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OpenStereo foi desenvolvido originalmente para preencher uma lacuna entre aplicativos de anáalise para geologia estrutural, como um software livre, gratuito e multi-plataforma. Ao longo dos anos ele adquiriu um grande núumero de usuários, com citações regulares. Este trabalho objetivou a reestruturação do OpenStereo como um todo, mudando-o para uma nova estrutura de interface gráfica e construíndo-o do zero visando desempenho, estabilidade e facilidade de manutenção e extensão. Diversas novas funcionalidades foram incluídas tais como projetos, conversão de notação de atitudes, ajuste de pequenos círculos, extração de atitudes de modelos tridimensionais e conversão de shapefiles de linhas para dados circulares. A pesquisa gerou dois subprodutos principais: um novo método gráfico para ajuste de pequenos círculos e a biblioteca de análise de dados estruturais Auttitude. / OpenStereo was originally developed to fill a gap among software packages for structural geology analysis, as a free open source cross-platform software. Over the years it has acquired a great number of users, with regular citations. This work aimed to restructure OpenStereo as a whole, changing to a new graphical interface framework and building it from the ground up for speed, stability, ease of maintenance and extension. Many new functionalities were also included, such as project management, structural attitudes notation handling, small circle fitting, extractions of attitudes from three-dimensional models and conversion of lines shapefiles to circular data. The research involved had two main byproducts, a new graphical method for small circle data fitting and a directional data analysis library, Auttitude.

Doctor of Philosophy / Collective actions of large animal groups result in elaborate behaviour, whose nature can be breathtaking in their complexity. Social organisation is the key to the origin of this behaviour and the mechanisms by which this organisation occurs are of particular interest. In this thesis, these mechanisms of social interactions and their consequences for group-level behaviour are explored. Social interactions amongst individuals are based on simple rules of attraction, alignment and orientation amongst neighbouring individuals. As part of this study, we will be interested in data that takes the form of a set of directions in space. In Chapter 2, we discuss relevant statistical measure and theory which will allow us to analyse directional data. These statistical tools will be employed on the results of the simulations of the mathematical models formulated in the course of the thesis. The first mathematical model for collective group behaviour is a Lagrangian self-organising model, which is formulated in Chapter 3. This model is based on basic social interactions between group members. Resulting collective behaviours and other related issues are examined during this chapter. Once we have an understanding of the model in Chapter 3, we use this model in Chapter 4 to investigate the idea of guidance of large groups by a select number of individuals. These individuals are privy to information regarding the location of a specific goal. This is used to explore a mechanism proposed for honeybee (Apis mellifera) swarm migrations. The spherical theory introduced in Chapter 2 will prove to be particularly useful in analysing the results of the modelling. In Chapter 5, we introduce a second mathematical model for aggregative behaviour. The model uses ideas from electromagnetic forces and particle physics, reinterpreting them in the context of social forces. While attraction and repulsion terms have been included in similar models in past literature, we introduce an orientation force to our model and show the requirement of a dissipative force to prevent individuals from escaping from the confines of the group.

Doctor of Philosophy / Collective actions of large animal groups result in elaborate behaviour, whose nature can be breathtaking in their complexity. Social organisation is the key to the origin of this behaviour and the mechanisms by which this organisation occurs are of particular interest. In this thesis, these mechanisms of social interactions and their consequences for group-level behaviour are explored. Social interactions amongst individuals are based on simple rules of attraction, alignment and orientation amongst neighbouring individuals. As part of this study, we will be interested in data that takes the form of a set of directions in space. In Chapter 2, we discuss relevant statistical measure and theory which will allow us to analyse directional data. These statistical tools will be employed on the results of the simulations of the mathematical models formulated in the course of the thesis. The first mathematical model for collective group behaviour is a Lagrangian self-organising model, which is formulated in Chapter 3. This model is based on basic social interactions between group members. Resulting collective behaviours and other related issues are examined during this chapter. Once we have an understanding of the model in Chapter 3, we use this model in Chapter 4 to investigate the idea of guidance of large groups by a select number of individuals. These individuals are privy to information regarding the location of a specific goal. This is used to explore a mechanism proposed for honeybee (Apis mellifera) swarm migrations. The spherical theory introduced in Chapter 2 will prove to be particularly useful in analysing the results of the modelling. In Chapter 5, we introduce a second mathematical model for aggregative behaviour. The model uses ideas from electromagnetic forces and particle physics, reinterpreting them in the context of social forces. While attraction and repulsion terms have been included in similar models in past literature, we introduce an orientation force to our model and show the requirement of a dissipative force to prevent individuals from escaping from the confines of the group.

OpenStereo foi desenvolvido originalmente para preencher uma lacuna entre aplicativos de anáalise para geologia estrutural, como um software livre, gratuito e multi-plataforma. Ao longo dos anos ele adquiriu um grande núumero de usuários, com citações regulares. Este trabalho objetivou a reestruturação do OpenStereo como um todo, mudando-o para uma nova estrutura de interface gráfica e construíndo-o do zero visando desempenho, estabilidade e facilidade de manutenção e extensão. Diversas novas funcionalidades foram incluídas tais como projetos, conversão de notação de atitudes, ajuste de pequenos círculos, extração de atitudes de modelos tridimensionais e conversão de shapefiles de linhas para dados circulares. A pesquisa gerou dois subprodutos principais: um novo método gráfico para ajuste de pequenos círculos e a biblioteca de análise de dados estruturais Auttitude. / OpenStereo was originally developed to fill a gap among software packages for structural geology analysis, as a free open source cross-platform software. Over the years it has acquired a great number of users, with regular citations. This work aimed to restructure OpenStereo as a whole, changing to a new graphical interface framework and building it from the ground up for speed, stability, ease of maintenance and extension. Many new functionalities were also included, such as project management, structural attitudes notation handling, small circle fitting, extractions of attitudes from three-dimensional models and conversion of lines shapefiles to circular data. The research involved had two main byproducts, a new graphical method for small circle data fitting and a directional data analysis library, Auttitude.

Dans cette thèse, nous nous intéressons au problème de tester en grande dimension l'uniformité sur la sphère-unité $S^{p_n-1}$ (la dimension des observations, $p_n$, dépend de leur nombre, $n$, et être en grande dimension signifie que $p_n$ tend vers l'infini en même temps que $n$). Nous nous restreignons dans un premier temps à des contre-hypothèses ``monotones'' de densité croissante le long d'une direction ${\pmb \theta}_n\in S^{p_n-1}$ et dépendant d'un paramètre de concentration $\kappa_n>0$. Nous commençons par identifier le taux $\kappa_n$ auquel ces contre-hypothèses sont contiguës à l'uniformité ;nous montrons ensuite grâce à des résultats de normalité locale asymptotique, que le test d'uniformité le plus classique, le test de Rayleigh, n'est pas optimal quand ${\pmb \theta}_n$ est connu mais qu'il le devient à $p$ fixé et dans le cas FvML en grande dimension quand ${\pmb \theta}_n$ est inconnu.Dans un second temps, nous considérons des contre-hypothèses ``axiales'', attribuant la même probabilité à des points diamétralement opposés. Elles dépendent aussi d'un paramètre de position ${\pmb \theta}_n\in S^{p_n-1}$ et d'un paramètre de concentration $\kappa_n\in\R$. Le taux de contiguïté s'avère ici plus élevé et suggère un problème plus difficile que dans le cas monotone. En effet, le test de Bingham, le test classique dans le cas axial, n'est pas optimal à ${\pmb \theta}_n$ inconnu et $p$ fixé, et ne détecte pas les contre-hypothèses contiguës en grande dimension. C'est pourquoi nous nous tournons vers des tests basés sur les plus grande et plus petite valeurs propres de la matrice de variance-covariance et nous déterminons leurs distributions asymptotiques sous les contre-hypothèses contiguës à $p$ fixé.Enfin, à l'aide d'un théorème central limite pour martingales, nous montrons que sous certaines conditions et après standardisation, les statistiques de Rayleigh et de Bingham sont asymptotiquement normales sous l'hypothèse d'invariance par rotation des observations. Ce résultat permet non seulement d'identifier le taux auquel le test de Bingham détecte des contre-hypothèses axiales mais aussi celui auquel il détecte des contre-hypothèses monotones. / In this thesis we are interested in testing uniformity in high dimensions on the unit sphere $S^{p_n-1}$ (the dimension of the observations, $p_n$, depends on their number, and high-dimensional data are such that $p_n$ diverges to infinity with $n$).We consider first ``monotone'' alternatives whose density increases along an axis ${\pmb \theta}_n\in S^{p_n-1}$ and depends on a concentration parameter $\kappa_n>0$. We start by identifying the rate at which these alternatives are contiguous to uniformity; then we show thanks to local asymptotic normality results that the most classical test of uniformity, the Rayleigh test, is not optimal when ${\pmb \theta}_n$ is specified but becomes optimal when $p$ is fixed and in the high-dimensional FvML case when ${\pmb \theta}_n$ is unspecified.We consider next ``axial'' alternatives, assigning the same probability to antipodal points. They also depend on a location parameter ${\pmb \theta}_n\in S^{p_n-1}$ and a concentration parameter $\kappa_n\in\R$. The contiguity rate proves to be higher in that case and implies that the problem is more difficult than in the monotone case. Indeed, the Bingham test, the classical test when dealing with axial data, is not optimal when $p$ is fixed and ${\pmb \theta}_n$ is not specified, and is blind to the contiguous alternatives in high dimensions. This is why we turn to tests based on the extreme eigenvalues of the covariance matrix and establish their fixed-$p$ asymptotic distributions under contiguous alternatives.Finally, thanks to a martingale central limit theorem, we show that, under some assumptions and after standardisation, the Rayleigh and Bingham test statistics are asymptotically normal under general rotationally symmetric distributions. It enables us to identify the rate at which the Bingham test detects axial alternatives and also monotone alternatives. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

yes / Archaeomagnetic dating offers a valuable chronological tool for archaeological investigations, particularly for dating fired material. The method depends on the establishment of a dated record of secular variation of the Earth's magnetic field and this paper presents new and updated archaeomagnetic directional data from the UK and geomagnetic secular variation curves arising from them. The data are taken from publications from the 1950's to the present day; 422 dated entries derived from existing archaeo and geomagnetic databases are re-evaluated and 487 new directions added, resulting in 909 entries with corresponding dates, the largest collection of dated archaeomagnetic directions from a single country. An approach to improving the largest source of uncertainty, the independent dating, is proposed and applied to the British Iron Age, resulting in 145 directions from currently available databases being updated with revised ages and/or uncertainties, and a large scale reassessment of age assignments prior to inclusion into the Magnetic Moments of the Past and GEOMAGIA50 databases. From the significantly improved dataset a new archaeomagnetic dating curve for the UK is derived through the development of a temporally continuous geomagnetic field model, and is compared with previous UK archaeomagnetic dating curves and global field models. The new model, ARCH-UK.1 allows model predictions for any location in the UK with associated uncertainties. It is shown to improve precision and accuracy in archaeomagnetic dating, and to provide new insight into past geomagnetic field changes. / Arts and Humanities Research Council

No / Many datasets are available in the form of conventional databases, or simplified comma separated values. The machines do not adequately handle these types of unstructured data. There are compatibility issues as well, which are not addressed well to manage the transformation. The literature describes several rigid techniques that do the transformation from unstructured or conventional data sources to Resource Description Framework (RDF) with data loss and limited customization. These techniques do not present any remote way that helps to avoid compatibility issues among these data forms simultaneous utilization. In this article, a new approach has been introduced that allows data mapping. This mapping can be used to understand their differences at the level of data representations. The mapping is done using Extensible Markup Language (XML) based data structures as intermediate data presenter. This approach also allows bi-directional data transformation from conventional data format and RDF without data loss and with improved remote availability of data. This is a solution to the issue concerning update when dealing with any change in the remote environment for the data. Thus, traditional systems can easily be transformed into Semantic Web-based system. The same is true when transforming data back to conventional data format, i.e. Database (DB). This bidirectional transformation results in no data loss, which creates compatibility between both traditional and semantic form of data. It will allow applying inference and reasoning on conventional systems. The census un-employment dataset is used which is being collected from US different states. Remote bi-directional transformation is mapped on the dataset and developed linkage using relationships between data elements. This approach will help to handle both types of data formats to co-exist at the same time, which will create opportunities for data compatibility, statistical powers and inference on linked data found in remote areas.

Dans la vie actuelle, les données directionnelles sont présentes dans la majorité des domaines, sous plusieurs formes, différents aspects et de grandes tailles/dimensions, d'où le besoin de méthodes d'étude efficaces des problématiques posées dans ce domaine. Pour aborder le problème de la classification automatique, l'approche probabiliste est devenue une approche classique, reposant sur l'idée simple : étant donné que les g classes sont différentes entre elles, on suppose que chacune suit une loi de probabilité connue, dont les paramètres sont en général différents d'une classe à une autre; on parle alors de modèle de mélange de lois de probabilités. Sous cette hypothèse, les données initiales sont considérées comme un échantillon d'une variable aléatoire d-dimensionnelle dont la densité est un mélange de g distributions de probabilités spécifiques à chaque classe. Dans cette thèse nous nous sommes intéressés à la classification automatique de données directionnelles, en utilisant des méthodes de classification les mieux adaptées sous deux approches: géométrique et probabiliste. Dans la première, en explorant et comparant des algorithmes de type kmeans; dans la seconde, en s'attaquant directement à l'estimation des paramètres à partir desquels se déduit une partition à travers la maximisation de la log-vraisemblance, représentée par l'algorithme EM. Pour cette dernière approche, nous avons repris le modèle de mélange de distributions de von Mises-Fisher, nous avons proposé des variantes de l'algorithme EMvMF, soit CEMvMF, le SEMvMF et le SAEMvMF, dans le même contexte, nous avons traité le problème de recherche du nombre de composants et le choix du modèle de mélange, ceci en utilisant quelques critères d'information : Bic, Aic, Aic3, Aic4, Aicc, Aicu, Caic, Clc, Icl-Bic, Ll, Icl, Awe. Nous terminons notre étude par une comparaison du modèle vMF avec un modèle exponentiel plus simple ; à l'origine ce modèle part du principe que l'ensemble des données est distribué sur une hypersphère de rayon ρ prédéfini, supérieur ou égal à un. Nous proposons une amélioration du modèle exponentiel qui sera basé sur une étape estimation du rayon ρ au cours de l'algorithme NEM. Ceci nous a permis dans la plupart de nos applications de trouver de meilleurs résultats; en proposant de nouvelles variantes de l'algorithme NEM qui sont le NEMρ , NCEMρ et le NSEMρ. L'expérimentation des algorithmes proposés dans ce travail a été faite sur une variété de données textuelles, de données génétiques et de données simulées suivant le modèle de von Mises-Fisher (vMF). Ces applications nous ont permis une meilleure compréhension des différentes approches étudiées le long de cette thèse. / In contemporary life directional data are present in most areas, in several forms, aspects and large sizes / dimensions; hence the need for effective methods of studying the existing problems in these fields. To solve the problem of clustering, the probabilistic approach has become a classic approach, based on the simple idea: since the g classes are different from each other, it is assumed that each class follows a distribution of probability, whose parameters are generally different from one class to another. We are concerned here with mixture modelling. Under this assumption, the initial data are considered as a sample of a d-dimensional random variable whose density is a mixture of g distributions of probability where each one is specific to a class. In this thesis we are interested in the clustering of directional data that has been treated using known classification methods which are the most appropriate for this case. In which both approaches the geometric and the probabilistic one have been considered. In the first, some kmeans like algorithms have been explored and considered. In the second, by directly handling the estimation of parameters from which is deduced the partition maximizing the log-likelihood, this approach is represented by the EM algorithm. For the latter approach, model mixtures of distributions of von Mises-Fisher have been used, proposing variants of the EM algorithm: EMvMF, the CEMvMF, the SEMvMF and the SAEMvMF. In the same context, the problem of finding the number of the components in the mixture and the choice of the model, using some information criteria {Bic, Aic, Aic3, Aic4, AICC, AICU, CAIC, Clc, Icl-Bic, LI, Icl, Awe} have been discussed. The study concludes with a comparison of the used vMF model with a simpler exponential model. In the latter, it is assumed that all data are distributed on a hypersphere of a predetermined radius greater than one, instead of a unit hypersphere in the case of the vMF model. An improvement of this method based on the estimation step of the radius in the algorithm NEMρ has been proposed: this allowed us in most of our applications to find the best partitions; we have developed also the NCEMρ and NSEMρ algorithms. The algorithms proposed in this work were performed on a variety of textual data, genetic data and simulated data according to the vMF model; these applications gave us a better understanding of the different studied approaches throughout this thesis.

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