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| 1 | GENERATING EXACT NONLINEAR RANKING FUNCTIONS BY SYMBOLIC-NUMERIC HYBRID METHOD显示文摘This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs.At last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients. | SHEN Liyong WU Min YANG Zhengfeng ZENG Zhenbing | 2013 | Journal of Systems Science & Complexity2013，26，2： | 5 |
| 2 | Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems显示文摘The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blondel’s technique. We give a complete answer to the open problem proposed by Patel et al., which auto-matically includes the solution to the original Champagne Problem. Based on the recent development in automated inequality-type theorem proving, a new stabiliz-ing controller design method is established. Our numerical examples significantly improve the relevant results in the literature. | GUAN Qiang WANG Long XIA BiCan YANG Lu YU WenSheng ZENG ZhenBing | 2007 | Science in China(Series F)2007，50，5： | 4 |
| 3 | Resultant Elimination via Implicit Equation Interpolation显示文摘It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems. | TANG Min YANG Zhengfeng ZENG Zhenbing | 2016 | Journal of Systems Science & Complexity2016，29，5： | 3 |
| 4 | Comparative study of de novo assembly and genome-guided assembly strategies for transcriptome reconstruction based on RNA-Seq显示文摘Transcriptome reconstruction is an important application of RNA-Seq,providing critical information for further analysis of transcriptome.Although RNA-Seq offers the potential to identify the whole picture of transcriptome,it still presents special challenges.To handle these difficulties and reconstruct transcriptome as completely as possible,current computational approaches mainly employ two strategies:de novo assembly and genome-guided assembly.In order to find the similarities and differences between them,we firstly chose five representative assemblers belonging to the two classes respectively,and then investigated and compared their algorithm features in theory and real performances in practice.We found that all the methods can be reduced to graph reduction problems,yet they have different conceptual and practical implementations,thus each assembly method has its specific advantages and disadvantages,performing worse than others in certain aspects while outperforming others in anther aspects at the same time.Finally we merged assemblies of the five assemblers and obtained a much better assembly.Additionally we evaluated an assembler using genome-guided de novo assembly approach,and achieved good performance.Based on these results,we suggest that to obtain a comprehensive set of recovered transcripts,it is better to use a combination of de novo assembly and genome-guided assembly. | LU BingXin ZENG ZhenBing SHI TieLiu | 2013 | Science China(Life Sciences)2013，56，2： | 2 |
| 5 | Parallel computation of determinants of matrices with multivariate polynomial entries显示文摘In this paper we present an extension to the work of Bjrck et al.for computing the determinants of matrices with univariate or bivariate polynomials as entries to multivariate case.The algorithm supports parallel computation and has been implemented on a multi-core cluster computer system.We show how to use our approach to calculate two unsolved problems,which arise from computational geometry optimization and electric power engineering,and analyze the time complexity as well as bits complexity. | CHEN LiangYu ZENG ZhenBing | 2013 | Science China(Information Sciences)2013，56，11： | 2 |
| 6 | Exact safety verification of hybrid systems using sums-of-squares representation显示文摘In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems.A hybrid symbolic-numeric method is presented to compute inequality inductive invariants of the given systems.A numerical invariant of the given system can be obtained by solving a parameterized polynomial optimization problem via sum-of-squares(SOS)relaxation.And a method based on Gauss-Newton refinement and rational vector recovery is used to obtain the invariants with rational coefficients,which exactly satisfy the conditions of invariants.Several examples are given to illustrate our algorithm. | LIN Wang WU Min YANG ZhengFeng ZENG ZhenBing | 2014 | Science China(Information Sciences)2014，57，5： | 1 |
| 7 | Linear invariant generation for verification of nonlinear hybrid systems via conservative approximation显示文摘Dear editor,Hybrid systems are widely used in modeling safetycritical systems[1].In recent years,safety verification of hybrid systems,whose aim is to decide whether the systems will reach a dangerous or un- | Xia ZENG Wang LIN Zhengfeng YANG Zhenbing ZENG | 2017 | Science China(Information Sciences)2017，60，3： | 1 |
| 8 | Weak centers and bifurcation of critical periods in reversible cubic systems显示文摘 | ZHANG Weinian HUO Xiaorong ZENG Zhenbing | 2000 | Computers&Mathematics with Applications2000，40，6： | 1 |
| 9 | A complete discrimination system for polynomials显示文摘 | Yang Lu Hou Xiaorong Zeng Zhenbing | 1996 | Science in China1996，39，6： | 1 |
| 10 | Weak cen- ters and bifurcation of critical periods in reversible cubicsystems显示文摘 | Zb:ang Weinian Hou Xiaorong Zeng Zhenbing | 2000 | Computers and Mathematics with Applica- tions2000，40，： | 1 |
| 11 | Weak centers and bifurcation of critical periods in revertible cubic system显示文摘 | Zhang Weinian Hou Xiaorong Zeng Zhenbing | 2000 | Computers & Mathematics with Ap- plications2000，40，： | 1 |
| 12 | Automated andreadable simplification of trigonometric expressions 显示文摘 | Fu Hongguang Zhong Xiuqin Zeng Zhenbing | 2006 | Math-ematical and Computer Modeling2006，44，11： | 1 |
| 13 | Heilbronn's Problem of Eight Points in the Square显示文摘In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the(38)triangles formed by them is maximal.Symbolic computations are employed to reduce the problem into a nonlinear programming problem and find its optimal solution.All computations are done using Maple. | DEHBI Lydia ZENG Zhenbing | 2022 | Journal of Systems Science & Complexity2022，35，6： | 0 |
| 14 | Proving total correctness and generating preconditions for loop programs via symbolic-numeric computation methods显示文摘我们在场一个符号数字的混合方法,基于 sum-of-squares (求救) 松驰和合理向量恢复,为证明正确性全部并且为程序产生前提计算不平等 invariants 和评价函数。求救松驰方法被用来计算近似 invariants 并且接近与浮点系数评价功能。然后,高斯牛顿精炼和合理向量恢复被用于近似多项式与合理系数获得候选人多项式,它确切满足 invariants 的条件,评价工作。最后,几个例子被给显示出我们的方法的有效性。 | Wang LIN Min WU Zhengfeng YANG Zhenbing ZENG | 2014 | Frontiers of Computer Science2014，8，2： | 0 |
| 15 | Computing Sparse GCD of Multivariate Polynomials via Polynomial Interpolation显示文摘作为在更多的一般范围的计算机代数学和符号的计算的最重要的任务之一,自从开始,计算 multivariate 多项式的最大的普通除数(GCD ) 的问题广泛地被学习了有计算机科学的数学学科交差。为象数字图象恢复和改进那样的许多真实应用程序,非线性的系统的柔韧的控制理论, L 1-norm 在察觉到技术压缩的凸的优化,以及芦苇贤明之人和 BCH 的代数学的译码编码,稀少的 GCD 的概念起仅仅的一个核心作用最大的普通除数与很,少数比原来的多项式由于问题或数据结构的性质具有兴趣的称为。这份报纸经由分别地基于 Zippels 方法和 Ben-Or/Tiwari 算法的变化的 multivariate 多项式插值论述二个方法。为了减少计算复杂性,概率的技术和随机化,被采用处理 univariate GCD 计算和 univariate 多项式插值。作者在例子的重要身体上表明我们的算法的实际表演。实现的实验说明那我们的算法为输入的一个相当宽的范围是有效的。 | TANG Min LI Bingyu ZENG Zhenbing | 2018 | Journal of Systems Science & Complexity2018，31，2： | 0 |
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