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| 1 | A Geometric Understanding of Deep Learning显示文摘This work introduces an optimal transportation(OT)view of generative adversarial networks(GANs).Natural datasets have intrinsic patterns,which can be summarized as the manifold distribution principle:the distribution of a class of data is close to a low-dimensional manifold.GANs mainly accomplish two tasks:manifold learning and probability distribution transformation.The latter can be carried out using the classical OT method.From the OT perspective,the generator computes the OT map,while the discriminator computes the Wasserstein distance between the generated data distribution and the real data distribution;both can be reduced to a convex geometric optimization process.Furthermore,OT theory discovers the intrinsic collaborative-instead of competitive-relation between the generator and the discriminator,and the fundamental reason for mode collapse.We also propose a novel generative model,which uses an autoencoder(AE)for manifold learning and OT map for probability distribution transformation.This AE–OT model improves the theoretical rigor and transparency,as well as the computational stability and efficiency;in particular,it eliminates the mode collapse.The experimental results validate our hypothesis,and demonstrate the advantages of our proposed model. | Na Lei Dongsheng An Yang Guo Kehua Su Shixia Liu Zhongxuan Luo Shing-Tung Yau Xianfeng Gu | 2020 | Engineering2020，6，3： | 10 |
| 2 | From a projective invariant to some new properties of algebraic hypersurfaces显示文摘Projective invariants are not only important objects in mathematics especially in geometry,but also widely used in many practical applications such as in computer vision and object recognition. In this work,we show a projective invariant named as characteristic number,from which we obtain an intrinsic property of an algebraic hypersurface involving the intersections of the hypersurface and some lines that constitute a closed loop. From this property,two high-dimensional generalizations of Pascal's theorem are given,one establishing the connection of hypersurfaces of distinct degrees,and the other concerned with the intersections of a hypersurface and a simplex. | LUO ZhongXuan ZHOU XinChen GU David XianFeng | 2014 | Science China Mathematics2014，57，11： | 8 |
| 3 | Desulfurization metabolite of Rhodococcus erythropolis LSSE8-1 and its related desulfurizational gene fragments显示文摘Rhodococcus erythropolis LSSE8-1 is a newly isolated biodesulfurizaion strain from the soil of Chishui gas field, Guizhou Province, China. The analysis of its metabo-lism product shows that the strain is a kind of biocatalyst able to oxidize dibenzothiophene (DBT) to 2-hydroxydi- phenyl (HBP), and therefore the sulfur in DBT is selectively removed. By using DBTO2 (dibenzothiophene 5,5-dioxide) as substrate, both DBT and HBP are found in the culture, which shows that the reaction from DBT to DBTO2 is re-versible in the cell. While using 0.5 mmol/L DBT as control, 0.01—0.4 mmol/L DBTO2 shows poisonous effect to the cell, which will explain why there is no DBTO2 accumulation in the process of biodesulfurization. After treatment by lysozme, the plasmid DNA of the strain is isolated by alkaline method to be used as the template of PCR reaction. Three dsz gene fragments of 1.3, 1.0 and 1.2 kb respectively were amplified. Each fragment is ligate with PGEM-T vector, and cloned into E. coli. DH5. The clone DNA is sequenced and the result shows that dsz related genes are highly conservative. The identities of dszA and dszB with respect to IGTS8 are 100%, and the identity of dszC with that of IGTS8 is 99%. | GOU Zhongxuan, LUO Mingfang, LI Xin, XING Jianmin & LIU Huizhou Laboratory of Separation Science and Engineering, State Key Laboratory of Biochemical Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100080, China Correspondence should be addressed to Liu Huizhou (e-mail: hzliu@ home.ipe.ac.cn) | 2003 | Chinese Science Bulletin2003，48，24： | 5 |
| 4 | Heat and moisture transfer with sorption and condensation in porous clothing assemblies and numerical simulation 显示文摘 | FAN Jintu LUO Zhongxuan LI Yi | 2000 | International Journal of Heat and Mass Transfer2000，，43： | 1 |
| 5 | Heat and moisture trans fer with sorption and condensation in porous clothing as- sembilies and numerical simulation 显示文摘 | Jintu Fan Zhongxuan Luo Yi Li | 2000 | International Jour- nal of Heat and Mass Transfer2000，，43： | 1 |
| 6 | Heat and moisture with sorption and condensation in porous clothing assemblies and numerical simulation显示文摘 | FAN Jintu LUO Zhongxuan LI Yi | 2000 | Int J Heat Mass Transfer2000，43，16： | 1 |
| 7 | Geometrically Continuous Interpolation in Spheres显示文摘In this paper, a new method for geometrically continuous interpolation in spheres is proposed. The method is entirely based on the spherical B′ezier curves defined by the generalized de Casteljau algorithm. Firstly we compute the tangent directions and curvature vectors at the endpoints of a spherical B′ezier curve. Then, based on the above results, we design a piecewise spherical B′ezier curve with G 1 and G 2 continuity. In order to get the optimal piecewise curve according to two different criteria, we also give a constructive method to determine the shape parameters of the curve. According to the method, any given spherical points can be directly interpolated in the sphere. Experimental results also demonstrate that the method performs well both in uniform speed and magnitude of covariant acceleration. | Zhongxuan LUO Qian WANG | 2012 | Journal of Mathematical Research with Applications2012，32，4： | 1 |
| 8 | A Cl-rational spline in range restricted interpolation of scattered data 显示文摘 | Zhongxuan Luo Xingxuan Peng | 2006 | Journal of Computational and Applied Mathematics2006，194，2： | 1 |
| 9 | Fast algorithm of imagematching 显示文摘 | Luo Zhongxuan Liu Chengming | 2005 | Journal of Computer-Aided DesignComputer Graphics2005，17，5： | 1 |
| 10 | An tmproved mathenatical simulation of the coupled diffusion of moisture and heat in wool fabric显示文摘 | Li Y Luo Zhongxuan | 1999 | Textile Res J1999，69，10： | 1 |
| 11 | Microbial desulfurization of dibenzothiophene and 4,6-dimethyldibenzothiophene in dodecane and straight-run diesel oil显示文摘 | Luo Mingfang Xing Jianmin Gou Zhongxuan Liu Huizhou Chen Jiayong | 2003 | Korean Journal of Chemical Engineering2003，，4： | 1 |
| 12 | Heat and moisture with sorption and condensation in porous clothing assemblies and numerical simulation 显示文摘 | FAN Jintu LUO Zhongxuan LI Yi | 2000 | International Journal of Heat and Mass Transfer2000，43，： | 1 |
| 13 | Desulfurization of Dibenzothiophene by Lyophilized Cells of Pseudomonas DelafieldiiR - 8 in the Presence of Dodecane显示文摘 | Luo Mingfang Xing Jianmin Gou Zhongxuan | 2003 | Biochem Eng J2003，13，1： | 1 |
| 14 | Feature based problem hardness understanding for requirements engineering显示文摘Heuristics and metaheuristics have achieved great accomplishments in various fields, and the investigation of the relationship between these algorithms and the problem hardness has been a hot topic in the research field. Related research work has contributed much to the understanding of the underlying mechanisms of the algorithms for problem solving. However, most existing studies consider traditional combinatorial problems as their case studies. In this study, taking the Next Release Problem(NRP) from the requirements engineering as a case study, we investigate the relationship between software engineering problem instances and heuristics. We employ an evolutionary algorithm to evolve NRP instances, which are uniquely hard or easy for the target heuristic(Greedy Randomized Adaptive Search Procedure and Randomized Hill Climbing in this paper). Then, we use a feature-based method to estimate the hardness of the evolved instances, with respect to the target heuristic. Experimental results demonstrate that, evolutionary algorithm can be used to evolve NRP instances that are uniquely hard or easy to solve. Moreover, the features enable the estimation of the target heuristics' performance. | Zhilei REN He JIANG Jifeng XUAN Shuwei ZHANG Zhongxuan LUO | 2017 | Science China(Information Sciences)2017，60，3： | 0 |
| 15 | Prismatic mesh generation based on anisotropic volume harmonic field显示文摘In this paper,we present an effective prismatic mesh generation method for viscous flow simulations.To address the prismatic mesh collisions in recessed cavities or slit areas,we exploit 3D tensors controlled anisotropic volume harmonic field to generate prismatic meshes.Specially,a well-fitting tetrahedral mesh is first constructed to serve as the discrete computation domain of volume harmonic fields.Then,3D tensors are exploited to control the volume harmonic field that better fits the shape geometry.From the topological perspective,the generation of the prismatic mesh can be treated as a topology-preserved morphing of the viscous wall.Therefore,iso-surfaces in the volume harmonic field should be homeomorphic to the viscous wall while fitting its shapes.Finally,a full prismatic mesh can be induced by estimating the forward directions and visible regions in the volume harmonic field.Moreover,to be compatible with different simulation situations,the thickness of prismatic meshes should be variable.Our approach provides local adjustable thickness of prismatic meshes,which can be achieved by controlling local 3D tensors.The proposed anisotropic volume harmonic field based prismatic meshes are efficient and robust,and a full prismatic mesh can be guaranteed without low quality collisions.Various experiments have shown that our proposed prismatic meshes have obvious advantages in terms of efficiency and effectiveness. | Yiming Zhu Shengfa Wang Xiaopeng Zheng Na Lei Zhongxuan Luo Bo Chen | 2021 | Advances in Aerodynamics2021，3，1： | 0 |
| 16 | A Class of Multivariate Hermite Interpolation of Total Degree显示文摘In this paper we study a class of multivariate Hermite interpolation problem on 2~d nodes with dimension d ≥ 2 which can be seen as a generalization of two classical Hermite interpolation problems of d = 2. Two combinatorial identities are firstly given and then the regularity of the proposed interpolation problem is proved. | Zhongyong HU Zhaoliang MENG Zhongxuan LUO | 2017 | Journal of Mathematical Research with Applications2017，37，3： | 0 |
| 17 | The Nearest Complex Polynomial with a Prescribed Zero显示文摘Nearest polynomial with given properties has many applications in control theory and applied mathematics. Given a complex univariate polynomial f(z) and a zero α, in this paper we explore the problem of computing a complex polynomial f(z) such that f(α) = 0 and the distance ∥f-f ∥ is minimal. Considering most of the existing works focus on either certain polynomial basis or certain vector norm, we propose a common computation framework based on both general polynomial basis and general vector norm, and summarize the computing process into a four-step algorithm. Further, to find the explicit expression of f(z), we focus on two specific norms which generalize the familiar lp-norm and mixed norm studied in the existing works, and then compute f(z) explicitly based on the proposed algorithm. We finally give a numerical example to show the effectiveness of our method. | Wenyu HU Zhongxuan LUO | 2015 | Journal of Mathematical Research with Applications2015，35，1： | 0 |
| 18 | A NODAL BASIS OF C~μ-RATIONAL SPLINE FUNCTIONS ON TRIANGULATIONS显示文摘Let ι be a triangulation of a polygonal domain DR2 with vertices V={v1:1≤i≤N,}andRSk(D,τ)={u∈Ck(D):(T∈τ, u|τis a rational function}.The purpose of this paper is to study the exist-ence and construction of C<sup>μ-rational spline functions on any triangulation τ for CAGD.The Hermite prob-lem Hμ(V,U)={find | Zhongxuan Luo Renhong Wang (Dalian University of Technology,China) | 1994 | Analysis in Theory and Applications1994，10，4： | 0 |
| 19 | Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions显示文摘A simple method is proposed for constructing fourth-degree cubature formulae over general product regions with no symmetric assumptions. The cubatureformulae that are constructed contain at most n2 + 7n + 3 nodes and they are likelythe first kind of fourth-degree cubature formulae with roughly n2 nodes for nonsymmetric integrations. Moreover, two special cases are given to reduce the numberof nodes further. A theoretical upper bound for minimal number of cubature nodesis also obtained. | Ran Yu Zhaoliang Meng Zhongxuan Luo | 2014 | Numerical Mathematics(Theory,Methods and Applications)2014，7，2： | 0 |
| 20 | A New Strategy to Construct Embedded Cubature Formulae over Two-Dimensional Regions显示文摘The purpose of this paper is to study a new strategy to construct embedded cubature formulae over two-dimensional regions.A new kind of embedded cubature formulae with some nodes along the selected algebraic curve is constructed.Some examples on the unit disk are presented to illustrate the validity of this strategy. | Ran YU Zhaoliang MENG Zhongxuan LUO | 2013 | Journal of Mathematical Research with Applications2013，33，2： | 0 |
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