Nombre de travaux contemporains en philosophie de la perception s’inspirent de l’ouvrage Sense and Sensibilia du philosophe anglais John L. Austin (1911-1960). En examinant le langage ordinaire pour reconnaître la diversité des phénomènes perceptifs, Austin vise entre autres à démontrer l’impossibilité de les réduire aux catégories métaphysiques traditionnelles. Charles Travis est de ceux qui se sont risqués à réinvestir la phénoménologie linguistique d’Austin. Se réclamant ouvertement d’Austin qui soutenait que « nos sens sont muets », il développera la thèse du silence des sens selon laquelle la perception n’aurait pas un contenu représentationnel. Cette thèse aura une grande influence sur Jocelyn Benoist, qui reprendra à son compte l’idée selon laquelle la perception n’est pas intentionnelle. Travis et Benoist s’entendent donc pour dire qu’en tant que la perception est silencieuse — et donc non-conceptuelle — elle ne peut être intentionnelle. Or, il s’en suivrait alors que la phénoménologie serait fondamentalement incompatible avec la radicalité de leur critique réciproque contre le représentationnalisme, basée sur la thèse d’inspiration austinienne du silence des sens. L’intuition à l’origine de ce mémoire réside dans la perspective selon laquelle ces conclusions constitueraient en fait une radicalisation de la thèse véritablement défendue par Austin, le mutisme n’étant pas synonyme de silence. Si Austin a pu démontrer très efficacement l’autonomie de la perception par rapport au langage, la reprise de cette idée chez Travis et Benoist les a menés à une thèse plus radicale selon laquelle la perception ne serait pas une activité que l’on pourrait qualifier de normative. Partant de cette idée, j’interroge la portée et les limites de la thèse d’Austin et de ses héritiers en examinant le rôle de la normativité en jeu dans la perception. Dans ce mémoire, je soutiens que les conclusions que Travis et Benoist tirent de la thèse du silence des sens qu’ils attribuent à Austin constituent en fait une radicalisation de la position véritablement défendue par l’Oxonien. La thèse de Travis et Benoist doit être nuancée dans la mesure où d’autres types de normes jouent un rôle transcendantal pour la perception. Dès lors que l’on considère l’expérience sensible, non pas comme une activité exclusivement épistémique et cognitive, mais comme une pratique incarnée, la thèse du mutisme des sens devient compatible avec une conception normative de la perception. / Much contemporary work in philosophy of perception draws on the work Sense and Sensibilia by the English philosopher John L. Austin (1911-1960). By examining ordinary language to recognize the diversity of perceptual phenomena, Austin aims, among other things, to demonstrate the impossibility of reducing them to traditional metaphysical categories. Charles Travis is one of those who have ventured to reinvest Austin's linguistic phenomenology. Following in the footsteps of Austin, who maintained that "our senses are dumb", he developed the thesis of the silence of the senses, according to which perception has no representational content. This thesis had a major influence on Jocelyn Benoist, who took up the idea that perception is not intentional. Travis and Benoist agree that since perception is silent - and therefore non-conceptual - it cannot be intentional. It would then follow that phenomenology would be fundamentally incompatible with the radicalness of their reciprocal critique of representationalism based on Austin’s inspired thesis of the silence of the senses. The intuition behind this dissertation lies in the prospect that these conclusions might in fact constitute a radicalization of the thesis actually defended by Austin, since mutism is not synonymous with silence. If Austin demonstrated very effectively the autonomy of perception in relation to language, the revival of this idea by Travis and Benoist led them to a much more radical thesis, according to which perception would not be an activity that can be described as normative. Based on this idea, I question the scope and limits of the thesis of Austin and his heirs by examining the role of normativity at play in perception. In this dissertation, I argue that the conclusions Travis and Benoist draw from the silence of the senses thesis they attribute to Austin are in fact a radicalization of the position actually defended by the Oxonian. Travis and Benoist's thesis must be tempered insofar as other types of norms play a transcendental role for perception. As soon as we consider sensible experience not as an exclusively epistemic and cognitive activity, but as an embodied practice, the thesis of the mutism of the senses becomes compatible with a normative conception of perception.

Many chemical engineering applications, such as safety verification and parameter estimation, require global optimization of dynamic models. Global optimization algorithms typically require obtaining global bounding information of the dynamic system, to aid in locating and verifying the global optimum. The typical approach for providing these bounds is to generate convex relaxations of the dynamic system and minimize them using a local optimization solver. Tighter convex relaxations typically lead to tighter lower bounds, so that the number of iterations in global optimization algorithms can be reduced. To carry out this local optimization efficiently, subgradient-based solvers require gradients or subgradients to be furnished. Smooth convex relaxations would aid local optimization even more. To address these issues and improve the computational performance of global dynamic optimization, this thesis proposes several novel formulations for constructing tight convex relaxations of dynamic systems. In some cases, these relaxations are smooth. Firstly, a new strategy is developed to generate convex relaxations of implicit functions, under minimal assumptions. These convex relaxations are described by parametric programs whose constraints are convex relaxations of the residual function. Compared with established methods for relaxing implicit functions, this new approach does not assume uniqueness of the implicit function and does not require the original residual function to be factorable. This new strategy was demonstrated to construct tighter convex relaxations in multiple numerical examples. Moreover, this new convex relaxation strategy extends to inverse functions, feasible-set mappings in constraint satisfaction problems, as well as parametric ordinary differential equations (ODEs). Using a proof-of-concept implementation in Julia, numerical examples are presented to illustrate the convex relaxations produced for various implicit functions and optimal-value functions. In certain cases, these convex relaxations are tighter than those generated with existing methods. Secondly, a novel optimization-based framework is introduced for computing time-varying interval bounds for ODEs. Such interval bounds are useful for constructing convex relaxations of ODEs, and tighter interval bounds typically translate into tighter convex relaxations. This framework includes several established bounding approaches, but also includes many new approaches. Some of these new methods can generate tighter interval bounds than established methods, which are potentially helpful for constructing tighter convex relaxations of ODEs. Several of these approaches have been implemented in Julia. Thirdly, a new approach is developed to improve a state-of-the-art ODE relaxation method and generate tighter and smooth convex relaxations. Unlike state-of-the-art methods, the auxiliary ODEs used in these new methods for computing convex relaxations have continuous right-hand side functions. Such continuity not only makes the new methods easier to implement, but also permits the evaluation of the subgradients of convex relaxations. Under some additional assumptions, differentiable convex relaxations can be constructed. Besides that, it is demonstrated that the new convex relaxations are at least as tight as state-of-the-art methods, which benefits global dynamic optimization. This approach has been implemented in Julia, and numerical examples are presented. Lastly, a new approach is proposed for generating a guaranteed lower bound for the optimal solution value of a nonconvex optimal control problem (OCP). This lower bound is obtained by constructing a relaxed convex OCP that satisfies the sufficient optimality conditions of Pontryagin's Minimum Principle. Such lower bounding information is useful for optimizing the original nonconvex OCP to a global minimum using deterministic global optimization algorithms. Compared with established methods for underestimating nonconvex OCPs, this new approach constructs tighter lower bounds. Moreover, since it does not involve any numerical approximation of the control and state trajectories, it provides lower bounds that are reliable and consistent. This approach has been implemented for control-affine systems, and numerical examples are presented. / Thesis / Doctor of Philosophy (PhD)

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Existing sufficient dimension reduction (SDR) methods typically consider cases with no missing data. The dissertation aims to propose methods to facilitate the SDR methods when the response can be missing. The first part of the dissertation focuses on the seminal sliced inverse regression (SIR) approach proposed by Li (1991). We show that missing responses generally affect the validity of the inverse regressions under the mechanism of missing at random. We then propose a simple and effective adjustment with inverse probability weighting that guarantees the validity of SIR. Furthermore, a marginal coordinate test is introduced for this adjusted estimator. The proposed method share the simplicity of SIR and requires the linear conditional mean assumption. The second part of the dissertation proposes two new estimating equation procedures: the complete case estimating equation approach and the inverse probability weighted estimating equation approach. The two approaches are applied to a family of dimension reduction methods, which includes ordinary least squares, principal Hessian directions, and SIR. By solving the estimating equations, the two approaches are able to avoid the common assumptions in the SDR literature, the linear conditional mean assumption, and the constant conditional variance assumption. For all the aforementioned methods, the asymptotic properties are established, and their superb finite sample performances are demonstrated through extensive numerical studies as well as a real data analysis. In addition, existing estimators of the central mean space have uneven performances across different types of link functions. To address this limitation, a new hybrid SDR estimator is proposed that successfully recovers the central mean space for a wide range of link functions. Based on the new hybrid estimator, we further study the order determination procedure and the marginal coordinate test. The superior performance of the hybrid estimator over existing methods is demonstrated in simulation studies. Note that the proposed procedures dealing with the missing response at random can be simply adapted to this hybrid method. / Statistics

No / Gazeau-Klauder coherent states for a one-mode system with sinusoidal potential, are introduced. Their quantum statistical properties and their uncertainties are studied. The effect of dissipation on these states is estimated. The evolution of the ordinary (Glauber) coherent states in this system, is also studied. It is shown that these states evolve into superpositions of many macroscopically distinguishable states (`multi-Schrödinger cats').

No / Surface blending with tangential continuity is most widely applied in computer-aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: (1) exact satisfaction of C1C1 continuous blending boundary constraints, (2) effective shape control of blending surfaces, (3) high computing efficiency due to explicit mathematical representation of blending surfaces, and (4) ability to blend multiple (more than two) primary surfaces.

The compositions of in-host microbial communities (microbiota) play a significant role in host health, and a better understanding of the microbiota's role in a host's transition from health to disease or vice versa could lead to novel medical treatments. One of the first steps toward this understanding is modeling interaction dynamics of the microbiota, which can be exceedingly challenging given the complexity of the dynamics and difficulties in collecting sufficient data. Methods such as principal differential analysis, dynamic flux estimation, and others have been developed to overcome these challenges for ordinary differential equation models. Despite their advantages, these methods are still vastly underutilized in mathematical biology, and one potential reason for this is their sophisticated implementation. While this work focuses on applying principal differential analysis to microbiota data, we also provide comprehensive details regarding the derivation and numerics of this method. For further validation of the method, we demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data. In working with these data, we capture experimentally confirmed dynamics while also revealing potential new insights into those dynamics. We also explore how we find the forward solution of the model differential equation in the context of principal differential analysis, which amounts to a least-squares finite element method. We provide alternative ideas for how to use the least-squares finite element method to find the forward solution and share the insights we gain from highlighting this piece of the larger parameter estimation problem. / Ph. D.