Graphs and Groups

This project is a combination of graphs and group theory in which the aim is to describe the automorphism group of some specific families of graphs. Finally, an example of the application of automorphism groups in reaction graphs is shown. The project is written in english.

Visualización interactiva de grafos con el programa Xglore

[ES] El presente manual describe el manejo de grafos de forma interactiva en el entorno 3D que proporciona el programa Xglore (http://sourceforge.net/projects/xglore/). Forma parte del proyecto “Nerthusv2: Base de datos léxica en 3D del inglés antiguo” patrocinado por el Ministerio de Ciencia e Innovación (nº: FFI08-04448/FILO).

Influencia del GSD en la orientación de un bloque fotogramétrico

Direcciones de correo electrónico de las autoras: Edurne Ortiz de Elguea (txintxe1989@holmail.com) y Priscila García (pelukina06@hotmail.com).

Communities in complex networks

The study of complex networks has attracted the attention of the scientific community for many obvious reasons. A vast number of systems, from the brain to ecosystems, power grid, and the Internet, can be represented as large complex networks, i.e, assemblies of many interacting components with nontrivial topological properties. The link between these components can describe a global behaviour such as the Internet traffic, electricity supply service, market trend, etc. One of the most relevant topological feature of graphs representing these complex systems is community structure which aims to identify the modules and, possibly, their hierarchical organization, by only using the information encoded in the graph topology. Deciphering network community structure is not only important in order to characterize the graph topologically, but gives some information both on the formation of the network and on its functionality.

Invariant-free deduction systems for temporal logic

In this thesis we propose a new approach to deduction methods for temporal logic. Our proposal is based on an inductive definition of eventualities that is different from the usual one. On the basis of this non-customary inductive definition for eventualities, we first provide dual systems of tableaux and sequents for Propositional Linear-time Temporal Logic (PLTL). Then, we adapt the deductive approach introduced by means of these dual tableau and sequent systems to the resolution framework and we present a clausal temporal resolution method for PLTL. Finally, we make use of this new clausal temporal resolution method for establishing logical foundations for declarative temporal logic programming languages. The key element in the deduction systems for temporal logic is to deal with eventualities and hidden invariants that may prevent the fulfillment of eventualities. Different ways of addressing this issue can be found in the works on deduction systems for temporal logic. Traditional tableau systems for temporal logic generate an auxiliary graph in a first pass.Then, in a second pass, unsatisfiable nodes are pruned. In particular, the second pass must check whether the eventualities are fulfilled. The one-pass tableau calculus introduced by S. Schwendimann requires an additional handling of information in order to detect cyclic branches that contain unfulfilled eventualities. Regarding traditional sequent calculi for temporal logic, the issue of eventualities and hidden invariants is tackled by making use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their automation. A remarkable consequence of using either a two-pass approach based on auxiliary graphs or aone-pass approach that requires an additional handling of information in the tableau framework, and either invariant-based rules or infinitary rules in the sequent framework, is that temporal logic fails to carry out the classical correspondence between tableaux and sequents. In this thesis, we first provide a one-pass tableau method TTM that instead of a graph obtains a cyclic tree to decide whether a set of PLTL-formulas is satisfiable. In TTM tableaux are classical-like. For unsatisfiable sets of formulas, TTM produces tableaux whose leaves contain a formula and its negation. In the case of satisfiable sets of formulas, TTM builds tableaux where each fully expanded open branch characterizes a collection of models for the set of formulas in the root. The tableau method TTM is complete and yields a decision procedure for PLTL. This tableau method is directly associated to a one-sided sequent calculus called TTC. Since TTM is free from all the structural rules that hinder the mechanization of deduction, e.g. weakening and contraction, then the resulting sequent calculus TTC is also free from this kind of structural rules. In particular, TTC is free of any kind of cut, including invariant-based cut. From the deduction system TTC, we obtain a two-sided sequent calculus GTC that preserves all these good freeness properties and is finitary, sound and complete for PLTL. Therefore, we show that the classical correspondence between tableaux and sequent calculi can be extended to temporal logic. The most fruitful approach in the literature on resolution methods for temporal logic, which was started with the seminal paper of M. Fisher, deals with PLTL and requires to generate invariants for performing resolution on eventualities. In this thesis, we present a new approach to resolution for PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Our method is based on the dual methods of tableaux and sequents for PLTL mentioned above. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called TRS-resolution, that extends classical propositional resolution. Finally, we prove that TRS-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL. In the field of temporal logic programming, the declarative proposals that provide a completeness result do not allow eventualities, whereas the proposals that follow the imperative future approach either restrict the use of eventualities or deal with them by calculating an upper bound based on the small model property for PLTL. In the latter, when the length of a derivation reaches the upper bound, the derivation is given up and backtracking is used to try another possible derivation. In this thesis we present a declarative propositional temporal logic programming language, called TeDiLog, that is a combination of the temporal and disjunctive paradigms in Logic Programming. We establish the logical foundations of our proposal by formally defining operational and logical semantics for TeDiLog and by proving their equivalence. Since TeDiLog is, syntactically, a sublanguage of PLTL, the logical semantics of TeDiLog is supported by PLTL logical consequence. The operational semantics of TeDiLog is based on TRS-resolution. TeDiLog allows both eventualities and always-formulas to occur in clause heads and also in clause bodies. To the best of our knowledge, TeDiLog is the first declarative temporal logic programming language that achieves this high degree of expressiveness. Since the tableau method presented in this thesis is able to detect that the fulfillment of an eventuality is prevented by a hidden invariant without checking for it by means of an extra process, since our finitary sequent calculi do not include invariant-based rules and since our resolution method dispenses with invariant generation, we say that our deduction methods are invariant-free.

Efficient learning of decomposable models with a bounded clique size

The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains.

Herramienta software para el análisis de rendimiento de redes 4G

[ES]El objetivo de este proyecto ha sido desarrollar una herramienta software que permita medir el rendimiento de redes con tecnología móvil 4G, también conocida como LTE. Para ello se ha creado un sistema software que está compuesto por una aplicación móvil y un servidor de aplicaciones. El sistema en conjunto realiza la función de recoger indicadores de calidad de la red móvil de diversa índole, que posteriormente son procesados utilizando herramientas software matemáticas, para así obtener gráficas y mapas que permiten analizar la situación y el rendimiento de una red 4G concreta. El desarrollo del software ha llegado a nivel de prototipo y se han realizado pruebas reales con él obteniendo resultados positivos de funcionamiento.

Treewidth: theory and applications to computer science

This report is an introduction to the concept of treewidth, a property of graphs that has important implications in algorithms. Some basic concepts of graph theory are presented in the first chapter for those readers that are not familiar with the notation. In Chapter 2, the definition of treewidth and some different ways of characterizing it are explained. The last two chapters focus on the algorithmic implications of treewidth, which are very relevant in Computer Science. An algorithm to compute the treewidth of a graph is presented and its result can be later applied to many other problems in graph theory, like those introduced in the last chapter.

Contributions on agreement in dynamic distributed systems

139 p.

Análisis de redes de los proyectos de innovación europeos “Leonardo da Vinci”: un ensayo empírico preliminar

[Castellano] En este trabajo se realiza un ensayo empírico preliminar de los proyectos de innovación europeos “Leonardo da Vinci”. La metodología que se utiliza a lo largo del trabajo es el análisis de redes. Se observan grafos e indicadores de redes y se comparan la situación de los agentes que forman las redes. Además no solamente se analiza la situación de los agentes, sino la similitud y causalidad estructural existente entre las redes que conforman dichos proyectos. Este ensayo empírico preliminar da lugar a una futura modelización o a la aplicación de la metodología en otras materias.

El juego en la educación infantil: cómo y por qué cambian las preferencias lúdicas

[ES] El interés por conocer la cultura lúdica de los niños y niñas de E. Infantil y los posibles cambios que en ella se han producido nos ha llevado a realizar 100 entrevistas sobre las preferencias lúdicas y algunas observaciones a infantes de 3-7 años. Para analizar los resultados se han categorizado las respuestas obtenidas siguiendo los criterios de clasificación de J. Piaget, R. Ortega y Mc Lloyd. Las gráficas de resultados han mostrado que la edad, el sexo y el juguete han sido determinantes en la preferencia lúdica. Por ello, nos ha parecido relevante en E. Infantil, dado que es la actividad por excelencia de la infancia.

Urte biko gelako gatazkak: izaera eta esku-hartzea

[EUS] Ikerketa lan honen helburua urte biko gela batean ematen diren egoera gatazkatsuak eta horietan burutzen diren esku-hartze mota desberdinak aztertzea izan da. Horretarako, bi alditan banandu da ikerketa honen zeregina: fase esploratzailean eta fase zientifikoan, hain zuzen. Lehenengoan, gaiari buruzko hausnarketa teoriko sakon bat gauzatzearekin batera, ikerketaren behaketa esparruak zehaztu dira, hala nola, zer, noiz, non eta nola behatuko den. Orduan, goizeko une gatazkatsuenak behatzea erabaki da; saio kolektiboa, txokoak eta batzeko unea, hain zuzen. Ondoren, fase zientifikoan, hiru esparru horietan behatutako datu guztiak bildu eta hainbat taula eta grafiko eratu dira. Lortutako emaitzen arabera, argi gelditu delarik eskolan biolentzia erabiltzea nahiko ohikoa dela; autoritarismoa, diziplina inposaketa eta boterearen erabilera bortitza. Hori dela eta, batetik garatutako lan enpirikoan eta bestetik Pikler-Lóczy eskolatze goiztiarraren hezkuntza-eredu arrakastatsuan oinarritutako hausnarketa egin da, gatazka egoeretan erabili daitezkeen baliabide nahiz esku-hartze mota kalitatezko eta egokiagoak eskaintzeko asmotan.