Symmetric product as moduli space of linear representations

We show that the $n-$th symmetric product of an affine scheme $X=\mathrm{Spec} A$ over a characteristic zero field is isomorphic as a scheme to the quotient by the general linear group of the scheme parameterizing $n-$dimensional linear representations of $A$. As a consequence we give generators and relations of the related rings of invariants as well as the equations of any symmetric products in term of traces. In positive characteristic we prove an analogous result for the associated varieties.Comment: 10 pages, from the talk given at ICM 2006 Madri

Machine learning for flux regression in discrete fracture networks

AbstractIn several applications concerning underground flow simulations in fractured media, the fractured rock matrix is modeled by means of the Discrete Fracture Network (DFN) model. The fractures are typically described through stochastic parameters sampled from known distributions. In this framework, it is worth considering the application of suitable complexity reduction techniques, also in view of possible uncertainty quantification analyses or other applications requiring a fast approximation of the flow through the network. Herein, we propose the application of Neural Networks to flux regression problems in a DFN characterized by stochastic trasmissivities as an approach to predict fluxes

Integrating social preferences in spatial analysis : the case of the Mendocinian piedmont natural areas

En esta investigación se estima el cambio en el bienestar social por un cambio de paisaje de los espacios naturales del piedemonte mendocino. Para ello, se utiliza el método de valoración contingente para inferir el valor social de un cambio de paisaje por la acción antrópica sobre tres cuencas hidrográficas ubicadas al oeste del Gran Mendoza. Los resultados del estudio muestran que un cambio de paisaje, simulado mediante una disminución de la cobertura vegetal, disminuye el bienestar de los ciudadanos del Gran Mendoza. En particular, el cambio de paisaje equivale en pérdida de bienestar individual, en promedio, a un gasto anual de 78 pesos en moneda de 2013, a partir de ahora y durante 10 años. Por consiguiente, la continuidad de un proceso de planificación territorial que no impida el deterioro del paisaje de los espacios naturales del piedemonte implica una pérdida de bienestar social. En este sentido, la valoración económica genera un nuevo espacio de participación ciudadana, al integrar las preferencias sociales al diseño de la gestión, y construir sobre esa base, en diálogo con el juicio experto, una gestión territorial eficiente y sustentable desde un punto de vista social.In this study is estimated the change in social welfare for a landscape change of the Mendocinian piedmont natural areas. It is used the contingent valuation method to elicit the social value for a landscape change of anthropogenic-pressures on three basins placed at the west of Gran Mendoza. The results show that a landscape change, simulated through plant cover reduction, reduces the social welfare of Gran Mendoza's citizens. In particular, this landscape change represents for each citizen a welfare lost equivalent, on average, to an annual expense of pesos 78 (in 2013 currency) in the coming 10 years. Consequently, a territorial programme omitting the landscape decline of the natural areas of the Mendocinian piedmont worsens social welfare. So, the economic valuation creates room for citizens' participation by integrating social preferences into programmes design, and allows with a team of experts to build an efficient and sustainable territorial planning, from a social perspective.Fil: Farreras, Verónica. CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas) - Universidad Nacional de CuyoFil: Salvador, Pablo F.. Universidad Nacional de Cuyo. Facultad de Ciencias EconómicasFil: Vaccarino, Emilce. Universidad Nacional de Cuyo. Facultad de Ciencias Económica

Scaling of Pseudo-Critical Couplings in Two-Flavour QCD

We study the scaling behaviour of the pseudo-critical couplings for the chiral phase transition in two-flavour QCD. We show that all existing results from lattice simulations on lattices with temporal extent $N_\tau = 4$, 6 and 8 can be mapped onto a universal scaling curve. The relevant combination of critical exponents, $\beta\delta$, is consistent with the scaling behaviour expected for a second order phase transition with $O(4)$ exponents. At present, scaling according to the $O(2)$ symmetry group can, however, not be ruled out.Comment: 8 pages, NSF-ITP 93-12

Meson Decay Constants from the Valence Approximation to Lattice QCD

We evaluate $f_{\pi}/ m_{\rho}$, $f_K/ m_{\rho}$, $1/f_{\rho}$, and $m_{\phi}/(f_{\phi} m_{\rho})$, extrapolated to physical quark mass, zero lattice spacing and infinite volume, for lattice QCD with Wilson quarks in the valence (quenched) approximation. The predicted ratios differ from experiment by amounts ranging from 12\% to 17\% equivalent to between 0.9 and 2.8 times the corresponding statistical uncertainties.Comment: uufiles encoded copy of 40 page Latex article, including 14 figures in Postscript. The long version of hep-lat/9302012, IBM/HET 93-