UMR CNRS 6205 Campus de Tohannic Vannes France université de bretagne sud Centre de Recherches en Psychologie Cognition Communication-CRPCC EA 1285 Campus de Tohannic Vannes France

Aspects of human behavior in cyber security allow more natural security to the user. This research focuses the appearance of anticipating cyber threats and their abstraction hierarchy levels on the mental picture levels of human. The study concerns the modeling of the behaviors of mental states of an individual under cyber attacks. The mental state of agents being not observable, we propose a non-stationary hidden Markov chain approach to model the agent mental behaviors. A renewal process based on a nonparametric estimation is also considered to investigate the spending time in a given mental state. In these approaches, the effects of the complexity of the cyber attacks are taken into account in the models.

关键词： Cyber Attacks Abstraction Hierarchy Hidden Markov Chain Nonparametric Estimation Renewal Process