Constructing an efficient parametrization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parametrization using the local tangent plane. Principal component analysis (PCA) is often the tool of choice, as it returns an optimal basis in the case of noise-free samples from a linear su...

Local and non local perturbation bounds for real continuous time coupled algebraic matrix Riccati equations are deriv ed using the technique of Ly apunov majorants and xed point principles Equations of this type arise in the robust analysis and design of linear control systems

where C is a convex closed cone in the Euclidean space IR, f : IR → IR and G : IR → Y is a mapping from IR into the space Y := S of m × m symmetric matrices. We refer to the above problem as a nonlinear semidefinite programming problem. In particular, if C = IR, the objective function is linear, i.e. f(x) := ∑n i=1 bixi, and the constraint mapping is affine, i.e. G(x) := A0 + ∑n i=1 xiAi where ...

Eigenproblem has wide range of applications in engineering disciplines, including compression and recognition. When building practical systems for these applications , we are interested in actual system performance. The actual system performance usually differs from the ideal system performance. One way to quantify the actual performance is to measure the ideal performance and the performance d...

Perturbation analysis is a powerful tool to study population and community dynamics. This article describes expressions for sensitivity metrics reflecting changes in equilibrium occupancy resulting from small changes in the vital rates of patch occupancy dynamics (i.e., probabilities of local patch colonization and extinction). We illustrate our approach with a case study of occupancy dynamics ...

Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models), feedback through the environment or the e...

Shallow water acoustics and the performance of sonar systems in littoral environments are critical areas of interest to the US Navy. In response to this, the Office of Naval Research sponsored a series of acoustics experiments in the East and South China Seas, hereafter referred to as ASIAEX. Components of these experiments included studies of shallow water reverberation, geoacoustic properties...

Patterns are a tool that enables the collective knowledge of a particular community to be recorded and transmitted in an efficient manner. Initially developed in the field of architecture and later developed by software engineers [Gamma et al. (1995)], they have now been adopted by the complex systems modelling community [Wiles and Watson (2005)]. It can be argued that, while most complex syste...

This note contributes to the technical nature of dynamic surface control (DSC) based on a class of strict-feedback nonlinear systems. The DSC technique prevents the complexity problem in integrator backstepping control (IBC). Yet, the stability results obtained by existing DSCs are conservative, and consequently, cannot fully reveal the technical nature of DSC. By the exploitation of the singul...