Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

Les codes de l'obligations : méta-analyses pragmatologiques de l'application de méthodes en sciences sociales

Cette thèse rassemble une série de méta-analyses, c'est-à-dire d'analyses ayant pour objet des analyses produites par des sociologues (notamment celles résultant de l'application de méthodes de traitement des entretiens). Il s'agit d'une démarche réflexive visant les pratiques concrètes des sociologues. Celles-ci sont envisagées comme des activités gouvernées par des règles. Une part importante de cette thèse sera donc consacrée au développement d'un outil d'analyse « pragmatologique » (E. Durkheim), c'est-à-dire permettant l'étude des pratiques et des règles en rapport avec elles. Pour aborder les règles, la philosophie analytique d'inspiration wittgensteinienne apporte plusieurs propositions importantes. Les règles sont ainsi considérées comme des concepts d'air de famille : il n'y a pas de définitions communes recouvrant l'ensemble des règles. Pour étudier les règles, il convient alors de faire des distinctions à partir de leurs usages. Une de ces distinctions concerne la différence entre règles constitutives et règles régulatives : une règle constitutive crée une pratique (e.g. le mariage), alors qu'une règle régulative s'applique à des activités qui peuvent exister sans elle (e.g. les règles du savoir-vivre). L'activité méthodologique des sociologues repose et est contrainte par ces types de règles, qui sont pour l'essentiel implicites. Cette thèse vise donc à rendre compte, par la description et la codification des règles, du caractère normatif des méthodes dans les pratiques d'analyse de la sociologie. Elle insiste en particulier sur les limites logiques qu'instituent les règles constitutives, celles-ci rendant impossibles (et non pas interdites) certaines actions des sociologues. This thesis brings together a series of meta-analyzes, that is, analyzes that tackle analyzes produced by sociologists (notably those resulting from the application of methods in treating interviews). The approach is reflexive and aimed at the concrete practices of sociologists, considered as activities governed by rules. An important part of this thesis is therefore devoted to the development of a "pragmatological" analytical tool (Durkheim) to conduct a study of such practices and of the rules that govern them. To approach these rules, Wittgenstein-inspired analytic philosophy offers several important proposals. The rules are, at first, seen as concepts of family resemblance, assuming that there is no common definition accounting for all rules. In order to conduct the study of such rules, it is therefore necessary to discern how they are respectively used. One of these distinctions concerns the difference between constitutive rules and regulative rules: a constitutive rule creates a practice (for example marriage), while a regulative rule applies to activities that can exist outside of the rule (for example, the rules of etiquette). The methodological activity of sociologists relies on, and is constrained by these types of rules, which are essentially implicit. Through the description and codification of rules, this thesis aims to account for the normative character of methods governing analytical practices in sociology. Particular emphasis is on the logical limits established by constitutive rules, limits that render several of the sociologist's actions impossible (rather than forbidden).

Correcting surface coil excitation inhomogeneities in single-shot SPEN MRI.

Given their high sensitivity and ability to limit the field of view (FOV), surface coils are often used in magnetic resonance spectroscopy (MRS) and imaging (MRI). A major downside of surface coils is their inherent radiofrequency (RF) B1 heterogeneity across the FOV, decreasing with increasing distance from the coil and giving rise to image distortions due to non-uniform spatial responses. A robust way to compensate for B1 inhomogeneities is to employ adiabatic inversion pulses, yet these are not well adapted to all imaging sequences - including to single-shot approaches like echo planar imaging (EPI). Hybrid spatiotemporal encoding (SPEN) sequences relying on frequency-swept pulses provide another ultrafast MRI alternative, that could help solve this problem thanks to their built-in heterogeneous spatial manipulations. This study explores how this intrinsic SPEN-based spatial discrimination, could be used to compensate for the B1 inhomogeneities inherent to surface coils. Experiments carried out in both phantoms and in vivo rat brains demonstrate that, by suitably modulating the amplitude of a SPEN chirp pulse that progressively excites the spins in a direction normal to the coil, it is possible to compensate for the RF transmit inhomogeneities and thus improve sensitivity and image fidelity.

Error models in hydrogeology applications

Notre consommation en eau souterraine, en particulier comme eau potable ou pour l'irrigation, a considérablement augmenté au cours des années. De nombreux problèmes font alors leur apparition, allant de la prospection de nouvelles ressources à la remédiation des aquifères pollués. Indépendamment du problème hydrogéologique considéré, le principal défi reste la caractérisation des propriétés du sous-sol. Une approche stochastique est alors nécessaire afin de représenter cette incertitude en considérant de multiples scénarios géologiques et en générant un grand nombre de réalisations géostatistiques. Nous rencontrons alors la principale limitation de ces approches qui est le coût de calcul dû à la simulation des processus d'écoulements complexes pour chacune de ces réalisations. Dans la première partie de la thèse, ce problème est investigué dans le contexte de propagation de l'incertitude, oú un ensemble de réalisations est identifié comme représentant les propriétés du sous-sol. Afin de propager cette incertitude à la quantité d'intérêt tout en limitant le coût de calcul, les méthodes actuelles font appel à des modèles d'écoulement approximés. Cela permet l'identification d'un sous-ensemble de réalisations représentant la variabilité de l'ensemble initial. Le modèle complexe d'écoulement est alors évalué uniquement pour ce sousensemble, et, sur la base de ces réponses complexes, l'inférence est faite. Notre objectif est d'améliorer la performance de cette approche en utilisant toute l'information à disposition. Pour cela, le sous-ensemble de réponses approximées et exactes est utilisé afin de construire un modèle d'erreur, qui sert ensuite à corriger le reste des réponses approximées et prédire la réponse du modèle complexe. Cette méthode permet de maximiser l'utilisation de l'information à disposition sans augmentation perceptible du temps de calcul. La propagation de l'incertitude est alors plus précise et plus robuste. La stratégie explorée dans le premier chapitre consiste à apprendre d'un sous-ensemble de réalisations la relation entre les modèles d'écoulement approximé et complexe. Dans la seconde partie de la thèse, cette méthodologie est formalisée mathématiquement en introduisant un modèle de régression entre les réponses fonctionnelles. Comme ce problème est mal posé, il est nécessaire d'en réduire la dimensionnalité. Dans cette optique, l'innovation du travail présenté provient de l'utilisation de l'analyse en composantes principales fonctionnelles (ACPF), qui non seulement effectue la réduction de dimensionnalités tout en maximisant l'information retenue, mais permet aussi de diagnostiquer la qualité du modèle d'erreur dans cet espace fonctionnel. La méthodologie proposée est appliquée à un problème de pollution par une phase liquide nonaqueuse et les résultats obtenus montrent que le modèle d'erreur permet une forte réduction du temps de calcul tout en estimant correctement l'incertitude. De plus, pour chaque réponse approximée, une prédiction de la réponse complexe est fournie par le modèle d'erreur. Le concept de modèle d'erreur fonctionnel est donc pertinent pour la propagation de l'incertitude, mais aussi pour les problèmes d'inférence bayésienne. Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont les algorithmes les plus communément utilisés afin de générer des réalisations géostatistiques en accord avec les observations. Cependant, ces méthodes souffrent d'un taux d'acceptation très bas pour les problèmes de grande dimensionnalité, résultant en un grand nombre de simulations d'écoulement gaspillées. Une approche en deux temps, le "MCMC en deux étapes", a été introduite afin d'éviter les simulations du modèle complexe inutiles par une évaluation préliminaire de la réalisation. Dans la troisième partie de la thèse, le modèle d'écoulement approximé couplé à un modèle d'erreur sert d'évaluation préliminaire pour le "MCMC en deux étapes". Nous démontrons une augmentation du taux d'acceptation par un facteur de 1.5 à 3 en comparaison avec une implémentation classique de MCMC. Une question reste sans réponse : comment choisir la taille de l'ensemble d'entrainement et comment identifier les réalisations permettant d'optimiser la construction du modèle d'erreur. Cela requiert une stratégie itérative afin que, à chaque nouvelle simulation d'écoulement, le modèle d'erreur soit amélioré en incorporant les nouvelles informations. Ceci est développé dans la quatrième partie de la thèse, oú cette méthodologie est appliquée à un problème d'intrusion saline dans un aquifère côtier. -- Our consumption of groundwater, in particular as drinking water and for irrigation, has considerably increased over the years and groundwater is becoming an increasingly scarce and endangered resource. Nofadays, we are facing many problems ranging from water prospection to sustainable management and remediation of polluted aquifers. Independently of the hydrogeological problem, the main challenge remains dealing with the incomplete knofledge of the underground properties. Stochastic approaches have been developed to represent this uncertainty by considering multiple geological scenarios and generating a large number of realizations. The main limitation of this approach is the computational cost associated with performing complex of simulations in each realization. In the first part of the thesis, we explore this issue in the context of uncertainty propagation, where an ensemble of geostatistical realizations is identified as representative of the subsurface uncertainty. To propagate this lack of knofledge to the quantity of interest (e.g., the concentration of pollutant in extracted water), it is necessary to evaluate the of response of each realization. Due to computational constraints, state-of-the-art methods make use of approximate of simulation, to identify a subset of realizations that represents the variability of the ensemble. The complex and computationally heavy of model is then run for this subset based on which inference is made. Our objective is to increase the performance of this approach by using all of the available information and not solely the subset of exact responses. Two error models are proposed to correct the approximate responses follofing a machine learning approach. For the subset identified by a classical approach (here the distance kernel method) both the approximate and the exact responses are knofn. This information is used to construct an error model and correct the ensemble of approximate responses to predict the "expected" responses of the exact model. The proposed methodology makes use of all the available information without perceptible additional computational costs and leads to an increase in accuracy and robustness of the uncertainty propagation. The strategy explored in the first chapter consists in learning from a subset of realizations the relationship between proxy and exact curves. In the second part of this thesis, the strategy is formalized in a rigorous mathematical framework by defining a regression model between functions. As this problem is ill-posed, it is necessary to reduce its dimensionality. The novelty of the work comes from the use of functional principal component analysis (FPCA), which not only performs the dimensionality reduction while maximizing the retained information, but also allofs a diagnostic of the quality of the error model in the functional space. The proposed methodology is applied to a pollution problem by a non-aqueous phase-liquid. The error model allofs a strong reduction of the computational cost while providing a good estimate of the uncertainty. The individual correction of the proxy response by the error model leads to an excellent prediction of the exact response, opening the door to many applications. The concept of functional error model is useful not only in the context of uncertainty propagation, but also, and maybe even more so, to perform Bayesian inference. Monte Carlo Markov Chain (MCMC) algorithms are the most common choice to ensure that the generated realizations are sampled in accordance with the observations. Hofever, this approach suffers from lof acceptance rate in high dimensional problems, resulting in a large number of wasted of simulations. This led to the introduction of two-stage MCMC, where the computational cost is decreased by avoiding unnecessary simulation of the exact of thanks to a preliminary evaluation of the proposal. In the third part of the thesis, a proxy is coupled to an error model to provide an approximate response for the two-stage MCMC set-up. We demonstrate an increase in acceptance rate by a factor three with respect to one-stage MCMC results. An open question remains: hof do we choose the size of the learning set and identify the realizations to optimize the construction of the error model. This requires devising an iterative strategy to construct the error model, such that, as new of simulations are performed, the error model is iteratively improved by incorporating the new information. This is discussed in the fourth part of the thesis, in which we apply this methodology to a problem of saline intrusion in a coastal aquifer.

Correcting Interdevice Bias of Horizontal White-to-White and Sulcus-to-Sulcus Measures Used for Implantable Collamer Lens Sizing.

PURPOSE: To assess the agreement and repeatability of horizontal white-to-white (WTW) and horizontal sulcus-to-sulcus (STS) diameter measurements and use these data in combination with available literature to correct for interdevice bias in preoperative implantable collamer lens (ICL) size selection. DESIGN: Interinstrument reliability and bias assessment study. METHODS: A total of 107 eyes from 56 patients assessed for ICL implantation at our institution were included in the study. This was a consecutive series of all patients with suitable available data. The agreement and bias between WTW (measured with the Pentacam and BioGraph devices) and STS (measured with the HiScan device) were estimated. RESULTS: The mean spherical equivalent was -8.93 ± 5.69 diopters. The BioGraph measures of WTW were wider than those taken with the Pentacam (bias = 0.26 mm, P < .01), and both horizontal WTW measures were wider than the horizontal STS measures (bias >0.91 mm, P < .01). The repeatability (Sr) of STS measured with the HiScan was 0.39 mm, which was significantly reduced (Sr = 0.15 mm) when the average of 2 measures was used. Agreement between the horizontal WTW measures and horizontal STS estimates when bias was accounted for was г = 0.54 with the Pentacam and г = 0.64 with the BioGraph. CONCLUSIONS: Large interdevice bias was observed for WTW and STS measures. STS measures demonstrated poor repeatability, but the average of repeated measures significantly improved repeatability. In order to conform to the US Food and Drug Administration's accepted guidelines for ICL sizing, clinicians should be aware of and account for the inconsistencies between devices.

The right dorsolateral prefrontal cortex prevents post-error slowing

Adjusting behavior following the detection of inappropriate actions allows flexible adaptation to task demands and environmental contingencies during goal-directed behaviors. Post-error behavioral adjustments typically consist in adopting more cautious response mode, which manifests as a slowing down of response speed. Although converging evidence involves the dorsolateral prefrontal cortex (DLPFC) in post-error behavioral adjustment, whether and when the left or right DLPFC is critical for post-error slowing (PES), as well as the underlying brain mechanisms, remain highly debated. To resolve these issues, we used single-pulse transcranial magnetic stimulation in healthy human adults to disrupt the left or right DLPFC selectively at various delays within the 30-180ms interval following false alarms commission, while participants preformed a standard visual Go/NoGo task. PES significantly increased after TMS disruption of the right, but not the left DLPFC at 150ms post-FA response. We discuss these results in terms of an involvement of the right DLPFC in reducing the detrimental effects of error detection on subsequent behavioral performance, as opposed to implementing adaptative error-induced slowing down of response speed.

The Impact of Supervisor's Advice, Codes of Conduct, Accountability and Moral Attentiveness of Individuals on Discriminatory Behaviour Against Immigrants.

Past studies on the personnel selection demonstrated that a supervisor's advice to discriminate can lead to compliant behaviours. This study had the aim to extend past findings by examining what can overcome the powerful influence of the hierarchy. 50 Swiss managers participated to an in-basket exercise. The main task was to evaluate Swiss candidates (in-group) and foreigners (out-groups: Spanish and Kosovo Albanians) and to select two applicants for a job interview. Main results were the effect of codes of conduct to prevent discrimination against out-group applicants in the presence of a supervisor's advice to prefer in-group members. But, when participants were accountable to an audience, this beneficial effect disappears because participants followed the supervisor's advice. The second aim was to assess if the difference in responses between participants was related to their difference in moral attentiveness. Results showed some significant relationships but not always in the direction expected.