Torelli theorem for the parabolic Deligne-Hitchin moduli space

We prove that, given the isomorphism class of the parabolic Deligne-Hitchin moduli space over a smooth projective curve, we can recover the isomorphism class of the curve and the parabolic points.Comment: 20 page

Automorphism group of the moduli space of parabolic bundles over a curve

We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking the dual, and Hecke transforms (using the filtrations given by the parabolic structure). A Torelli theorem for parabolic bundles with arbitrary rank and generic weights is also obtained. These results are extended to the classification of birational equivalences which are defined over "big" open subsets (3-birational maps, i.e. birational maps giving an isomorphism between open subsets with complement of codimension at least 3). Finally, an analysis of the stability chambers for the parabolic weights is performed in order to determine precisely when two moduli spaces of parabolic vector bundles with different parameters (curve, rank, determinant and weights) can be isomorphic.Comment: 99 page

Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces

Let $\mathcal{L}=(L,[\cdot\,,\cdot],\delta)$ be an algebraic Lie algebroid over a smooth projective curve of genus $g\geq 2$ such that $L$ is a line bundle whose degree is less than $2-2g$. Let $r$ and $d$ be coprime numbers. We prove that the motivic class (in the Grothendieck ring of varieties) of the moduli space of $\mathcal{L}$-connections of rank $r$ and degree $d$ over $X$ does not depend on the Lie algebroid structure $[\cdot\,,\cdot]$ and $\delta$ of $\mathcal{L}$ and neither on the line bundle $L$ itself, but only the degree of $L$ (and of course on $r,d,g$ and $X$). In particular it is equal to the motivic class of the moduli space of $K_X(D)$-twisted Higgs bundles of rank $r$ and degree $d$, for $D$ any divisor of positive degree. As a consequence, similar results (actually a little stronger) are obtained for the corresponding $E$-polynomials. Some applications of these results are then deduced.Comment: 55 pages. Typos corrected; added a new subsection (7.4.4) and also new reference

Automorphism group of the moduli space of parabolic vector bundles over a curve

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 26-10-2018The main objective of this thesis is the computation of the automorphism group of the moduli space of parabolic vector bundles over a smooth complex projective curve. We will start by de ning the notion of a parabolic -module { a module over a sheaf of rings of di erential operators with a parabolic structure at certain marked points { and building their moduli space. This will provide us a common theoretical framework that allows us to work with several kinds of moduli spaces of bundles with parabolic structure such parabolic vector bundles, parabolic (L-twisted) Higgs bundles, parabolic connections or parabolic -connections. As an application, we build the parabolic Hodge moduli space and the parabolic Deligne{Hitchin moduli space. Then, we will address the computation of the automorphism group of the moduli space of parabolic bundles. Let X and X0 be irreducible smooth complex projective curves with sets of marked points D X and D0 X0 and genus g 6 and g0 6 respectively. LetM(X; r; ; ) be the moduli space of rank r stable parabolic vector bundles on (X;D) with parabolic weights and determinant . We classify the possible isomorphisms : M(X; r; ; ) ���! M(X0; r0; 0; 0). First, a Torelli type theorem is proved, implying that for to exist it is necessary that (X;D) = (X0;D0) and r = r0. Then we prove that the possible isomorphisms are generated by automorphisms of the pointed curve (X;D), tensorization with suitable line bundles, dualization of parabolic vector bundles and Hecke transformations at the parabolic points. These results are extended to birational equivalences : M(X; r; ; ) 99K M(X0; r0; 0; 0) which are de ned over \big" open subsets. The particular case of \concentrated" weights (corresponding to \small" stability parameters) is studied further. In this case Hecke transformations give rise to birational morphisms that do not extend to automorphisms of the moduli space. Moreover, an analysis of the stability chambers for the weights allows us to determine an explicit computable presentation of the group of automorphisms of the moduli space for arbitrary generic weights. Finally, the automorphism group of the moduli space of framed bundles over a smooth complex projective curve X of genus g > 2 with a framing over a point x 2 X is also described. It is shown that this group is generated by pullbacks using automorphisms of the curve X that x the marked point x, tensorization with certain line bundles over X and the action of PGLr(C) by composition with the framing

Automatic aspect extraction in information retrieval diversity

In this master thesis we describe a new automatic aspect extraction algorithm by incorporating relevance information to the dynamics of the Probabilistic Latent Semantic Analysis. An utility-biased likelihood statistical framework is described to formalize the incorporation of prior relevance information to the dynamics of the algorithm intrinsically. Moreover, a general abstract algorithm is presented to incorporate any arbitrary new feature variables to the analysis. A tempering procedure is inferred for this general algorithm as an entropic regularization of the utility-biased likelihood functional and a geometric interpretation of the algorithm is described, showing the intrinsic changes in the information space of the problem produced when di erent sources of prior utility estimations are provided over the same data. The general algorithm is applied to several information retrieval, recommendation and personalization tasks. Moreover, a set of post-processing aspect lters is presented. Some characteristics of the aspect distributions such as sparsity or low entropy are identi ed to enhance the overall diversity attained by the diversi cation algorithm. Proposed lters assure that the nal aspect space has those properties, thus leading to better diversity levels. An experimental setup over TREC web track 09-12 data shows that the algorithm surpasses classic pLSA as an aspect extraction tool for the search diversi cation. Additional theoretical applications of the general procedure to information retrieval, recommendation and personalization tasks are given, leading to new relevanceaware models incorporating several variables to the latent semantic analysis. Finally the problem of optimizing the aspect space size for diversi cation is addressed. Analytical formulas for the dependency of diversity metrics on the choice of an automatically extracted aspect space are given under a simpli ed generative model for the relation between system aspects and evaluation true aspects. An experimental analysis of this dependence is performed over TREC web track data using pLSA as aspect extraction algorithm

Optimización y control en cascada de temperatura de registro mediante sistemas de refrigeración

Este artículo analiza la eficiencia energética de un ciclo de refrigeración, generando un optimizador de referencias para el control basado en aproximaciones lineales. Se plantean dos enfoques de control: el control de potencia, en el cual se propone un controlador robusto descentralizado para la regulación de la potencia frigorífica dada por el ciclo, y el control de temperatura de recinto, en el cual se considera también la dinámica del recinto a refrigerar y se propone una estructura de control en cascada donde un controlador externo genera las referencias de potencia frigorífica al controlador interno del ciclo de refrigeración. Se analizan en simulación y también experimentalmente el seguimiento de referencias y el rechazo de perturbaciones en ambas estrategias de control.Ministerio de Ciencia e Innovación (España) proyecto DPI2015-70973-RMinisterio de Ciencia e Innovación (España) proyecto DPI2016-79444-

Optimización y control en cascada de temperatura de registro mediante sistemas de refrigeración

[Resumen] Este artículo analiza la eficiencia energética de un ciclo de refrigeración, generando un optimizador de referencias para el control basado en aproximaciones lineales. Se plantean dos enfoques de control: el control de potencia, en el cual se propone un controlador robusto descentralizado para la regulación de la potencia frigorífica dada por el ciclo, y el control de temperatura de recinto, en el cual se considera también la dinámica del recinto a refrigerar y se propone una estructura de control en cascada donde un controlador externo genera las referencias de potencia frigorífica al controlador interno del ciclo de refrigeración. Se analizan en simulación y también experimentalmente el seguimiento de referencias y el rechazo de perturbaciones en ambas estrategias de control.Ministerio de Ciencia e Innovación; DPI2015-70973-RMinisterio de Ciencia e Innovación; DPI2016-79444-

Identificación paramétrica del condensador de una planta experimental de refrigeración

[Resumen] Este artículo describe el procedimiento seguido para la identificación del condensador de un ciclo de refrigeración por compresión de vapor. El condensador se ha identificado de forma aislada, bajo la premisa de la existencia de tres zonas diferenciadas: zona de vapor sobrecalentado, zona bifásica y zona de líquido subenfriado, condición respaldada de forma empírica, y basándose en datos experimentales de equilibrio. Además se han tenido en cuenta las pérdidas de carga debido al diseño del circuito del refrigerante.Los autores quieren expresar su gratitud al MCeI por la financiación de este trabajo, a través de los proyectos DPI2015-70973-R y DPI2013-44135-Rhttps://doi.org/10.17979/spudc.978849749808

Benthic diversity and assemblage structure of a north Patagonian rocky shore: a monitoring legacy of the NaGISA project

The rocky shore of Punta Este, Golfo Nuevo (Patagonia, Argentina), was sampled using the standardized NaGISA (CoML) protocol aimed to generate biodiversity baseline data in 6 levels, from high intertidal to 10m depth. Based on the generated data, we studied the benthic assemblage structure, species richness, mean abundance and the distribution pattern of invertebrate functional groups, typifying species in each intertidal and subtidal level. The rocky shore studied, as other in north Patagonia is understudied, factors driven its assemblage structure are not clear yet. The intertidal sampled is exposed to extreme physical conditions higher than any other studied rocky shore systems, with air temperature variation of 40°C during the year, maximum winds of 90 km/h and semidiurnal tides of 5m amplitude; on the other hand subtidal presents less thermal variation (DeltaT 10°C along the year) and more homogeneous physical conditions. We identified 65 taxa represented by six animal phyla: Mollusca, Arthropoda, Annelida (Polychaeta), Echinodermata, Cnidaria and Nemertea; and three algal phyla: Chlorophyta, Rhodophyta and Heterokontophyta (class: Phaeophyceae). Ordination nMDS plots showed three different assemblages in terms of species composition (intertidal, subtidal 1m level and subtidal 5-10m samples). The intertidal was represented by suspension feeders mainly Mollusca. The tiny mussels Brachidontes rodriguezii and Brachidontes purpuratus, and the algae Corallina officinalis dominated the intertidal and acts as a buffer that prevent other species for physical stress. The subtidal was mainly represented by grazers. Our results showed a tendency of suspension feeders decreasing and increasing of grazers and predators from high intertidal to subtidal, probably driven by decreasing in physical stress. The gastropod Tegula patagonica, the sea urchins Arbacia dufresnii and Pseudechinus magellanicus and the non native algae Undaria pinnatifida were the most abundant in 1m-10m level. Based on previous works performed in the region, we hypothesize that the differences registered between intertidal and subtidal samples could be explained in part by an increase in physical stress in the intertidal with low predation pressure that promotes positive interactions, while in the subtidal the increasing in consumers and decreasing of physical stress could lead to associational defenses. Competition for primary substrate at the intertidal and subtidal must be explored in future experiments. Our results could be useful to compare data and to develop a sustainable network for long-term monitoring benthic community changes due to anthropogenic activities.Fil: Rechimont, Maria Emilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Galvan, David Edgardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Sueiro, Maria Cruz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Casas, Graciela Noemi. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Piriz, Maria Luz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Diez, María Emilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Primost, Monica Angelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Zabala, Maria Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Marquez, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Brogger, Martin Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales; ArgentinaFil: Fernandez Alfaya, Jose Elias. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; ArgentinaFil: Bigatti, Gregorio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentin