A Consistent and Stable Approach to Generalized Sampling

We consider the problem of generalized sampling, in which one seeks to obtain reconstructions in arbitrary finite dimensional spaces from a finite number of samples taken with respect to an arbitrary orthonormal basis. Typical approaches to this problem consider solutions obtained via the consistent reconstruction technique or as solutions of an overcomplete linear systems. However, the consistent reconstruction technique is known to be non-convergent and ill-conditioned in important cases, such as the recovery of wavelet coefficients from Fourier samples, and whilst the latter approach presents solutions which are convergent and well-conditioned when the system is sufficiently overcomplete, the solution becomes inconsistent with the original measurements. In this paper, we consider generalized sampling via a non-linear minimization problem and prove that the minimizers present solutions which are convergent, stable and consistent with the original measurements. We also provide analysis in the case of recovering wavelets coefficients from Fourier samples. We show that for compactly supported wavelets of sufficient smoothness, there is a linear relationship between the number of wavelet coefficients which can be accurately recovered and the number of Fourier samples available.     

Deuterium N.M.R. of liquid crystal solutions with proton–proton dipolar decoupling

Abstract

Deuterium N.M.R. of solute molecules in liquid crystal solutions with the removal of proton–proton dipolar coupling has been explored. The deuterium N.M.R. spectrum of a partially deuterated compound dissolved in a liquid crystal solvent is usually complex or unresolved because of proton–deuterium coupling and extensive proton–proton dipolar coupling. When the latter is removed by a special dipolar decoupling sequence, the deuterium N.M.R. spectrum becomes first order, and deuterium–proton dipolar coupling constants can be readily obtained from the spectrum. Results of monodeuterated hexanes and heptanes dissolved in ZLI 2142 are reported.     

Co growth on Si(0 0 1) and Si(1 1 1) surfaces: Interfacial interaction and growth dynamics

In situ X-ray photoelectron spectroscopy (XPS) and ex situ atomic force microscopy (AFM) were used to study the growth of thin cobalt films at room temperature (RT) on both clean and H-terminated Si(0 0 1) and Si(1 1 1) surfaces. The growth proceeds by first forming an initial CoSi₂-like phase at the growth front of the Si substrate. With increasing Co coverage the interfacial layer composition becomes richer in Co and eventually a metallic Co film is formed on top. Hydrogen termination of the Si surface did not suppress the reaction of Co and Si. A pseudo-layer-by-layer growth mode is proposed to describe the growth of Co on H-terminated Si surfaces, while closed-packed small island growth occurs on clean Si surfaces. The difference in growth mode can be attributed to the increase in the surface mobility of Co adatoms in the presence of hydrogen.     

DEFORMATIONS OF HYPERCOMPLEX STRUCTURES ASSOCIATED TO HEISENBERG GROUPS

Let X be a compact quotient of the product of the real Heisenberggroup H_4m+1 of dimension 4m + 1 and the three-dimensional realEuclidean space R³. A left-invariant hypercomplex structureon H_4m+1 x R³ descends onto the compact quotient X. The spaceX is a hyperholomorphic fibration of 4-tori over a 4m-torus.We calculate the parameter space and obstructions to deformationsof this hypercomplex structure on X. Using our calculations,we show that all small deformations generate invariant hypercomplexstructures on X but not all of them arise from deformationsof the lattice. This is in contrast to the deformations on the4m-torus.     

Review on theory and applications of wavefront recording plane framework in generation and processing of digital holograms

The wavefront recording plane (WRP), subsequently generalized to be known as the virtual diffraction plane (VDP), is a recent concept that has been successfully deployed in fast generation and processing of digital holograms. In brief, the WRP and its extension, the VDP, is a hypothetical plane that is located between the hologram and the object scene, and which is at close proximity to the latter. As such, the fringe patterns on the hypothetical plane are carrying the holistic information of the hologram, as well as the local optical properties of the object scene. This important property enables a hologram to be processed with classical image processing techniques that are normally unsuitable for handling holographic information. In this paper we shall review a number of works, that have been developed based on the framework of the WRP and the VDP.     

Eliashberg function in amorphous superconductors

The conventional approach to tunnelling and critical temperature analysis for amorphous superconductors is discussed. Comparison is made on the effect of structural disorder on the electron-phonon coupling in nearly-free-electron and nearly-localized-electron metals. The results are in good agreement with tunnelling data.     

Generation of dangling bonds by high temperature annealing and hopping conduction in amorphous silicon films

By annealing evaporated a-Si films between 450°C and 620°C, it is found that new dangling bonds are generated. These dangling bonds can act as hopping centres. Quantitative analysis of experimental results on electrical resistivity and ESR measurements favours a conduction mechanism of hopping to nearest neighbours between room temperature and ?100°C. Films annealed just before crystallisation temperature have a density of states near Fermi level of about 3 × 10¹⁸ cm^?3 eV^?1.     

Polyelectrolyte complex materials consisting of antibacterial and cell-supporting layers

The characterization of a polyelectrolyte complex material comprised of two biopolymers, a chitosan upper layer and a gellan gum under layer, is reported. It is shown that the upper layer of chitosan with incorporated levofloxacin displays an antibacterial activity, while the under layer of a gellan gum/TiO(2) composite supports the growth of fibroblastic cells.     

Model-based clustering of high-dimensional data: Variable selection versus facet determination

Variable selection is an important problem for cluster analysis of high-dimensional data. It is also a difficult one. The difficulty originates not only from the lack of class information but also the fact that high-dimensional data are often multifaceted and can be meaningfully clustered in multiple ways. In such a case the effort to find one subset of attributes that presumably gives the “best” clustering may be misguided. It makes more sense to identify various facets of a data set (each being based on a subset of attributes), cluster the data along each one, and present the results to the domain experts for appraisal and selection. In this paper, we propose a generalization of the Gaussian mixture models and demonstrate its ability to automatically identify natural facets of data and cluster data along each of those facets simultaneously. We present empirical results to show that facet determination usually leads to better clustering results than variable selection.