Principle of Learning Metrics for Exploratory Data Analysis

Visualization and clustering of multivariate data are usually based on mutual distances of samples, measured by heuristic means such as the Euclidean distance of vectors of extracted features. Our recently developed methods remove this arbitrariness by learning to measure important differences. The effect is equivalent to changing the metric of the data space. It is assumed that variation of the data is important only to the extent it causes variation in auxiliary data which is available paired to the primary data. The learning of the metric is supervised by the auxiliary data, whereas the data analysis in the new metric is unsupervised. We review two approaches: a clustering algorithm and another that is based on an explicitly generated metric. Applications have so far been in exploratory analysis of texts, gene function, and bankruptcy. Relationships of the two approaches are derived, which leads to new promising approaches to the clustering problem.     

Interference and interactions in mesoscopic rings

We consider a mesoscopic ring connected to external reservoirs by tunnel junctions. The ring is capacitively coupled to an external gate electrode and may be pierced by a magnetic field. Due to strong electron–electron interactions within the ring the conductance shows Coulomb blockade oscillations as a function of the gate voltage, while Aharonov–Bohm interference effects lead to a dependence on the magnetic flux. The Hamiltonian of the ring is given by a Luttinger model that allows for an exact treatment of both interaction and interference effects. We conclude that the positions of conductance maxima as a function the external parameters can be used to determine the interaction parameter , and the shapes of conductance peaks are strongly affected by electron correlations within the ring.     

Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

We construct the asymptotics (as ε→0) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance ε>0. To cite this article: G. Cardone et al., C. R. Mecanique 335 (2007).     

A note about Volterra operators on weighted Banach spaces of entire functions

We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with sup‐norms in terms of the symbol g; thus we complement recent work by Bassallote, Contreras, Hernández‐Mancera, Martín and Paul 3 for spaces of holomorphic functions on the disc and by Constantin and Peláez 16 for reflexive weighted Fock spaces.     

The Use of Carousel Interferometer in Fourier-Transform Ultraviolet Spectroscopy

The carousel interferometer is a new type of an interferometer, which has been invented at the University of Turku. It consists of a beamsplitter and five plane mirrors. Four of the mirrors are mounted on a carousel, which rotates back and forth. We have modified the interferometer for use in the Fourier-transform ultraviolet (FT-UV) spectroscopy. Test measurement with plasma radiation gives favourable results. The most important property, which makes the carousel interferometer suitable for UV measurements, is its good stability in modulation.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27–29, Saitama, Japan.     

A fast direct solver for elliptic problems with a divergence constraint

A fast direct solution method for a discretized vector‐valued elliptic partial differential equation with a divergence constraint is considered. Such problems are typical in many disciplines such as fluid dynamics, elasticity and electromagnetics. The method requires the problem to be posed in a rectangle and boundary conditions to be either periodic boundary conditions or the so‐called slip boundary conditions in one co‐ordinate direction. The arising saddle‐point matrix has a separable form when bilinear finite elements are used in the discretization. Based on a result for so‐called p‐circulant matrices, the saddle‐point matrix can be transformed into a block‐diagonal form by fast Fourier transformations. Thus, the fast direct solver has the same structure as methods for scalar‐valued problems which are based on Fourier analysis and, therefore, it has the same computational cost ??(N log N). Numerical experiments demonstrate the good efficiency and accuracy of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

On Extended Polar Decomposition

In this study, we considered the extended polar decomposition using a more general approach than the one provided by Boulanger and Hayes [Int. J. Non-Linear Mech. 36 (2001) 399–420]. We showed that the procedure of the decomposition could be simplified by considering its rotation tensor. Our method is illustrated by examples.