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Cascade algorithm and multiresolution analysis on the Heisenberg group

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Progress in Natural science:Materials International 2005年第7期15卷 602-608页

作者： LIU Heping, LIU Yu, PENG Lizhong and CHU Xiaoyong (lmam, school of mathematical sciences, Peking University, Beijing 100871, China) lmam School of Mathematical Sciences Peking University Beijing 100871 China

In this paper we investigate the relationship between the convergence of cascade algorithm and orthogonal (or biorthogo-nal) multiresolution analysis on the Heisenberg group. It is proved that the (strong) convergence of cascade algorithm together with the perfect reconstruction condition induces an orthogonal multiresolution analysis and vice versa . Similar results are also proved for biorthogo-nal multiresolution analysis.

关键词： Heisenberg group cascade algorithm multiresolution analysis refinable functions.

MODEL ANALYSIS AND PARAMETER EXTRACTION FOR MOS CAPACITOR INCLUDING QUANTUM MECHANICAL EFFECTS

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Journal of Computational Mathematics 2006年第3期24卷 401-411页

作者： Hai-yan Jiang Ping-wen Zhang lmam CCSE and School of Mathematical Sciences.Peking University Beijing 100871 China

The high frequency CV curves of MOS capacitor have been studied. It is shown that semiclassical model is a good approximation to quantum model and approaches to classical model when the oxide layer is thick. This conclusion provides us an efficient （semiclassical） model including quantum mechanical effects to do parameter extraction for ultrathin oxide device. Here the effective extracting strategy is designed and numerical experiments demonstrate the validity of the strategy.

关键词： Poisson Equation SchrSdinger Equation MOS Capacitor Quantum Effect,Sensitivity Parameter Extraction.

Geodesic discs in Teichmiiller space

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science China Mathematics 2005年第8期48卷 1075-1082页

作者： LI Zhong lmam & school of mathematical sciences Peking University Beijing 100871 China

Let T(S) be the Teichmuller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincare disc into T(S). It is shown in this paper that for any non-Strebe... 详细信息

关键词： Teichmiiller space geodesic discs

Discovering causes and effects of a given node in Bayesian networks

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Frontiers of Mathematics in China 2013年第3期8卷 643-663页

作者： Changzhang WANG You ZHOU Zhi GENG school of mathematical sciences LMAM Peking University Beijing 100871 China

Causal relationships among variables can be depicted by a causal network of these variables. We propose a local structure learning approach for discovering the direct causes and the direct effects of a given target variable. In the approach, we first find the variable set of parents, children, and maybe some descendants （PCD） of the target variable, but generally we cannot distinguish the parents from the children in the PCD of the target variable. Next, to distinguish the causes from the effects of the target variable, we find the PCD of each variable in the PCD of the target variable, and we repeat the process of finding PCDs along the paths starting from the target variable. Without constructing a whole network over all variables, we find only a local structure around the target variable. Theoretically, we show the correctness of the proposed approach under the assumptions of faithfulness, causal sufficiency, and that conditional independencies are correctly checked.

关键词： Directed acyclic graphs causal networks graphical models structure learning

Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 1-16页

作者： Yong Liu Zi-yu Liu lmam School of Mathematical SciencePeking UniversityBeijing100871China

We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish *** precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous MarkovFeller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior,then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.

关键词： Markov-Feller semigroup ergodicity e-property eventual continuity

A Branching Random Walk Method for Many-Body Wigner Quantum Dynamics

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 21-71页

作者： Sihong Shao Yunfeng Xiong lmam and school of mathematical sciences Peking UniversityBeijing 100871China

A branching random walk algorithm for many-body Wigner equations and its numerical applications for quantum dynamics in phase space are proposed and ana-lyzed in this *** an auxiliary function,the truncated Wigner equation and its adjoint form are cast into integral formulations,which can be then reformulated into renewal-type equations with probabilistic *** prove that the first mo-ment of a branching random walk is the solution for the adjoint *** the help of the additional degree of freedom offered by the auxiliary function,we are able to produce a weighted-particle implementation of the branching random *** contrast to existing signed-particle implementations,this weighted-particle one shows a key ca-pacity of variance reduction by increasing the constant auxiliary function and has no time discretization *** canonical numerical experiments on the 2D Gaussian barrier scattering and a 4D Helium-like system validate our theoretical findings,and demonstrate the accuracy,the efficiency,and thus the computability of the proposed weighted-particle Wigner branching random walk algorithm.

关键词： Wigner equation branching random walk quantum dynamics variance reduction signed-particle Monte Carlo method adjoint equation renewal-type equations importance sam-pling resampling

A variational hardcut EM algorithm for the mixtures of Gaussian processes

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science China(Information sciences) 2023年第3期66卷 291-292页

作者： Tao LI Jinwen MA Department of Information and Computational sciences School of Mathematical Sciences and LMAM Peking University

Gaussian process(GP) is the dominant model in the nonparametric Bayesian community, but it is not flexible enough to model non-stationary/multi-modal data, because a conventionally trained Gaussian process is stationary. To overcome this problem, the mixture of Gaussian processes(MGP) [1] was proposed. Compared with GP,

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Empirical Likelihood for Generalized Linear Models with Longitudinal Data

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Journal of Systems science & Complexity 2023年第5期36卷 2100-2124页

作者： YIN Changming AI Mingyao CHEN Xia KONG Xiangshun school of Mathematics and Information science Guangxi UniversityNanning 530004China lmam School of Mathematical Sciences and Center for Statistical SciencePeking UniversityBeijing 100871China school of Mathematics and Statistics Shaanxi Normal UniversityXi'an 710062China school of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

Generalized linear models are usually adopted to model the discrete or nonnegative *** this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is *** some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also *** with the existing results,the new conditions are more weak and easy to *** simulations are presented to illustrate these asymptotic properties.

关键词： Empirical likelihood ratio generalized linear model longitudinal data maximum empirical likelihood estimator

Hausdorff dimension of quasi-cirles of polygonal mappings and its applications

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science China Mathematics 2013年第5期56卷 1033-1040页

作者： HUO ShengJin TANG ShuAn WU ShengJian lmam and school of mathematical sciences Peking University school of Mathematics and Computer science Guizhou Normal University

We show that the Hausdorff dimension of quasi-circles of polygonal mappings is one. Furthermore, we apply this result to the theory of extremal quasiconformal mappings. Let [μ] be a point in the universal Teichmiiller space such that the Hausdorff dimension of fμ（δ△） is bigger than one. We show that for every kn ∈ （0, 1） and polygonal differentials δn, n = 1, 2, the sequence {[kn δn/｜δn｜} cannot converge to [μ] under the Teichmiiller metric.

关键词： Hausdorff dimension Teichmiiller space quasi-circle polygonal mapping