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Rational Solutions of First Order Algebraic Ordinary Differential Equations

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Journal of Systems science & Complexity 2024年第2期37卷 567-580页

作者： FENG Shuang SHEN Liyong School of Physical and Mathematical sciences Nanjing Tech UniversityNanjing 211816China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Let f(t,y,y')=∑ _(i=0)^(n )a_(i)(t,y)y'^(i)=0 be an irreducible first order ordinary differential equation with polynomial *** in 1998 proved that there exists a constant C such that every rational solution of f(t,y,y')=0 is of degree not greater than *** show that this degree bound C depends not only on the degrees of f in t,y,y' but also on the coefficients of f viewed as the polynomial in t,y,y'.In this paper,the authors show that if f satisfies deg(f,y)0,then the degree bound C only depends on the degrees of f in t,y,y',and furthermore we present an explicit expression for C in terms of the degrees of f in t,y,y'.

关键词： Degree bound first order AODE height rational solution

Tool Orientation Optimization and Path Planning for 5-Axis Machining

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Journal of Systems science & Complexity 2021年第1期34卷 83-106页

作者： YUAN Chunming MI zhenpeng JIA Xiaohong LIN Fengming SHEN Liyong KLMM Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Tool path generation is a fundamental problem in 5-axis CNC machining, which consists of tool orientation planning and cutter-contact(CC) point planning. The planning strategy highly depends on the type of tool cutters. For ball-end cutters, the tool orientation and CC point location can be planned separately;while for flat end cutters, the two are highly dependent on each other. This paper generates a smooth tool path of workpiece surfaces for flat end mills from two stages: Computing smooth tool orientations on the surface without gouging and collisions and then designing the CC point path. By solving the tool posture optimization problem the authors achieve both the path smoothness and the machining efficiency. Experimental results are provided to show the effectiveness of the method.

关键词： 5-axis CNC machining flat end cutter tool path planning tool posture optimization

Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models

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Journal of Systems science & Complexity 2021年第3期34卷 1135-1155页

作者： LIU Yan REN Mingyang zHANG Sanguo School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of SciencesBeijing 100190China

This paper considers tests for regression coefficients in high dimensional partially linear *** authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly ***,the authors propose an empirical likelihood method to test regression *** authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null *** addition,the method is extended to test with nuisance *** show that the proposed method have a good performance in control of type-I error rate and *** proposed method is also employed to analyze a data of Skin Cutaneous Melanoma(SKCM).

关键词： Empirical likelihood test high dimensional analysis partially linear models regression coefficients

6D Object Pose Estimation in Cluttered Scenes from RGB Images

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Journal of Computer science & Technology 2022年第3期37卷 719-730页

作者： Xiao-Long Yang Xiao-Hong Jia Yuan Liang Lu-Bin Fan Academy of Mathematics and Systems science Chinese Academy of SciencesBeijing 100190China University of Chinese Academy of sciences Beijing 100049China Alibaba DAMO Academy Alibaba GroupHangzhou 311121China

We propose a feature-fusion network for pose estimation directly from RGB images without any depth information in this ***,we introduce a two-stream architecture consisting of segmentation and regression *** segmentation stream processes the spatial embedding features and obtains the corresponding image *** features are further coupled with the image crop in the fusion ***,we use an efficient perspective-n-point(E-PnP)algorithm in the regression stream to extract robust spatial features between 3D and 2D ***,we perform iterative refinement with an end-to-end mechanism to improve the estimation *** conduct experiments on two public datasets of YCB-Video and the challenging *** results show that our method outperforms state-of-the-art approaches in both the speed and the accuracy.

关键词： two-stream network 6D pose estimation fusion feature

Analyzing Multiple Phenotypes Based on Principal Component Analysis

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 843-860页

作者： De-liang BU San-guo zHANG Na LI School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of SciencesBeijing 100049China LSC NCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Joint analysis of multiple phenotypes can have better interpretation of complex diseases and increase statistical power to detect more significant single nucleotide polymorphisms(SNPs)compare to traditional single phenotype analysis in genome-wide association *** component analysis(PCA),as a popular dimension reduction method,has been broadly used in the analysis of multiple *** PCA transforms the original phenotypes into principal components(PCs),it is natural to think that by analyzing these PCs,we can combine information across *** PCA-based methods can be divided into two categories,either selecting one particular PC manually or combining information from all *** this paper,we propose an adaptive principle component test(APCT)which selects and combines the PCs adaptively by using Cauchy combination *** proposed method can be seen as a generalization of traditional PCA based method since it contains two existing methods as special *** simulation shows that our method is robust and can generate powerful result in various *** real data analysis of stock mice data also demonstrate that our proposed APCT can identify significant SNPs that are missed by traditional methods.

关键词： multiple phenotypes principal component analysis cauchy combination method

A Survey of the Representations of Rational Ruled Surfaces

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Journal of Systems science & Complexity 2021年第6期34卷 2357-2377页

作者： YUAN Chun-Ming PEREz-DIAz Sonia SHEN Li-Yong KLMM Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China Grupo ASYNACS Dpto.de Fisica y MatematicasUniversidad de Alcala28871-Alcala de HenaresMadridSpain

The rational ruled surface is a typical modeling surface in computer aided geometric design.A rational ruled surface may have different representations with respective advantages and *** this paper,the authors revisit the representations of ruled surfaces including the parametric form,algebraic form,homogenous form and Plucker ***,the transformations between these representations are proposed such as parametrization for an algebraic form,implicitization for a parametric form,proper reparametrization of an improper one and standardized reparametrization for a general *** on these transformation algorithms,one can give a complete interchange graph for the different representations of a rational ruled *** rational surfaces given in algebraic form or parametric form not in the standard form of ruled surfaces,the characterization methods are recalled to identify the ruled surfaces from them.

关键词： Birational transformation characterization implicitization parametrization rational ruled surface reparametrization

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A framework from point clouds to workpieces

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Visual Computing for Industry,Biomedicine,and Art 2022年第1期5卷 250-267页

作者： Li‑Yong Shen Meng‑Xing Wang Hong‑Yu Ma Yi‑Fei Feng Chun‑Ming Yuan School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China KLMM Academy of Mathematics and Systems SciencesUniversity of Chinese Academy of SciencesBeijing 100049China

Combining computer-aided design and computer numerical control(CNC)with global technical connections have become interesting topics in the manufacturing industry.A framework was implemented that includes point clouds to workpieces and consists of a mesh generation from geometric data,optimal surface segmentation for CNC,and tool path planning with a certified scallop *** latest methods were introduced into the mesh generation with implicit geometric regularization and total generalized *** the mesh model was obtained,a fast and robust optimal surface segmentation method is provided by establishing a weighted graph and searching for the minimum spanning tree of the graph for extraordinary *** method is easy to implement,and the number of segmented patches can be controlled while preserving the sharp features of the ***,a contour parallel tool-path with a confined scallop height is generated on each patch based on B-spline *** results show that the proposed framework is effective and robust.

关键词： Computer numerical control Mesh reconstruction Mesh segmentation Path planning Scallop height

Tool Path Planning with Confined Scallop Height Error Using Optimal Connected Fermat Spirals

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Communications in Mathematics and Statistics 2024年第1期12卷 55-78页

作者： Hong-Yu Ma Chun-Ming Yuan Li-Yong Shen KLMM Academy of Mathematics and Systems SciencesCASBeijing 100190People’s Republic of China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049People’s Republic of China

In CNC machining,the tool path planning of the cutter plays an important *** this paper,we generate a space-filling and continuous tool path for free-form surface represented by the triangular mesh with a confined scallop *** tool path is constructed from connected Fermat spirals(CFS)but with fewer inflection *** with the newly developed CFS method,only about half of the number of inflection points are ***,the kinematic constraints are simultaneously taken into account to increase the feedrates in ***,we use a micro-line trajectory technique to smooth the tool *** results and physical cutting tests are provided to illustrate and clarify our method.

关键词： Tool path planning Connected Fermat spirals Scallop height Kinematic constraints

Distance-Based Regression Analysis for Measuring Associations

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Journal of Systems science & Complexity 2023年第1期36卷 393-411页

作者： SHI Yuke zHANG Wei LIU Aiyi LI Qizhai LSC Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of sciences Beijing 100049China Biostatistics and Bioinformatics Branch Eunice Kennedy Shriver National Institute of Child Health Human Development National Institutes of HealthBethesdaMD 20847USA

Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research *** on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the *** the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the *** fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random *** that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square *** asymptotic null distribution of the new test statistic and power of both tests are also *** studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F *** test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.

关键词： Asymptotic distribution chi-squared-type mixture nonparametric test pseudo-F test similarity matrix