Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.

In literature Trefftz method normally has geometric (exponential) convergence. Recently many scholars have found that spectral method in some cases can converge faster than exponential, which is called super-geometric convergence. Since Trefftz method can be regarded as a kind of spectral method, we expect it might possess super-geometric convergence too. In this thesis, we classify all types of super-geometric convergence and compare their speeds. We develop a method to decide the convergent type of given error data. Finally we can observe in many numerical experiments the super-geometric convergence of Trefftz method to solve Helmholtz boundary value problems.

In this thesis, the analysis of the method of fundamental solution(MFS) is expanded for biharmonic equations. The bounds of errors are derived for the traditional and the Almansi's approaches in bounded simply-connected domains. The exponential and the polynomial convergence rates are obtained from highly and finite smooth solutions, respectively. Also the bounds of condition number are derived for the disk domains, to show the exponential growth rates. The analysis in this thesis is the first time to provide the rigor analysis of the CTM for biharmonic equations, and the intrinsic nature of accuracy and stability is similar to that of Laplace's equation. Numerical experiment are carried out for both smooth and singularity problems. The numerical results coincide with the theoretical analysis made. When the particular solutions satisfying the biharmonic equation can be found, the method of particular solutions(MPS) is always superior to MFS, supported by numerical examples. However, if such singular particular solutions near the singular points can not be found, the local refinement of collocation nodes and the greedy adaptive techniques can be used. It seems that the greedy adaptive techniques may provide a better solution for singularity problems. Beside, the numerical solutions by Almansi's approaches are slightly better in accuracy and stability than those by the traditional FS. Hence, the MFS with Almansi's approaches is recommended, due to the simple analysis, which can be obtained directly from the analysis of MFS for Laplace's equation.

Boundary approximation method, also known as the collocation Trefftz method in engineering, is used to solve Laplace boundary value problem on rectanglular domain. Suppose the particular solutions are chosen for the whole domain. If there is no singularity on other vertices, it should have exponential convergence. Otherwise, it will degenerate to polynomial convergence. In the latter case, the order of convergence has some relation with the intensity of singularity. So, it is easy to design models with desired convergent orders. On a sectorial domain, when one side of the boundary conditions is a transcendental function, it needs to be approximated by power series. The truncation of this power series will generate an artificial singularity when solving Laplace equation on polygon. So it will greatly slow down the expected order of convergence. This thesis study how the truncation error affects the convergent speed. Moreover, we focus on the transition behavior of the convergence from one order to another. In the end, we also apply our results to boundary approximation method with enriched basis.

Early detection of breast cancer on screening mammograms is crucial to reduce mortality rates. Computer-aided detection (CADe) systems for mammography are of great importance since they have been shown to positively assist radiologists in detecting early cancer. However, one area where CADe systems for mammography need improvement is in the early detection and annotation of spiculated lesions, which may represent invasive malignancies, and hence, early detection is crucial. Spicule annotation is important since it can yield useful discriminative information about the suspect lesion location on the mammogram and can also provide rich visual evidence to the interpreting radiologist to make the right follow-up decision. However, spicule annotation is a non-trivial task since spicules are fine scale curvilinear structures that are often not clearly visible amidst the surrounding breast parenchyma. The first contribution of this dissertation is an active contour algorithm called snakules for the annotation of spicules on mammography. Observer studies with experienced radiologists to evaluate the performance of snakules demonstrate the potential of the algorithm as an annotation tool that could be used to augment existing spiculated mass CADe systems. Mammography suffers from a major limitation: the 3-D to 2-D projection process results in anatomical noise due to overlapping of out of plane tissue structures, which hinders both radiologists and CADe systems in finding early cancers. This has motivated the development of 3-D breast imaging in the form of breast tomosynthesis, stereoscopic (stereo) mammography, and breast computed tomography (CT) to augment mammography for early cancer detection. Our second contribution is a novel computational stereo model for estimating a dense disparity map from a pair of stereo mammograms. This problem is very important since this is the first step towards elucidating 3-D information that is essential for conducting 3-D digital analysis on the stereo mammogram images. Nearly all of the 3-D structural information of interest on a stereo mammogram exists as a complex network of multi-layered, heavily occluded curvilinear structures, which is unlike what is seen on optical images of the real world. Our proposed stereo model employs a new singularity index as a constraint in a global optimization framework to obtain better estimates of disparity along critical curvilinear structures. The new singularity index is an important contribution of this work. In-depth theoretical analyses and experiments on several real world images demonstrate the efficacy of the index for detecting multi-scale curvilinear structures. Experiments on synthetic images with known ground truth and on real stereo mammograms highlight the advantages of the proposed stereo model over the canonical stereo model. The final contribution of this dissertation is an observer study, which demonstrates the feasibility of viewing breast tomosynthesis projection images stereoscopically. Unlike stereo mammogram images, each tomosynthesis projection image is acquired at a much lower dose. Stereo viewing of tomosynthesis projection images has the potential to reveal the 3-D structure of the breast, unlike the current cine or slice-by slice viewing modes. The results from our study suggest that stereo viewing could be a viable reading mode for breast tomosynthesis data in the future. / text

Η περιγραφή των αλληλεπιδράσεων που αναπτύσσονται μεταξύ ενός συνόλου σωμάτων που είτε είναι ακίνητα είτε κινούνται και ενός ρευστού, ρέοντος ή ηρεμούντος, βρίσκεται στον πυρήνα ενός μεγάλου αριθμού επιστημονικών προσπαθειών. Η μοντελοποίηση των αλληλεπιδράσεων αυτών μπορεί να γίνει με πολλούς τρόπους, καθένας από τους οποίους εμφανίζει πλεονεκτήματα και μειονεκτήματα, ανάλογα με το είδος του συστήματος στο οποίο επιχειρείται να εφαρμοστεί. Σκοπός της εργασίας αυτής είναι η ανάδειξη ενός εξ αυτών που είναι η Μέθοδος των Προτύπων Ροών. / The description of interactions between a number of solid particles, which may be in motion or fixed in space and a fluid which in turn may either be flowing or resting, is placed at the core of a large number of scientific publications. Modelling such interactions may follow a variety of approaches. Each approach has its own pros and cons, regarding the nature and the specific features of the system which is aimed to describe. Current thesis goal is to describe one of these approaches, which is the approach of Singularities or the Method of Elementary Flows.

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The Singularity is a hypothetical moment in the not-so-distant future when machine intelligence will supplant human intelligence as the dominant force in the world. There is a growing movement of scientists, authors, and advocates who believe the Singularity is not just possible, but inevitable. There is maybe no more eloquent or influential argument for the Singularity than futurist Ray Kurzweil’s 2005 book, The Singularity is Near: When Humans Transcend Biology. Kurzweil predicts a utopian future of advanced human/machine hybrid intelligence and radically extended life by the year 2045. This thesis applies Kenneth Burke’s system of dramatism, specifically the pentad, to The Singularity is Near as well as a sample of technology articles from The New York Times and The Wall Street Journal to examine Kurzweil’s motives and the way Singularity discourse “chains out” through other media. I will also draw on movement theory to examine the discourse of Singularity advocates to determine if Singularity discourse qualifies as a rhetorical movement. / Department of Telecommunications

La recherche de sens peut se poser comme une nécessité pour les dirigeants dont on attend une capacité à communiquer la mission, la vocation ou la raison d'être de l’organisation dont ils ont la charge. Lorsque dans les organisations confrontées à des incertitudes, la quête de sens et d'avenir des équipes devient cruciale, il arrive que les dirigeants fassent appel à des tiers, tels que des consultants, des experts ou autres professionnels du conseil pour les accompagner. Ces derniers utilisent de nombreux outils dans leurs prestations. La conscience de l’identité organisationnelle permet de générer de la confiance au sein des équipes mais elle n’est pas toujours immédiate pour le dirigeant. Le tiers extérieur peut aider à sa clarification : ses effets peuvent alors créer une révélation identitaire pour le dirigeant et les collaborateurs à propos de l'organisation.Pour étudier ce phénomène une approche ethnographique a été adoptée. Elle est fondée sur une observation participante au sein d'une société de recherche et de conseil utilisant un outil donnant accès à la singularité identitaire : avec à l’appui une étude longitudinale au cours d'une mission de conseil dans une entreprise et deux études monographiques menées auprès de participants à une session de formation et auprès de dirigeants.La recherche établit comment des dirigeants accèdent au sens de l‘organisation dans le processus de l'identité révélée. Elle ouvre également à un paradigme émergeant : celui de la singularité identitaire comme une théorie de l'identité avec des implications sur la conduite managériale. Elle permet au dirigeant d'aligner le cadre stratégique, de formaliser des principes rationnels, émotionnels et spirituels pour la mobilisation et l'action des équipes. / The search for meaning can be a necessity for the leaders who are expected to be able to communicate the mission, vocation or reason of being of the organization which they are responsible for. When in organizations facing uncertainties, the quest for meaning and future of the teams becomes crucial, managers sometimes use third parties, such as consultants or experts to help them. The consultants use a large array of tools to perform their task. Awareness of organizational identity helps building trust among work teams but is not always immediately tangible for the leader. As an outsider, the consultant can help clarifying, up to the point of bringing a revelation to the leader and collaborators about their own organization.To study this phenomenon an ethnographic approach has been selected. On one hand this approach was based on a participant observation conducted by a research and consulting company via the use of a specific tool giving access to identitarian singularity. On the other hand, two studies were done: a longitudinal one, during a consulting mission and two monographic studies conducted one with participants in a training session and one with leaders. During the process when the identity of an organization is revealed the research establishes how leaders gain access to the meaning of their organization. It also opens up to an emergent paradigm named identitarian singularity which could be defined as a theory of identity with implications for managerial behavior. It allows the leader to align the strategic framework, to formalize rational, emotional and spiritual principles for the mobilization and the action of the teams.