Energy concentration and explicit Sommerfeld radiation condition for the electromagnetic Helmholtz equation

We study the electromagnetic Helmholtz equation \notag (\nabla + ib(x))^{2}u(x) + n(x)u(x) = f(x), \quad x\in\Rd with the magnetic vector potential $b(x)$ and $n(x)$ a variable index of refraction that does not necessarily converge to a constant at infinity, but can have an angular dependency like $n(x) \to n_{\infty}(\frac{x}{|x|})$ as $|x|\to\infty$. We prove an explicit Sommerfeld radiation condition \notag \int_{\Rd} |\D u - in_{\infty}^{1/2}\frac{x}{|x|}u|^{2} \frac{dx}{1+|x)} < + \infty for solutions obtained from the limiting absorption principle and we also give a new energy estimate \notag \int_{\Rd}| \nabla_{\omega}n_{\infty}(\frac{x}{|x|})|^{2}\frac{|u|^{2}}{1+|x|} dx < +\infty, which explains the main physical effect of the angular dependence of $n$ at infinity and deduces that the energy concentrates in the directions given by the critical points of the potential

The acquisition of spanish perfective aspect : A study on children's production and comprehension

This paper presents the acquisition of Spanish perfective aspect in production and comprehension. It argues that, although young children use perfective aspect to talk about completed events, young children have difficulty in assessing perfective meaning from perfective morphology. This paper proposes that in the process of acquiring aspectual meaning, children use local strategies to decode aspectual meaning from form: when analyzing a completed situation, young children depend on certain learnability factors to correctly assess the entailment of completion of the perfective, namely, their ability to determine if the object of the event measures out the event as a whole or not, and their ability to read the agent’s intentions. When those factors are removed from the situation, young children had difficulty determining the entailment of completion of perfective aspect. This study also suggests that the manner in which aspectual information is conveyed in a language, may play a role on the readiness of the acquisition of the semantic morphology of the language (e.g., verb+object vs. verb+affixes). The results of this study indicate that successful performance on the semantics of Spanish perfective aspect develops around the age of 5-6

Mathematical optimization in deep learning

Mathematical Optimization plays a pillar role in Machine Learning (ML) and Neural Networks (NN) are amongst the most popular and effective ML architectures and are the subject of a very intense investigation. They have also been proven immensely powerful at solving prediction tasks in areas such as speech recognition, image classification, robotics and quantum physics. In this work we present the problem of training a Deep Neural Network (DNN), specifically the continuous optimization problem arising in Feed-Forward Networks with Rectified Linear Unit (ReLU) activation. Then we will discuss the inverse problem, presenting a model for a trained DNN as a 0-1 Mixed Integer Linear Program (MILP). Some applications, such as feature visualization and the construction of adversarial examples will be outlined. Computational experiments are reported for both direct and inverse problem. The remainder of the text contains the AMPL codes used for solving the posed problems.La optimización matemática juega un papel fundamental en el aprendizaje automático (AA), y las redes neuronales (NN) se encuentran entre las estructuras más populares y efectivas dentro de este campo. Por ello, son objecto de una intensa investigación. Además, han demostrado ser inmensamente potentes resolviendo tareas de predicción en áreas como reconocimiento automático del habla, clasificación de imágenes, robótica y física cuántica. En este trabajo, se presenta el problema de entrenar una red neuronal profunda (DNN), específicamente el problema de optimización continua que surge en las redes neuronales prealimentadas (FNN) con rectificador (ReLU) como función de activación. Posteriormente, se discutirá el problema inverso, presentaremos un modelo para una DNN que ya ha sido entrenada como un problema de programación lineal en enteros mixta. Describiremos algunas aplicaciones, como visualización de características y la construcción de ejemplos maliciosos. Se realizarán los experimentos computacionales para ambos problemas, el directo y el inverso. Los códigos de AMPL para los problemas planteados se encuentran al final del documento.Universidad de Sevilla. Doble Grado en Física y Matemática

European integration, FDI and the internal geography of trade : evidence from Western European border regions

In this paper we use a gravity model to study the trade performance of French and Spanish border regions relatively to non-border regions, over the past two decades. We find that, controlling for their size, proximity and location characteristics, border regions trade on average between 62% and 193% more with their neighbouring country than other regions, and twice as much if they are endowed with good cross border transport infrastructures. Despite European integration, however, this trade outperformance has fallen for the most peripheral regions within the EU. We show that this trend was linked in part to a shift in the propensity of foreign investors to move their affiliates from the regions near their home market to the regions bordering the EU core.- En aquest article analitzem el rendiment comercial relatiu de les regions frontereres a França i Espanya, mitjançant un model de gravetat. Els nostres resultats mostren que, controlant per la dimensió, la proximitat i les característiques de les localitzacions, les regions frontereres comercien en mitjana entre un 62% i un 193% més que les altres regions amb els estats veïns, i més del doble si estan dotades amb bones infrastructures transfrontereres de transport. Ara bé, malgrat el procés d'integració europeu, aquest rendiment superior ha disminuït per les regions més perifèriques de la UE. Mostrem que aquesta tendència està lligada en part a un canvi en la propensió dels inversors estrangers a localitzar les seves filials des de les regions més properes al seu mercat d'origen cap a les regions properes al centre de la UE

European integration, FDI and the geography of French trade

This paper uses an augmented gravity model to investigate whether the 1978-2000 process of European integration has changed the geography of trade within France, with a particular focus on the trends experienced by border regions. We support the conclusion that, once controlled for bilateral distance, origin- and destination-specific characteristics, French border regions trade on average 72% more with nearby countries than predicted by the gravity norm. They perform even better (114%) if they have good cross-border transport connections to the neighboring country. However, this outperformance eroded drastically for the French border regions located at the periphery of Europe throughout integration. We show that this trend is partly due to a decreasing propensity of foreign affliates to trade with their home country. This trade reorientation is less pronounced for the Belgian-Luxembourgian and German firms located in the regions which have better access to the EU core.trade ; gravity ; border regions ; European integration ; foreign direct investment

Steam curing effect on the properties of fly ash high performance recycled aggregates concrete

The aim of this study is to encourage the use of Recycled Concrete Aggregate (RCA) in High Performance Concrete (HPC) with fly ash. Three types of coarse RCA sourced from medium to high strength concretes were employed in 100% replacement. In order to boost their mechanical performance at early age, steam curing was assessed. The physical, mechanical and durability properties of Recycled Aggregate Concretes (RAC) were compared to those from Natural Aggregate Concrete (NAC). According to the results, natural aggregates could be completely replaced by RCA if they are sourced from similar parent HPC. Lower quality RCAs decreased the mechanical and durability behavior of HPC. However, the properties of RAC had higher long-term improvements than those from NAC due to the influence of fly ash. Despite steam curing produced higher early-age compressive strength, it had longterm negative effects. Nevertheless, RACs were less affected by long term effects of steam curing.Postprint (published version

Properties of plain concrete produced employing recycled aggregates and sea water

The final publication is available at Springer via http://dx.doi.org/10.1007/s40999-017-0229-0The generation of construction and demolition waste (C&DW) is a noteworthy environmental and economic concern. The development of new applications in which Recycled Mixed Aggregates (RMA) can be used will lead to a reduction of landfills growth. Moreover, the use of seawater shall represent another advance in sustainability due to the consequent reduction of fresh water consumption, which can be a limited resource in certain areas. Although seawater is not generally recommended for concrete production, especially in reinforced concretes, seawater could be a viable replacement for fresh water in the production of plain concretes. This study intends to analyse the possibility of using RMA and seawater in the production of concrete to be used in port sites. This study is based on three different parameters: cement class, water source and RMA content. The results highlighted the beneficial effects of using type III cement, especially with regard to durability properties. The concretes produced employing RMA and type III cement achieved lower value of sorptivity coefficient and higher values of ultrasonic pulse velocity (UPV), chloride ion penetration resistance and electrical resistivity than those produced with natural aggregates and type I cement. Moreover, the use of seawater in concretes with type III cement not only produced higher density and lower absorption capacity but also higher mechanical properties by creating a denser cement matrix, which proved to suffer low decrease by RMA addition.Peer ReviewedPostprint (author's final draft