Colouring random graphs and maximising local diversity

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.Comment: 10 pages, 10 figure

An exact dynamic programming approach to segmented isotonic regression

This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on dynamic programming and is built on the basis that said curve-fitting task can be tackled as a shortest-path type of problem. Numerical results on synthetic and realistic data sets reveal that our algorithm is able to provide the globally optimal monotone stepwise curve fit for samples with thousands of data points in less than a few hours. Furthermore, the algorithm gives a certificate on the optimality gap of any incumbent solution it generates. From a practical standpoint, this piece of research is motivated by the roll-out of smart grids and the increasing role played by the small flexible consumption of electricity in the large-scale integration of renewable energy sources into current power systems. Within this context, our algorithm constitutes an useful tool to generate bidding curves for a pool of small flexible consumers to partake in wholesale electricity markets.This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 755705). This work was also supported in part by the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (ERDF) through project ENE2017-83775-P. Martine Labbé has been partially supported by the Fonds de la Recherche Scientifique - FNRS under Grant(s) no PDR T0098.18

Exploiting graph structure in Active SLAM

Aplicando análisis provenientes de la teoría de grafos, la teoría espectral de grafos, la exploración de grafos en línea, generamos un sistema de SLAM activo que incluye la planificación de rutas bajo incertidumbre, extracción de grafos topológicos de entornos y SLAM activo \'optimo.En la planificación de trayectorias bajo incertidumbre, incluimos el análisis de la probabilidad de asociación correcta de datos. Reconociendo la naturaleza estocástica de la incertidumbre, demostramos que planificar para minimizar su valor esperado es más fiable que los actuales algoritmos de planificación de trayectorias con incertidumbre.Considerando el entorno como un conjunto de regiones convexas conectadas podemos tratar la exploración robótica como una exploración de grafos en línea. Se garantiza una cobertura total si el robot visita cada región. La mayoría de los métodos para segmentar el entorno están basados en píxeles y no garantizan que las regiones resultantes sean convexas, además pocos son algoritmos incrementales. En base a esto, modificamos un algoritmo basado en contornos en el que el entorno se representa como un conjunto de polígonos que debe segmentarse en un conjunto de polígonos pseudo convexos. El resultado es un algoritmo de segmentación que produjo regiones pseudo-convexas, robustas al ruido, estables y que obtienen un gran rendimiento en los conjuntos de datos de pruebas.La calidad de un algoritmo se puede medir en términos de cuan cercano al óptimo está su rendimiento. Con esta motivación definimos la esencia de la tarea de exploración en SLAM activo donde las únicas variables son la distancia recorrida y la calidad de la reconstrucción. Restringiendo el dominio al grafo que representa el entorno y probando la relación entre la matriz asociada a la exploración y la asociada al grafo subyacente, podemos calcular la ruta de exploración óptima.A diferencia de la mayoría de la literatura en SLAM activo, proponemos que la heurística para la exploración de grafos consiste en atravesar cada arco una vez. Demostramos que el tipo de grafos resultantes tiene un gran rendimiento con respecto a la trayectoria \'optima, con resultados superiores al 97 \% del \'optimo en algunas medidas de calidad.El algoritmo de SLAM activo TIGRE integra el algoritmo de extracción de grafos propuesto con nuestra versión del algoritmo de exploración incremental que atraviesa cada arco una vez. Nuestro algoritmo se basa en una modificación del algoritmo clásico de Tarry para la búsqueda en laberintos que logra el l\'imite inferior en la aproximación para un algoritmo incremental. Probamos nuestro sistema incremental en un escenario de exploración típico y demostramos que logra un rendimiento similar a los métodos fuera de línea y también demostramos que incluso el método \'optimo que visita todos los nodos calculado fuera de línea tiene un peor rendimiento que el nuestro.<br /

Navigability and synchronization in complex networks: a computational approach

Les xarxes complexes han demostrat ser una eina molt valuosa per estudiar sistemes reals, en part, gràcies a la creixent capacitat de computació. En aquesta tesi abordem computacionalment diversos problemes dividits en dos blocs. El primer bloc està motivat pels problemes que planteja la ràpida evolució de la Internet. D’una banda, el creixement exponencial de la xarxa està comprometent la seva escalabilitat per les dependències a les taules d’enrutament globals. Al Capítol 4 proposem un esquema d’enrutament descentralitzat que fa servir la projecció TSVD de l’estructura mesoscòpica de la xarxa com a mapa. Els resultats mostren que fent servir informació local podem guiar amb èxit en l’enrutament. Al Capítol 3 també avaluem la fiabilitat d’aquesta projecció davant el creixement de la xarxa. Els resultats indiquen que aquest mapa és robust i no necessita actualitzacions contínues. D’altra banda, la creixent demanda d’ample de banda és un factor potencial per produir congestió. Al Capítol 5 estenem un esquema d’enrutament dinàmic en el context de les xarxes multiplex, i l’analitzem amb xarxes sintètiques amb diferents assortativitats d’acoblament. Els resultats mostren que tenir en compte el volum de trànsit en l’enrutament retarda l’inici de la congestió. Tot i això, la distribució uniforme del trànsit produeix una transició de fase abrupta. Amb tot, l’acoblament assortatiu es presenta com la millor opció per a dissenys de xarxes òptimes. El segon bloc ve motivat per l’actual crisi financera mundial. Al Capítol 6 proposem estudiar la propagació de les crisis econòmiques utilitzant un model simple de xarxa formada per oscil·ladors integrate-and-fire, i caracteritzar la seva sincronització durant l’evolució de la xarxa de comerç. Els resultats mostren l’aparició d’un procés de globalització que dilueix les fronteres topològiques i accelera la propagació de les crisis financeres.Las redes complejas han demostrado ser una herramienta muy valiosa para estudiar sistemas reales, en parte, gracias a la creciente capacidad de computación. En esta tesis abordamos computacionalmente varios problemas divididos en dos bloques. El primer bloque está motivado por los problemas que plantea la rápida evolución de Internet. Por un lado, el crecimiento exponencial de la red está comprometiendo su escalabilidad por las dependencias a las tablas de enrutado globales. En el Capítulo 4 proponemos un esquema de enrutamiento descentralizado que utiliza la proyección TSVD de la estructura mesoscópica de la red como mapa. Los resultados muestran que utilizando información local podemos guiar con éxito el enrutado. En el Calítulo 3 también evaluamos la fiabilidad de esta proyección bajo cambios en la topología de la red. Los resultados indican que este mapa es robusto y no necesita actualizaciones continuas. Por otra parte, la creciente demanda de ancho de banda es un factor potencial de congestión. En el Capítulo 5 extendemos un esquema de enrutamiento dinámico en el marco de las redes multiplex, y lo analizamos en redes sintéticas con distintas asortatividades de acoplamiento. Los resultados muestran que tener en cuenta el volumen de tráfico en el enrutado retrasa la congestión. Sin embargo, la distribución uniforme del tráfico produce una transición de fase abrupta. Además, el acoplamiento asortativo se presenta como la mejor opción para diseños de redes óptimas. El segundo bloque viene motivado por la actual crisis financiera mundial. En el Capítulo 6 proponemos estudiar la propagación de las crisis económicas utilizando un modelo simple de red formada por osciladores integrate-and-fire, y caracterizar su sincronización durante la evolución de la red de comercio. Los resultados muestran la aparición de un proceso de globalización que diluye las fronteras topológicas y acelera la propagación de las crisis financieras.Complex networks are a powerful tool to study many real systems, partly thanks to the increasing capacity of computational resources. In this dissertation we address computationally a broad scope of problems that are framed in two parts. The first part is motivated by the issues posed by the rapid evolution of the Internet. On one side, the exponential growth of the network is compromising its scalability due to dependencies on global routing tables. In Chapter 4 we propose a decentralized routing scheme that exploits the TSVD projection of the mesoscopic structure of the network as a map. The results show that, using only local information, we can achieve good success rates in the routing process. Additionally, Chapter 3 evaluates the reliability of this projection when network topology changes. The results indicate that this map is very robust and does not need continual updates. On the other side, the increasing bandwidth demand is a potential trigger for congestion episodes. In Chapter 5 we extend a dynamic traffic-aware routing scheme to the context of multiplex networks, and we conduct the analysis on synthetic networks with different coupling assortativity. The results show that considering the traffic load in the transmission process delays the congestion onset. However, the uniform distribution of traffic produces an abrupt phase transition from free-flow to congested state. Withal, assortative coupling is depicted as the best consideration for optimal network designs. The second part is motivated by the current global financial crises. Chapter 6 presents a study on the spreading of economic crises using a simple model of networked integrate-and-fire oscillators and we characterize synchronization process on the evolving trade network. The results show the emergence of a globalization process that dilutes the topological borders and accelerates the spreading of financial crashes

Charged-hadrons production in pp and A-A collisions and characterization of the components for the upgrade of the Inner Tracking System of the ALICE experiment at LHC

L'abstract è presente nell'allegato / the abstract is in the attachmen

Angular resolution improvement of slumped thin glass optics for x-ray telescopes.

Current X-ray telescopes such as Chandra and XMM were designed and built to privilege the angular resolution or the collecting area respectively, but using two different manufacturing techniques, and these two key aspects could not be optimised at the same time. The result is that the high-redshift X-ray Universe is still too unresolved to provide us with the understanding of the time evolution of the universe as we see it nowadays. Now the ATHENA mission, approved for the L2 slot in the Cosmic Vision program, is required to have an effective area of 2 m2 at 1 keV and an angular resolution better than 5 arcsec Half-Energy Width (HEW). At this regard, in addition to the baseline solution based on Silicon Pore Optics (SPO), thin glass foils are considered a viable alternative. Slumped glass foils are also considered as substrates for X-ray optics being developed in other projects; for example, the X-ray Surveyor mission being developed at SAO/CfA in USA, and the AXYOM project being developed in Italy. They both foresee the use of piezo-electric actuators to correct the shape errors of the mirrors. The Brera Astronomical Observatory (INAF-OAB, Merate - Italy) has been working, from 2009 till 2013, under ESA contract aimed to develop in Europe a Slumped Glass Optics (SGO) technology, alternative to the one based on silicon pores, and based on the slumping of thin glass foils, in parallel to the work being carried out at NASA/GSFC and other institutes. The INAFOAB innovation is the use of pressure in the hot slumping process to replicate the mould figure. This technology is coupled with an integration process able to damp low frequency errors. My Ph.D. activity, carried out at the INAF-OAB, is devoted to the advancement in the hot slumping technology assisted by pressure, for the production of glass mirrors for future X-ray telescopes. As a preliminary work, I have developed a new method to precisely characterise the mid frequency errors of the glass foils. An existing model, developed by Jimenez-Garate in 2003 to account for the relaxation of ripples in the slumped glass foil when in contact with the slumping mould, was modified to include the application of pressure, and the model was compared to the experimental results. The pressure was found to be essential, also from the the theory viewpoint, to reduce mid-frequency errors in the profile of slumped glass foils, which crucially degrade the performances of the optics. As for the slumping process, I have introduced a new glass material (Corning Eagle XG) combined with the Schott Zerodur K20, already chosen at earlier times as slumping mould material for its anti-sticking properties. I have developed cleaning protocols, used different thermal cycles and different pressures conditions, and reconditioned the pressure control system. I have also optimised the mould height with experiments based on Finite Element Analysis, and reduced the thermal gradients inside the mould and the glass foils. The final result obtained in this research are slumped glass foils with angular resolution improved from the initial 7 arcsec to 2.2\ub10.3 arcsec in single reflection, as expected from metrology at 1 keV X-ray energy and 0.7 incidence angle, and computed by simulating a perfect integration. This result has to be compared with 2 arcsec defined as the error budget allocated for the slumped glass foils. About 1 arcsec is due to replication of the mid-frequency errors in the slumping mould which, owing to the improved result in the slumping, are now a limiting factor in the quality of the slumped glass foils. From the roughness point of view, the contribution to the HEW is guaranteed to be less then 1 arcsec at 1 keV, with an rms improvement from 21 to 11 \uc5 throughout my Ph.D. Moreover, the last tests carried out proved that the roughness of the slumped glass foils can be further reduced to _ 7 \uc5, making the technology attractive also for higher X-ray energies and higher incidence angles. The glass foils slumped during this Ph.D. have been used for the production of two SGO Proof Of Concept prototypes (POC) for the ATHENA mission: the POC#3, (with 2 glass foils assembled) is characterised by HEW value of 5.5 arcsec at 0.27 keV in the best portion of the module, as tested at the PANTER facility; the POC#4 (with 8 glass foils) has expected HEW of about 15 arcsec from metrological data, but the result in X-ray was much higher because of accidental problems during the integration. The next prototype, the POC#5 (with the best eight glass foils produced during my Ph.D. activity), will soon be integrated and tested in X-rays, to assess the improvement already proven by metrology and simulations. Some of the produced slumped glass foils have also been used for studies of active profile corrections with piezoelectric elements, both for the AXYOM project and X-ray Surveyor mission. Alternative materials and techniques have been used in this research to further improve the result. To reduce the surface micro-roughness of the slumped glass foils, I have proven that the slumping technique with pressure application can also be suited in the indirect slumping, in which the optical surface of the glass is not in contact with the mould, thus preserving its initial surface smoothness. Moreover, the dip coating technique was studied to fill the micro-pores present on the surface of the glass foils slumped with the direct technique. Alternative materials for the slumping mould were tested, defining Si3N4 as a very promising candidate, owing to its higher rigidity with respect to Zerodur K20 and therefore preferable to avoid mould deformations with the slumping, as experienced with K20. The Gorilla glass (normally used for smartphones and tablets), was proven to preserve the surface quality of the glass foils, once slumped and chemically tempered to increase the mirror endurance against the vibrations experienced at launch. Finally, I have also studied the scattering and the reflectivity properties of multilayer coatings for X-ray optics. I have upgraded an IDL code to simulate the roughness growth in the multilayer deposition process, extending the computations from periodic to the more general case of graded multilayers. I have also contributed to the X-ray measurements at the BEAR beamline of the Elettra synchrotron in Trieste, on multilayers deposited on glass, silicon and electroformed nickel, for the polarimetric LAMP projec