Global complete observability and output-to-state stability imply the existence of a globally convergent observer

We consider systems which are globally completely observable and output-to-state stable. The former property guarantees the existence of coordinates such that the dynamics can be expressed in observability form. The latter property guarantees the existence of a state norm observer and therefore the possibility of bounding any continuous state functions. Both properties allow to conceptually build an observer from an approximation of an exponentially attractive invariant manifold in the space of the system state and an output driven dynamic extension. The proposed observer provides convergence to zero of the estimation error within the domain of definition of the solutions. The work of A. Astolfi is partly supported by the Leverhulme Trust.     

Laplace spectra as fingerprints for image recognition

In the area of image retrieval from data bases and for copyright protection of large image collections there is a growing demand for unique but easily computable fingerprints for images. These fingerprints can be used to quickly identify every image within a larger set of possibly similar images. This paper introduces a novel method to automatically obtain such fingerprints from an image. It is based on a reinterpretation of an image as a Riemannian manifold. This representation is feasible for gray value images and color images. We discuss the use of the spectrum of eigenvalues of different variants of the Laplace operator as a fingerprint and show the usability of this approach in several use cases. Contrary to existing works in this area we do not only use the discrete Laplacian, but also with a particular emphasis the underlying continuous operator. This allows better results in comparing the resulting spectra and deeper insights in the problems arising. We show how the well known discrete Laplacian is related to the continuous Laplace-Beltrami operator. Furthermore, we introduce the new concept of solid height functions to overcome some potential limitations of the method.     

基于关系型发散的黎曼流形分类图像识别

针对图像识别中传统的嵌入流形算法通常只考虑切线空间却忽略了流形结构以致不能准确建模的问题,提出一种基于关系型发散的黎曼流形分类(RMC)算法。首先从底层黎曼流形建立训练集,并在流形上建立一组表示黎曼点的参考点;然后,借助于最近提出的斯坦因发散计算黎曼点与各个类之间的相似性,从而有效地将流形分类问题转换成寻找合适的相似空间问题;最后,利用经典的线性判别分析进行特征提取,最近邻分类器完成最终的分类、识别。通过纹理分类、人脸识别、人体识别实验验证了所提算法的有效性及高效性。实验结果表明,相比其他几种较为先进的流形算法,提出的算法不仅提高了识别率,同时大大减少了训练、分类所耗时间,有望应用于实时图像识别系统。     

Patchy solution of a Francis–Byrnes–Isidori partial differential equation

The solution to the nonlinear output regulation problem requires one to solve a first‐order partial differential equation, known as the Francis–Byrnes–Isidori equations. In this paper, we propose a method to compute approximate solutions to the Francis–Byrnes–Isidori equations when the zero dynamics of the plant are hyperbolic and the exosystem is two dimensional. With our method, we are able to produce approximations that converge uniformly to the true solution. Our method relies on the periodic nature of two‐dimensional analytic center manifolds. Copyright © 2012 John Wiley & Sons, Ltd.     

Shareability-Exclusivity Representation on Product Grassmann Manifolds for Multi-camera video clustering

With the rapid popularity of multi-camera networks, one human action is usually captured by multiple cameras located at different angles simultaneously. Multi-camera videos contain the distinct perspectives of one action, therefore multiple views can overcome the impacts of illumination and occlusion. In this paper, we propose a novel multi-camera video clustering model, named Shareability-Exclusivity Representation on Product Grassmann Manifolds (PGM-SER), to address two key issues in traditional multi-view clustering methods (MVC): (1) Most MVC methods directly construct a shared similarity matrix by fusing multi-view data or their corresponding similarity matrices, which ignores the exclusive information in each view; (2) Most MVC methods are designed for multi-view vectorial data, which cannot handle the nonlinear manifold structure hidden in multi-camera videos. The proposed PGM-SER firstly adopts Product Grassmann Manifolds to represent multi-camera videos, then simultaneously learn their shared and exclusive information in global structures to achieve multi-camera video clustering. We provide an effective optimization algorithm to solve PGM-SER and present the corresponding convergence analysis. Finally, PGM-SER is tested on three multi-camera human action video datasets and obtain satisfied experimental results.     

Fast computation of equispaced Pareto manifolds and Pareto fronts for multiobjective optimization problems

In this paper, we consider the problem of generating a well sampled discrete representation of the Pareto manifold or the Pareto front corresponding to the equilibrium points of a multi-objective optimization problem. We show how the introduction of simple additional constraints into a continuation procedure produces equispaced points in either of those two sets. Moreover, we describe in detail a novel algorithm for global continuation that requires two orders of magnitude less function evaluations than evolutionary algorithms commonly used to solve this problem. The performance of the methods is demonstrated on problems from the current literature.     

A family of approximate inertial manifolds for a Van der Pol/FitzHugh–Nagumo perturbation problem

We investigate the stability of a family of approximate inertial manifolds (AIMs) obtained from an ODE containing a perturbation parameter. For two choices of the parameter, the dynamics associated with the equations are already well known: in one case, we have a Van der Pol equation, while in the other setting we obtain a FitzHugh–Nagumo equation. Recently, it has been shown that (a modified version of) each equation admits a sequence of AIMs which converges to the inertial manifold. We show that our model admits a family of AIMs depending on the perturbation parameter. We then investigate the stability of the family of AIMs as the perturbation parameter approaches two different vanishing coefficient limits. These results are intended to shed insight into the continuity properties of inertial manifolds.     

Thermal explosion in a hot gas mixture with organic gel fuel droplets

Recent experimental evidence has uncovered the peculiar behavior of certain gel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion. In this work a preliminary foray is made into the theoretical analysis of the nature of the evolution of a hot gas mixture containing organic gel fuel droplets with oscillatory evaporation within the context of thermal-explosion theory. The problem is modeled as a system of highly nonlinear singularly perturbed ordinary differential equations. Non-dimensionalization of the equations enables identification of the parameters that play a major role in determining the dynamical regimes of the system of equations. The method of integral manifolds is exploited for the analysis and it is found, that for certain parametric regions, the system exhibits new dynamical behavior that is quite different from that found for conventional liquid droplets.     

Numerical comparison of sampling strategies for BRDF data manifolds

The bidirectional reflectance distribution function (BRDF) is one of the fundamental concepts in such diverse fields as multidimensional reflectometry, computer graphics and computer vision. BRDF manifolds form an infinite-dimensional space, but typically the available measurements are very scarce. Therefore, an efficient learning strategy is crucial when performing the measurements.In this paper, we perform simulation studies within a mathematical framework that allows to establish more efficient BRDF sampling and measurement strategies in the sense of statistical design of experiments and generalized proactive learning. Our simulation studies suggest that the default BRDF measurement strategy is suboptimal for a wide class of loss functions.     

ITER blanket manifold system: Integration,assembly and maintenance

The ITER Tokamak Cooling Water System (TCWS) provides coolant for blankets and divertor. The blanket system consists of 440 blanket modules (BMs). The blanket manifold consists of a system of seamless pipes arranged in bundles and routed in poloidal direction from the upper ports of the Vacuum Vessel (VV) to the bottom of the machine. In each of the 18 upper ports there are 20 inlet and 20 outlet pipes, which split at the port exit in two directions, supplying cooling water to either the inboard or the outboard blanket modules. The manifold is routed between the VV and BMs. Branch pipes provide the connection between the manifold and the blanket cooling circuits through a coaxial connector welded to the shield block. A complex, sequential installation sequence has been developed in order to enable the assembly. Once installed the manifold is considered a semi-permanent component, but since failure would prevent ITER operation a maintenance strategy has been planned.