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Dimension reduction based on weighted variance estimate

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Science china Mathematics 2009年第3期52卷 539-560页

作者： ZHAO JunLong1 & XU XingZhong2.1 department of Mathematics, Beihang University Laboratory of Mathematics, Information and Behavior of the Ministry of Education, beijing 100083,{2. 2.department of Mathematics, beijing institute of technology, beijing 100081,{2. department of Mathematics Beihang University Laboratory of Mathematics Information and Behavior of the Ministry of Education Beijing 100083 China department of Mathematics Beijing Institute of Technology Beijing 100081 China

In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE.

关键词： central subspace contour regression sliced average variance estimate sliced inverse regression sufficient dimension reduction weight function 62.08 62.05

Fiducial inference in the pivotal family of distributions

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Science china Mathematics 2006年第3期49卷 410-432页

作者： XU Xingzhong & LI Guoying department of Mathematics, beijing {2. of technology, beijing 100081, china Academy of Mathematics and Systems Science, Chinese Academy of Sciences, beijing 100080, china 1. department of Mathematics Beijing Institute of Technology Beijing 100081 China 2. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is *** method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

关键词： confidence bounds, fiducial distributions, fiducial model, frequentist prop-erty, generalized pivotal model, pivotal family of distributions, testing hypotheses.

The discrete multiple-parameter fractional Fourier transform

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Science china(Information Sciences) 2010年第11期53卷 2287-2299页

作者： LANG Jun, TAO Ran& WANG Yue department of Electronic Engineering, beijing {2. of technology, beijing 100081, china 1. department of Electronic Engineering Beijing Institute of Technology Beijing 100081 China

As a generalization of the Fourier transform (FT), the fractional Fourier transform (FRFT) has many applications in the areas of optics, signal processing, information security, etc. Therefore, the efficient discrete computational method is the vital fundament for the application of the fractional Fourier transform. The multiple-parameter fractional Fourier transform (MPFRFT) is a generalized fractional Fourier transform, which not only includes FRFT as special cases, but also provides a unified framework for the study of FRFT. In this paper, we present in detail the discretization method of the MPFRFT and define the discrete multiple-parameter fractional Fourier transform (DMPFRFT). Then, we utilize the tensor product to define two-dimensional multiple-parameter fractional Fourier transform (2.-MPFRFT) and the corresponding two-dimensional discrete multiple-parameter fractional Fourier transform (2.-DMPFRFT). Finally, as an application, a novel image encryption method based on 2.-DMPFRFT is proposed. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

关键词： multiple-parameter fractional Fourier transform fractional Fourier transform image encryption information security

Entropy Squeezing in Coupled Field-Superconducting Charge Qubit with Intrinsic Decoherence

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Communications in Theoretical Physics 2007年第7期48卷 63-66页

作者： YAN Xue-Qun SHAO Bin ZOU Jian department of Physic,School of Science,beijing {2. of technology,beijing 100081,china department of Physic School of Science Beijing Institute of Technology

We investigate the entropy squeezing in the system of a superconducting charge qubit coupled to a singlemode *** find an exact solution of the Milburn equation for the system and discuss the influence of intrinsicdecoherence on entropy *** a comparison,we also consider the variance *** results show that inthe absence of the intrinsic decoherence both entropy and variance squeezings have the same periodic properties of time,and occur at the same range of ***,when the intrinsic decoherence is considered,we find that as the timegoing on the entropy squeezing disappears fast than the variance squeezing,there exists a range of time where entropysqueezing can occur but variance squeezing cannot.

关键词： entropy squeezing intrinsic decoherence superconducting charge qubit

Image stylization with enhanced structure on GPU

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Science china(Information Sciences) 2012年第5期55卷 1093-1105页

作者： LI Ping 1,SUN HanQiu 1,SHENG Bin 1,2.& SHEN JianBing 3 1 department of computer Science and Engineering,The Chinese University of Hong Kong,Hong Kong,{2. 2.department of computer Science and Engineering,Shanghai Jiao Tong University,Shanghai 2.02.0,{2. 3 School of computer Science and technology,beijing institute of technology,beijing {12.,{2. 1. department of computer Science and Engineering The Chinese University of Hong Kong Hong Kong China2. Department of Computer Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China3. School of Computer Science and Technology Beijing Institute of Technology Beijing 100081 China

This paper presents a graphics processing unit (GPU) based stylization approach that preserves the fine structure between the original and the stylized images using gradient *** abstraction and painterly stylization methods focused on contrast manipulation only,and thus the detailed salient structures of the input images are always destroyed when performing the current stylization techniques because of limitations like unavoidable salience information loss caused by contrast *** propose an image structure map to naturally model the fine structure existing in the original ***-based structure tangent generation and tangent-guided image morphology are used to construct the structure *** image structure map,unlike an edge map,not only systematically models the boundary information within the imagery but also accentuates the underlying inner structure detail for further *** facilitate the final stylization via parallel bilateral grid and structure-aware stylizing optimization on a GPU-CUDA platform in real *** multiple experiments,the proposed method consistently demonstrates efficient and high quality image stylization performance.

关键词： image stylization non-photorealistic rendering real-time processing GPU image abstraction

Oscillatory periodic solutions of differential-delay equations with multiple lags

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Chinese Science Bulletin 1997年第6期42卷 444-447页

作者： GE Weigaodepartment of Applied Mathematics, beijing {2. of technology, beijing 100081, china department of Applied Mathematics Beijing Institute of Technology Beijing 100081 China

BASED on the Nussbaum’s results, we studied in ref. [2. the conditions for the existence of oscillatory periodic solutions to the differential-delay equations (DDEs)

关键词： differential-delay equation periodic solution multiple lags.

Modeling and characteristic analysis of underwater acoustic signal of the accelerating propeller

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Science china(Information Sciences) 2012年第2期55卷 270-280页

作者： FENG Yuan1,2.TAO Ran1 & WANG Yue11department of Electronic Engineering,beijing {2. of technology,beijing 100081,china 2.cience Research {2. of china North Industries Group Corporation,beijing 100081,china 1. department of Electronic Engineering Beijing Institute of Technology Beijing 100081 China2. Science Research Institute of China North Industries Group Corporation Beijing 100081 China

The signal feature of propeller cavitation noise during acceleration or deceleration procedure can be used to passively detect and classify moving vessels and underwater vehicles in the port *** analyzing the chirp periodicity of the variation of propeller wake velocity under acceleration situation,this paper presents a time domain expression of the modulation envelope signal of the accelerating propeller noise,treating the signal as a Gaussian-shaped chirp periodic pulse train with increasing trend and fluctuating pulse *** paper investigates the characteristics of simplified fractional Fourier transform(SFRFT)spectrum of the chirp periodic signal,and thus obtains the relation between the chirp periodic signal and its chirp harmonics under the conditions of underwater passive ***,the experimental data of the cavitation tunnel satisfy the results obtained by simulation,which verifies the correctness of the proposed signal model.

关键词： accelerating propeller modeling of underwater acoustic signal chirp periodic signal simplified fractional Fourier transform

Lie symmetry and conservation law of Birkhoffian system

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Chinese Science Bulletin 1999年第4期44卷 318-320页

作者： MEI Fengxiangdepartment of Applied Mechanics , beijing {2. of technology, beijing 100081, china department of Applied Mechanics Beijing Institute of Technology Beijing China

The Lie symmetry of Birkhoffian system was studied, the condition under which the system admits the one-parameter Lie group of transformation with infinitesimal generator was given, and the structural equation and the... 详细信息

关键词： symmetry conservation law Birknoffian system.

Non-Noether conserved quantity for differential equations of motion in the phase space

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Chinese Science Bulletin 2002年第24期47卷 2049-2050页

作者： MEI Fengxiangdepartment of Applied Mechanics, beijing {2. of technology, beijing 100081, china department of Applied Mechanics Beijing Institute of Technology Beijing China

A non-Noether conserved quantity for the differential equations of motion of mechanical systems in the phase space is studied. The differential equations of motion of the systems are established and the determining equations of Lie symmetry are given. An existence theorem of non-Noether conserved quantity is obtained. An example is given to illustrate the application of the result.

关键词： mechanical system phase space non-Noether conserved quantity.