Iterant recombination with one-norm minimization for multilevel Markov chain algorithms via the ellipsoid method

Recently, it was shown how the convergence of a class of multigrid methods for computing the stationary distribution of sparse, irreducible Markov chains can be accelerated by the addition of an outer iteration based on iterant recombination. The acceleration was performed by selecting a linear combination of previous fine-level iterates with probability constraints to minimize the two-norm of the residual using a quadratic programming method. In this paper we investigate the alternative of minimizing the one-norm of the residual. This gives rise to a nonlinear convex program which must be solved at each acceleration step. To solve this minimization problem we propose to use a deep-cuts ellipsoid method for nonlinear convex programs. The main purpose of this paper is to investigate whether an iterant recombination approach can be obtained in this way that is competitive in terms of execution time and robustness. We derive formulas for subgradients of the one-norm objective function and the constraint functions, and show how an initial ellipsoid can be constructed that is guaranteed to contain the exact solution and give conditions for its existence. We also investigate using the ellipsoid method to minimize the two-norm. Numerical tests show that the one-norm and two-norm acceleration procedures yield a similar reduction in the number of multigrid cycles. The tests also indicate that one-norm ellipsoid acceleration is competitive with two-norm quadratic programming acceleration in terms of running time with improved robustness.     

Digital Elevation Model generation for historical landscape analysis based on LiDAR data,a case study in Flanders (Belgium)

This paper discusses the generation of a high precision DEM (Digital Elevation Model) based on high density airborne LiDAR (Light Detection and Ranging) data for an interdisciplinary landscape archaeological study concerning the settlement history and environment in Sandy Flanders, a region to the north of Ghent (Belgium). The objective was to create a detailed topographical surface free of artificial features and topographical artefacts, in the form of a DEM, visualizing the natural and current topography through the implementation of true ground points only. The semi-automatical removal of these features and artefacts was based on topographical vector data, visual interpretations and slope analysis. Ultimately two DEM’s were constructed (1) a TIN (Triangulated Irregular Network) model, whereby the inherent large file format restricts the usability to large scale and (2) a grid model which can be used for small-, medium- and large-scale applications. Both datasets were used as an image that is interpreted using ancillary data from historical sources. Its usefulness is illustrated in a case of field pattern and microfield topography. Starting from this DEM, the approach of this landscape historical study is mainly retrogressive, i.e. starting from the landscape structures and elements that are still present in the contemporary landscape and moving into the past.     

Loss and gain functions for CBR retrieval

The method described in this article evaluates case similarity in the retrieval stage of case-based reasoning (CBR). It thus plays a key role in deciding which case to select, and therefore, in deciding which solution will be eventually applied. In CBR, there are many retrieval techniques. One feature shared by most is that case retrieval is based on attribute similarity and importance. However, there are other crucial factors that should be considered, such as the possible consequences of a given solution, in other words its potential loss and gain. As their name clearly implies, these concepts are defined as functions measuring loss and gain when a given retrieval case solution is applied. Moreover, these functions help the user to choose the best solution so that when a mistake is made the resulting loss is minimal. In this way, the highest benefit is always obtained.     

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.