La température est un paramètre crucial dans le fonctionnement du monde vivant, notamment de la machinerie moléculaire (les protéines) dont la stabilité et l’activité en dépendent sensiblement. Celles-ci sont souvent considérées comme étant équivalentes : si une protéine fonctionne, c’est qu’elle est stable, et vice-versa. Cependant, les protéines des organismes thermophiles, qui prolifèrent dans de températures élevées, sont stables à température ambiante, mais y présentent une faible activité. Cette dernière est optimale à la température de croissance de l’organisme hôte. Lorsqu’on parle de stabilité et d’activité protéique, la rigidité mécanique est souvent utilisée comme paramètre pertinent, offrant une explication simple et attractive à la fois pour la stabilité thermodynamique à haute température et au manque d’activité à des températures plus modérés. La réalité s’avère souvent plus complexe, et les mécanismes moléculaires reliant rigidité/flexibilité avec la stabilité et l’activité sont encore mal compris. Dans ce travail, nous abordons le problème au travers de trois systèmes. Nous avons examiné l’activation thermique des modes fonctionnels du domaine G de la protéine EF ainsi que les homologues mésophiles et thermophiles de la déshydrogénase Lactate/Malate. Par ailleurs, nous avons mis en évidence l’existence d’un paramètre unique (la moyenne des fluctuations atomiques) permettant d’expliquer la dynamique de la protéine lysozyme près de son point de fusion, et ce quelle que soit la nature de l’environnement autour de la protéine (qui décale le point de fusion). Nos conclusions se basent principalement sur une approche in silico où la dynamique moléculaire et des techniques d’échantillonnage améliorées sont utilisées et sont complémentées par des expériences de diffraction de neutrons / Temperature is one of the major factors governing life as demonstrated by the fine tuning of stability and activity of the molecular machinery, proteins in particular. The structural stability and activity of proteins have been often presented as equivalent. However, the thermophilic proteins are stable at ambient condition, but lack activity, the latter recovered only when the temperature increases to match that of the optimal growth condition for the hosting organism. In discussing the protein stability and activity, mechanical rigidity is often used as a relevant parameter, offering a simple and appealing explanation of both the extreme thermodynamic stability and the lack of activity at low temperature. The reality, however, illustrates the complexity of the rigidity/flexibility trade off in ensuring stability and activity through intricate thermodynamic and molecular mechanisms. Here we investigate the problem by studying three study cases. These are used to relate the thermal effects on mechanical properties and the stability and activity of the proteins. For instance, we have probed the thermal activation of functional modes in EF G-domain and Lactate/Malate dehydrogenase mesophilic and thermophilic homologues and verified a “universal” scaling of atomistic fluctuation of the Lysozyme approaching the melting in different environmental conditions. Our conclusions largely rest on an in silico approach, where molecular dynamics and enhanced sampling techniques are utilized, and are often complemented with neutron scattering experiments

In the first part of this thesis, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Some attention will be given to finding approximations to solutions which are themselves flows. Moreover, we will address the writing of one component in terms of another in the case of a planar system. In the second part of this thesis, we will explore the Michaelis-Menten mechanism of a single enzyme-substrate reaction. The focus is an analysis of the planar reduction in phase space or, equivalently, solutions of the scalar reduction. In particular, we will prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Also, we will determine the concavity of all solutions in the first quadrant. Moreover, we will establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we will determine the asymptotic behaviour of the slow manifold at infinity. Additionally, we will study the planar reduction. In particular, we will find non-trivial bounds on the length of the pre-steady-state period, determine the asymptotic behaviour of solutions as time tends to infinity, and determine bounds on the solutions valid for all time. In the third part of this thesis, we explore the (nonlinear) Lindemann mechanism of unimolecular decay. The analysis will be similar to that for the Michaelis-Menten mechanism with an emphasis on the differences. In the fourth and final part of this thesis, we will present some open problems.

In the first part of this thesis, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Some attention will be given to finding approximations to solutions which are themselves flows. Moreover, we will address the writing of one component in terms of another in the case of a planar system. In the second part of this thesis, we will explore the Michaelis-Menten mechanism of a single enzyme-substrate reaction. The focus is an analysis of the planar reduction in phase space or, equivalently, solutions of the scalar reduction. In particular, we will prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Also, we will determine the concavity of all solutions in the first quadrant. Moreover, we will establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we will determine the asymptotic behaviour of the slow manifold at infinity. Additionally, we will study the planar reduction. In particular, we will find non-trivial bounds on the length of the pre-steady-state period, determine the asymptotic behaviour of solutions as time tends to infinity, and determine bounds on the solutions valid for all time. In the third part of this thesis, we explore the (nonlinear) Lindemann mechanism of unimolecular decay. The analysis will be similar to that for the Michaelis-Menten mechanism with an emphasis on the differences. In the fourth and final part of this thesis, we will present some open problems.

This thesis aims to prove the following statement, where the Weierstrass p-function has algebraic invariants and complex multiplication by Q(alpha): "If beta_1,..., beta_n are algebraic numbers which are linearly independent over Q(alpha), then p(beta_1),...,p(beta_n) are algebraically independent over Q." This was proven by Philippon in 1983, and the proof in this thesis follows his ideas. The difference lies in the strength of the tools used, allowing certain arguments to be simplified. This thesis shows that the above result is equivalent to imposing the restriction (beta_1,...,beta_n)=(1,beta,...,beta^{n-1}), where n=[Q(alpha,beta):Q(alpha)]. The core of the proof consists of developing height estimates, constructing representations for morphisms between products of elliptic curves, and finding height and degree estimates on large families of polynomials which are small at a point in Q(alpha,beta,g_2,g_3)(p(1),p'(1),...,p(beta^{n-1}),p'(beta^{n-1})). An application of Philippon's zero estimate (1986) and his criterion of algebraic independence (1984) is then used to obtain the main result.

The kinetics of the pressure dependent O + SO2 + Ar reaction have been investigated using laser photolysis resonance fluorescence at temperatures of 289 K, 399 K, 581 K, 699 K, 842 K and 1040 K and at pressures from 30-665 torr. Falloff was observed for the first time in the pressure dependence. Application of Lindemann theory yielded an Arrhenius expression of k(T) = 3.3 x 10-32exp(-992/T) cm6 molecule-1 s-1 for the low pressure limit and k(T) = 8.47 x 10-14exp(-468/T) cm3 molecule-1 s-1 for the high pressure limit at temperatures between 289 and 842 K. The reaction is unusual as it possesses a positive activation energy at low temperature, yet at higher temperatures the activation energy is negative, illustrating a reaction barrier.

La conjecture de Zilber-Pink est une conjecture diophantienne concernant les intersections atypiques dans les variétés de Shimura mixtes. C’est une généralisation commune de la conjecture d’André-Oort et de la conjecture de Mordell-Lang. Le but de cette thèse est d’étudier Zilber-Pink. Plus concrètement, nous étudions la conjecture d’André-Oort, selon laquelle une sous-variété d’une variété de Shimura mixte est spéciale si son intersection avec l’ensemble des points spéciaux est dense, et la conjecture d’André-Pink-Zannier, selon laquelle une sous-variété d’une variété de Shimura mixte est faiblement spéciale si son intersection avec une orbite de Hecke généralisée est dense. Cette dernière conjecture généralise Mordell-Lang comme expliqué par Pink.Dans la méthode de Pila-Zannier, un point clef pour étudier la conjecture de Zilber-Pink est de démontrer le théorème d’Ax-Lindemann qui est une généralisation du théorème classique de Lindemann-Weierstrass dans un cadre fonctionnel. Un des résultats principaux de cette thèse est la démonstration du théorème d’Ax-Lindemann dans sa forme la plus générale, c’est- à-dire le théorème d’Ax-Lindemann mixte. Ceci généralise les résultats de Pila, Pila-Tsimerman, Ullmo-Yafaev et Klingler-Ullmo-Yafaev concernant Ax-Lindemann pour les variétés de Shimura pures.Un autre résultat de cette thèse est la démonstration de la conjecture d’André-Oort pour une grande collection de variétés de Shimura mixtes : in- conditionnellement pour une variété de Shimura mixte arbitraire dont la par- tie pure est une sous-variété de AN6 (par exemple les produits des familles universelles des variétés abéliennes de dimension 6 et le fibré de Poincaré sur A6) et sous GRH pour toutes les variétés de Shimura mixtes de type abélien. Ceci généralise des théorèmes connus de Klinger-Ullmo-Yafaev, Pila, Pila-Tsimerman et Ullmo pour les variétés de Shimura pures.Quant à la conjecture d’André-Pink-Zannier, nous démontrons plusieurs cas valables lorsque la variété de Shimura mixte ambiante est la famille universelle des variétés abéliennes. Tout d’abord nous démontrons l’intersection d’André-Oort et André-Pink-Zannier, c’est-à-dire que l’on étudie l’orbite de Hecke généralisée d’un point spécial. Ceci généralise des résultats d’Edixhoven-Yafaev et Klingler-Ullmo-Yafaev pour Ag. Nous prouvons ensuite la conjecture dans le cas suivant : une sous-variété d’un schéma abélien au dessus d’une courbe est faiblement spéciale si son intersection avec l’orbite de Hecke généralisée d’un point de torsion d’une fibre non CM est Zariski dense. Finalement pour une orbite de Hecke généralisée d’un point algébrique arbitraire, nous démontrons la conjecture pour toutes les courbes. Ces deux derniers cas généralisent des résultats de Habegger-Pila et Orr pour Ag.Dans toutes les démonstrations, la théorie o-minimale, en particulier le théorème de comptage de Pila-Wilkie, joue un rôle important. / The Zilber-Pink conjecture is a diophantine conjecture concerning unlikely intersections in mixed Shimura varieties. It is a common generalization of the André-Oort conjecture and the Mordell-Lang conjecture. This dissertation is aimed to study the Zilber-Pink conjecture. More concretely, we will study the André-Oort conjecture, which predicts that a subvariety of a mixed Shimura variety having dense intersection with the set of special points is special, and the André-Pink-Zannier conjecture which predicts that a subvariety of a mixed Shimura variety having dense intersection with a generalized Hecke orbit is weakly special. The latter conjecture generalizes the Mordell-Lang conjecture as explained by Pink.In the Pila-Zannier method, a key point to study the Zilber-Pink conjec- ture is to prove the Ax-Lindemann theorem, which is a generalization of the functional analogue of the classical Lindemann-Weierstrass theorem. One of the main results of this dissertation is to prove the Ax-Lindemann theorem in its most general form, i.e. the mixed Ax-Lindemann theorem. This generalizes results of Pila, Pila-Tsimerman, Ullmo-Yafaev and Klingler-Ullmo-Yafaev concerning the Ax-Lindemann theorem for pure Shimura varieties.Another main result of this dissertation is to prove the André-Oort conjecture for a large class of mixed Shimura varieties: unconditionally for any mixed Shimura variety whose pure part is a subvariety of AN6 (e.g. products of universal families of abelian varieties of dimension 6 and the Poincaré bundle over A6) and under GRH for all mixed Shimura varieties of abelian type. This generalizes existing theorems of Klinger-Ullmo-Yafaev, Pila, Pila-Tsimerman and Ullmo concerning pure Shimura varieties.As for the André-Pink-Zannier conjecture, we prove several cases when the ambient mixed Shimura variety is the universal family of abelian varieties. First we prove the overlap of André-Oort and André-Pink-Zannier, i.e. we study the generalized Hecke orbit of a special point. This generalizes results of Edixhoven-Yafaev and Klingler-Ullmo-Yafaev for Ag. Secondly we prove the conjecture in the following case: a subvariety of an abelian scheme over a curve is weakly special if its intersection with the generalized Hecke orbit of a torsion point of a non CM fiber is Zariski dense. Finally for the generalized Hecke orbit of an arbitrary algebraic point, we prove the conjecture for curves. These generalize existing results of Habegger-Pila and Orr for Ag.In all these proofs, the o-minimal theory, in particular the Pila-Wilkie counting theorems, plays an important role.

Living Disability: Ways Forward from Decontextual Models of Disability consists of six articles that provide both theoretical and pragmatic commentaries on decontextual approaches to vulnerability and disability. In What Contemporary Models of Disability Miss: The Case for a Phenomenological Hermeneutic Analysis I argue many commonly accepted models for understanding disability use a vertical method in which disability is defined as a category into which people are slotted based on whether or not they fit its definitional criteria. This method inevitably homogenizes the experiences of disabled people. A hermeneutic investigation of commonly accepted models for understanding disability will provide an epistemological tool to critique and to augment contemporary models of disability. In A Phenomenological Hermeneutic Resolution to the Principlist- Narrative Bioethics Debate Narrative, I note narrative approaches to bioethics and principlist approaches to bioethics have often been presented in fundamental opposition to each other. I argue that a phenomenological hermeneutic approach to the debate finds a compromise between both positions that maintains what is valuable in each of them. Justifying an Adequate Response to the Vulnerable Other examines the possibility of endorsing the position that I, as a moral agent, ought to do my best to respond adequately to the other’s vulnerability. I contend that, insofar as I value my personal identity, it is consistent to work toward responding adequately to the vulnerability of the other both ontologically and ethically. Who Can Make a Yes?: Disability, Gender, Sexual Consent and ‘Yes Means Yes’ examines the ‘yes means yes’ model of sexual consent, and the political and ethical commitments that underpin this model, noting three fundamental Ph.D. Thesis – C. Kavanagh; McMaster University - Philosophy v disadvantages. This position unfairly polices the sexual expression of participants, particularly vulnerable participants such as disabled people, it demands an unreasonably high standard for defining sexual interaction as consensual, and allows perpetrators of sexual violence to define consent. In Craving Sameness, Accepting Difference: The Possibility of Solidarity and Social Justice I note realist accounts typically define solidarity on the basis of a static feature of human nature. We stand in solidarity with some other person, or group of people, because we share important features in common. In opposition to such realist accounts, Richard Rorty defines solidarity as a practical tool, within which there is always an ‘us’, with whom we stand in solidarity, and a ‘them’, with whom we are contrasted. I argue that by understanding Rorty’s pragmatic solidarity in terms of the relational view of solidarity offered by Alexis Shotwell, it is possible to conceptualise solidarity in a manner that allows for extending the boundaries of the community with whom we stand in solidarity. In Translating Non-Human Actors I examine Bruno Latour’s position that nonhuman things can be made to leave interpretable statements, and have a place in democracy. With the right types of mediators, the scientist can translate for non-humans, and those voices will allow for nonhuman political representation. I wish to suggest that, like scientists, people with disabilities are particularly capable of building networks that facilitate translation between humans and non-humans. / Thesis / Doctor of Philosophy (PhD) / Living Disability: Ways Forward from Decontextual Models of Disability consists of six separate articles that provide both theoretical and pragmatic commentaries on decontextual approaches to vulnerability and disability. The first three articles examine contemporary approaches to understanding vulnerability and disability, and explore what a contextual theoretical approach, one that puts the experiences of people with disabilities at the centre, might look like. The second three articles provide a bioethical examination of practical ethical questions associated with the treatment of people with disabilities when it comes to social and political positions on disability and sexuality, solidarity with people with disabilities, and the relationship between people with disabilities and objects.