Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel

Extraordinary transverse magneto-optical Kerr effect in a superlens

It has been shown that a slab of a negative index material can behave as a superlens enhancing the imaging resolution beyond the wavelength limit. We show here that if such a slab possesses in addition some magneto-optical activity, it could act as an ideal optical filter and exhibit an extraordinary transverse magneto-optical Kerr effect. Moreover, we show that losses, which spoil the imaging resolution of these lenses, are a necessary ingredient to observe this effect.Comment: 5 pages, 6 figure

Pilot study of vegetation in the Alchichica-Perote region by remote sensing

A study of the application of satellite images to the identification of vegetation in a small area corresponding to the arid zone of Veracruz and part of Puebla is presented. This study is accomplished by means of images from the LANDSAT satellite obtained on January 19 and May 23, 1973. The interpretation of the different maps is made on the basis of information from the data bank of the Flora de Veracruz program, and various surveys made by land and air

The Snapshot Hubble U-Band Cluster Survey (SHUCS) II. Star Cluster Population of NGC 2997

We study the star cluster population of NGC 2997, a giant spiral galaxy located at 9.5 Mpc and targeted by the Snapshot Hubble U-band Cluster Survey (SHUCS). Combining our U-band imaging from SHUCS with archival BVI imaging from HST, we select a high confidence sample of clusters in the circumnuclear ring and disk through a combination of automatic detection procedures and visual inspection. The cluster luminosity functions in all four filters can be approximated by power-laws with indices of $-1.7$ to $-2.3$. Some deviations from pure power-law shape are observed, hinting at the presence of a high-mass truncation in the cluster mass function. However, upon inspection of the cluster mass function, we find it is consistent with a pure power-law of index $-2.2\pm0.2$ despite a slight bend at $\sim$$2.5\times10^{4}$ M$_{\odot}$. No statistically significant truncation is observed. From the cluster age distributions, we find a low rate of disruption ($\zeta\sim-0.1$) in both the disk and circumnuclear ring. Finally, we estimate the cluster formation efficiency ($\Gamma$) over the last 100 Myr in each region, finding $7\pm2$% for the disk, $12\pm4$% for the circumnuclear ring, and $10\pm3$% for the entire UBVI footprint. This study highlights the need for wide-field UBVI coverage of galaxies to study cluster populations in detail, though a small sample of clusters can provide significant insight into the characteristics of the population.Comment: 31 pages, 9 figures, accepted to the A