Dissertations / Theses on the topic 'Variation graph'

Thesis advisor: Gabor T. Marth
This thesis concerns itself with the development of methods for comparing genomes. Chapter 2 is a comparative genomics investigation of coding regions across multiple species. Regions of the genome coding for proteins show higher conservation than non-coding regions. Furthermore, we show that a portion of coding regions are conserved beyond the requirements of protein conservation, supporting functions such as microRNA binding and splicing enhancement, providing the non-coding functional impetus to conservation. In Chapter 3, we focus on the detection and characterization of a particular type of structural variation - mobile element insertions (MEIs). While there are many types of mobile elements in the human genome, three of these are active and cause most of the MEI variation observed in humans: ALU, L1 and SVA elements. We detect variation across 1000 Genomes Pilot populations caused by these elements, assemble ALU elements to single nucleotide resolution, and determine actively copying species of this element. We've developed a variety of algorithmic approaches to MEI detection, and present these. Chapter 4 outlines an approach to remedy reference bias via the incorporation of variation data into the reference. In particular, we construct a pan-genome reference, demonstrated concretely via resolving ALU regions, and develop new alignment software to align against this enriched reference structure
Thesis (PhD) — Boston College, 2014
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Biology

Les variants structuraux (SVs), des variations génomiques de plus de 50 pb, contribuent de manière significative à la diversité génétique et à l'évolution des espèces. La détection et le génotypage précis des SVs est crucial pour comprendre leur rôle dans la variation phénotypique et l'adaptation. Les graphes de variation (VGs) et graphes de pangénomes (PGs), qui représentent les variations génomiques comme des chemins alternatifs dans un graphe, offrent une approche prometteuse pour l'analyse des SVs. Cette thèse explore l'utilisation des VGs et PGs pour la détection et le génotypage des SVs, en se concentrant sur un complexe de quatre espèces de papillons Coenonympha alpins. Deux outils bio-informatiques ont été développés au cours de cette thèse : (1) SVJedi-graph, le premier génotypeur de SVs à partir de lectures longues utilisant un VG pour représenter les SVs, fournissant une précision de génotypage supérieure aux outils de l’état de l’art, en particulier pour les SVs proches et chevauchants, et (2) INVPG-annot, un outil d’identification des inversions dans les PGs, qui a permi de démontrer que les inversions sont représentées par différentes topologies dans les PGs selon l’outil de construction utilisé. L'analyse comparative des génomes des papillons Coenonympha a permis d'identifier douze grandes inversions (≥ 100 kbp) entre les quatre espèces, dont certaines pourraient jouer un rôle dans l'isolement reproductif et l'adaptation locale de deux de ces espèces. Bien que l'approche basée sur les PGs présente des avantages pour la comparaison de génomes, des défis restent à relever pour l'analyse des grands variants comme les inversions
Structural variants (SVs), genomic variations of more than 50 bp, contribute significantly to genetic diversity and species evolution. Accurate detection and genotyping SVs is crucial to understanding their role in phenotypic variation and adaptation. Variation graphs (VGs) and pangenome graphs (PGs), which represent genomic variations as alternative paths in a graph, offer a promising approach for the analysis of SVs. This thesis explores the use of VGs and PGs for the detection and genotyping of SVs, focusing on a complex of four species of alpine Coenonympha butterflies. Two bioinformatics tools were developed during this thesis: (1) SVJedi-graph, the first long-read SV genotyper using a VG to represent SVs, providing a genotyping accuracy superior to state-of-the-art tools, particularly for close and overlapping SVs, and (2) INVPG-annot, a tool for identifying inversions in PGs, which demonstrated that inversions are represented by different topologies in PGs depending on the construction tool used. Comparative analysis of the Coenonympha butterfly genomes identified twelve large inversions (≥ 100 kbp) between the four species, some of which could play a role in the reproductive isolation and local adaptation of two of these species. While the PG-based approach offers advantages for genome comparison, challenges remain for the analysis of large variants such as inversions

Mieux comprendre les mécanismes de la résistance aux antibiotique est un enjeu important dans la lutte contre les maladies infectieuses, qui fait face à la propagation de bactéries multi-résistantes. Les études d'association à l'échelle des génomes sont des outils puissants pour explorer les polymorphismes liés aux variations phénotypiques dans une population. Leur cadre méthodologique est très documenté pour les eucaryotes, mais leur application aux bactéries est très récente. Durant cette thèse, j'ai cherché à rendre ces outils mieux adaptés aux génomes plastiques des bactéries, principalement en travaillant sur la représentation des variations génétiques. En effet, parce que les bactéries ont la capacité à échanger du matériel génétique avec leur environnement, leurs génomes peuvent être trop différents au sein d'une espèce pour être alignés contre une référence. La description des variations par des fragments de séquence de longueur k, les k-mers, offre la flexibilité nécessaire mais ne permet pas une interprétation directe des résultats obtenus. La méthode mise au point teste l'association de ces k-mers avec le phénotype, et s'appuie sur un graphe de De Bruijn pour permettre la visualisation du contexte génomique des k-mers identifiés par le test, sous forme de graphes. Cette vue synthétique renseigne sur la nature de la séquence identifiée: il peut par exemple s'agir de polymorphisme local dans un gène ou de l'acquisition d'un gène dans un plasmide. Le type de variant représenté dans un graphe peut être prédit avec une bonne performance à partir de descripteurs du graphe, rendant plus opérationnelles les approches par k-mers pour l'étude des génomes bactériens
The emergence and spread of multi-drug resistance has become a major worldwide public health concern, calling for better understanding of the underlying resistance mechanisms. Genome-wide association studies are powerful tools to finely map the genetic polymorphism linked to the phenotypic variability observed in a population. However well documented for eukaryotic genome analysis, these studies were only recently applied to prokaryota.Through this PhD project, I searched how to better adapt these tools to the highly plastic bacterial genomes, mainly by working on the representation of the genetic variations in these genomes. Indeed, because the bacteria have the faculty to acquire genetic material by a means other than direct inheritance from a parent cell, their genomes can differ too much within a species to be aligned against a reference. A representation using sequence fragments of length k - the so-called k-mers - offers the required flexibility but generates redundancy and does not allow for a direct interpretation of the identified associations. The method we set up tests the association of these k-mers with the phenotype, and takes advantage of a De Bruijn graph (DBG) built over all genomes to remove the local redundancy of k-mers, and offer a visualisation of the genomic context of the k-mers identified by the test. This synthetic view as DBG subgraphs informs on the nature of the identified sequence: e.g. local polymorphism in a gene or gene acquired through a plasmid. The type of variant can be predicted correctly in 96% of the cases from descriptors of the subgraphs, providing a tractable framework for k-mer-based association studies

Objectives: One of the most prominent features of schizophrenia is relatively lower general cognitive ability (GCA). An emerging approach to understanding the roots of variation in GCA relies on network properties of the brain. In this multi-center study, we determined global characteristics of brain networks using graph theory and related these to GCA in healthy controls and individuals with schizophrenia. Methods: Participants (N = 116 controls, 80 patients with schizophrenia) were recruited from four sites. GCA was represented by the first principal component of a large battery of neurocognitive tests. Graph metrics were derived from diffusion-weighted imaging. Results: The global metrics of longer characteristic path length and reduced overall connectivity predicted lower GCA across groups, and group differences were noted for both variables. Measures of clustering, efficiency, and modularity did not differ across groups or predict GCA. Follow-up analyses investigated three topological types of connectivity—connections among high degree “rich club” nodes, “feeder” connections to these rich club nodes, and “local” connections not involving the rich club. Rich club and local connectivity predicted performance across groups. In a subsample (N = 101 controls, 56 patients), a genetic measure reflecting mutation load, based on rare copy number deletions, was associated with longer characteristic path length. Conclusions: Results highlight the importance of characteristic path lengths and rich club connectivity for GCA and provide no evidence for group differences in the relationships between graph metrics and GCA.

Aquesta tesi proposa una estructura de dades per emmagatzemar imatges tridimensionals. L'estructura da dades té forma d'arbre i codifica les components connexes dels conjunts de nivell de la imatge. Aquesta estructura és la eina bàsica per moltes aplicacions proposades: operadors morfològics tridimensionals, visualització d'imatges mèdiques, anàlisi d'histogrames de color, seguiment d'objectes en vídeo i detecció de vores. Motivada pel problema de la completació de vores, la tesi conté un estudi de com l'eliminació de soroll mitjançant variació total anisòtropa es pot fer servir per calcular conjunts de Cheeger en mètriques anisòtropes. Aquests conjunts de Cheeger anisòtrops es poden utilitzar per trobar òptims globals d'alguns funcionals per completar vores. També estan relacionats amb certs invariants afins que s'utilitzen en reconeixement d'objectes, i en la tesi s'explicita aquesta relació.
This thesis proposes a tree data structure to encode the connected components of level sets of 3D images. This data structure is applied as a main tool in several proposed applications: 3D morphological operators, medical image visualization, analysis of color histograms, object tracking in videos and edge detection. Motivated by the problem of edge linking, the thesis contains also an study of anisotropic total variation denoising as a tool for computing anisotropic Cheeger sets. These anisotropic Cheeger sets can be used to find global optima of a class of edge linking functionals. They are also related to some affine invariant descriptors which are used in object recognition, and this relationship is laid out explicitly.

In this thesis we consider cutsets in graphs which can be expressed as unionsof sets each of which is spanned by a tree of diameter at most d-1 for someinteger d ≥ 1; we call these sets galaxy cutsets. These galaxycutsets generalise both star-cutsets and vertex-cuts, and serve as simple models for virus-like attacks on or cascading failures in networks,the crucial property being that neighbours of affected vertices may alsofail and cease to function. We approach our subject from four different pointsof view. We begin by exploring the connection between galaxiesand a suitable type of flow, proving a min-max result for planargraphs. Then, after tackling the fundamental issue of recognising whethera given graph is susceptible to virus-like attacks, i.e. whether it contains a galaxy cutset, we consider a weighted version of the flows that are dualto the galaxies, and prove Θ(log n) lower and upper approximability boundsfor the problem of finding a maximum such flow. We then investigate the problem of network design, that is tosay, the problem of constructing low cost spanning subgraphs of a given graph which are not vulnerable to cascading failures. Finally, weembark on a detailed analysis of the structure of star-cutsets in planar graphs and useour results to derive a polynomial time algorithm for the problem ofneutralising every star-cutset by protecting edges.
Dans cette thèse, nous considerons des séparateurs dans les graphes qui peuvent être éxprimés sous forme d'une union d'ensembles de sommets dans laquelle chaque ensemble est couvert par un arbre de diamètre d-1 pour un nombre entier d ≥ 1; nous appellons ces séparateurs des galaxies séparatrices. Les galaxies séparatrices genéralisent les étoiles séparatrices et les séparateurs formés par un ensemble de sommets, et elles servent comme simple modèle pour des attaques de virus sur ou des cascades de défaillances dans un réseau, la proprieté distinguante étant que les voisins des sommets qui sont affectés peuvent eux aussi faillir. Nous approchons le sujet depuis quatre points de vue différents. Nous commençons par explorer le lien entre les galaxies et un type de flot approprié, et nous prouvons un résultat de type min max pour les graphes planaires. Ensuite, après avoir résolu la question fondamentale de reconnaitre si un graphe donné est sensible aux attaques de virus, c'est-à-dire s'il contient une galaxie séparatrice, nous introduisons des capacités dans les flots correspondants aux galaxies, et demontrons une borne d'approximabilité inférieure et supérieure de Θ(log n)pour le problème de trouver un flot maximum. Ensuite, nous enquêtons sur le problème de dessein de réseau, c'est-à-dire le problème de construire des sous-graphes couvrants peu coûteux qui ne sont pas sensibles aux cascades de défaillances. Finalement, nous nous lançons dans une analyse détaillée de la structure des étoiles séparatrices dans les graphes planaires, et nous utilisons nos résultats pour développer un algorithme polynomial qui résout le problème de neutraliser toutes les étoiles séparatrices en protégeant des arêtes.

The main goal of this thesis is to develop tools that enable us to study the convergence of minimizers of functionals defined on point clouds towards minimizers of equivalent functionals in the continuum; the point clouds we consider are samples of a ground-truth distribution. In particular, we investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground-truth distribution). Moreover, we obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the consistency to hold. We provide results for two-way and for multi-way cuts. The results are obtained by using the notion of Γ-convergence and an appropriate choice of metric which allows us to compare functions defined on point clouds with functions defined on continuous domains.

Many computer vision applications such as image filtering, segmentation and stereovision can be formulated as optimization problems. Recently discrete, convex, globally optimal methods have received a lot of attention. Many graph-based methods suffer from metrication artefacts, segmented contours are blocky in areas where contour information is lacking. In the first part of this work, we develop a discrete yet isotropic energy minimization formulation for the continuous maximum flow problem that prevents metrication errors. This new convex formulation leads us to a provably globally optimal solution. The employed interior point method can optimize the problem faster than the existing continuous methods. The energy formulation is then adapted and extended to multi-label problems, and shows improvements over existing methods. Fast parallel proximal optimization tools have been tested and adapted for the optimization of this problem. In the second part of this work, we introduce a framework that generalizes several state-of-the-art graph-based segmentation algorithms, namely graph cuts, random walker, shortest paths, and watershed. This generalization allowed us to exhibit a new case, for which we developed a globally optimal optimization method, named "Power watershed''. Our proposed power watershed algorithm computes a unique global solution to multi labeling problems, and is very fast. We further generalize and extend the framework to applications beyond image segmentation, for example image filtering optimizing an L0 norm energy, stereovision and fast and smooth surface reconstruction from a noisy cloud of 3D points

"Department of Horticulture, Viticulture and Oenology, Faculty of Agriculture and Natural Resource Sciences, The University of Adelaide, Waite Campus, Glen Osmond S.A." Bibliography: leaves 136-149 This investigated focussed on selected aspects of berry development and ripening that were subject to variation. Shiraz and Chardonnay were chosen as experimental varieties because these cultivars presented a large range of variability in the field. The extent of the variation within each of the recorded berry parameters was assessed using the coefficient of variation (CV), a unitless measure of sample variability relative to the sample mean, ideally suited to comparative studies.

L’opérateur du p-Laplacien non local, l’équation d’évolution et la régularisation variationnelle associées régies par un noyau donné ont des applications dans divers domaines de la science et de l’ingénierie. En particulier, ils sont devenus des outils modernes pour le traitement massif des données (y compris les signaux, les images, la géométrie) et dans les tâches d’apprentissage automatique telles que la classification. En pratique, cependant, ces modèles sont implémentés sous forme discrète (en espace et en temps, ou en espace pour la régularisation variationnelle) comme approximation numérique d’un problème continu, où le noyau est remplacé par la matrice d’adjacence d’un graphe. Pourtant, peu de résultats sur la consistence de ces discrétisations sont disponibles. En particulier, il est largement ouvert de déterminer quand les solutions de l’équation d’évolution ou du problème variationnel des tâches basées sur des graphes convergent (dans un sens approprié) à mesure que le nombre de sommets augmente, vers un objet bien défini dans le domaine continu, et si oui, à quelle vitesse. Dans ce manuscrit, nous posons les bases pour aborder ces questions.En combinant des outils de la théorie des graphes, de l’analyse convexe, de la théorie des semi- groupes non linéaires et des équations d’évolution, nous interprétons rigoureusement la limite continue du problème d’évolution et du problème variationnel du p-Laplacien discrets sur graphes. Plus précisé- ment, nous considérons une suite de graphes (déterministes) convergeant vers un objet connu sous le nom de graphon. Si les problèmes d’évolution et variationnel associés au p-Laplacien continu non local sont discrétisés de manière appropriée sur cette suite de graphes, nous montrons que la suite des solutions des problèmes discrets converge vers la solution du problème continu régi par le graphon, lorsque le nombre de sommets tend vers l’infini. Ce faisant, nous fournissons des bornes d’erreur/consistance.Cela permet à son tour d’établir les taux de convergence pour différents modèles de graphes. En parti- culier, nous mettons en exergue le rôle de la géométrie/régularité des graphons. Pour les séquences de graphes aléatoires, en utilisant des inégalités de déviation (concentration), nous fournissons des taux de convergence nonasymptotiques en probabilité et présentons les différents régimes en fonction de p, de la régularité du graphon et des données initiales
The non-local p-Laplacian operator, the associated evolution equation and variational regularization, governed by a given kernel, have applications in various areas of science and engineering. In particular, they are modern tools for massive data processing (including signals, images, geometry), and machine learning tasks such as classification. In practice, however, these models are implemented in discrete form (in space and time, or in space for variational regularization) as a numerical approximation to a continuous problem, where the kernel is replaced by an adjacency matrix of a graph. Yet, few results on the consistency of these discretization are available. In particular it is largely open to determine when do the solutions of either the evolution equation or the variational problem of graph-based tasks converge (in an appropriate sense), as the number of vertices increases, to a well-defined object in the continuum setting, and if yes, at which rate. In this manuscript, we lay the foundations to address these questions.Combining tools from graph theory, convex analysis, nonlinear semigroup theory and evolution equa- tions, we give a rigorous interpretation to the continuous limit of the discrete nonlocal p-Laplacian evolution and variational problems on graphs. More specifically, we consider a sequence of (determin- istic) graphs converging to a so-called limit object known as the graphon. If the continuous p-Laplacian evolution and variational problems are properly discretized on this graph sequence, we prove that the solutions of the sequence of discrete problems converge to the solution of the continuous problem governed by the graphon, as the number of graph vertices grows to infinity. Along the way, we provide a consistency/error bounds. In turn, this allows to establish the convergence rates for different graph models. In particular, we highlight the role of the graphon geometry/regularity. For random graph se- quences, using sharp deviation inequalities, we deliver nonasymptotic convergence rates in probability and exhibit the different regimes depending on p, the regularity of the graphon and the initial data

The solution for the edge-isoperimetric problem (EIP) of the square tessellation of plane is investigated and solved. Summaries of the stabilization theory and previous research dealing with the EIP are stated. These techniques enable us to solve the EIP of the cubical tessellation.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.
Includes bibliographical references (leaves 259-271).
Stochastic processes defined on graphs arise in a tremendous variety of fields, including statistical physics, signal processing, computer vision, artificial intelligence, and information theory. The formalism of graphical models provides a useful language with which to formulate fundamental problems common to all of these fields, including estimation, model fitting, and sampling. For graphs without cycles, known as trees, all of these problems are relatively well-understood, and can be solved efficiently with algorithms whose complexity scales in a tractable manner with problem size. In contrast, these same problems present considerable challenges in general graphs with cycles. The focus of this thesis is the development and analysis of methods, both exact and approximate, for problems on graphs with cycles. Our contributions are in developing and analyzing techniques for estimation, as well as methods for computing upper and lower bounds on quantities of interest (e.g., marginal probabilities; partition functions). In order to do so, we make use of exponential representations of distributions, as well as insight from the associated information geometry and Legendre duality. Our results demonstrate the power of exponential representations for graphical models, as well as the utility of studying collections of modified problems defined on trees embedded within the original graph with cycles. The specific contributions of this thesis include the following. We develop a method for performing exact estimation of Gaussian processes on graphs with cycles by solving a sequence of modified problems on embedded spanning trees.
(cont.) We introduce the tree-based reparameterization framework for approximate estimation of discrete processes. This perspective leads to a number of theoretical results on belief propagation and related algorithms, including characterizations of their fixed points and the associated approximation error. Next we extend the notion of reparameterization to a much broader class of methods for approximate inference, including Kikuchi methods, and present results on their fixed points and accuracy. Finally, we develop and analyze a novel class of upper bounds on the log partition function based on convex combinations of distributions in the exponential domain. In the special case of combining tree-structured distributions, the associated dual function gives an interesting perspective on the Bethe free energy.
by Martn J. Wainwright.
Ph.D.

La vigne est une plante cultivée dans le monde entier dont l’importance économique est principalement liée à la production de vin. La baie de raisin est également l’un des principaux modèles d’étude pour les fruits non-climatériques notamment pour l’étude des mécanismes contrôlant le mûrissement des baies. Le développement de la baie de raisin est caractérisé par deux phases de croissance séparées par une phase de latence se produisant au moment de la véraison. La baie de raisin est composée de trois tissus principaux: la peau, la pulpe et les graines. La peau et la pulpe présentent une structure et une composition en métabolites distinctes et contribuent de manière différente à la qualité du vin, la pulpe fournissant essentiellement le sucre, les acides aminés et organiques alors que la peau est riche en anthocyanes. A l'heure actuelle, les mécanismes moléculaires impliqués dans le contrôle de la maturation des baies de raisin sont encore mal compris. Si l'ABA, le sucre et différents facteurs de transcription jouent un rôle important dans le contrôle de cette phase de développement, les mécanismes épigénétiques, en particulier la méthylation de l’ADN, apparaissent aussi comme des régulateurs importants du développement et du mûrissement des fruits charnus. Dans ce contexte, Le projet de thèse présenté vise à analyser le rôle de la méthylation de l’ADN (1) dans la maturation des baies de raisin et (2) dans la synthèse des anthocyanes en utilisant comme système modèle des cellules de baie de raisin cultivées in vitro.La culture in vitro de baies de raisin en présence d’inhibiteurs de la méthylation de l'ADN, aboutit à une inhibition de la maturation, suggérant que la méthylation de l’ADN joue un rôle crucial pour cette étape du développement chez la vigne. La pellicule et la chair de baies de raisin récoltées à divers stades de développement ont ensuite été analysées séparément pour déterminer les variations des transcriptomes, de l’abondance de différents métabolites, et de la méthylation de l'ADN. Les principaux résultats indiquent des variations des métabolites et du transcriptome, avec des spécificités liés au tissu analysé. En outre, l'analyse des variations de méthylation de l'ADN à deux stades de développement dans chacun de ces deux tissus révèle l’existence de variations de méthylation spécifiques à chaque tissu, tandis que les variations communes aux deux tissus restent limitées. Ces résultats suggèrent un contrôle de la méthylation de l’ADN spécifique à chaque tissu lors de la maturation de la baie. Cependant les régions différentiellement méthylées identifiées dans chaque tissu, ne sont pas associées à des gènes exprimés différentiellement au cours de la maturation des baies, ce qui pose la question du rôle de la méthylation de l’ADN dans le contrôle de l’expression génique dans les baies.Pour analyser le rôle de la méthylation de l’ADN dans le contrôle de la synthèse des anthocyanes, nous avons utilisé des suspensions de cellules de raisin du génotype Gamay Teinturier (GT), connues pour accumuler des anthocyanes lorsqu’elles sont cultivées à la lumière. L’utilisation de la zébularine, un inhibiteur de la méthylation d’ADN, permet de stimuler l’accumulation d'anthocyanes dans les cellules GT en présence de lumière, et de l’induire à l’obscurité. Les traitements à la zébularine provoquent en outre une limitation de la croissance cellulaire, une modification de l’accumulation des sucres solubles et acides organiques ainsi qu’une reprogrammation importante du transcriptome. Ces résultats suggèrent un effet général de la zébularine sur les cellules GT plutôt qu’un effet spécifique sur l’accumulation d’anthocyanes.Dans l'ensemble, les résultats indiquent que la méthylation de l'ADN est importante pour le contrôle de la maturation des fruits de la vigne, bien que les mécanismes qui sous-tendent les variations de la méthylation et leurs rôles dans les différents tissus de la baie de raisin restent à préciser
Grapevine is a worldwide cultivated fruit crop with high economic importance mainly because of its usage for vine production. Grape berry is also one of the main models for non-climacteric fruits to study the mechanisms controlling the ripening process. Grape berry development is characterized by two phases of rapid size increase separated by a lag phase at the time of ripening induction. Grape berries are composed of three main tissues, the peel, the pulp and the seeds. Peel and pulp present distinct structure and metabolite composition and contribute in a different way to wine quality, the pulp providing sugar, amino and organic acids whereas the peel is important for anthocyanins and other phenolic compound abundance. At the present time, the molecular mechanisms involved in the control of grape berry ripening are still poorly understood. Recent results indicate that both ABA and sugar may be important signals together with various transcription factors. In addition, epigenetic mechanisms are now emerging as important regulators of fleshy fruit development, DNA methylation being critically important for tomato, sweet range and strawberry ripening.The present project aims at analyzing the potential role of DNA methylation in the control grape berry ripening. It also investigates the potential role of DNA methylation in the synthesis of anthocyanins, a compound of primary importance in peel of red grape berries, using in vitro grown fruit cells. To address these questions, grape berries cultivated in vitro were treated with DNA methylation inhibitors. Treatments resulted in delayed and reduced grape berry ripening, therefore sustaining the idea that DNA methylation plays critical roles at this developmental step. Grape berries harvested at various developmental stages were then dissected and each tissue was separately analyzed for transcriptomic, metabolic and DNA methylation variations. Main results indicate significant and distinct metabolic and transcriptomic variations consistent with each tissue following specific modifications during ripening. In addition, analysis of DNA methylation variations at two developmental stages in each tissue indicates both common and tissue specific changes in DNA methylation patterns during fruit ripening. A very small proportion of DMRs is found similarly in the pup and the peel, but most are tissue specific, also consistent with tissue specific control at this developmental phase. Of note, among the different DMRs identified in each tissue, only a few were associated with differentially expressed genes (DEG) during ripening, whereas most were not, questioning the general role of DNA methylation in the control of gene expression at this developmental transition in grape.As Anthocyanins are the most abundant polyphenolic compounds in the skin of red grape berries, we used grape cell suspensions of the Gamay Teinturier genotype, that are known to accumulate anthocyanins when grown in light conditions, to analyze the potential role of DNA methylation in their synthesis. GT cells cultivated in light conditions were treated with the DNA methyltransferase inhibitor zebularine, they accumulate higher quantities of anthocyanins. Of note, GT cells grown in the absence of light do not accumulate anthocyanins. However, zebularine was sufficient to induce anthocyanin accumulation in the absence of light. Zebularine treatments had significant additional effects on grape cells including, cell growth limitation, and modification of soluble sugar, organic acid or stilbene accumulation, together with important transcriptomic reprogramming, consistent with a general effect on cells rather than a specific effect on anthocyanin accumulation.Taken together, results are consistent with DNA methylation being important in the control of grape fruit ripening, although the precise mechanisms underlying methylation variations and roles in grape berries remain to be deciphered

Field and greenhouse studies were carried out to determine the effects of Al and Mn individually or collectively on the growth and elemental composition of various grape cultivars. Soil and plant tissue analyses were evaluated in two vineyard locations on which several grape varieties were established on a White House soil series. Soils at both locations were treated with soil amendments and N fertilizers. The results show that both soils are acidic at the top 30 cm surface and have a high extractable Al, Fe and in some cases Mn content. The field results further indicate that grape varieties respond differently to soil acidity in terms of their mineral composition. High soil Al, Fe and Mn resulted in a higher accumulation of these elements in grape leaves whereas the cation uptake especially P, Ca, Zn, and Cu were reduced. Field plants exhibiting P deficiency symptoms resulting from high soil Al and Fe had a 950 Mg kg⁻¹ Al and 400 mg kg⁻¹ Mn in their leaves. Furthermore, these plants had a deficient range of P, K, Ca and Zn. The Al treatments reduced shoot growth and decreased number of leaves. The growth reduction resulted from higher Al, Mn and Fe content of plant leaves and lower P, Ca and Cu. Furthermore high Al treatments of 30 mg 1⁻¹ and more in the nutrient solution resulted in lower accumulation of P, Ca, K, Mg, Fe and Cu. The different parameters were affected by Al levels to different degrees and were more pronounced at a later stage of growth than the earlier stage of growth. The concentration of Al in plant tops at which Al toxicity symptoms appeared was 800 mg kg⁻¹ Al or more. Mn treatments reduced plant growth, decreased number of leaves and induced toxicity symptoms. The percent reduction of growth parameters was greatest at highest Mn levels. The reduced growth resulted from the deficiency of several mineral elements such as Ca, Fe, Zn and Cu and higher accumulation of Mn in plant tissue. The effect of Mn levels on the elemental composition especially Fe, Zn, Cu, Ca and P increased progressively as plant growth progressed. The 10% reduction in growth occurred when plant had accumulated 400 mg kg⁻¹ Mn in their tops. The accumulation of elements in plant leaves was varied at various stages of growth as a function of time and Mn and/or Al concentration in the nutrient solution. The growth reduction and the severity of toxicity symptoms were proportional to either Al, Mn or Al + Mn concentrations in the nutrient solution as well as their accumulation in plant tops.

Variational analysis, a relatively new area of research in mathematics, has become one of the most powerful tools in nonsmooth optimisation and neighbouring areas. The extremal principle, a tool to substitute the conventional separation theorem in the general nonconvex environment, is a fundamental result in variational analysis. There have seen many attempts to generalise the conventional extremal principle in order to tackle certain optimisation models. Models involving collections of sets, initiated by the extremal principle, have proved their usefulness in analysis and optimisation, with non-intersection properties (or their absence) being at the core of many applications: recall the ubiquitous convex separation theorem, extremal principle, Dubovitskii Milyutin formalism and various transversality/regularity properties. We study elementary nonintersection properties of collections of sets, making the core of the conventional definitions of extremality and stationarity. In the setting of general Banach/Asplund spaces, we establish nonlinear primal (slope) and linear/nonlinear dual (generalised separation) characterisations of these non-intersection properties. We establish a series of consequences of our main results covering all known formulations of extremality/ stationarity and generalised separability properties. This research develops a universal theory, unifying all the current extensions of the extremal principle, providing new results and better understanding for the exquisite theory of variational analysis. This new study also results in direct solutions for many open questions and new future research directions in the fields of variational analysis and optimisation. Some new nonlinear characterisations of the conventional extremality/stationarity properties are obtained. For the first time, the intrinsic transversality property is characterised in primal space without involving normal cones. This characterisation brings a new perspective on intrinsic transversality. In the process, we thoroughly expose and classify all quantitative geometric and metric characterisations of transversality properties of collections of sets and regularity properties of set-valued mappings.
Doctor of Philosophy

La modélisation de processus complexes peut impliquer un grand nombre de variables ayant entre elles une structure de corrélation compliquée. Par exemple, les phénomènes spatiaux possèdent souvent une forte régularité spatiale, se traduisant par une corrélation entre variables d’autant plus forte que les régions correspondantes sont proches. Le formalisme des graphes pondérés permet de capturer de manière compacte ces relations entre variables, autorisant la formalisation mathématique de nombreux problèmes d’analyse de données spatiales. La première partie du manuscrit se concentre sur la résolution efficace de problèmes de régularisation spatiale, mettant en jeu des pénalités telle que la variation totale ou la longueur totale des contours. Nous présentons une stratégie de préconditionnement pour l’algorithme generalized forward-backward, spécifiquement adaptée à la résolution de problèmes structurés par des graphes pondérés présentant une grande variabilité de configurations et de poids. Nous présentons ensuite un nouvel algorithme appelé cut pursuit, qui exploite les relations entre les algorithmes de flots et la variation totale au travers d’une stratégie de working set. Ces algorithmes présentent des performances supérieures à l’état de l’art pour des tâches d’agrégations de données geostatistiques. La seconde partie de ce document se concentre sur le développement d’un nouveau modèle qui étend les chaînes de Markov à temps continu au cas des graphes pondérés non orientés généraux. Ce modèle autorise la prise en compte plus fine des interactions entre noeuds voisins pour la prédiction structurée, comme illustré pour la classification supervisée de tissus urbains
Modeling complex processes often involve a high number of variables with anintricate correlation structure. For example, many spatially-localized processes display spatial regularity, as variables corresponding to neighboring regions are more correlated than distant ones. The formalism of weighted graphs allows us to capture relationships between interacting variables in a compact manner, permitting the mathematical formulation of many spatial analysis tasks. The first part of this manuscript focuses on optimization problems with graph-structure dregularizers, such as the total variation or the total boundary size. We first present the convex formulation and its resolution with proximal splitting algorithms. We introduce a new preconditioning scheme for the existing generalized forward-backward proximal splitting algorithm, specifically designed for graphs with high variability in neighbourhood configurations and edge weights. We then introduce a new algorithm, cut pursuit, which used the links between graph cuts and total variation in a working set scheme. We also present a variation of this algorithm which solved the problem regularized by the non convex total boundary length penalty. We show that our proposed approaches reach or outperform state-of-the-art for geostatistical aggregation as well as image recovery problems. The second part focuses on the development of a new model, expanding continuous-time Markov chain models to general undirected weighted graphs. This allows us to take into account the interactions between neighbouring nodes in structured classification, as demonstrated for a supervised land-use classification task from cadastral data

Variational methods and Partial Differential Equations (PDEs) have been extensively employed for the mathematical formulation of a myriad of problems describing physical phenomena such as heat propagation, thermodynamic transformations and many more. In imaging, PDEs following variational principles are often considered. In their general form these models combine a regularisation and a data fitting term, balancing one against the other appropriately. Total variation (TV) regularisation is often used due to its edgepreserving and smoothing properties. In this thesis, we focus on the design of TV-based models for several different applications. We start considering PDE models encoding higher-order derivatives to overcome wellknown TV reconstruction drawbacks. Due to their high differential order and nonlinear nature, the computation of the numerical solution of these equations is often challenging. In this thesis, we propose directional splitting techniques and use Newton-type methods that despite these numerical hurdles render reliable and efficient computational schemes. Next, we discuss the problem of choosing the appropriate data fitting term in the case when multiple noise statistics in the data are present due, for instance, to different acquisition and transmission problems. We propose a novel variational model which encodes appropriately and consistently the different noise distributions in this case. Balancing the effect of the regularisation against the data fitting is also crucial. For this sake, we consider a learning approach which estimates the optimal ratio between the two by using training sets of examples via bilevel optimisation. Numerically, we use a combination of SemiSmooth (SSN) and quasi-Newton methods to solve the problem efficiently. Finally, we consider TV-based models in the framework of graphs for image segmentation problems. Here, spectral properties combined with matrix completion techniques are needed to overcome the computational limitations due to the large amount of image data. Further, a semi-supervised technique for the measurement of the segmented region by means of the Hough transform is proposed.

This thesis essentially deals with two basic problems, one in Rieinannian, the other in Conformal Geometry, described in Part I resp. Part III. Part II can be considered as an interlude serving as a sort of bridge between Riemannian and Comformal Geometry.

Des questions d'approximations des regularisations et de convergence, liees au domaine de l'analyse non lineaire, sont traitees. En premier lieu, on donne une caracterisation de la convergence de certaines fonctionnelles integrales en terme de convergence des coefficients de leurs integrandes. On se consacre ensuite a l'etude de l'approximee de lasry-lions d'une fonction definie sur un espace de hilbert, pour un choix critique des parametres. Par ailleurs, le resultat d'equivalence entre convergence au sens d'attouch-wets d'une suite de fonctions definies sur un espace super reflexif et convergence au meme sens des graphes de leur sous differentiels est precisee. On introduit enfin, une notion de recession pour un operateur maximal monotone defini sur un espace de hilbert. L'un des objectifs est la resolution d'equations gouvernees par des maximaux monotones non coercifs

L'exploitation de la variation clonale est une des voies d'amélioration utilisée chez un grand nombre de plantes d'intérêts agronomiques telles que la pomme de terre, le café et la vigne. En effet, après plusieurs cycles de reproduction végétative, des caractéristiques agronomiques stables apparaissent donnant naissance à une diversité phénotypique remarquable, appelée « diversité clonale ». Chez la vigne, cette diversité clonale est d'une importance majeure pour les viticulteurs puisqu'elle permet une amélioration variétale sans changer d'identité de cépage en conformité avec la réglementation fixée par Appellations d'Origine Protégée. L'hypothèse la plus parcimonieuse expliquant cette diversité phénotypique clonale est l'accumulation de mutations somatiques au cours des cycles de reproduction végétative. L'objectif de cette thèse a été de dresser un panorama le plus exhaustif possible des différents polymorphismes moléculaires entre les génomes de plusieurs clones. Dans un premier temps trois clones de Pinot ont été séquencés par la technique 454 GS-FLX puis dans un second temps 11 clones de quatre cépages ont été séquencés la technique Illumina HiSeq 2000. Afin d'analyser la grande quantité de données obtenues, nous avons construit un pipeline d'analyse (Bacchus pipeline) permettant d'identifier tous les types de polymorphismes moléculaires entre les différents génomes.Nos résultats permettent, pour la première fois un inventaire exhaustif des polymorphismes moléculaires dans un contexte multiplication végétatif. L'ensemble des mutations polymorphes entre deux clones a pu être identifié, SNPs, indels (2,5 SNPs et 11,5 indels par Mb en moyenne) ainsi que des variations d'ordre structural (larges insertions ou délétions) représentant la classe la plus fréquente (129 évènements par Mb entre deux clones en moyenne). Afin d'évaluer le polymorphisme d'insertion généré par ces éléments nous en avons étudié quatre par une approche S-SAP sur plusieurs niveaux de diversité (inter-espèces, inter-cépages, inter-clones et entre plusieurs tissus d'un même individu). L'analyse phylogénétique au niveau des espèces est conforme à celle réalisée avec d'autres types de marqueurs moléculaires (SSR, SNP). Cependant, une forte instabilité de ces insertions a été confirmée entre les clones et entre les tissus d'un même d'individu. L'identification des clones par une méthodologie moléculaire serait d'une grande importance pour la filère. Pour cet objectif, nos résultats indiquent que les mutations de types SNP et petits indels qui sont certes moins fréquentes que les variations structurales mais qui sont plus stables semblent plus pertinentes pour la mise en place d'une méthodologie d'identification des clones
Clonal variation is considered as an effective contribution to breeding programs of vegetatively propagated species with major agronomical interest such as banana, potato, coffee and grape. Indeed, after several propagation cycles, stable and heritable phenotypic variations appear giving rise to a phenotypic variation termed “clonal diversity”. This clonal diversity is very important for wine-growers because it allows preserving cultivars identity in the strict respect of Appellation (A.O.P) wines specifications The most parsimonious hypothesis explaining clonal phenotypic diversity is the accumulation of somatic mutations. The objective of my thesis was to provide a broad description of molecular polymorphisms in the context of vegetative propagation. Three clones were first sequenced by 454 GS-FLX technology and eleven clones were then sequenced with Illumina Hiseq2000 technique. To analyse the high quantity of data obtained, we built a pipeline (Bacchus pipeline) allowing the identification of all existing molecular polymorphisms between different genomes.All polymorphism types were observed: indels and SNPs which have a low polymorphism frequency (2.5 SNPs and 11.5 indels per Mb between two clones in average) and structural variations (large insertions or deletions) which have a high polymorphism frequency (129 per Mb between two clones in average) but are unstable. To evaluate stability and polymorphism level of these transposable elements, we have studied 4 elements using S-SAP method at different diversity levels (inter-species, inter-cultivars, inter-clones and between organs/tissues of a single individual). Our interspecific phylogenetic analysis is similar to other phylogenies performed with SSR or SNPs markers. However, we confirm the high instability of these elements between clones and between tissues in single individuals.Clone identification through molecular methods would be of high significance for the wine industry. SNP or small indels mutations are less frequent but more stable than structural variation and could be used for accurate clone identification

This thesis addresses the problem of inference in factor graphs, especially the LDPC codes, almost solved by message-passing algorithms. In particular, the Belief Propagation algorithm (BP) is investigated as a particular message-passing algorithm whose suboptimality is discussed in the case where the factor graph has a loop-like topology. From the equivalence between the BP and the Bethe approximation in statistical physics that is generalized to the region-based approximation, is detailed the Generalized Belief Propagation algorithm (GBP), a message-passing algorithm between clusters of the factor graph. It is experimentally shown to surpass the BP in the cases where the clustering deals with the harmful topological structures that prevents the BP from rightly decoding any LDPC code, namely the trapping sets. We do not only confront the BP and the GBP algorithms according to their performance from the point of view of the channel coding with the error-rate, but also according to their dynamical behaviors for non-trivial error-events for which both algorithms can exhibit chaotic beahviors. By means of classical and original dynamical quantifiers, it is shown that the GBP algorithm can overcome the BP algorithm.

Durant la guerre de Sécession (1861-1865), des milliers de soldats, de chaque côté du front, prirent leur plume afin de s'enquérir de leur famille et de donner des nouvelles du front. Généralement peu lettrés, la plupart de ces soldats ne maîtrisaient que très partiellement les codes de l'écrit. Le corpus sur lequel se base la présente recherche doctorale se compose de 366 lettres (soit environ 170 000 mots) rédigées par 80 soldats de première et deuxième classes originaires de Virginie. L'orthographe idiosyncratique et approximative de leurs écrits ainsi que les nombreuses variations morphosyntaxiques non standard permettent de mieux saisir ce que pouvait être le vernaculaire des locuteurs blancs issus des couches les plus basses de la société virginienne durant la première moitié du XIXe siècle.Selon Guy Bailey (1997), certaines caractéristiques du vernaculaire du Sud des Etats-Unis (Southern American English) seraient apparues après la guerre de Sécession et seraient le fruit d'une réaction identitaire face à la domination du Nord et à l'humiliation causée par la défaite. Les variations non standard répertoriées dans le Virginia Civil War Corpus nous invitent à nuancer cette assertion. Malgré une orthographe phonétique et l'emploi de nombreuses variations morphosyntaxiques et lexicales non standard, leurs écrits révèlent la tension constante entre le registre paritaire et disparitaire. Cette perpétuelle oscillation est-elle le fruit d'un conflit interne entre différents modèles linguistiques ou est-elle, au contraire, le signe d'opérations énonciatives spécifiques ?
Throughout the Civil War (1861-1865), thousands of low ranking soldiers on both sides of the conflict took up their pens to inquire after their families and give news from the front. Usually semiliterate, most of these soldiers were far from mastering written conventions. The 170,000-word corpus, on which this thesis is based, is composed of 366 letters written by 80 privates, corporals and sergeants from Virginia. Their idiosyncratic and ingenuous spellings as well as their use of non-standard morphosyntactic variations offer a great opportunity to gain further insight into the vernacular spoken by white lower-class people in Virginia around the middle of the 19th century.According to Guy Bailey (1997), certain specificities of the Southern American Vernacular English (SAVE) appeared after the Civil War, as a reaction against Northern domination and the humiliation caused by the defeat. The non standard variations found in the Virginia Civil War Corpus tend to question this hypothesis and reveal that most of the features, that are today associated with SAVE, were already present in low ranking soldiers' writings.Despite the phonetic spelling and the use of non-standard grammatical and lexical forms, the letters reveal that the soldiers were fully aware that their vernacular speech was not in line with academic conventions. We thus observe a constant tension between the academic prescriptive norm and non-standard variations. We may wonder if this constant oscillation is only triggered by an internal conflict between different linguistic models or if, on the contrary, the presence of these dialectal variations must be understood as signs of specific enunciative operations

Cette thèse traite des fondements et modalités d'une didactique de l'intercompréhension entre les langues qui, au cours de leur histoire, ont été en contact avec la langue et l'écriture chinoises, et dont les lexiques contemporains conservent une trace profonde. Cette étude explore dans quelle mesure il est possible de concevoir un enseignement-apprentissage qui tiendrait compte des acquis d'une première expérience d'apprentissage d'une de ces langues pour en apprendre une autre. La thèse défendue repose sur une refondation didactique du sinogramme au moyen d'une réévaluation non plus seulement graphique mais surtout phonologique afin d'entraîner les apprenants à émettre des hypothèses quant à la réalisation de ces sinogrammes dans la langue-cible. Il y a trois parties. Premièrement, il s'agit d'une discussion épistémologique sur la connaissance de l'écriture chinoise en Europe, la réduction de ce système à sa seule dimension graphique - voire idéographique - et l'incapacité des savants européens à intégrer la culture phonologique très développée qui constitue selon cette thèse la matrice sur laquelle fonder l'intercompréhension entre les langues d'Asie Orientale à l'instar de la grammaire contrastive pour les langues romanes. Ensuite, après une recontextualisation des différentes approches didactique des sinogrammes, sont traitées les modalités mises en œuvre pour préparer à l'intercompréhension : tout d'abord, une refondation de l'enseignement-apprentissage du système sinogrammique non plus au moyen de la programmation des types les plus fréquents dans les lexiques contemporains, mais à travers une approche globale incluant la compréhension des principes de toute l'économie du système graphique . Enfin, il est procédé à la présentation de la transposition sinogrammique, ultime contribution de cette thèse et opération qui permet à l'apprenant de passer de la lecture d'un sinogramme dans une langue-pont à celle dans une langue-cible
This doctoral thesis analyzes the current teaching and learning models among languages that were, and still are, in contact with the Chinese script, and that retain this influence in their modern lexicon : the sinogramic languages. This thesis asserts that such a course can be designed through a complete didactic reformulation of how to teach sinograms, not only in their graphic dimension, but also their phonological identity, in order for the student to imagine pronouncing a sinogram in the target-language according to his/her understanding of an already acquired 'bridge-language'. The thesis is divided into three parts. First, there is an epistemological discussion of the European approach to Chinese language and script, with the sole graphic - «ideographic» - focus, which shadowed traditional phonological practices. Next, the design of an alternative approach is proposed in which sinogram-based learning is not rooted in the so called concentrated approach, according to which sinogram types are selected in order of their frequency and adaptability within the contemporary lexicon. This alternative approach is discussed based on the training of the sinogramic system as a whole: the global approach. Finally, the main process for mutual understanding, which is called sinogramic transposition, is introduced to show how students can be trained to understand and produce readings of sinograms in the target-language

The cross-situational word learning paradigm argues that word meanings can be approximated by word-object associations, computed from co-occurrence statistics between words and entities in the world. Lexicon acquisition involves simultaneously guessing (1) which objects are being talked about (the ”meaning”) and (2) which words relate to those objects. However, most modeling work focuses on acquiring meanings for isolated words, largely neglecting relationships between words or physical entities, which can play an important role in learning. Semantic parsing, on the other hand, aims to learn a mapping between entire utterances and compositional meaning representations where such relations are central. The focus is the mapping between meaning and words, while utterance meanings are treated as observed quantities. Here, we extend the joint inference problem of word learning to account for compositional meanings by incorporating a semantic parsing model for relating utterances to non-linguistic context. Integrating semantic parsing and word learning permits us to explore the impact of word-word and concept-concept relations. The result is a joint-inference problem inherited from the word learning setting where we must simultaneously learn utterance-level and individual word meanings, only now we also contend with the many possible relationships between concepts in the meaning and words in the sentence. To simplify design, we factorize the model into separate modules, one for each of the world, the meaning, and the words, and merge them into a single synchronous grammar for joint inference. There are three main contributions. First, we introduce a novel word learning model and accompanying semantic parser. Second, we produce a corpus which allows us to demonstrate the importance of structure in word learning. Finally, we also present a number of technical innovations required for implementing such a model.

Esta pesquisa traz um estudo sobre a construção inicial dos conceitos de limites e taxa de variação, com alunos do segundo ano do Ensino Médio da Escola Antônio de Castro Alves. Como metodologia utilizamos a perspectiva do Estudo de Caso (PONTE, 2006). O trabalho propõe a utilização do software Tracker Physics, que possibilita a análise de objetos em movimento gravados por vídeo a partir de diferentes registros gerados pelo software, tais como gráficos, tabelas e registros algébricos. Com o uso deste software e da teoria de Duval, procuramos responder à seguinte pergunta norteadora: como os alunos do Ensino Médio compreendem os conceitos de taxa de variação e de limite a partir de objetos em movimento analisados com o Tracker Physics? Por tratar-se de objetos em movimento, utilizamos a Física como meio para trabalharmos os conceitos matemáticos. Antes de chegarmos ao debate sobre limite e taxa de variação, a proposta levanta questões acerca da interpretação de gráficos, tabelas, equações e cálculos numéricos, que não são o escopo principal do trabalho, mas que são importantes para o processo de construção dos conceitos propostos, e a análise dos dados aponta resultados interessantes. Os dados da pesquisa são analisados à luz da teoria dos Registros Semióticos de Duval. Podemos apontar, ao final da pesquisa, que os alunos avançaram na compreensão dos conceitos abordados nas situações apresentadas e analisadas.
This research brings a study about the initial construction of the concepts of limits and rate of variation, with students of the second year of High School of the School Antônio de Castro Alves. As methodology we use the case study perspective (PONTE, 2006). The work proposes the use of Tracker Physics software, which enables the analysis of moving objects recorded by video from different records generated by the software, such as graphs, tables and algebraic records. With the use of this software and Duval's theory, we try to answer the following guiding question: how do the students of the High School understand the concepts of rate of variation and limit from moving objects analyzed with Tracker Physics? Because we are dealing with moving objects, we use Physics as the means to work on mathematical concepts. Before we reach the debate about limit and rate of variation, the proposal raises questions about the interpretation of graphs, tables, equations and numerical calculations, which are not the main scope of the work, but which are important for the process of construction of the proposed concepts , And the analysis of the data points interesting results. The data of the research is analyzed in light of the theory of the Duval Semiotic Registers. We can point out, at the end of the research, that the students advanced in understanding the concepts addressed in the situations presented and analyzed.

Global climate model simulations indicate 1.3°C to 1.8°C increase in the Earth’s average temperature by middle of this century above the 1980 to 1999 average. The magnitude and rate of change of this projected warming is greater than the average warming during the last century. Global climate models project an even higher degree of warming later in the century also due to increasing grrenhouse gases concentrations in the atmosphere from human activity. Impacts of future climate change on viticulture are likely to be significant as viticulture requires a narrow climate range to produce grapes of suitable quality for premium wine production.In this thesis, impacts of climate change on winegrape growing conditions across the Western Australian wine regions were spatially and temporally examined by utilising fine resolution downscaled climate projections. Relationships between climate variation and grape maturity or key quality attributes of Cabernet Sauvignon, Shiraz and Chardonnay were modelled from measured fruit and climate data along a natural climate gradient encompassing a 5°C range in winegrape growing season average temperature. Potential future climate change impacts on grape quality were quantitatively evaluated by driving the grape quality models with the downscaled climate projections.Analyses of climate conditions for winegrape growth were carried out under future climate projections for the Western Australian wine regions. A total of 10 global climate models forced with an A2 emission scenario were downscaled. Of these models, the MEDRES Miroc3.2 and CSIRO Mk3.5 climate models, which indicated the low and high warming ranges (projections of these models will be referred as low and high range warming, hereafter) across the study regions, were selected to take into account the uncertainty of future climate change for impact assessment. Our results indicate increasingly warmer and drier climate conditions for the Western Australian wine regions. The current October to April average temperature (averaged across the regions) is projected to be 0.5°C to 1.5°C warmer by 2030, respectively. The magnitude of the warming will likely be uneven across the regions. For example, 0.1 to 0.3°C higher average temperature during October to April period has been projected for the northern regions than the southern regions by 2030, depending on the warming ranges. On the other hand, rainfall is projected to decrease across the regions under the future scenario we assessed in this study. By 2030, annual rainfall, averaged across the regions, is projected to decline by 5 to 8%, respectively, under the low and high warming ranges of climate change under the A2 emission scenario. Among seasons, the greatest decline in rainfall is projected to occur during spring. On average, up to 8% and 19% decline in spring rainfall is projected respectively under the low and high warming ranges by 2030.The magnitude of these changes are projected to increase as time progresses. For example, by 2070, averaged across the study regions, our modelling results show current mean temperature during October to April is projected to be between 1.1°C and 3.9°C warmer, but the annual rainfall is likely to be 15 to 24% lower than the current climate averages (1975 to 2005) under the A2 scenario.Maturity dates of the studied varieties are projected to advance asymmetrically across the study regions. For example, Cabernet Sauvignon may reach 22 °Brix total soluble solid maturity about 4 and 7 days earlier respectively for the northern and the southern regions by 2030 under the low warming range. Our results also indicate maturity date shifting a further 8 and 18 days earlier by 2070 for the northern and the southern regions respectively under the same warming range. Patterns of this maturity date shifting is likely to be similar under the high warming range. However, the magnitude of advancement is projected to be doubled.If no adaptive measures are implemented future climate change will likely reduce wine quality due to declining concentrations of berry anthocyanins and acidity under a warmer climate. The reductions of berry quality attributes are likely to be more pronounced in the warmer northern wine regions compared to the cooler southern regions. For example, Cabernet Sauvignon current median anthocyanins concentration is projected to decline by about 12% and 33% for the warmer northern regions, and about 6 to 18% for the cooler southern wine regions respectively by 2030 and 2070 under the high warming range. In contrast, the maximum decline in Cabernet Sauvignon anthocyanin concentration under the lower warming range is projected to be small, up to 5% for the cooler southern and up to 8% for the warmer northern regions by 2070. Shiraz anthocyanins concentration decrease pattern is similar to that of Cabernet Sauvignon, however, our modelling indicates the magnitude is smaller, with maximum of 18% for Swan District and about 11% for the southern regions by 2070 under the high warming range.Modelled impacts of climate change on grape titratable acidity are also region and variety specific. Among the varieties studied, Chardonnay exhibits the highest decline in median titratable acidity across the regions (17% for the Margaret River and 42% for the Swan District regions), followed by Shiraz (7% for the Margaret River and 15% for the Peel regions) and Cabernet Sauvignon (no change for Blackwood and 12% for the Swan District regions) by 2070 under high climate warming. On the other hand, the median titratable acidity levels are less impacted by low warming scenario (maximum decline is 4% for Shiraz only by 2070).Under the future warming scenarios studied in this thesis currently established wine regions and wine styles across the Western Australian wine regions are likely to be affected to the extent that some regions may not be conducive to premium wine production, while for some regions changing the variety may be the only option to adapt to the climate change. For example, by 2070, under high warming range Swan District, Perth Hills, and some parts of the Peel and Geographe regions are projected to be suited more to producing fortified wines or table grapes due to high average growing season temperature (>24°C). In this future climate the present cool climate southern regions are likely to have the same climate conditions that currently prevail in the warmer Swan District. Apparent differences in currently planted varieties between the cooler southern and warmer northern regions clearly indicate the need to adapt to the warming climate in the southern wine regions.Analysis of other potential factors that influence viticulture such as frequency of hot days, vapour pressure deficit and disease pressure were examined. The results indicated that winegrape fungal disease pressure will likely decrease across the regions due to the declining rainfall, potentially lessening the need for spraying during the growing season. On the other hand, there will likely be increased frequency of hot days and elevated vapour pressure deficit. The impacts of these, combined with the decreasing rainfall during growing season will potentially drive irrigation demand higher requiring altered water management under climate change.Climatically, most of the Western Australian wine regions are known as premium wine producing areas. The results from this study indicate potential challenges of climate change for the Western Australian wine industry. Under the future climate scenarios examined, some currently warmer regions may become less suitable for premium quality wines due to the increased temperature, which is projected to be out of the optimum temperature range for premium wine production. For most of the other regions, the challenge will likely be a decreased grape quality required to produce premium wine with the current varieties. Suitable adaptation strategies may be required to maintain the current market reputation. Furthermore, the warmer and drier conditions under climate change is likely to necessitate revised water management across the wine growing regions, especially some regions which are already limited by available water for grape production. However, the magnitude of the impacts is projected to be dependent upon the magnitude of future climate change.

Ces dernières années, de nouveaux matériaux bidimensionnels aux propriétés surprenantes ont été découverts, le plus connu étant le graphène. Dans ces matériaux, les électrons du niveau de Fermi ont une masse apparente nulle, et peuvent être décrits par l’équation de Dirac sans masse. Un tel phénomène apparaît dans des situations très générales, pour les matériaux bidimensionnels ayant une structure périodique en « nid d’abeille ». De plus, la prise en compte d’interactions mène à des équations de Dirac non linéaires. Ces équations apparaissent également dans l’étude des paquets d’ondes lumineuses dans certaines fibres optiques. Le but de cette thèse est d’étudier l’existence et la stabilité de solutions stationnaires de ces équations avec termes non linéaires sous-critiques et critiques, et de montrer qu’ils sont la limite de solutions stationnaires de l’équation de Schrödinger non linéaire à potentiel périodique dans certains régimes de paramètres. Du point de vue mathématique, on devra résoudre les équations d’Euler-Lagrange de fonctionnelles d'énergie fortement indéfinies faisant intervenir l’opérateur de Dirac. Il s’agira en particulier d’étudier le cas des non-linéarités avec exposant critique, encore mal comprises pour ce type de fonctionnelle, et qui apparaissent naturellement en optique non linéaire. Les résultats de cette thèse pourraient avoir un impact important en physique, en particulier en physique du solide et optique non linéaire
Recently, new two-dimensional materials possessing unique properties have been discovered, the most famous being the graphene. In this materials, electrons at the Fermi level behave as massless particles and can be described by the massless Dirac equation. This phenomenon is quite general, and it is a common features of "honeycomb" periodic structures. Moreover, taking into account interaction leads to non-linear Dirac equations, which also appear in the description of light propagation in particular waveguides. The aim of the thesis is to study existence and stability of stationary solutions for those equations with both sub-critical and critical nonlinearities, and to show that they are limit of stationary solutions to the Schroedinger equation with honeycomb potential, for a suitable choice of parameters. This amounts to solving the Euler-Lagrange equation for strongly indefinite energy functionals, involving the Dirac operator. We will deal with critical nonlinearities, which are still poorly understood, and appear naturally in non-linear optics. This results may have an impact on the understanding some solid state or nonlinear optics systems

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Secretaria da Educação do Estado de São Paulo
This study aims to identify the perception of variability and the level of reasoning about this peculiarity, with students of the sixth year at basic education at a state school in Cotia. We discussed what are the concepts and procedures deployed when they resolve issues that involve reading, interpretation and construction of graphs. In particular, diagnose which operative invariants related to the notion of variability that these students mobilized in these activities. As theoretical references, we consider the levels of understanding graphical mobilized by students who are solving problems in statistical context. We also considered the theory of Conceptual Fields seeking to identify the operational invariants by observing the students in situations of problem solving. We performed a qualitative research, with application of a diagnostic instrument, with voluntary participation by two pairs of students. The results pointed to the difficulties of students in reading, interpreting and constructing graphs in specific situations, such as graphs with non-unit scales and null often. For calculating the range, the results showed a stable procedure, especially on the part of one of the pairs studied, in other words, a possible operational invariant, the confusion between the variable frequency and the variable
O presente trabalho tem como objetivo identificar a percepção da variabilidade e o nível de raciocínio sobre essa característica, junto a alunos do sexto ano do Ensino Fundamental de uma escola pública estadual de Cotia. Discutimos quais são os conceitos e procedimentos mobilizados quando estes resolvem questões que envolvem leitura, interpretação e construção de gráficos. Particularmente, diagnosticar quais invariantes operatórios relacionados à noção de variabilidade que estes alunos mobilizaram nessas atividades. Como referências teóricas, consideramos os níveis de compreensão gráfica mobilizados pelos alunos em situação de resolução de problemas em contexto estatístico. Consideramos também a teoria dos Campos Conceituais, buscando identificar os invariantes operatórios por meio da observação dos alunos em situações de resolução de problemas. Foi realizada uma pesquisa qualitativa, com aplicação de um instrumento diagnóstico, com participação voluntária de duas duplas de alunas. Os resultados apontaram para as dificuldades dos alunos na leitura, interpretação e construção de gráficos em situações específicas, como gráficos com escalas não unitárias e o com freqüência nula. Quanto ao cálculo da amplitude, os resultados mostraram um procedimento estável, por parte principalmente de uma das duplas pesquisadas, ou seja, um possível invariante operatório, a confusão entre freqüência da variável e a variável

Les méthodes d’assimilation de données et plus particulièrement les méthodes variationnelles sont mises à profit dans le domaine industriel pour deux grands types d’applications que sont la reconstruction de champ physique et le recalage de paramètres. Une des difficultés de mise en œuvre des algorithmes d’assimilation est que la structure de matrices de covariance d’erreurs, surtout celle d’ébauche, n’est souvent pas ou mal connue. Dans cette thèse, on s’intéresse à la spécification et la localisation de matrices de covariance dans des systèmes multivariés et multidimensionels, et dans un cadre industriel. Dans un premier temps, on cherche à adapter/améliorer notre connaissance sur les covariances d’analyse à l’aide d’un processus itératif. Dans ce but nous avons développé deux nouvelles méthodes itératives pour la construction de matrices de covariance d’erreur d’ébauche. L’efficacité de ces méthodes est montrée numériquement en expériences jumelles avec des erreurs indépendantes ou relatives aux états vrais. On propose ensuite un nouveau concept de localisation pour le diagnostic et l’amélioration des covariances des erreurs. Au lieu de s’appuyer sur une distance spatiale, cette localisation est établie exclusivement à partir de liens entre les variables d’état et les observations. Finalement, on applique une combinaison de ces nouvelles approches et de méthodes plus classiques existantes, pour un modèle hydrologique multivarié développé à EDF. L’assimilation de données est mise en œuvre pour corriger la quantité de précipitation observée afin d’obtenir une meilleure prévision du débit d’une rivière en un point donné
Data assimilation techniques are widely applied in industrial problems of field reconstruction or parameter identification. The error covariance matrices, especially the background matrix in data assimilation are often difficult to specify. In this thesis, we are interested in the specification and localization of covariance matrices in multivariate and multidimensional systems in an industrial context. We propose to improve the covariance specification by iterative processes. Hence, we developed two new iterative methods for background matrix recognition. The power of these methods is demonstrated numerically in twin experiments with independent errors or relative to true states. We then propose a new concept of localization and applied it for error covariance tuning. Instead of relying on spatial distance, this localization is established purely on links between state variables and observations. Finally, we apply these new approaches, together with other classical methods for comparison, to a multivariate hydrological model. Variational assimilation is implemented to correct the observed precipitation in order to obtain a better river flow forecast

La production du raisin à l’origine de vins AOC (Appellation d’Origine Contrôlée) est soumise à des cahiers de charges imposant des exigences en termes de rendement, de qualité des produits et de pratiques. En plus de ces exigences, le viticulteur doit désormais faire évoluer ses itinéraires techniques viticoles pour en améliorer les performances environnementales. Or, définir des lignes directrices d’action pour une amélioration des pratiques viticoles en s'appuyant sur les évaluations environnementales et de qualité du raisin est complexe tant ces évaluations fournissent un nombre important d'indicateurs. L’objectif de la thèse est la construction d’une méthode d’évaluation prenant en compte en parallèle l’évaluation de la performance environnementale des itinéraires techniques viticoles avec la qualité du raisin et permettant d’aider le viticulteur et son conseiller à identifier les pratiques assurant le meilleur compromis entre « performance environnementale » et « qualité de production ». Cette méthode permet d’analyser un itinéraire technique viticole mais aussi de comparer ce dernier à d’autres. Cette méthode a été développée et testée à l’aide de cinq itinéraires techniques viticoles aux pratiques différenciées sur le cépage Chenin blanc en moyenne vallée de la Loire pendant deux années aux climats contrastés. Les travaux ont permis de (i) faire une adaptation du calcul d’Analyse du Cycle de Vie (ACV) spécifique au système de production viticole, (ii) montrer l’importance de la variabilité interannuelle dans les résultats d’évaluation environnementale par ACV. Les travaux ont aussi abouti à l’élaboration d’un modèle explicatif de la qualité du raisin à partir des pratiques viticoles et des facteurs pédoclimatiques permettant d’étudier l’incidence potentielle d’un changement de pratiques sur les critères d’évaluation de la qualité du raisin. La construction de la méthode multicritères CONTRA-QUALENVIC pour la viticulture, principale issue de ce travail, comporte (i) la construction de règles de décision et de fonctions mathématiques pour y répondre et (ii) des réunions d’experts pour caractériser les critères à agréger et les pondérer. La méthode CONTRA-QUALENVIC a été éprouvée en la comparant à d’autres méthodes. Pour conclure, la méthode CONTRA-QUALENVIC est une méthode pertinente pour l’aide à la décision dans le cadre d’une amélioration continue des pratiques viticoles vers un meilleur respect de l’environnement tout en préservant la qualité du raisin
Grape production from PDO wines (Protected Designation of Origin) is subjected to tender specifications, imposing requirements in terms of performance, as well as practices and products quality. In addition to these requirements, the winemaker must now make its viticultural technical management routes evolve, to improve its environmental performances. But, defining actions guidelines for the improvement of viticultural practices based on environmental assessments and grape qualityis very complex, since each one of these assessments provide a significant number of indicators. The aim of the thesis is to construct an evaluation method that takes into consideration both evaluating the environmental performance of viticultural technical management routes with grape quality and assisting the winemaker and advisor to identify practices to ensure the best compromise between "environmental performance" and " product quality". This method allows to analyze a technical management route as well as to compare it to others. This method was developed and tested on five technical management routes with differentiated practices, on the Chenin Blanc grape variety in the middle Loire Valley, for two years with contrasted climates.The study helped (i) analyzing the Life Cycle Assessment (LCA) results specifically for viticulture, (ii) showing the importance of interannual variability in the results of environmental assessment by LCA. The work also led to the development of a model to explain the grapes quality linked with viticultural practices, and soil and climate factors, to study the potential impact of a practice change, on the grape quality evaluation. The CONTRA-QUALENVIC multi-criteria method construction for viticulture is the main outcome of this study, and includes (i) the construction of decision rules and mathematical functions to meet them, and (ii) experts’ meetings to characterize the criteria to aggregate and weight. The CONTRA-QUALENVIC method has been tested by comparing it to other methods.To conclude, the CONTRA-QUALENVIC method is an effective method for decision support as part of a continuous improvement of viticultural practices towards a better respect of the environment, while maintaining the grape quality

Cette thèse est réalisée dans le cadre du projet BPI DeepTech, en collaboration avec la société Fair&Smart, veillant principalement à la protection des données personnelles conformément au Règlement Général sur la Protection des Données (RGPD). Dans ce contexte, nous avons proposé un modèle neuronal profond pour l'extraction d'informations dans les documents administratifs semi-structurés (DSSs). En raison du manque de données d'entraînement publiques, nous avons proposé un générateur artificiel de DSSs qui peut générer plusieurs classes de documents avec une large variation de contenu et de mise en page. Les documents sont générés à l'aide de variables aléatoires permettant de gérer le contenu et la mise en page en respectant des contraintes visant à garantir leur proximité avec des documents réels. Des métriques ont été introduites pour évaluer la diversité des DSSs générés en termes de contenu et de mise en page. Les résultats de l'évaluation ont montré que les jeux de données générés pour trois types de DSSs (fiches de paie, tickets de caisse et factures) présentent un degré élevé de diversité, ce qui permet d'éviter le sur-apprentissage lors de l'entraînement des systèmes d'extraction d'informations. En s'appuyant sur le format spécifique des DSSs, constitué de paires de mots (mots-clés, informations) situés dans des voisinages proches spatialement, le document est modélisé sous forme de graphe où les nœuds représentent les mots et les arcs, les relations de voisinage. Le graphe est incorporé dans un réseau d'attention à graphe (GAT) multi-couches (Multi-GAT). Celui-ci applique le mécanisme d'attention multi-têtes permettant d'apprendre l'importance des voisins de chaque mot pour mieux le classer. Une première version de ce modèle a été utilisée en mode supervisé et a obtenu un score F1 de 96 % sur deux jeux de données de factures et de fiches de paie générées, et de 89 % sur un ensemble de tickets de caisse réels (SROIE). Nous avons ensuite enrichi le Multi-GAT avec un plongement multimodal de l'information au niveau des mots (avec des composantes textuelle, visuelle et positionnelle), et l'avons associé à un auto-encodeur variationnel à graphe (VGAE). Ce modèle fonctionne en mode semi-supervisé, capable d'apprendre à partir des données annotées et non annotées simultanément. Pour optimiser au mieux la classification des nœuds du graphe, nous avons proposé un semi-VGAE dont l'encodeur partage ses premières couches avec le classifieur Multi-GAT. Cette optimisation est encore renforcée par la proposition d'une fonction de perte VGAE gérée par la perte de classification. En utilisant une petite base de données non annotées, nous avons pu améliorer de plus de 3 % le score F1 obtenu sur un ensemble de factures générées. Destiné à fonctionner dans un environnement protégé, nous avons adapté l'architecture du modèle pour son chiffrement homomorphe. Nous avons étudié une méthode de réduction de la dimensionnalité du modèle Multi-GAT. Ensuite, nous avons proposé une approche d'approximation polynomiale des fonctions non-linéaires dans le modèle. Pour réduire la dimension du modèle, nous avons proposé une méthode de fusion de caractéristiques multimodales qui nécessite peu de paramètres supplémentaires et qui réduit les dimensions du modèle tout en améliorant ses performances. Pour l'adaptation au chiffrement, nous avons étudié des approximations polynomiales de degrés faibles aux fonctions non-linéaires avec une utilisation des techniques de distillation de connaissance et de fine tuning pour mieux adapter le modèle aux nouvelles approximations. Nous avons pu minimiser la perte lors de l'approximation d'environ 3 % pour deux jeux de données de factures ainsi qu'un jeu de données de fiches de paie et de 5 % pour SROIE
This thesis is being carried out as part of the BPI DeepTech project, in collaboration with the company Fair&Smart, primarily looking after the protection of personal data in accordance with the General Data Protection Regulation (RGPD). In this context, we have proposed a deep neural model for extracting information in semi-structured administrative documents (SSDs). Due to the lack of public training datasets, we have proposed an artificial generator of SSDs that can generate several classes of documents with a wide variation in content and layout. Documents are generated using random variables to manage content and layout, while respecting constraints aimed at ensuring their similarity to real documents. Metrics were introduced to evaluate the content and layout diversity of the generated SSDs. The results of the evaluation have shown that the generated datasets for three SSD types (payslips, receipts and invoices) present a high diversity level, thus avoiding overfitting when training the information extraction systems. Based on the specific format of SSDs, consisting specifically of word pairs (keywords-information) located in spatially close neighborhoods, the document is modeled as a graph where nodes represent words and edges, neighborhood connections. The graph is fed into a multi-layer graph attention network (Multi-GAT). The latter applies the multi-head attention mechanism to learn the importance of each word's neighbors in order to better classify it. A first version of this model was used in supervised mode and obtained an F1 score of 96% on two generated invoice and payslip datasets, and 89% on a real receipt dataset (SROIE). We then enriched the multi-GAT with multimodal embedding of word-level information (textual, visual and positional), and combined it with a variational graph auto-encoder (VGAE). This model operates in semi-supervised mode, being able to learn on both labeled and unlabeled data simultaneously. To further optimize the graph node classification, we have proposed a semi-VGAE whose encoder shares its first layers with the multi-GAT classifier. This is also reinforced by the proposal of a VGAE loss function managed by the classification loss. Using a small unlabeled dataset, we were able to improve the F1 score obtained on a generated invoice dataset by over 3%. Intended to operate in a protected environment, we have adapted the architecture of the model to suit its homomorphic encryption. We studied a method of dimensionality reduction of the Multi-GAT model. We then proposed a polynomial approximation approach for the non-linear functions in the model. To reduce the dimensionality of the model, we proposed a multimodal feature fusion method that requires few additional parameters and reduces the dimensions of the model while improving its performance. For the encryption adaptation, we studied low-degree polynomial approximations of nonlinear functions, using knowledge distillation and fine-tuning techniques to better adapt the model to the new approximations. We were able to minimize the approximation loss by around 3% on two invoice datasets as well as one payslip dataset and by 5% on SROIE

Lau, Siu Cheong.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.
Includes bibliographical references (leaves 51-52).
Abstracts in English and Chinese.
Chapter 1 --- In search of minimal cycles --- p.9
Chapter 1.1 --- What do we mean by cycles? --- p.9
Chapter 1.2 --- Integral currents --- p.10
Chapter 1.3 --- Calibration theory --- p.13
Chapter 2 --- Motivation from the Hodge Conjecture --- p.17
Chapter 2.1 --- Hodge theory on Riemannian manifolds --- p.17
Chapter 2.2 --- Hodge decomposition in Kahler manifolds --- p.19
Chapter 2.3 --- The Hodge conjecture --- p.22
Chapter 3 --- Variation of cycles in symmetric orbit --- p.26
Chapter 3.1 --- Variational formulae --- p.26
Chapter 3.2 --- Stability of cycles in Sm and CPn --- p.29
Chapter 3.3 --- Symmetric orbit in Euclidean space --- p.31
Chapter 3.4 --- Projective spaces in simple Jordan algebra --- p.39
Chapter 3.4.1 --- Introduction to simple Jordan algebra --- p.39
Chapter 3.4.2 --- Projective spaces as symmetric orbits --- p.41
Chapter 3.4.3 --- Computation of second fundamental form --- p.43
Chapter 3.4.4 --- The main theorem --- p.45
Chapter 3.5 --- Future directions --- p.49
Bibliography --- p.51

This thesis investigates three areas of the theory of graph homomorphisms: cores of graphs, the homomorphism order, and quantum homomorphisms. A core of a graph X is a vertex minimal subgraph to which X admits a homomorphism. Hahn and Tardif have shown that, for vertex transitive graphs, the size of the core must divide the size of the graph. This motivates the following question: when can the vertex set of a vertex transitive graph be partitioned into sets which each induce a copy of its core? We show that normal Cayley graphs and vertex transitive graphs with cores half their size always admit such partitions. We also show that the vertex sets of vertex transitive graphs with cores less than half their size do not, in general, have such partitions. Next we examine the restriction of the homomorphism order of graphs to line graphs. Our main focus is in comparing this restriction to the whole order. The primary tool we use in our investigation is that, as a consequence of Vizing's theorem, this partial order can be partitioned into intervals which can then be studied independently. We denote the line graph of X by L(X). We show that for all n ≥ 2, for any line graph Y strictly greater than the complete graph Kₙ, there exists a line graph X sitting strictly between Kₙ and Y. In contrast, we prove that there does not exist any connected line graph which sits strictly between L(Kₙ) and Kₙ, for n odd. We refer to this property as being ``n-maximal", and we show that any such line graph must be a core and the line graph of a regular graph of degree n. Finally, we introduce quantum homomorphisms as a generalization of, and framework for, quantum colorings. Using quantum homomorphisms, we are able to define several other quantum parameters in addition to the previously defined quantum chromatic number. We also define two other parameters, projective rank and projective packing number, which satisfy a reciprocal relationship similar to that of fractional chromatic number and independence number, and are closely related to quantum homomorphisms. Using the projective packing number, we show that there exists a quantum homomorphism from X to Y if and only if the quantum independence number of a certain product graph achieves |V(X)|. This parallels a well known classical result, and allows us to construct examples of graphs whose independence and quantum independence numbers differ. Most importantly, we show that if there exists a quantum homomorphism from a graph X to a graph Y, then ϑ̄(X) ≤ ϑ̄(Y), where ϑ̄ denotes the Lovász theta function of the complement. We prove similar monotonicity results for projective rank and the projective packing number of the complement, as well as for two variants of ϑ̄. These immediately imply that all of these parameters lie between the quantum clique and quantum chromatic numbers, in particular yielding a quantum analog of the well known ``sandwich theorem". We also briefly investigate the quantum homomorphism order of graphs.

Tese de Doutoramento em Genética Molecular Comparativa apresentada à Universidade de Trás-os-Montes e Alto Douro
Grapevine (Vitis vinifera L.) is one of the oldest perennial domesticated fruit crops in the world and has been widely cultivated and appreciated both for its fruit and wine. During the domestication process of the wild Vitis vinifera subsp. sylvestris to Vitis vinifera subsp. sativa, a complex and long-term evolutionary process led to dramatic changes on grape biology. Since early, vine growers selected the grapevine phenotypes capable of ensuring a greater and regular fruit production and quality, maintaining them through vegetative propagation, thus multiplying highly desirable genotypes. However, natural crossings between newly introduced cultivars and the local germplasm also occurred, alongside with the emergence of somatic events. One of the major contributors for the existing diversity in cultivated grapevine has been the appearance of somatic mutations that affect berry skin color leading to various phenotypes. Indeed, this feature has been used as basis for selection on breeding programs due to its influence on vine growers, winemakers and consumers, representing an important economic factor on this crop. Grapes are not obviously only red or white, instead they provide a huge assortment of colors ranging from whitish, yellow, green, to pink, grey, and to darker red, purple and black berries. This broad range of color cannot be explained by the simple presence of a specific group of molecules, thus, the present study intended to deepen the current knowledge about how grape berry skin color variation is affected by the synthesis of phenolic compounds and their underlying genetic factors. Primarily, the identification of grape berry skin color mutants was performed by genotyping a germplasm set of twenty-five grapevine accessions with twelve microsatellite loci. Among the eleven groups of putative berry skin color mutants genotyped, nine accessions, which were grouped in four different families, were identified as true color mutants, including related black, grey or red and white-skinned variants derived from a single variety. The phenolic profile of the confirmed berry skin color mutants revealed that they could be distinguished according to their non-colored compounds and anthocyanins composition. Moreover, this work benefits from the complementary use of molecular and chemical approaches for the correct identification of the berry skin color mutants studied. The change of berry skin color, from green to white/yellow in non-colored cultivars or from green to pink-red/blue-black in colored cultivars due to anthocyanin synthesis and accumulation occurs during the onset of ripening (veraison). Based on these facts, a first attempt to characterize these changes by means of an integrative approach combining colorimetric (CIELab measurement), metabolic (phenolic profile by HPLC-DAD) and genotypic (allelic composition of MYBA1 and MYBA2 genes) data was performed. This study was focused on the changes that occur during berry development, to improve the knowledge regarding grape berry skin color diversity using somatic variants for berry skin color. Overall, the process of anthocyanin biosynthesis/ accumulation showed a correlation with the colorimetric parameters analysed. Despite the berry skin color variability observed among the somatic variants analyzed was not fully explained by the berry color locus genotype, the phenolic profiles allowed to infer about specific interferences, namely some possible dysfunctions at different levels of the biosynthetic pathway, which could be behind the color variation observed. Additionally, a case study focused on an extremely skin-pigmented Portuguese cultivar (cv. ‘Vinhão’) was conducted throughout berry development, providing the first insights into the genetic and transcriptomic background that may be responsible for the skin color properties of this cultivar. Several types of mutations have been identified at the berry color locus as being responsible for color reversions in grapevine. Through a layer-specific approach, the molecular mechanisms responsible for berry skin color reversion were determined on a subset of somatic variants for berry skin color never investigated before, by the genetic characterization of the berry color locus and its surrounding genomic region. In addition to the observation and description of the most well-known models and mechanisms behind berry skin color reversions, a novel mechanism for the genetic make-up of less-pigmented variants evolving from an unpigmented ancestor was also proposed, in which color gain seems to result from the recovery of the functional G allele on MYBA2. Moreover, it was observed that the mutational events responsible for color gain/ recovery are less understood and different from those described for color loss. On this way, a case study of a white-to-red berry skin color reversion was also performed, in order to better understand its transcriptomic and metabolic consequences in grapevine, specifically in the cv. ‘Moscatel Galego’. The results obtained showed that the coloration of the red-skinned variant was recovered from the white-skinned phenotype of cv. ‘Moscatel Galego Branco’ by the partial activation of the berry color locus. The red-skinned coloration in cv. ‘Moscatel Galego Roxo’ was also associated with the reduced activity of the flavonoid trihydroxylated sub-branch and decreased anthocyanins methylation/acylation.
A videira (Vitis vinifera L.) é uma das mais antigas culturas perenes domesticadas no mundo e tem sido extensamente cultivada e apreciada tanto pelos seus frutos como pelo vinho. Ao longo do processo de domesticação de Vitis vinifera subsp. sylvestris para Vitis vinifera subsp. sativa, um processo evolutivo complexo e de longa duração levou a alterações dramáticas na biologia da uva. Desde cedo, os vitivinicultores selecionaram os fenótipos de videira capazes de assegurar uma maior e mais regular produção e qualidade do fruto, mantendo-os através de propagação vegetativa, multiplicando assim, genótipos altamente desejáveis. No entanto, também ocorreram cruzamentos naturais entre as novas cultivares introduzidas e o germoplama local, juntamente com o aparecimento de eventos somáticos. Uma das maiores contribuições para a diversidade existente na videira cultivada foi o aparecimento de mutações somáticas que afetam a cor do bago levando a vários fenótipos. De facto, esta característica tem sido usada como base de seleção em programas de melhoramento devido à sua influência sobre os vitivinicultores, enólogos e consumidores, representando um importante fator económico nesta cultura. As uvas não são obviamente só tintas ou brancas, em vez disso apresentam uma enorme seleção de cores variando desde uvas esbranquiçadas, amarelas, verdes, a rosadas, rosa-pálido, e até vermelhas mais escuras, roxas e pretas. Este grande intervalo de cor não pode ser explicado pela simples presença de um determinado grupo de moléculas, assim, o presente estudo destinou-se a aprofundar o conhecimento atual sobre como a variação da cor do bago é afetada pela síntese de compostos fenólicos e os seus fatores genéticos subjacentes. Primeiramente, foi efetuada a identificação de mutantes para a cor do bago num conjunto de germoplasma contendo vinte e cinco acessos de videira através da genotipagem com doze loci de microssatélites. Entre os onze grupos de putativos mutantes para a cor do bago genotipados, nove acessos, agrupados em quatro famílias diferentes, foram identificados como verdadeiros mutantes para a cor, incluindo variantes com película de cor tinta, roxa ou rosada e branca derivados de uma única variedade. O perfil fenólico dos mutantes para a cor do bago confirmados revelou que estes podem ser distinguidos de acordo com a sua composição em compostos não-corados e antocianinas. Além disso, este trabalho beneficiou do uso complementar de técnicas moleculares e químicas para a correta identificação dos mutantes para a cor do bago estudados. A alteração da cor do bago, de verde para branco/amarelo em cultivares não-corados ou de verde para rosa-avermelhado/preto-azulado em cultivares corados devido à síntese e acumulação de antocianinas ocorre no início do amadurecimento (pintor). Com base nestes factos, foi realizada uma primeira tentativa de caracterizar estas mudanças recorrendo a uma abordagem integrada combinando dados colorimétricos (medição CIELab), metabólicos (perfil fenólico através de HPLC-DAD) e genotípicos (composição alélica dos genes MYBA1 e MYBA2). Este estudo focou-se nas alterações ocorridas durante o desenvolvimento do bago, de forma a melhorar o conhecimento acerca da diversidade da cor do bago em videira utilizando variantes somáticos para a cor do bago. No geral, o processo de biossíntese/ acumulação de antocianinas demonstrou uma correlação com os parâmetros colorimétricos analisados. Apesar da variabilidade da cor do bago observada entre os variantes somáticos analisados não ser totalmente explicada pelo genótipo do locus da cor do bago, os perfis fenólicos permitiram inferir sobre interferências específicas, nomeadamente sobre possíveis disfunções a diversos níveis da via biossintética, que poderão estar por detrás da variação de cor observada. Adicionalmente, um estudo de caso focado num cultivar Português extremamente pigmentado (cv. ‘Vinhão’) foi conduzido durante o desenvolvimento do bago, fornecendo as primeiras descobertas sobre o fundo genético e transcritómico que poderá ser responsável pelas propriedades colorimétricas deste cultivar. Vários tipos de mutações têm sido identificados no locus da cor do bago como sendo responsáveis por reversões de cor em videira. Através de uma abordagem específica em camadas, os mecanismos moleculares responsáveis por reversões de cor foram determinados num conjunto de variantes somáticos para a cor da película do bago, nunca estudados anteriormente, através da caracterização genética do locus da cor do bago e da região genómica adjacente. Além da observação e descrição dos modelos e mecanismos responsáveis pela reversão de cor mais conhecidos, foi também proposto um novo mecanismo responsável pela composição genética de variantes pouco pigmentados descendentes de um ancestral não pigmentado, no qual o ganho de cor parece resultar da recuperação do alelo funcional G no gene MYBA2. Além disso, foi observado que os eventos mutacionais responsáveis pelo ganho/ recuperação de cor são menos compreendidos e diferentes dos descritos para a perda de cor. Desta forma, foi realizado o estudo de um caso de reversão de cor, de branco para rosado, de forma a melhor compreender as suas consequências a nível transcritómico e metabólico em videira, especificamente no cv. ‘Moscatel Galego’. Os resultados obtidos demonstraram que a coloração do variante roxo foi recuperada a partir do fenótipo branco do cv. ‘Moscatel Galego Branco’ através da ativação parcial do locus da cor do bago. A coloração roxa do cv. ‘Moscatel Galego Roxo’ foi também associada à reduzida atividade da sub-via dos flavonoides tri-hidroxilados e à diminuição da metilação/ acilação das antocianinas

Research Doctorate - Doctor of Philosophy (PhD)
Interconnection networks form an important research area which has received much attention, both in theoretical research and in practice. Design of interconnection networks is much concerned with the topology of networks. The topology of a network is usually studied in terms of extremal graph theory. Consequently, from the extremal graph theory point of view, designing the topology of a network involves various extremal graph problems. One of these problems is the well-known fundamental problem called the degree/diameter problem, which is to determine the largest (in terms of the number of vertices) graphs or digraphs of given maximum degree and given diameter. General upper bounds, called Moore bounds, exist for the largest possible order of such graphs and digraphs of given maximum degree ∆ (respectively, out-degree d) and diameter D. However, quite a number of open problems regarding the degree/diameter problem do still exist. Some of these problems, such as constructing a Moore graph of degree ∆ = 57 and diameter D = 2, have been open for over 50 years. Another extremal graph problem regarding the design of the topology of a network is called the construction of EX graphs, which is to obtain graphs of the largest size (in terms of the number of edges), given order and forbidden cycle lengths. In this thesis, we obtain large graphs whose sizes either improve the lower bound of the size of EX graphs, or even reach the optimal value. We deal with designing the topology of a network, but we are also interested in the issue of fault tolerance of interconnection networks. This leads us to another extremal graph problem, that is, connectivity. In this thesis, we provide an overview of the current state of research in connectivity of graphs and digraphs. We also present our contributions to the connectivity of general regular graphs with small diameter, and the connectivity of EX graphs.

Research Doctorate - Doctor of Philosophy (PhD)
Interconnection networks form an important research area which has received much attention, both in theoretical research and in practice. Design of interconnection networks is much concerned with the topology of networks. The topology of a network is usually studied in terms of extremal graph theory. Consequently, from the extremal graph theory point of view, designing the topology of a network involves various extremal graph problems. One of these problems is the well-known fundamental problem called the degree/diameter problem, which is to determine the largest (in terms of the number of vertices) graphs or digraphs of given maximum degree and given diameter. General upper bounds, called Moore bounds, exist for the largest possible order of such graphs and digraphs of given maximum degree ∆ (respectively, out-degree d) and diameter D. However, quite a number of open problems regarding the degree/diameter problem do still exist. Some of these problems, such as constructing a Moore graph of degree ∆ = 57 and diameter D = 2, have been open for over 50 years. Another extremal graph problem regarding the design of the topology of a network is called the construction of EX graphs, which is to obtain graphs of the largest size (in terms of the number of edges), given order and forbidden cycle lengths. In this thesis, we obtain large graphs whose sizes either improve the lower bound of the size of EX graphs, or even reach the optimal value. We deal with designing the topology of a network, but we are also interested in the issue of fault tolerance of interconnection networks. This leads us to another extremal graph problem, that is, connectivity. In this thesis, we provide an overview of the current state of research in connectivity of graphs and digraphs. We also present our contributions to the connectivity of general regular graphs with small diameter, and the connectivity of EX graphs.

Let G = (V, E) be a graph. For any real valued function f : V >R and SCV, let f (s) = z ues f(u). The weight of f is defined as f(V). A signed k-subdominating function (signed kSF) of G is defined as a function f : V > {-I, I} such that f(N[v]) > 1 for at least k vertices of G, where N[v] denotes the closed neighborhood of v. The signed k-subdomination number of a graph G, denoted by yks-11(G), is equal to min{f(V) I f is a signed kSF of G}. If instead of the range {-I, I}, we require the range {-I, 0, I}, then we obtain the concept of a minus k-subdominating function. Its associated parameter, called the minus k-subdomination number of G, is denoted by ytks-101(G). In chapter 2 we survey recent results on signed and minus k-subdomination in graphs. In Chapter 3, we compute the signed and minus k-subdomination numbers for certain complete multipartite graphs and their complements, generalizing results due to Holm [30]. In Chapter 4, we give a lower bound on the total signed k-subdomination number in terms of the minimum degree, maximum degree and the order of the graph. A lower bound in terms of the degree sequence is also given. We then compute the total signed k-subdomination number of a cycle, and present a characterization of graphs G with equal total signed k-subdomination and total signed l-subdomination numbers. Finally, we establish a sharp upper bound on the total signed k-subdomination number of a tree in terms of its order n and k where 1 < k < n, and characterize trees attaining these bounds for certain values of k. For this purpose, we first establish the total signed k-subdomination number of simple structures, including paths and spiders. In Chapter 5, we show that the decision problem corresponding to the computation of the total minus domination number of a graph is NP-complete, even when restricted to bipartite graphs or chordal graphs. For a fixed k, we show that the decision problem corresponding to determining whether a graph has a total minus domination function of weight at most k may be NP-complete, even when restricted to bipartite or chordal graphs. Also in Chapter 5, linear time algorithms for computing Ytns-11(T) and Ytns-101(T) for an arbitrary tree T are presented, where n = n(T). In Chapter 6, we present cubic time algorithms to compute Ytks-11(T) and Ytks-101l(T) for a tree T. We show that the decision problem corresponding to the computation of Ytks-11(G) is NP-complete, and that the decision problem corresponding to the computation of Ytks-101 (T) is NP-complete, even for bipartite graphs. In addition, we present cubic time algorithms to computeYks-11(T) and Yks-101(T) for a tree T, solving problems appearing in [25].
Thesis (Ph.D.)-University of Natal, Pietermaritzburg, 2003.

Table grape (cv. Menindee Seedless) production from a vineyard in Emerald, Central Queensland, demonstrated a strong alternate bearing pattern in seven consecutive seasons (P < 0.02) and irregular bearing in another seven seasons. Variation in vine yield was 78–90% attributable to the variation in bunch number. A sampling methodology for estimation of vine yield was recommended, and a machine vision-based system for rapid estimation of berry number and size was introduced. Low yields were attributed to low bud fertility, with only one inflorescence primordium (IP) in fruitful buds, and to poor development of IP during hot summers. IP developmental stages stretched across two seasons, with IP initiation and development in season 1 and floral primordia formation on IP in season 2. The hypothesis that IP initiation and survival is related to carbohydrate availability was not supported by the results of a two season sucrose supplementation trial. Total non-structural carbohydrate (TNC) reserves did not recover between flowering and harvest in untreated (control) plants, and decreased in root and trunk tissues from 13.5% and 7.5% w/dw at leaf fall to 7.2% and 3.7% w/dw at flowering, respectively. A continuous low pressure (69 kPa) stem injection system delivered an average of 150 g of sucrose per season into vines estimated to contain 500 g of carbohydrate at flowering but this did not alter the root or trunk TNC reserve content. Tissue δ13C (‰) values were consistent with partitioning of injected sucrose to young shoots. The comparatively low sucrose loading and variability between vines in the field by stem injection was ascribed to necrotic xylem and a decline in hydraulic conductance. Sucrose equivalent to 37% of the total plant dry weight was introduced into shoot cuttings through transpiration flow over four days, however photosynthetic rate is decreased, limiting impact of sucrose injection on TNC status. Hydraulic conductance of shoot cuttings was enhanced about 20% by perfusion with 10 mM KCl compared to water, a result attributed to an effect on pectin hydrogels in pit membranes, but conductance nevertheless had declined by approximately 90% in 72 hours. Gibberellic acid (GA3) applied at earlier stages of flowering (10% and 30% caps-off) increased inflorescence count per vine in the following season by 93% to 122% per vine relative to a control with no GA3 application, justifying a proposed split application strategy. Future research should test the proposal that inter-seasonal yield variation in Menindee Seedless is linked to low bud fruitfulness, triggered by extreme temperatures during IP formation.

The common grapevine, Vitis vinifera subsp. sativa L. (2n=6x=38) is one of the major fruit crops worldwide in terms of economic value and cultivated area. In the panorama of Italian viticulture and oenology, Campania region is characterized by a rich biodiversity, which includes a distinctive number of very ancient varieties (more than one hundred years old). This biodiversity needs to be preserved to protect producers and consumers from frauds, and on the counterpart is an essential genetic resource for breeding. The recent sequencing of grape genome represents an essential step forward for structural and functional genomics studies. In this context, one major objective of this research was to investigate the molecular basis of Campania grape germplasm. Microsatellite and retrotransposon-based markers were used in a collection of 62 grapevines. Homonymies and synonymies were found, pointing out that molecular evaluations can provide further insights into genetic structure and differentiation of Vitis germplasm accumulated during centuries of cultivation and selection. Indeed, Procidana and Coglionara are grapes cultivated and sampled on the island of Ischia and we classified them as synonymous. In our effort, we were able to identify 19 grape-specific alleles, which represent useful tools for many purposes such as traceability, typicity preservation and varietal identification. Within the collection analyzed, Aglianico del Taburno is a model for astringency and the strong resveratrol content confers high positive nutriceutical properties to its grapes and wines. For this reason, a transcriptomic analysis of key genes of the phenyl-propanoid pathway was carried out in different tissues of the berry during fruit maturation. This part of the study was correlated with the spectrophotometric assay of total phenols, flavans, anthocyanins and tannins detected in skin and berry. Anthocyanin analysis revealed the highest amount of these molecules in ripening berry skin and the lowest in seed. Correlating the transcriptomic and chemical data, the key-genes able to control production of poly-phenolic compounds in berry tissues were determined. Poly-phenolic compounds are key molecules of grapevine defense and in particular of PTI (PAMP-Triggered Immunity). Indeed, they are produced as defense compounds after pathogen recognition. Nowadays, much has been written about defense mechanisms and chitin perception in Arabidopsis, but little is known in grapevine. Considering powdery mildew as the most destructive disease of grapevines world-wide, an intense structural and functional study of PTI-involved grape genes was conducted. Grapevines are highly resistant to many powdery mildews of other species, called non-adapted (e.g. E. cichoracearum). Using Arabidopsis as model species, we identified and functionally studied the grape genes involved in the perception of chitin in the epidermal cells apoplast, as LysM-RLK, and in the intracellular signal transduction. Our findings suggest that three candidates, VvLYK1, VvLYK2 and VvLYK3, can play a different role in chitin signaling in V. vinifera. We demonstrated that a total resistance to powdery mildew was re-established in the A. thaliana cerk1 mutant only by VvLYK1, but not by VvLYK2 and VvLYK3. Further experiments also suggested an inactive VvLYK2 gene and an active but unknown function of VvLYK3. Regarding the signal transduction pathways, we found that VvMAPK3 and VvMAPK6 are not involved in the biotic response, since they both did not show expression differences in powdery mildew infection and chitin treatment time courses. The transcriptomic data generated in this study allowed us to identify VvWRKY24 as the positive regulatory factor of grape defense to powdery mildew, but excluded VvWRKY16. Indeed, VvWRKY24 had the strongest up-regulation in response to powdery mildew infection and chitin treatment. To better understand the possible interactions between two or more genes and regulatory mechanisms, an over-expression and silencing transformation was conducted. The transformations gave rise to few positive embryos after ten months from co-cultivation with Agrobacterium. This result is strictly correlated with the known recalcitrance of grapevine to transformation. As far as we know, this represents the first complete structural and functional genomics study in grapevine aimed to the identification of the major genes involved in chitin perception and signal transduction.

In this dissertation, we study etale correspondence of hyperbolic curves with unbounded dynamics. Mochizuki proved that over a field of characteristic 0, such curves are always Shimura curves. We explore variants of this question in positive characteristic, using graph theory, l-adic local systems, and Barsotti-Tate groups. Given a correspondence with unbounded dynamics, we construct an infinite graph with a large group of ”algebraic” automorphisms and roughly measures the ”generic dynamics” of the correspondence. We construct a specialization map to a graph representing the actual dynamics. Along the way, we formulate conjectures that etale correspondences with unbounded dynamics behave similarly to Hecke correspondences of Shimura curves. Using graph theory, we show that type (3,3) etale correspondences verify various parts of this philosophy. Key in the second half of this dissertation is a recent p-adic Langlands correspondence, due to Abe, which answers affirmatively the petites camarades conjecture of Deligne in the case of curves. This allows us the build a correspondence between rank 2 l-adic local systems with trivial determinant and Frobenius traces in Q and certain height 2, dimension 1 Barsotti-Tate groups. We formulate a conjecture on the fields of definitions of certain compatible systems of l-adic representations. Relatedly, we conjecture that the Barsotti-Tate groups over complete curves in positive characteristic may be ”algebraized” to abelian schemes.