Testing an Optimised Expansion on Z_2 Lattice Models

We test an optimised hopping parameter expansion on various Z_2 lattice scalar field models: the Ising model, a spin-one model and lambda (phi)^4. We do this by studying the critical indices for a variety of optimisation criteria, in a range of dimensions and with various trial actions. We work up to seventh order, thus going well beyond previous studies. We demonstrate how to use numerical methods to generate the high order diagrams and their corresponding expressions. These are then used to calculate results numerically and, in the case of the Ising model, we obtain some analytic results. We highlight problems with several optimisation schemes and show for the best scheme that the critical exponents are consistent with mean field results to at least 8 significant figures. We conclude that in its present form, such optimised lattice expansions do not seem to be capturing the non-perturbative infra-red physics near the critical points of scalar models.Comment: 47 pages, some figures in colour but will display fine in B

optimización da planificación de adquisición de datos LIDAR cara ó modelado 3D de interiores

The main objective of this doctoral thesis is the design, validation and implementation of methodologies that allow the geometric and topological modelling of navigable spaces, whether inside buildings or urban environments, to be integrated into three-dimensional geographic information systems (GIS-3D). The input data of this work will consist mainly of point clouds (which can be classified) acquired by LiDAR systems both indoors and outdoors. In addition, the use of BIM infrastructure models and cadastral maps is proposed depending on their availability. Point clouds provide a large amount of environmental information with high accuracy compared to data offered by other acquisition technologies. However, the lack of data structure and volume requires a great deal of processing effort. For this reason, the first step is to structure the data by dividing the input cloud into simpler entities that facilitate subsequent processes. For this first division, the physical elements present in the cloud will be considered, since they can be walls in the case of interior environments or kerbs in the case of exteriors. In order to generate navigation routes adapted to different mobile agents, the next objective will try to establish a semantic subdivision of space according to the functionalities of space. In the case of internal environments, it is possible to use BIM models to evaluate the results and the use of cadastral maps that support the division of the urban environment. Once the navigable space is divided, the design of topologically coherent navigation networks will be parameterized both geometrically and topologically. For this purpose, several spatial discretization techniques, such as 3D tessellations, will be studied to facilitate the establishment of topological relationships, adjacency, connectivity and inclusion between subspaces. Based on the geometric characterization and the topological relations established in the previous phase, the creation of three-dimensional navigation networks with multimodal support will be addressed and different levels of detail will be considered according to the mobility specifications of each agent and its purpose. Finally, the possibility of integrating the networks generated in a GIS-3D visualization system will be considered. For the correct visualization, the level of detail can be adjusted according to geometry and semantics. Aspects such as the type of user or transport, mobility, rights of access to spaces, etc. They must be considered at all times.El objetivo principal de esta tesis doctoral es el diseño, la validación y la implementación de metodologías que permitan el modelado geométrico y topológico de espacios navegables, ya sea de interiores de edificios o entornos urbanos, para integrarse en sistemas de información geográfica tridimensional (SIG). -3D). Los datos de partida de este trabajo consistirán principalmente en nubes de puntos (que pueden estar clasificados) adquiridas por sistemas LiDAR tanto en interiores como en exteriores. Además, se propone el uso de modelos BIM de infraestructuras y mapas catastrales en función de su disponibilidad. Las nubes de puntos proporcionan una gran cantidad de información del entorno con gran precisión con respecto a los datos ofrecidos por otras tecnologías de adquisición. Sin embargo, la falta de estructura de datos y su volumen requiere un gran esfuerzo de procesamiento. Por este motivo, el primer paso que se debe realizar consiste en estructurar los datos dividiendo la nube de entrada en entidades más simples que facilitan los procesos posteriores. Para esta primera división se considerarán los elementos físicos presentes en la nube, ya que pueden ser paredes en el caso de entornos interiores o bordillos en el caso de los exteriores. Con el propósito de generar rutas de navegación adaptadas a diferentes agentes móviles, el próximo objetivo intentará establecer una subdivisión semántica del espacio de acuerdo con las funcionalidades del espacio. En el caso de entornos internos, es posible utilizar modelos BIM para evaluar los resultados y el uso de mapas catastrales que sirven de apoyo en la división del entorno urbano. Una vez que se divide el espacio navegable, se parametrizará tanto geométrica como topológicamente al diseño de redes de navegación topológicamente coherentes. Para este propósito, se estudiarán varias técnicas de discretización espacial, como las teselaciones 3D, para facilitar el establecimiento de relaciones topológicas, la adyacencia, la conectividad y la inclusión entre subespacios. A partir de la caracterización geométrica y las relaciones topológicas establecidas en la fase anterior, se abordará la creación de redes de navegación tridimensionales con soporte multimodal y se considerarán diversos niveles de detalle según las especificaciones de movilidad de cada agente y su propósito. Finalmente, se contemplará la posibilidad de integrar las redes generadas en un sistema de visualización tridimensional 3D SIG 3D. Para la correcta visualización, el nivel de detalle se puede ajustar en función de la geometría y la semántica. Aspectos como el tipo de usuario o transporte, movilidad, derechos de acceso a espacios, etc. Deben ser considerados en todo momento.O obxectivo principal desta tese doutoral é o deseño, validación e implementación de metodoloxías que permitan o modelado xeométrico e topolóxico de espazos navegables, ben sexa de interiores de edificios ou de entornos urbanos, ca fin de seren integrados en Sistemas de Información Xeográfica tridimensionais (SIX-3D). Os datos de partida deste traballo constarán principalmente de nubes de puntos (que poden estar clasificadas) adquiridas por sistemas LiDAR tanto en interiores como en exteriores. Ademáis plantease o uso de modelos BIM de infraestruturas e mapas catastrais dependendo da súa dispoñibilidade. As nubes de puntos proporcionan unha gran cantidade de información do entorno cunha gran precisión respecto os datos que ofrecen outras tecnoloxías de adquisición. Sen embargo, a falta de estrutura dos datos e a seu volume esixe un amplo esforzo de procesado. Por este motivo o primeiro paso a levar a cabo consiste nunha estruturación dos datos mediante a división da nube de entrada en entidades máis sinxelas que faciliten os procesos posteriores. Para esta primeira división consideraranse elementos físicos presentes na nube como poden ser paredes no caso de entornos interiores ou bordillos no caso de exteriores. Coa finalidade de xerar rutas de navegación adaptadas a distintos axentes móbiles, o seguinte obxectivo tratará de establecer unha subdivisión semántica do espazo de acordo as funcionalidades do espazo. No caso de entornos interiores plantease a posibilidade de empregar modelos BIM para avaliar os resultados e o uso de mapas catastrais que sirvan de apoio na división do entorno urbano. Unha vez divido o espazo navigable parametrizarase tanto xeométricamente como topolóxicamene de cara ao deseño de redes de navegación topolóxicamente coherentes. Para este fin estudaranse varias técnicas de discretización de espazos como como son as teselacións 3D co obxectivo de facilitar establecer relacións topolóxicas, de adxacencia, conectividade e inclusión entre subespazos. A partir da caracterización xeométrica e das relación topolóxicas establecidas na fase previa abordarase a creación de redes de navegación tridimensionais con soporte multi-modal e considerando varios niveis de detalle de acordo as especificacións de mobilidade de cada axente e a súa finalidade. Finalmente comtemplarase a posibilidade de integrar as redes xeradas nun sistema SIX 3D visualización tridimensional. Para a correcta visualización o nivel de detalle poderá axustarse en base a xeometría e a semántica. Aspectos como o tipo de usuario ou transporte, mobilidade, dereitos de acceso a espazos, etc. deberán ser considerados en todo momento

Modelling Seismic Wave Propagation for Geophysical Imaging

International audienceThe Earth is an heterogeneous complex media from the mineral composition scale (10−6m) to the global scale ( 106m). The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods (Günther et al., 2006; Rücker et al., 2006), diffusive methods (Cognon, 1971; Druskin & Knizhnerman, 1988; Goldman & Stover, 1983; Hohmann, 1988; Kuo & Cho, 1980; Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968; Bolt & Smith, 1976; Dablain, 1986; Kelly et al., 1976; Levander, 1988; Marfurt, 1984; Virieux, 1986). Seismic waves belong to the last category. We shall concentrate in this chapter on the forward problem which will be at the heart of any inverse problem for imaging the Earth. The forward problem is dedicated to the estimation of seismic wavefields when one knows the medium properties while the inverse problem is devoted to the estimation of medium properties from recorded seismic wavefields

An adaptive ant colony optimization algorithm for rule-based classification

Classification is an important data mining task with different applications in many fields. Various classification algorithms have been developed to produce classification models with high accuracy. Differing from other complex and difficult classification models, rules-based classification algorithms produce models which are understandable for users. Ant-Miner is a variant of ant colony optimisation and a prominent intelligent algorithm widely use in rules-based classification. However, the Ant-Miner has overfitting and easily falls into local optima problems which resulted in low classification accuracy and complex classification rules. In this study, a new Ant-Miner classifier is developed, named Adaptive Genetic Iterated-AntMiner (AGI-AntMiner) that aims to avoid local optima and overfitting problems. The components of AGI-AntMiner includes: i) an Adaptive AntMiner which is a prepruning technique to dynamically select the appropriate threshold based on the quality of the rules; ii) Genetic AntMiner that improves the post-pruning by adding/removing terms in a dual manner; and, iii) an Iterated Local Search-AntMiner that improves exploitation based on multiple-neighbourhood structure. The proposed AGI-AntMiner algorithm is evaluated on 16 benchmark datasets of medical, financial, gaming and social domains obtained from the University California Irvine repository. The algorithm’s performance was compared with other variants of Ant-Miner and state-of-the-art rules-based classification algorithms based on classification accuracy and model complexity. Experimental results proved that the proposed AGI-AntMiner algorithm is superior in two (2) aspects. Hybridization of local search in AGI-AntMiner has improved the exploitation mechanism which leads to the discovery of more accurate classification rules. The new pre-pruning and postpruning techniques have improved the pruning ability to produce shorter classification rules which are easier to interpret by the users. Thus, the proposed AGI-AntMiner algorithm is capable in conducting an efficient search in finding the best classification rules that balance the classification accuracy and model complexity to overcome overfitting and local optima problems

Problems and results on linear hypergraphs

In this thesis, we tackle several problems involving the study of 3-uniform, linear hypergraphs satisfying some additional structural constraint. We begin with a problem of Hrushovski concerning Latin squares satisfying a partial associativity condition. From an $n\times n$ Latin square $A$ one can define a binary operation $\circ:[n]\times[n]\to [n]$, and $\circ$ is associative if and only if $A$ is a group multiplication table. Hrushovski asked whether, if $\circ$ is only associative a positive proportion of the time, $A$ must still in some sense be close to a group multiplication table. This problem manifests a well-studied combinatorial theme, in which a local structural constraint is relaxed (first to a `99$\%$' version and then to a `1$\%$' version) and the global consequences of the relaxed constraints are analysed. We show that the partial associativity condition is sufficient to deduce powerful global information, allowing us to find within $A$ a large subset with group-like structure. Since Latin squares can be regarded as 3-uniform, linear hypergraphs, and the partial associativity condition can be formulated in terms of the count of a particular subhypergraph, we are able to apply purely combinatorial methods to a problem that touches algebra, model theory and geometric group theory. We then take this problem further. A condition due to Thomsen provides a combinatorial constraint which, if satisfied by the Latin square $A$, proves that $A$ is in fact the multiplication table of an abelian group. It is then natural to ask whether a relaxed version of this result is also attainable, and by extending our methods we are able to prove a result of this flavour. Since the combinatorial obstructions to commutativity of $\circ$ are far more complex than those for associativity, topological complications arise that are not present in the earlier work. We also study a problem of Loh concerning sequences of triples of integers from $[n]$ satisfying a certain `increasing' property. Loh studied the maximum length of such a sequence, improving a trivial upper bound of $n^2$ to $n^2/\exp(\log^*n)$ using the triangle removal lemma and conjecturing that a natural construction of length $n^{3/2}$ is best possible. We provide the first power-type improvement to the upper bound, showing that there exists $\epsilon>0$ such that the length is bounded by $n^{2-\epsilon}$. By viewing the triples as edges in a 3-uniform hypergraph, the increasing property shows that the hypergraph is linear and provides further restrictions in terms of forbidden subhypergraphs. By considering this formulation, we provide links to various important open problems including the Brown--Erd\H os--S\'os conjecture. Finally, we present a collection of shorter results. In work connecting to the earlier chapters, we resolve the Brown--Erd\H os--S\'os conjecture in the context of hypergraphs with a group structure, and show moreover that subsets of group multiplication tables exhibit local density far beyond what can be hoped for in general. In work less closely connected to the main theme of the thesis, we also answer a question of Leader, Mili\'cevi\'c and Tan concerning partitions of boxes, consider a problem on projective cubes in $\mathbb{Z}_{2^n}$, and resolve a conjecture concerning a diffusion process on graphs

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field