Academic literature on the topic 'Algèbre médiane'
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Dissertations / Theses on the topic "Algèbre médiane"
Messaci, Mohamed Lamine. "Espaces médians." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4119.
Full textThe subject of this thesis are median spaces and the main direction concerns the study of isometric actions on complete connected locally compact median space of finite rank. We first give a characterization of the local compactness in this context. Then we give a classification theorem in this class for median spaces which admit a transitive action. We show that such median spaces are necessarily isometric to mathbb{R}^n endowed with the ell^1 metric. Finally, we prove that when the isometry group of a median space X verifies certain conditions, then the orbits of any action on X is discrete
Durrleman, Stanley. "Statistical models of currents for measuring the variability of anatomical curves, surfaces and their evolution." Nice, 2010. http://www.theses.fr/2010NICE4072.
Full textThis thesis is about the definition, the implementation and the evaluation of statistical models of variability of curves and surfaces based on currents in the context of Computational Anatomy. Currents were introduced in medical imaging by Joan Glaun\`es and Marc Vaillant in order to define a metric between curves and surfaces which does not assume point correspondence between structures. This metric was used to drive the registration of anatomical data. In this thesis, we propose to extend this tool to analyze the variability of anatomical structures via the inference of generative statistical models. Besides the definition and discussion of these models, we provide a numerical framework to deal efficiently with their estimation. Several applications on real anatomical database in brain and cardiac imaging tend to show the generality and relevance of the approach. In the first part of the manuscript, we extend the work of Joan Glaun\`es and introduce new numerical tools to deal with currents. First, a discretization framework based on linearly spaced grids is provided: it enables to give finite-dimensional projection of currents which converges to the initial continuous representation as the grids become finer. This leads to a generic way to derive robust and efficient algorithms on currents, while controlling the numerical precision. This gives for instance a more stable numerical implementation of the registration algorithm of currents. Then, we define an approximation algorithm which gives a sparse representation of any currents at any desired accuracy via the search of an adapted basis for currents decomposition. This sparse representation is of great interest to compress large sets of anatomical data and to give interpretable representation of statistics on such data sets. In the second part, we define a statistical model which considers a set of curves or surfaces as the result of random deformations of an unknown template plus random residual perturbations in the space of currents. The inference of such models on anatomical data enables to decompose the variability into a geometrical part (captured by diffeomorphisms) and a ``texture'' part (captured by the residual currents). Three applications are provided: first, the analysis of variability of a set of sulcal lines is used to describe the variability of the cortex surface, second, the inference of the model on set of white matter fiber bundles shows that both the geometrical part and the texture part may contain relevant anatomical information and, third, the variability analysis is used in a clinical context for the prediction of the remodeling of the right ventricle of the heart in patients suffering from Tetralogy of Fallot. In the third part, we define statistical models for shape evolution. First, we define a spatiotemporal registration scheme which maps successive scans of one subject to the set of successive scans of another subject. This registration does not only account for the morphological differences between subjects but also for the difference in terms of speed of evolution. Then, we propose a statistical model which estimates a mean scenario of evolution from a set of longitudinal data along with its spatiotemporal variability in the population
Dai, Wei-Wen. "Études de la méthode des éléments frontière : développement d'un algorithme de reconstruction en imagerie d'impédance." Toulouse, INPT, 1994. http://www.theses.fr/1994INPT018H.
Full textDurrleman, Stanley. "Modèles statistiques de courants pour mesurer la variabilité anatomique de courbes, de surfaces et de leur évolution." Phd thesis, Université de Nice Sophia-Antipolis, 2010. http://tel.archives-ouvertes.fr/tel-00631382.
Full textGloaguen, Arnaud. "A statistical and computational framework for multiblock and multiway data analysis." Electronic Thesis or Diss., université Paris-Saclay, 2020. http://www.theses.fr/2020UPASG016.
Full textA challenging problem in multivariate statistics is to study relationships between several sets of variables measured on the same set of individuals. In the literature, this paradigm can be stated under several names as “learning from multimodal data”, “data integration”, “data fusion” or “multiblock data analysis”. Typical examples are found in a large variety of fields such as biology, chemistry, sensory analysis, marketing, food research, where the common general objective is to identify variables of each block that are active in the relationships with other blocks. Moreover, each block can be composed of a high number of measurements (~1M), which involves the computation of billion(s) of associations. A successful investigation of such a dataset requires developing a computational and statistical framework that fits both the peculiar structure of the data as well as its heterogeneous nature.The development of multivariate statistical methods constitutes the core of this work. All these developments find their foundations on Regularized Generalized Canonical Correlation Analysis (RGCCA), a flexible framework for multiblock data analysis that grasps in a single optimization problem many well known multiblock methods. The RGCCA algorithm consists in a single yet very simple update repeated until convergence. If this update is gifted with certain conditions, the global convergence of the procedure is guaranteed. Throughout this work, the optimization framework of RGCCA has been extended in several directions:(i) From sequential to global. We extend RGCCA from a sequential procedure to a global one by extracting all the block components simultaneously with a single optimization problem.(ii) From matrix to higher order tensors. Multiway Generalized Canonical Correlation Analysis (MGCCA) has been proposed as an extension of RGCCA to higher order tensors. Sequential and global strategies have been designed for extracting several components per block. The different variants of the MGCCA algorithm are globally convergent under mild conditions.(iii) From sparsity to structured sparsity. The core of the Sparse Generalized Canonical Correlation Analysis (SGCCA) algorithm has been improved. It provides a much faster globally convergent algorithm. SGCCA has been extended to handle structured sparse penalties.In the second part, the versatility and usefulness of the proposed methods have been investigated on various studies: (i) two imaging-genetic studies, (ii) two Electroencephalography studies and (iii) one Raman Microscopy study. For these analyses, the focus is made on the interpretation of the results eased by considering explicitly the multiblock, tensor and sparse structures