Explicit formulas for ellipsoids approximating attainable sets: II

Ellipsoidal estimates of attainable sets for linear control systems that are globally optimal in the sense of the ellipsoid volume are studied. The following two basic results are reported: a rapidly converging iteration method for explicit determination of optimal ellipsoids is described, and asymptotics of parameters of optimal ellipsoids for an autonomous control system for large time of motion is determined.     

Explicit formulas for stability radii of nonnegative and Metzlerianmatrices

We address stability issues pertaining to uncertain nonnegative and Metzlerian matrices. The problem under consideration is the computation of the stability radius when matrix perturbations are both unstructured and structured. We show that the stability radius can be obtained in the former case by computing the largest singular value of a constant matrix and in the latter case by computing the spectral radius of a constant matrix     

Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization

For a class of nonlinear systems having triangular structure, we provide explicit formulas for feedback controllers, that exhibit global stabilization. The global part of our analysis is mainly based on a version of Sontag's input-to-state-stability property, and constitutes a generalization of previous works of the second author.     

Explicit formulas for the Nörlund polynomials Bn(χ) and bn(χ)

In this paper, the authors establish some explicit formulas and representations for the Nörlund polynomial B_n^(χ) and b_n^(χ) Several identities involving Bernoulli numbers, Nörlund numbers, Stirling numbers and the associated Stirling numbers are also presented.     

Non-asymptotic confidence ellipsoids for the least-squares estimate

In this paper, we consider the finite sample properties of least-squares system identification, and derive non-asymptotic confidence ellipsoids for the estimate. The shape of the confidence ellipsoids is similar to the shape of the ellipsoids derived using asymptotic theory, but unlike asymptotic theory, they are valid for a finite number of data points. The probability that the estimate belongs to a certain ellipsoid has a natural dependence on the volume of the ellipsoid, the data generating mechanism, the model order and the number of data points available.     

Invariance attainability conditions for power plant control systems

Consideration was given to the characteristics of the power plants for which the control systems invariant in input and deviation to external actions can be designed. The solvability conditions for design of systems invariant in the G.V. Shchipanov and V.S. Kulebakin sense were compared.     

Controllability and attainability criteria for linear differential-algebraic systems

For linear stationary regular differential-algebraic systems, the problems of complete controllability and attainability, controllability in the space ? ⁿ and null-controllability, spectrum control are stated. For the designated problems, the spectrum and rank solvability criteria are formulated and proved, and constructive methods of solving are also presented. The approach effectiveness and problematic issues are illustrated by featured examples of controlled plants.     

Some algorithms for approximating convolutions

This paper presents some algorithms for approximating two-dimensional convolution operators of size n × n, n odd, by a product, or sum of products, of 3 × 3 convolutions. Inaccuracies resulting from the approximation as well as from fixed point computation are discussed and examples are given.     

A parallel algorithm for approximating the minimum cycle cover

We address the problem of approximating aminimum cycle cover in parallel. We give the first efficient parallel algorithm for finding an approximation to aminimum cycle cover. Our algorithm finds a cycle cover whose size is within a factor of 0(1 +n logn/(m + n) of the minimum-sized cover usingO(log² n) time on (m + n)/logn processors.Research supported by ONR Grant N00014-88-K-0243 and DARPA Grant N00039-88-C0113 at Harvard University.Research supported by a graduate fellowship from GE. Additional support provided by Air Force Contract AFOSR-86-0078, and by an NSF PYI awarded to David Shmoys, with matching funds from IBM, Sun Microsystems, and UPS.     

两种近似EMD的图像检索方法

相似度量是图像检索的关键,EMD是一种有效的度量距离,但其计算比较复杂,而且赖于基本距离的选择。采用Lloyd聚类算法对图像进行高斯混合建模,并以聚类失真作为基本距离提出了两种近似EMD的方法计算相似度。实验结果验证了该方法的有效性,其检索效率与EMD方接近,而且计算复杂度比EMD方法低,基本距离的选择不敏感。     

Advantages of cubics for approximating element boundaries

A finite element is constructed with two straight sides and one cubic side. A cubic isoparametric transformation chosen to satisfy particular curve-matching requirements while ensuring a positive transformation Jacobian over the element is investigated.     

CIM algorithm for approximating three-dimensional polygonal curves

The polygonal approximation problem is a primary problem in computer graphics,pattern recognition,CAD/CAM,etc.In R^2,the cone intersection method(CIM) is one of the most efficient algorithms for approximating polygonal curves,With CIM Eu and Toussaint,by imposing an additional constraint and changing the given error criteria,resolve the three-dimensional weighted minimum number polygonal approximation problem with the parallel-strip error criterion(PS-WMN)under L2 norm.In this paper,without any additional constraint and change of the error criteria,a CIM solution to the same problem with the line segment error criterion(LS-WMN)is presented,which is more frequently encountered than the PS-WMN is .Its time complexity is O(n^3),and the space complexity is O(n^2) .An approximation algorithm is also presented,which takes O(n^2) time and O(n) space.Results of some examples are given to illustrate the efficiency of these algorithms.     

Complete memory structures for approximating nonlineardiscrete-time mappings

This paper introduces a general structure that is capable of approximating input-output maps of nonlinear discrete-time systems. The structure is comprised of two stages, a dynamical stage followed by a memoryless nonlinear stage. A theorem is presented which gives a simple necessary and sufficient condition for a large set of structures of this form to be capable of modeling a wide class of nonlinear discrete time systems. In particular, we introduce the concept of a "complete memory". A structure with a complete memory dynamical stage and a sufficiently powerful memoryless stage is shown to be capable of approximating arbitrarily wide class of continuous, causal, time invariant, approximately-finite-memory mappings between discrete-time signal spaces. Furthermore, we show that any bounded-input bounded output, time-invariant, causal memory structure has such an approximation capability if and only if it is a complete memory. Several examples of linear and nonlinear complete memories are presented. The proposed complete memory structure provides a template for designing a wide variety of artificial neural networks for nonlinear spatiotemporal processing.     

An accurate sampling-based method for approximating geometry

We present a sampling-based method for approximating the boundary of a geometry defined by various geometric operations. Based on a novel adaptive sampling condition, we first construct volumetric grids such that an error-minimizing point can be found in each cell to capture all the geometric objects inside the cell. We then construct a polygonal model from the grid. We guarantee the boundary approximation has the same topology as the exact surfaces, and the maximum approximation error from the exact surfaces is bounded by a user specified tolerance. Our method is robust and easy to implement. We have applied it in various applications such as remeshing of polygonal models, Boolean operations, and offsetting operations. We report experimental results on a variety of CAD models.     

Alphabet indexing for approximating features of symbols

We consider two maximization problems to find a mapping from a large alphabet forming given two sets of strings to a set of a very few symbols specifying a symbol wise transformation of strings. First we show that the problem to find a mapping that transforms the most of the strings as to form disjoint sets cannot be approximated within a ratio n^1/16 in polynomial time, unless P = NP. Next we consider a mapping that retains the difference of the maximum number of pairs of strings over the given sets. We present a polynomial-time approximation algorithm that guarantees a ratio k/(k − 1) for mappings to k symbols, as well as proving that the problem is hard to approximate within an arbitrary small ratio in polynomial time. Furthermore, we extend this algorithm as to deal with not only pairs but also tuples of strings and show that it achieves a constant approximation ratio.     

基于Cauchy-Schwarz逼近的网络坐标导引

针对拓扑结构突变时网络坐标系统存在的剧烈抖动问题, 定义节点导引步和误差修正步, 通过坐标的延迟发布实现突变抑制。在导引步节点保持坐标广播静默, 并基于Cauchy-Schwarz不等式生成迭代序列, 逼近节点坐标的较优初值; 在修正步执行Vivaldi算法, 修正自身坐标并广播更新。仿真实验显示, 该方法能在保证定位精度的前提下, 有效抑制拓扑结构突变对网络坐标系统产生的剧烈影响, 显著提升网络坐标系统泛化能力。     

Bicubic patches for approximating non-rectangular control-point meshes

The application of surface modelling techniques within solid modelling requires the use of arbitrary meshes of control points to define a solid. A method using bicubic patches is presented which is valid for a number of cases. The faces of the mesh must have four edges, and at all vertices either three or four, or at all vertices an odd number of edges are allowed to meet. Sample applications are presented.     

High order algorithms for approximating nth roots

In this article, by means of a modification of the Newton method, we obtain a family of iterative processes which approximates the nth root of a real number with a prefixed order of convergence q, q?≥?2.