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Xylella fastidiosa (g-Proteobacteria: Xanthomonadaceae) es uno de los patógenos de plantas más importantes a nivel mundial, transmitido exclusivamente por insectos que se alimentan del xilema. El principal vector de esta enfermedad en Europa es Philaenus spumarius (Hemiptera: Aphrophoridae). Su control químico es aún limitado y apenas se conocen agentes con potencial para su control biológico. La espuma producida por las ninfas de P. spumarius podría ser un micro-ambiente propicio para la supervivencia de los juveniles infectivos (JIs) de los nematodos entomopatógenos (NEPs) lejos de su hábitat natural, el suelo, posibilitando su aplicación aérea frente a esta plaga. Las hipótesis planteadas fueron: (i) los JIs tienen capacidad infectiva frente a ninfas de P. spumarius en ausencia de espuma, (ii) la espuma inhibe la patogenicidad de los JIs; y (iii) en un sistema espumaninfa-planta las tasas de patogenicidad serán menores a las registradas en ausencia de espuma. La exposición directa de 30 JIs de Steinernema feltiae (Rhabditida: Steinernematidae) supuso una mortalidad de ninfas a dos días del 77%, frente al 10% en ausencia de NEPs. La inoculación de 3 JIs en espuma no implicó una reducción de su patogenicidad tras exposiciones de 24 y 72 h. Estudios preliminares evidencian una menor eficacia infectiva en el sistema espuma-ninfa-planta, aunque aún son necesarios estudios adicionales para establecer el potencial de control. Se confirmó que S. feltiae tiene la capacidad de completar su ciclo biológico dentro de la ninfa hasta la emergencia de una nueva generación de JIs. Asimismo, estudios preliminares paralelos demostraron que otros NEPs como Heterorhabditis bacteriophora y Steinernema riojaense n. sp. tienen capacidad infectiva y colonizadora de ninfas de P. spumarius. Concluimos que el desarrollo de bio-herramientas basadas en el uso de NEPs puede ser una alternativa real y prometedora en el control biológico de vectores de X. fastidiosa.

Entomopathogenic nematodes (EPNs) are well-studied biocontrol agents of soil-dwelling arthropod pests. The insecticidal efficiency of EPNs is modulated by food web dynamics. EPNs can reproduce in freeze-killed insect larvae, even in competition with free-living bacterivorous nematodes (FLBNs) in the genus Oscheius. The objective of this study was to assess the efficiency of EPNs as scavengers when competing with free-living saprophagous nematodes and fungi, and to determine the possible impact on subsequent EPN offspring fitness. Live and freeze-killed larvae of Galleria mellonella were used to evaluate the reproduction rate and progeny fitness of two EPN species, Heterorhabditis bacteriophora and Steinernema feltiae, applied individually or combined with the FLBN species Oscheius onirici or Pristionchus maupasi, or Aspergillus flavus, an opportunistic saprophytic fungus. We hypothesized that (1) EPN scavenging behaviors previously observed (for H. megidis and S. kraussei) apply to other EPN species, (2) infective juveniles (IJs) emerging from freeze-killed larvae will display reduced pathogenicity and reproduction, and (3) fitness reduction will be amplified by exposure to other organisms competing for the resources. The reproduction rate of S. feltiae was lower in freeze-killed larvae than in larvae infected and killed by the nematode, whereas H. bacteriophora failed to reproduce as a scavenger. The S. feltiae F1 IJs that emerged from freeze-killed larvae exhibited lower pathogenicity rates than IJs resulting from entomopathogenic activity, and also lower reproductive rates if they experienced high FLBN competitive pressure during development. This study illustrates that scavenging is a suboptimal alternative pathway for EPNs, especially in the face of scavenger competition, even though it provides a means for some EPN species to complete their life-cycle.

Esta memoria explica, en primer lugar, como funcionan sistemas de pregunta y respuesta existentes en la actualidad. En concreto, se estudian diversos sistemas relacionados con la medicina, debido que en un primer momento, en este trabajo se pretendía implementar un chat médico. A partir de conocer cómo funcionan los sistemas existentes y tener claro lo que se quiere conseguir, se sigue explicando los fundamentos técnico-teóricos más importantes del Deep Learning de cara a la implementación final del sistema de preguntas y respuestas. En concreto se hace mucho énfasis en los fundamentos del Machine Learning, los tipos diferentes de Redes Neuronales Recurrentes y como usarlas, y la arquitectura Encoder-Decoder. En el siguiente capítulo se explica la teoría del procesamiento del lenguaje natural. Este apartado de la memoria se explica en conjunto con Spacy, para darle también un enfoque más práctico. Al finalizar se explican los diferentes métodos de representación del lenguaje en vectores numéricos. Después empezará la segunda parte, y la más importante del TFG, que es como se han aplicado estos conceptos teóricos al sistema de preguntas y respuestas final. Se empieza por explicar lo que hace el código de manera secuencial y muy abstracta evadiéndose en todo momento del código en sí, para ahondar en por qué funciona de una forma más conceptual y teórica. A continuación, se hace mención a cada uno de los experimentos a los que se sometió el sistema y se comentan los resultados. Finalmente se procede a dar una opinión personal de por qué se han obtenido tales resultados y las soluciones que se le darían, haciendo hincapié en que se tienen que demostrar todos de manera empírica., This report explains, first of all, how question answering systems currently exist. Specifically, various systems related to medicine are studied, because at first, in this work was intended to implement a medical chat. From knowing how the existing systems work and being aware about what we wanted to achieve, this document continues explaining the most important technical-theoretical foundations of Deep Learning for the final implementation of the question answering system. In particular, much emphasis is placed on the fundamentals of Machine Learning, the different types of Recurrent Neural Networks and how to use them, and the Encoder-Decoder architecture. The theory of natural language processing is explained in the next chapter. This section of the report is explained in conjunction with Spacy, to also give you a more practical approach. At the end, the different methods of representing the language in numerical vectors are explained. Then the second and most important part of the TFG begins, which explains how these theoretical concepts have been applied to the final question answering system. It begins by explaining what the code does in a very abstract and sequential manner, evading the code itself at all times, to focus into why it works in a more conceptual and theoretical way. Next, each of the experiments to which the system was underwent is mentioned and the results are discussed. Finally we proceed to give a personal opinion of why such results have been obtained and the solutions that would be given to it, emphasizing that they have to be demonstrated empirically.

Viticulture is a worldwide valuable sector, with special relevance in Spain for their socio-economic impact. Vineyards are threatened by numerous pests and diseases, and their management relies primarily on use of conventional agrochemicals. Current paradigm of sustainability pursues the implementation of ecologically sound strategies. The use of cover crops is arising as an alternative with numerous benefits, including favouring above-belowground biodiversity. We hypothesize that vineyard with cover crops might increase the prevalence of entomopathogenic nematodes (EPNs), biocontrol agents of soil pests, modulating the assemblage of other associated organisms. The presence and activity of native EPNs were evaluated in an ongoing experiment in La Grajera (Logroño, Spain) on Vitis vinifera var Tempranillo (clon RJ-26, rootstock “110-Richter”) investigating tillage, and three types of covers: spontaneous, flower-driven, and seeded with Bromus perenne (Poaceae) (n = 3 per treatment). During late-spring and early-autumn 2017, 48 composite soil samples (12 cores, 2.5 cm diam X 20 cm depth) were taken to ensure balanced spatial distribution (two pair’s rows/inter-rows per plot). Each sample was assessed for the presence and abundance of 9 EPNs and other related organisms: 6 nematophagous fungi, 5 free-living nematodes (FLNs), and 2 ectoparasitic bacteria, by qPCR approaches. Moreover, traditional insect-bait provided the measurement of EPN activity. In spring 2017, nematode activity was slightly higher (P = 0.068) in inter-rows than in rows. However, this trend was only observed for the tillage and seeded treatments in later autumn (P < 0.05). Two EPN species were isolated: Steinernema feltiae and, for the first time in La Rioja, Heterorhabditis bacteriophora. The insect-baits detected low EPN-FLN incidence in the isolates, indicating that EPNs could suffer low competition with other nematodes for the cadaver under this scenario. The ongoing surveys in 2018 will supply ad

We show that a radial continuous valuation defined on the n-dimensional star bodies extends uniquely to a continuous valuation on the n-dimensional bounded star sets. Moreover, we provide an integral representation of every such valuation, in terms of the radial function, which is valid on the dense subset of the simple Borel star sets. Along the way, we also show that every radial continuous valuation defined on the n-dimensional star bodies can be decomposed as a sum V=V+−V−, where both V+ and V− are positive radial continuous valuations., Ministerio de Economía, Comercio y Empresa (España), Comunidad de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random instances of such bipartite correlations. The main question we are interested in is: given a quantum correlation, taken at random, how likely is it that it is truly non-explainable by a classical model? We show that, under very general assumptions on the considered distribution, a random correlation which lies on the border of the quantum set is with high probability outside the classical set. What is more, we are able to provide the Bell inequality certifying this fact. On the technical side, our results follow from (i) estimating precisely the “quantum norm” of a random matrix and (ii) lower-bounding sharply enough its “classical norm”, hence proving a gap between the two. Along the way, we need a non-trivial upper bound on the ∞→1∞→1 norm of a random orthogonal matrix, which might be of independent interest., Unión Europea, Ministerio de Economía, Comercio y Empresa (España), Comunidad de Madrid, Generalitat de Catalunya, French CNRS (ANR), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

[ES] Se trata de acondicionar a la vez de ajardinar un parque público, en el que se ubica el circuito municipal de ciclismo de la Pobla de Vallbona. El terreno está localizado en el camino Mas de Tous, con una superficie 47.000 m2. El problema que encontramos en este espacio es que únicamente esta aprovechado para uso del circuito oval. Este proyecto se basa en la necesidad de dotar de valor social y lúdico al terreno a la vez que se genera un espacio verde alrededor de su pista oval, siempre buscando un equilibrio entre la estética paisajística, la funcionalidad y la sostenibilidad e integrándolo en el entorno circundante. Se realiza con el objetivo de convertir este espacio en un entorno de referencia para la gente del pueblo en el que puedan realizar diferentes actividades, como por ejemplo ir a disfrutar del deporte en la pista oval ya ubicada o simplemente pasar un domingo de picnic. Para su ajardinamiento se aprovechara que en el interior del circuito ya existe una arboleda de pinos que nos servirá de punto de inicio a la hora de elegir variedades y plantas acordes al entorno. El diseño de la rehabilitación del espacio ajardinado quedara extensamente detallado en la memoria del proyecto, incluyendo aquellos arboles existentes, las nuevas variedades y más mobiliario para nuestro parque. Además, incluirá un presupuesto detallado de los trabajos a realizar, una planificación y programación de las tareas y ejecución de las mismas, un estudio de seguridad y salud, el correspondiente pliego de condiciones generales así como los planos necesarios y correspondientes del terreno., [EN] Today, it is necessary to conditioning and landscape a public park, is located the municipal cycling circuit of Pobla de Vallbona. The ground is on the road Mas de Tous, with a surface area of 47.000 m2. We find a problem in this space is that it¿s only the oval circuit is used. This project is based on the need to provide social and recreational value to the ground while generating a green space around its oval track, always seeking a balance between landscape aesthetics, functionality and sustainability and integrating it into the environment surrounding. It is done with the aim of turning this space into a reference environment for the people of the town where they can perform different activities, such as going to enjoy the sport on the oval track already located or pass the Sunday picnic. For your landscaping will take advantage of the fact that inside the circuit there is already a pine grove that will serve as a starting point when choosing varieties and plants according to the environment. The design of the rehabilitation of the garden space will be extensively detailed in the project's memory, including those existing trees, new varieties and more furniture for our park. In addition, it will include a detailed budget of the work to be carried out, planning and scheduling of the tasks and execution thereof, a safety and health study, the corresponding general specifications and the necessary and corresponding plans of the ground.

Background: The global pandemic of obesity has led to an increased risk for prediabetes and type-2 diabetes (T2D). The aims of the current project are: (1) to evaluate the effect of a 22-week family based intervention program, including supervised exercise, on insulin resistance syndrome (IRS) risk in children with a high risk of developing T2D and (2) to identify the profile of microRNA in circulating exosomes and in peripheral blood mononuclear cells in children with a high risk of developing T2D and its response to a multidisciplinary intervention program including exercise. Methods: A total of 84 children, aged 8-12 years, with a high risk of T2D will be included and randomly assigned to control (N = 42) or intervention (N = 42) groups. The control group will receive a family based lifestyle education and psycho-educational program (2 days/month), while the intervention group will attend the same lifestyle education and psycho-educational program plus the exercise program (3 days/week, 90 min per session including warm-up, moderate to vigorous aerobic activities, and strength exercises). The following measurements will be evaluated at baseline prior to randomization and after the intervention: fasting insulin, glucose and hemoglobin A1c; body composition (dual-energy X-ray absorptiometry); ectopic fat (magnetic resonance imaging); microRNA expression in circulating exosomes and in peripheral blood mononuclear cells (MiSeq; Illumina); cardiorespiratory fitness (cardiopulmonary exercise testing); dietary habits and physical activity (accelerometry). Discussion: Prevention and identification of children with a high risk of developing T2D could help to improve their cardiovascular health and to reduce the comorbidities associated with obesity.

Objectives: More than 3.5 million invasive coronary angiographies (ICA) are performed in Europe annually. Approximately 2 million of these invasive procedures might be reduced by noninvasive tests because no coronary intervention is performed. Computed tomography (CT) is the most accurate noninvasive test for detection and exclusion of coronary artery disease (CAD). To investigate the comparative effectiveness of CT and ICA, we designed the European pragmatic multicentre DISCHARGE trial funded by the 7th Framework Programme of the European Union (EC-GA 603266). Methods: In this trial, patients with a low-to-intermediate pretest probability (10–60 %) of suspected CAD and a clinical indication for ICA because of stable chest pain will be randomised in a 1-to-1 ratio to CT or ICA. CT and ICA findings guide subsequent management decisions by the local heart teams according to current evidence and European guidelines. Results: Major adverse cardiovascular events (MACE) defined as cardiovascular death, myocardial infarction and stroke as a composite endpoint will be the primary outcome measure. Secondary and other outcomes include cost-effectiveness, radiation exposure, health-related quality of life (HRQoL), socioeconomic status, lifestyle, adverse events related to CT/ICA, and gender differences. Conclusions: The DISCHARGE trial will assess the comparative effectiveness of CT and ICA. Key Points: • Coronary artery disease (CAD) is a major cause of morbidity and mortality.• Invasive coronary angiography (ICA) is the reference standard for detection of CAD.• Noninvasive computed tomography angiography excludes CAD with high sensitivity.• CT may effectively reduce the approximately 2 million negative ICAs in Europe.• DISCHARGE addresses this hypothesis in patients with low-to-intermediate pretest probability for CAD.

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.)., Ministerio de Economía, Comercio y Empresa (España), Comunidad de Madrid, Ramón y Cajal” program and ICMAT Severo Ochoa, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Ministerio de Economía, Comercio y Empresa (España), Comunidad de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form γ=(⟨ui,vj⟩)ni,j=1, where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of α=mnα=mn, where the previous vectors are sampled according to the Haar measure in the unit sphere of RmRm. In particular, we prove the existence of an α0>0 such that if α≤α0, γ is nonlocal with probability tending to 1 as n→∞, while for α>2, γ is local with probability tending to 1 as n→∞.

We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated with it. To do this, we use tools from the theory of multilinear operators on spaces of continuous functions. Along the way we reprove, with these same techniques, a recently found characterization of the dual mixed volume., Ministerio de Economía, Comercio y Empresa (España), Mexico's National Council for Science and Technology postdoctoral grant, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. Along the way we reprove, with these same techniques, a recently found characterization of the dual mixed volume.

The aim of this thesis is to characterise a sample of High Mass X-ray Binaries (HMXBs) formed by: IGR J00370+6122, XTE J1855-026, AX J1841.0-0535 and AX J1845.0-0433. These objects are composed of pulsars (rotating neutron stars) accreting material from the wind of their supergiant companions. The X-rays are produced in the interaction of the accreted material with the strong gravitational field of the neutron star that accelerates this material and heats it up to ~ 107 K. The study of HMXBs has strong implications in several areas of Physics and Astrophysics. They contain neutron stars whose study is essential to constrain the equation of state of nuclear dense matter, and provides insights on the astrophysical models of core collapse and Supernovae explosions. HMXBs considered as a population give information on the properties of the galaxy. In addition they are excellent test-beds to study accretion physics and outflows. The X-ray behaviour of these systems determines the class of system (classical HMXBs, Supergiant Fast X-ray Transients, Be/X-ray Binaries). The differences in the X-ray emission are supposed to be due to the different properties of the binary systems, such as the orbital properties, the magnetic field of the neutron star or the spectral type of the donor star. HMXBs in this thesis are wind-fed systems, therefore, the properties of the wind (which depend on the spectral type) and the interaction of this wind with the gravitational field of the compact object are key elements to understand the X-ray emission. Therefore, in this thesis an orbital solution for each target of study has been determined using optical spectra of the donor star. Moreover, to check if wind variability is related to the orbit of the binary system, analysis of Ha variations have been carried out. Furthermore, in the case of IGR J00370+6122 and XTE J1855-026 we have obtained an atmosphere model for each of the donor stars allowing us to characterise the atmospheres of these s

Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely., Unión Europea, Ministerio de Economía, Comercio y Empresa (España), Comunidad de Madrid, Ministerio de Educación, Formación Profesional y Deportes (España), Templeton Foundation, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a mathematical theory of the macroscopic fluctuations generated by ensembles of independent microscopic discrete systems. We provide algorithms to decide which multivariate Gaussian distributions can be approximated by sums of finitely valued random vectors. We study non-trivial cases where the microscopic variables have an unbounded range, as well as asymptotic scenarios with infinitely many macroscopic variables. From a foundational point of view, our results imply that bipartite Gaussian states of light cannot be understood as beams of independent d-dimensional particle pairs. It is also shown that the classical description of certain macroscopic optical experiments, as opposed to the quantum one, requires variables with infinite cardinality spectra., Unión Europea, Comunidad de Madrid, Templeton Foundation, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Las estrellas masivas desempeñan un papel fundamental en la evolución de las Galaxias, siendo la fuente primordial de generación y dispersión de elementos como el oxígeno, silicio, etc., en el medio interestelar. La masa de la estrella es el parámetro más determinante en los procesos de evolución de la estrella, pero su determinación no siempre es posible sin el uso de calibraciones externas. Afortunadamente, la naturaleza nos ofrece las estrellas binarias como laboratorios astrofísicos, donde es posible la determinación de las masas de sus componentes a partir del movimiento orbital de las mismas. En esta tesis se presentan el análisis espectroscópico y fotométrico de cuatros sistemas binarios cuyas componentes son estrellas masivas.

The strong* topology s_(X) of a Banach space X is defined as the locally convex topology generated by the seminorms x 7! kSxk for bounded linear maps S from X into Hilbert spaces. The w-right topology for X, _(X), is a stronger locally convex topology, which may be analogously characterised by taking reflexive Banach spaces in place of Hilbert spaces. For any Banach space Y , a linear map T : X ! Y is known to be weakly compact precisely when T is continuous from the w-right topology to the norm topology of Y . The main results deal with conditions for, and consequences of, the coincidence of these two topologies on norm bounded sets. A large class of Banach spaces, including all C_-algebras, and more generally, all JB_-triples, exhibit this behaviour., I+D Madrid Ciencia y Tecnología, Junta de Andalucía, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order Ω(√n∕Log2n) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative Lp embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise., Unión Europea - FP7, Comunidad de Madrid, National Science Foundation (Estados Unidos), Danish Center for Quantum Optics, Danish Natural Science Research Council, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We introduce the concept of quasi-completely continuous multilinear operators and use this concept to characterize, for a wide class of Banach spaces X1, …, Xk, the multilinear operators T : X1 × … × Xk → X with an X-valued Aron–Berner extension., I+D Madrid Ciencia y Tecnología, Junta de Andalucía, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In recent papers, the Right mid the Strong* topologies have been. introduced and studied on general Banach spaces We characterize different types of continuity for multilinear operators (joint, uniform, etc) with respect to the above topologies We also study the relations between them. Finally, in the last section, we relate the joint Strong*-to-norm continuity of a multilinear operator T defined on C*-algebras (respectively, JB*-triples) to C*-summability (respectively, JB*-triple-summability)., I+D Madrid Ciencia y Tecnología project, Universidad Complutense de Madrid, Junta de Andalucía, Becas UCM 2005, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Short (non-technical) version, In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We illustrate the power of this connection by showing that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\frac{\sqrt{n}}{\log^2n}$ when observables with n possible outcomes are used. Applications to resistance to noise, Hilbert space dimension estimates and communication complexity are given., Unión Europea, QUANTOP, e Danish Natural Science Research Council, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. In order to derive all these physical consequences, we wil have to obtain new mathematical results in the theories of operator spaces and tensor norms. In particular, we will prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We show that for every orthogonally additive scalar n-homogeneous polynomial P on a C*-algebra A there exists phi in A* satisfying P(x) = phi(x(n)), for each element x in A. The vector-valued analogue follows as a corollary., I+D Marid Ciencia y Tecnología, Comunidad de Madrid, Junta de Andalucía, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub