Estimating the higher symmetric topological complexity of spheres

We study questions of the following type: Can one assign continuously and $\Sigma_m$-equivariantly to any $m$-tuple of distinct points on the sphere $S^n$ a multipath in $S^n$ spanning these points? A \emph{multipath} is a continuous map of the wedge of $m$ segments to the sphere. This question is connected with the \emph{higher symmetric topological complexity} of spheres, introduced and studied by I. Basabe, J. Gonz\'alez, Yu. B. Rudyak, and D. Tamaki. In all cases we can handle, the answer is negative. Our arguments are in the spirit of the definition of the Hopf invariant of a map $f: S^{2n-1} \to S^n$ by means of the mapping cone and the cup product.Comment: This version has minor corrections compared to what published in AG

From Perturbation Theory to Confinement: How the String Tension is built up

We study the spatial volume dependence of electric flux energies for SU(2) Yang-Mills fields on the torus with twisted boundary conditions. The results approach smoothly the rotational invariant Confinement regime. The would-be string tension is very close to the infinite volume result already for volumes of $(1.2 \ {\rm fm.})^3$. We speculate on the consequences of our result for the Confinement mechanism.Comment: 6p, ps-file (uuencoded). Contribution to Lattice'93 Conference (Dallas, 1993). Preprint INLO-PUB 18/93, FTUAM-93/4

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

New objects in old structures: The Iron Age hoard of the Palacio III megalithic funerary complex (Almadén de la Plata, Seville, Spain)

Cultural contact, exchange and interaction feature high in the list of challenging topics of current research on European Prehistory. Not far off is the issue of the changing role of monuments in the making and maintaining of key cultural devices such as memory and identity. Addressing both these highly-debated issues from a science-based perspective, in this paper we look at an unusual case study set in southern Iberia and illustrate how these archaeological questions can benefit from robust materials-science approaches.We present the contextual, morphological and analytical study of an exceptional Early Iron Age hoard composed of a number of different (and mostly exotic) materials such as amber, quartz, silver and ceramic. This hoard, found under the fallen orthostat of a megalithic structure built at least 2000 years earlier, throws new light on long-distance exchange networks and the effect they could have had on the cultural identities and social relations of local Iberian Early Iron Age communities. Moreover, the archaeometric study reveals how diverse and distant the sources of these item are (Northern Europe to Eastern and Western Mediterranean raw materials, as well as local and eastern technologies), therefore raising questions concerning the social mechanisms used to establish change and resistance in contexts of colonial encounter