An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators

This paper proposes an original method for obtaining analytical approximations of the invariant probability density function of multi-dimensional Hamiltonian dissipative dynamic systems under Gaussian white noise excitations, with linear non-conservative parts and nonlinear conservative parts. The method is based on an exact result and a heuristic argument. Its pertinence is attested by numerical tests.     

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.     

Ergodicity of filtering process by vanishing discount approach

A new approach to study ergodicity of filtering processes is presented. It is based on the vanishing discount approach to discounted functional of filtering process. We show that limit superior of the Cesaro averages of the functionals is the same for all initial conditions from which the uniqueness of invariant measures of filtering processes follows. The approach is based on certain assumption for which we provide a sufficient condition using concavity arguments. In addition we show the existence of solutions to the Poisson equation corresponding to filtering process with concave functional. The assumptions are then extended to the controlled case and using similar concave arguments we obtain the existence of solutions to the Bellman equation corresponding to partially observed average cost per unit time problem.     

Self-calibration based on invariant view recognition: Dynamic approach to navigation

We extend a dynamic approach of behavior generation to the representation of spatial information. Two levels of dynamics integrate dead-reckoning, dominant far from home bases, and piloting, dominant near home bases. When the view-based piloting system recognizes a home base, visual place information recalibrates the dead-reckoning system, inverting the hierarchical ordering of the two dynamic levels by time scale inversion. Reference views taken at discrete home bases are recognized invariantly under rotation of views. This process yields compass information. Continuous translational information is obtained as a neural place representation built from view correlations with a scattered set of local views. This self-calibrating cognitive map couples into a dynamics of heading direction integrating the behaviors of obstacle avoidance and target acquisition. Targets can be designated in terms of the cognitive map. We demonstrate the dynamical model in simulation.     

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.     

A remark on bilinear systems and moduli spaces of instantons

Explicit equations are given for the moduli space of framed instantons as a quasi-affine variety, based on the representation theory of noncommutative power series, or equivalently, the minimal realization theory of bilinear systems.     

FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

Pattern recognition for characterization of pharmaceutical powders

A large part of pharmaceutical manufacturing involves the use of particulate materials. It is well known that both particle size and shape affect the physical characteristics of tablets. An image processing and analysis algorithm based on the invariant image moment technique was developed in this work to determine the particle shape by comparing features (moments) extracted from templates to those extracted from each of the objects in the image. First it determines the particle shape (rectangle, circle, etc.) and then calculates its specific dimensions (diameter, aspect ratio).The statistical validation of the vision system obtained a repeatability of 0.0012 in and 0.5% relative standard deviation and accuracy within 0.1 to 0.9% of the average value considered as true value. Also the pattern recognition technique indicated high precision and accuracy for images containing particles with some level of contact between them. The shape recognition of microcrystalline cellulose (MCC) indicated that particles of equant and acicular shape as defined by USP are predominant. The results suggest that image processing and analysis would be a suitable tool for pharmaceutical process analytical technologies (PAT) and process optimization.     

基于NSST和RI-LPQ的纹理图像检索

针对采用单一方法提取图像特征时检索率不高的问题,结合非下采样剪切波变换(NSST)统计特征和旋转不变的局部相位量化(RI-LPQ)原理,提出一种纹理图像检索方法。非下采样剪切波不仅具有方向选择性及平移不变性,而且可以对图像进行有效的稀疏表示,与传统小波相比,可有效捕捉图像的边缘轮廓等纹理信息,与非下采样轮廓波相比,具有更高的计算效率。利用广义高斯分布函数对图像NSST高频子带系数的统计特征进行分析,RI-LPQ描述算子直接提取图像特征,采用具有权重系数的相似性测度公式对Brodatz图像库进行纹理图像检索。实验结果表明,与传统小波和轮廓波的方法相比,NSST统计特征方法的平均检索率分别提高4.77%和1.44%,纹理图像检索方法的平均检索率分别提高7.36%和1.98%。