The genus of the configuration spaces for Artin groups of affine type

Let $(W,S)$ be a Coxeter system, $S$ finite, and let $G_{W}$ be the associated Artin group. One has configuration spaces $Y,\ Y_{W},$ where $G_{W}=\pi_1(Y_{W}),$ and a natural $W$-covering $f_{W}:\ Y\to Y_{W}.$ The Schwarz genus $g(f_{W})$ is a natural topological invariant to consider. In this paper we generalize this result by computing the Schwarz genus for a class of Artin groups, which includes the affine-type Artin groups. Let $K=K(W,S)$ be the simplicial scheme of all subsets $J\subset S$ such that the parabolic group $W_J$ is finite. We introduce the class of groups for which $dim(K)$ equals the homological dimension of $K,$ and we show that $g(f_{W})$ is always the maximum possible for such class of groups. For affine Artin groups, such maximum reduces to the rank of the group. In general, it is given by $dim(X_{W})+1,$ where $X_{ W}\subset Y_{ W}$ is a well-known $CW$-complex which has the same homotopy type as $Y_{ W}.$Comment: To appear in Atti Accad. Naz. Lincei Rend. Lincei Mat. App

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

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

Experiment Investigating the Connection between Weak Values and Contextuality

Weak value measurements have recently given rise to a large interest for both the possibility of measurement amplification and the chance of further quantum mechanics foundations investigation. In particular, a question emerged about weak values being proof of the incompatibility between Quantum Mechanics and Non-Contextual Hidden Variables Theories (NCHVT). A test to provide a conclusive answer to this question was given in [M. Pusey, Phys. Rev. Lett. 113, 200401 (2014)], where a theorem was derived showing the NCHVT incompatibility with the observation of anomalous weak values under specific conditions. In this paper we realize this proposal, clearly pointing out the strict connection between weak values and the contextual nature of Quantum Mechanics.Comment: 5 pages, 4 figure

The effect of spatial resolution on optical and near-IR studies of stellar clusters: Implications for the origin of the red excess

Recent ground based near-IR studies of stellar clusters in nearby galaxies have suggested that young clusters remain embedded for 7-10Myr in their progenitor molecular cloud, in conflict with optical based studies which find that clusters are exposed after 1-3Myr. Here, we investigate the role that spatial resolution plays in this apparent conflict. We use a recent catalogue of young ($5000$~\msun) clusters in the nearby spiral galaxy, M83, along with Hubble Space Telescope (HST) imaging in the optical and near-IR, and ground based near-IR imaging, to see how the colours (and hence estimated properties such as age and extinction) are affected by the aperture size employed, in order to simulate studies of differing resolution. We find that the near-IR is heavily affected by the resolution, and when aperture sizes $>40$~pc are used, all young/blue clusters move red-ward in colour space, which results in their appearance as heavily extincted clusters. However, this is due to contamination from nearby sources and nebular emission, and is not an extinction effect. Optical colours are much less affected by resolution. Due to the larger affect of contamination in the near-IR, we find that, in some cases, clusters will appear to show near-IR excess when large ($>20$~pc) apertures are used. Our results explain why few young ($<6$~Myr), low extinction (\av < 1~mag) clusters have been found in recent ground based near-IR studies of cluster populations, while many such clusters have been found in higher resolution HST based studies. Additionally, resolution effects appear to (at least partially) explain the origin of the near-IR excess that has been found in a number of extragalactic YMCs.Comment: 8 pages, 5 figures, accepted for publication in MNRA