Incremental Linear Discriminant Analysis Using Sufficient Spanning Sets and Its Applications

This paper presents an incremental learning solution for Linear Discriminant Analysis (LDA) and its applications to object recognition problems. We apply the sufficient spanning set approximation in three steps i.e. update for the total scatter matrix, between-class scatter matrix and the projected data matrix, which leads an online solution which closely agrees with the batch solution in accuracy while significantly reducing the computational complexity. The algorithm yields an efficient solution to incremental LDA even when the number of classes as well as the set size is large. The incremental LDA method has been also shown useful for semi-supervised online learning. Label propagation is done by integrating the incremental LDA into an EM framework. The method has been demonstrated in the task of merging large datasets which were collected during MPEG standardization for face image retrieval, face authentication using the BANCA dataset, and object categorisation using the Caltech101 dataset. © 2010 Springer Science+Business Media, LLC.

Using Level Sets as the basis for a scalable, parallel geometry engine and mesh generation system

The background to this review paper is research we have performed over recent years aimed at developing a simulation system capable of handling large scale, real world applications implemented in an end-to-end parallel, scalable manner. The particular focus of this paper is the use of a Level Set solid modeling geometry kernel within this parallel framework to enable automated design optimization without topological restrictions and on geometries of arbitrary complexity. Also described is another interesting application of Level Sets: their use in guiding the export of a body-conformal mesh from our basic cut-Cartesian background octree - mesh - this permits third party flow solvers to be deployed. As a practical demonstrations meshes of guaranteed quality are generated and flow-solved for a B747 in full landing configuration and an automated optimization is performed on a cooled turbine tip geometry. Copyright © 2009 by W.N.Dawes.

High order schemes on three-dimensional general polyhedral meshes - Application to the level set method

In this article, we detail the methodology developed to construct arbitrarily high order schemes - linear and WENO - on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set. © 2012 Global-Science Press.

Raman scattering of non-planar graphite: arched edges, polyhedral crystals, whiskers and cones

Planar graphite has been extensively studied by Raman scattering for years. A comparative Raman study of several different and less common non-planar graphitic materials is given here. New kinds of graphite whiskers and tubular graphite cones (synthetic and natural) have been introduced. Raman spectroscopy has been applied to the characterization of natural graphite crystal edge planes, an individual graphite whisker graphite polyhedral crystals and tubular graphite cones. Almost all of the observed Raman modes were assigned according to the selection rules and the double-resonance Raman mechanism. The polarization properties related to the structural features, the line shape of the first-order dispersive mode and its combination modes, the frequency variation of some modes in different carbon materials and other unique Raman spectral features are discussed here in detail.

Large-scale, rapid synthesis and application in surface-enhanced Raman spectroscopy of sub-micrometer polyhedral gold nanocrystals

Macromolecule-protected sub-micrometer polyhedral gold nanocrystals have been facilely prepared by heating an aqueous solution containing poly (N-vinyl-2-pyrrolidone) (PVP) and HAuCl4 without adding other reducing agents. Scanning electron microscopy (SEM), energy-dispersive x-ray spectroscopy (EDX), ultraviolet-visible-near-infrared spectroscopy (UV-vis-NIR), and x-ray diffraction (XRD) were employed to characterize the obtained polyhedral gold nanocrystals. It is found that the 10:1 molar ratio of PVP to gold is a key factor for obtaining quasi-monodisperse polyhedral gold nanocrystals. Furthermore, the application of polyhedral gold nanocrystals in surface-enhanced Raman scattering (SERS) was investigated by using 4-aminothiophenol (4-ATP) as a probe molecule. The results indicated that the sub-micrometer polyhedral gold nanocrystals modified on the ITO substrate exhibited higher SERS activity compared to the traditional gold nanoparticle modified film. The enhancement factor (EF) on polyhedral gold nanocrystals was about six times larger than that obtained on aggregated gold nanoparticles (similar to 25 nm).

Polyhedral oligomeric silsesquioxane nanocomposite thin films via layer-by-layer electrostatic self-assembly

Fabrication of ultrathin polymer composite films with low dielectric constants has been demonstrated. Octa( aminophenyl) silsesquioxane (OAPS) was synthesized and assembled with poly( acrylic acid) (PAA) and poly( styrene sulfonate) (PSS) via a layer-by-layer electrostatic self-assembly technique to yield nanoporous ultrathin films. The OAPS was soluble in water at pH 3 or lower, and suitable pH conditions for the OAPS/PAA and OAPS/PSS assemblies were determined. The multilayer formation process was studied by contact angle analysis, X-ray photoelectron spectroscopy, atomic force microscopy, quartz crystal microgravimetry, UV-vis spectroscopy, and ellipsometry. The multilayer growth was found to be steady and uniform, and the analysis of the film surface revealed a rough topography due to OAPS aggregates. The incorporation of porous OAPS molecules into the thin films significantly lowered their dielectric constants. The OAPS/PAA multilayer thin film thus prepared exhibited a dielectric constant of 2.06 compared to 2.58 for pure PAA film. The OAPS/PAA multilayer film was heated to effect cross-linking between the OAPS and the PAA layers, and the transformation was verified by reflection-absorption Fourier transform infrared spectroscopy.