Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.Comment: v1: 17 pages, Talk presented in the "MAT.ES2005: 1st Joint Meeting of Mathematics RSME-SCM-SEIO-SEMA" (Valencia, Spain 2005, http://www.uv.es/mat.es2005/); v3: published versio

The impact of population ageing on international capital flows

This paper is oriented to study the relationship between demographical factors and international capital flows. We analyse the impact of ageing on foreign direct investments (FDI) and foreign portfolio investments (FPI) on a bilateral level. Firstly we present a theoretical foundation of the relationship and then we test it by an empirical model. Theoretical foundations are based on the lifecycle hypothesis and overlapping generations model in a demographic context. The bilateral FDI and FPI are modelled by using fixed effects balanced panel data. The results suggest that the current and future age structure of the nation has significant effect on current international capital flows.International Capital Flows; Demography; Capital Mobility; FDI; Portfolio Investment

Refugees and “Missing” Arms Trade

Millions of people are killed or wounded by small arms each year. The aim of this study is to enhance our understanding of “missing” arms trade across countries. We proceed in two steps. First, we measure the extent of missing arms trade on the basis of official trade statistics. We construct a measure of the gap in arms trade based on the discrepancy between the value of arms exports reported by the exporting country and the value of arms imports recorded by the importing country. Second, we uncover the link between refugee movements and missing arms trade. Refugee flows, by reducing the ability of the receiving country to patrol its borders and its customs, are found to be correlated with arms smuggling across the border into the importing country. A series of robustness checks confirm the above findings.international trade, refugees, arms, customs.

The effect of mafia on public transfers

Organized crime is a worldwide, widespread phenomenon, which affects developing as well as developed countries, and entails deep economic and social consequences. The purpose of this study is to enhance our understanding of organized crime activities. By using an innovative data set on Sicilian mafia activity available at municipality level, we test whether firms located in municipalities with mafia-related crimes obtain more public subsidies. In order to deal with the endogeneity of the relationship, we explore the origins of mafia. We instrument current mafia activity with exogenous historical and geographical shifters of land productivity, i.e. rainfall in the XIX century and geographical features at municipality level. We provide evidence that the presence of mafia affects the allocation of public transfers: municipalities with mafia activity receive larger public funding. The estimated impact of mafia is also economically relevant and equals one standard deviation of the dependent variable. According to our estimates the presence of mafia increases the total amounts of funds by about 35% on average. A series of robustness checks confirms the above findings.organized crime, public transfers

I. Apples to apples A2A^2: realistic galaxy simulated catalogs and photometric redshift predictions for next-generation surveys

We present new mock catalogues for two of the largest stage-IV next-generation surveys in the optical and infrared: LSST and Euclid, based on an N-body simulation+semi-analytical cone with a posterior modification with \texttt{PhotReal}. This technique modifies the original photometry by using an empirical library of spectral templates to make it more realistic. The reliability of the catalogues is confirmed by comparing the obtained color-magnitude relation, the luminosity and mass function and the angular correlation function with those of real data. Consistent comparisons between the expected photometric redshifts for different surveys are also provided. Very deep near infrared surveys such as Euclid will provide very good performance ($\Delta z/(1+z) \sim 0.025-0.053$) down to $H\sim24$ AB mag and up to $z\sim3$ depending on the optical observations available from the ground whereas extremely deep optical surveys such as LSST will obtain an overall lower photometric redshift resolution ($\Delta z/(1+z) \sim 0.045$) down to $i\sim27.5$ AB mag, being considerably improved ($\Delta z/(1+z) \sim 0.035$) if we restrict the sample down to i$\sim$24 AB mag. Those numbers can be substantially upgraded by selecting a subsample of galaxies with the best quality photometric redshifts. We finally discuss the impact that these surveys will have for the community in terms of photometric redshift legacy. This is the first of a series of papers where we set a framework for comparability between mock catalogues and observations with a particular focus on cluster surveys. The Euclid and LSST mocks are made publicly available in the following link: http://photmocks.obspm.fr/.Comment: accepted in MNRAS. Mocks available in the following link: http://photmocks.obspm.fr

Multisymplectic unified formalism for Einstein-Hilbert gravity

We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified Lagrangian-Hamiltonian formalism is particularly interest- ing when it is applied to these kinds of theories, since it simplifies the treatment of them; in particular, the implementation of the constraint algorithm, the retrieval of the Lagrangian description, and the construction of the covariant Hamiltonian formalism. In order to apply this algorithm to the co- variant field equations, they must be written in a suitable geometrical way, which consists of using integrable distributions, represented by multivector fields of a certain type. We apply all these tools to the Einstein-Hilbert model without and with energy-matter sources. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomen- tum (covariant) Hamiltonian formalisms in both cases. As a consequence of the gauge freedom and the constraint algorithm, we see how this model is equivalent to a first-order regular theory, without gauge freedom. In the case of presence of energy-matter sources, we show how some relevant geo- metrical and physical characteristics of the theory depend on the type of source. In all the cases, we obtain explicitly multivector fields which are solutions to the gravitational field equations. Finally, a brief study of symmetries and conservation laws is done in this context.Peer ReviewedPostprint (author's final draft

Video Prioritization for Unequal Error Protection

We analyze the effect of packet losses in video sequences and propose a lightweight Unequal Error Protection strategy which, by choosing which packet is discarded, reduces strongly the Mean Square Error of the received sequenc

Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics

The consequences of the projectability of Poincar\'e-Cartan forms in a third-order jet bundle $J^3\pi$ to a lower-order jet bundle are analyzed using the constraint algorithm for the Euler-Lagrange equations in $J^3\pi$. The results are applied to the Hilbert Lagrangian for the Einstein equations. Furthermore, the case of higher-order mechanics is also studied as a particular situation.Peer ReviewedPostprint (author's final draft