Thesis (M. Sc.), Memorial University of Newfoundland, 1998. / Restricted until November 1999. Bibliography: leaves p. 97-104.

Master of Science / Department of Mathematics / Bacim Alali / Nonlocal vector calculus, introduced in generalizes differential operators' calculus to nonlocal calculus of integral operators. Nonlocal vector calculus has been applied to many fields including peridynamics, nonlocal diffusion, and image analysis. In this report, we present a vector calculus for nonlocal operators such as a nonlocal divergence, a nonlocal gradient, and a nonlocal Laplacian. In Chapter 1, we review the local (differential) divergence, gradient, and Laplacian operators. In addition, we discuss their adjoints, the divergence theorem, Green's identities, and integration by parts. In Chapter 2, we define nonlocal analogues of the divergence and gradient operators, and derive the corresponding adjoint operators. In Chapter 3, we present a nonlocal divergence theorem, nonlocal Green's identities, and integration by parts for nonlocal operators. In Chapter 4, we establish a connection between the local and nonlocal operators. In particular, we show that, for specific integral kernels, the nonlocal operators converge to their local counterparts in the limit of vanishing nonlocality.

In systems with female heterogamety (e.g. WZ/ZZ; female/male), the Z chromosome has several characteristics that distinguish it from autosomes, such as different effective population size (Ne) and hemizygosity in the heterogametic sex. These characteristics may lead to an accelerated rate of adaptive changes for the Z-linked genes compared to autosomal coding sequences, often referred to as the Fast-Z effect. This work is the first attempt to test the Fast Z effect in Lepidoptera by using two methodological approaches. These included comparative fluorescence in situ hybridizations and comparisons of substitution rates in coding sequences.

No description available.

Knowledge of phylogenetic relationships among organisms is essential for anchoring evolutionary studies. Phylogenomic studies use large amounts of genetic data in analyses, which is particularly important for highly phenotypically variable taxa that are difficult to distinguish from one another without the use of genetic data, due to the abundance of homoplasy in morphological characters typically used in morphological classification. Use of genome-scale molecular data has thus become the gold standard for identifying these phylogenetic relationships, specifically in comparison to past studies based on fewer genes. Greater quantities of genetic data, in addition to finer taxon sampling, may lead to different conclusions about phylogenetic relationships among organisms compared to previous studies, necessitating new analyses on organisms when new discoveries of populations and new sources of genetic data arise. Ranitomeya poison frogs (Amphibia: Dendrobatidae) are an Amazonian lineage of dendrobatid frogs consisting of 16 species possessing remarkable diversity in color pattern, range size, and parental care behavior. I present the first phylogeny based on genomic data for all species in Ranitomeya, using maximum likelihood and multi-species coalescent methods. I used ultraconserved elements (UCEs), a genome-scale nuclear marker, as my source of molecular data to construct the tree. I also present divergence time estimations using the MCMCTree program. My results indicate several differences from previous analyses in terms of interspecific relationships. Notably, I find R. toraro and R. defleri constitute different species groups, and recover R. uakarii as paraphyletic. I also designate former populations of R. fantastica from Isla Pongo, Peru and Tarapoto as R. summersi, and transfer the French Guianan R. amazonica populations to R. variabilis. My study clarifies both interspecific and intraspecific relationships within Ranitomeya, and provides key insights into phylogeny that pave the way for future studies testing hypotheses on color pattern evolution and historical biogeography.

Thesis (MSc (Botany and Zoology))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: It is thought that a large proportion of the great variety of floral structures in flowering plants reflect adaptations to different biotic pollen vectors. Divergence in flower traits and pollinators is linked to speciation. Pollinator-driven speciation is thought to have played a large role in the spectacular floral diversity found in South African Iridaceae and the genus Tritoniopsis is a particularly good example of this. This study focuses on Tritoniopsis revoluta, a pink irid occurring in the Swartberg and Langeberg Mountains, as well as Potberg Mountain. I tested the hypothesis that variation in flower tube-lengths of Tritoniopsis revoluta are related to the geographic distribution of pollinators and the variation of their tongue lengths. It was determined that this species is highly variable in respect to corolla tube-length and is pollinated by different fly species across its range. Also, the tongue-lengths of the fly pollinators corresponded almost exactly with the tube-length of the flowers they were pollinating in each population. In some populations, where long-proboscid flies were absent, bees were observed visiting T. revoluta flowers. This presents evidence for pollinator-driven floral variation within a single plant species, and most of this vast diversification in floral morphology has probably been driven by morphological variation found within a single fly family. In one population I found variable tube-lengths which appeared to exhibit a bimodal distribution of corolla tubelengths. I hypothesized that the two Tritoniopsis revoluta ecotypes at this population are pollinated by two different pollinators, leading to assortative mating, and ultimately strong inter-ecotype incompatibility. Tritoniopsis revoluta is self-incompatible and exists as two discrete entities (morphotypes) at the Gysmanshoek Pass site, and these entities differ in tubelength, color, nectar volume and sugar content. These morphotypes were not pollinated by long-proboscid flies, but seems to represent a recent shift to pollination by Amegilla bees. However, ecotypes are not reproductively isolated as short and long flowers can produce offspring, rather tube-length differences are possibly maintained through spatial separation. To compliment the correlatory data between flower tube-lengths and pollinator tongue-lengths, I used molecular tools (chloroplast markers and AFLPs) to elucidate the patterns of tube-length evolution in Tritoniopsis revoluta. I aimed to determine the directionality and frequency of transitions between tube-length categories. Tube-length transitions would be suggestive of flower morphology being labile, and together with the tube-tongue length correlation it suggests pollinator shifts may drive the changes in tube length. Character state reconstructions using tube-length as character determined that four evolutionary transitions to shorter tube-length categories and two transitions to longer categories occurred. I also tested whether morphological divergence between populations corresponds to patterns of divergence from neutral genetic markers. Population genetic structure in this system showed that the different populations of T. revoluta are vicariant and tube-length differences between them could have evolved through selection. / AFRIKAANSE OPSOMMING: Dit is ‘n algemene gedagte dat die groot verskeidenheid blom strukture in die angiosperme dui op aanpassings tot verskillende biotiese stuifmeel draers. Die diverse blom strukture in baie van die groot Kaapse genera kan verduidelik word deur aanpassings tot veranderinge in bestuiwings-sisteme. ‘n Aantal studies hieroor stel voor dat bestuiwers nie net die veranderinge in blom morfologie bewerkstellig nie, maar ook ‘n rol speel in die aanpassende uiteenlopendheid van blomplant kenmerke. Spesiasie bewerkstellig deur bestuiwers het moontlik ‘n groot rol gespeel in die blom-diversiteit wat gevind word in die Suid-Afrikaanse Iridaceae familie, en die genus Tritoniopsis is ‘n baie goeie voorbeeld hiervan. Hierdie studie fokus spesifiek op Tritoniopsis revoluta, ‘n pienk iris wat voorkom in die Swart- en Langeberge, asook by Potberg. Die hipotese dat die variasie in buis-lengtes van T. revoluta verwant is aan die geografiese verspreiding van bestuiwers en die variasie in hul tong-lengtes is hier getoets. Dit is bepaal dat hierdie spesie groot variasie toon in terme van buis-lengtes en bestuif word deur verskillende vlieg spesies regoor sy verspreiding. Die tong-lengtes van hierdie vlieë korrespondeer ook met die buis-lengtes van die blomme wat hul bestuif in elkeen van die T. revoluta populasies. In sommige van die populasies, waar lang-tong vlieë afwesig was, is bye wat die T. revoluta blomme besoek, opgemerk. Hierdie resultate lewer bewyse vir die hipotese dat bestuiwers blom morfologie kan beïnvloed; die interessante hiervan is dat die variasie in buis-lengtes in hierdie spesie heel moontlik te danke is aan die morfologies variasie wat gevind word in ‘n enkele lang-tong vlieg familie. In een van die populasies het ek ‘n bimodale verspreiding van buis-lengtes gevind. ‘n Logiese afleiding is dat hierdie twee verskillende buislengtes – ekotipes – deur twee verskillende bestuiwers besoek word, en dat dit lei tot sterk onversoenbaarheid tussen ekotipes. Tritoniopsis revoluta is nie instaat tot self-bestuiwing nie en die twee ekotipes verskil in terme van buis-lengtes, kleur, nektar volume en suiker inhoud. Kort- en lang-buis blomme word nie eksklusief bestuif deur lang-tong vlieë in die Gysmanshoek Pas nie, maar word in die algemeen ook bestuif deur bye van die genus Amegilla. Die twee ekotipes is in staat om te reproduseer met mekaar, so die buis-lengte verskille word moontlik in stand gehou deur hul geografiese skeiding. Om die korrelasie analise tussen blom buislengtes en vlieg tong-lengtes te komplimenteer, het ek molekulêre tegnieke (chloroplast merkers en AFLPs) gebruik om die patrone van buis-lengte evolusie in Tritoniopsis revoluta duidelik te maak. Ten eerste het ek bepaal of verkortings en verlengings van buis-lengtes een keer in die verlede gebeur het, of as meermalige gebeurtenisse. Meermalige veranderinge in buis-lengtes kan moontlik dui op verskuiwings tussen verskillende bestuiwers, asook taksonomiese verdelings wat korrespondeer met bestuiwer veranderinge. Ek het ook bepaal of die buis-lengte verskille in die verskillende populasies toegeskryf kan word aan seleksie prosesse. Deur buis-lengte as karakter te gebruik, het ek karakter-status rekonstruksies gedoen en bepaal dat vier ewolutionêre transisies na korter buis-lengte kategorieë, en twee transisies na langer kategorieë plaasgevind het. Populasie genetiese struktuur in die sisteem dui daarop dat T. revoluta populasies geïsoleer is deur afstand. Die konklusie wat ek trek gebasseer op hierdie resultate is dat verskille in buis-lengtes in hierdie sisteem moontlik ontstaan het as gevolg van die verskillende bestuiwers wat aktief is in die verskillende T. revoluta populasies, en dat natuurlike prosesse nie die hoofrol spelers in hierdie sisteem is ten opsigte van buis-lengte evolusie nie.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

4D flow MRI is an imaging technique able to provide relevant information on patients’ cardiac health condition both from a visual and a quantitative point of view. Its applicability is however limited by uncertainty in the data due to the presence of noise. A new class of filters, called divergence free filters, was recently proposed. They incorporate physical knowledge into the filtering of 4D flow data. One way to implement divergence filters is via wavelet transform. The filtering process using the Divergence Free Wavelet Transform can be carried out in a completely automated fashion and was shown to hold promising results. The focus of this thesis was thus put towards assessing the effect produced by these filters on a large cohort of patients. Time-resolved segmentations were incorporated into the filtering process as this was thought to enhance divergence reduction. They were also used to investigate the filtering in every region of the thoracic cardiovascular system. The assessment of the filters was carried out both from a visual and a quantitative perspective. In-house tools were used to compute clinically used parameters on the data before and after the filtering to investigate the introduced change. The results showed that the used method was able to reduce divergence like noise while preserving all the relevant information contained in the original data, in all the regions of the heart. Flow quantifications were essentially unchanged by the filtering suggesting that the method can be safely applied on 4D flow data.

Cette thèse s'inscrit dans le contexte de l'optimisation convexe. Elle apporte à ce domaine deux contributions principales. La première porte sur les méthodes d'optimisation convexe non lisse appliquées à la vision par ordinateur. Quant à la seconde, elle fournit de nouveaux résultats théoriques concernant la manipulation de mesures de divergences, telles que celles utilisées en théorie de l'information et dans divers problèmes d'optimisation. Le principe de la stéréovision consiste à exploiter deux images d'une même scène prises sous deux points de vue, afin de retrouver les pixels homologues et de se ramener ainsi à un problème d'estimation d'un champ de disparité. Dans ce travail, le problème de l'estimation de la disparité est considéré en présence de variations d'illumination. Ceci se traduit par l'ajout, dans la fonction objective globale à minimiser, d'un facteur multiplicatif variant spatialement, estimé conjointement avec la disparité. Nous avons mis l'accent sur l'avantage de considérer plusieurs critères convexes et non-nécessairement différentiables, et d'exploiter des images multicomposantes (par exemple, des images couleurs) pour améliorer les performances de notre méthode. Le problème d'estimation posé est résolu en utilisant un algorithme parallèle proximal basé sur des développements récents en analyse convexe. Dans une seconde partie, nous avons étendu notre approche au cas multi-vues qui est un sujet de recherche relativement nouveau. Cette extension s'avère particulièrement utile dans le cadre d'applications où les zones d'occultation sont très larges et posent de nombreuses difficultés. Pour résoudre le problème d'optimisation associé, nous avons utilisé des algorithmes proximaux en suivant des approches multi-étiquettes relaxés de manière convexe. Les algorithmes employés présentent l'avantage de pouvoir gérer simultanément un grand nombre d'images et de contraintes, ainsi que des critères convexes et non convexes. Des résultats sur des images synthétiques ont permis de valider l'efficacité de ces méthodes, pour différentes mesures d'erreur. La dernière partie de cette thèse porte sur les problèmes d'optimisation convexe impliquant des mesures d'information (Phi-divergences), qui sont largement utilisés dans le codage source et le codage canal. Ces mesures peuvent être également employées avec succès dans des problèmes inverses rencontrés dans le traitement du signal et de l'image. Les problèmes d'optimisation associés sont souvent difficiles à résoudre en raison de leur grande taille. Dans ce travail, nous avons établi les expressions des opérateurs proximaux de ces divergences. En s'appuyant sur ces résultats, nous avons développé une approche proximale reposant sur l'usage de méthodes primales-duales. Ceci nous a permis de répondre à une large gamme de problèmes d'optimisation convexe dont la fonction objective comprend un terme qui s'exprime sous la forme de l'une de ces divergences / Convex optimization aims at searching for the minimum of a convex function over a convex set. While the theory of convex optimization has been largely explored for about a century, several related developments have stimulated a new interest in the topic. The first one is the emergence of efficient optimization algorithms, such as proximal methods, which allow one to easily solve large-size nonsmooth convex problems in a parallel manner. The second development is the discovery of the fact that convex optimization problems are more ubiquitous in practice than was thought previously. In this thesis, we address two different problems within the framework of convex optimization. The first one is an application to computer stereo vision, where the goal is to recover the depth information of a scene from a pair of images taken from the left and right positions. The second one is the proposition of new mathematical tools to deal with convex optimization problems involving information measures, where the objective is to minimize the divergence between two statistical objects such as random variables or probability distributions. We propose a convex approach to address the problem of dense disparity estimation under varying illumination conditions. A convex energy function is derived for jointly estimating the disparity and the illumination variation. The resulting problem is tackled in a set theoretic framework and solved using proximal tools. It is worth emphasizing the ability of this method to process multicomponent images under illumination variation. The conducted experiments indicate that this approach can effectively deal with the local illumination changes and yields better results compared with existing methods. We then extend the previous approach to the problem of multi-view disparity estimation. Rather than estimating a single depth map, we estimate a sequence of disparity maps, one for each input image. We address this problem by adopting a discrete reformulation that can be efficiently solved through a convex relaxation. This approach offers the advantage of handling both convex and nonconvex similarity measures within the same framework. We have shown that the additional complexity required by the application of our method to the multi-view case is small with respect to the stereo case. Finally, we have proposed a novel approach to handle a broad class of statistical distances, called $varphi$-divergences, within the framework of proximal algorithms. In particular, we have developed the expression of the proximity operators of several $varphi$-divergences, such as Kulback-Leibler, Jeffrey-Kulback, Hellinger, Chi-Square, I$_{alpha}$, and Renyi divergences. This allows proximal algorithms to deal with problems involving such divergences, thus overcoming the limitations of current state-of-the-art approaches for similar problems. The proposed approach is validated in two different contexts. The first is an application to image restoration that illustrates how to employ divergences as a regularization term, while the second is an application to image registration that employs divergences as a data fidelity term