Fourier-Mukai transforms for coherent systems on elliptic curves

We determine all the Fourier-Mukai transforms for coherent systems consisting of a vector bundle over an elliptic curve and a subspace of its global sections, showing that these transforms are indexed by the positive integers. We prove that the natural stability condition for coherent systems, which depends on a parameter, is preserved by these transforms for small and large values of the parameter. By means of the Fourier-Mukai transforms we prove that certain moduli spaces of coherent systems corresponding to small and large values of the parameter are isomorphic. Using these results we draw some conclusions about the possible birational type of the moduli spaces. We prove that for a given degree $d$ of the vector bundle and a given dimension of the subspace of its global sections there are at most $d$ different possible birational types for the moduli spaces.Comment: LaTeX2e, 21 pages, some proofs simplified, typos corrected. Final version to appear in Journal of the London Mathematical Societ

A multivariate generalized independent factor GARCH model with an application to financial stock returns

We propose a new multivariate factor GARCH model, the GICA-GARCH model , where the data are assumed to be generated by a set of independent components (ICs). This model applies independent component analysis (ICA) to search the conditionally heteroskedastic latent factors. We will use two ICA approaches to estimate the ICs. The first one estimates the components maximizing their non-gaussianity, and the second one exploits the temporal structure of the data. After estimating the ICs, we fit an univariate GARCH model to the volatility of each IC. Thus, the GICA-GARCH reduces the complexity to estimate a multivariate GARCH model by transforming it into a small number of univariate volatility models. We report some simulation experiments to show the ability of ICA to discover leading factors in a multivariate vector of financial data. An empirical application to the Madrid stock market will be presented, where we compare the forecasting accuracy of the GICA-GARCH model versus the orthogonal GARCH one

Tower systems for Linearly repetitive Delone sets

In this paper we study linearly repetitive Delone sets and prove, following the work of Bellissard, Benedetti and Gambaudo, that the hull of a linearly repetitive Delone set admits a properly nested sequence of box decompositions (tower system) with strictly positive and uniformly bounded (in size and norm) transition matrices. This generalizes a result of Durand for linearly recurrent symbolic systems. Furthermore, we apply this result to give a new proof of a classic estimation of Lagarias and Pleasants on the rate of convergence of patch-frequencies.Comment: 27 pages, 2 figures

Exploring ICA for time series decomposition

In this paper, we apply independent component analysis (ICA) for prediction and signal extraction in multivariate time series data. We compare the performance of three different ICA procedures, JADE, SOBI, and FOTBI that estimate the components exploiting either the non-Gaussianity, or the temporal structure of the data, or combining both, non-Gaussianity as well as temporal dependence. Some Monte Carlo simulation experiments are carried out to investigate the performance of these algorithms in order to extract components such as trend, cycle, and seasonal components. Moreover, we empirically test the performance of those three ICA procedures on capturing the dynamic relationships among the industrial production index (IPI) time series of four European countries. We also compare the accuracy of the IPI time series forecasts using a few JADE, SOBI, and FOTBI components, at different time horizons. According to the results, FOTBI seems to be a good starting point for automatic time series signal extraction procedures, and it also provides quite accurate forecasts for the IPIs.ICA, Signal extraction, Multivariate time series, Forecasting

A multivariate generalized independent factor GARCH model with an application to financial stock returns

We propose a new multivariate factor GARCH model, the GICA-GARCH model , where the data are assumed to be generated by a set of independent components (ICs). This model applies independent component analysis (ICA) to search the conditionally heteroskedastic latent factors. We will use two ICA approaches to estimate the ICs. The first one estimates the components maximizing their non-gaussianity, and the second one exploits the temporal structure of the data. After estimating the ICs, we fit an univariate GARCH model to the volatility of each IC. Thus, the GICA-GARCH reduces the complexity to estimate a multivariate GARCH model by transforming it into a small number of univariate volatility models. We report some simulation experiments to show the ability of ICA to discover leading factors in a multivariate vector of financial data. An empirical application to the Madrid stock market will be presented, where we compare the forecasting accuracy of the GICA-GARCH model versus the orthogonal GARCH one.ICA, Multivariate GARCH, Factor models, Forecasting volatility

Variational Principles for multisymplectic second-order classical field theories

We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.Comment: 6 pp. Minor corrections. Clarifications and comments have been added. Two new sections ("Introduction" and "The higher-order case") have been added. Bibliography enlarge

Microbiological analysis of natural waters

Traballo fin de grao (UDC.CIE). Bioloxía. Curso 2016/2017[Resumen] En el Ayuntamiento de Ribadeo (Lugo) se estimó la carga microbiológica presente en el agua de cuatro fuentes (fuente del Valín, Sta. Cruz, Ove y fuente de Cedofeita), un río (río de Esteiro) y un pozo para determinar si cumplían los parámetros microbiológicos establecidos en el Real Decreto 140/2003 referidos a la calidad del agua de consumo humano. Los microorganismos analizados fueron los indicadores de contaminación fecal (grupo coliforme, enterococos y Clostridium perfringens), los microorganismos totales cultivables a 22ºC y 37ºC y Pseudomonas aeruginosa. Los resultados obtenidos mostraron una baja abundancia de microorganismos cultivables y ausencia total del resto de indicadores en las cuatro fuentes y el pozo, mientras que la muestra de río presentó contaminación de origen fecal, siendo así sus aguas una posible fuente de transmisión de microorganismos patógenos.[Resumo] No Concello de Ribadeo (Lugo) estimouse a carga microbiolóxica presente na auga de catro fontes (fonte do Valín, Sta. Cruz, Ove e fonte de Cedofeita), un río e un pozo para determinar se cumprían os parámetros microbiolóxicos establecidos no Real Decreto 140/2003 referidos á calidade da auga de consumo humano. Os microorganismos analizados foron os indicadores de contaminación fecal (grupo coliforme, enterococos e Clostridium perfringens), os microorganismos cultivables a 22ºC e 37ºC e Pseudomonas aeruginosa. Os resultados obtidos amosaron unha baixa abundancia de microorganismos cultivables e ausencia total do resto nas catro fontes e no pozo, mentres que no río supéranse amplamente tódolos parámetros analizados, sendo así as súas augas unha posible fonte de transmisión de microorganismos patóxenos.[Abstract] Microbiological analyses of water from different points in Ribadeo village were carried out: four fountains (Fuente del Valín, fuente de Sta. Cruz, fuente de Ove y fuente de Cedofeita), one well and one river (río de Esteiro). Microbiological parameters related to water quality were estimated taking into account the normative published in the Real Decreto 140/2003 referred to potability of water. The microorganisms analysed were the indicators of faecal pollution (“coliform group”, enterococci and Clostridium perfrigens), the cultivable microorganisms at a 22 and 37ºC and Pseudomonas aeruginosa. The results obtained show a low concentrations of cultivable microorganisms and a complete absence of the remaining indicators in the four fountains and the well, while in the river all parameters analysed are substantially exceeded. Therefore, the river waters could be a potential source of transmission of pathogenic microorganisms

THREE-DIMENSIONAL CONTOURING WITH DIGITAL HOLOGRAPHY

Presentamos una técnica para determinar contornos tridimensionales de objetos con dimensiones de al menos cuatro órdenes de magnitud mayor que la longitud de onda de la iluminación. Nuestra propuesta esta basada en la reconstrucción numérica del frente de onda objeto a partir de un holograma registrado digitalmente. El mapa de fase módulo-2π requerido en cualquier proceso de contorneado es obtenido por medio de la substracción directa de dos imágenes de fase (imagen de diferencia de fase) de un objeto bajo diferentes ángulos de iluminación. La obtención de la imagen de diferencia de fase es posible gracias a la capacidad de reconstrucción numérica del campo óptico complejo proporcionado por la holografía digital. Esta característica particular nos proporciona un robusto, confiable y rápido procedimiento que sólo requiere de dos imágenes para su ejecución. La propuesta es soportada con el análisis teórico del sistema de contorneado y verificado por medio de resultados numéricos y experimentales.We report on a technique to determine the 3D contour of objects with dimensions of at least four orders of magnitude larger than the illumination optical wavelength. Our proposal is based on the numerical reconstruction of the object optical wave field of digitally recorded holograms. The re-quired 2π-module phase map in any contouring process is obtained by means of the direct subtraction of two phase-contrast images (phase-difference image) of a still object under different illumination angles. Obtaining phase difference images is only possible by using the capability of numerical reconstruction of the complex optical field provided by the digital holography. This unique characteristic leads us to a robust, reliable, and fast procedure that only requires of two images. We support our proposal with the theoretical means of numerical and experimental results.Presentamos una técnica para determinar contornos tridimensionales de objetos con dimensiones de al menos cuatro órdenes de magnitud mayor que la longitud de onda de la iluminación. Nuestra propuesta esta basada en la reconstrucción numérica del frente de onda objeto a partir de un holograma registrado digitalmente. El mapa de fase módulo-2π requerido en cualquier proceso de contorneado es obtenido por medio de la substracción directa de dos imágenes de fase (imagen de diferencia de fase) de un objeto bajo diferentes ángulos de iluminación. La obtención de la imagen de diferencia de fase es posible gracias a la capacidad de reconstrucción numérica del campo óptico complejo proporcionado por la holografía digital. Esta característica particular nos proporciona un robusto, confiable y rápido procedimiento que sólo requiere de dos imágenes para su ejecución. La propuesta es soportada con el análisis teórico del sistema de contorneado y verificado por medio de resultados numéricos y experimentales

Cluster identification using projections

This artiele describes a procedure to identify elusters in multivariate data using information obtained from the univariate projections of the sample data onto certain directions. The directions are chosen as those that minimize and maximize the kurtosis coefficlent of the projected data. It is shown that, under certain conditions, these directions provide the largest separatlOn for the dlfferent clusters. The projected univariate data are used to group the observations according to the values of the gaps or spacings between consecutive-ordered observations. These groupings are then combined over all projection directions. The behavior of the method is tested on several examples, and compared to k-means, MCLUST, and the procedure proposed by Jones and Sibson in 1987. The proposed algonthm is iterative, affine equivariant, flexible, robust to outliers, fast to implement, and seems to work well in practiceThis research was supported by Spanish grant BEC2000-0167Publicad

Combining random and specific directions for outlier detection and robust estimation in high-dimensional multivariate data

A powerful procedure for outlier detection and robust estimation of shape and location with multivariate data in high dimension is proposed. The procedure searches for outliers in univariate projections on directions that are obtained both randomly, as in the Stahel-Donoho method, and by maximizing and minimizing the kurtosis coefficient of the projected data, as in the Pe˜na and Prieto method.We propose modifications of both methods to improve their computational efficiency and combine them in a procedure which is affine equivariant, has a high breakdown point, is fast to compute and can be applied when the dimension is large. Its performance is illustrated with a Monte Carlo experiment and in a real dataset.Publicad