Exhaustive generation of kk-critical H\mathcal H-free graphs

We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$. We also show that there are only finitely many $4$-critical graphs $(P_8,C_4)$-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the $3$-colorability problem in the respective classes. Moreover, we prove that for every $t$, the class of 4-critical planar $P_t$-free graphs is finite. We also determine all 27 4-critical planar $(P_7,C_6)$-free graphs. We also prove that every $P_{10}$-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic $P_{12}$-free graph of girth five. Moreover, we show that every $P_{13}$-free graph of girth at least six and every $P_{16}$-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697

Implementazione ed ottimizzazione di algoritmi per l'analisi di Biomedical Big Data

Big Data Analytics poses many challenges to the research community who has to handle several computational problems related to the vast amount of data. An increasing interest involves Biomedical data, aiming to get the so-called personalized medicine, where therapy plans are designed on the specific genotype and phenotype of an individual patient and algorithm optimization plays a key role to this purpose. In this work we discuss about several topics related to Biomedical Big Data Analytics, with a special attention to numerical issues and algorithmic solutions related to them. We introduce a novel feature selection algorithm tailored on omics datasets, proving its efficiency on synthetic and real high-throughput genomic datasets. We tested our algorithm against other state-of-art methods obtaining better or comparable results. We also implemented and optimized different types of deep learning models, testing their efficiency on biomedical image processing tasks. Three novel frameworks for deep learning neural network models development are discussed and used to describe the numerical improvements proposed on various topics. In the first implementation we optimize two Super Resolution models showing their results on NMR images and proving their efficiency in generalization tasks without a retraining. The second optimization involves a state-of-art Object Detection neural network architecture, obtaining a significant speedup in computational performance. In the third application we discuss about femur head segmentation problem on CT images using deep learning algorithms. The last section of this work involves the implementation of a novel biomedical database obtained by the harmonization of multiple data sources, that provides network-like relationships between biomedical entities. Data related to diseases and other biological relates were mined using web-scraping methods and a novel natural language processing pipeline was designed to maximize the overlap between the different data sources involved in this project

Model for WCET prediction, scheduling and task allocation for emergent agent-behaviours in real-time scenarios

[ES]Hasta el momento no se conocen modelos de tiempo real específicamente desarrollados para su uso en sistemas abiertos, como las Organizaciones Virtuales de Agentes (OVs). Convencionalmente, los modelos de tiempo real se aplican a sistemas cerrados donde todas las variables se conocen a priori. Esta tesis presenta nuevas contribuciones y la novedosa integración de agentes en tiempo real dentro de OVs. Hasta donde alcanza nuestro conocimiento, éste es el primer modelo específicamente diseñado para su aplicación en OVs con restricciones temporales estrictas. Esta tesis proporciona una nueva perspectiva que combina la apertura y dinamicidad necesarias en una OV con las restricciones de tiempo real. Ésto es una aspecto complicado ya que el primer paradigma no es estricto, como el propio término de sistema abierto indica, sin embargo, el segundo paradigma debe cumplir estrictas restricciones. En resumen, el modelo que se presenta permite definir las acciones que una OV debe llevar a cabo con un plazo concreto, considerando los cambios que pueden ocurrir durante la ejecución de un plan particular. Es una planificación de tiempo real en una OV. Otra de las principales contribuciones de esta tesis es un modelo para el cálculo del tiempo de ejecución en el peor caso (WCET). La propuesta es un modelo efectivo para calcular el peor escenario cuando un agente desea formar parte de una OV y para ello, debe incluir sus tareas o comportamientos dentro del sistema de tiempo real, es decir, se calcula el WCET de comportamientos emergentes en tiempo de ejecución. También se incluye una planificación local para cada nodo de ejecución basada en el algoritmo FPS y una distribución de tareas entre los nodos disponibles en el sistema. Para ambos modelos se usan modelos matemáticos y estadísticos avanzados para crear un mecanismo adaptable, robusto y eficiente para agentes inteligentes en OVs. El desconocimiento, pese al estudio realizado, de una plataforma para sistemas abiertos que soporte agentes con restricciones de tiempo real y los mecanismos necesarios para el control y la gestión de OVs, es la principal motivación para el desarrollo de la plataforma de agentes PANGEA+RT. PANGEA+RT es una innovadora plataforma multi-agente que proporciona soporte para la ejecución de agentes en ambientes de tiempo real. Finalmente, se presenta un caso de estudio donde robots heterogéneos colaboran para realizar tareas de vigilancia. El caso de estudio se ha desarrollado con la plataforma PANGEA+RT donde el modelo propuesto está integrado. Por tanto al final de la tesis, con este caso de estudio se obtienen los resultados y conclusiones que validan el modelo

Hegartymaths: gimmick or game changer?

This research examines the effectiveness of Hegartymaths, an online platform comprised of mathematical instructional video tutorials and quizzes used in approximately a third of mainstream secondary schools in England. The study employed mixed methods from an objectivist epistemological standpoint and used quasiexperiments to assess how schools who use Hegartymaths compare with ones that do not, as well as exploring how schools’ implementation of Hegartymaths impacts GCSE performance for the pupils that use it. In order to explore the impact Hegartymaths on GCSE performance, and specifically on the topics/types of questions which are part of the GCSE, data was collected and cleaned from the Gov.uk website, which publishes KS4 data for all 5,512 schools in England, and the Hegartymaths data team, who shared a snapshot of the big data analytics for 37 United Learning schools (30,501 pupils). A teacher survey, which included 106 responses from United Learning teachers of mathematics, considered which Hegartymaths practices increase its efficacy. The findings indicate that there are significant and positive relationships between the time spent on Hegartymaths and the performance of students in several categories, and the time spent completing quizzes was more effective than watching the video tutorials. Hegartymaths was seen to be more aligned to questions that test for procedural knowledge, rather than conceptual knowledge, and the schools that were identified to be more successful indicate there seems to be merit in the following practices: setting more Hegartymaths tasks at a time; allowing some topics to be taught solely through Hegartymaths; directing pupils to write notes when watching the tutorials. The research design and analyses in the study harness the power of big data with learning analytics to contribute to the literature from a methodological point of view, whereas the findings contribute to the limited existing literature on using video tutorials within a blended learning approach

Proceedings of the 15th ISWC workshop on Ontology Matching (OM 2020)

15th International Workshop on Ontology Matching co-located with the 19th International Semantic Web Conference (ISWC 2020)International audienc

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition