A new representation of systems with frictional unilateral constraints and its Baumgarte-like relaxation

This paper proposes a new representation of multibody mechanical systems involving three-dimensional frictional unilateral constraints. The new representation is of the form of a differential algebraic inclusion (DAI) employing a normal cone with a non-Euclidean, singular norm metric. It can be seen as a generalization of a differential algebraic equation (DAE) using Lagrange multipliers, which has been used to represent mechanical systems with equality constraints. The paper also presents an approach to approximate the aforementioned DAI by another form of DAI, which can be equivalently converted into an ordinary differential equation (ODE). The approach can be seen as a generalization of the Baumgarte stabilization, which was originally developed for DAEs. The new DAI representation and its ODE approximation are illustrated with some simple examples.     

Gradient-based adaptation of general gaussian kernels

Gradient-based optimizing of gaussian kernel functions is considered. The gradient for the adaptation of scaling and rotation of the input space is computed to achieve invariance against linear transformations. This is done by using the exponential map as a parameterization of the kernel parameter manifold. By restricting the optimization to a constant trace subspace, the kernel size can be controlled. This is, for example, useful to prevent overfitting when minimizing radius-margin generalization performance measures. The concepts are demonstrated by training hard margin support vector machines on toy data.     

Compatibility of parameter passing and implementation of parameterized data types

The basis for this paper are the concepts of parameterization and implementation of abstract data types which have been developed in the theory of algebraic specifications with initial algebra semantics. In this paper we combine both concepts defining implementations of parameterized data types and studying the compatibility of parameter passing and implementation of parameterized data types. In our main result we show that parameter passing commutes with implementation. This is an important step in order to apply the theory of algebraic specifications to development and stepwise refinement of software systems. We illustrate our notion and results by a small example implementing binary trees over arbitrary data by corresponding strings with brackets. Finally we consider the problem of 2-dimensional compatibility of parameter passing and implementation and discuss the kind of compatibility results which have been shown by other authors in the case of loose and final algebra semantics.     

Design Sensitivity Analysis and Optimization tool (DSO) for shape design applications

The Design Sensitivity Analysis and Optimization (DSO) tool, developed initially for sizing design application, has been extended to support shape design applications of structural components. The new capabilities including shape design parameterization, error analysis and mesh adaptation, design velocity field computation, shape design sensitivity analysis, and interactive design steps, are discussed. These capabilities are integrated on the top of the DSO framework that includes databases, user interface, foundation class and remote module. The DSO allows the design engineer to easily create geometric, design, and analysis models; define performance measures; perform design sensitivity analysis (DSA); and carry out a four-step interactive design process that includes visual display of design sensitivity, what-if study, trade-off analysis, and interactive design optimization. Additionally, a 3-D tracked vehicle clevis is presented in this paper to demonstrate the new capabilities.     

Techniques for cubic algebraic surfaces

A survey of some techniques that may have potential for free-form modeling with algebraic surfaces is continued. Classical results as well as several recent innovations are included. Specific attention is paid to cubic algebraic surfaces, although many of the ideas presented have application to algebraic surfaces of any degree. Topics addressed include piecewise constructions, interpolation to points and space curves, and parameterization     

基于三次PH 曲线误差可控代数曲线等距线逼近算法

论文提出一种用三次PH 曲线逼近代数曲线的方法及其误差分析。使用该 方法,给出一种用PH 曲线的等距线来逼近原来代数曲线等距线的算法。逼近曲线保持了原 曲线的一些重要几何性质,如单调性、凹凸性、G1 连续性等。数值实验表明,该算法提供 了代数曲线近似参数化的一条有效途径。并在此基础上提出了一种计算代数曲线等距线的有 理参数表示的新方法。     

Toward the adaptation of component‐based architectures by model transformation: behind smart user interfaces

Graphical user interfaces are not always developed for remaining static. There are GUIs with the need of implementing some variability mechanisms. Component‐based GUIs are an ideal target for incorporating this kind of operations, because they can adapt their functionality at run‐time when their structure is updated by adding or removing components or by modifying the relationships between them. Mashup user interfaces are a good example of this type of GUI, and they allow to combine services through the assembly of graphical components. We intend to adapt component‐based user interfaces for obtaining smart user interfaces. With this goal, our proposal attempts to adapt abstract component‐based architectures by using model transformation. Our aim is to generate at run‐time a dynamic model transformation, because the rules describing their behavior are not pre‐set but are selected from a repository depending on the context. The proposal describes an adaptation schema based on model transformation providing a solution to this dynamic transformation. Context information is processed to select at run‐time a rule subset from a repository. Selected rules are used to generate, through a higher‐order transformation, the dynamic model transformation. This approach has been tested through a case study which applies different repositories to the same architecture and context. Moreover, a web tool has been developed for validation and demonstration of its applicability. The novelty of our proposal arises from the adaptation schema that creates a non pre‐set transformation, which enables the dynamic adaptation of component‐based architectures. Copyright © 2014 Copyright © 2014 John Wiley & Sons, Ltd.     

A vegetarian approach to optimal parameterizations

According to a recent result by Farouki (1997), the optimal bilinear parameter transformation of an integral Bézier curve (which produces a rational parameterization whose parametric speed is as uniform as possible) can be computed by solving a quadratic equation. This note presents a simplified derivation of this result. In addition we outline its generalization to rational curves.     

Parameterization in Finite Precision

Certain classes of algebraic curves and surfaces admit both parametric and implicit representations. Such dual forms are highly useful in geometric modeling since they combine the strengths of the two representations. We consider the problem of computing the rational parameterization of an implicit curve or surface in a finite precision domain. Known algorithms for this problem are based on classical algebraic geometry, and assume exact arithmetic involving algebraic numbers. In this work we investigate the behavior of published parameterization algorithms in a finite precision domain and derive succinct algebraic and geometric error characterizations. We then indicate numerically robust methods for parameterizing curves and surfaces which yield no error in extended finite precision arithmetic and, alternatively, minimize the output error under fixed finite precision calculations. Received January 8, 1997; revised August 27, 1998.     

A Computational Global Tangential Krylov Subspace Method for Model Reduction of Large-Scale MIMO Dynamical Systems

In this paper, we present a new approach for model order reduction problems, with multiple inputs and multiple outputs, named: Adaptive Global Tangential Arnoldi Algorithm. This method is based on a generalization of the global Arnoldi algorithm. The selection of the shifts and the tangent directions are done with an adaptive procedure. We give some algebraic properties and present some numerical examples to show the effectiveness of the proposed algorithm.     

Gradient-based adaptation of continuous dynamic model structures

A gradient-based method of symbolic adaptation is introduced for a class of continuous dynamic models. The proposed model structure adaptation method starts with the first-principles model of the system and adapts its structure after adjusting its individual components in symbolic form. A key contribution of this work is its introduction of the model’s parameter sensitivity as the measure of symbolic changes to the model. This measure, which is essential to defining the structural sensitivity of the model, not only accommodates algebraic evaluation of candidate models in lieu of more computationally expensive simulation-based evaluation, but also makes possible the implementation of gradient-based optimisation in symbolic adaptation. The proposed method is applied to models of several virtual and real-world systems that demonstrate its potential utility.     

On decentralized dynamic pole placement and feedback stabilization

In this paper we study the feedback control problem using an r-channel decentralized dynamic feedback control scheme. We will develop the theory in the behavioral framework. Using this framework we introduce an algebraic parameterization of the space of all possible feedback compensators having a bounded McMillan degree, and we show that this parameterization has the structure of an algebraic variety. We define the pole-placement map for this problem, and we give exact conditions when this map is onto, and almost onto. Finally we provide new necessary and sufficient conditions which guarantee that the set of stabilizable plants is a generic set     

基于几何约束的三次代数曲线插值

尽管三次参数曲线在曲线曲面造型中扮演着主要角色,但是计算几何专家也一直没有放弃对三次代数曲线的性质及应用进行研究。该文首先综述了近年来有关三次代数曲线研究的最新进展,对各主要方法的优缺点进行了客观的评价。然后提出了一种基于几何约束的三次代数曲线的插值方法,该方法守完全通过几何量如控制顶点、切线和曲率来控制三次代数曲线的形状,使得对三次代数曲线的编辑与对三次B－样条曲线的编辑一样灵活方便。该文提出的代数曲线的结构有两种,一种是插值平面上四点及两端点切线的三次代数曲线;另一种是插值两端点、两切线及两曲率的三次代数曲线。在第二种情况下对曲率的情况进行了详细的分类。并且从理论上对曲线的连续性及保凸性进行了严格的证明。     

Lower bounds for the non-linear complexity of algebraic computation trees with integer inputs

Andrew Yao proved some lower bounds for algebraic computation trees with integer inputs. In his key result he proved bounds on the number of components of the leaf space of a homogeneous decision tree derived from a computation tree. In this paper we present a shorter and more conceptual proof. We introduce the concept of aregulated tree as a generalization of a regular tree which has the advantage of allowing the same lower bounds on the non-linear portion of the complexity. The proof is an application of a result of Ben-Or.     

Generalizing rational degree elevation

A generalization of the well-known degree elevation algorithms for Bézier curves is presented. This generalized degree elevation extends the expressive power of rational polynomials. In particular, it allows a given curve to be represented equivalently by a family of control point and weight distributions, without affecting its parameterization. Some control over the control point distribution is demonstrated. The effects of reparameterization in conjunction with degree elevation are also explored, and techniques for detecting degeneracy in the presence of reparameterization are described.     

Algebra of Systems: A Metalanguage for Model Synthesis and Evaluation

This paper represents system models as algebraic entities and formulates model transformation activities as algebraic operations. We call this modeling framework ldquoalgebra of systemsrdquo (AoS). To show that AoS can automate complex model reasoning tasks in system design projects, we implemented the abstract algebraic specification as an executable metalanguage named object-process network, which serves as a tool for automatic model transformation, enumeration, and evaluation. A case study of the Apollo lunar landing mission design is developed using this algebraic modeling approach.     

代数曲线的分段有理二次B样条插值

通过对代数曲线的合理分割,定义了曲线段的三角形凸包。给出了由三角形凸包确定控制多边形的方案。重点讨论了代数曲线参数化的分段有理二次B样条插值算法。插值曲线保持了原始曲线的一些重要几何性质,如单调性、凹凸性、G1连续性。数值实验验证了算法的有效性。