<p> The aim of this thesis is to construct some smooth Einstein manifolds with nonzero Einstein constant, and then to investigate their topological and geometric properties.</p> <p> In the negative case, we are able to construct conformally compact Einstein metrics on 1. products of an arbitrary closed Einstein manifold and a certain even-dimensional ball bundle over products of Hodge Kähler-Einstein manifolds, 2. certain solid torus bundles over a single Fano Kähler-Einstein manifold. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in odd dimensions. As by-products, we obtain many Riemannian manifolds with vanishing Q-curvature.</p> <p> In the positive case, we are able to construct complete Einstein metrics on certain 3-sphere bundles over a Fano Kähler-Einstein manifold. We classify the homeomorphism and diffeomorphism types of the total spaces when the base manifold is the complex projective plane.</p> / Thesis / Doctor of Philosophy (PhD)

This dissertation presents the results of a comparison of human skeletons from two historic villages (the Larson site, 39WW2, and the Leavenworth site, 39CO9), which were inhabited by Great Plains Village Horticulturalists following the arrival of Europeans and Americans. The people living at these villages are suspected to have experienced changes to their cultural practices, with Larson occupied during the beginning of the Post-Contact period and Leavenworth occupied just before the complete abandonment of the Plains Village lifeway. This study examines whether observed differences in the strength of the bones of their limbs resulted from different activities performed at each village or if the introduction of new genes may have altered limb bone shape during the Post-Contact period. The analysis relies on the examination of limb bone strength (cross-sectional properties) to identify patterns related to activities, but unlike previous studies that examine cross-sectional properties, this analysis includes a measure of biological distance to determine if biological kin share limb bone shape. The results indicate some general trends in limb strength during the Post-Contact period including a reduction in male lower limb bone strength and increased asymmetry in the lower limbs of the women at the later village, and many variables indicate greater variation in limb bone strength among women from both villages. While it is difficult to draw any definitive conclusions about activity, the patterns seem to support accounts from the archaeological and historic records regarding the introduction of new cultural practices and a reduction in mobility, especially among males. The interpretation that these patterns may result from changing activities is bolstered by the analysis of biological distance. Mantel results comparing biodistance scores based on odontometry and distance scores based on limb geometry indicate that intragroup pairwise distance scores rarely correlate, with the left humeri being the most consistent exception to this pattern. The left humeri (and potentially the radius and ulna) may exhibit similarities among related individuals due to these non-dominant bones receiving relatively less biomechanical stress during activities. A seeming paradox developed in the analysis when groups (male and female samples from each site) were compared. Unlike biodistance between individuals, the groups exhibiting the greatest genetic similarities also exhibit the greatest similarity in the cross-sectional shape of their right and left femora, right humeri, and right radii, with the mid-section of the femur exhibiting the most consistent correlation regardless of the side used in the analyses. These bones seem to be the ones experiencing the greatest biomechanical stress during activities. At the group level, shape for those bones experiencing a relatively high degree of biomechanical stress during activity seem to mirror genetic relationships. These correlations may result from a convergence between genetic patterns and activity patterns. Despite greater univariate variation within each sample, females across the two sites exhibit closer biological distances than do the males. This result may be due to both matrilocality, which creates less variation within the female population over time, and continuity in female activity over time. By contrast, males exhibit a greater degree of divergence, suggesting that males from each site are more genetically dissimilar than females and that they may have experienced a greater degree of change to their activities.

Femoral and tibial diaphyseal geometry has frequently been used to evaluate mobility and other patterns of physical activity in past populations. The high antero-posterior (A-P) to medio-lateral (M-L) bending rigidity ratio (IX/IY) typical of many hunter-gatherer femora, for instance, may reflect mechanical loads associated with long distance travel. The possible confounding effect of physical terrain on lower limb diaphyseal morphology is rarely evaluated. This study investigated the possible effect of terrain on lower limb shape ratios (IX/IY) and bending and torsional strength (ZP) in adult skeletons from Europe, North America, Africa, and Asia, covering a time span from around 30,000 BP to the present. Midshaft femoral and tibial cross-sectional geometric properties for 3515 individuals were gathered from databases kindly provided by researchers. Geographic coordinates were found for each archaeological site. Local terrain for each site was quantified with ArcGIS 10 mapping software using USGS elevation data, and characterized as flat, hilly, or mountainous. Analysis of variance shows significant differences (pP) of both femoral and tibial midshaft among the three terrain categories, with more A-P oriented diaphyseal shapes and greater strength in hilly and mountainous groups, even after correcting for the effect of subsistence on these cross-sectional properties. These results suggest that terrain needs to be taken into account in analyses of lower limb diaphyseal structure and mobility. Latitude and coastal proximity were also investigated as possible biogeographic factors in the morphology of lower limb diaphyses.

La plupart des méthodes de surveillance des systèmes sont basées sur l'analyse et la caractérisation de grandeurs physiques qui sont par nature tridimensionnelles. Tracées dans un repère euclidien à trois dimensions, ces grandeurs parcourent en fonction du temps une trajectoire dont les caractéristiques géométriques sont représentatives de l'état du système surveillé. Les techniques classiques de surveillance des systèmes étudient les grandeurs mesurées composante par composante, sans prendre en compte leur nature tridimensionnelle et les propriétés géométriques de leur trajectoire. Une part importante de l'information est ainsi ignorée. Dans le cadre de ce travail de recherche, on se propose de développer une méthode d'analyse et de traitement de grandeurs à trois composantes permettant de mettre en évidence les spécificités géométriques des données et de fournir une information complémentaire pour la surveillance des systèmes. La méthode proposée a été appliquée à deux cas différents : la surveillance des creux de tension des réseaux de puissance triphasés et la surveillance des défauts de roulement des machines électriques tournantes. Dans ces deux cas, les résultats obtenus sont prometteurs et montrent que les indicateurs géométriques estimés mènent à de l'information complémentaire qui peut être utile pour la surveillance des systèmes. / Most methods for condition monitoring are based on the analysis and characterization of physical quantities that are three-dimensional in nature. Plotted in a three-dimensional Euclidean space as a function of time, these quantities follow a trajectory whose geometric characteristics are representative of the state of the monitored system. Usual techniques of condition monitoring study the measured quantities component by component, without taking into account their three-dimensional nature and the geometric properties of their trajectory. A significant part of the information is thus ignored. In this research work, we would therefore like to develop a method for the analysis and processing of three-component quantities capable of highlighting the special geometric features of such data and providing complementary information for condition monitoring. The proposed method has been applied to two different cases: voltage dips monitoring in three-phase power networks and bearing faults monitoring in rotating electrical machines. In this two cases, the results obtained are promising and show that the estimated geometric indicators lead to complementary information that can be useful for condition monitoring.

No description available.

À l’holocène, le développement de l'agriculture par les populations humaines a modifié la morphologique du squelette humain. Dans ce cadre, plusieurs recherches se sont intéressées à la biomécanique des populations passées et modernes. Elles supposent qu’une activité physique répétée affecte la structure de l’os. Cette réponse osseuse est analysée par les propriétés géométriques de l’os qui permettent de reconstruire le comportement passé et présent des individus. La distribution osseuse en coupe a donc été étudiée sur les membres supérieurs et inférieurs de populations centrafricaines (du Cameroun et de la République Démocratique du Congo). La première hypothèse de ce mémoire est la suivante, les agriculteurs centrafricains, au mode de vie sédentaire, auraient les membres supérieurs plus robustes, tandis que les chasseurs-cueilleurs, plus mobiles, auraient les membres inférieurs plus robustes. La deuxième hypothèse suppose que les populations d’un milieu/terrain plus accidenté auraient les membres, supérieurs et/ou inférieurs, plus robustes. Nos résultats indiquent plutôt que les chasseurs-cueilleurs et les agriculteurs ont la même robustesse générale, bien que les peuples non sédentarisés soient plus robustes à la mi-diaphyse des radius droits. Contrairement à ce qui était attendu, les fémurs sont plus résistants (CSA) chez les agriculteurs, quand ils sont standardisés par la masse corporelle. En revanche, la moitié supérieure des tibias semblent être plus robuste chez les chasseurs-cueilleurs, quand les propriétés sont standardisées par la longueur de l’os. Les radius et les ulnas des chasseurs-cueilleurs vivant en forêt et en montagne ont la même robustesse. Enfin, seule la section distale des fibulas est plus résistante (CSA) chez les chasseurs-cueilleurs de la montagne que chez les chasseurs-cueilleurs de la forêt. En conclusion, ce mémoire ne nous permet pas d’affirmer que la transition vers l’agriculture s’accompagne d’une réduction de la mobilité et de la robustesse en Afrique centrale. En revanche, il montre que ces individus sont quand même influencés par leur stratégie de subsistance. Un plus grand échantillon est nécessaire pour mieux documenter la transition agricole et l’influence du milieu sur la structure osseuse en Afrique centrale. / The emergence of farming in the Holocene had major impacts on human populations. Many biomechanical studies have explored past and recent populations and have suggested that physical activity affects bone structure. Cross-sectional geometric properties of bones are measured to reconstruct past and recent human behavior. The present study analyses bone cross-sectional geometry of upper and lower limbs long bones of Central African populations (from Cameroon and the Democratic Republic of Congo). This study is based on the premise that agriculturalists, a sedentary group using their upper limbs for farming activities, have more robust upper limbs, while hunter-gatherers, that have an extremely mobile lifestyle, have more robust lower limbs. In addition, it is assumed that populations in more rugged environments/terrains would have more robust upper and/or lower limbs. Against expectation, the upper limbs of non-sedentary and sedentary populations have the same robusticity, although the right radius midshafts of hunter-gatherers are more robust. The femora are more robust in agriculturalists when the significant properties are normalized by body mass. In contrast, the upper part of the tibiae is more robust in hunter-gatherers when the properties are standardised by bone length. Against expectation, it was found that the upper limbs (radii and ulnae) of hunter-gatherers living in the lowland forests and in the mountains have the same robustness. Meanwhile, for the lower limbs, the fibula is more robust in people living in the mountains than those in the forest. In conclusion, these findings do not allow us to assert that the transition to agriculture is accompanied by a reduction in mobility and robusticity in the lower limbs or an increase in robusticity of the upper limb. Nonetheless, this study suggests that individuals are influenced by their economic strategy. However, a larger sample will be needed to better evaluate the role of the transition to agriculture on bone structure in Central Africa.