Symbolic parametrization of curves

If algebraic varieties like curves or surfaces are to be manipulated by computers, it is essential to be able to represent these geometric objects in an appropriate way. For some applications an implicit representation by algebraic equations is desirable, whereas for others an explicit or parametric representation is more suitable. Therefore, transformation algorithms from one representation to the other are of utmost importance.We investigate the transformation of an implicit representation of a plane algebraic curve into a parametric representation. Various methods for computing a rational parametrization, if one exists, are described. As a new idea we introduce the concept of working with classes of conjugate (singular or simple) points on curves. All the necessary operations, like determining the multiplicity and the character of the singular points or passing a linear system of curves through these points, can be applied to such classes of conjugate points. Using this idea one can parametrize a curve if one knows only one simple point on it. We do not propose any new method for finding such a simple point. By classical methods a rational point on a rational curve can be computed, if such a point exists. Otherwise, one can express the coordinates of such a point in an algebraic extension of degree 2 over the ground field.     

一种基于切片技术度量Java耦合性的框架

在研究面向对象的度量问题时,人们通过简单的统计方法和基于信息源的方法来度量其中的一些特征,例如基本度量、CK度量和AoKi度量等。文中采用一种基于程序切片的方法来度量Java的耦合性问题,通过对J ava源程序中存在的耦合关系的度量,得到了一种比传统方法更精确的耦合度量方法。     

Monte Carlo methods for matrix computations on the grid

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors.     

Real Solving for Positive Dimensional Systems

Finding one point on each semi-algebraically connected component of a real algebraic variety, or at least deciding if such a variety is empty or not, is a fundamental problem of computational real algebraic geometry. Although numerous studies have been done on the subject, only a small number of efficient implementations exist.In this paper, we propose a new efficient and practical algorithm for computing such points. By studying the critical points of the restriction to the variety of the distance function to one well chosen point, we show how to provide a set of zero-dimensional systems whose zeros contain at least one point on each semi-algebraically connected component of the studied variety, without any assumption either on the variety (smoothness or compactness for example) or on the system of equations which define it.From the output of our algorithm, one can then apply, for each computed zero-dimensional system, any symbolic or numerical algorithm for counting or approximating the real solutions. We report some experiments using a set of pure exact methods. The practical efficiency of our method is due to the fact that we do not apply any infinitesimal deformations, unlike the existing methods based on a similar strategy.     

Some techniques for geometric searching with implicit set representations

Summary There are many efficient ways of searching a set when all its elements can be represented in memory. Often, however, the domain of the search is too large to have each element stored separately, and some implicit representation must be used. Whether it is still possible to search efficiently in these conditions is the underlying theme of this paper. We look at several occurrences of this problem in computational geometry and we propose various lines of attack. In the course of doing so, we improve the solutions of several specific problems; for example, computing order statistics, performing polygonal range searching, testing algebraic predicates, etc.     

Robust segmentation of primitives from range data in the presenceof geometric degeneracy

This paper addresses a common problem in the segmentation of range images. We present methods for the least-squares fitting of spheres, cylinders, cones, and tori to 3D point data, and their application within a segmentation framework. Least-squares fitting of surfaces other than planes, even of simple geometric type, has rarely been studied. Our main application areas of this research are reverse engineering of solid models from depth-maps and automated 3D inspection where reliable extraction of these surfaces is essential. Our fitting method has the particular advantage of being robust in the presence of geometric degeneracy, i.e., as the principal curvatures of the surfaces being fitted decrease, the results returned naturally become closer and closer to those surfaces of “simpler type”, i.e., planes, cylinders, cones, or spheres, which best describe the data. Many other methods diverge because, in such cases, various parameters or their combination become infinite     

Gradual Numbers and Their Application to Fuzzy Interval Analysis

In this paper, we introduce a new way of looking at fuzzy intervals. Instead of considering them as fuzzy sets, we see them as crisp sets of entities we call gradual (real) numbers. They are a gradual extension of real numbers, not of intervals. Such a concept is apparently missing in fuzzy set theory. Gradual numbers basically have the same algebraic properties as real numbers, but they are functions. A fuzzy interval is then viewed as a pair of fuzzy thresholds, which are monotonic gradual real numbers. This view enables interval analysis to be directly extended to fuzzy intervals, without resorting to alpha-cuts, in agreement with Zadeh's extension principle. Several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end- points of intervals are changed into left and right fuzzy bounds. Our approach is illustrated on two known problems: computing fuzzy weighted averages and determining fuzzy floats and latest starting times in activity network scheduling.     

A finite element method for diffusion dominated unsteady viscous flows

A general conforming finite element scheme for computing viscous flows is presented which is of second-order accuracy in space and time. Viscous terms are treated implicitly and advection terms are treated explicitly in the time marching segment of the algorithm. A method for solving the algebraic equations at each time step is given. The method is demonstrated on two test problems, one of them being a plane vortex flow for which asymptotic methods are used to obtain suitable numerical boundary conditions at each time step.     

Approximating sets on a plane with optimal sets of circles

We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles.     

Projective Visual Hulls

This article presents a novel method for computing the visual hull of a solid bounded by a smooth surface and observed by a finite set of cameras. The visual hull is the intersection of the visual cones formed by back-projecting the silhouettes found in the corresponding images. We characterize its surface as a generalized polyhedron whose faces are visual cone patches; edges are intersection curves between two viewing cones; and vertices are frontier points where the intersection of two cones is singular, or intersection points where triples of cones meet. We use the mathematical framework of oriented projective differential geometry to develop an image-based algorithm for computing the visual hull. This algorithm works in a weakly calibrated setting–-that is, it only requires projective camera matrices or, equivalently, fundamental matrices for each pair of cameras. The promise of the proposed algorithm is demonstrated with experiments on several challenging data sets and a comparison to another state-of-the-art method.     

IFS与L系统的统一描述语言及其分类

为了更高效地表示分形图形,依据形式语言的文法结构及正则表达式的文法规则,通过引入代数运算,提出了一个能够对L系统和迭代函数系统(IFS)统一描述的语言代数系统。根据语言代数系统产生式的文法规则,将此系统的产生式集划分为五类。结合分形理论,此语言代数系统着重将DOL系统、迭代函数系统(IFS)、带凝聚集迭代函数系统(凝聚IFS)、随机迭代函数系统(IFSP)和再归迭代函数系统(RIFS)等进行描述,同时用此系统的正则表达式方程解将分形吸引子进行代数表示,并给出一些实例。通过实例表明,分形图形可以用该语言代数系统简单、明了、高效地表示。     

Matching 3-D Models to 2-D Images

We consider the problem of analytically characterizing the set of all 2-D images that a group of 3-D features may produce, and demonstrate that this is a useful thing to do. Our results apply for simple point features and point features with associated orientation vectors when we model projection as a 3-D to 2-D affine transformation. We show how to represent the set of images that a group of 3-D points produces with two lines (1-D subspaces), one in each of two orthogonal, high-dimensional spaces, where a single image group corresponds to one point in each space. The images of groups of oriented point features can be represented by a 2-D hyperbolic surface in a single high-dimensional space. The problem of matching an image to models is essentially reduced to the problem of matching a point to simple geometric structures. Moreover, we show that these are the simplest and lowest dimensional representations possible for these cases.We demonstrate the value of this way of approaching matching by applying our results to a variety of vision problems. In particular, we use this result to build a space-efficient indexing system that performs 3-D to 2-D matching by table lookup. This system is analytically built and accessed, accounts for the effects of sensing error, and is tested on real images. We also derive new results concerning the existence of invariants and non-accidental properties in this domain. Finally, we show that oriented points present unexpected difficulties: indexing requires fundamentally more space with oriented than with simple points, we must use more images in a motion sequence to determine the affine structure of oriented points, and the linear combinations result does not hold for oriented points.     

A unified approach to finding good stable matchings in the hospitals/residents setting

The hospitals/residents (HR) problem is a many-to-one generalization of the stable marriage (SM) problem. Researchers have been interested in variants of stable matchings that either satisfy a set of additional contraints or are optimal with respect to some cost function. In this paper, we show that broad classes of feasibility and optimization stable matching problems in the HR setting can be solved efficiently provided certain tasks (such as checking the feasibility of a stable matching or computing the cost of a stable matching) can also be done efficiently. To prove our results, we make use of an HR instance’s meta-rotation poset to explore its stable matchings. An algorithm that can discover all the meta-rotations of the instance serves as a starting point for all our algorithms.     

Managers,spreadsheets and computing growth: contagion or control?

Abstract. It is widely accepted that managers do not make the most of the opportunities offered by information technology (IT). This study set out to investigate why by establishing what computing facilities managers actually use, and how they use them. The original hypothesis was that adoption of technology was limited by poor training and lack of interest in IT. We set out to establish empirical findings by interviewing managers face to face at their place of work. An exploratory investigation of this nature must adopt a non-directive approach which is not amenable to questionnaire-type survey techniques, and which produces 'soft' rather than quantitative data. As the 'soft' nature of the data ruled out strict statistical methods we used a 'search and refine' technique, to build a structure from all the information we received during the interviews until a clear body of results emerged and could be clarified and confirmed. The research broadly supports the lack of training hypothesis but finds that far from being uninterested, managers are very interested in using IT, but only where it is directly relevant to their own work. The study suggests that training is not enough and must be supplemented by control. The findings support but also refute aspects of Nolan's stage theoy of computing growth. Further research to confirm these findings would be useful, as would comparative studies in organizations where controls on spreadsheets are in place.     

基于推广B 样条细分方法的曲面混合

提出用推广B 样条细分曲面来混合多张曲面的方法,既适用于一般网格曲面,又适 用于推广B 样条参数曲面混合。根据需要选择阶数和张力参数,可全局调整整张混合曲面的形状。 中心点和谷点的计算都设置了形状参数,可局部调整混合部分形状。推导出二次曲面细分初始网 格计算公式,并将3 阶推广B 样条细分曲面混合方法用于多张二次曲面混合,与已有的二次曲面 混合方法相比具有明显的优势。     

对区间二型模糊集的EKM降型法的改进

二型模糊集的质心计算称为降型,目前的降型方法大多计算成本较高,其中EKM (Enhanced Karnik-Mendel)法可计算区间二型模糊集的质心。然而,由于EKM算法中求取切换点的初始化方法还不完善,计算时间较长,使其在实际应用中受到一定限制。对此,提出一种新的改进EKM法,对原有方法进行了两处改进：更改切换点的初始化条件和改进查找切换点的方法。所提出的方法可实现向上和向下搜索,计算量大大减小,降型更有效。仿真结果验证了新的改进EKM法的有效性。     

Advances in feedforward neural networks: demystifying knowledgeacquiring black boxes

We survey research of recent years on the supervised training of feedforward neural networks. The goal is to expose how the networks work, how to engineer them so they can learn data with less extraneous noise, how to train them efficiently, and how to assure that the training is valid. The scope covers gradient descent and polynomial line search, from backpropagation through conjugate gradients and quasi Newton methods. There is a consensus among researchers that adaptive step gains (learning rates) can stabilize and accelerate convergence and that a good starting weight set improves both the training speed and the learning quality. The training problem includes both the design of a network function and the fitting of the function to a set of input and output data points by computing a set of coefficient weights. The form of the function can be adjusted by adjoining new neurons and pruning existing ones and setting other parameters such as biases and exponential rates. Our exposition reveals several useful results that are readily implementable     

The computation of hitting sets: Review and new algorithms

In model-based diagnosis or other research fields, the hitting sets of a set cluster are usually used. In this paper we introduce some algorithms, including the new BHS-tree and Boolean algebraic algorithms. In the BHS-tree algorithm, a binary-tree is used for the computation of hitting sets, and in the Boolean algebraic algorithm, components are represented by Boolean variables. It runs just for one time to catch the minimal hitting sets. We implemented the algorithms and present empirical results in order to show their superiority over other algorithms for computing hitting sets.