[ES] Los espacios libres Lipschitz F(M) son linearizaciones canónicas de espacios métricos M cualesquiera. Más concretamente, F(M) es el único espacio de Banach que contiene una copia isométrica de M que es linearmente densa, y tal que toda aplicación Lipschitz de M en cualquier espacio de Banach X puede extenderse a un operador linear continuo de F(M) en X. Estos espacios suponen una herramienta muy potente para el estudio de la geometría no lineal de espacios de Banach, al permitir la aplicación de las técnicas lineales clásicas, bien conocidas, a problemas no lineales. Pero este esfuerzo sólo merece la pena si se dispone de un conocimiento lo bastante detallado de la estructura de F(M). El estudio sistemático de los espacios libres Lipschitz es bastante reciente y, por ello, dicho conocimiento es todavía más bien limitado. Esta tesis se enmarca en el programa general de estudio de la estructura espacios libres Lipschitz genéricos. Empezamos nuestro estudio desarrollando algunas herramientas básicas para la teoría general de espacios libres Lipschitz. Primero definimos operadores de ponderación en espacios Lipschitz y los usamos para demostrar la conjetura de Weaver de que todos los funcionales normales del bidual F(M)** son débil* continuos. A continuación demostramos el teorema de la intersección, que en esencia dice que la intersección de espacios libres Lipschitz es de nuevo un espacio libre Lipschitz. Este resultado nos permite desarrollar el concepto de soporte de un elemento de F(M), análogo al de soporte de una medida. Además, extendemos el uso de estas herramientas al bidual F(M) y las usamos para establecer una descomposición del bidual en espacios de funcionales que están "concentrados en el infinito" y "separados del infinito", respectivamente. Con estas herramientas en nuestro poder, emprendemos el estudio de dos aspectos concretos de los espacios libres Lipschitz. En primer lugar analizamos la relación entre F(M) y los espacios de medidas sobre M. En particular, obtenemos caracterizaciones de los elementos de F(M) que pueden representarse como la integración con respecto a una medida de Borel (no necesariamente finita) sobre M y viceversa, y probamos que el soporte coincide con el de la medida asociada. También identificamos los espacios métricos M en los cuales todo elemento de F(M) puede ser representado como una medida de Borel. Este análisis se generaliza al bidual F(M)**, utilizando en este caso medidas sobre la compactificación uniforme de M y llegando a resultados similares. Obtenemos también algunas consecuencias para los elementos de F(M) y F(M)** que pueden expresarse como diferencia de dos elementos positivos, como la existencia de un análogo de la descomposición de Jordan para medidas. En segundo lugar, estudiamos la estructura extremal de la bola unidad de F(M) y hacemos algunas contribuciones al programa general consistente en encontrar caracterizaciones puramente geométricas de todos sus elementos extremales. Concretamente, caracterizamos los puntos extremos preservados de la bola, así como aquellos puntos extremos y expuestos que tienen soporte finito. Además damos una descripción completa de la estructura extremal de la parte positiva de la bola unidad. La teoría de los soportes en F(M) desarrollada anteriormente juega un papel crucial en las demostraciones de estos resultados. / [CA] Els espais lliures Lipschitz F(M) són linearitzacions canòniques d'espais mètrics M qualssevol. Més concretament, F(M) és l'únic espai de Banach que conté una còpia isomètrica de M que és linealment densa, i tal que tota aplicació Lipschitz de M en qualsevol espai de Banach X pot ser estesa a un operador lineal continu de F(M) en X. Aquests espais són una eina molt potent per a l'estudi de la geometria no lineal d'espais de Banach, ja que permeten l'aplicació de les tècniques lineals clàssiques, ben conegudes, a problemes no lineals. Però aquest esforç nomes val la pena si es disposa d'un coneixement bastant detallat de l'estructura de F(M). L'estudi sistemàtic dels espais lliures Lipschitz és bastant recent i, per això, aquest coneixement és encara prou limitat. Aquesta tesi s'emmarca en el programa general d'estudi de l'estructura dels espais lliures Lipschitz genèrics. Comencem el nostre estudi desenvolupant algunes eines bàsiques per a la teoria general d'espais lliures Lipschitz. Primer definim operadors de ponderació en espais Lipschitz i els fem servir per demostrar la conjectura de Weaver que tots els funcionals normals del bidual F(M)** son feble* continus. A continuació demostrem el teorema de la intersecció, que en essència diu que la intersecció d'espais lliures Lipschitz és de nou un espai lliure Lipschitz. Aquest resultat ens permet desenvolupar el concepte de suport d'un element de F(M), anàleg al de suport d'una mesura. A més, estenem l'ús d'aquestes eines al bidual F(M)** i les fem servir per establir una descomposició del bidual en espais de funcionals que estan "concentrats a l'infinit" i "separats de l'infinit", respectivament. Amb aquestes eines al nostre abast, emprenem l'estudi de dos aspectes concrets dels espais lliures Lipschitz. En primer lloc, analitzem la relació entre F(M) i els espais de mesures sobre M. En particular, obtenim caracteritzacions dels elements de F(M) que poden representar-se com la integració respecte a una mesura de Borel (no necessàriament finita) sobre M i viceversa, i provem que el suport coincideix amb el de la mesura associada. També identifiquem els espais mètrics M on tot element de F(M) pot ser representat com una mesura de Borel. Aquesta anàlisi es generalitza al bidual F(M)**, utilitzant en aquest cas mesures sobre la compactificació uniforme de M i arribant a resultats similars. També obtenim algunes conseqüències per als elements de F(M) i F(M)** que poden expressar-se com a diferència de dos elements positius, com ara l'existència d'un anàleg de la descomposició de Jordan per a mesures. En segon lloc, estudiem l'estructura extremal de la bola unitat de F(M) i fem algunes contribucions al programa general consistent en trobar caracteritzacions purament geomètriques de tots els seus elements extremals. Concretament, caracteritzem els punts extrems preservats de la bola, així com aquells punts extrems i exposats que tenen suport finit. A més fem una descripció completa de l'estructura extremal de la part positiva de la bola unitat. La teoria dels suports en F(M) desenvolupada anteriorment juga un paper crucial en les demostracions d'aquests resultats. / [EN] Lipschitz-free spaces F(M) are canonical linearizations of arbitrary complete metric spaces M. More specifically, F(M) is the unique Banach space that contains an isometric copy of M that is linearly dense, and such that any Lipschitz mapping from M into some Banach space X extends to a bounded linear operator from F(M) into X. Those spaces are a very powerful tool for studies of the nonlinear geometry of Banach spaces, as they allow the application of well-known classical linear techniques to nonlinear problems. But this effort is only worthwhile if we have sufficient knowledge about the structure of F(M). The systematic study of Lipschitz-free spaces is rather recent and so the current understanding of their structure is still quite limited. This thesis is framed within the general program of studying the structure of general Lipschitz-free spaces. We start our study by developing some basic tools for the general theory of Lipschitz-free spaces. First we introduce weighting operators and use them to solve Weaver's conjecture that all normal functionals in the bidual F(M)** are weak* continuous. Next we prove the intersection theorem, which essentially says that the intersection of Lipschitz-free spaces is again a Lipschitz-free space. That result allows us to develop the concept of support of an element of F(M), analogous to the support of a measure. Furthermore, we extend the use of these tools to the bidual F(M)** and apply them to establish a decomposition of the bidual into spaces of functionals that are "concentrated at infinity" and "separated from infinity", respectively. With these tools at our disposal, we undertake the study of two particular aspects of Lipschitz-free spaces. First we analyze the relationship between F(M) and spaces of measures on M. In particular, we obtain characterizations of those elements of F(M) that can be represented as integration against a (not necessarily finite) Borel measure on M and vice versa, and we show that their supports agree. We also identify those metric spaces such that every element of F(M) can be represented by a Borel measure. This analysis is generalized to the bidual F(M)**, using measures on the uniform compactification of M in that case and obtaining similar results. We also derive some consequences for those elements of F(M) and F(M)** that can be expressed as the difference between two positive elements, such as the existence of an analog of the Jordan decomposition for measures. Secondly, we study the extremal structure of the unit ball of F(M) and provide some contributions to the general program of finding purely geometric characterizations of all of its extremal elements. Namely, we characterize all of its preserved extreme points, and its extreme and exposed points of finite support. We also give a full description of the extremal structure of the positive unit ball. The theory of supports developed previously plays a crucial role in the proofs of these results / The author would like to thank Marek Cúth, Michal Doucha, Antonio José Guirao, Gilles Lancien and Eva Pernecká for their careful reading and correction of this document or parts of it. Some activities related to this thesis were partially supported by the Spanish Ministry of Economy, Industry and Competitiveness under Grant MTM2017-83262-C2-2-P, and by a travel grant of the Institute of Mathematics (IEMath-GR) of the University of Granada. Part of this research was conducted during visits to the Czech Technical University in Prague in 2018 and 2020, the Laboratoire de Mathématiques de Besançon in 2019, and the University of Granada in 2020. The author wishes to express his gratitude for the hospitality and the excellent working conditions during his visits. / Aliaga Varea, RJ. (2020). Geometry and structure of Lipschitz-free spaces and their biduals [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/159256

Yes / Satellite QKD/FSO systems, which facilitate quantum key distribution (QKD) over free-space optical (FSO) links between satellites and ground stations, present a promising pathway toward achieving global security in upcoming sixth-generation (6G) wireless communications. Our study focuses on a superior type of these systems, the satellite EB/CV-QKD/FSO, which utilizes the continuous-variable (CV) method for quantum state representation and the entanglement-based (EB) scheme for QKD implementation. We propose the use of optical phase-shift keying (QPSK) signaling and dual-threshold/heterodyne detection (DT/HD) receivers to bolster the reliability and feasibility of satellite EB/CV-QKD/FSO systems. Closed-form expressions for key system performance metrics are derived using improved channel modeling. Numerical results are presented to showcase the effects of channel impairments on the system performance. We also provide recommendations for optimal system setup parameters, aiming to enhance performance. / Ministry of Information and Communications (Vietnam) (Grant Number: DT.26/23). Asia Pacific Network Information Centre (APNIC) Foundation under the Switch! Project

Die Quantenschlüsselverteilung (QKD), die erste anwendbare Quantentechnologie, verspricht informationstheoretisch sichere Kommunikation. In der vorliegenden Arbeit wurde das Zeit-Frequenz (TF)-QKD-Protokoll untersucht, das Zeit und Frequenz, nämlich Puls-Positionsmodulation (PPM) im Zeitbereich und Frequenzumtastung (FSK) im Frequenzbereich als die beiden komplementären Basen verwendet. Seine Sicherheit beruht den Quanteneigenschaften von Licht und auf der Zeit-Frequenz-Unschärferelation. TF-QKD kann mit größtenteils Standard-Telekommunikationstechnologie im 1550-nm-Band implementiert werden. Die PPM-Basis kann mit Modulatoren und die FSK-Basis mit Hilfe der Wellenlängenmultiplex-Technologie realisiert werden. Das TF-QKD-Protokoll ist in der Lage, ein beliebig großes Alphabet bereitzustellen, was mehr als 1 bit/Photon ermöglicht. Darüber hinaus ist es robust gegenüber athmosphärischen Störungen und somit für die Übertragung über den Freiraumkanal geeignet. In der vorliegenden Arbeit wird das TF-QKD-Protokoll theoretisch bewertet, mit Standardkomponenten für 1 bit/Photon implementiert und die Freiraumübertragung mit optischem Tracking über eine 388 m Teststrecke wird bei Tageslicht demonstriert. Unter Verwendung der vorhandenen Komponenten konnte eine sichere Schlüsselrate von 364 kbit/s back-to-back und 9 kbit/s über den Freiraumkanal demonstriert werden. / Quantum key distribution (QKD), the first applicable quantum technology, promises information theoretically secure communication. In the presented work the time-frequency (TF)-QKD protocol was examined, which uses time and frequency, namely pulse position modulation (PPM) in the time domain and frequency shift keying (FSK) in the frequency domain as the two complementary bases. Its security relies on the quantum properties of light and the time-frequency uncertainty relation. TF-QKD can be implemented mostly with standard telecom-technology in the 1550 nm band. The PPM basis can be implemented with modulators and the FSK basis with help of wavelength-division multiplexing technology. The TF-QKD protocol is capable of providing an arbitrarily large alphabet enabling more than 1 bit/photon. Moreover, it is robust in the atmosphere making it suitable for transmission over the free-space channel. In the present work the TF-QKD protocol is assessed theoretically, implemented with off-the-shelf components for 1 bit/photon and free-space transmission with optical tracking over a 388 m testbed is demonstrated in daylight. Using components at hand, secret key rates of 364 kbit/s back-to-back and 9 kbit/s over the free-space channel could be demonstrated.

[pt] Este trabalho apresenta o estudo de comunicação óptica quântica no infravermelho, utilizando um sistema híbrido fibra-óptica – espaço-livre, como prova de princípio para o estabelecimento de chaves secretas a fim de utilização em criptografia do tipo one-time pad. Ao modular a polarização da luz de um laser em polarizações ortogonais, podem-se codificar os bits clássicos 1 e 0 em cada uma dessas polarizações, sendo detectadas por detectores contadores de fótons únicos, e, assim, utilizar o canal quântico para transmissão dos bits quânticos entre dois interlocutores, utilizandoos para o estabelecimento da chave criptográfica, que pode ser usada em qualquer tipo de informação a ser transmitida por um canal clássico ou quântico. Ao realizar a transmissão em espaço-livre, sujeita a variações climáticas, como temperatura atmosférica, luz solar, presença de nuvens, chuva e vento, foi também estudada a influência destes fenômenos na qualidade da transmissão e dos dados obtidos. Os resultados experimentais demonstraram consistência com a teoria e com outros trabalhos publicados na área até esta data com relação às taxas de erro de bit quântico e também à taxa de transmissão de bits. As taxas de erro obtidas, por estarem abaixo do limiar teórico para segurança da informação em comunicação quântica, provam, ainda, a possibilidade de estabelecimento de chave secreta para criptografia através do uso de distribuição quântica das chaves (QKD). Os resultados também apresentaram boa qualidade da informação recuperada após a descriptografia. / [en] This work presents the study of optical quantum communication in the infrared region, using a hybrid optical-fiber – free-space system, as proof of principle for the agreement on secret keys by two parties for use in one-time pad encryption. By modulating the polarization of laser light into orthogonal polarizations, one can encode the classic bits 1 and 0 in each of these polarizations, being detected by single photon counter detectors, and can use the quantum channel to transmit the quantum bits between two interlocutors. It is then possible to use those bits to establish the cryptographic key, which can be used in any type of information to be transmitted by a classic or quantum channel. While carrying out transmission in free space optics, subject to climatic variations, such as atmospheric temperature, sunlight, presence of clouds and rain, and the presence of wind, the influence of these phenomena on the quality of transmission and on the data obtained was also studied. The experimental results showed consistency with the theory and with other works published to date with regard to quantum bit error rates and to the bit rate. The error rates obtained, being below the theoretical threshold for information security in quantum communication, further proves the possibility of establishing a secret key for encryption through the use of quantum key distribution (QKD). It also presented good quality on the information recovered after decryption.

Cette thèse porte sur la caractérisation non destructive de structures 2D magnéto-diélectriques inhomogènes complexes. L’ensemble des étapes allant de l’expérience au traitement du problème inverse est traité. Dans un premier temps, un modèle direct reliant le champ diffusé aux propriétés électromagnétiques du matériau a été mis en place. Ce modèle requiert des calculs par éléments finis de la propagation de l’onde électromagnétique, en présence de l’objet observé lorsque celui-ci est positionné sur un support métallique. Une validation expérimentale a été réalisée via la mise en place d'un banc de mesure multi statique. Différentes étapes d'ajustements et d'étalonnages ont permis la réduction du bruit de mesure ainsi que des biais. L’inversion est traitée principalement par une approche linéaire, avec un choix attentif de la valeur des hyper paramètres qui y sont associés. Une fois les outils mis en place, six études ont été réalisées pour la validation de notre système d’imagerie 2D des propriétés électromagnétiques de matériaux magnéto-diélectriques inhomogènes. Cela comprend l’évaluation des incertitudes de mesure, de la résolution spatiale, la mesure de différents matériaux magnétiques et l’utilisation de différents supports à géométries variées. L’ensemble des résultats expérimentaux réalisés se place dans une hypothèse de géométrie 2D. C’est pourquoi, nous avons ensuite orienté nos travaux vers la recherche d’un design innovant permettant de faire évoluer le banc de mesure en un dispositif d’imagerie 3D. Dans cette perspective, une source secondaire vient se déplacer proche de la cible pour acquérir de l’information selon la troisième dimension. / The subject of this thesis is the non-destructive characterization of complex inhomogeneous magneto-dielectric structures. Successively, the experimental developments, the modelling and the data treatments stages are addressed. A forward model that links the scattered field to the electromagnetic properties is established. This model requires some finite element computations in order to estimate the propagation of the electromagnetic wave in presence of the magneto-dielectric object which is glued on a metallic support. A multistatic bench has been designed and constructed in order to collect measured scattered fields. Several adjustments and calibration procedures have been carried out to reduce the measurement noise and biases. Next, the inverse problem has been dealt with, in order to retrieve the electromagnetic properties of the samples, from the measured scattered field. The inverse problem is mainly solved with a linear approach, with a careful selection of the hyperparameters. Once the system has been fine tuned, six studies have been realized to validate our 2D imaging system. The assessment of the measurement uncertainty, the evaluation of the spatial resolution, the characterization of various magnetics materials and the use of different supports with variable geometries have been performed. So far, all the developments were done under a 2D hypothesis. That is why, we have then focused our research on the design of a 3D innovative imaging setup. To this end, a secondary source moving close to the target has been added in order to gain information in the third direction. A numerical study has been performed to assess the expected performances of this new setup.

We present robust explicit construction of 3D configuration spaces using controlled linear perturbation. The input is two planar parts: a fixed set and a moving set, where each set is bounded by circle segments. The configuration space is the three-dimensional space of Euclidean transformation (translations plus rotations) of the moving set relative to the fixed set. The goal of constructing the 3D configuration space is to determine the boundary representation of the free space where the intersection of the moving set and fixed set is empty. To construct the configuration space, we use the controlled linear perturbation algorithm. The controlled linear perturbation algorithm assigns function signs that are correct for a nearly minimal input perturbation. The output of the algorithm is a consistent set of function signs. This approach is algorithm-independent, and the overhead over traditional floating point methods is reasonable. If the fixed and moving sets are computer representations of physical objects, then computing the configuration space greatly aids in many computational geometry problems. The main focus of computing the configuration space is for the path planning problem. We must find if a path exists from the start to the goal, where the fixed set is the obstacle, and the moving set is the object trying to reach the goal.

No description available.

Made available in DSpace on 2014-12-17T15:48:12Z (GMT). No. of bitstreams: 1 LeonardoDO_DISSERT.pdf: 3357434 bytes, checksum: 75c2c837997e2220e8de164c844c9b5d (MD5) Previous issue date: 2014-06-05 / Due to the constantly increasing use of wireless networks in domestic, business and industrial environments, new challenges have emerged. The prototyping of new protocols in these environments is typically restricted to simulation environments, where there is the need of double implementation, one in the simulation environment where an initial proof of concept is performed and the other one in a real environment. Also, if real environments are used, it is not trivial to create a testbed for high density wireless networks given the need to use various real equipment as well as attenuators and power reducers to try to reduce the physical space required to create these laboratories. In this context, LVWNet (Linux Virtual Wireless Network) project was originally designed to create completely virtual testbeds for IEEE 802.11 networks on the Linux operating system. This paper aims to extend the current project LVWNet, adding to it the features like the ability to interact with real wireless hardware, provides a initial mobility ability using the positioning of the nodes in a space coordinates environment based on meters, with loss calculations due to attenuation in free space, enables some scalability increase by creating an own protocol that allows the communication between nodes without an intermediate host and dynamic registration of nodes, allowing new nodes to be inserted into in already in operation network / Com o crescimento constante da utiliza??o de redes sem fio em ambientes dom?sticos, empresariais e at? industriais, aparecem novos desafios. A prototipa??o de novos protocolos nesses ambientes tipicamente ? restrita a ambientes de simula??o, onde existe a necessidade de uma dupla implementa??o, uma no ambiente de simula??o, onde se realiza uma prova de conceito inicial e outra em um ambiente real. Al?m disso, uma vez que se parta para ambientes reais, n?o ? trivial a cria??o de um testbed para redes sem fio de alta densidade, dada a necessidade de uso de v?rios equipamentos reais, e uso de atenuadores, redutores de pot?ncia, para tentar reduzir o espa?o f?sico necess?rio para cria??o desses laborat?rios. Nessa lacuna, o projeto LVWNet (Linux Virtual Wireless Network) foi inicialmente concebido para cria??o de testbeds completamente virtuais para redes IEEE 802.11 sobre o sistema operacional Linux. Este trabalho tem como objetivo extender o atual projeto LVWNet adicionando a ele os recursos de possibilitar a intera??o com hardwares wireless reais, dar um suporte inicial ? mobilidade atrav?s do posicionamento dos n?s em um ambiente de coordenadas no espa?o baseado em metros, j? com c?lculos de perda decorrente da atenua??o em espa?o livre, aumentar a escalabilidade com a cria??o de um mecanismo que permita a comunica??o direta entre os n?s sem necessidade de um host intermedi?rio al?m do registro din?mico de n?s, de modo que novos n?s podem ser inseridos na rede com a mesma j? em opera??o

Le travail de cette thèse est consacré à l’étude et l’optimisation d’un cas particulier de la diffusion des ondes électromagnétiques. Elle porte plus particulièrement sur un phénomène appelé le « jet photonique ou jet électromagnétique (jet EM)». Il s’agit d’un faisceau de lumière étroit et concentré en champ proche avec des caractéristiques physiques remarquables. Dans ce travail, un guide d’onde terminé par un embout de forme particulière est utilisé pour générer le jet photonique. Cette thèse a pour objectif l’étude, la caractérisation expérimentale et l’optimisation de jets photoniques pour des applications dans le domaine optique et hyperfréquences. Une méthode robuste et rapide a été développée pour calculer le champ électromagnétique généré par un objet diélectrique ou en sortie d’un guide d'onde avec un embout de forme particulière. Elle est basée sur la Méthode d'Equation Intégrale aux Frontière (MEIF) qui utilise la seconde identité Green. La caractérisation expérimentale des jets photoniques a été réalisée dans le domaine micro-ondes à des fréquences autour de 30 GHz. La possibilité de générer un jet simple et double en utilisant un guide d’onde à embout a été montrée expérimentalement et théoriquement par la méthode MEIF. Les jets EM simples et doubles ont été utilisés pour la détection d’objets métalliques de taille plus petite que la longueur d’onde et l'imagerie en champ proche à travers des structures optiquement opaques. Une procédure d’optimisation basée sur le couplage entre la MEIF et les algorithmes génétiques a été mise au point afin de générer des jets photoniques avec des caractéristiques a priori bien définie. Des optimisations des jets photoniques générés par un objet diélectrique et en sortie d’un guide d’onde avec embout ont été effectuées pour la micro-gravure laser et l’imagerie HF / The work of this thesis is devoted to the study and optimization of a particular case of the scattering of electromagnetic waves. Particularly, it is about a phenomenon called the "photonic jet or electromagnetic jet (EM jet)". This is a narrow light beam concentrated in near-field with remarkable physical characteristics. In this work, a waveguide terminated by a tip with special form is used to generate the photonic jet. This thesis performs the electromagnetic modeling, the experimental characterization and the optimization of photonic jets for applications in optic and microwave field. A robust and fast method was developed to calculate the electromagnetic field generated by a dielectric object or by a waveguide terminated with a tip. It is based on the boundary integral equation method (BIEM) which uses the second Green identity. Experimental characterization of photonic jets was conducted in the microwave field around 30 GHz. The ability to generate a single and double EM jet using a tipped waveguide has been shown experimentally and theoretically by BEIM method. The single and double EM jets were used for the detection of metal objects with a size smaller than the wavelength and for imaging through opaque structures in near field. An optimization procedure based on the coupling between the BEIM and genetic algorithms has been developed to generate photonic jets with properties well defined. Optimizations of photonic jets generated by a dielectric object and by a tipped waveguide have been realized for laser micro-etching and RF imaging

This Master’s thesis analizes technologies suitable for metropolitan area networks. In this thesis there are mentioned technologies used for wireless transfer with speeds above 1 Gbps. There are described basic features and parameters of microwave radio relay links in 70/80GHz range and free space optic links. These technologies are compared with classic optical networks. Practical part of thesis was focused on development of application which calculates signal attenuation caused by the passage of the atmosphere for both technologies. Results gained from this application are mentioned in this Master’s thesis.