Transmission and Coding of Information

2018/201

Transmission and coding of information - problem list

2018/201

Completion and decomposition of hypergraphs by domination hypergraphs

A graph consists of a finite non-empty set of vertices and a set of unordered pairs of vertices, called edges. A dominating set of a graph is a set of vertices D such that every vertex not in D is adjacent to some vertex in D. A hypergraph on a finite set X is a collection of subsets of X, none of which is a proper subset of another. The domination hypergraph of a graph is the collection of all the minimal vertex dominating sets of the graph. A hypergraph is a domination hypergraph if it is the domination hypergraph of a graph. In general, a hypergraph is not a domination hypergraph. The objective of this work is to approximate a hypergraph by domination hypergraphs and that the optimal approximations determine uniquely the hypergraph. In Chapter 1 we introduce two structures of distributive lattices on the set of hypergraphs on a finite set and also define some operations: the complementary hypergraph and two transversal operations. We study the behavior of these operations with respect to the partial orders and the lattice structures. In Chapter 2 we first introduce several hypergraphs associated with a graph, the most important one being the domination hypergraph, and we establish several relationships among them. Then we compute the domination hypergraph of all graphs, modulo isomorphism, up to order 5. We also investigate when a given hypergraph is a domination hypergraph and find all domination hypergraphs in some cases. In Chapter 3 we present the problem of approximating a hypergraph by domination hypergraphs. We introduce four families of approximations of a hypergraph, which we call completions, depending on which partial order we use and on which side we approximate. We set some sufficient conditions for the existence of completions, introduce the sets of minimal or maximal completions of a hypergraph and study the concept of decomposition, which leads to the decomposition index of a hypergraph. Avoidance properties turn out to be an essential ingredient for the existence of domination completions. In Chapter 4 we give some computational techniques and calculate the upper minimal domination completions and the decomposition indices of some hypergraphs. In the appendices we give the SAGE code developed to perform the calculations of the thesis and we list all the domination hypergraphs of all graphs of order 5 and all the graphs of order 5 with the same domination hypergraph.Un grafo consiste en un conjunto no vacío de vértices y un conjunto de pares no ordenados de vértices denominados aristas. Un conjunto de vértices D es dominante si todo vértice que no esté en D es adyacente a algún vértice de D. Un hipergrafo sobre un conjunto finito X es una colección de subconjuntos de X, ninguno de los cuales es un subconjunto de ningún otro. El hipergrafo de dominación de un grafo es la colección de los conjuntos dominantes minimales del grafo. Un hipergrafo es de dominación si es el hipergrafo de dominación de un grafo. En el capítulo 1 introducimos dos estructuras de retículo distributivo en el conjunto de hipergrafos sobre un conjunto finito y también definimos algunas operaciones: el complementario de un hipergrafo y las dos operaciones de transversal correspondientes a cada una de las estructuras de retículo. Estudiamos el comportamiento de estas operaciones con respecto a los órdenes parciales y las estructuras de retículo. En el capítulo 2 introducimos varios hipergrafos asociados a un grafo, siendo los más importantes el hipergrafo de dominación y el hipergrafo de independencia-dominación del grafo, cuyos elementos son los conjuntos independientes maximales del grafo, y establecemos varias relaciones entre ellos. Después calculamos el hipergrafo de dominación de todos los grafos de orden 5, salvo isomorfismo. También investigamos cuándo un hipergrafo es un hipergrafo de dominación y encontramos todos los hipergrafos de dominación en algunos casos. En el capítulo 3 presentamos el problema de la aproximación de un hipergrafo por hipergrafos de una familia dada. Dado un hipergrafo, definimos cuatro familias de aproximaciones, que llamamos compleciones, dependiendo del orden parcial usado y de por dónde aproximemos el hipergrafo. Establecemos condiciones suficientes para la existencia de compleciones, introducimos los conjuntos de compleciones minimales o maximales de un hipergrafo y estudiamos el concepto de descomposición, que conduce al índice de descomposición de un hipergrafo. Las propiedades de evitación resultan ser cruciales en el estudio de la existencia de descomposiciones. En el capítulo 4 presentamos técnicas de cálculo y calculamos las compleciones de dominación minimales superiores y los índices de descomposición de algunos hipergrafos. En los apéndices damos el código SAGE, desarrollado para realizar los cálculos de esta tesis, y damos la lista de los hipergrafos de dominación de todos los grafos de orden 5 así como todos los grafos de orden 5 que poseen el mismo hipergrafo de dominación

Error-tolerant Graph Matching on Huge Graphs and Learning Strategies on the Edit Costs

Els grafs són estructures de dades abstractes que s'utilitzen per a modelar problemes reals amb dues entitats bàsiques: nodes i arestes. Cada node o vèrtex representa un punt d'interès rellevant d'un problema, i cada aresta representa la relació entre aquests vèrtexs. Els nodes i les arestes podrien incorporar atributs per augmentar la precisió del problema modelat. Degut a aquesta versatilitat, s'han trobat moltes aplicacions en camps com la visió per computador, biomèdics, anàlisi de xarxes, etc. La Distància d'edició de grafs (GED) s'ha convertit en una eina important en el reconeixement de patrons estructurals, ja que permet mesurar la dissimilitud dels grafs. A la primera part d'aquesta tesi es presenta un mètode per generar una parella grafs juntament amb la seva correspondència en un cost computacional lineal. A continuació, se centra en com mesurar la dissimilitud entre dos grafs enormes (més de 10.000 nodes), utilitzant un nou algoritme de aparellament de grafs anomenat Belief Propagation. Té un cost computacional O(d^3.5N). Aquesta tesi també presenta un marc general per aprendre els costos d'edició implicats en els càlculs de la GED automàticament. Després, concretem aquest marc en dos models diferents basats en xarxes neuronals i funcions de densitat de probabilitat. S'ha realitzat una validació pràctica exhaustiva en 14 bases de dades públiques. Aquesta validació mostra que la precisió és major amb els costos d'edició apresos, que amb alguns costos impostos manualment o altres costos apresos automàticament per mètodes anteriors. Finalment proposem una aplicació de l'algoritme Belief propagation utilitzat en la simulació de la mecànica muscular.Los grafos son estructuras de datos abstractos que se utilizan para modelar problemas reales con dos entidades básicas: nodos y aristas. Cada nodo o vértice representa un punto de interés relevante de un problema, y cada arista representa la relación entre estos vértices. Los nodos y las aristas podrían incorporar atributos para aumentar la precisión del problema modelado. Debido a esta versatilidad, se han encontrado muchas aplicaciones en campos como la visión por computador, biomédicos, análisis de redes, etc. La Distancia de edición de grafos (GED) se ha convertido en una herramienta importante en el reconocimiento de patrones estructurales, ya que permite medir la disimilitud de los grafos. En la primera parte de esta tesis se presenta un método para generar una pareja grafos junto con su correspondencia en un coste computacional lineal. A continuación, se centra en cómo medir la disimilitud entre dos grafos enormes (más de 10.000 nodos), utilizando un nuevo algoritmo de emparejamiento de grafos llamado Belief Propagation. Tiene un coste computacional O(d^3.5n). Esta tesis también presenta un marco general para aprender los costos de edición implicados en los cálculos de GED automáticamente. Luego, concretamos este marco en dos modelos diferentes basados en redes neuronales y funciones de densidad de probabilidad. Se ha realizado una validación práctica exhaustiva en 14 bases de datos públicas. Esta validación muestra que la precisión es mayor con los costos de edición aprendidos, que con algunos costos impuestos manualmente u otros costos aprendidos automáticamente por métodos anteriores. Finalmente proponemos una aplicación del algoritmo Belief propagation utilizado en la simulación de la mecánica muscular.Graphs are abstract data structures used to model real problems with two basic entities: nodes and edges. Each node or vertex represents a relevant point of interest of a problem, and each edge represents the relationship between these points. Nodes and edges could be attributed to increase the accuracy of the modeled problem, which means that these attributes could vary from feature vectors to description labels. Due to this versatility, many applications have been found in fields such as computer vision, bio-medics, network analysis, etc. Graph Edit Distance (GED) has become an important tool in structural pattern recognition since it allows to measure the dissimilarity of attributed graphs. The first part presents a method is presented to generate graphs together with an upper and lower bound distance and a correspondence in a linear computational cost. Through this method, the behaviour of the known -or the new- sub-optimal Error-Tolerant graph matching algorithm can be tested against a lower and an upper bound GED on large graphs, even though we do not have the true distance. Next, the present is focused on how to measure the dissimilarity between two huge graphs (more than 10.000 nodes), using a new Error-Tolerant graph matching algorithm called Belief Propagation algorithm. It has a O(d^3.5n) computational cost.This thesis also presents a general framework to learn the edit costs involved in the GED calculations automatically. Then, we concretise this framework in two different models based on neural networks and probability density functions. An exhaustive practical validation on 14 public databases has been performed. This validation shows that the accuracy is higher with the learned edit costs, than with some manually imposed costs or other costs automatically learned by previous methods. Finally we propose an application of the Belief propagation algorithm applied to muscle mechanics

The SmartSantander project

The SmartSantander project has deployed during the past two years a unique in the world city-scale experimental research facility in support of typical applications and services for a smart city. This facility is sufficiently large, open and flexible to enable horizontal and vertical federation with other experimental facilities, and to stimulate the development of new applications by end-users. Besides, it provides support to the experimental advanced research on IoT technologies, and allows a realistic assessment on new services by means of users’ acceptability tests. The facility already counts with more than 10,000 IoT devices (March 2013), and by the end of 2013 it will comprise of more than 12,000. The core of the facility is being installed in the city of Santander (Spain), the capital of the region of Cantabria situated on the north coast of Spain, and its surroundings. Besides Santander, other deployments have been placed in Lübeck (Germany), Guilford (UK) and Belgrade (Serbia). SmartSantander will enable the Future Internet of Things to become a reality

Los viernes creativos

Los viernes creativos es una actividad semanal para el aula de Matemáticas, que se plantea con el fin de motivar al alumnado de la ESO. Tiene como objetivo que los alumnos realicen sus propias creaciones matemáticas, en diferentes formatos, eligiendo aquellas actividades que más les atraigan de entre el abanico ofertado. Cada viernes, el profesor realiza una propuesta de actividad y se convierte en intermediario matemático del alumno

Fuzzy heterogeneous neurons for imprecise classification problems

In the classical neuron model, inputs are continuous real-valued quantities. However, in many important domains from the real world, objects are described by a mixture of continuous and discrete variables, usually containing missing information and uncertainty. In this paper, a general class of neuron models accepting heterogeneous inputs in the form of mixtures of continuous (crisp and/or fuzzy) and discrete quantities admitting missing data is presented. From these, several particular models can be derived as instances and different neural architectures constructed with them. Such models deal in a natural way with problems for which information is imprecise or even missing. Their possibilities in classification and diagnostic problems are here illustrated by experiments with data from a real-world domain in the field of environmental studies. These experiments show that such neurons can both learn and classify complex data very effectively in the presence of uncertain information.Peer ReviewedPostprint (author's final draft

Efficacy and safety of preoperative preparation with Lugol's iodine solution in euthyroid patients with Graves’ disease (LIGRADIS Trial): Study protocol for a multicenter randomized trial

"Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAM"Background: Currently, both the American Thyroid Association and the European Thyroid Association recommend preoperative preparation with Lugol's Solution (LS) for patients undergoing thyroidectomy for Graves’ Disease (GD), but their recommendations are based on low-quality evidence. The LIGRADIS trial aims to provide evidence either to support or refute the systematic use of LS in euthyroid patients undergoing thyroidectomy for GD. Methods: A multicenter randomized controlled trial will be performed. Patients ≥18 years of age, diagnosed with GD, treated with antithyroid drugs, euthyroid and proposed for total thyroidectomy will be eligible for inclusion. Exclusion criteria will be prior thyroid or parathyroid surgery, hyperparathyroidism that requires associated parathyroidectomy, thyroid cancer that requires adding a lymph node dissection, iodine allergy, consumption of lithium or amiodarone, medically unfit patients (ASA-IV), breastfeeding women, preoperative vocal cord palsy and planned endoscopic, video-assisted or remote access surgery. Between January 2020 and January 2022, 270 patients will be randomized for either receiving or not preoperative preparation with LS. Researchers will be blinded to treatment assignment. The primary outcome will be the rate of postoperative complications: hypoparathyroidism, recurrent laryngeal nerve injury, hematoma, surgical site infection or death. Secondary outcomes will be intraoperative events (Thyroidectomy Difficulty Scale score, blood loss, recurrent laryngeal nerve neuromonitoring signal loss), operative time, postoperative length of stay, hospital readmissions, permanent complications and adverse events associated to LS. Conclusions: There is no conclusive evidence supporting the benefits of preoperative treatment with LS in this setting. This trial aims to provide new insights into future Clinical Practice Guidelines recommendations. Trial registration: ClinicalTrials.gov identifier: NCT03980132.This project is funded by the Spanish Association of Surgeons by a competitive grant for multicenter studies. This Association has no influ- ence on any part of the design, data collection, analysis or interpreta- tion of the results, all of which will be carried out by the main investiga- tors (JLMN and JMVM