Cette thèse porte sur l’étude des familles de polynômes orthogonaux et leurs liens avec les modèles exactement résolubles. Elle se décline en deux parties. Dans la première, on caractérise quatre nouvelles familles de polynômes orthogonaux à l’aide de processus limites appliqués à des familles appartenant aux schéma d’Askey et de Bannai-Ito. Des troncations singulières des polynômes de Wilson et d’Askey-Wilson sont considérées. Deux premières extensions bivariées de polynômes appartenant au tableau de Bannai-Ito sont également introduites. La deuxième partie présente quatre modèles exactement résolubles en lien avec la théorie des polynômes orthogonaux. Les propriétés de transfert parfait d’information quantique et de partage d’intrication d’un modèle de chaîne de spin XX dont les couplage sont liés aux polynômes de para-Racah sont examinées. Deux modèles superintégrables contenant des opérateurs de réflexions sont proposés. Leurs solutions sont obtenues et leurs symétries s’encodent respectivement dans l’algèbre de Bannai-Ito de rang deux et de rang arbitraire ce qui mène à conjecturer l’apparition des polynômes de Bannai-Ito multivariés comme coefficients de connection. Finalement, par la théorie des représentations de la superalgèbre osp(1|2), deux identités de convolution pour des familles de polynômes du tableau de Bannai-Ito sont offertes. Une réalisation en termes d’opérateurs de Dunkl conduit à une fonction génératrice bilinéaire pour les polynômes de Big −1 Jacobi. / This thesis is concerned with the study of families of orthogonal polynomials and their connection to exactly solvable models. It comprises two parts. In the first one, four novel families of orthogonal polynomials are caracterized through limit processes applied to families belonging to the Askey and Bannai-Ito schemes. Singular truncations of the Wilson and Askey-Wilson polynomials are considered. The first two bivariate extensions of families of the Bannai-Ito tableau are also introduced. The second part presents four exactly solvable models connected to the theory of orthogonal polynomials. The perfect transfer of quantum information and entanglement generation properties of an XX spin chain model whose couplings are linked to the para-Racah polynomials are examined. Two superintegrable models containing reflexion operators are proposed. Their solutions are obtained and their symmetries are encoded respectively in the rank two and arbitrary rank Bannai-Ito algebra which leads to conjecture the apparition of multivariate Bannai-Ito polynomials as overlaps. Finally, via the representation theory of the osp(1|2) Lie superalgebra, two convolution identities for families of orthogonal polynomials of the Bannai-Ito tableau are offered. Realizations in terms of Dunkl operators lead to a bilinear generating function for the Big −1 Jacobi polynomials.

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<p dir="ltr">Distributed energy resources (DERs), such as rooftop solar generation and energy storage systems, are becoming more prevalent in distribution systems. DERs are connected to the distribution system via power electronic converters, introducing faster dynamics in the system. Understanding the system dynamics under a high penetration of inverter-based DERs is critical for power system researchers and practitioners, driving the development of modeling techniques and simulation software. Aiming to reduce computational complexity, existing tools and techniques often employ various approximations. Meanwhile, modern advancements in computational hardware capabilities provide opportunities to include the faster time-scale dynamics. To address this, the primary objective of this thesis is to develop an open-source Python simulation package, Dynamic Simulation using Sparse Tableau Approach in Python, DynaSTPy (pronounced “dynasty”), capable of capturing the dynamics of all components in a distribution feeder. The distribution feeder is modeled as a system of Differential-Algebraic Equations (DAEs). Further, each component in the feeder is modeled based on the Sparse Tableau Approach (STA), which involves the representation of component model equations using sparse matrices, facilitating a systematic procedure to model the components and construct the system DAEs. In sinusoidal steady state, the DAEs can be represented in phasor form, extending the approach to perform power flow analysis of distribution feeders.</p>

The modal satisfiability problem has to date been solved using either a specifically designed algorithm, or by translating the modal logic formula into a different class of problem, such as a first-order logic, a propositional satisfiability problem or a constraint satisfaction problem. These approaches and the solvers developed to support them are surveyed and a synthesis thereof is presented. The translation of a modal K formula into a constraint satisfaction problem, as developed by Brand et al. [18], is further enhanced. The modal formula, which must be in conjunctive normal form, is translated into layered propositional formulae. Each of these layers is translated into a constraint satisfaction problem and solved using the constraint solver ECLiPSe. I extend this translation to deal with reflexive and transitive accessibility relations, thereby providing for the modal logics KT and S4. Two of the difficulties that arise when these accessibility relations are added are that the resultant formula increases considerably in complexity, and that it is no longer in conjunctive normal form (CNF). I eliminate the need for the conversion of the formula to CNF and deal instead with formulae that are in negation normal form (NNF). I apply a number of enhancements to the formula at each modal layer before it is translated into a constraint satisfaction problem. These include extensive simplification, the assignment of a single value to propositional variables that occur only positively or only negatively, and caching the status of the formula at each node of the search tree. All of these significantly prune the search space. The final results I achieve compare favorably with those obtained by other solvers. / Computing / M.Sc. (Computer Science)

Ce travail de recherche porte sur la diffusion de la stratégie au sein de la banque. En effet, nous avons cherché à déterminer les étapes clés de la mise en évidence d’un processus de diffusion au sein de la banque, de déterminer les freins que peuvent rencontrés les banquiers lors de ce processus et d’évaluer leur impact sur la mise en oeuvre de la stratégie. En effet, la diffusion est le processus par lequel la stratégie est déclinée à travers toute la banque. Or, la compréhension et le soutien qu’accordent les membres de la banque dépendent, entre autres, du processus grâce auquel iles en prennent connaissance. C’est pourquoi, l’étude de la diffusion apparait pertinente. Ainsi, comprendre en profondeur le processus de la diffusion en termes de modalités et de contenus, nous a permis de détecter les éléments qui peuvent freiner le développement d’une représentation stratégique partagée et comprise par l’ensemble de la banque, de la stratégie envisagée, et influencer la qualité de la mise en oeuvre. Notre analyse s’est essentiellement basée sur une démarche abductive qui consiste à procéder par allers retours entre théorie et terrain et qui nous a permis de renforcer la validité de notre cadre conceptuel et de le compléter par les éléments de notre analyse des cas. Au final, nous avons détecté un ensemble de freins à la diffusion de la stratégie au sein de la banque qui sont essentiellement : la sur information, les capacités cognitives, la résistance au changement, la nature de la stratégie et le nombre des niveaux hiérarchiques et dont l’impact le plus marquant est le dérapage de la mise en oeuvre. / This study deals with the communication of strategy within the banking sector. Our aim was to highlight the key steps involved in the communication process of banks, identify the challenges faced by bankers regarding that process and assess their role in the promotion of the strategy. Indeed, communication is the channel through which the strategy will be spread throughout the bank. Yet, the understanding and defense of the strategy by the employees, greatly depends on the way it has been conveyed to them; hence the importance and relevance of communication studies. Thus, a deep understanding of communication processes in terms of form as well as content, allowed us to pinpoint the elements that might prevent the development of a common strategic representation, understood by all, and affect the quality of its implementation. Our study is essentially based on an abductive approach that consists in going back and forth between theory and confirmation on the field. This method allowed us to strengthen the validity of our conceptual framework and supplement it with examples derived from our study case. In the end, we came up with the conclusion that many elements prevent the good circulation of strategy information within a bank. The main ones being: over-information, cognitive capacities, the resistance to change, the nature of the strategy as well as the number of hierarchical levels whose most striking consequence is the failure of implementation.

L’activité de chantier se caractérise par un mode de production in situ. Dès lors, nombreux sont les dysfonctionnements qui peuvent apparaître. La coordination du chantier repose sur un mélange subtil entre interactions implicites et explicites, où l’organisation prend de multiples configurations (hiérarchique, adhocratique ou transversale), et où la qualité du processus collectif repose sur l’autonomie et le sens des responsabilités de chacun des intervenants. Nous faisons l’hypothèse qu’un tel contexte est largement fondé sur la notion de confiance, car celle-ci a la capacité de réduire la perception du risque et de permettre l’action dans un environnement incertain. En conséquence, nous suggérons un rapprochement entre les outils d’assistance à la coordination et la notion de confiance, et nous proposons une nouvelle approche du pilotage de l’activité collective à partir de la représentation de la confiance. Ce travail de doctorat se structure autour de la notion de « confiance dans le bon déroulement de l’activité ». Notre méthode consiste d’abord en l’identification des divers critères de confiance, consolidés par une étude de terrain. Puis, nous établissons un modèle mathématique destiné à évaluer cette confiance à partir des informations issues d’un contexte de coopération. Sur base de ces éléments, s’en suit la proposition d’un prototype dénommé Bat’iTrust. La navigation au sein de ce prototype est guidée par un tableau de bord centré sur le concept de confiance. Enfin, la validation de cette proposition repose sur des enquêtes et une phase d’expérimentation qui nous ont permis de confronter nos résultats à des sujets expérimentaux représentatifs du domaine / The building construction is an “on-site” production activity. Therefore numerous dysfunctions can appear during the activity. The coordination of building construction depends on a subtle combination between explicit vs. implicit interactions, where organization takes various forms (i.e. hierarchic, adhocratic and transversal). Quality of the collective process is thus largely dependent on autonomy capability and responsibility sharing of each of the involved actors. Our hypothesis is that such a collective context is mainly based on the notion of trust. Indeed trust has the capability to reduce the perception of risk and to enable action in uncertain environments. Consequently, we suggest applying trust notion to the issue of design of cooperation support tools, towards a new vision of collective activity management based on trust representation. This Ph.D. research introduces the notion of “trust in the good progress of the activity”. Our methodology consists firstly in identifying the various trust criterions that we validate through a terrain survey. Secondly we establish a mathematical model aiming at evaluating trust level based on cooperation context information. Then the proposition suggests a prototype tool, called Bat’iTrust. User-navigation inside the prototype is guided by a dashboard view centred on the trust concept. Finally the validation is assessed through both surveys and an experimentation stage. These ones allow us to confront our results to experimenters subjects representative of the construction domain

This dissertation is concerned with the potential multistability of protein concentrations in the cell that can arise in biochemical networks. That is, situations where one, or a family of, proteins may sit at one of two or more different steady state concentrations in otherwise identical cells, and in spite of them being in the same environment. Models of multisite protein phosphorylation have shown that this mechanism is able to exhibit unlimited multistability. Nevertheless, these models have not considered enzyme docking, the binding of the enzymes to one or more substrate docking sites, which are separate from the motif that is chemically modified. Enzyme docking is, however, increasingly being recognised as a method to achieve specificity in protein phosphorylation and dephosphorylation cycles. Most models in the literature for these systems are deterministic i.e. based on Ordinary Differential Equations, despite the fact that these are accurate only in the limit of large molecule numbers. For small molecule numbers, a discrete probabilistic, stochastic, approach is more suitable. However, when compared to the tools available in the deterministic framework, the tools available for stochastic analysis offer inadequate visualisation and intuition. We firstly try to bridge that gap, by developing three tools: a) a discrete `nullclines' construct applicable to stochastic systems - an analogue to the ODE nullcines, b) a stochastic tool based on a Weakly Chained Diagonally Dominant M-matrix formulation of the Chemical Master Equation and c) an algorithm that is able to construct non-reversible Markov chains with desired stationary probability distributions. We subsequently prove that, for multisite protein phosphorylation and similar models, in the deterministic domain, enzyme docking and the consequent substrate enzyme-sequestration must inevitably limit the extent of multistability, ultimately to one steady state. In contrast, bimodality can be obtained in the stochastic domain even in situations where bistability is not possible for large molecule numbers. We finally extend our results to cases where we have an autophosphorylating kinase, as for example is the case with $Ca^{2+}$/calmodulin-dependent protein kinase II (CaMKII), a key enzyme in synaptic plasticity.

Résumé : Cette recherche aborde la problématique de la relation à la formation dans un processus d’autoformation en ligne. Elle pose la question du rapport au pouvoir dans ce type de situation d’apprentissage. La médiation pédagogique humaine et la médiatisation technologique y sont au centre des préoccupations. Il s’agit d’aborder, au travers de la conception même des instruments d’investigation, les concepts: de contrôle, d’autodirection, d’autonomie, d’efficacité, de compétence, d’autodétermination en relation avec la notion de motif d’engagement. Les dispositions et les prédispositions liées à l'autoformation sont également observées. On se propose de comprendre les orientations motivationnelles et les motifs qui éclairent l’engagement au regard de la perception de soi dans un contexte d’autoformation. Nos réflexions portent également sur le concept d'alterdidaxie par opposition aux démarches autodidactes dans un contexte d'autoformation./ Summary: This research approaches the problems in relation to training in the process of e-learning. It raises the question of the self-directed learning’s power in this type of training situation. The human teaching mediation and the technological mediatization are both in the center of the concerns. This research is an approach, through the design even of instruments of investigation, to the concepts : control, autodirection, autonomy, effectiveness, competence, self-determination in relation with the engagement. Competences and readiness scales related to the adults’ self-training are also observed. One proposes to observe motivational directions and the engagement’s reasons in relation with the perception of oneself as self-directed learners in a context of self-training. Our reflections also relate to the concept of Alterdidacticism in opposition to the self-educated steps, to the Autodidacticism in a context of adults’ self-training.

The main problem addressed by this dissertation is the accurate and automated determination of electron microscope imaging conditions. This enables the restoration of the object wave, which confers direct structural information about the specimen, from sets of differently aberrated images. An important member in the imaging chain is the image recording device, in many cases now a charge-coupled device (CCD) camera. Previous characterisations of these cameras often relied on the unjustified assumption that the Modulation Transfer Function (MTF) also correctly describes the spatial frequency dependent attenuation of the electron shot noise. A new theory is therefore presented that distinguishes between signal and noise transfer. This facilitates the evaluation of both properties using a detailed Monte-Carlo simulation model for the electron and photon scattering in the scintillator of the camera. Furthermore, methods for the accurate experimental determination of the signal and noise transfer functions are presented. In agreement with the Monte-Carlo simulations, experimental results for commercially available CCD cameras show that the signal transfer is significantly poorer than the noise transfer. The centrepiece of this dissertation is the development of new methods for determining the relative aberrations in a set of images and the absolute symmetric aberrations in the restored wave. Both are based on the analysis of the phase information in the Fourier domain and give each Fourier component a weight independent of its strength. This makes the method suitable even for largely crystalline samples with little amorphous contamination, where conventional methods, such as automated diffractogram fitting, usually fail. The method is then extended to also cover the antisymmetric aberrations, using combined beam tilt and focal series. The applicability of the new method is demonstrated with object wave restorations from tilt and focal series of complex inorganic block oxides and of carbon nanotubes filled with one-dimensional inorganic crystals. The latter specimens allowed for the first time a direct comparison between the phase shift in the restored object wave of a specimen with precisely known thickness and the value predicted by simulations.

The modal satisfiability problem has to date been solved using either a specifically designed algorithm, or by translating the modal logic formula into a different class of problem, such as a first-order logic, a propositional satisfiability problem or a constraint satisfaction problem. These approaches and the solvers developed to support them are surveyed and a synthesis thereof is presented. The translation of a modal K formula into a constraint satisfaction problem, as developed by Brand et al. [18], is further enhanced. The modal formula, which must be in conjunctive normal form, is translated into layered propositional formulae. Each of these layers is translated into a constraint satisfaction problem and solved using the constraint solver ECLiPSe. I extend this translation to deal with reflexive and transitive accessibility relations, thereby providing for the modal logics KT and S4. Two of the difficulties that arise when these accessibility relations are added are that the resultant formula increases considerably in complexity, and that it is no longer in conjunctive normal form (CNF). I eliminate the need for the conversion of the formula to CNF and deal instead with formulae that are in negation normal form (NNF). I apply a number of enhancements to the formula at each modal layer before it is translated into a constraint satisfaction problem. These include extensive simplification, the assignment of a single value to propositional variables that occur only positively or only negatively, and caching the status of the formula at each node of the search tree. All of these significantly prune the search space. The final results I achieve compare favorably with those obtained by other solvers. / Computing / M.Sc. (Computer Science)