Artus de Bretagne est un roman du XIVe siècle conservé dans de nombreux manuscrits, ce qui établit son succès. Le fils d'un duc de Bretagne y gagne le royaume de Sorrolois, devenant ainsi le roi Artus. Il existe des continuations du roman au XVe siècle, conservées dans quatre manuscrits. Ils contiennent des textes proches qui constituent une version longue du roman. La thèse édite les 229 premiers folios du manuscrit BnF fr 19 163. Le texte est établi grâce aux trois autres manuscrits et au manuscrit BnF fr 761 qui contient la version courte. Le texte pose peu de problèmes de lecture et utilise le moyen français de manière régulière, avec un vocabulaire déjà connu par ailleurs, même si plusieurs copistes ont travaillé. L'analyse littéraire s'intéresse aux problèmes posés par l'écriture de continuation. Comment l'auteur de la version longue d'Artus de Bretagne les a-t-il résolus ? L'auteur commence son texte avant la fin de la version courte et en reprend la matière sans différence significative. Il faut penser qu'il y a là de quoi intéresser le lecteur médiéval, grand amateur de variations sur le même sujet. Pour autant comment ne pas lasser ? La thèse s'attache à étudier les solutions mises en oeuvre par l'auteur qui conduisent à s'interroger sur une nouvelle esthétique fondée sur le mélange des matières - antique, bretonne, française - et le mélange de l'épique, du merveilleux, du lyrisme. Le roman est aussi un roman favorable à la France et aux Français qu'il valorise, considérant le roi Artus comme un Français.. Le roman se révèle aussi porteur d'une vision du monde qui permet au XVe siècle de mieux se vivre et de préserver une image favorable de lui-même / Artus de Bretagne is a 14th century novel. Its presence in several manuscripts helped establish its popularity. The narrative follows Artus, the son of a duke from Brittany, winning the kingdom of Sorrolois and therefor becoming king Arthus. There are sequel to the novel dating from the 15th century disseminated in four manuscripts. They contain stories close that constitute a longer version of the original novel. This thesis edits the first 229 folios of the BnF fr 19 163 manuscript. This text is based on three other manuscript and the short version of the novel, contained in the BnF fr 761 manuscript. The BnF fr 19163 text is easily readable and uses moyen français throughout ; the vocabulary is known even though several copists worked on it. The literary analysis focuses on the problems surfacing from continuation writing. How did the author of the long version of Artus de Bretagne overcome them? The author starts the text before the end of the short version and uses the content without any significant differences. There is enough to interest medieval readers, fond of variations on the same subjects. However, this raises the question, how to keeo the audience engaged? This thesis aims at studying solutions used by the author and how they lead to a reflexion on new aesthetics based on merging genres: antiquity, breton, french - and styles, epic, fantasy and lyrism. The novel is also complimentary towards France and French people, valorised through Artus being considered French. The novel reveals itself as the bearer of a vision of the world allowing the 15th century to live better

Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers' published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage.

Les instabilités hydrodynamiques en cavité chauffée latéralement jouent un rôle important dans certains processus de fabrication de matériaux tels que le procédé de Bridgman horizontal. En effet, le fluide (métal liquide qui va se solidifier) est le siège d’une circulation thermoconvective due à l’existence d’un gradient de température horizontal qui est susceptible de devenir instationnaire via des instabilités oscillatoires. La connaissance et la maîtrise de ces instabilités sont donc primordiales afin de pouvoir améliorer la qualité des cristaux obtenus par cette technique. Dans cette thèse, nous nous sommes intéressés en premier aux instabilités affectant la circulation convective dans une cavité tridimensionnelle de dimensions 4×2×1. (longueur × largeur × hauteur). Grâce aux techniques numériques de continuation, nous avons pu obtenir les solutions stationnaires et oscillatoires, ainsi que leur stabilité, jusqu’à l’apparition de la quasi-périodicité en fonction du nombre de Grashof Gr et pour un nombre de Prandtl allant de 0 à 0,025. Ensuite, pour un éventuel contrôle des instabilités, nous nous sommes intéressés aux effets induits par la rotation de la cavité. Nous avons tout d’abord considéré un modèle monodimensionnel que nous avons développé durant cette thèse. Ce modèle analytique, bien que simplifié, est en très bon accord avec les observations en dynamique des écoulements atmosphériques (déviation des masses fluides vers la droite de la composante de vitesse dominante et vents thermiques). La stabilité linéaire de cet écoulement est ensuite effectuée en fonction du taux de rotation donné par le nombre de Taylor et du nombre de Grashof pour un nombre de Prandtl allant de 0 à 10. Nous avons pu montrer à travers ce modèle que la rotation possède un caractère stabilisant vis-à-vis de ce type d’écoulement. Enfin, nous nous sommes focalisés sur les effets de la rotation sur l’écoulement pleinement tridimensionnel dans la cavité de dimensions 4×2×1. Nous avons mis en évidence deux régimes d’écoulements : un régime dominé par la convection, où la circulation du fluide est déviée par la rotation dans la diagonale de la cavité, et un deuxième régime dominé par la rotation où la circulation du fluide est concentrée dans les couches limites dites d’Ekman et de Stewartson. Un très bon accord est observé entre le modèle analytique simplifié et la simulation numérique tridimensionnelle. / Hydrodynamic instabilities in laterally heated cavities play an important role in some material processing techniques such as the horizontal Bridgman process. Indeed, the fluid (liquid metal to be solidified) is the seat of a thermoconvective circulation due to the existence of a horizontal temperature gradient which is likely to become unsteady via oscillatory instabilities. The knowledge and the control of these instabilities are thus essential in order to be able to improve the quality of the crystals obtained by this technique. In this thesis, we are first interested in the instabilities of the convective circulation in a three-dimensional cavity of dimensions 4×2×1 (length × width × height). Thanks to the numerical continuation techniques, we were able to obtain the stationary and oscillatory solutions, as well as their stability, until the appearance of the quasi-periodicity according to the Grashof number Gr and for a Prandtl number Pr ranging from 0 to 0.025.Then, the effects induced by a rotation of the cavity around the vertical axis parallel to gravity (for a possible control of the instabilities) are studied and a one-dimensional model developed during this thesis was first considered. This analytical model, although simplified, is in very good agreement with the observations of the atmospheric flows (deviation of the fluid masses towards the right of the component of the dominant velocity and thermal winds). The linear stability of this flow as well as an energy analysis at the thresholds are then performed as a function of the rotation rate given by the Taylor number Ta and the Grashof number Gr for a Prandtl number Pr ranging from 0 to 10. Through this model, we have been able to show that the rotation has a stabilizing effect on this type of flow.We finally focused on the effects of this type of rotation on the steady fully threedimensional flow observed in the cavity 4×2×1 at low Grashof numbers.We have highlighted two flow regimes: a regime dominated by convection where the fluid circulation, deviated by the rotation, occurs in the diagonal of the cavity, and a second regime dominated by rotation where the fluid circulation is concentrated in the so-called Ekman and Stewartson boundary layers. A very good agreement is observed between the simplified analytical model and the three-dimensional numerical simulation.

The spectral zeta function, introduced by Minakshisundaram and Pleijel in [36] and denoted by ζg(s), encodes important spectral information for the Laplacian on Riemannian manifolds. For instance, the important notions of the determinant of the Laplacian and Casimir energy are defined via the spectral zeta function. On homogeneous manifolds, it is known that the spectral zeta function is critical with respect to conformal metric perturbations, (see e.g Richardson ([47]) and Okikiolu ([41])). In this thesis, we compute a second variation formula of ζg(s) on closed homogeneous Riemannian manifolds under conformal metric perturbations. It is well known that the quadratic form corresponding to this second variation is given by a certain pseudodifferential operator that depends meromorphically on s. The symbol of this operator was analysed by Okikiolu in ([42]). We analyse it in more detail on homogeneous spaces, in particular on the spheres Sn. The case n = 3 is treated in great detail. In order to describe the second variation we introduce a certain distributional integral kernel, analyse its meromorphic properties and the pole structure. The Casimir energy defined as the finite part of ζg(-½) on the n-sphere and other points of ζg(s) are used to illustrate our results. The techniques employed are heat kernel asymptotics on Riemannian manifolds, the associated meromorphic continuation of the zeta function, harmonic analysis on spheres, and asymptotic analysis.

In many important economic situations, decision makers influence each other. The subject of game theory offers a mathematical framework to describe such strategic interaction. This dissertation focuses largely on helping to answering the question,"What will someone do in a particular strategic situation?" In order to do this, it is useful to interweave theory with experimentation. After all, observation of what people really do is a necessity when attempting to create models of what people really do. At the same time, theory can help significantly when formulating interesting hypotheses to test. The chapters in my dissertation illustrate this interweaving of theory and experiments.

In the thesis we study a method for determining resonance energies - gen- eralization of the method of analytical continuation in the coupling constant, which is based on continuation of the coupling constant λ as a function of the momentum k. A formula for λ(k) is derived for spherically symmetric potential consisting of finite number of δ-functions and its Taylor series is studied. Taylor series of λ(k) and its asymptotic behavior is studied for sep- arable potential. Proper choice of added potential parameters is studied on examples. A method for determining λ(k) poles is described for spherically symmetric potential with added δ-function. It is tested whether the knowl- edge of λ(k) poles can be useful to improve the accuracy of the determination of the resonance parameters of the original potential.

This research will be of interest to global higher education policy makers, researchers and practitioners engaged in student retention, widening access and managing strategic interventions to deliver step improvements in performance. Widening access policies continue to have contemporary relevance. Effectively and efficiently reducing student non-continuation rates, without compromising widening access performance, remains a challenge for many HEIs. A new system level Management Model for Improving Student Retention Performance and its supporting performance framework is derived from empirical data gathered from a longitudinal instrumental case study and informed by the literature. They have specific validity for HEIs with strong widening access performances and general applicability to others. The dominant theoretical model informing the research is Tinto's longitudinal model of institutional departure (Tinto, 1993). The Management Model for Improving Student Retention Performance is presented around three primary categories: students, faculty and institution. Each interacts with each other and operates within individual and mutually inclusive environmental systems. There is also a supporting Improving Student Retention KPI Framework and Improving Student Retention Performance Monitoring Information System to provide the mechanisms and tools that influence the effective and efficient application of the model to deliver a step improvement in student retention. Evidence of considerable improvements [50%] in student retention performances1 for widening access students is evidenced by the case institution which is not shared by comparable HEIs in Wales. Two new performance indicators are also derived: the Specific Widening Participation Indicator (SWPi) and the Multiple Widening Participation Index (MWPi). These support a new paradigm for understanding widening access and student non- continuation performances and challenge the algorithm used to calculate institution non-continuation benchmarks. They are included in the new performance framework and inform the third primary research contribution which exposes the significant discrepancies between the funding allocations made by HEFCW, the demands on HEIs relating to widening participation policy and the extent of their MWPi>0 and retention performances. Incongruence between HEFCW funding methodology and Welsh policy is evidenced.

Non-convex optimization of deep neural networks is a well-researched problem. We present a novel application of continuation methods for deep learning optimization that can potentially arrive at a better solution. In our method, we first decompose the original optimization problem into a sequence of problems using a homotopy method. To achieve this in neural networks, we derive the Continuation(C)- Activation function. First, C-Activation is a homotopic formulation of existing activation functions such as Sigmoid, ReLU or Tanh. Second, we apply a method which is standard in the parameter continuation domain, but to the best of our knowledge, novel to the deep learning domain. In particular, we use Natural Parameter Continuation with Secant approximation(NPCS), an effective training strategy that may find a superior local minimum for a non-convex optimization problem. Additionally, we extend our work on Step-up GANs, a data continuation approach, by deriving a method called Continuous(C)-SMOTE which is an extension of standard oversampling algorithms. We demonstrate the improvements made by our methods and establish a categorization of recent work done on continuation methods in the context of deep learning.

On analyse des problèmes de completude géodésique par rapport aux metriques méromorphes sur variétés complexes. Les métriques sont des formes symmetriques doublement covariantes et les géodésiques sont immersions de surfaces de Riemann dans le variétes.

In this dissertation, I try to advance our understanding of how managerial discretion and corporate financial flexibility affect various corporate outcomes such as failure, excessive (sub-optimal) continuation, firm growth and investment, in three novel ways. First, I show that the empirical effect of finance is not merely a misspecified real influence but rather that the financial structure of firms matter for firm growth and investment where the real effects of finance arise out of the imperfect substitutability between internal funding and external private credit. Second, using managerial mergers and acquisitions (M&A) investment decisions as an identification mechanism, I find that managerial discretion combined with corporate financial flexibility may lead to distortions in corporate investment and financing policies, and those distortions cost the various stakeholders of the firm dearly. Furthermore, using another sample of distressed firms worth more dead than alive, I, along with a co-author, show that most of these firms continue operations long after the optimal exit time. The failure to liquidate costs the typical sample firm over three years 8.7% of its assets in lost earnings relative to the industry median. Finally, I find that capital market does not fully internalize the costs associated with managerial sub-optimal behaviors in the short run. Although the market disciplines managerial sub-optimal behaviors in the long run, the market disciplinary mechanisms may not be swift enough to forestall falling values for the various stakeholders of the firm. Succinctly, the findings in this dissertation suggest that managerial discretion and corporate financial flexibility entail real consequences for various firm dynamics. The traditional line of argument, ``Blame It on the Market," may not be well grounded, and firms need to carefully examine their investments and financing policies in good times to cushion against systematic shocks in bad times.