Nous étudions la régression bayésienne sous contraintes de régularité et de forme. Pour cela,on considère une base de B-spline pour obtenir une courbe lisse et nous démontrons que la forme d'une spline engendrée par une base de B-spline est contrôlée par un ensemble de points de contrôle qui ne sont pas situés sur la courbe de la spline. On propose différents types de contraintes de forme (monotonie, unimodalité, convexité, etc). Ces contraintes sont prises en compte grâce à la loi a priori. L'inférence bayésienne a permis de dériver la distribution posteriori sous forme explicite à une constante près. En utilisant un algorithme hybride de type Metropolis-Hastings avec une étape de Gibbs, on propose des simulations suivant la distribution a posteriori tronquée. Nous estimons la fonction de régression par le mode a posteriori. Un algorithme de type recuit simulé a permis de calculer le mode a posteriori. La convergence des algorithmes de simulations et du calcul de l'estimateur est prouvée. En particulier, quand les noeuds des B-splines sont variables, l'analyse bayésienne de la régression sous contrainte devient complexe. On propose des schémas de simulations originaux permettant de générer suivant la loi a posteriori lorsque la densité tronquée des coefficients de régression prend des dimensions variables. / We investigate the Bayesian regression under shape and smoothness constraints. We first elicita Bayesian method for regression under shape restrictions and smoothness conditions. Theregression function is built from B-spline basis that controls its regularity. Then we show thatits shape can be controlled simply from its coefficients in the B-spline basis. This is achievedthrough the control polygon whose definition and some properties are given in this article.The regression function is estimated by the posterior mode. This mode is calculated by asimulated annealing algorithm which allows to take into account the constraints of form inthe proposal distribution. A credible interval is obtained from simulations using Metropolis-Hastings algorithm with the same proposal distribution as the simulated annealing algorithm.The convergence of algorithms for simulations and calculation of the estimator is proved. Inparticular, in the case of Bayesian regression under constraints and with free knots, Bayesiananalysis becomes complex. we propose original simulation schemes which allows to simulatefrom the truncated posterior distribution with free dimension.

Le domaine des problèmes inverses est une discipline qui se trouve à la frontière des mathématiques appliquées et de la physique et qui réunit les différentes solutions pour résoudre les problèmes d'optimisation mathématique. Dans le cas de la déconvolution 1D, ce domaine apporte un formalisme pour proposer des solutions avec deux grands types d'approche: les problèmes inverses avec régularisation et les problèmes inverses bayésiens. Sous l'effet du déluge de données, les géosciences et la planétologie nécessitent des algorithmes de plus en plus plus complexe pour obtenir des informations pertinentes. Dans le cadre de cette thèse, nous proposons d'apporter des connaissances dans trois problèmes de déconvolution 1D sous contrainte avec régularisation dans le domaine de l'hydrologie, la sismologie et de la spectroscopie. Pour chaque problème nous posons le modèle direct, le modèle inverse, et nous proposons un algorithme spécifique pour atteindre la solution. Les algorithmes sont définis ainsi que les différentes stratégies pour déterminer les hyper-paramètres. Aussi, des tests sur des données synthétiques et sur des données réelles sont exposés et discuté du point de vue de l'optimisation mathématique et du point de vue du domaine de l'application choisi. Finalement, les algorithmes proposés ont l'objectif de mettre à portée de main l'utilisation des méthodes des problèmes inverses pour la communauté des Géosciences. / The inverse problem field is a domain at the border between applied mathematics and physics that encompasses the solutions for solving mathematical optimization problems. In the case of 1D deconvolution, the discipline provides a formalism to designing solutions in the frames of its two main approaches: regularization based inverse problems and bayesian based inverse problems. Under the data deluge, geosciences and planetary sciences require more and more complex algorithms for obtaining pertinent information. In this thesis, we solve three 1D deconvolution problems under constraints with regularization based inverse problem methodology: in hydrology, in seismology and in spectroscopy. For every of the three problems, we pose the direct problem, the inverse problem, and we propose a specific algorithm to reach the solution. Algorithms are defined but also the different strategies to determine the hyper-parameters. Furthermore, tests on synthetic data and on real data are presented and commented from the point of view of the inverse problem formulation and that of the application field. Finally, the proposed algorithms aim at making approachable the use of inverse problem methodology for the Geoscience community.

Prieš rengiant kelių investicinius projektus surenkami ir detaliai analizuojami esami kelių eksploatacinių rodiklių duomenys ir jų reglamentuotų norminių reikšmių atitiktis. Baigiamajame darbe išanalizuoti automobilių kelių asfaltbetonio dangos būklės, patikimumo bei šių rodiklių gavimo ir apdorojimo metodai. Pateikiamas automobilių kelių asfaltbetonio dangos reikiamų eksploatacinių rodiklių teorinis pagrindimas, reglamentuotos norminės reikšmės bei eksploatacinių rodiklių gerinimo svarba. Naudojantis tyrimų, atliktų Lietuvos svarbiausiuose magistraliniuose keliuose A1 Vilnius – Kaunas - Klaipėda ir A5 Kaunas – Marijampolė - Suvalkai, duomenimis, atlikta pagrindinių eksploatacinių rodiklių - dangos lygumo, rato su danga sukibimo koeficiento, dangos suirimo masto rodiklio, konstrukcijos deformacijos modulio bei provėžų gylio analizė ir šių rodiklių kitimas laiko atžvilgiu. Nustatyta dangos būklę apibūdinančių rodiklių sietis. Analizės pagrindu pateikti rekomenduojami leistinieji dangos lygumo rodikliai. Pateiktos išvados ir rekomendacijos. Baigiamojo darbo aprašomojo skyriaus apimtis – 89 psl., 17 lentelių, 90 paveikslų, 44 bibliografiniai šaltiniai. / Before the preparation of highway investment projects, the available data of highway maintenance indices are collected and analysed and their conformity with the standard values is established. The thesis deals with the analysis of reliability of the condition of highway asphalt concrete pavement and the indices collection and procession methods. The thesis includes the theoretical grounding of the necessary maintenance indices of the highway asphalt concrete pavement, standard values and the importance of improvement of the maintenance indices. Using the data of the testing performed in the main Lithuanian highways A1 Vilnius – Kaunas - Klaipėda and A5 Kaunas – Marijampolė - Suvalkai, the analysis of the basic maintenance indices, i.e. pavement smoothness, wheel adherence coefficient, pavement breakup degree index, construction deformation module and furrow depth, and the change of such indices in the terms of time has been carried out. The link between the indices characterising the condition of the pavement has been determined. Basing on the analysis, the recommended permitted pavement smoothness indices are presented. The conclusions and recommendations of the thesis are introduced. Theses consist of: 89 p. text without appendixes, 90 pictures, 17 tables, 44 bibliographical entries.

O objetivo deste trabalho é estudar aproximação na esfera por uma soma com pesos de harmônicos esféricos. Apresentamos condições necessárias e suficientes sobre os pesos para garantir a convergência, tanto no caso contínuo quanto no caso Lp. Analisamos a ordem de convergência dos processos aproximatórios usando um módulo de suavidade esférico relacionado à derivada forte de Laplace-Beltrami. Incluímos provas para vários resultados sobre a derivada forte de Laplace-Beltrami, já que não conseguimos encontrá-las na literatura / The subject of this work is to study approximation on the sphere by weighted sums of spherical harmonics. We present necessary and sufficient conditions on the weights for convergence in both, the continuous and the Lp cases. We analyse the convergence rates of the approximation processes using a modulus of smoothness related to the strong Laplace- Beltrami derivative. We include proofs for several results related to such a derivative, since we were unable to find them in the literature

O objetivo deste trabalho é estudar aproximação na esfera por uma soma com pesos de harmônicos esféricos. Apresentamos condições necessárias e suficientes sobre os pesos para garantir a convergência, tanto no caso contínuo quanto no caso Lp. Analisamos a ordem de convergência dos processos aproximatórios usando um módulo de suavidade esférico relacionado à derivada forte de Laplace-Beltrami. Incluímos provas para vários resultados sobre a derivada forte de Laplace-Beltrami, já que não conseguimos encontrá-las na literatura / The subject of this work is to study approximation on the sphere by weighted sums of spherical harmonics. We present necessary and sufficient conditions on the weights for convergence in both, the continuous and the Lp cases. We analyse the convergence rates of the approximation processes using a modulus of smoothness related to the strong Laplace- Beltrami derivative. We include proofs for several results related to such a derivative, since we were unable to find them in the literature

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / In this work we establish local regularity estimates for at solutions to non-convex fully nonlinear elliptic equations and we study cavitation type equations modeled within coef- icients bounded and measurable. / Neste trabalho estabelecemos estimativas de regularidade local para soluÃÃes "flat" de equaÃÃes elÃpticas totalmente nÃo-lineares nÃo-convexas e estudamos equations do tipo cavidade com coeficientes meramente mensurÃveis.

Thesis Across the Line of the World: On Poetics of Being on the Road in the Central and East European Novel of the second half of the Twentieth Century dissert on the phenomen of vagabondism in a given space and time. Analysis of eight texts (Albahari, Bachmannová, Bernhard, Bondy, Chwin, Miłosz, Müllerová, Sebald, Velikić) through the concept of smooth and striated space (Gilles Deleuze, Félix Guattari), and Milan Balaban's exegesis on the Biblical Exodus shows four basic principals of this rather intensive than extensive vagabondism: nothingness, sense for smoothness, melancholy and fragmentarization. Central and East European Novel Vagabondism Smooth and striated space (Gilles Deleuze, Félix Guattari) Exodus (Milan Balabán) Melancholy Nothingness Sense for smoothness Fragmentarization

Annual bluegrass (Poa annua L.) and roughstalk bluegrass (Poa trivialis L.) are among the most troublesome grass weeds on golf courses throughout the United States. Herbicides for selective control of these weeds in cool-season fairways are limited and ineffective. Methiozolin is a new isoxazoline herbicide that controls annual bluegrass on putting greens and shows promise for possible weed control in fairways. Kentucky bluegrass (Poa pratensis L.) is among the most common turfgrass species used for golf fairways in the Northern United States and its response to methiozolin has scarcely been tested. A 2.5-yr field study was conducted at four Virginia locations to evaluate methiozolin efficacy for selective annual bluegrass and roughstalk bluegrass control in creeping bentgrass (Agrostis stolonifera L.) or Kentucky bluegrass fairways. Another study evaluated the response of 110 Kentucky bluegrass varieties to three rates of methiozolin. Annual bluegrass has long been presumed to impact putting green trueness, or the ability of the greens canopy to provide a smooth and directionally-consistent ball roll. Although much research has evaluated the impact of greens management on ball roll distance, no peer-reviewed research has evaluated how canopy surface factors, such as weedy annual bluegrass, will influence ball roll direction. Laboratory and field research was conducted to elucidate and overcome experimental errors that may be limiting assessment of ball directional imprecision caused by greens canopy anomalies. Techniques to minimize experimental error were employed in field studies at two Virginia golf courses to determine the influence of annual bluegrass on ball directional imprecision, bounce, and acceleration. Study results suggest that annual bluegrass patches in a creeping bentgrass putting surface can cause subtle increases in ball directional imprecision and bounce but several sources of error must be controlled before these effects can be measured. By using a mechanical putter to avoid directional errors associated with simulated-putt devices, selecting golf balls with balanced centers of gravity, eliminating legacy or "tracking" effects of repeated ball rolls via canopy brushing, and scoring ball direction 30 cm prior to terminal acceleration, we were able to detect an increase in ball directional imprecision of 8 mm m⁻¹ when balls rolled over a single patch of annual bluegrass compared to adjacent rolls on visually-pure creeping bentgrass. In herbicide efficacy studies, methiozolin-only treatments did not significantly injure creeping bentgrass or Kentucky bluegrass, reduce quality, or reduce normalized difference vegetative index regardless of application timings and rates. In general, fall applications of methiozolin reduced roughstalk bluegrass and annual bluegrass cover more than the spring-only treatments. At 1 year after the last treatment, methiozolin at 1500 g ha⁻¹ applied four times in fall at 2-wk intervals for two consecutive years controlled roughstalk bluegrass and annual bluegrass ≥85% and more consistently than other herbicides or treatment regimes. Spanning 110 Kentucky bluegrass varieties, a commercially-acceptable threshold of 30% Kentucky bluegrass injury required between 3.4 to more than 10 times the methiozolin rate needed for annual bluegrass control. Results indicate that annual bluegrass increases directional imprecision and bounce of golf balls rolling across a greens canopy. Methiozolin could be a viable herbicide for managing annual and roughstalk bluegrass in Kentucky bluegrass and creeping bentgrass fairways but weed control efficacy may be dependent on application timing. By measuring small differences in ball directional imprecision as influenced by greens canopy factors, future research efforts will aim to help turf managers choose appropriate greens management techniques. / Ph. D. / Annual bluegrass and roughstalk bluegrass are among the most troublesome grass weeds on golf courses throughout the United States. Both these weedy bluegrass species reduces the aesthetics and playability of golf turf, including fairways, tees, and putting greens. Since both annual bluegrass and roughstalk bluegrass favors growing conditions very similar to that of desirable cool-season grasses, especially Kentucky bluegrass and creeping bentgrass – the most prominent cool-season grasses on golf courses throughout the Northern USA, selective removal of these weedy bluegrass species from the desirable turf sward is very difficult. Moreover, genetic similarity of annual bluegrass and roughstalk bluegrass to Kentucky bluegrass accentuates the difficulty in selective control even more. Commercially-available herbicides for selective control of these weedy bluegrass species in cool-season golf fairways are limited and often ineffective for long-term control. Methiozolin (PoaCure®) is a new herbicide that has been extensively studied and shown to control annual bluegrass on golf putting greens and shows promise for possible weed control in fairways. However, PoaCure® has scarcely been tested to selectively and safely control annual bluegrass and roughstalk bluegrass in cool-season golf fairways. Therefore, field research was conducted at four Virginia locations to evaluate PoaCure® efficacy for selective, long-term annual bluegrass and roughstalk bluegrass control in creeping bentgrass or Kentucky bluegrass fairways. To assess the weed-control potential of PoaCure® on a broader spectrum of Kentucky bluegrass varieties grown here in VA and other cool-season grass growing parts of the nation, another field research was conducted to evaluate the response of 110 Kentucky bluegrass varieties to three different field application rates of PoaCure®. In PoaCure® weed control efficacy studies, PoaCure® by itself did not injure or reduced quality of creeping bentgrass or Kentucky bluegrass regardless of application timings and rates. In general, fall applications of PoaCure® reduced roughstalk bluegrass and annual bluegrass green cover more than the spring-only treatments. At trial completion, which was 2.5 years after trial initiation and 1 year after the last herbicidal treatment, PoaCure® at 82 fl oz/A applied four times in fall at 2-wk intervals for two consecutive years provided ≥85% control of annual bluegrass and roughstalk bluegrass and did so more consistently than other herbicides or treatment regimes in the study. In the tolerance study of 110 Kentucky bluegrass varieties, a commercially-acceptable threshold of 30% injury required between 3.4 to more than 10 times the PoaCure® rate needed for annual bluegrass control. Results from herbicide efficacy and tolerance studies indicate that PoaCure® could be a viable herbicide for managing annual and roughstalk bluegrass in Kentucky bluegrass and creeping bentgrass fairways but weed control efficacy may be dependent on application timing. In addition to being difficult to control and aesthetically unpleasing to view, annual bluegrass has also long been blamed for missed golf putts. Some researchers have surmised that a golf ball's direction may be altered when the ball traverses an anomaly in the greens surface, such as annual bluegrass, but no scientific studies have tested this assumption. Laboratory and field research was conducted to elucidate and overcome experimental errors that may be limiting assessment of ball directional imprecision caused by greens canopy anomalies. Study results suggest that an isolated patch of annual bluegrass increases ball directional imprecision by 8 mm m^-1 compared to visibly-pure creeping bentgrass and that tools and methodology currently reported in scientific literature are not precise enough to discern these subtle changes in direction. At Virginia Tech, we devised a new methodology to discern subtle changes in ball roll directional precision and bounce as influenced by an isolated patch of annual bluegrass in an otherwise visually-pure creeping bentgrass canopy. We used a mechanical putter to minimize directional errors associated with commercially-available simulated putt-devices, selected balanced golf balls, eliminated legacy of repeated ball rolls by brushing putting green surface canopy between ball rolls, scored ball direction prior to terminal acceleration with pressuresensitive paper, and used high-speed video and motion tracking software to measure ball wobble and bounce. Results indicate that annual bluegrass increases directional imprecision and bounce of golf balls rolling across a greens canopy.

The objective of our studies is the combination of electromagnetic and direct current (DC) resistivity methods in a joint inversion approach to improve the reconstruction of a given conductivity distribution. We utilize the distinct sensitivity patterns of different methods to enhance the overall resolution power and ensure a more reliable imaging result. In order to simplify the work with more than one electromagnetic method and establish a flexible and state-of-the-art software basis, we developed new DC resistivity and electromagnetic forward modeling and inversion codes based on finite elements of second order on unstructured grids. The forward operators are verified using analytical solutions and convergence studies before we apply a regularized Gauss-Newton scheme and successfully invert synthetic data sets. Finally, we link both codes with each other in a joint inversion. In contrast to most widely used joint inversion strategies, where different data sets are combined in a single least-squares problem resulting in a large system of equations, we introduce a sequential approach that cycles through the different methods iteratively. This way, we avoid several difficulties such as the determination of the full set of regularization parameters or a weighting of the distinct data sets. The sequential approach makes use of a smoothness regularization operator which penalizes the deviation of the model parameters from a given reference model. In our sequential strategy, we use the result of the preceding individual inversion scheme as reference model for the following one. We successfully apply this approach to synthetic data sets and show that the combination of at least two methods yields a significantly improved parameter model compared to the individual inversion results. / Ziel der vorliegenden Arbeit ist die gemeinsame Inversion (\"joint inversion\") elektromagnetischer und geoelektrischer Daten zur Verbesserung des rekonstruierten Leitfähigkeitsmodells. Dabei nutzen wir die verschiedenartigen Sensitivitäten der Methoden aus, um die Auflösung zu erhöhen und ein zuverlässigeres Ergebnis zu erhalten. Um die Arbeit mit mehr als einer Methode zu vereinfachen und eine flexible Softwarebasis auf dem neuesten Stand der Forschung zu etablieren, wurden zwei Codes zur Modellierung und Inversion geoelektrischer als auch elektromagnetischer Daten neu entwickelt, die mit finiten Elementen zweiter Ordnung auf unstrukturierten Gittern arbeiten. Die Vorwärtsoperatoren werden mithilfe analytischer Lösungen und Konvergenzstudien verifiziert, bevor wir ein regularisiertes Gauß-Newton-Verfahren zur Inversion synthetischer Datensätze anwenden. Im Gegensatz zur meistgenutzten \"joint inversion\"-Strategie, bei der verschiedene Daten in einem einzigen Minimierungsproblem kombiniert werden, was in einem großen Gleichungssystem resultiert, stellen wir schließlich einen sequentiellen Ansatz vor, der zyklisch durch die einzelnen Methoden iteriert. So vermeiden wir u.a. eine komplizierte Wichtung der verschiedenen Daten und die Bestimmung aller Regularisierungsparameter in einem Schritt. Der sequentielle Ansatz wird über die Anwendung einer Glättungsregularisierung umgesetzt, bei der die Abweichung der Modellparameter zu einem gegebenen Referenzmodell bestraft wird. Wir nutzen das Ergebnis der vorangegangenen Einzelinversion als Referenzmodell für die folgende Inversion. Der Ansatz wird erfolgreich auf synthetische Datensätze angewendet und wir zeigen, dass die Kombination von mehreren Methoden eine erhebliche Verbesserung des Inversionsergebnisses im Vergleich zu den Einzelinversionen liefert.

Pro optimalizaci letových trajektorií ve velmi malé nadmorské výšce, terenní vlastnosti musí být zahrnuty velice přesne. Proto rychlá a efektivní evaluace terenních dat je velice důležitá vzhledem nato, že čas potrebný pro optimalizaci musí být co nejkratší. Navyše, na optimalizaci letové trajektorie se využívájí metody založené na výpočtu gradientu. Proto musí být aproximační funkce terenních dat spojitá do určitého stupne derivace. Velice nádejná metoda na aproximaci terenních dat je aplikace víceroměrných simplex polynomů. Cílem této práce je implementovat funkci, která vyhodnotí dané terenní data na určitých bodech spolu s gradientem pomocí vícerozměrných splajnů. Program by měl vyčíslit více bodů najednou a měl by pracovat v $n$-dimensionálním prostoru.