Unfolding kernel embeddings of graphs:enhancing class separation through manifold learning

In this paper, we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels. The idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels, the resulting data tends to be clustered along a curve that wraps around the embedding space, a behavior that suggests that long range distances are not estimated accurately, resulting in an increased curvature of the embedding space. Hence, we propose to use a number of manifold learning techniques to compute a low-dimensional embedding of the graphs in an attempt to unfold the embedding manifold, and increase the class separation. We perform an extensive experimental evaluation on a number of standard graph datasets using the shortest-path (Borgwardt and Kriegel, 2005), graphlet (Shervashidze et al., 2009), random walk (Kashima et al., 2003) and Weisfeiler-Lehman (Shervashidze et al., 2011) kernels. We observe the most significant improvement in the case of the graphlet kernel, which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold. On the other hand, the Weisfeiler-Lehman kernel partially mitigates the locality problem by using the node labels information, and thus does not clearly benefit from the manifold learning. Interestingly, our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels.

Investigation of the effects of low energy high dose ion bombardment in metals and compound semiconductors

The effect of low energy nitrogen molecular ion beam bombardment on metals and compound semiconductors has been studied, with the aim to investigate at the effects of ion and target properties. For this purpose, nitrogen ion implantation in aluminium, iron, copper, gold, GaAs and AIGaAs is studied using XPS and Angle Resolve XPS. A series of experimental studies on N+2 bombardment induced compositional changes, especially the amount of nitrogen retained in the target, were accomplished. Both monoenergetic implantation and non-monoenergetic ion implantation were investigated, using the VG Scientific ESCALAB 200D system and a d. c. plasma cell, respectively. When the samples, with the exception of gold, are exposed to air, native oxide layers are formed on the surfaces. In the case of monoenergetic implantation, the surfaces were cleaned using Ar+ beam bombardment prior to implantation. The materials were then bombarded with N2+ beam and eight sets of successful experiments were performed on each sample, using a rastered N2+ ion beam of energy of 2, 3, 4 and 5 keV with current densities of 1 μA/cm2 and 5 μA/cm22 for each energy. The bombarded samples were examined by ARXPS. After each complete implantation, XPS depth profiles were created using Ar+ beam at energy 2 ke V and current density 2 μA/cm2 . As the current density was chosen as one of the parameters, accurate determination of current density was very important. In the case of glow discharge, two sets of successful experiments were performed in each case, by exposing the samples to nitrogen plasma for the two conditions: at low pressure and high voltage and high pressure and low voltage. These samples were then examined by ARXPS. On the theoretical side, the major problem was prediction of the number of ions of an element that can be implanted in a given matrix. Although the programme is essentially on experimental study, but an attempt is being made to understand the current theoretical models, such as SATVAL, SUSPRE and TRIM. The experimental results were compared with theoretical predictions, in order to gain a better understanding of the mechanisms responsible. From the experimental results, considering possible experimental uncertainties, there is no evidence of significant variation in nitrogen saturation concentration with ion energy or ion current density in the range of 2-5 ke V, however, the retention characteristics of implantant seem to strongly depend on the chemical reactivity between ion species and target material. The experimental data suggests the presence of at least one thermal process. The discrepancy between the theoretical and experimental results could be the inability of the codes to account for molecular ion impact and thermal processes.

The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz transform. For spatial images there exist two Riesz transformed signals and one original signal from which orientation, phase and energy may be represented as a vector in 3-D signal space. We show that these image properties may be represented by a Singular Value Decomposition (SVD) of the higher-order derivatives of the original and the Riesz transformed signals. We further show that the expected responses of even and odd symmetric filters from the Riesz transform may be represented by a single signal autocorrelation function, which is beneficial in simplifying Bayesian computations for spatial orientation. Importantly, the Riesz transform allows one to weight linearly across orientation using both symmetric and asymmetric filters to account for some perceptual phase distortions observed in image signals - notably one's perception of edge structure within plaid patterns whose component gratings are either equal or unequal in contrast. Finally, exploiting the benefits that arise from the Riesz definition of local energy as a scalar quantity, we demonstrate the utility of Riesz signal representations in estimating the spatial orientation of second-order image signals. We conclude that the Riesz transform may be employed as a general tool for 2-D visual pattern recognition by its virtue of representing phase, orientation and energy as orthogonal signal quantities.

Can surface energy measurements predict the impact of catalyst hydrophobicity upon fatty acid esterification over sulfonic acid functionalised periodic mesoporous organosilicas?

Sulfonic acid functionalised periodic mesoporous organosilicas (PrSO3 H-PMOs) with tunable hydrophobicity were synthesised via a surfactant-templating route, and characterised by porosimetry, TEM, XRD, XPS, inverse gas chromatography (IGC) and ammonia pulse chemisorption. IGC reveals that incorporation of ethyl or benzyl moieties into a mesoporous SBA-15 silica framework significantly increases the non-specific dispersive surface energy of adsorption for alkane adsorption, while decreasing the free energy of adsorption of methanol, reflecting increased surface hydrophobicity. The non-specific dispersive surface energy of adsorption of PMO-SO3H materials is strongly correlated with their activity towards palmitic acid esterification with methanol, demonstrating the power of IGC as an analytical tool for identifying promising solid acid catalysts for the esterification of free fatty acids. A new parameter [-ΔGCNP-P], defined as the per carbon difference in Gibbs free energy of adsorption between alkane and polar probe molecules, provides a simple predictor of surface hydrophobicity and corresponding catalyst activity in fatty acid esterification. © 2014 Elsevier B.V.