The aim of this thesis is to analyze two major indicators representing the processes of natural changes in population, which are not influenced by age structure -- age specific fertility rate and age specific mortality rate and to introduce functional data analysis, which has recently become increasingly applied in many scientific fields. The functional data analysis is introduced on the Czech demographic data set for more than last sixty years. The thesis briefly describes historical development of mortality and fertility and also describes selected methods of functional data analysis by using statistical program R. Functional data analysis provides a wide variety of graphics tools to explore the data which we called functional and help us to explore all typical and atypical features, identify outliers etc.

[ES] En esta Tesis Doctoral se plantea un nuevo modelado biomecánico del cuello para su aplicación en los campos de la valoración funcional y la ergonomía. Se ha realizado un estudio cinemático para describir los axoides asociados a los ejes instantáneos de rotación (EIR) del movimiento de la cabeza respecto del tórax, así como las variables cinemáticas (posiciones, velocidades y aceleraciones), que se describen como funciones continuas mediante técnicas de Análisis de Datos Funcionales (FDA). Se han analizado movimientos cíclicos continuos. El movimiento más reproducible es el de flexo-extensión. Para el análisis dinámico, se ha elaborado un modelo articular de dinámica inversa, que permite estimar las fuerzas, momentos a nivel de C7 y potencia desarrollada, a partir de la cinemática del movimiento y de las características inerciales del sistema cuello-cabeza, obtenidas a partir de estudios previos y ajustadas mediante un procedimiento de calibración. El modelo ha sido validado experimentalmente y se ha cuantificado su fiabilidad, que resulta suficiente para aplicaciones clínicas. Se han estudiado una muestra de sujetos sanos (n=45) con la finalidad de obtener una base de normalidad, analizar el efecto de características individuales (edad, sexo y características antropométricas), y una muestra de pacientes con dolor inespecífico de cuello (n=24), para analizar las diferencias asociados a la patología. Este es el primer estudio en el que se obtiene una representación continua del EIR y se realiza una descripción de la cinemática y dinámica usando funciones continuas mediante técnicas estadísticas de FDA. Los resultados muestran que los patrones cinemáticos y dinámicos están influidos por el sexo y por la longitud del cuello. Las mujeres presentan más movilidad que los hombres y una mayor longitud del cuello va asociada a movimientos más lentos. El efecto de la edad no es demasiado acusado en la muestra analizada, con edades inferiores a 50 años en la mayoría de casos. Las diferencias cinemáticas entre personas sanas y con dolor de cuello son muy claras, siendo mayores en las variables de posición y de aceleración que en los rangos, por lo que son éstas variables más adecuadas para definir protocolos de valoración biomecánica clínica. Desde el punto de vista dinámico, hay diferencias muy claras en las fuerzas y en la potencia desarrollada, aunque no tanto en el momento articular. Las diferencias en las variables funcionales son mucho más evidentes que en las correspondientes variables numéricas extraídas de éstas (rangos, valores máximos y mínimos). En definitiva, se demuestra que el registro de movimientos continuo y el uso conjunto de información cinemática y dinámica ofrece una visión más completa de los patrones biomecánicos de movimiento del cuello y puede mejorar los actuales sistemas de valoración funcional. / [CA] En aquesta tesi doctoral es planteja un nou modelatge biomecànic de el coll per la seva aplicació en els camps de la valoració funcional i l'ergonomia. S'ha realitzat un estudi cinemàtic per descriure els axoides associats als eixos instantanis de rotació (EIR) de el moviment del cap respecte de tòrax, així com les variables cinemàtiques (posicions, velocitats i acceleracions), que es descriuen com a funcions contínues mitjançant tècniques d'Anàlisi de Dades Funcionals (FDA). S'han analitzat moviments cíclics continus. El moviment més reproduïble és el de flexo-extensió. Per a l'anàlisi dinàmic, s'ha elaborat un model articular de dinàmica inversa, que permet estimar les forces, moments a nivell de C7 i potència desenvolupada, a partir de la cinemàtica de el moviment i de les característiques inercials de sistema coll-cap, obtingudes a partir d'estudis previs i ajustades mitjançant un procediment de calibratge. El model ha estat validat experimentalment i s'ha quantificat la seva fiabilitat, que resulta suficient per a aplicacions clíniques. S'han estudiat una mostra de subjectes sans (n = 45) amb la finalitat d'obtenir una base de normalitat, analitzar l'efecte de característiques individuals (edat, sexe i característiques antropomètriques), i una mostra de pacients amb dolor inespecífic de coll (n = 24), per analitzar les diferències associats a la patologia. Aquest és el primer estudi en el qual s'obté una representació contínua de l'AIR i es realitza una descripció de la cinemàtica i dinàmica usant funcions contínues mitjançant tècniques estadístiques de FDA. Els resultats mostren que els patrons cinemàtics i dinàmics estan influïts pel sexe i per la longitud de coll. Les dones presenten més mobilitat que els homes i una major longitud de coll va associada a moviments més lents. L'efecte de l'edat no és massa acusat en la mostra analitzada, amb edats inferiors a 50 anys en la majoria de casos. Les diferències cinemàtiques entre persones sanes i amb mal de coll són molt clares, sent majors en les variables de posició i d'acceleració que en els rangs, de manera que són aquestes variables més adequades per definir protocols de valoració biomecànica clínica. Des del punt de vista dinàmic, hi ha diferències molt clares en les forces i en la potència desenvolupada, encara que no tant en el moment articular. Les diferències en les variables funcionals són molt més evidents que en les corresponents variables numèriques extretes d'aquestes (rangs, valors màxims i mínims). En definitiva, es demostra que el registre de moviments continu i l'ús conjunt d'informació cinemàtica i dinàmica ofereix una visió més completa dels patrons biomecànics de moviment de coll i pot millorar els actuals sistemes de valoració funcional. / [EN] In this Doctoral Thesis, a new biomechanical modeling of the neck is proposed for its application in the fields of functional assessment and ergonomics. A kinematic study has been carried out to describe the axoids associated with the instantaneous axes of rotation (EIR) of the movement of the head with respect to the thorax, as well as the kinematic variables (positions, velocities and accelerations), which are described as continuous functions using techniques of Functional Data Analysis (FDA). Continuous cyclical movements have been analyzed. The most reproducible movement is flexion-extension. For the dynamic analysis, a joint model of inverse dynamics has been developed, which allows estimating the forces, moments at the C7 level and developed power, from the kinematics of the movement and the inertial characteristics of the neck-head system, obtained from starting from previous studies and adjusted by means of a calibration procedure. The model has been experimentally validated and its reliability has been quantified, which is sufficient for clinical applications. A sample of healthy subjects (n = 45) were studied in order to obtain a normality base, analyze the effect of individual characteristics (age, sex and anthropometric characteristics), and a sample of patients with nonspecific neck pain (n = 24), to analyze the differences associated with the pathology. This is the first study in which a continuous representation of the EIR is obtained and a description of the kinematics and dynamics is made using continuous functions using FDA statistical techniques. The results show that the kinematic and dynamic patterns are influenced by gender and neck length. Women are more mobile than men and longer neck length is associated with slower movements. The effect of age is not too pronounced in the analyzed sample, with ages less than 50 years in most cases. The kinematic differences between healthy people and those with neck pain are very clear, being greater in the position and acceleration variables than in the ranges, making these variables more suitable for defining clinical biomechanical assessment protocols. From the dynamic point of view, there are very clear differences in the forces and the power developed, although not so much in the articulation moment. The differences in the functional variables are much more evident than in the corresponding numerical variables extracted from them (ranges, maximum and minimum values). In short, it has been shown that continuous movement recording and the joint use of kinematic and dynamic information offers a more complete view of the biomechanical patterns of neck movement and can improve current functional assessment systems. / Este trabajo ha sido desarrollado en el Instituto Universitario de Ingeniería Mecánica y Biomecánica de la Universitat Politècnica de València, y ha sido financiado con el proyecto de investigación Junior PIJ-15-08 de la Escuela Politécnica Nacional de Quito-Ecuador. / Venegas Toro, WR. (2021). Modelado biomecánico del cuello basado en la imagen cinemática de la función articular para su aplicación en tecnologías para la salud y el bienestar del ser humano [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/174522 / TESIS

An vielen verschiedenen Stellen der angewandten Statistik sind die zu untersuchenden Objekte abhängig von stetigen Parametern. Typische Beispiele in Finanzmarktapplikationen sind implizierte Volatilitäten, risikoneutrale Dichten oder Zinskurven. Aufgrund der Marktkonventionen sowie weiteren technisch bedingten Gründen sind diese Objekte nur an diskreten Punkten, wie zum Beispiel an Ausübungspreise und Maturitäten, für die ein Geschäft in einem bestimmten Zeitraum abgeschlossen wurde, beobachtbar. Ein funktionaler Datensatz ist dann vorhanden, wenn diese Funktionen für verschiedene Zeitpunkte (z.B. Tage) oder verschiedene zugrundeliegende Aktiva gesammelt werden. Das erste Thema, das in dieser Dissertation betrachtet wird, behandelt die nichtparametrischen Methoden der Schätzung dieser Objekte (wie z.B. implizierte Volatilitäten) aus den beobachteten Daten. Neben den bekannten Glättungsmethoden wird eine Prozedur für die Glättung der implizierten Volatilitäten vorgeschlagen, die auf einer Kombination von nichtparametrischer Glättung und den Ergebnissen der arbitragefreien Theorie basiert. Der zweite Teil der Dissertation ist der funktionalen Datenanalyse (FDA), speziell im Zusammenhang mit den Problemen, der empirischen Finanzmarktanalyse gewidmet. Der theoretische Teil der Arbeit konzentriert sich auf die funktionale Hauptkomponentenanalyse -- das funktionale Ebenbild der bekannten Dimensionsreduktionstechnik. Ein umfangreicher überblick der existierenden Methoden wird gegeben, eine Schätzmethode, die von der Lösung des dualen Problems motiviert ist und die Zwei-Stichproben-Inferenz basierend auf der funktionalen Hauptkomponentenanalyse werden behandelt. Die FDA-Techniken sind auf die Analyse der implizierten Volatilitäten- und Zinskurvendynamik angewandt worden. Darüber hinaus, wird die Implementation der FDA-Techniken zusammen mit einer FDA-Bibliothek für die statistische Software Xplore behandelt. / In many different fields of applied statistics an object of interest is depending on some continuous parameter. Typical examples in finance are implied volatility functions, yield curves or risk-neutral densities. Due to the different market conventions and further technical reasons, these objects are observable only on a discrete grid, e.g. for a grid of strikes and maturities for which the trade has been settled at a given time-point. By collecting these functions for several time points (e.g. days) or for different underlyings, a bunch (sample) of functions is obtained - a functional data set. The first topic considered in this thesis concerns the strategies of recovering the functional objects (e.g. implied volatilities function) from the observed data based on the nonparametric smoothing methods. Besides the standard smoothing methods, a procedure based on a combination of nonparametric smoothing and the no-arbitrage-theory results is proposed for implied volatility smoothing. The second part of the thesis is devoted to the functional data analysis (FDA) and its connection to the problems present in the empirical analysis of the financial markets. The theoretical part of the thesis focuses on the functional principal components analysis -- functional counterpart of the well known multivariate dimension-reduction-technique. A comprehensive overview of the existing methods is given, an estimation method based on the dual problem as well as the two-sample inference based on the functional principal component analysis are discussed. The FDA techniques are applied to the analysis of the implied volatility and yield curve dynamics. In addition, the implementation of the FDA techniques together with a FDA library for the statistical environment XploRe are presented.

High-dimensional data such as multi-modal neuroimaging data and large-scale networks carry excessive amount of information, and can be used to test various scientific hypotheses or discover important patterns in complicated systems. While considerable efforts have been made to analyze high-dimensional data, existing approaches often rely on simple summaries which could miss important information, and many challenges on modeling complex structures in data remain unaddressed. In this proposal, we focus on analyzing structured high-dimensional data, including functional data with important local regions and network data with community structures. The first part of this dissertation concerns the detection of ``important'' regions in functional data. We propose a novel Bayesian approach that enables region selection in the functional data regression framework. The selection of regions is achieved through encouraging sparse estimation of the regression coefficient, where nonzero regions correspond to regions that are selected. To achieve sparse estimation, we adopt compactly supported and potentially over-complete basis to capture local features of the regression coefficient function, and assume a spike-slab prior to the coefficients of the bases functions. To encourage continuous shrinkage of nearby regions, we assume an Ising hyper-prior which takes into account the neighboring structure of the bases functions. This neighboring structure is represented by an undirected graph. We perform posterior sampling through Markov chain Monte Carlo algorithms. The practical performance of the proposed approach is demonstrated through simulations as well as near-infrared and sonar data. The second part of this dissertation focuses on constructing diversified portfolios using stock return data in the Center for Research in Security Prices (CRSP) database maintained by the University of Chicago. Diversification is a risk management strategy that involves mixing a variety of financial assets in a portfolio. This strategy helps reduce the overall risk of the investment and improve performance of the portfolio. To construct portfolios that effectively diversify risks, we first construct a co-movement network using the correlations between stock returns over a training time period. Correlation characterizes the synchrony among stock returns thus helps us understand whether two or multiple stocks have common risk attributes. Based on the co-movement network, we apply multiple network community detection algorithms to detect groups of stocks with common co-movement patterns. Stocks within the same community tend to be highly correlated, while stocks across different communities tend to be less correlated. A portfolio is then constructed by selecting stocks from different communities. The average return of the constructed portfolio over a testing time period is finally compared with the SandP 500 market index. Our constructed portfolios demonstrate outstanding performance during a non-crisis period (2004-2006) and good performance during a financial crisis period (2008-2010). / PHD / High dimensional data, which are composed by data points with a tremendous number of features (a.k.a. attributes, independent variables, explanatory variables), brings challenges to statistical analysis due to their “high-dimensionality” and complicated structure. In this dissertation work, I consider two types of high-dimension data. The first type is functional data in which each observation is a function. The second type is network data whose internal structure can be described as a network. I aim to detect “important” regions in functional data by using a novel statistical model, and I treat stock market data as network data to construct quality portfolios efficiently

In-service pavements require maintenance and rehabilitation (MandR) interventions to keep them in compliance with structural and functional standards. With the increased focus on the sustainability of our roadway systems, it has become important to document the cost and environmental impacts of different MandR strategies over the life cycle of the pavement to facilitate project selection decisions in the future. Asphalt pavement recycling, while cost-effective and environmentally friendly compared to other traditional MandR treatments, still faces some widespread implementation push-back, leading to policy enactments by the FHWA aimed at encouraging the use of recycling in road projects. Many agencies and contractors have cited the lack of project selection criteria, and uncertainty about long-term performance of these recycling alternatives as reasons impeding rapid implementation of these treatments in road projects. One of the gray areas of the FHWA's 2015 Recycled Material Policy in project selection was, until recently, the lack of guidelines or tools for the assessment of the environmental suitability of candidate MandR treatments. Today, it is almost impossible to evaluate the environmental suitability of various recycling-based end-of-service-life treatments because available databases do not have relevant information on the details of unit processes, construction equipment and activities, and use-stage roughness data. Development of future MandR plans throughout the service life of pavements rehabilitated with recycling-based treatments is somewhat limited as deterioration is not fully understood. Also, available modeling tools no not address all LCA phases, or in cases where they do, key life cycle phases including the MandR, and use phases are not well covered due to the lack of quantification highlighted earlier. To address the highlighted concerns, this dissertation developed a user-friendly comprehensive LCA tool that was further validated with a case study to quantify the service life (when the pavement has reached a critical threshold performance value) and potential environmental benefits of pavement recycling projects executed by the Virginia Department of Transportation over the past decade. The tool, pySuPave, includes an excel spreadsheet user-inputs interface, and database of economic flows for unit processes used in the production of pavement materials and subsequent construction of the pavement system, considering transportation of materials and construction machinery to plants and construction site. A python-based program was used to perform matrix-based computations to generate the environmental burdens from the available public LCA Ecoinvent database. A substantive part of the dissertation was dedicated to evaluating the performance of in-service pavements rehabilitated with cold recycling and full-depth reclamation treatments, focusing on developing pavement performance prediction models (PPPM) that goes on to improve modelling of the MandR and use stages in the pavement LCA and ultimately bridges the knowledge gap on how these treatments perform in the long term. This part of the dissertation was presented in two chapters; trends in pavement recycling and performance data collection, and development of PPPMs for recycled asphalt pavements. The first provides an update and examines the current state of pavement recycling techniques, highlighting trends in the various recycling methods, examining what is and is not working from the agency perspective, and assessing the progress made in the last decade through a web-based survey. The survey results did not indicate significant changes in the adoption of the asphalt pavement recycling concept in the last decade. However, recycling techniques, such as hot in-place recycling, are being used less and more agencies seem to be adopting lower temperature techniques such as cold in-place recycling, cold central plant recycling and full depth reclamation. Improvements in mix design methods were noticeable, as more agencies have adopted contemporary methods, such as the Superpave design. Among states, very few agencies collected performance data for completed asphalt pavement recycling projects. The second chapter on performance focused on developing individual and family-type PPPMs from the data collected from the states of Virginia and Colorado, respectively. While regression modeling forms the backbone of the approach used, the chapter also presents an approach to developing family-type models using functional data analysis to find groups of projects with similar deterioration trends. In the case of Colorado, cold in-place recycling (CIR) projects completed with an initial IRI between 71 and 91 in/mi are most likely to deteriorate at an average group rate of 1.37 in/mi/year. Similarly, full depth reclamation (FDR) projects will most likely deteriorate following an average group rate of 1.40 in/mi/yr, with an initial IRI between 52 and 70 in/mi. These projects will stay in service well over 30 years if a threshold IRI of 140 in/mi were used a failure criterion. For the individual roughness models developed for VDOT, the initial IRI values and the rate of change for the treatments analyzed were found to range between 48 and 85 in/mi and between 0.70 and 5.20 in/mi/year, respectively, depending on the recycling method and type of stabilization treatment. Finally, a context-based life cycle assessment case study was conducted to benchmark and compare the environmental impacts associated with rehabilitating a low-volume road with various recycled-based and equivalent conventional methods. Several impact indicators were assessed but only the global warming (GW) score and the single score index that combines all the environmental impact indicators into a single number using normalization and weighting factors were reported in this study for the sake of brevity. Four restorative maintenance projects including two CIR (4-in. HMA over a 5-in. CIR with foamed asphalt and emulsion stabilization), one cold central plant recycling (CCPR): 4-in. HMA over a 5-in. foamed asphalt CCPR (CCPR FA), and one non-recycling structural overlay (8-in. HMA over an existing pavement) were evaluated. In addition, the following reconstruction projects were assessed; two FDR (4-in. HMA over a 12-in. FDR with foamed asphalt with 1% cement additive, and a 4-in. HMA over 10.5-in. cement stabilized FDR), and a non-recycling reconstruction project (a new reconstruction project with 8-in. HMA over a 16-in. aggregate base and subbase). The functional unit was a two lane-mile length, 12 feet wide project with a traffic volume of 1000 vehicles (3% trucks) and the analysis was conducted for 50 years. The GW score and a few other impact indicators showed an increase in the observed results where cement is used as a main stabilizer or as an additive. Between the asphalt stabilized projects, the difference in impact scores is only seen when cement is used as an additive as highlighted in the case of foamed asphalt applications. Even for the low-volume road under study, the use stage contributes the largest share to global warming and is—among several factors—attributed to the initial surface roughness of completed projects. Thus, for state DOTs looking to reduce the environmental footprints for road infrastructure projects and achieve federal legislative goals, building smoother roads and taking steps to keep the annual deterioration rate low would be an important measure, in addition to pavement recycling. Comparing the projects based on the overall single score derived from weighting factors from the National Institute of Standards and Technology (NIST) ranks the projects as follows (listed in order decreasing impacts per rehabilitation category); restorative maintenance projects: T. OVERLAY (non-recycling structural overlay—8 in. HMA over an existing pavement) - 1.06 pts, CCPR FA (4 in. HMA over a 5 in. cold central plant recycling with foamed asphalt) - 1.02 pts, CIR FA (4 in. HMA over a 5 in. cold in-place recycling with foamed asphalt) - 1.00 pts, CIR AE (4 in. HMA over a 5 in. cold in-place recycling with emulsion)- 0.86 pts; reconstruction projects: RECONS (a new reconstruction project—8 in. HMA over a 16 in. aggregate base and subbase) -1.42 pts, FDR FA+C (4 in. HMA over a 12 in. FDR with foamed asphalt with 1% cement additive) - 1.15 pts, FDR C (4 in. HMA over 10.5 in. cement stabilized FDR) - 1.02 pts. / Doctor of Philosophy / Due to harsh environmental conditions and continual damage from moving traffic, highway pavements or roadways deteriorate and grow weak over time. Throughout their life in service, different maintenance and rehabilitation (MandR) activities are performed with the intention of slowing down the deterioration to always keep the highway at a certain level of service to road users. For a long time, these MandR activities have included the use of virgin materials in techniques ranging from minor treatment applications such as fog seals, chip seals, thin overlays through more heavy treatments such as mill and fills, thicker overlays all the way to total reconstruction. Other MandR alternatives include pavement recycling which reuses materials from the existing distressed roadways either in-place or at a nearby mobile plant have gained popularity among several state highway agencies over the last decade. The advantages of using the recycling alternatives compared to non-recycling options are many and have been known to include cost savings, less construction time, and low environmental footprint. Many highway agencies, however, have expressed the lack of information on project selection criteria and the uncertainty about long-term performance of these recycling alternatives as reasons impeding rapid and widespread implementation in road projects. Agencies need selection criteria to help them identify the right treatments to apply to the right road at the right time. In a bid to encourage the use of pavement recycling treatments, the Federal Highway Administration (FHWA) enacted the Recycled Materials Policy in 2006 (revised 2015) but the policy did not fully address certain aspects of project selection. Directives on assessing the environmental suitability of recycling projects, for instance, was not given. There are no tools with modern databases incorporating the various unit processes for pavement recycling to aid agencies carry out this environmental assessment. To address the highlighted concerns, we developed a user-friendly comprehensive environmental assessment tool called pySuPave as part of this dissertation. We later validated the tool with a case study to quantify the potential environmental benefits of pavement recycling projects executed by the Virginia Department of Transportation over the past decade. Next, we conducted a survey of the departments of transportation (DOT) around the United States and Canada to collect performance data from agencies with active in-place recycling programs. Approximately 18% of the DOTs surveyed were able to provide performance data. Data received from Colorado and Virginia were subsequently used to developed models to predict deterioration in recycled pavements. In the case of Colorado, CIR projects completed with an initial roughness (IRI) between 71 and 91 in/mi are most likely to deteriorate at a rate of 1.37 in/mi/year. Similarly, FDR projects will most likely deteriorate following an average group rate of 1.40 in/mi/yr, with an initial IRI between 52 and 70 in/mi. These projects will stay in service well over 30 years if a threshold IRI of 140 in/mi were used a failure criterion. For the individual roughness models developed for VDOT, the initial IRI values and the rate of change for the treatments analyzed were found to range between 48 and 85 in/mi and between 0.70 and 5.20 in/mi/year, respectively, depending on the recycling method and type of stabilization treatment Finally, we conducted an environmental assessment case study to benchmark and compare the environmental burdens i.e., global warming (GW) and other impacts associated with rehabilitating a low-volume road with various recycled-based and equivalent non-recycling methods. Four restorative maintenance projects including two CIR (4-in. HMA over a 5-in. CIR with foamed asphalt and emulsion stabilization), one CCPR (4-in. HMA over a 5-in. foamed asphalt CCPR [CCPR FA]), and one non-recycling structural overlay (8-in. HMA over an existing pavement) were evaluate. In addition, the following reconstruction projects were assessed; two FDR (4-in. HMA over a 12-in. FDR with foamed asphalt with 1% cement additive, and a 4-in. HMA over 10.5-in. cement stabilized FDR), and a non-recycling reconstruction project (a new reconstruction project with 8-in. HMA over a 16-in. aggregate base and subbase). The functional unit was a two lane-mile length, 12 feet wide project with a traffic volume of 1000 vehicles (3% trucks) and the analysis was conducted for 50 years. The study results showed that the recycling-based projects had lower overall environmental burdens compared to their equivalent non-recycling alternatives. The GW score and a few other environmental impact indicators were higher when cement is used as a main stabilizer or as an additive in the recycling projects. Between the asphalt stabilized recycling projects, the difference in impact scores is only seen when cement is used as an additive as emphasized in the case of foamed asphalt applications. Even for the low-volume roads under study, the use stage (when the project is open to road-users) in the pavement life cycle contributes the largest share to global warming and is—among several factors—attributed to the initial surface roughness of completed projects. Thus, for state DOTs looking to reduce the environmental footprints for road infrastructure projects and achieve federal legislative goals, building smoother roads and taking steps to keep the annual deterioration rate low would be an important measure, in addition to pavement recycling. The results from this research support the hypothesis that pavement recycling can reduce global warming and other environmental burdens compared to non-recycling methods. Therefore, agencies should encourage more pavement recycling programs.

La radiothérapie occupe une place majeure dans l’arsenal thérapeutique des cancers.Malgré des progrès technologiques importants depuis près de vingt ans, des tissus sains au voisinage ou à distance de la tumeur cible continuent à être inévitablement irradiés à des niveaux de doses très différents. Ces doses sont à l’origine d’effets secondaires précoces (Œdème, radionécrose, Dysphagie, Cystite) ou tardifs (rectorragies, télangiectasie, effets carcinogènes, les pathologie cérébrovasculaires).Il est donc primordial de quantifier et de prévenir ces effets secondaires afin d'améliorer la qualité de vie des patients pendant et après leur traitement.La modélisation du risque d'événements iatrogènes radio-induits repose sur la connaissance précise de la distribution de doses au tissu sain d'intérêt ainsi que sur un modèle de risque capable d'intégrer un maximum d'informations sur le profil d'irradiation et des autres facteurs de risques non dosimétriques. L'objectif de ce travail de thèse a été de développer des méthodes de modélisation capables de répondre à des questions spécifiques aux deux aspects, dosimétriques et statistiques, intervenant dans la modélisation du risque de survenue d'événements iatrogènes radio-induits.Nous nous sommes intéressé dans un premier temps au développement d'un modèle de calcul permettant de déterminer avec précision la dose à distance due au rayonnements de diffusion et de fuite lors d'un traitement par radiothérapie externe et ce, pour différentes tailles des champs et à différentes distances de l'axe du faisceau. Ensuite, nous avons utilisé des méthodes d'analyse de données fonctionnelles pour développer un modèle de risque de toxicité rectales après irradiation de la loge prostatique. Le modèle proposé a montré des performances supérieures aux modèles de risque existants particulièrement pour décrire le risque de toxicités rectales de grade 3. Dans le contexte d'une régression de Cox flexible sur données réelles, nous avons proposé une application originale des méthodes de statistique fonctionnelle permettant d'améliorer les performances d'une modélisation via fonctions B-splines de la relation dose-effet entre la dose de radiation à la thyroïde.Nous avons également proposé dans le domaine de la radiobiologie une méthodes basée sur l’analyse en composantes principales multiniveau pour quantifier la part de la variabilité expérimentale dans la variabilité des courbes de fluorescence mesurées. / Radiotherapy plays a major role in the therapeutic arsenal against cancer. Despite significant advances in technology for nearly twenty years, healthy tissues near or away from the target tumor remain inevitably irradiated at very different levels of doses. These doses are at the origin of early side effects (edema, radiation necrosis, dysphagia, cystitis) or late (rectal bleeding, telangiectasia, carcinogenic, cerebrovascular diseases). It is therefore essential to quantify and prevent these side effects to improve the patient quality of life after their cancer treatment.The objective of this thesis was to propose modelling methods able to answer specific questions asked in both aspects, dosimetry and statistics, involved in the modeling risk of developing radiation-induced iatrogenic pathologies.Our purpose was firstly to assess the out-of-field dose component related to head scatter radiation in high-energy photon therapy beams and then derive a multisource model for this dose component. For measured doses under out-of-field conditions, the average local difference between the calculated and measured photon dose is 10%, including doses as low as 0.01% of the maximum dose on the beam axis. We secondly described a novel method to explore radiation dose-volume effects. Functional data analysis is used to investigate the information contained in differential dose-volume histograms. The method is applied to the normal tissue complication probability modeling of rectal bleeding for In the flexible Cox model context, we proposed a new dimension reduction technique based on a functional principal component analysis to estimate a dose-response relationship. A two-stage knots selection scheme was performed: a potential set of knots is chosen based on information from the rotated functional principal components and the final knots selection is then based on statistical model selection. Finally, a multilevel functional principal component analysis was applied to radiobiological data in order to quantify the experimental Variability for replicate measurements of fluorescence signals of telomere length.

L’objectif de cette thèse est de contribuer à l’amélioration du processus de dépouillement d’essais de sûreté visant étudier le comportement d'un combustible nucléaire en contexte d’accident d’injection de réactivité (RIA), via la technique de contrôle par émission acoustique. Il s’agit notamment d’identifier clairement les mécanismes physiques pouvant intervenir au cours des essais à travers leur signature acoustique. Dans un premier temps, au travers de calculs analytiques et des simulation numériques conduites au moyen d’une méthode d’éléments finis spectraux, l’impact du dispositif d’essais sur la propagation des ondes est étudié. Une fréquence de résonance du dispositif est identifiée. On établit également que les mécanismes basses fréquences ne sont pas impactés par le dispositif d'essais. En second lieu, diverses techniques de traitement du signal (soustraction spectrale, analyse spectrale singulière, ondelettes. . . ) sont expérimentées, afin de proposer des outils permettant de traiter différent types de bruit survenant lors des essais RIA. La soustraction spectrale s’avère être la méthode la plus robuste aux changements de nature du bruit, avec un fort potentiel d’amélioration du rapport signal-à-bruit. Enfin, des méthodes d’analyse de données multivariées et d’analyse de données fonctionnelles ont été appliquées, afin de proposer un algorithme de classification statistique permettant de mieux comprendre la phénoménologie des accidents de type RIA et d’identifier les mécanismes physiques. Selon l’approche (multivariée ou fonctionnelle), les algorithmes obtenus permettent de reconnaître le mécanisme associé à une salve dans plus de 80% des cas. / The objective of the thesis is to contribute to the improvement of the monitoring process of nuclear safety experiments dedicated to study the behavior of the nuclear fuel in a reactivity initiated accident (RIA) context, by using the acoustic emission technique. In particular, we want to identify the physical mechanisms occurring during the experiments through their acoustic signatures. Firstly, analytical derivations and numerical simulations using the spectral finite element method have been performed in order to evaluate the impact of the wave travelpath in the test device on the recorded signals. A resonant frequency has been identified and it has been shown that the geometry and the configuration of the test device may not influence the wave propagation in the low frequency range. Secondly, signal processing methods (spectral subtraction, singular spectrum analysis, wavelets,…) have been explored in order to propose different denoising strategies according to the type of noise observed during the experiments. If we consider only the global SNR improvement ratio, the spectral subtraction method is the most robust to changes in the stochastic behavior of noise. Finally, classical multivariate and functional data analysis tools are used in order to create a machine learning algorithm dedicated to contribute to a better understanding of the phenomenology of RIA accidents. According to the method (multivariate or functional), the obtained algorithms allow to identify the mechanisms in more than 80 % of cases.

L'Analyse des Données Fonctionnelles est un domaine important et dynamique en statistique. Elle offre des outils efficaces et propose de nouveaux développements méthodologiques et théoriques en présence de données de type fonctionnel (fonctions, courbes, surfaces, ...). Le travail exposé dans cette thèse apporte une nouvelle contribution aux thèmes de l'apprentissage statistique et des quantiles conditionnels lorsque les données sont assimilables à des fonctions. Une attention particulière a été réservée à l'utilisation de la technique Support Vector Machines (SVM). Cette technique fait intervenir la notion d'Espace de Hilbert à Noyau Reproduisant. Dans ce cadre, l'objectif principal est d'étendre cette technique non-paramétrique d'estimation aux modèles conditionnels où les données sont fonctionnelles. Nous avons étudié les aspects théoriques et le comportement pratique de la technique présentée et adaptée sur les modèles de régression suivants. Le premier modèle est le modèle fonctionnel de quantiles de régression quand la variable réponse est réelle, les variables explicatives sont à valeurs dans un espace fonctionnel de dimension infinie et les observations sont i.i.d.. Le deuxième modèle est le modèle additif fonctionnel de quantiles de régression où la variable d'intérêt réelle dépend d'un vecteur de variables explicatives fonctionnelles. Le dernier modèle est le modèle fonctionnel de quantiles de régression quand les observations sont dépendantes. Nous avons obtenu des résultats sur la consistance et les vitesses de convergence des estimateurs dans ces modèles. Des simulations ont été effectuées afin d'évaluer la performance des procédures d'inférence. Des applications sur des jeux de données réelles ont été considérées. Le bon comportement de l'estimateur SVM est ainsi mis en évidence. / Functional Data Analysis is an important and dynamic area of statistics. It offers effective new tools and proposes new methodological and theoretical developments in the presence of functional type data (functions, curves, surfaces, ...). The work outlined in this dissertation provides a new contribution to the themes of statistical learning and quantile regression when data can be considered as functions. Special attention is devoted to use the Support Vector Machines (SVM) technique, which involves the notion of a Reproducing Kernel Hilbert Space. In this context, the main goal is to extend this nonparametric estimation technique to conditional models that take into account functional data. We investigated the theoretical aspects and practical attitude of the proposed and adapted technique to the following regression models.The first model is the conditional quantile functional model when the covariate takes its values in a bounded subspace of the functional space of infinite dimension, the response variable takes its values in a compact of the real line, and the observations are i.i.d.. The second model is the functional additive quantile regression model where the response variable depends on a vector of functional covariates. The last model is the conditional quantile functional model in the dependent functional data case. We obtained the weak consistency and a convergence rate of these estimators. Simulation studies are performed to evaluate the performance of the inference procedures. Applications to chemometrics, environmental and climatic data analysis are considered. The good behavior of the SVM estimator is thus highlighted.

Given current rates of anthropogenic environmental change, combined with the increasing lethal and non-lethal mortality threat that human activities pose, there is a vital need to understand wildlife movement and behaviour in human-dominated landscapes to help inform conservation efforts and wildlife management. As long-term monitoring of wildlife populations using Global Positioning System (GPS) telemetry increases, there are new opportunities to quantify change in wildlife movement and behaviour. The objective of this PhD research is to develop novel methodological approaches for quantifying change in spatial-temporal patterns of wildlife movement and habitat by leveraging long time series of GPS telemetry and remotely sensed data. Analyses were focused on the habitat and movement of individuals in the threatened grizzly bear (Ursus arctos) population of Alberta, Canada, which occupies a human-dominated and heterogeneous landscape. Using methods in functional data analysis, a multivariate regionalization approach was developed that effectively summarizes complex spatial-temporal patterns associated with landscape disturbance, as well as recovery, which is often left unaccounted in studies quantifying patterns associated with disturbance. Next, the quasi-experimental framework afforded by a hunting moratorium was used to compare the influence of lethal (i.e., hunting) and non-lethal (i.e., anthropogenic disturbance) human-induced risk on antipredator behaviour of an apex predator, the grizzly bear. In support of the predation risk allocation hypothesis, male bears significantly decrease risky daytime behaviours by 122% during periods of high lethal human-induced risk. Rapid behavioural restoration occurred following the end of the hunt, characterized by diel bimodal movement patterns which may promote coexistence of large predators in human-dominated landscapes. A multi-scale approach using hierarchical Bayesian models, combined with post hoc trend tests and change point detection, was developed to test the influence of landscape disturbance and conditions on grizzly bear home range and movement selection over time. The results, representing the first longitudinal empirical analysis of grizzly bear habitat selection, revealed selection for habitat security at broad scales and for resource availability and habitat permeability at finer spatial scales, which has influenced potential landscape connectivity over time. Finally, combining approaches in movement ecology and conservation physiology, a body condition index was used to characterize how the physiological condition (i.e., internal state) of grizzly bears influences behavioral patterns due to costs and benefits associated with risk avoidance and resource acquisition. The results demonstrated individuals in poorer condition were more likely to engage in risky behaviour associated with anthropogenic disturbance, which highlights complex challenges for carnivore conservation and management of human-carnivore conflict. In summary, this dissertation contributes 1) a multivariate regionalization approach for quantifying spatial-temporal patterns of landscape disturbance and recovery applicable across diverse natural systems, 2) support for the growing theory that apex predators modify behavioural patterns to account for temporal overlap with lethal and non-lethal human-induced risk associated with humans, 3) an integrated approach for considering multi-scale spatial-temporal change in patterns of wildlife habitat selection and landscape connectivity associated with landscape change, 4) a cross-disciplinary framework for considering the impacts of the internal state on behavioural patterns and risk tolerance. / Graduate

Cette thèse porte sur l'utilisation de données de vols pour l'optimisation de trajectoires de montée vis-à-vis de la consommation de carburant.Dans un premier temps nous nous sommes intéressé au problème d'identification de modèles de la dynamique de l'avion dans le but de les utiliser pour poser le problème d'optimisation de trajectoire à résoudre. Nous commençont par proposer une formulation statique du problème d'identification de la dynamique. Nous l'interpretons comme un problème de régression multi-tâche à structure latente, pour lequel nous proposons un modèle paramétrique. L'estimation des paramètres est faite par l'application de quelques variations de la méthode du maximum de vraisemblance.Nous suggérons également dans ce contexte d'employer des méthodes de sélection de variable pour construire une structure de modèle de régression polynomiale dépendant des données. L'approche proposée est une extension à un contexte multi-tâche structuré du bootstrap Lasso. Elle nous permet en effet de sélectionner les variables du modèle dans un contexte à fortes corrélations, tout en conservant la structure du problème inhérente à nos connaissances métier.Dans un deuxième temps, nous traitons la caractérisation des solutions du problème d'optimisation de trajectoire relativement au domaine de validité des modèles identifiés. Dans cette optique, nous proposons un critère probabiliste pour quantifier la proximité entre une courbe arbitraire et un ensemble de trajectoires échantillonnées à partir d'un même processus stochastique. Nous proposons une classe d'estimateurs de cette quantitée et nous étudions de façon plus pratique une implémentation nonparamétrique basé sur des estimateurs à noyau, et une implémentation paramétrique faisant intervenir des mélanges Gaussiens. Ce dernier est introduit comme pénalité dans le critère d'optimisation de trajectoire dans l'objectif l'intention d'obtenir directement des trajectoires consommant peu sans trop s'éloigner des régions de validité. / This thesis deals with the use of flight data for the optimization of climb trajectories with relation to fuel consumption.We first focus on methods for identifying the aircraft dynamics, in order to plug it in the trajectory optimization problem. We suggest a static formulation of the identification problem, which we interpret as a structured multi-task regression problem. In this framework, we propose parametric models and use different maximum likelihood approaches to learn the unknown parameters.Furthermore, polynomial models are considered and an extension to the structured multi-task setting of the bootstrap Lasso is used to make a consistent selection of the monomials despite the high correlations among them.Next, we consider the problem of assessing the optimized trajectories relatively to the validity region of the identified models. For this, we propose a probabilistic criterion for quantifying the closeness between an arbitrary curve and a set of trajectories sampled from the same stochastic process. We propose a class of estimators of this quantity and prove their consistency in some sense. A nonparemetric implementation based on kernel density estimators, as well as a parametric implementation based on Gaussian mixtures are presented. We introduce the later as a penalty term in the trajectory optimization problem, which allows us to control the trade-off between trajectory acceptability and consumption reduction.