Optimal approximate merging of a pair of Bézier curves with G2-continuity

We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^2-continuity. Instead of moving the control points, we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bezier curve＇s discrete structure, where the approximation error is measured by L2-norm. We use geometric information about the curves to generate the merged curve, and the approximation error is smaller. We can obtain control points of the merged curve regardless of the degrees of the two original curves. We also discuss the merged curve with point constraints. Numerical examples are provided to demonstrate the effectiveness of our algorithms.     

Optimal approximate merging of a pair of Bézier curves with G2-continuity

We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier curves with G2-continuity. Instead of moving the control points, we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bezier curve's discrete structure, where the approximation error is measured by L2-norm. We use geometric information about the curves to generate the merged curve, and the approximation error is smaller. We can obtain control points of the merged curve regardless of the degrees of the two original curves. We also discuss the merged curve with point constraints. Numerical examples are provided to demonstrate the effectiveness of our algorithms.     

On the approximate zero of Newton method

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Tree kernel-based semantic role labeling with enriched parse tree structure

Shallow semantic parsing assigns a simple structure (such as WHO did WHAT to WHOM, WHEN, WHERE, WHY, and HOW) to each predicate in a sentence. It plays a critical role in event-based information extraction and thus is important for deep information processing and management. This paper proposes a tree kernel method for a particular shallow semantic parsing task, called semantic role labeling (SRL), with an enriched parse tree structure. First, a new tree kernel is presented to effectively capture the inherent structured knowledge in a parse tree by enabling the standard convolution tree kernel with context-sensitiveness via considering ancestral information of substructures and approximate matching via allowing insertion/deletion/substitution of tree nodes in the substructures. Second, an enriched parse tree structure is proposed to both well preserve the necessary structured information and effectively avoid noise by differentiating various portions of the parse tree structure. Evaluation on the CoNLL’2005 shared task shows that both the new tree kernel and the enriched parse tree structure contribute much in SRL and our tree kernel method significantly outperforms the state-of-the-art tree kernel methods. Moreover, our tree kernel method is proven rather complementary to the state-of-the-art feature-based methods in that it can better capture structural parse tree information.     

构建有意义的英语精读课堂教学模式

精读课要想摆脱传统的以教师为中心的讲座式课堂教学模式,增强学生学习的兴趣、动机和效果,促进他们思维能力的发展,教师一方面可以通过从教材中提取挖掘能引起学生共鸣的富于化性、意义性的思想内容并设置相关的学习任务和活动;另一方面可以通过在课堂教学中适当地运用“近体原则”,从而帮助学生进行具有个人意义的建构。只有通过对学习来说有意义的学习,精读教学才能更富于成效。     

On the approximate zero of Newton method

A judgment criterion to guarantee a point to be a Chen's approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero; assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen's approximate zero may not be a Smale's approximate zero. The error estimate obtained indicated the convergent order when we use |f(x)|<ε to stop computation in software. The result can also be applied for solving partial derivative and integration equations. Project supported by the Special Funds for Major State Basic Research (973) Program(No. 19990328) and the National Natural Science Foundation of China(No. 10271112), and Y. C. Tang Disciplinary Development Fund of Zhejiang University, China     

Comparison of two approximal proximal point algorithms for monotone variational inequalities

Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions of PPA (APPA) are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as predic- tion-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm I; in the same way, Algorithm II is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm II usually outperforms Algorithm I. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm II to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some nu- merical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.     

模糊广义正则蕴涵代数

模糊蕴涵代数是取值于[0,1]区间上的模糊逻辑系统的一种代数抽象。通过引入模糊广义正则蕴涵代数的概念,对其性质进行了讨论,并给出了广义正则模糊蕴涵代数的一些等价刻画。     

浅谈物理学问题中的近似条件

物理学中近似条件在理论学习和解题中占有比较重要的地位。因此 ,熟练掌握近似方法及应用 ,对物理学习会带来很多方便之处     

s-grams: Defining generalized n-grams for information retrieval

n-grams have been used widely and successfully for approximate string matching in many areas. s-grams have been introduced recently as an n-gram based matching technique, where di-grams are formed of both adjacent and non-adjacent characters. s-grams have proved successful in approximate string matching across language boundaries in Information Retrieval (IR). s-grams however lack precise definitions. Also their similarity comparison lacks precise definition. In this paper, we give precise definitions for both. Our definitions are developed in a bottom-up manner, only assuming character strings and elementary mathematical concepts. Extending established practices, we provide novel definitions of s-gram profiles and the L₁ distance metric for them. This is a stronger string proximity measure than the popular Jaccard similarity measure because Jaccard is insensitive to the counts of each n-gram in the strings to be compared. However, due to the popularity of Jaccard in IR experiments, we define the reduction of s-gram profiles to binary profiles in order to precisely define the (extended) Jaccard similarity function for s-grams. We also show that n-gram similarity/distance computations are special cases of our generalized definitions.