An algebraic characterization of the optimum of regularized kernel methods

The representer theorem for kernel methods states that the solution of the associated variational problem can be expressed as the linear combination of a finite number of kernel functions. However, for non-smooth loss functions, the analytic characterization of the coefficients poses nontrivial problems. Standard approaches resort to constrained optimization reformulations which, in general, lack a closed-form solution. Herein, by a proper change of variable, it is shown that, for any convex loss function, the coefficients satisfy a system of algebraic equations in a fixed-point form, which may be directly obtained from the primal formulation. The algebraic characterization is specialized to regression and classification methods and the fixed-point equations are explicitly characterized for many loss functions of practical interest. The consequences of the main result are then investigated along two directions. First, the existence of an unconstrained smooth reformulation of the original non-smooth problem is proven. Second, in the context of SURE (Stein’s Unbiased Risk Estimation), a general formula for the degrees of freedom of kernel regression methods is derived.     

A stable multimodel scheme control for the regulation of the transient behavior of a tunnel-diode trigger circuit

A multimodel scheme is designed for a triggering tunnel-diode circuit. The scheme improves the transient behavior during the transition time period after switching from a stable system equilibrium point to another one which is known as a triggering process. Each model is obtained by a linearization of the circuit near an equilibrium point. Moreover, each of these models can be described as a combination of two other transfer functions describing the linearized plant behavior near two different equilibrium points. The scheme chooses online the model with the best tracking performance in order to generate the control law. Different reference transfer functions are proposed with the aim of generating the desired transient in the triggering process. Some simulations show the usefulness of this scheme.     

Rhodium coated mirrors deposited by magnetron sputtering for fusion applications

Metallic mirrors will be essential components of all optical spectroscopy and imaging systems for ITER plasma diagnostics. Any change in the mirror performance, in particular, its reflectivity, due to erosion of the surface by charge exchange neutrals or deposition of impurities will influence the quality and reliability of the detected signals. Due to its high reflectivity in the visible wavelength range and its low sputtering yield, rhodium appears as an attractive material for first mirrors in ITER. However, the very high price of the raw material calls for using it in the form of a film deposited onto metallic substrates. The development of a reliable technique for the preparation of high reflectivity rhodium films is therefore of the highest importance. Rhodium layers with thicknesses of up to 2 microm were produced on different substrates of interest (Mo, stainless steel, Cu) by magnetron sputtering. Produced films exhibit a low roughness and crystallite size of about 10 nm with a dense columnar structure. No impurities were detected on the surface after deposition. Scratch tests demonstrate that adhesion properties increase with substrate hardness. Detailed optical characterizations of Rh-coated mirrors as well as results of erosion tests performed both under laboratory conditions and in the TEXTOR tokamak are presented in this paper.     

Identification of stable models in subspace identification by usingregularization

In subspace identification methods, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. For a finite number of data points, the estimated system matrix is not guaranteed to be stable, even when the true linear system is known to be stable. In this paper, stability is imposed by using regularization. The regularization term used here is the trace of a matrix which involves the dynamical system matrix and a positive (semi) definite weighting matrix. The amount of regularization can be determined from a generalized eigenvalue problem. The data augmentation method of Chui and Maciejowski (1996) is obtained by using specific choices for the weighting matrix in the regularization term     

On the output regulation for linear systems in the presence ofinput saturation

Some results on the problem of achieving output regulation in the presence of sinusoidal/constant exogenous signals for linear systems subject to input saturation are presented. In particular, the issue of enlarging the set of initial conditions for which the problem has solutions is addressed     

EuLisp in education

We present our experience withEuLisp as a teaching language, focussing on the level of the language which was specifically designed for this purpose (level-0).EuLisp has been used in undergraduate and postgraduate teaching since 1990, in lectures and laboratories, where in many cases it has replaced Scheme or Common Lisp. It has been used extensively in programming courses, parallelism courses, as a vehicle for advanced courses in symbolic computing and programming language design; it has also been used as a platform for final year undergraduate projects. This experience has demonstrated thatEuLisp is well suited to teaching and far reaching in its capabilities: it supports the relevant concepts in a consistent and versatile framework, so that the language serves to facilitate the educational process. The discussion is illustrated with examples, and where appropriate we draw a comparison with the Lisp dialects used previously in these courses.     

Digital Image Analysis to Standardize a Photometric Method in Colorimetric Quantification

Abstract

Techniques applying digital images increasingly have been used in biology, medicine, physics, and other research areas. The image coordinates can represent light intensities values to be detected by a CCD. Based on this concept, a photometric system composed of a LED source and a digital camera as a detector was used for optical density measurements. Standards for permanganate, glucose, and protein solutions were determined by colorimetric methods using our device. Samples of protein of Pasteurella mutocida bacteria membrane and, also, fractions of rabbit kidney membrane, rich in Na, K‐ATPase, with unknown concentrations were dosed through the Hartree method using our photometric system.     

A universal topological transformation group inL 2 (G × G)

LetG denote an infinite,-compact, locally compact topological group. In this paper a construction is given for a topological transformation groupH _G with the Hilbert spaceL ² (G × G) as a phase space such that any topological transformation group (G, X, ) can be embedded inH _G , providedX is a separable metrizable space and is a bounded action. The class of such topological transformation groups contains all actions ofG on separable, metrizable, locally compact spaces.