Simultaneous inner and outer approximation of shapes

For compact Euclidean bodiesP, Q, we define (P, Q) to be the smallest ratior/s wherer > 0,s > 0 satisfy . HeresQ denotes a scaling ofQ by the factors, andQ,Q are some translates ofQ. This function gives us a new distance function between bodies which, unlike previously studied measures, is invariant under affine transformations. If homothetic bodies are identified, the logarithm of this function is a metric. (Two bodies arehomothetic if one can be obtained from the other by scaling and translation.)For integerk 3, define (k) to be the minimum value such that for each convex polygonP there exists a convexk-gonQ with (P, Q) (k). Among other results, we prove that 2.118 ... <-(3) 2.25 and (k) = 1 + (k ^–2). We give anO(n ² log² n)-time algorithm which, for any input convexn-gonP, finds a triangleT that minimizes (T, P) among triangles. However, in linear time we can find a trianglet with (t, P)<-2.25.Our study is motivated by the attempt to reduce the complexity of the polygon containment problem, and also the motion-planning problem. In each case we describe algorithms which run faster when certain implicitslackness parameters of the input are bounded away from 1. These algorithms illustrate a new algorithmic paradigm in computational geometry for coping with complexity.Work of all authors was partially supported by the ESPRIT II Basic Research Actions Program of the EC under Contract No. 3075 (project ALCOM). Rudolf Fleischer and Kurt Mehlhorn acknowledge also DFG (Grant SPP Me 620/6). Chee Yap acknowledges also DFG (Grant Be 142/46-1) and NSF (Grants DCR-84-01898 and CCR-87-03458). This research was performed when Günter Rote and Chee Yap were at the Freie Universität Berlin.     

Polygonal approximation of 2-D shapes through boundary merging

In this paper we present a shape approximation method which yields accurate and unique polygonal approximations. The approach first looks for arcs with two or three runs along the shape boundary whose arc-to-chord deviations are not only the smallest in their local areas but also smaller than a tolerance value. These arcs are then replaced by their respective chords. This process goes on iteratively until no arc can be reduced for the given tolerance.     

轴承内外套圈自动检测与分级设备的研究

基于全新的V型块三点圆度解析测量法及labview软件平台，设计了一种在线式轴承内外套圈自动检测与分级设备。该设备采用最新的激光位移式传感器，实现了非接触高精度测量。     

管状药柱识别及平均内外径检测

某管状药柱塑性较大,在生产过程中,由于挤压等原因,端面不是规则的圆环形,其平均内外径尺寸直接关系到弹药的性能。目前的内外径尺寸检测技术只能检测单个目标,检测平均内外径需要拍摄多幅图像,取这多幅图像目标尺寸平均值。为此,提出了利用面阵电荷耦合器件(面阵CCD)摄像机获取目标图像,每幅图像可包含多个目标,然后,采用二维傅里叶描述子对不同目标进行识别,根据药柱是否相同判断其是否离开视场,实现了对多个药柱尺寸同时检测,极大地提高了检测速度,采用多项式插值技术进行亚像素边缘检测,使测量精度高于0.01mm,达到微米级。     

Recursive algorithms for inner ellipsoidal approximation of convex polytopes

In this paper, fast recursive algorithms for the approximation of an n-dimensional convex polytope by means of an inscribed ellipsoid are presented. These algorithms consider at each step a single inequality describing the polytope and, under mild assumptions, they are guaranteed to converge in a finite number of steps. For their recursive nature, the proposed algorithms are better suited to treat a quite large number of constraints than standard off-line solutions, and have their natural application to problems where the set of constraints is iteratively updated, as on-line estimation problems, nonlinear convex optimization procedures and set membership identification.     

Kernel shapes of fuzzy sets in fuzzy systems for function approximation

The shapes of if-part fuzzy sets affect the approximating capability of fuzzy systems. In this paper, the fuzzy systems with the kernel-shaped if-part fuzzy sets are built directly from the training data. It is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single-input-single-output (SISO) case. On the basis of these rates, the relationships between the approximating capability and the shapes of if-part fuzzy sets are developed for the fuzzy systems. Furthermore, the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions. The theoretical results are confirmed from the simulation data. In addition, the estimations of the uniform approximation rates are extended to the multi-input-single-output (MISO) case.     

三线圈内外层电感磨粒传感器研究

磨损颗粒是造成机械故障的重要因素,对磨粒的检测一般采用螺线管传感器。以螺线管传感器为基础,研究线圈多层缠绕的情况,并提出一种三线圈内外层结构传感器。依据电路理论,推导传感器工作等效电路和多层线圈磁感应强度、电感公式。基于Maxwell软件,比较内外层式和平行式磨粒传感器的磁场,分析线圈缠绕层数对传感器输出特性的影响。仿真结果验证了公式的正确性,为多层线圈磨粒传感器的设计、优化提供了基础。     

Boundary evaluation using inner and outer sets: the ISOS method

A boundary-evaluation algorithm for constructive solid geometry is presented for representations in which the primitives can be bounded by complex surfaces (such as splines) as well as by simpler polynomial surfaces. A fundamental part of the algorithm is the spatial decomposition of each primitive in a way that yields three planar bounded volumes, one containing the primitive (outer set), one contained within the primitive (inner set), and the third being the set difference of the first two, containing the boundary of the primitive. A positive feature of this approach is that the geometric coverage can be extended to any family of solid primitives for which an initial inner-solid-outer-solid segmentation and a subdivision procedure can be devices. Satisfying these two requirements ensures that the resulting primitive definitions are in the canonical form necessary for evaluation. Therefore the cost in terms of software development of adding primitive types does not depend on the number or type of existing primitives     

The inner and outer approaches to the design of recursive neural architectures

Feedforward neural network architectures work well for numerical data of fixed size, such as images. For variable size, structured data, such as sequences, d dimensional grids, trees, and other graphs, recursive architectures must be used. We distinguish two general approaches for the design of recursive architectures in deep learning, the inner and the outer approach. The inner approach uses neural networks recursively inside the data graphs, essentially to “crawl” the edges of the graphs in order to compute the final output. It requires acyclic orientations of the underlying graphs. The outer approach uses neural networks recursively outside the data graphs and regardless of their orientation. These neural networks operate orthogonally to the data graph and progressively “fold” or aggregate the input structure to produce the final output. The distinction is illustrated using several examples from the fields of natural language processing, chemoinformatics, and bioinformatics, and applied to the problem of learning from variable-size sets.     

An outer approximation algorithm for equilibrium problems in Hilbert spaces

We introduce an algorithm for solving non-smooth equilibrium problems in real Hilbert spaces. At each iteration, a regularized proximal-like equilibrium problem on a suitable outer approximation of the original constraint set is considered. We prove, under standard assumptions, that the sequence generated by the algorithm converges weakly to a solution of the problem. Some numerical experience with the algorithm is reported.     

Structural optimization with several discrete design variables per part by outer approximation

The article proposes an optimal design approach to minimize the mass of load carrying structures with discrete design variables. The design variables are chosen from catalogues, and several variables are assigned to each part of the structure. This allows for more design freedom than only choosing parts from a catalogue. The problems are modelled as mixed 0–1 nonlinear problems with nonconvex continuous relaxations. An algorithm based on outer approximation is proposed to find optimized designs. The capabilities of the approach are demonstrated by optimal design of a space frame (jacket) structure for offshore wind turbines, with requirements on natural frequencies, strength, and fatigue lifetime.     

回转体逆时序右特征识别及内外轮廓自动重构

特征自动化识别与解读是回转体零件加工代码自适应生成的重要基础,而回转体内外轮廓的几何特征信息是加工轨迹生成的重要依据。针对多种信息混合的CAD载体中回转体零件几何特征解读问题,提出了顺时序最右侧判别法自动识别回转体零件的内外轮廓特征。利用DXF结构化存储的图形信息和回转体零件对称性的特点去除尺寸标注,剖面线、粗糙度标注,形位公差标注等多余线,最后沿着逆时针寻找相对于当前轮廓最右侧的路径为下一轮廓。与传统方法相比,所提出算法的复杂度进一步降低,能够准确可靠地在干扰信息中识别出零件的内外轮廓精确信息。     

Combined inner and outer loop feedback in an intelligent tutoring system for statistics in higher education

Intelligent tutoring systems (ITSs) can provide inner loop feedback about steps within tasks, and outer loop feedback about performance on multiple tasks. While research typically addresses these feedback types separately, many ITSs offer them simultaneously. This study evaluates the effects of providing combined inner and outer loop feedback on social sciences students' learning process and performance in a first-year university statistics course. In a 2 x 2 factorial design (elaborate inner loop vs. minimal inner loop and outer loop vs. no outer loop feedback) with 521 participants, the effects of both feedback types and their combination were assessed through multiple linear regression models. Results showed mixed effects, depending on students' prior knowledge and experience, and no overall effects on course performance. Students tended to use outer loop feedback less when also receiving elaborate inner loop feedback. We therefore recommend introducing feedback types one by one and offering them for substantial periods of time.     

Power spectrum reduction by optimal Hankel norm approximation of the phase of the outer spectral factor

A new approach to stochastic processes power spectrum reduction, based on Akaike's canonical correlation between the process past and future, is developed. As a first result, the correlation between the canonical past and the canonical future is given its precise functional-analytic interpretation as the Hankel operator generated lay the all-pass function characterizing the phase of the process outer spectral factor. The canonical correlation coefficients turn out to he nothing else but the singular values of this Hankel operator. Next, the all-pass function characterizing the phase of the outer spectral factor is reduced using the optimal Hankel-norm procedure of Adamjan, Arov, and Krein. The reduction of the all-pass phase function is implemented with the safeguards necessary for the magnitude information to be carried all the way through. This involves Bode's relations between the gain and the phase of an outer function, Nehari's extension, and the winding number of the all-pass phase function which is itself shown to be related to the definition of the past and the future. Finally, the net result is a reduced-order, outer spectral factor that matches the high-order spectral factor, fairly well.     

The inner and the outer model in explanatory design theory: the case of designing electronic feedback systems

Both Information Technology (IT) artifacts and design theories are important elements for knowledge capture in design science research in information systems. Building on a rich tradition of constructing and evaluating artifacts, recent design science research has made significant advances toward better understanding the explanatory aspect of design theory. Researchers have stressed the importance of mid-range theories that relate IT artifact features (causes) with measures and goals (effects). Against this background, design theorizing reveals certain commonalities with theorizing in the behavioral science field. In this paper, we explore differences and similarities between theorizing in these areas. We develop a framework that allows for a better understanding of the relationships between manifest design decisions, kernel theory constructs and their evaluation metrics. We identify common issues that arise from conceptual distances between these ideas and show their potential impact on both the design and evaluation of artifacts. The field of electronic feedback systems is used as an illustrative example.     

Simultaneous estimation of odor classes and concentrations using an electronic nose with function approximation model ensembles

This paper sets up a practical electronic nose for simultaneously estimating many kinds of odor classes and concentrations. Mathematically, such simultaneous estimation problems can be regarded as multi-input/multi-output (MIMO) function approximation problems. After decomposing an MIMO approximation task into multiple many-to-one tasks, we can use multiple many-to-one approximation model ensembles to implement them one after another. A single approximation model may be a multivariate logarithmic regression, a quadratic multivariate logarithmic regression, a multilayer perceptron, or a support vector machine. An ensemble is made up of the above four models, represents a special kind of odor, and realizes the relationship between sensor array responses and the represented odor concentrations. Naturally, all members in the ensemble are trained only by the samples from the represented odor. The real outputs of ensembles are the average predicted concentrations and the relative standard deviations (R.S.D.s). The ensemble with the smallest R.S.D. finally gives the label and concentration of an odor sample, which can be looked upon as the use of the average and the minimum combination rules. The predicted results for four kinds of fragrant materials, ethanol, ethyl acetate, ethyl caproate, and ethyl lactate, 21 concentrations in total, show that the proposed approximation model ensembles and combination strategies with the electronic nose are effective for simultaneously estimating many kinds of odor classes and concentrations.