Einstein's equations in vacuum spacetimes with two spacelike killing vectors are explored using affine projection tensor geometry. By doing a semi-conformal transformation on the metric, a new "fiducial" geometry is constructed using a projection tensor fields. This fiducial geometry provides coordinate independent information about the underlying structure of the spacetime without the use of an explicit form of the metric tensor.

La conception classique de l'organisation des réseaux cérébraux participant au langage décrit deux zones corticales, l'une frontale (Broca), l'autre temporale intervenant respectivement dans la production et la compréhension du langage, unies par un faisceau de substance blanche: le faisceau longitudinal supérieur. L'imagerie par résonance magnétique d'activation (IRMf) a rendu possible la visualisation de zones d'activation corticales, et l'imagerie en tenseur de diffusion avec la tractographie celle des faisceaux de substance blanche. Ces données nouvelles permettent de repenser l'organisation corticale et sous-corticale du langage. L'ensemble des travaux en imagerie d'activation étaye l'hypothèse d'une dissociation dorso-ventrale du traitement du langage. Les zones de traitement de l'information phonétique étant dorsales, et les centres impliqués dans le traitement sémantique plus ventraux. Imagerie d'activation, imagerie du tenseur de diffusion, stimulations corticales et sous-corticales ont permis d'aboutir à un modèle de réseau du langage impliquant une voie dorsale, essentiellement phonologique et une voie ventrale, sémantique présentant deux composantes. La première est directe, par le faisceau fronto-occipital inférieur connectant les aires temporales postérieures à la région orbito-frontale. La seconde est une voie indirecte qui connecte successivement la région occipito-temporale au pôle temporal par l'intermédiaire du faisceau longitudinal inférieur puis le pôle temporal aux aires basifrontales par le faisceau unciné. Cette dernière voie est compensée après résection ou lors des stimulations per-opératoires, suggérant la possibilité de réseaux de suppléance parallèles et bilatéraux. Dans cette vision d'une voie ventrale sémantique bilatérale, notre travail a pour objet par l'utilisation de l'imagerie fonctionnelle d'activation, d'une part, et de l'imagerie en tenseur de diffusion d'autre part, 1) de vérifier le nombre de faisceaux qui sous-tendent cette voie et en particulier de la part attribuable au faisceau longitudinal moyen; 2) de caractériser les réorganisations de la connectivité fonctionnelle du réseau du langage après une chirurgie de tumeur gliale hémisphérique gauche. Dans la première partie de ce travail, après avoir rappelé la filiation phylogénétique de l'homme et du primate non-humain, en insistant sur les dissemblances qui existent dans leur anatomie corticale et sous-corticale, nous exposons comment ces données ont permis d'aboutir à la découverte du faisceau longitudinal moyen chez l'homme. Nous confirmons la visibilité en imagerie du tenseur de diffusion de ce faisceau et nous précisons ses rapports avec les différents faisceaux de substance blanche constitutifs des voies ventrales et dorsales du langage. Enfin nous discutons ces données tractographiques à la lumière de la dissection et discutons du rôle présumé du faisceau dans le langage. Dans un deuxième temps, nous présentons les concepts de connectivité anatomique, fonctionnelle et effective. Puis nous appliquons un outil d'analyse de la connectivité fonctionnelle à des données périopératoires en tâches de fluence afin de réaliser une cartographie de la plasticité périopératoire de la composante sémantique du langage. Les résultats de cette deuxième étude suggèrent un recrutement de l'hémisphère ipsilatéral à la lésion au décours de la chirurgie. Enfin, nous évoquons la possibilité d'induire une désynchronisation (i.e. une altération de la connectivité) du réseau du mode par défaut par une stimulation peropératoire de la partie postérieure du faisceau cingulaire, induisant une sensation de dépersonnalisation, ces résultats suggérant qu'une des fonctions du noeud le plus postérieur du réseau soit de maintenir un état de conscience du monde extérieur. / According to classical conception of the anatomo-functional organization of language, there are two main cortical areas: a frontal area (Broca) and a temporal one (Wernicke) respectively involved in language production and comprehension. Functional magnetic resonance Imaging (fMRI) reveals cortical areas of activation and diffusion tensor imaging-based tractography (DTI) makes feasible the visualization of white-matter tracts in the human brain. On the basis of these techniques, a new conception of language cortical and sub-cortical organization arose, supporting the hypothesis that language processing network is dissociated in an dorso-ventral way. Dorsal areas of the brain being devoted to phonologic processing and its ventral areas to semantic processing of speech. Different techniques such as fMRI, DTI, intraoperative cortical and subcortical mapping made possible to describe two pathways involved in the language network: a dorsal stream and a ventral stream respectively involved in phonologic and semantic processing. As the dorsal route is composed of a unique pathway, the superior longitudinal fasciculus, the ventral stream appears to be composed of two different pathways. First a direct pathway, the inferior occipitofrontal fasciculus, connecting the posterior temporal areas to the orbitofrontal region. The second one, an indirect pathway, the inferior longitudinal fasciculus links the posterior occipitotemporal to the temporal pole, then relayed by the uncinate fasciculus connecting the temporal pole to the basifrontal areas. According to these observations the aim of our work is In the present work, we aim (1) to confirm that the MdLF is constantly found in control subjects and that it can be delineated from the other fiber tracts that constitute language pathways, (2) to characterize the reorganization of language network's functional connectivity follmowing surgical removal of left hemisphere low grade gliomas. In this study, we confirmed that the MdLF is constantly found in healthy volunteers and we clearly delineate the MdLF from the other fascicles that constitute language pathways, especially the ventral pathway. Considering language plasticity, our findings suggest that in the postoperative period, brain plasticity occurs with an ipsilateral recrutment and increased fonctional connectivity in the left hemisphere. Finally, we report a collaborative work observing that intraoperative electrostimulations of the white matter underlying the left posterior cingulate, while performing a naming task, systematically induced an unresponsive state for few seconds in relationship with a dream-like state. This result provides direct evidence that connectivity underlying the posterior node of the default mode network permits maintained consciousness of the external world.

3 Title: Moment-tensor inversion of earthquakes in Greece, method ISOLA Author: Dana Červinková Department: Department of Geophysics Supervisor: Prof. RNDr. Jiří Zahradník, DrSc. Supervisor's e-mail address: jz@karel.troja.mff.cuni.cz Abstract: The possibility of obtaining a reliable moment tensor using a low-frequency waveform inversion from a single seismic station is studied. Deviatoric part of the moment tensor is described in usual way, using its orientation (angles strike, dip, rake), scalar seismic moment M0 and the double-couple percentage (DC%), and also by means of the coefficients of linear combination of elementary mechanisms. We estimate the formal error of the coefficients and study conditionality of the inverse problem. Data from earthquakes Trichonis (Mw = 5.2, April 2007) and Leonidio (Mw = 6.2, January 2008), Greece, are processed using software ISOLA (Sokos and Zahradník). The moment tensor is calculated from many stations and its stability is tested. This reference solution is compared to those independently obtained from single stations. Synthetic tests are performed to understand why the single-station estimates are sufficient for Trichonis, but not for Leonidio, paying attention to the focal depth, station azimuth and epicentral distance. It is found that the depth is crucial at...

This work deals with the linear analysis of plasma waves, especially with the methods of solution of a hot plasma dispersion relation. There are cited some results achieved in the space plasma research and mapped current numerical methods of their analysis. Besides, this work introduces a new numeric procedure, computer code PDRS (Plasma Dispersion Relation Solver), which allows finding solution of a dispersion function of a cold or hot plasma with general distribution function. It also demonstrates the usage of the PDRS methods on real examples of waves in space plasma based on the spacecraft Cluster measurement.

<p>The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.</p><p>We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode. </p><p>We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.</p><p>The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.</p><p>Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.</p><p>The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.</p> / Dissertation

Les dernières décennies ont donné lieux à d'énormes progrès dans la simulation numérique des phénomènes physiques. D'une part grâce au raffinement des méthodes de discrétisation des équations aux dérivées partielles. Et d'autre part grâce à l'explosion de la puissance de calcul disponible. Pourtant, de nombreux problèmes soulevés en ingénierie tels que les simulations multi-physiques, les problèmes d'optimisation et de contrôle restent souvent hors de portée. Le dénominateur commun de ces problèmes est le fléau des dimensions. Un simple problème tridimensionnel requiert des centaines de millions de points de discrétisation auxquels il faut souvent ajouter des milliers de pas de temps pour capturer des dynamiques complexes. L'avènement des supercalculateurs permet de générer des simulations de plus en plus fines au prix de données gigantesques qui sont régulièrement de l'ordre du pétaoctet. Malgré tout, cela n'autorise pas une résolution ``exacte'' des problèmes requérant l'utilisation de plusieurs paramètres. L'une des voies envisagées pour résoudre ces difficultés est de proposer des représentations ne souffrant plus du fléau de la dimension. Ces représentations que l'on appelle séparées sont en fait un changement de paradigme. Elles vont convertir des objets tensoriels dont la croissance est exponentielle $n^d$ en fonction du nombre de dimensions $d$ en une représentation approchée dont la taille est linéaire en $d$. Pour le traitement des données tensorielles, une vaste littérature a émergé ces dernières années dans le domaine des mathématiques appliquées.Afin de faciliter leurs utilisations dans la communauté des mécaniciens et en particulier pour la simulation en mécanique des fluides, ce manuscrit présente dans un vocabulaire rigoureux mais accessible les formats de représentation des tenseurs et propose une étude détaillée des algorithmes de décomposition de données qui y sont associées. L'accent est porté sur l'utilisation de ces méthodes, aussi la bibliothèque de calcul texttt{pydecomp} développée est utilisée pour comparer l'efficacité de ces méthodes sur un ensemble de cas qui se veut représentatif. La seconde partie de ce manuscrit met en avant l'étude de l'écoulement dans une cavité entraînée à haut nombre de Reynolds. Cet écoulement propose une physique très riche (séquence de bifurcation de Hopf) qui doit être étudiée en amont de la construction de modèle réduit. Cette étude est enrichie par l'utilisation de la décomposition orthogonale aux valeurs propres (POD). Enfin une approche de construction ``physique'', qui diffère notablement des développements récents pour les modèles d'ordre réduit, est proposée. La connaissance détaillée de l'écoulement permet de construire un modèle réduit simple basé sur la mise à l'échelle des fréquences d'oscillation (time-scaling) et des techniques d'interpolation classiques (Lagrange,..). / Numerical simulation has experienced tremendous improvements in the last decadesdriven by massive growth of computing power. Exascale computing has beenachieved this year and will allow solving ever more complex problems. But suchlarge systems produce colossal amounts of data which leads to its own difficulties.Moreover, many engineering problems such as multiphysics or optimisation andcontrol, require far more power that any computer architecture could achievewithin the current scientific computing paradigm. In this thesis, we proposeto shift the paradigm in order to break the curse of dimensionality byintroducing decomposition and building reduced order models (ROM) for complexfluid flows.This manuscript is organized into two parts. The first one proposes an extendedreview of data reduction techniques and intends to bridge between appliedmathematics community and the computational mechanics one. Thus, foundingbivariate separation is studied, including discussions on the equivalence ofproper orthogonal decomposition (POD, continuous framework) and singular valuedecomposition (SVD, discrete matrices). Then a wide review of tensor formats andtheir approximation is proposed. Such work has already been provided in theliterature but either on separate papers or into a purely applied mathematicsframework. Here, we offer to the data enthusiast scientist a comparison ofCanonical, Tucker, Hierarchical and Tensor train formats including theirapproximation algorithms. Their relative benefits are studied both theoreticallyand numerically thanks to the python library texttt{pydecomp} that wasdeveloped during this thesis. A careful analysis of the link between continuousand discrete methods is performed. Finally, we conclude that for mostapplications ST-HOSVD is best when the number of dimensions $d$ lower than fourand TT-SVD (or their POD equivalent) when $d$ grows larger.The second part is centered on a complex fluid dynamics flow, in particular thesingular lid driven cavity at high Reynolds number. This flow exhibits a seriesof Hopf bifurcation which are known to be hard to capture accurately which iswhy a detailed analysis was performed both with classical tools and POD. Oncethis flow has been characterized, emph{time-scaling}, a new ``physics based''interpolation ROM is presented on internal and external flows. This methodsgives encouraging results while excluding recent advanced developments in thearea such as EIM or Grassmann manifold interpolation.

Mild traumatic brain injuries (MTBI) are the leading type of head injuries with appreciable risque of sequelae leading to functional and psychological deficits. Although mild traumatic brain injuries are frequently underdiagnosed by conventional imaging modalities, rapidly evolving techniques such as diffusion tensor imaging (DTI) reveal subtle changes in white matter integrity as a result of head trauma and play an important role in refining diagnosis, therapeutic interventions and management of MTBI. In this dissertation we use diffusion tensor imaging to detect the microstructural changes induced by axonal injuries and to monitor their evolution during the recovery process. DTI data were previously acquired from 11 subjects, football players of age 19-23 years (median age 20 years). Three players had suffered a mild traumatic brain injury during the season and underwent scanning within 24 hours after the injury with follow-ups after one and two weeks. A set of diffusion indices, such as fractional anisotropy, axial, radial and mean diffusivity were derived from the diffusion tensor. Changes in diffusion indices in concussed subjects were analyzed based on two different approaches: whole brain analysis, using tract-based spatial statistics (TBSS) and region of interest analysis (ROI). In both approaches we use a voxelwise analysis to examine group differences in diffusion indices between five controls and three concussed subjects for all DTI scans. Additional statistical analysis was performed between control groups consisting of five and three non-injured players. Both analyses demonstrated that the MTBI group reveals increase in fractional anisotropy and decreases in transversal and mean diffusivity in cortical and subcortical areas within 24 hours after the injury. / No changes were detected in TBSS analysis for the follow-up data sets. Furthermore, our ROI approach revealed multiples regions with significantly different voxels, non-uniformly distributed throughout the brain, for all diffusion indices in all three scans. Three of the diffusion indices fractional anisotropy, mean and transversal diffusivity showed higher vulnerability to head trauma in subcortical and cortical areas than in regions in the lower brain. Recovery of white matter pathways occured at different locations in the brain at one and two weeks after head trauma. Strong recovery was observed in mean and transversal diffusivity in subcortical areas that correspond to the corticospinal tract. No recovery was found for fractional anisotropy and axial diffusivity in the same region. Also, decreases in fractional anisotropy and increases in transversal and axial diffusivity were observed in the spleninum of the corpus callosum. As voxelwise analysis performed on DTI data revealed white matter regions, which exhibit changes in diffusion parameters in the concussed group for all three scans, we conclude that diffusion tensor imaging is a powerful technique for early detection of axonal injuries and may serve as an important tool for monitoring microstructural changes during the recovery process. / by Angelica Hotiu. / Thesis (Ph.D.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

Étant donné une variété symplectique $(M,\omega)$, il existe toujours des structures presque complexes $\omega$-compatibles positives. La question qui nous intéresse est de trouver des méthodes de sélection de certaines de ces structures. Des réponses ont déjà été données par V. Apostolov et T.Draghici, J.G. Evans, et J. Keller et M. Lejmi. Nous nous intéressons ici principalement à des méthodes de sélection définies en termes du tenseur de Nijenhuis. De manière très générale, lorsqu'on veut sélectionner certaines données géométriques, on peut aborder le problème de différentes manières. L’une d’entre elles consiste à regarder la décomposition en composantes irréductibles de certains tenseurs naturellement associés à la structure considérée et poser des conditions sur certaines composantes. Nous avons montré que le tenseur de Nijenhuis est irréductible sous l'action du groupe unitaire. Cette irréductibilité ne nous permet pas d'imposer d'autre condition linéaire à ce tenseur que son annulation, qui correspond aux variétés de Kähler. Une autre méthode possible de sélection est d’imposer des conditions à certaines distributions liées au problème. Nous avons étudié des distributions liées au tenseur de Nijenhuis. Nous nous sommes intéressés ici aux dimensions et propriétés d’involutivité possibles de ces distributions. Nous donnons des exemples invariants sous l’action d’un groupe, construits sur des groupes symplectiques ou sur des fibrés de twisteurs sur une variété riemannienne. La dernière méthode envisagée dans ce travail est la considération de fonctionnelles définies à partir des données. Pour construire une fonctionnelle la plus simple possible en termes du tenseur de Nijenhuis, nous intégrons une fonction polynomiale du second degré en les composantes du tenseur de Nijenhuis. On montre qu’un tel polynôme est toujours un multiple de la norme au carré de ce tenseur. La fonctionnelle obtenue est celle étudiée par Evans. Elle est a priori peu intéressante pour notre problème de sélection car il a prouvé qu’on peut trouver des exemples de variétés symplectiques n’admettant aucune structure kählérienne mais telle que l’infimum de la fonctionnelle soit nul / Given a symplectic manifold $(M,\omega)$, there always exist almost complex $\omega,$-compatible positive structures. The problem studied in this thesis is to find methods to select some of these structures. Answers have already been suggested by V. Apostolov and T.Draghici, J. G. Evans, and J. Keller and M. Lejmi. We are mainly interested here in selection methods defined in terms of the Nijenhuis tensor. The problem of selecting geometric objects can be tackled in various ways. One of them is to decompose into irreducible components some tensors naturally associated with the structure, and to impose conditions on some of those components. We prove that the Nijenhuis tensor is irreducible under the action of the unitary group. This irreducibility does not allow to impose any linear condition on the Nijenhuis tensor, except the vanishing of it, which corresponds to Kähler manifolds. Another possible method of selection is to impose conditions on distributions related to the problem. We study distributions defined by the Nijenhuis tensor. Our results concern the possible dimensions and properties of involutivity of these distributions. We give examples which are invariant under the action of a group, on some symplectic groups and on twisted bundles over some Riemannian manifolds. The last method considered in this work consists in looking for extremals of functionals defined from the data. To construct the simplest functional defined in terms of the Nijenhuis tensor, we integrate a polynomial function of the second degree into the components of this tensor. All such polynomials are multiple of the square of the norm of this tensor. This functional is the one studied by Evans; the drawback for our selection problem is that there exist examples of compact symplectic manifolds which do not admit any K\"ahler structure but such that the infimum of the functional is zero

Freeform curve design has existed in various forms for at least two millennia, and is important throughout computer-aided design and manufacture. With the increasing importance of animation and robotics, coupled with the increasing power of computers, there is now interest in freeform motion design, which, in part, extends techniques from curve design, as well as introducing some entirely distinct challenges. There are several approaches to freeform motion construction, and the first step in designing freeform motions is to choose a representation. Unlike for curves, there is no "standard" way of representing freeform motions, and the different tools available each have different properties. A motion can be viewed as a continuously-varying pose, where a pose is a position and an orientation. This immediately presents a problem; the dimensions of rotations and translations are different, and it is not clear how the two can be compared, such as to define distance along a motion. One solution is to treat the rotational and translational components of a motion separately, but this is inelegant and clumsy. The philosophy of this thesis is that a motion is not defined purely by rotations and translations, but that the body following a motion is a part of that motion. Specifically, the part of the body that is accounted for is its inertia tensor. The significance of the inertia tensor is that it allows the rotational and translational parts of a motion to be, in some sense, compared in a dimensionally- consistent way. Using the inertia tensor, this thesis finds the form of kinetic energy in <;1'4, and also discusses extensions of the concepts of arc length and curvature to the space of motions, allowing techniques from curve fairing to be applied to motion fairing. Two measures of motion fairness are constructed, and motion fairing is the process of minimizing the measure of a motion by adjusting degrees of freedom present in the motion's construction. This thesis uses the geometric algebra <;1'4 in the generation offreeform motions, and the fairing of such motions. <;1'4 is chosen for its particular elegance in representing rigid-body transforms, coupled with an equivalence relation between elements representing transforms more general than for ordinary homogeneous coordinates. The properties of the algebra germane to freeform motion design and improvement are given, and two distinct frameworks for freeform motion construction and modification are studied in detail.

Pedestrian detection is a canonical instance of object detection that remains a popular topic of research and a key problem in computer vision due to its diverse applications. These applications have the potential to positively improve the quality of life. In recent years, the number of approaches to detecting pedestrians in monocular and binocular images has grown steadily. However, the use of multispectral imaging is still uncommon. This thesis work presents a novel approach to data and feature fusion of a multispectral imaging system for pedestrian detection. It also includes the design and building of a test rig which allows for quick data collection of real-world driving. An application of the mathematical theory of trifocal tensor is used to post process this data. This allows for pixel level data fusion across a multispectral set of data. Performance results based on commonly used SVM classification architectures are evaluated against the collected data set. Lastly, a novel cascaded SVM architecture used in both classification and detection is discussed. Performance improvements through the use of feature fusion is demonstrated.