Hyperspaces, shape theory and computational topology

Esta tesis trata sobre aproximaciones de espacios métricos compactos. La aproximación y reconstrucción de espacios topológicos mediante otros más sencillos es un tema antigüo en topología geométrica. La idea es construir un espacio muy sencillo lo más parecido posible al espacio original. Como es muy difícil (o incluso no tiene sentido) intentar obtener una copia homeomorfa, el objetivo será encontrar un espacio que preserve algunas propriedades topológicas (algebraicas o no) como compacidad, conexión, axiomas de separación, tipo de homotopía, grupos de homotopía y homología, etc. Los primeros candidatos como espacios sencillos con propiedades del espacio original son los poliedros. Ver el artículo [45] para los resultados principales. En el germen de esta idea, destacamos los estudios de Alexandroff en los años 20, relacionando la dimensión del compacto métrico con la dimensión de ciertos poliedros a través de aplicaciones con imágenes o preimágenes controladas (en términos de distancias). En un contexto más moderno, la idea de aproximación puede ser realizada construyendo un complejo simplicial basado en el espacio original, como el complejo de Vietoris-Rips o el complejo de Cech y comparar su realización con él. En este sentido, tenemos el clásico lema del nervio [12, 21] el cual establece que para un recubrimiento por abiertos “suficientemente bueno" del espacio (es decir, un recubrimiento con miembros e intersecciones contractibles o vacías), el nervio del recubrimiento tiene el tipo de homotopía del espacio original. El problema es encontrar estos recubrimientos (si es que existen). Para variedades Riemannianas, existen algunos resultados en este sentido, utilizando los complejos de Vietoris-Rips. Hausmann demostró [35] que la realización del complejo de Vietoris-Rips de la variedad, para valores suficientemente bajos del parámetro, tiene el tipo de homotopía de dicha variedad. En [40], Latschev demostró una conjetura establecida por Hausmann: El tipo de homotopía de la variedad se puede recuperar utilizando un conjunto finito de puntos (suficientemente denso) para el complejo de Vietoris-Rips. Los resultados de Petersen [58], comparando la distancia Gromov-Hausdorff de los compactos métricos con su tipo de homotopía, son también interesantes. Aquí, los poliedros salen a relucir en las demostraciones, no en los resultados...

The role of impurities in the shape, structure and physical properties of semiconducting oxide nanostructures grown by thermal evaporation

A thermal evaporation method developed in the research group enables to grow and design several morphologies of semiconducting oxide nanostructures, such as Ga_2O_3, GeO_2 or Sb_2O_3, among others, and some ternary oxide compounds (ZnGa_2O_4, Zn_2GeO_4). In order to tailor physical properties, a successful doping of these nanostructures is required. However, for nanostructured materials, doping may affect not only their physical properties, but also their morphology during the thermal growth process. In this paper, we will show some examples of how the addition of impurities may result into the formation of complex structures, or changes in the structural phase of the material. In particular, we will consider the addition of Sn and Cr impurities into the precursors used to grow Ga_2O_3, Zn_2GeO_4 and Sb_2O_3 nanowires, nanorods or complex nanostructures, such as crossing wires or hierarchical structures. Structural and optical properties were assessed by electron microscopy (SEM and TEM), confocal microscopy, spatially resolved cathodoluminescence (CL), photoluminescence, and Raman spectroscopies. The growth mechanisms, the luminescence bands and the optical confinement in the obtained oxide nanostructures will be discussed. In particular, some of these nanostructures have been found to be of interest as optical microcavities. These nanomaterials may have applications in optical sensing and energy devices.

Bone morphology of the femur and tibia captured by statistical shape modelling predicts rapid bone loss in acute spinal cord injury patients

We would like to thank the study participants and the clinical and research staff at the Queen Elizabeth National Spinal Injury Unit, as without them this study would not have been possible. We are grateful for the funding received from Glasgow Research Partnership in Engineering for the employment of SC during data collection for this study. We would like to thank the Royal Society of Edinburgh's Scottish Crucible scheme for providing the opportunity for this collaboration to occur. We are also indebted to Maria Dumitrascuta for her time and effort in producing inter-repeatability results for the shape models.

Variations in hip shape are associated with radiographic knee osteoarthritis : cross-sectional and longitudinal analyses of the Johnston County Osteoarthritis Project

Funding was provided in part by the US National Institute of Arthritis and Musculoskeletal and Skin Diseases (NIAMS) K23 AR061406 (Nelson); US National Institutes of Health (NIH)/NIAMS P60AR30701 (Jordan/Renner/Schwartz); US Centers for Disease Control/Association of Schools of Public Health S043 and S3486 (Jordan/Renner); K24-AR04884, P50-AR063043, and P50-AR060752 (Lane); and NIH/National Center for Advancing Translational Sciences KL2TR001109 (Golightly).

Bone morphology of the femur and tibia captured by statistical shape modelling predicts rapid bone loss in acute spinal cord injury patients

We would like to thank the study participants and the clinical and research staff at the Queen Elizabeth National Spinal Injury Unit, as without them this study would not have been possible. We are grateful for the funding received from Glasgow Research Partnership in Engineering for the employment of SC during data collection for this study. We would like to thank the Royal Society of Edinburgh's Scottish Crucible scheme for providing the opportunity for this collaboration to occur. We are also indebted to Maria Dumitrascuta for her time and effort in producing inter-repeatability results for the shape models.

Variations in hip shape are associated with radiographic knee osteoarthritis : cross-sectional and longitudinal analyses of the Johnston County Osteoarthritis Project

Funding was provided in part by the US National Institute of Arthritis and Musculoskeletal and Skin Diseases (NIAMS) K23 AR061406 (Nelson); US National Institutes of Health (NIH)/NIAMS P60AR30701 (Jordan/Renner/Schwartz); US Centers for Disease Control/Association of Schools of Public Health S043 and S3486 (Jordan/Renner); K24-AR04884, P50-AR063043, and P50-AR060752 (Lane); and NIH/National Center for Advancing Translational Sciences KL2TR001109 (Golightly).

Performance Related Pay, Efficiency Wages and the Shape of the Tenure-Earnings Profile

Peer reviewed

Multi-impurity adsorption model for modeling crystal purity and shape evolution during crystallization processes in impure media

Peer reviewed

Widespread range expansions shape latitudinal variation in insect thermal limits

I thank the authors of previous studies on global variation in insect thermal tolerances who have generously provided open access use of their data sets.

Windscapes shape seabird instantaneous energy costs but adult behavior buffers impact on offspring

Acknowledgements K. Ashbrook, M. Barrueto, K. Elner, A. Hargreaves, S. Jacobs, G. Lancton, M. LeVaillant, E. Grosbellet, A. Moody, A. Ronston, J. Provencher, P. Smith, K. Woo and P. Woodward helped in the field. J. Nakoolak kept us safe from bears. N. Sapir and two anonymous reviewers provided very useful comments on an earlier version of our manuscript. R. Armstrong at the Nunavut Research Institute, M. Mallory at the Canadian Wildlife Service Northern Research Division and C. Eberl at National Wildlife Research Centre in Ottawa provided logistical support. F. Crenner, N. Chatelain and M. Brucker customized the GPS at the IPHC-CNRS. KHE received financial support through a NSERC Vanier Canada Graduate Scholarship, ACUNS Garfield Weston Northern Studies scholarship and AINA Jennifer Robinson Scholarship and JFH received NSERC Discovery Grant funding. J. Welcker generously loaned some accelerometers. All procedures were approved under the guidelines of the Canadian Council for Animal Care.

Shape-keeping elements in tRNA

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Pupillary shapes in response to electrical stimulation of the sclera of peripheral cornea in cats and porcines

Purpose: We have reported that the changes in the pupillary shape in response to electrical stimulation of the branches of the ciliary nerves in cats. (Miyagawa et al. PLoS One, 2014). This study investigates the changes in the pupillary shapes in response to electrical stimulations of the sclera of peripheral cornea in cats and porcines. Methods: Two enucleated eyes of two cats and three enucleated porcine eyes were studied. Trains of biphasic pulses (current, 3 mA; duration, 2 ms/phase; frequency, 40 Hz) were applied using a tungsten electrode (0.3mm diameter). The stimulation was performed at every 45 degree over the entire circular region on the sclera near the cornea. The pupillary images were recorded before and 4 s (cat) and 10 s (pig) after the stimulation and the change in the pupil diameter (Δr) was quantified. The pupillary images were obtained with a custom-built compact wavefront aberrometer (Uday et al. J Cataract Refract Surg, 2013). Results: In a cat eye, the pupil was dilated by the electrical stimulation at six out of eight orientations (before stimulation pupil diameter r=10.10±0.49 mm, Δr=0.33±0.12 mm). The pupil dilated only toward the electrode (relative eccentricity of the pupil center to the pupil diameter change amount rdec=1.15±0.28). In the porcine eyes, the pupils were constricted by the electrical stimulations at the temporal and nasal orientations (r=10.04±0.57 mm, Δr=1.52±0.70 mm). The pupils contracted symmetrically (rdec=0.30±0.12). Conclusions: With electrical stimulation in the sclera of the peripheral cornea, asymmetric mydriasis in cat eyes and symmetrical miosis in porcine eyes were observed. Under the assumption that the electrical stimulation stimulated both muscles that contribute to the pupil control, our hypothesis proposed here is that the pupil dilator is stronger than the pupil sphincter in cat, and pupil sphincter is stronger than pupil dilator in porcine.

Shape from photographs:a multi-view stereo pipeline

Acquiring 3D shape from images is a classic problem in Computer Vision occupying researchers for at least 20 years. Only recently however have these ideas matured enough to provide highly accurate results. We present a complete algorithm to reconstruct 3D objects from images using the stereo correspondence cue. The technique can be described as a pipeline of four basic building blocks: camera calibration, image segmentation, photo-consistency estimation from images, and surface extraction from photo-consistency. In this Chapter we will put more emphasis on the latter two: namely how to extract geometric information from a set of photographs without explicit camera visibility, and how to combine different geometry estimates in an optimal way. © 2010 Springer-Verlag Berlin Heidelberg.

Host genotype and age shape the leaf and root microbiomes of a wild perennial plant.

Bacteria living on and in leaves and roots influence many aspects of plant health, so the extent of a plant's genetic control over its microbiota is of great interest to crop breeders and evolutionary biologists. Laboratory-based studies, because they poorly simulate true environmental heterogeneity, may misestimate or totally miss the influence of certain host genes on the microbiome. Here we report a large-scale field experiment to disentangle the effects of genotype, environment, age and year of harvest on bacterial communities associated with leaves and roots of Boechera stricta (Brassicaceae), a perennial wild mustard. Host genetic control of the microbiome is evident in leaves but not roots, and varies substantially among sites. Microbiome composition also shifts as plants age. Furthermore, a large proportion of leaf bacterial groups are shared with roots, suggesting inoculation from soil. Our results demonstrate how genotype-by-environment interactions contribute to the complexity of microbiome assembly in natural environments.

Statistical methods for polyhedral shape classification with incomplete data - application to cryo-electron tomographic images

A certain type of bacterial inclusion, known as a bacterial microcompartment, was recently identified and imaged through cryo-electron tomography. A reconstructed 3D object from single-axis limited angle tilt-series cryo-electron tomography contains missing regions and this problem is known as the missing wedge problem. Due to missing regions on the reconstructed images, analyzing their 3D structures is a challenging problem. The existing methods overcome this problem by aligning and averaging several similar shaped objects. These schemes work well if the objects are symmetric and several objects with almost similar shapes and sizes are available. Since the bacterial inclusions studied here are not symmetric, are deformed, and show a wide range of shapes and sizes, the existing approaches are not appropriate. This research develops new statistical methods for analyzing geometric properties, such as volume, symmetry, aspect ratio, polyhedral structures etc., of these bacterial inclusions in presence of missing data. These methods work with deformed and non-symmetric varied shaped objects and do not necessitate multiple objects for handling the missing wedge problem. The developed methods and contributions include: (a) an improved method for manual image segmentation, (b) a new approach to 'complete' the segmented and reconstructed incomplete 3D images, (c) a polyhedral structural distance model to predict the polyhedral shapes of these microstructures, (d) a new shape descriptor for polyhedral shapes, named as polyhedron profile statistic, and (e) the Bayes classifier, linear discriminant analysis and support vector machine based classifiers for supervised incomplete polyhedral shape classification. Finally, the predicted 3D shapes for these bacterial microstructures belong to the Johnson solids family, and these shapes along with their other geometric properties are important for better understanding of their chemical and biological characteristics.