On some sampling-related frames in U-invariant spaces

This paper concerns the characterization as frames of some sequences in U-invariant spaces of a separable Hilbert space H where U denotes an unitary operator defined on H ; besides, the dual frames having the same form are also found. This general setting includes, in particular, shift-invariant or modulation-invariant subspaces in L2 (R), where these frames are intimately related to the generalized sampling problem. We also deal with some related perturbation problems. In so doing, we need that the unitary operator U belongs to a continuous group of unitary operators.

NFC based remote control of services for interactive spaces

Ubiquitous computing (one person, many computers) is the third era in the history of computing. It follows the mainframe era (many people, one computer) and the PC era (one person, one computer). Ubiquitous computing empowers people to communicate with services by interacting with their surroundings. Most of these so called smart environments contain sensors sensing users’ actions and try to predict the users’ intentions and necessities based on sensor data. The main drawback of this approach is that the system might perform unexpected or unwanted actions, making the user feel out of control. In this master thesis we propose a different procedure based on Interactive Spaces: instead of predicting users’ intentions based on sensor data, the system reacts to users’ explicit predefined actions. To that end, we present REACHeS, a server platform which enables communication among services, resources and users located in the same environment. With REACHeS, a user controls services and resources by interacting with everyday life objects and using a mobile phone as a mediator between himself/herself, the system and the environment. REACHeS’ interfaces with a user are built upon NFC (Near Field Communication) technology. NFC tags are attached to objects in the environment. A tag stores commands that are sent to services when a user touches the tag with his/her NFC enabled device. The prototypes and usability tests presented in this thesis show the great potential of NFC to build such user interfaces.

Análisis y modelización de la dinámica emergente durante el proceso de difusión de información en las redes sociales de internet

Durante la actividad diaria, la sociedad actual interactúa constantemente por medio de dispositivos electrónicos y servicios de telecomunicaciones, tales como el teléfono, correo electrónico, transacciones bancarias o redes sociales de Internet. Sin saberlo, masivamente dejamos rastros de nuestra actividad en las bases de datos de empresas proveedoras de servicios. Estas nuevas fuentes de datos tienen las dimensiones necesarias para que se puedan observar patrones de comportamiento humano a grandes escalas. Como resultado, ha surgido una reciente explosión sin precedentes de estudios de sistemas sociales, dirigidos por el análisis de datos y procesos computacionales. En esta tesis desarrollamos métodos computacionales y matemáticos para analizar sistemas sociales por medio del estudio combinado de datos derivados de la actividad humana y la teoría de redes complejas. Nuestro objetivo es caracterizar y entender los sistemas emergentes de interacciones sociales en los nuevos espacios tecnológicos, tales como la red social Twitter y la telefonía móvil. Analizamos los sistemas por medio de la construcción de redes complejas y series temporales, estudiando su estructura, funcionamiento y evolución en el tiempo. También, investigamos la naturaleza de los patrones observados por medio de los mecanismos que rigen las interacciones entre individuos, así como medimos el impacto de eventos críticos en el comportamiento del sistema. Para ello, hemos propuesto modelos que explican las estructuras globales y la dinámica emergente con que fluye la información en el sistema. Para los estudios de la red social Twitter, hemos basado nuestros análisis en conversaciones puntuales, tales como protestas políticas, grandes acontecimientos o procesos electorales. A partir de los mensajes de las conversaciones, identificamos a los usuarios que participan y construimos redes de interacciones entre los mismos. Específicamente, construimos una red para representar quién recibe los mensajes de quién y otra red para representar quién propaga los mensajes de quién. En general, hemos encontrado que estas estructuras tienen propiedades complejas, tales como crecimiento explosivo y distribuciones de grado libres de escala. En base a la topología de estas redes, hemos indentificado tres tipos de usuarios que determinan el flujo de información según su actividad e influencia. Para medir la influencia de los usuarios en las conversaciones, hemos introducido una nueva medida llamada eficiencia de usuario. La eficiencia se define como el número de retransmisiones obtenidas por mensaje enviado, y mide los efectos que tienen los esfuerzos individuales sobre la reacción colectiva. Hemos observado que la distribución de esta propiedad es ubicua en varias conversaciones de Twitter, sin importar sus dimensiones ni contextos. Con lo cual, sugerimos que existe universalidad en la relación entre esfuerzos individuales y reacciones colectivas en Twitter. Para explicar los factores que determinan la emergencia de la distribución de eficiencia, hemos desarrollado un modelo computacional que simula la propagación de mensajes en la red social de Twitter, basado en el mecanismo de cascadas independientes. Este modelo nos permite medir el efecto que tienen sobre la distribución de eficiencia, tanto la topología de la red social subyacente, como la forma en que los usuarios envían mensajes. Los resultados indican que la emergencia de un grupo selecto de usuarios altamente eficientes depende de la heterogeneidad de la red subyacente y no del comportamiento individual. Por otro lado, hemos desarrollado técnicas para inferir el grado de polarización política en redes sociales. Proponemos una metodología para estimar opiniones en redes sociales y medir el grado de polarización en las opiniones obtenidas. Hemos diseñado un modelo donde estudiamos el efecto que tiene la opinión de un pequeño grupo de usuarios influyentes, llamado élite, sobre las opiniones de la mayoría de usuarios. El modelo da como resultado una distribución de opiniones sobre la cual medimos el grado de polarización. Aplicamos nuestra metodología para medir la polarización en redes de difusión de mensajes, durante una conversación en Twitter de una sociedad políticamente polarizada. Los resultados obtenidos presentan una alta correspondencia con los datos offline. Con este estudio, hemos demostrado que la metodología propuesta es capaz de determinar diferentes grados de polarización dependiendo de la estructura de la red. Finalmente, hemos estudiado el comportamiento humano a partir de datos de telefonía móvil. Por una parte, hemos caracterizado el impacto que tienen desastres naturales, como innundaciones, sobre el comportamiento colectivo. Encontramos que los patrones de comunicación se alteran de forma abrupta en las áreas afectadas por la catástofre. Con lo cual, demostramos que se podría medir el impacto en la región casi en tiempo real y sin necesidad de desplegar esfuerzos en el terreno. Por otra parte, hemos estudiado los patrones de actividad y movilidad humana para caracterizar las interacciones entre regiones de un país en desarrollo. Encontramos que las redes de llamadas y trayectorias humanas tienen estructuras de comunidades asociadas a regiones y centros urbanos. En resumen, hemos mostrado que es posible entender procesos sociales complejos por medio del análisis de datos de actividad humana y la teoría de redes complejas. A lo largo de la tesis, hemos comprobado que fenómenos sociales como la influencia, polarización política o reacción a eventos críticos quedan reflejados en los patrones estructurales y dinámicos que presentan la redes construidas a partir de datos de conversaciones en redes sociales de Internet o telefonía móvil. ABSTRACT During daily routines, we are constantly interacting with electronic devices and telecommunication services. Unconsciously, we are massively leaving traces of our activity in the service providers’ databases. These new data sources have the dimensions required to enable the observation of human behavioral patterns at large scales. As a result, there has been an unprecedented explosion of data-driven social research. In this thesis, we develop computational and mathematical methods to analyze social systems by means of the combined study of human activity data and the theory of complex networks. Our goal is to characterize and understand the emergent systems from human interactions on the new technological spaces, such as the online social network Twitter and mobile phones. We analyze systems by means of the construction of complex networks and temporal series, studying their structure, functioning and temporal evolution. We also investigate on the nature of the observed patterns, by means of the mechanisms that rule the interactions among individuals, as well as on the impact of critical events on the system’s behavior. For this purpose, we have proposed models that explain the global structures and the emergent dynamics of information flow in the system. In the studies of the online social network Twitter, we have based our analysis on specific conversations, such as political protests, important announcements and electoral processes. From the messages related to the conversations, we identify the participant users and build networks of interactions with them. We specifically build one network to represent whoreceives- whose-messages and another to represent who-propagates-whose-messages. In general, we have found that these structures have complex properties, such as explosive growth and scale-free degree distributions. Based on the topological properties of these networks, we have identified three types of user behavior that determine the information flow dynamics due to their influence. In order to measure the users’ influence on the conversations, we have introduced a new measure called user efficiency. It is defined as the number of retransmissions obtained by message posted, and it measures the effects of the individual activity on the collective reacixtions. We have observed that the probability distribution of this property is ubiquitous across several Twitter conversation, regardlessly of their dimension or social context. Therefore, we suggest that there is a universal behavior in the relationship between individual efforts and collective reactions on Twitter. In order to explain the different factors that determine the user efficiency distribution, we have developed a computational model to simulate the diffusion of messages on Twitter, based on the mechanism of independent cascades. This model, allows us to measure the impact on the emergent efficiency distribution of the underlying network topology, as well as the way that users post messages. The results indicate that the emergence of an exclusive group of highly efficient users depends upon the heterogeneity of the underlying network instead of the individual behavior. Moreover, we have also developed techniques to infer the degree of polarization in social networks. We propose a methodology to estimate opinions in social networks and to measure the degree of polarization in the obtained opinions. We have designed a model to study the effects of the opinions of a small group of influential users, called elite, on the opinions of the majority of users. The model results in an opinions distribution to which we measure the degree of polarization. We apply our methodology to measure the polarization on graphs from the messages diffusion process, during a conversation on Twitter from a polarized society. The results are in very good agreement with offline and contextual data. With this study, we have shown that our methodology is capable of detecting several degrees of polarization depending on the structure of the networks. Finally, we have also inferred the human behavior from mobile phones’ data. On the one hand, we have characterized the impact of natural disasters, like flooding, on the collective behavior. We found that the communication patterns are abruptly altered in the areas affected by the catastrophe. Therefore, we demonstrate that we could measure the impact of the disaster on the region, almost in real-time and without needing to deploy further efforts. On the other hand, we have studied human activity and mobility patterns in order to characterize regional interactions on a developing country. We found that the calls and trajectories networks present community structure associated to regional and urban areas. In summary, we have shown that it is possible to understand complex social processes by means of analyzing human activity data and the theory of complex networks. Along the thesis, we have demonstrated that social phenomena, like influence, polarization and reaction to critical events, are reflected in the structural and dynamical patterns of the networks constructed from data regarding conversations on online social networks and mobile phones.

Urban voids, spaces of great expectations

Study and progress of urban voids. opportunities for new urban design.

Identification of pore spaces in 3D CT soil images using a PFCM partitional clustering

Recent advances in non-destructive imaging techniques, such as X-ray computed tomography (CT), make it possible to analyse pore space features from the direct visualisation from soil structures. A quantitative characterisation of the three-dimensional solid-pore architecture is important to understand soil mechanics, as they relate to the control of biological, chemical, and physical processes across scales. This analysis technique therefore offers an opportunity to better interpret soil strata, as new and relevant information can be obtained. In this work, we propose an approach to automatically identify the pore structure of a set of 200-2D images that represent slices of an original 3D CT image of a soil sample, which can be accomplished through non-linear enhancement of the pixel grey levels and an image segmentation based on a PFCM (Possibilistic Fuzzy C-Means) algorithm. Once the solids and pore spaces have been identified, the set of 200-2D images is then used to reconstruct an approximation of the soil sample by projecting only the pore spaces. This reconstruction shows the structure of the soil and its pores, which become more bounded, less bounded, or unbounded with changes in depth. If the soil sample image quality is sufficiently favourable in terms of contrast, noise and sharpness, the pore identification is less complicated, and the PFCM clustering algorithm can be used without additional processing; otherwise, images require pre-processing before using this algorithm. Promising results were obtained with four soil samples, the first of which was used to show the algorithm validity and the additional three were used to demonstrate the robustness of our proposal. The methodology we present here can better detect the solid soil and pore spaces on CT images, enabling the generation of better 2D?3D representations of pore structures from segmented 2D images.

Challenges for future of Natural Spaces of Canary Islands, Spain

The preservation of biodiversity is a fundamental objective of a ll policies related to a more sustainable development in any modern society. The rain forest and pine forests are two unique Canarian ecosystems with high importance to global biodiversity, holding a large number of endemic species and subspecies that is a priority to preserve. In this work the challenges that will face the natural areas of the Canary Islands are studied, as well as their fundamental value for economic and environmental development of the islands.

Numerical issues in Lagrangian tracking and topological evolution of fluid particles in wallbounded turbulent flows

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.