La méthode LS-STAG est une méthode cartésienne pour le calcul d’écoulements incompressibles en géométries complexes, qui propose une discrétisation précise des équations de Navier-Stokes dans les cut-cells, cellules polyédriques de forme complexe créées par l’intersection du maillage cartésien avec la frontière du solide immergé. Originalement développée pour les géométries 2D, son extension aux géométries 3D se heurte au défi posé par le grand nombre de types de cut-cells (108) à considérer. Récemment, la méthode LS-STAG a été étendue aux géométries complexes 3D dont la frontière est parallèle à l’un des axes du repère cartésien, où sont uniquement présentes les contreparties extrudées des cut-cells 2D. Cette étude a notamment souligné deux points à élucider pour le développement d’une méthode totalement 3D : premièrement, le calcul des flux diffusifs par un simple schéma à deux points s’est révélé insuffisamment précis dans les cut-cells 3D-extrudées du fait de la non orthogonalité. Ensuite, l’implémentation de ces flux à la paroi, qui s’effectue en imposant une discrétisation distincte pour chaque type de cut-cell extrudée, se révèle trop complexe pour être étendue avec succès aux nombreux types supplémentaires de cut-cells 3D, et doit être simplifiée et rationalisée. Dans cette thèse, le premier point est résolu en utilisant l’outil des schémas diamants, d’abord étudié en 2D pour l’équation de la chaleur puis les équations de Navier-Stokes dans l’approximation de Boussinesq, puis étendu en 3D. En outre, les schémas diamants ont permis de revisiter intégralement la discrétisation du tenseur des contraintes des équations de Navier-Stokes, où disparaît le traitement au cas par cas selon la disposition de la frontière solide dans les cut-cells. Cela a permis d’aboutir à une discrétisation systématique, précise et algorithmiquement efficace pour les écoulements en géométries totalement 3D. La validation numérique de la méthode LS-STAG avec schémas diamants est présentée pour une série de cas tests en géométries complexes 2D et 3D. Sa précision est d’abord évaluée par comparaison avec des solutions analytiques en 2D, puis en 3D par la simulation d’un écoulement de Stokes entre deux sphères concentriques. La robustesse de la méthode est notamment mise en évidence par l’étude d’écoulements autour d’une sphère en rotation, dans les régimes laminaires (stationnaire et instationnaire), ainsi que pour un régime faiblement turbulent. / The LS-STAG method is a cartesian method for the computations of incompressible flows in complex geometries, which consists in an accurate discretisation of the Navier-Stokes equations in cut-cells, polyhedral cells with complex shape made by the intersection of cartesian mesh and the immersed boundary. Originally developed for 2D geometries, where only three types of generic cut-cells appear, its extension to 3D geometries has to deal with the large amount of cut-cells types (108). Recently, the LS-STAG method had been extended to 3D complex geometries whose boundary is parallel to an axis of the cartesian coordinate system, where there are only the extruded counterparts of 2D cut-cells. This study highlighted two points to deal with in order to develop a totally 3D method: firstly, the computation of diffusive fluxes by a simple 2-points scheme has shown to be insufficiently accurate in 3D-extruded cut-cells due to the non-orthogonality. In addition to that, implementation of these fluxes on the immersed boundary, which is done with a case by case discretisation according to the type of the cut-cells, appears to be too difficult for its successful extension to the several extra types of 3D cut-cells, and needs to be simplified and rationalized. In this thesis, the first point is solved by using the diamond scheme tool, firstly studied in 2D for the heat equation then for the Navier-Stokes equations in Boussinesq approximation, and finally extended to 3D. Moreover, the diamond schemes have been used to fully revisit the discretisation of shear stresses from Navier-Stokes equations, where the case by case procedure is removed. These modifications have permitted to come up with a systematic discretisation that is accurate and algorithmically efficient for flows in totally 3D geometries. The numerical validation of the LS-STAG method with diamond schemes is presented for a series of test cases in 2D and 3D complex geometries. The precision is firstly assessed by comparison with analytical solutions in 2D, then in 3D by the simulation of Stokes flow between two concentric spheres. The robustess of the method is highlighted by the simulations of flows past a rotating sphere, in laminar modes (steady and unsteady), as well as in a weakly turbulent mode.

The traditional first-order analysis in Euclidean spaces relies on the Sobolev spaces W1,p(Ω), where Ω ⊂ Rn is open and p ∈ [1, ∞].The Sobolev norm is then defined as the sum of Lp norms of a function and its distributional gradient.We generalize the notion of Sobolev spaces in two different ways. First, the underlying function norm will be replaced by the “norm” of a quasi-Banach function lattice. Second, we will investigate functions defined on an abstract metric measure space and that is why the distributional gradients need to be substituted. The thesis consists of two papers. The first one builds up the elementary theory of Newtonian spaces based on quasi-Banach function lattices. These lattices are complete linear spaces of measurable functions with a topology given by a quasinorm satisfying the lattice property. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces, where the role of weak derivatives is passed on to upper gradients. Tools such asmoduli of curve families and the Sobolev capacity are developed, which allows us to study basic properties of the Newtonian functions.We will see that Newtonian spaces can be equivalently defined using the notion of weak upper gradients, which increases the number of techniques available to study these spaces. The absolute continuity of Newtonian functions along curves and the completeness of Newtonian spaces in this general setting are also established. The second paper in the thesis then continues with investigation of properties of Newtonian spaces based on quasi-Banach function lattices. The set of all weak upper gradients of a Newtonian function is of particular interest.We will prove that minimalweak upper gradients exist in this general setting.Assuming that Lebesgue’s differentiation theoremholds for the underlyingmetricmeasure space,wewill find a family of representation formulae. Furthermore, the connection between pointwise convergence of a sequence of Newtonian functions and its convergence in norm is studied.

In this thesis we study three stochastic partial differential equations (SPDE) that arise as stochastic gradient flows via the fluctuation-dissipation principle. For the first equation we establish a finer regularity statement based on a generalized Taylor expansion which is inspired by the theory of rough paths. The second equation is the thin-film equation with thermal noise which is a singular SPDE. In order to circumvent the issue of dealing with possible renormalization, we discretize the gradient flow structure of the deterministic thin-film equation. Choosing a specific discretization of the metric tensor, we resdiscover a well-known discretization of the thin-film equation introduced by Grün and Rumpf that satisfies a discrete entropy estimate. By proving a stochastic entropy estimate in this discrete setting, we obtain positivity of the scheme in the case of no-slip boundary conditions. Moreover, we analyze the associated rate functional and perform numerical experiments which suggest that the scheme converges. The third equation is the massive $\varphi^4_2$-model on the torus which is also a singular SPDE. In the spirit of Bakry and Émery, we obtain a gradient bound on the Markov semigroup. The proof relies on an $L^2$-estimate for the linearization of the equation. Due to the required renormalization, we use a stopping time argument in order to ensure stochastic integrability of the random constant in the estimate. A postprocessing of this estimate yields an even sharper gradient bound. As a corollary, for large enough mass, we establish a local spectral gap inequality which by ergodicity yields a spectral gap inequality for the $\varphi^4_2$- measure.

This thesis investigates the integration of Stein Variational Gradient Descent (SVGD) with Joint Energy Models (JEMs), comparing its performance to Stochastic Gradient Langevin Dynamics (SGLD). We incorporated a generative loss term with an entropy component to enhance diversity and a smoothing factor to mitigate numerical instability issues commonly associated with the energy function in energy-based models. Experiments on the CIFAR-10 dataset demonstrate that SGLD, particularly with Sharpness-Aware Minimization (SAM), outperforms SVGD in classification accuracy. However, SVGD without SAM, despite its lower classification accuracy, exhibits lower calibration error underscoring its potential for developing well-calibrated classifiers required in safety-critical applications. Our results emphasize the importance of adaptive tuning of the SVGD smoothing factor ($alpha$) to balance generative and classification objectives. This thesis highlights the trade-offs between computational cost and performance, with SVGD demanding significant resources. Our findings stress the need for adaptive scaling and robust optimization techniques to enhance the stability and efficacy of JEMs. This thesis lays the groundwork for exploring more efficient and robust sampling techniques within the JEM framework, offering insights into the integration of SVGD with JEMs. / Master of Science / This thesis explores advanced techniques for improving machine learning models with a focus on developing well-calibrated and robust classifiers. We concentrated on two methods, Stein Variational Gradient Descent (SVGD) and Stochastic Gradient Langevin Dynamics (SGLD), to evaluate their effectiveness in enhancing classification accuracy and reliability. Our research introduced a new mathematical approach to improve the stability and performance of Joint Energy Models (JEMs). By leveraging the generative capabilities of SVGD, the model is guided to learn better data representations, which are crucial for robust classification. Using the CIFAR-10 image dataset, we confirmed prior research indicating that SGLD, particularly when combined with an optimization method called Sharpness-Aware Minimization (SAM), delivered the best results in terms of accuracy and stability. Notably, SVGD without SAM, despite yielding slightly lower classification accuracy, exhibited significantly lower calibration error, making it particularly valuable for safety-critical applications. However, SVGD required careful tuning of hyperparameters and substantial computational resources. This study lays the groundwork for future efforts to enhance the efficiency and reliability of these advanced sampling techniques, with the overarching goal of improving classifier calibration and robustness with JEMs.

Scania has been working with statistics for a long time but has invested in becoming a data driven company more recently and uses data science in almost all business functions. The algorithms developed by the data scientists need to be optimized to be fully utilized and traditionally this is a manual and time consuming process. What this thesis investigates is if and how well evolutionary algorithms can be used to automate the optimization process. The evaluation was done by implementing and analyzing four variations of genetic algorithms with different levels of complexity and tuning parameters. The algorithm subject to optimization was XGBoost, a gradient boosted tree model, applied to data that had previously been modelled in a competition. The results show that evolutionary algorithms are applicable in finding good models but also emphasizes the importance of proper data preparation. / Scania har länge jobbat med statistik men har på senare år investerat i att bli ett mer datadrivet företag och använder nu data science i nästan alla avdelningar på företaget. De algoritmer som utvecklas av data scientists måste optimeras för att kunna utnyttjas till fullo och detta är traditionellt sett en manuell och tidskrävade process. Detta examensarbete utreder om och hur väl evolutionära algoritmer kan användas för att automatisera optimeringsprocessen. Utvärderingen gjordes genom att implementera och analysera fyra varianter avgenetiska algoritmer med olika grader av komplexitet och trimningsparameterar. Algoritmen som var målet för optimering var XGBoost, som är en gradient boosted trädbaserad modell. Denna applicerades på data som tidigare hade modellerats i entävling. Resultatet visar att evolutionära algoritmer är applicerbara i att hitta bra modellermen påvisar även hur fundamentalt det är att arbeta med databearbetning innan modellering.

Les plantes se distribuent dans des habitats présentant une disponibilité variable en nutriment et s'y adaptent en ajustant leur taux de croissance relatif. Les espèces adaptées aux habitats infertiles, affichent un taux de croissance plus faible que celles adaptées aux habitats fertiles. Les adaptations expliquant cette distribution ont été identifiées, premièrement, au niveau des feuilles. Un fort taux de fixation du carbone et d’allocation de ce dernier à la croissance sont favorisés en investissant davantage dans des tissus foliaires contenant des enzymes photosynthétiques riches en azote, par rapport aux tissus structuraux riches en carbone. Inversement, les feuilles favorisant une croissance lente présentent une plus grande quantité de tissus structuraux que de tissus riches en enzymes photosynthétiques, ce qui prolonge leur longévité, mais restreint leur taux d'assimilation du carbone. Étant donné que les adaptations foliaires dépendent de l'utilisation des nutriments acquis par les racines, les adaptations de ces dernières sont essentielles pour comprendre la distribution des plantes. Le fonctionnement des racines est influencé par les mêmes variations dans le ratio entre les tissus à forte teneur en protéines riches en azote et les tissus structuraux. Les fortes valeurs de ce ratio améliorent l’acquisition des nutriments et soutiennent une croissance rapide, tandis que les faibles valeurs prolongent la longévité des racines, mais restreignent leur taux d'acquisition. Cependant, les racines doivent également explorer le sol dû à la mobilité limitée des nutriments. Cette fonction est réalisée en établissant des relations symbiotiques avec des champignons ou par l'allongement de leurs racines. Cependant, contrairement aux adaptations foliaires, la relation entre ces adaptations racinaires et la disponibilité des nutriments présente des résultats contradictoires. De plus, ces adaptations n'influencent pas l'acquisition des nutriments non directement disponibles, comme les nutriments organiques, qui peuvent représenter une proportion importante des nutriments du sol. Cela limite notre compréhension de la nutrition des plantes et entrave notre compréhension des mécanismes expliquant leur distribution. Afin de mieux comprendre la nutrition des plantes, des feuilles et des racines furent échantillonnées le long de gradients de fertilité. Les résultats ont montré que l'utilisation de nutriments organiques par le biais d'enzymes hydrolytiques augmentait à mesure que la fertilité des sols diminuait. De plus, une forte corrélation entre cette adaptation et les adaptations racinaires liées aux taux d'acquisition des nutriments a été observée, mais aucune corrélation n'a été constatée avec celles liées à l'exploration du sol. En revanche, dans un autre système d'étude, les résultats ont indiqué que les adaptations racinaires liées à l'exploration du sol, plutôt que celles associées aux taux d'acquisition des nutriments, s'alignaient avec la variation de la disponibilité des nutriments et se coordonnaient avec les adaptations foliaires qui permettent d’expliquer en partie la distribution des plantes. Dans l'ensemble, ces études ont approfondi notre compréhension de la nutrition des plantes et ont révélé différentes relations entre la variation de la disponibilité des nutriments et les adaptations racinaires influençant l'acquisition des nutriments et l'exploration du sol. Cela suggère qu’une généralisation des adaptations racinaires répondant systématiquement aux demandes nutritionnelles des feuilles est peu probable. / Plants are distributed across habitats of varying nutrient availability and adapt by adjusting, notably, their relative growth rates. Species adapted to nutrient-poor habitats exhibit lower growth rates than those adapted to nutrient-rich habitats. The adaptations explaining this distribution have been identified, first and foremost, at the leaf level. Leaves promoting rapid growth enhance net carbon assimilation by investing more in nitrogen-rich photosynthetic enzymes compared to carbon-rich structural tissues. This extends their lifespan, enhances their nutrient-use efficiency but limits carbon assimilation. Given that foliar adaptations depend on the utilization of nutrients acquired by roots, root adaptations are essential to understanding plant distribution. Plants possess also the ability to modify the ratio between nitrogen-rich protein tissues and carbonrich structural tissues in their roots. Similarly to leaf functioning, increasing this ratio enhances the efficiency of nutrient acquisition while minimizing carbon investment, enabling optimal carbon allocation for growth. On the other hand, they can decrease this ratio to prioritize nutrient conservation, which extends their longevity but restricts nutrient acquisition rate. However, roots must also explore the soil due to the limited mobility of nutrients. Soil exploration is achieved by establishing symbiotic relationships with fungi or through the elongation of their roots. Unlike leaf adaptations, the relationship between these root adaptations and nutrient availability yields contradictory results. Additionally, these adaptations do not directly influence the acquisition of non-readily available soil nutrients, such as organic nutrients, which can represent a significant proportion of the total nutrient pool. Thus, our understanding of plant nutrition is limited, impeding our understanding of the mechanisms explaining their distributions. To contribute to an enriched understanding of plant nutrition, leaves and roots were sampled along strong fertility gradients. The results revealed an increase in the utilization of organic nutrients through hydrolytic enzymes as the availability of directly accessible nutrients declined. Furthermore, a strong correlation between this adaptation and root adaptations related to nutrient acquisition rates has been observed, but no correlation was found with adaptations related to soil exploration. On the other hand, in another study system, the results indicated that root adaptations related to soil exploration, rather than those associated with nutrient acquisition rates, aligned with the variation in nutrient availability and coordinated with foliar adaptations influencing net carbon assimilation. As a result, a high degree of mycorrhizal symbiosis was associated with leaves favoring rapid growth in fertile soil. Overall, roots displaying a high density of structural tissues and a high degree of symbiotic association were associated with fertile soil across two different study systems. Altogether, these results have deepened our understanding of plant nutrition and revealed different possible relationships between nutrient availability variation and root adaptations influencing nutrient acquisition and soil exploration. This suggests that generalizing root adaptations that consistently meet the nutrient demands of leaves is unlikely.

The thesis presents a novel computational method for analysing the static and dynamic behaviour of a multi-damaged beam using local and non-local elasticity theories. Most of the lumped damage beam models proposed to date are based on slender beam theory in classical (local) elasticity and are limited by inaccuracies caused by the implicit assumption of the Euler-Bernoulli beam model and by the spring model itself, which simplifies the real beam behaviour around the crack. In addition, size effects and material heterogeneity cannot be taken into account using the classical elasticity theory due to the absence of any microstructural parameter. The proposed work is based on the inhomogeneous Euler-Bernoulli beam theory in which a Dirac's delta function is added to the bending flexibility at the position of each crack: that is, the severer the damage, the larger is the resulting impulsive term. The crack is assumed to be always open, resulting in a linear system (i.e. nonlinear phenomena associated with breathing cracks are not considered). In order to provide an accurate representation of the structure's behaviour, a new multi-cracked beam element including shear effects and rotatory inertia is developed using the flexibility approach for the concentrated damage. The resulting stiffness matrix and load vector terms are evaluated by the unit-displacement method, employing the closed-form solutions for the multi-cracked beam problem. The same deformed shapes are used to derive the consistent mass matrix, also including the rotatory inertia terms. The two-node multi-damaged beam model has been validated through comparison of the results of static and dynamic analyses for two numerical examples against those provided by a commercial finite element code. The proposed model is shown to improve the computational efficiency as well as the accuracy, thanks to the inclusion of both shear deformations and rotatory inertia. The inaccuracy of the spring model, where for example for a rotational spring a finite jump appears on the rotations' profile, has been tackled by the enrichment of the elastic constitutive law with higher order stress and strain gradients. In particular, a new phenomenological approach based upon a convenient form of non-local elasticity beam theory has been presented. This hybrid non-local beam model is able to take into account the distortion on the stress/strain field around the crack as well as to include the microstructure of the material, without introducing any additional crack related parameters. The Laplace's transform method applied to the differential equation of the problem allowed deriving the static closed-form solution for the multi-cracked Euler-Bernoulli beams with hybrid non-local elasticity. The dynamic analysis has been performed using a new computational meshless method, where the equation of motions are discretised by a Galerkin-type approximation, with convenient shape functions able to ensure the same grade of approximation as the beam element for the classical elasticity. The importance of the inclusion of microstructural parameters is addressed and their effects are quantified also in comparison with those obtained using the classical elasticity theory.

Cette thèse est consacrée à l'étude de méthodes numériques pour la simulation des écoulements polyphasiques en milieu poreux, en vue de leur application à des problèmes d'ingénierie pétrolière ou environnementale. Nous présentons une formulation générique du modèle d'écoulements à nombre quelconque de composants présents dans un nombre quelconque de phases. Dans notre approche l'approximation des flux diffusifs (issus, par exemple, de la loi de Darcy) s'appuie sur de nouveaux schémas, appelés schémas gradient, qui ont plusieurs avantages sur les schémas industriels standard : ces derniers, qui sont des schémas volumes finis multi-points centrés aux mailles, ne sont généralement pas symétriques et convergent difficilement sur des cas à forts rapports d'anisotropie. Nous montrons en revanche que les schémas gradient conduisent naturellement à des approximations symétriques et convergentes. Parmi cette classe de schémas, nous étudions plus particulièrement le schéma "VAG" qui fait intervenir des inconnues au centre des mailles et aux sommets du maillage. Ce schéma conduit à la définition de flux entre le centre d'une maille et ses sommets, qui sont utilisés pour généraliser la méthode "VAG" au contexte polyphasique. Des tests numériques montrent alors que ce schéma est robuste, et conduit à un très bon compromis précision/coût, ce qui en fait un candidat idoine pour les applications industrielles. Nous présentons notamment un cas test, basé sur des observations de terrains, d'injection et de dissolution de CO2 dans la région proche d'un puits foré dans un aquifère salin. Nous montrons alors que le schéma numérique permet de simuler l'assèchement et la précipitation de minéral observée en pratique. Un chapitre de la thèse est enfin consacré à l'étude pratique et théorique d'une méthode numérique générique pour contrôler l'effet d'axe lors de l'utilisation de schémas industriels / This thesis is focused on numerical methods dedicated to the simulation of multiphase flow in porous media, involved in petroleum or environmental engineering. We present a generic formulation of the flow model which is able to take into account any number of components within any number of phases. In our approach the approximation of the diffusive fluxes (mainly resulting from Darcy's law) is based on new schemes, called gradient schemes, which show several advantages over the standard industrial numerical schemes : these schemes, which belong to the class of the cell-centred MultiPoint Flux Approximation finite volume schemes, are not symmetric and may lead to difficulties of convergence in the case of high anisotropy ratios. We indeed show that gradient schemes are naturally providing symmetric and convergent approximations. We particularly study the Vertex Approximate Gradient scheme (called the VAG scheme), whose discrete unknowns are the values at the cell centres and at the vertices of the mesh. This scheme implies the definition of fluxes between the centre of a given cell and its vertices, used for the extension of the scheme to multiphase flow. Numerical tests show the robustness and the accuracy of the method for a low computational cost, which enables the use of the VAG scheme in an industrial framework. A test case, based on experimental data of injection and dissolution of CO2 in the near-well region within a saline aquifer, shows the aptitude of the scheme for reproducing drying and salt precipitation, which are practically observed. Finally, a chapter of the thesis is devoted to the theoretical and practical study of a general numerical method for controlling Grid Orientation Effect in industrial simulators

Η παρούσα ειδική ερευνητική εργασία εκπονήθηκε στα πλαίσια του Διατμηματικού Προγράμματος Μεταπτυχιακών Σπουδών στην “Ηλεκτρονική και Επεξεργασία της Πληροφορίας”, στο Τμήμα Φυσικής του Πανεπιστημίου Πατρών. Αντικείμενο της παρούσας εργασίας είναι η “Υλοποίηση σε FPGA του περιγραφέα HOG για ανίχνευση ανθρώπων σε εικόνες και βίντεο”. Το πρώτο κεφάλαιο αποτελεί μια εισαγωγή στις βασικότερες έννοιες που χρησιμοποιούνται στην παρούσα εργασία. Περιγράφεται επίσης η αναπτυξιακή πλακέτα που χρησιμοποιήθηκε καθώς και τα επί μέρους στοιχεία που τη συνθέτουν. Τέλος γίνεται μια συνοπτική αναφορά σε εργασίες με παρόμοιο αντικείμενο, οι οποίες με επηρέασαν στο σχεδιασμό και την υλοποίηση του συστήματός μου. Στο δεύτερο κεφάλαιο αναλύεται ο περιγραφέας Ιστογραμμάτων Προσανατολισμού της Βάθμωσης ή όπως είναι ευρύτερα γνωστός Histograms of Oriented Gradient Descriptor. Παρουσιάζονται τα βήματα όπως περιγράφονται στην εργασία των Dalal&Triggs[4] και οι βέλτιστες τιμές των παραμέτρων του περιγραφέα. Στο τρίτο κεφάλαιο ακολουθώντας τα βήματα του δευτέρου κεφαλαίου, παρουσιάζεται η διαδικασία υλοποίησης του περιγραφέα στο Matlab. Εκτός της υλοποίησης έγινε και μια προεργασία για τη μεταφορά του σε γλώσσα περιγραφής υλικού. Η προεργασία αυτή περιλαμβάνει απλοποιήσεις και τροποποιήσεις με σκοπό να μειωθεί το υπολογιστικό κόστος. Τέλος παρουσιάζονται τα αποτελέσματα δοκιμών της απόδοσης του περιγραφέα για τις διάφορες απλοποιήσεις. Στο τέταρτο κεφάλαιο γίνεται μια μικρή αναφορά στους ταξινομητές. Περιγράφονται οι ταξινομητές που δοκιμάστηκαν στην παρούσα εργασία ως προς συγκεκριμένα χαρακτηριστικά τους καθώς και την υπολογιστική τους πολυπλοκότητα για την συγκεκριμένη εφαρμογή. Το πέμπτο και τελευταίο κεφάλαιο περιλαμβάνει την περιγραφή της υλοποίησης σε VHDL. Αναλύονται τα επί μέρους κυκλώματα και όπου κρίθηκε αναγκαίο χρησιμοποιήθηκαν σχήματα ή πίνακες. Σε κάποιες περιπτώσεις δίνονται και οι κυματομορφές των κυκλωμάτων. / This thesis took place within the frame work of the Interdeparmental Master’s Program in “Electronics and Information Processing”, at the Department of Physics of University of Patras. The objective of this work is the implementation in FPGA of the HOG descriptor for the detection of people, images and videos. The first chapter is an introduction about the basic concepts, which are used across the manuscript. (Additional descriptions concern the development board which was used as well as the individual parts that compose it.) In the end, there is a brief reference to past projects focusing on similar objectives, which influenced the design and the implementation of my system. The second chapter concerns the presentation and discussion of the Histograms of Oriented Gradient descriptor. The steps of the procedure and the best parameter values of the descriptor are presented in a similar way as they are described in the paper of Dalal and Triggs. In the third chapter, following the steps of the previous one, the focus shifts to the descriptor’s implementation procedure in Matlab. Besides the implementation, there is a preparation for the transference of the descriptor in a Hardware Description Language. This preparation includes simplifications and modifications aiming at the reduction of the computational cost. Finally, we see the tests’ results of the descriptor’s performance concerning the various simplifications. The fourth chapter is a partial reference to the classifiers. The description is about the classifiers that were used in the present work with respect to their features and their computational complexity of this particular application. The fifth and final chapter refers to the description of the implementation in VHDL. There is an analysis of the partial circuits and, when necessary, shapes and tables were used. In some cases, the waveforms of the circuits are being presented.

Le changement climatique rapide auquel nous assistons actuellement est déjà en train de modifier le cycle de vie d’un grand nombre d’organismes. Des études basées sur des modèles d’enveloppe bioclimatique apportent des réponses mais ces prédictions de nouvelles aires de répartition ne tiennent pas compte d’une part de l’adaptation rapide des espèces (plasticité phénotypique et diversité génétique non neutre), et d’autre part des interactions interspécifiques ou de la dynamique des populations. Ce travail de recherche est centré sur les mécanismes permettant la persistance des individus dans un environnement changeant.Nous avons travaillé dans les Pyrénées françaises sur deux espèces à large répartition européenne (chêne sessile et hêtre commun) sur un gradient altitudinal de 1500 m de dénivelé correspondant en moyenne à 8°C d’amplitude thermique. Ce gradient a été répété dans deux vallées parallèles, distantes de 30 km. Basée sur l’étude de traits fonctionnels, nous avons caractérisé les variations altitudinales de traits morphologiques et physiologiques de ces caractères dans des conditions naturelles. Les capacités écophysiologiques apparaissent plus élevée pour le chêne et pour les populations de haute altitude, suggérant une adaptation locale à un environnement stressant. Dans une étude préliminaire, nous avons établi qu’il était nécessaire d’intégrer les variations de pression partielle de dioxyde de carbone et non se concentration dans les mesures d’échanges gazeux. Tous les traits fonctionnels mesurés en populations naturelles varient avec l’altitude. Ainsi la taille des feuilles diminue avec l’altitude tandis que les autres traits augmentent, avec des valeurs de 1.3 à 3.9 fois supérieures entre le haut et le bas du gradient tous traits confondus. Nous avons ensuite cherché à déterminer l’origine de ces variations phénotypiques. Une expérimentation en test de provenance a ainsi permis de déterminer les traits dont la variation in situ était en partie sous contrôle génétique. Les résultats de notre étude montrent que le gradient altitudinal a induit une différenciation génétique au niveau de la croissance, de la phénologie et de traits fonctionnels foliaires pour ces espèces, malgré la proximité des populations étudiées dans leur milieu naturel. Néanmoins, les capacités photosynthétiques pour le hêtre et la surface spécifique foliaire pour le chêne ne montre aucune différentiation génétique, ainsi que la densité stomatique pour les deux espèces. D’autre part, l’expérimentation de transplantations réciproques le long du gradient, a mis en évidence une forte plasticité phénotypique pour les deux espèces, ce qui suggère que les populations peuvent dans une certaine mesure répondre immédiatement aux variations climatiques rencontrées le long de ce gradient. Cependant, tandis que la température optimale pour la longueur de saison de végétation ne semble pas encore atteinte, les populations pourraient réagir négativement à une élévation de la température en terme de croissance. En conclusion, les mécanismes adaptatifs mis en évidence le long d’un gradient climatique naturel, pourraient permettre aux populations de faire face au changement climatique actuel. / The rapid climate change, which we are currently witnessing, is already modifying the physiology and distribution of species. Predictions of changes in species distributions do not take evolutionary mechanisms and biotic interactions into account. Our main objective was to assess the inherent adaptive capacities of tree populations by i) quantifying the phenotypic variations of functional traits with altitude and ii) studying the extent to which these variations are environmentally driven (phenotypic plasticity) and/or genetically fixed (adaptation). The study took place in the French Pyrenees along an altitudinal gradient range of 1500 m corresponding on average to 8°C of thermal amplitude. We focused on two broadleaved species with a wide European distribution (sessile oak and common beech). This gradient was repeated in two parallel valleys, distant from 30 km. Altitudinal trends were investigated for several morphological, physiological and phenological traits in natural conditions (in situ), in a common garden experiment and in reciprocal transplant experiments (RTEs). The phenotypic variability observed in situ showed significant altitudinal trends for all the studied traits and followed similar patterns for both species. We established that together with temperature, it was also necessary to integrate the variations of atmospheric gas partial pressure along the altitudinal gradient. In the common garden experiment, our results showed that the altitudinal gradient induced genetic differentiations for growth, leaf phenology and several morphological and physiological traits. This experiment made it possible to demonstrate, for both species, a weaker effect of genetic variations than in situ observed variations, suggesting a strong effect of the environment on leaf functional traits. A higher intrapopulation than interpopulation genetic variability was also observed for all traits. Finally, the reciprocal transplant experiments highlighted a high magnitude of phenotypic plasticity whatever the trait and the species.