High-breakdown linear discriminant analysis

The classification rules of linear discriminant analysis are defined by the true mean vectors and the common covariance matrix of the populations from which the data come. Because these true parameters are generally unknown, they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population. However, these sample statistics are notoriously susceptible to contamination by outliers, a problem compounded by the fact that the outliers may be invisible to conventional diagnostics. High-breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers, regardless of their severity. In this article we motivate and develop a high-breakdown criterion for linear discriminant analysis and give an algorithm for its implementation. The procedure is intended to supplement rather than replace the usual sample-moment methodology of discriminant analysis either by providing indications that the dataset is not seriously affected by outliers (supporting the usual analysis) or by identifying apparently aberrant points and giving resistant estimators that are not affected by them.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

Improvement of the electrolytic properties of Y2O3-based materials using a crystallographic index

Y2O3 is a c-type rare earth oxide with a fluorite-related structure. This material has been used to refractory because of its high thermal stability and excellent resistance to hydration. In this study, the effective index was suggested in order to improve the electrolytic properties of Y2O3-based oxide. (CexY1-x)(2)O3+delta (x = 0.25 and 0.3) and [LaaSrbCe0.25Y(1-a-b)](2)O3+delta (a = 0.05, 0.1 and 0.15, b = 0, 0.006 and 0.0125) were prepared as the examples with intermediate and high index, respectively. The specimens with high index value such as (La0.15Ce0.25Y0.60)(2)O-3.25 and (La0.1Sr0.0125Ce0.25Y0.6375)(2)O-3.24 consisted of two phases such as c-type and fluorite, although (Ce0.25Y0.75)(2)O-3.25 with intermediate index value had a single phase of c-type rare earth oxide. Microanalysis indicates that a grain in the (La0.1Sr0.0125Ce0.25Y0.6375)(2)O-3.23(7) sintered body consists of c-type and fluorite phases. An interface between c-type and fluorite phases is coherent in a grain. This suggests that this effective index guides the crystal structure in the specimen to fluorite and the examined composition introduces the interface between c-type and fluorite in the microstructure. The electrochemical properties of specimens including Y2O3 were characterized on the basis of the suggested index. The electrical conductivity of Y2O3-based materials increased with an increase of the index. The apparent activation energy of Y2O3-based materials decreased with increasing index. The ionic transport number of oxygen of the specimens was improved by enhancement of the index, confirming validity of the index. The oxide ionic conductive region of (La0.1Sr0.0125Ce0.25Y0.(6375))(2)O-3.23(7) with high effective index extended up to P-O2 = 10(-18) atm at 800 degreesC, although the specimens with low or intermediate index showed p- or n-type semi-conduction in the same P-O2 region at 800 and 1000 degreesC. These results suggest that the interface between c-type and fluorite phases also contributes to improve the electrolytic properties in the grain. It is concluded that the improvement of electrolytic properties in Y2O3-based materials is attributable to the microstructure with interface between two phases in a grain and the fluorite structure guided by the suggested index. (C) 2001 Published by Elsevier Science B.V.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Novel colloidal materials for high-throughput screening applications in drug discovery and genomics

Tracking the reaction history is the means of choice to identify bioactive compounds in large combinatorial libraries. The authors describe two approaches to synthesis on silica beads: a) addition of a reporter dye tag during each synthesis step (see Figure), which attaches itself to the bead by colloidal forces, and b) encapsulating arrays of fluorescent dyes into the beads to encode them uniquely, for recognition with a flow cytometer after each reaction step.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.