Agency problems with non-smooth decision profiles: the case of monopoly under product quality

A method for dealing with monotonicity constraints in optimal control problems is used to generalize some results in the context of monopoly theory, also extending the generalization to a large family of principal-agent programs. Our main conclusion is that many results on diverse economic topics, achieved under assumptions of continuity and piecewise differentiability in connection with the endogenous variables of the problem, still remain valid after replacing such assumptions by two minimal requirements.

Kaksiakselisen välijäähdytyksellä, välipoltolla ja rekuperaattorilla varustetun mikrokaasuturbiinin osakuormahyötysuhteen säilyvyyden optimointi

Työssä pyrittiin etsimään differentiaalievoluutioalgoritmilla kaksiakseliselle, välijäähdytyksellä, välipoltolla ja rekuperaattorilla varustetulle mikrokaasuturbiinille sellaiset kompressorien painesuhteet ja rekuperaattorin rekuperaatioaste, että saavutettaisiin mandollisimman hyvä osakuormahyötysuhteen säilyvyys. Osakuormatehon säätömenetelmäksi oli valittu pyörimisnopeussäädön ja turbiinien sisääntulolämpötilan alentamisen yhdistelmä, jossa generaattorilla varustetun akselin pyörimisnopeus sekä molempien turbiinien sisääntulolämpötilat olivat toisistaan riippumatta vapaasti säädettävissä. Työssä löydettiin optimaalinen säätömenetelmien yhdistelmä, jolla saavutetaan parempi osakuormahyötysuhteen säilyvyys, kuin millään käytetyistä menetelmistä yksinään. Lisäksi havaittiin, ettei optimaalinen säätömenetelmä merkittävästi riipu koneikolle valituista suunnittelupisteen parametreista. Osakuormahyötysuhteen säilyvyyden kannalta optimaalinen koneikko ei merkittävästi poikennut suunnittelupisteen hyötysuhteen kannalta optimaalisesta.

Qualité des jeux de bataille père-enfant et adaptation sociale de l'enfant d'âge préscolaire

Les pères s’impliquent aujourd’hui davantage qu’auparavant auprès de leurs enfants. À l’âge préscolaire, les jeux physiques (incluant les jeux de bataille) sont une caractéristique distinctive du style paternel d’interaction. Quelques études tendent à suggérer un lien entre ce type de jeu et l’adaptation sociale des enfants. Cependant,des contradictions se dégagent de la littérature, notamment quant au lien entre la quantité de jeu physique père-enfant et des mesures d’adaptation sociale, quant aux différentes opérationnalisations de la qualité du jeu physique, ainsi qu’en ce qui a trait au genre de l’enfant. Il y a également un débat entourant le degré optimal de contrôle ou de mutualité) au cours du jeu, de même qu’un nombre très limité d’études sur le lien entre le jeu physique père-enfant et l’anxiété/retrait. Dans ce contexte de divergences entre les chercheurs, la présente thèse vise quatre objectifs, soit : 1)vérifier si la quantité de jeux de bataille père-enfant est liée à l’adaptation sociale des enfants d’âge préscolaire (via des mesures de compétence sociale, d’agressivité/irritabilité, d’agression physique et d’anxiété/retrait); 2) tester si des mesures de mutualité ou de contrôle modèrent la relation entre la quantité de jeux de bataille père-enfant et les mesures d’adaptation sociale; 3) explorer le rôle potentiel d’autres indices de qualité du jeu de bataille; 4) clarifier le rôle du genre de l’enfant. L’échantillon est composé de 100 dyades père-enfant de Montréal et les environs. Les résultats des analyses corrélationnelles suggèrent que la fréquence et la durée de jeu de bataille ne sont pas reliées directement à l’adaptation sociale des enfants et mettent en lumière des variables qui pourraient jouer un rôle modérateur. Les régressions pour modèles modérateurs indiquent que la mutualité père-enfant dans les initiations au jeu de bataille et la peur exprimée par l’enfant au cours de ce type de jeu modèrent la relation entre la durée des jeux de bataille et la compétence sociale de l’enfant d’âge préscolaire. La mutualité modère également le lien entre la durée du jeu et l’agressivité/irritabilité de l’enfant. Les initiations autoritaires faites par le père modèrent le lien entre la durée du jeu et les agressions physiques, alors qu’aucune variable ne modère le lien entre la durée du jeu et l’anxiété/retrait des enfants. Les analyses post-hoc donnent davantage d’informations sur la nature des liens de modération. Bien que les pères rapportent ne pas faire davantage de jeux de bataille, ni jouer plus longtemps à se batailler avec leurs garçons qu’avec leurs filles, trois modèles modérateurs sur quatre demeurent significatifs uniquement pour les garçons. Ces données sont interprétées à la lumière des théories éthologique et développementale. Il est suggéré que plutôt que de traiter l’agression et la compétence sociale comme des variables opposées de l’adaptation, une mesure de compétition permettrait peut-être de réconcilier les deux mondes.

Problèmes de premier passage et de commande optimale pour des chaînes de Markov à temps discret.

Nous considérons des processus de diffusion, définis par des équations différentielles stochastiques, et puis nous nous intéressons à des problèmes de premier passage pour les chaînes de Markov en temps discret correspon- dant à ces processus de diffusion. Comme il est connu dans la littérature, ces chaînes convergent en loi vers la solution des équations différentielles stochas- tiques considérées. Notre contribution consiste à trouver des formules expli- cites pour la probabilité de premier passage et la durée de la partie pour ces chaînes de Markov à temps discret. Nous montrons aussi que les résultats ob- tenus convergent selon la métrique euclidienne (i.e topologie euclidienne) vers les quantités correspondantes pour les processus de diffusion. En dernier lieu, nous étudions un problème de commande optimale pour des chaînes de Markov en temps discret. L’objectif est de trouver la valeur qui mi- nimise l’espérance mathématique d’une certaine fonction de coût. Contraire- ment au cas continu, il n’existe pas de formule explicite pour cette valeur op- timale dans le cas discret. Ainsi, nous avons étudié dans cette thèse quelques cas particuliers pour lesquels nous avons trouvé cette valeur optimale.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Optimizing Robust Quantum Gates in Open Quantum Systems

We are currently at the cusp of a revolution in quantum technology that relies not just on the passive use of quantum effects, but on their active control. At the forefront of this revolution is the implementation of a quantum computer. Encoding information in quantum states as “qubits” allows to use entanglement and quantum superposition to perform calculations that are infeasible on classical computers. The fundamental challenge in the realization of quantum computers is to avoid decoherence – the loss of quantum properties – due to unwanted interaction with the environment. This thesis addresses the problem of implementing entangling two-qubit quantum gates that are robust with respect to both decoherence and classical noise. It covers three aspects: the use of efficient numerical tools for the simulation and optimal control of open and closed quantum systems, the role of advanced optimization functionals in facilitating robustness, and the application of these techniques to two of the leading implementations of quantum computation, trapped atoms and superconducting circuits. After a review of the theoretical and numerical foundations, the central part of the thesis starts with the idea of using ensemble optimization to achieve robustness with respect to both classical fluctuations in the system parameters, and decoherence. For the example of a controlled phasegate implemented with trapped Rydberg atoms, this approach is demonstrated to yield a gate that is at least one order of magnitude more robust than the best known analytic scheme. Moreover this robustness is maintained even for gate durations significantly shorter than those obtained in the analytic scheme. Superconducting circuits are a particularly promising architecture for the implementation of a quantum computer. Their flexibility is demonstrated by performing optimizations for both diagonal and non-diagonal quantum gates. In order to achieve robustness with respect to decoherence, it is essential to implement quantum gates in the shortest possible amount of time. This may be facilitated by using an optimization functional that targets an arbitrary perfect entangler, based on a geometric theory of two-qubit gates. For the example of superconducting qubits, it is shown that this approach leads to significantly shorter gate durations, higher fidelities, and faster convergence than the optimization towards specific two-qubit gates. Performing optimization in Liouville space in order to properly take into account decoherence poses significant numerical challenges, as the dimension scales quadratically compared to Hilbert space. However, it can be shown that for a unitary target, the optimization only requires propagation of at most three states, instead of a full basis of Liouville space. Both for the example of trapped Rydberg atoms, and for superconducting qubits, the successful optimization of quantum gates is demonstrated, at a significantly reduced numerical cost than was previously thought possible. Together, the results of this thesis point towards a comprehensive framework for the optimization of robust quantum gates, paving the way for the future realization of quantum computers.

Implementación de la administración de costos de calidad en TGS : impresora de valores

Basándose en la necesidad manifiesta de la empresa Thomas Greg & Sons de Colombia por controlar los costos en los que incurre por adoptar un Sistema de Gestión de Calidad, se realizó una investigación de los procesos que realiza la empresa a nivel productivo y el esquema de costos que utiliza a nivel organizacional, con el fin de proponer y concebir un modelo de administración de costos de la calidad y de la no calidad que sea conforme a lo esperado por la alta gerencia y que contribuya significativamente al control de costos.

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

Large-scale functional expression of WT and truncated human adenosine A(2A) receptor in Pichia pastoris bioreactor cultures

Background: The large-scale production of G-protein coupled receptors (GPCRs) for functional and structural studies remains a challenge. Recent successes have been made in the expression of a range of GPCRs using Pichia pastoris as an expression host. P. pastoris has a number of advantages over other expression systems including ability to post-translationally modify expressed proteins, relative low cost for production and ability to grow to very high cell densities. Several previous studies have described the expression of GPCRs in P. pastoris using shaker flasks, which allow culturing of small volumes (500 ml) with moderate cell densities (OD600 similar to 15). The use of bioreactors, which allow straightforward culturing of large volumes, together with optimal control of growth parameters including pH and dissolved oxygen to maximise cell densities and expression of the target receptors, are an attractive alternative. The aim of this study was to compare the levels of expression of the human Adenosine 2A receptor (A(2A)R) in P. pastoris under control of a methanol-inducible promoter in both flask and bioreactor cultures. Results: Bioreactor cultures yielded an approximately five times increase in cell density (OD600 similar to 75) compared to flask cultures prior to induction and a doubling in functional expression level per mg of membrane protein, representing a significant optimisation. Furthermore, analysis of a C-terminally truncated A2AR, terminating at residue V334 yielded the highest levels (200 pmol/mg) so far reported for expression of this receptor in P. pastoris. This truncated form of the receptor was also revealed to be resistant to C-terminal degradation in contrast to the WT A(2A)R, and therefore more suitable for further functional and structural studies. Conclusion: Large-scale expression of the A(2A)R in P. pastoris bioreactor cultures results in significant increases in functional expression compared to traditional flask cultures.

Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

An implicit pole-assignment self-tuning regulator

A new self-tuning implicit pole-assignment algorithm is presented which, through the use of a pole compression factor and different RLS model and control structures, overcomes stability and convergence problems encountered in previously available algorithms. Computational requirements of the technique are much reduced when compared to explicit pole-assignment schemes, whereas the inherent robustness of the strategy is retained.

Auto-weighted minimum-variance self-tuning controller

A self-tuning controller which automatically assigns weightings to control and set-point following is introduced. This discrete-time single-input single-output controller is based on a generalized minimum-variance control strategy. The automatic on-line selection of weightings is very convenient, especially when the system parameters are unknown or slowly varying with respect to time, which is generally considered to be the type of systems for which self-tuning control is useful. This feature also enables the controller to overcome difficulties with non-minimum phase systems.

New developments in batch process input profile optimisation

A novel algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses dynamic integrated system optimisation and parameter estimation (DISOPE) which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimisation procedure. A new method for approximating some Jacobian trajectories required by the algorithm is introduced. It is shown that the iterative procedure associated with the algorithm naturally suits applications to batch chemical processes.

Some necessary and sufficient conditions for eigenstructure assignment

Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.