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

Metaldehyde removal from drinking water by adsorption onto filtration media: mechanisms and optimisation

Trace micropollutants should be removed during drinking water production without increasing the disinfection-by-product formation potential or energy demand of the treatment process. We demonstrate the efficacy of different filtration media to remove metaldehyde through controlled batch experiments on water augmented with metaldehyde. Equilibrium concentrations of metaldehyde and surrogate organics were successfully described by the Freundlich isotherm. Metaldehyde can be attenuated to varying degrees with activated carbon and sand with an active and inactive biofilm with kf values ranging from 0.006–0.3 (mg g−1)(L mg−1)1/n. The presence of the active biofilm improved metaldehyde adsorption by sand media, due to additional biosorption mechanisms, a greater surface area or biodegradation. Baseline levels of competing natural organic matter surrogates (NOM) reduced overall adsorption efficacy but increasing concentrations of NOM did not impact metaldehyde removal efficacy in a significant way. Biological activated carbon was identified as the most suitable adsorbent of metaldehyde (94% removal) but sand with an acclimated biofilm was capable of acting as a bio-adsorbent of metaldehyde even under environmentally relevant concentrations (41% adsorption from 0.002.5 mg L−1). Moreover, we observed that thermal hydrolysis of metaldehyde occurred at 60 °C, suggesting that thermal regeneration of GAC for this pesticide was possible at relatively low temperatures. Biological adsorption and thermal hydrolysis approaches presented herein offered a way forward to increase efficiency and cost effectiveness of existing treatments for metaldehyde

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

Energy Saving and Carbon Trading - Two Ways to Control CO2 Emissions in the Finnish Forest Industry

The major effort of international environmental politics is to control of greenhouse gas (GHG) emissions. Those industrialized countries that have ratified the Kyoto Protocol (KP) are committed to reducing their GHG emissions during the first commitment period of 2008-2012. To reach reduction targets, one of the mechanisms accepted in the KP was emissions trading. Trading offers cost savings to producers of GHGs who are responsible for decreasing their emissions. Each economic unit has its own marginal cost for reductions of GHG emissions, and this variation in abatement costs between different producers' profits the selling and buying of emission licenses on emission markets. The pulp and paper industry is one of those branches of industry that has to reduce its GHG emissions, mainly carbon dioxide (CO2). In this study two ways of controlling CO2 emissions were investigated: energy saving and carbon trading. The study objects were three Finnish mills of the forest consolidated corporation: (1) a chemical pulp mill with a sawmill, (2) a chemical pulp mill with two paper machines, and (3) an integrate containing mechanical and chemical pulping, paper machines of woodfree and woodcontaining paper grades, cardboard production and a sawmill. According to reports delivered to MOTIVA (Information Center for Energy Efficiency) in Finland, reductions in CO2 emissions resulting from energy saving by means of technical improvements in processes were calculated, and were in total 230,341 tCO2 (of which 78,246 tCO2 was from wood) at the previously mentioned mills. Total CO2 emissions of both bio- and fossil fuels were, on average, 3,913,446 tCO2, of which 357,948 tCO2 originated from fossil fuels. Carbon trading was simulated with carbon trading games played between the abovementioned mills. Three different institutions for trading were tested, namely, bilateral trading with open information, bilateral trading with restricted information and double auction with restricted information. The more information on abatement costs of the other mills a participant had, the more profitable was trading for the mill represented by a participant. Carbon trading was mainly a tool to help the mills to reduce their abatement costs, contrary to the situation if they had just invested in abatement technology themselves without trading