Les réseaux optiques à très haut-débit sont à la base des technologies de l’information d’aujourd’hui et le sujet d’intenses recherches. Alors que l’innovation permet de rendre les transpondeurs flexibles et versatiles, les réseaux de transmission par fibres optiques sont encore configurés manuellement et surtout rarement modifiés au cours de la vie du réseau. Un des points bloquants pour aller vers la reconfiguration et l’automatisation des réseaux optiques est le besoin de prédiction de la performance de tous les liens du réseau de façon précise et rapide. Cependant, la prédiction est rendue plus complexe par la diversité du type de fibres optiques déployées et les régimes de propagation utilisés.Au cours de mes travaux, j’ai étudié expérimentalement les distorsions du signal provenant des effets non-linéaires de type Kerr, accumulées sur des centaines de kilomètres de fibres optiques. Au travers d’expériences spécifiques et contrôlées, j’ai mesuré et mis en évidence les propriétés fondamentales des distorsions non-linéaires. Ces analyses m’ont permis de concevoir l’estimateur d’un modèle de performance destiné à des liens optiques hétérogènes, qui s’applique pour différents types de fibre et différents régimes de propagation.La flexibilité des transpondeurs associés à un estimateur de performance permettront de concevoir, d’optimiser et d’adapter de façon dynamique les canaux en fonction de la demande et de la topologie du réseau, ainsi que de calculer la protection et la restauration des chemins. / Nowadays, high-speed fiber-optic communication networks are the basis of information technology and the subject of intense research. Innovation enables transponders to be flexible and versatile, but fiber optical networks are still configured manually and especially almost never tuned during the life of the network. One of the blocking points toward reconfigurable and automated optical networks is the need of performance prediction for any link of the network in an accurate and fast way. However, the prediction is made even more complex by the diversity of deployed optical fiber types and propagation regimes.During my work, I addressed experimentally the signal distortions coming from nonlinear Kerr effects accumulated on hundreds of kilometers of optical fibers. Based on specific and controlled experiments, I have measured and highlighted the properties of the nonlinear distortions. These analyses allowed me to design a performance model estimator that can be applied to heterogeneous optical links with various optical fiber types and propagation regimes.The flexibility of transponders associated with a performance estimator will optimize and tune the channels dynamically depending on the load and the topology of the network, as well as compute the protection and restoration links.

This PhD thesis is comprised of 3 results in computational geometry and graph theory. In the first paper, I demonstrate that the piercing number of a set S of pairwise intersecting convex shapes in the plane is bounded by O(\alpha(S)), where \alpha(S) is the fatness of the set S, improving upon the previous upper-bound of O(\alpha(S)^2). In the second article, I show that anagram-free vertex colouring of a 2\times n square grid requires a number of colours that increases with n. This answers an open question in Wilson's thesis and shows that even graphs of pathwidth 2 do not have anagram-free colouring with a bounded number of colours. The third article is a study on the geodesic anagram-free chromatic number of chordal and interval graphs. \emph{Geodesic anagram-free chromatic number} is defined as the minimum number of colours required to colour a graph such that all shortest paths between any pair of vertices are coloured anagram-free. In particular, I prove that the geodesic anagram-free chromatic number of a chordal graph G is 32p'w, where p' is the pathwidth of the subtree intersection representation graph (tree) of G, and w is the clique number of G. Additionally, I prove that the geodesic anagram-free chromatic number of an interval graph is bounded by 32p, where p is the pathwidth of the interval graph. This PhD thesis is comprised of 3 results in computational geometry and graph theory.

The project examines, in an experimental way, how differences in massing, aperture, and sectioning are affecting the natural resonant frequency of an architectural space. An investigation of boxes with these different qualities resulted in more than 200 minutes of sound material. By creating visual representations of the sounds, a catalogue and scheme for amassment of the boxes, could be organized. With the knowledge of how resonant frequency in prehistoric megalithic structures could have been used to support ritual chanting and the parallel to historic and contemporary religious buildings, a chapel was designed. Each room of the chapel has its own reign of resonant frequencies, with the third node being generated from my own voice and a monologue. Since the sound is a big part of the project, the main representation of the project is a series of soundscapes of each room of the chapel. This illustrates that architecture should not always only be looked at, but also listened to.

This work will explore the musical ideas and philosophy discussed by George Russell in his book “The Lydian Chromatic Concept of Tonal Organization” (2001). Through the lens of a performing musician, improviser and composer/arranger, it will explore how the ideas of unity (vertical) and duality (horizontal), interact with each other through Tonal Gravity, and how they can be practically implemented as tools used to expand the scope of vertical (harmonic) consciousness and individual expression. Through my studies of the LCC, I have composed new music, in addition to contextualizing familiar jazz repertoire, in new and refreshing ways. Russell describes the Lydian Chromatic scale and its eleven member scales, as well as three different coexistent levels of Tonal Gravity in his River Trip analogy (Vertical, Horizontal and Supra-Vertical), which together opens up both ingoing and outgoing tonal resources. I have been exploring ways of integrating these elements in my expression. George Russell’s 50 years of work on The Concept was explicitly made to inspire future innovators to develop “[…] intellectual brilliance, intuitive perception, emotional fire, and spiritual depth.” (Russell, 2001, p. 98). Studying the Concept has helped me find my own expression more believable. By avoiding mechanical playing and rather developing my ears and fluency on the instrument, it allows for harmonic color and expression to be felt and created, instead of prepared licks and patterns. / <p><strong>For my exam concert I chose to play my own compositions in a quartet with the following contributing musicians:</strong></p><p>Trumpet and compositions - Øyvind Solheim</p><p>Piano - Rasmus Mannervik</p><p>Double bass - Anton Berndts</p><p>Drums - Richard Andersson Rasheed</p><p>The concert took place at the Royal College of Music in Stockholm on the 26th of March 2024. The set list consisted of six pieces, some of which had seamless transitions in-between each other. Since we had rehearsed with an open approach, we went in to the performance with the same attitude of playing something new.</p><p><strong>Repertoire (with timestamps from the recording)</strong></p><p>1. [00:00:40 – 00:05:40] October March - Øyvind Solheim</p><p>2. [00:06:35 – 00:15:40] Reaching - Øyvind Solheim</p><p>3. [00:16:30 – 00:25:40] Acrimony - Øyvind Solheim</p><p>4. [00:25:40 – 00:36:32] Wheelez - Øyvind Solheim</p><p>5. [00:38:02 – 00:47:40] Acending, Decending - Øyvind Solheim</p><p>6. [00:49:29 – 00:58:47] Lam-ent - Øyvind Solheim</p>

Tesis por compendio / [EN] The management of Rhynchophorus ferrugineus (Coleoptera: Dryophthoridae), the worst threat for palm trees worldwide, consists in several preventive and curative techniques, but because of its low efficacy the insect still causes major economic and landscape losses. In order to define aspects that have facilitated its rapid dispersal and contribute to improving its management, the effects of vision and flight, which influence the mobility of R. ferrugineus, have been analysed. The chromatic preference of R. ferrugineus has been studied by analysing their captures in coloured bucket traps. Black traps capture the highest number of insects compared with the other colours studied, both when they contain olfactory attractants, as when these compounds are not used, demonstrating that colour by itself is a crucial attraction factor. Moreover, the spectral reflectance of studied colours and of some P. canariensis tissues has been analysed. The wavelength spectrum of black shows great similarity to that of fibres of P. canariensis, so this may be the reason why R. ferrugineus prefers this colour. Regarding sex ratio of the insect in traps, female captures are significantly greater in those baited with olfactory attractants. However, a higher number of female captures does not always occur when these compounds are not used. On the other hand, the study of sex ratio in natural populations of the insect demonstrates that the proportion is one female per male. Therefore, the greater number of captures of females in commercial traps is due exclusively to their greater attraction towards the olfactory attractants used. Another of the analysed aspects has been the flight potential of R. ferrugineus under laboratory conditions. In order to know more about the mobility of this insect, different parameters have been studied using a computer-monitored flight mill. The selected parameters used to define the R. ferrugineus flight potential have been the number of flights, total distance flown, longest single flight, flight duration, and average and maximum speed. Moreover, the influence of sex, body size, and age of the adults on the aforementioned parameters has been examined. R. ferrugineus sex does not have a significant effect on the compared flight parameters. The body size in females is significantly greater, but this does not influence their flight potential. A higher percentage of flight is observed for adults with an age range of 8-23 days old, compared to the 1-7 day old adults. However, age does not significantly influence their flight potential. By analysing the longest single flight undertaken by each adult, up to 63% of the insects can be classified as short-distance flyers (<500m), 27.3% as medium-distance flyers (500-5000m), and >9% as long-distance flyers (>5000m). Finally, the flight behaviour and dispersal of R. ferrugineus have been analysed under field conditions using the mark-release-recapture method. This test focused on detecting the influence of different factors, such as sex, temperature, relative humidity, and solar radiation, in the take-off and dispersal of the adult insects. Take-off probability of R. ferrugineus adults is significantly greater in males Moreover, this probability increases when temperature and solar radiation rise. Concerning the insect dispersal by flying, the number of recaptures is influenced by temperature, increasing significantly when this factor increases. Likewise, dispersal distances also increase significantly as temperatures rise. The insect tends to fly distances <500m (77.1% of recaptured adults), following the same tendency observed in studies performed using the flight mill. However, R. ferrugineus is able to travel up to 7km, being recorded under laboratory conditions a potential flight up to 20km. To conclude, dispersal time of the adults is very short (more than 90% of the adults were recaptured during the first 7 days), being significantly lower when relative humidity increases. / [ES] El manejo de Rhynchophorus ferrugineus (Coleoptera: Dryophthoridae), una de las peores amenazas para las palmeras en el mundo, se lleva a cabo mediante la aplicación de diversas técnicas de prevención y control, pero debido a la baja eficacia de éstas la plaga continúa causando importantes pérdidas económicas y paisajísticas. Para definir los aspectos que han intervenido en su dispersión y contribuir a mejorar su manejo, se ha analizado el efecto de la visión y el vuelo en la movilidad de los adultos de R. ferrugineus. Se ha estudiado la preferencia cromática mediante el análisis de sus capturas en trampas cubo coloreadas. Las trampas negras capturan el mayor nº de insectos en comparación con el resto de colores estudiados, tanto cuando contienen atrayentes olfativos como cuando no los contienen, demostrando que el color por sí mismo es un factor importante de atracción. Además, se ha analizado el espectro de longitud de onda de los colores estudiados y de diversos tejidos de P. canariensis. El espectro del color negro muestra gran similitud con el de las fibras de P. canariensis, es por esto por lo que R. ferrugineus podría presentar esta preferencia. En relación a la proporción de sexos en trampas que contienen atrayentes olfativos, las capturas de hembras son significativamente más elevadas. En cambio, sin éstos no siempre se produce un mayor nº de capturas de este sexo. Por otro lado, el estudio de la proporción de sexos en poblaciones naturales muestra una ratio de una hembra por macho. Por tanto, las mayores capturas de hembras en trampas se deben a una mayor atracción de éstas hacia los atrayentes olfativos. Otro aspecto estudiado ha sido el potencial de vuelo de R. ferrugineus bajo condiciones de laboratorio. Con la finalidad de conocer la movilidad de este insecto se han analizado diversos parámetros mediante la utilización de un molinillo de vuelo computerizado. Los parámetros estudiados han sido: nº vuelos, distancia total volada, vuelo más largo, duración del vuelo y velocidades media y máxima. Además, se ha analizado como influye el sexo, el tamaño del cuerpo y la edad de los adultos en dichos parámetros de vuelo. El sexo de R. ferrugineus no muestra un efecto significativo sobre los parámetros de vuelo comparados. El tamaño del cuerpo de las hembras es significativamente mayor, pero no influye estadísticamente en su potencial de vuelo. En adultos con edades de entre 8-23 días se observa un mayor porcentaje de vuelo que en aquellos con 1-7 días de edad. En cambio, la edad no influye significativamente sobre su potencial de vuelo. Al analizar el vuelo más largo, obtenemos que >63% de los insectos se clasifican como voladores de corta distancia (<500m), el 27.3% de media distancia (500-5000m), y >9% de larga distancia (>5000m). Finalmente, se ha analizado en campo el comportamiento de vuelo y dispersión de R. ferrugineus mediante la técnica de marcaje-suelta-recaptura. Este ensayo ha permitido estudiar la influencia del sexo, la temperatura (Tª), la humedad relativa y la radiación solar, en el despegue y dispersión de los adultos. La probabilidad de despegue de R. ferrugineus es significativamente mayor en machos. Además, esta probabilidad se incrementa cuando la Tª y la radiación solar aumentan. Respecto a la dispersión del insecto mediante el vuelo, el nº de recapturas se ve influenciado por la Tª, aumentando significativamente cuando ésta se incrementa. De la misma manera, las distancias de dispersión también se incrementan significativamente a media que lo hace la Tª. El insecto tiende a volar distancias <500m (77.1% de los adultos recapturados), siguiendo la misma tendencia observada en laboratorio. No obstante, R. ferrugineus es capaz de recorrer hasta 7km, llegando a registrarse vuelos potenciales en laboratorio de hasta 20km. Por último, el tiempo de dispersión de los adultos es muy corto (>90% se recapturaron en los 7 primeros días), reduciéndose / [CA] El maneig de Rhynchophorus ferrugineus (Coleoptera: Dryophthoridae), una de les pitjors amenaces per a les palmeres en tot el món, es porta a terme mitjançant l'aplicació de diverses tècniques de prevenció i control, però degut a la baixa eficàcia d'aquestes l'insecte continua causant importants pèrdues econòmiques i paisatgístiques. Per a definir els aspectes que han intervingut en la seua dispersió i contribuir a la millora del seu maneig, s'ha analitzat l'efecte que tenen la visió i el vol en la mobilitat dels adults de R. ferrugineus. S'ha estudiat la preferència cromàtica mitjançant l'anàlisi de les seues captures en trampes poal acolorides. Les trampes negres capturen el major nombre d'insectes en comparació amb la resta de colors estudiats, tant quan contenen atraients olfactius com quan no els contenen, demostrant que el color per ell mateix és un factor important d'atracció. A més, s'ha analitzat l'espectre de longitud d'ona dels colors estudiats i de diversos teixits de P. canariensis. L'espectre del color negre mostra gran similitud amb el de les fibres de P. canariensis, és per açò pel que R. ferrugineus podria presentar aquesta preferència. En relació a la proporció de sexes a les trampes que contenen atraients olfactius, les captures de femelles són significativament més elevades. En canvi, sense aquests no sempre es produeix un major nombre de captures d'aquest sexe. Per altra banda, l'estudi de la proporció de sexes en poblacions naturals demostra que la ràtio és d'una femella per mascle. Per tant, les majors captures de femelles en trampes es deuen a una major atracció d'aquestes cap als atraients olfactius utilitzats. Altre aspecte estudiat ha sigut el potencial de vol de R. ferrugineus sota condicions de laboratori. Amb la finalitat de conèixer la mobilitat d'aquest insecte s'han analitzat diversos paràmetres mitjançant la utilització d'un molinet de vol computeritzat. Els paràmetres estudiats han sigut: nombre de vols, distància total volada, vol més llarg, duració del vol i velocitats mitjana i màxima dels vols. A més, s'ha analitzat com influeixen el sexe, el tamany del cos i l'edat dels adults en dits paràmetres de vol. El sexe de R. ferrugineus no mostra un efecte significatiu sobre els paràmetres de vol comparats. El tamany del cos de les femelles és significativament major, però no influeix estadísticament en el seu potencial de vol. En adults amb edats d'entre 8-23 dies s'observa un major percentatge de vol que en aquells amb 1-7 dies d'edat. En canvi, l'edat no influeix significativament sobre el seu potencial de vol. En analitzar el vol més llarg, obtenim que més del 63% dels insectes es classifiquen com voladors de curta distància (<500m), el 27.3% de mitja distància (500-5000m), i >9% de llarga distància (>5000m). Finalment, s'ha analitzat en camp el comportament de vol i dispersió de R. ferrugineus mitjançant la tècnica de marcatge-solta-recaptura. Aquest assaig ha permès estudiar la influència del sexe, la temperatura, la humitat relativa i la radiació solar, en l'enlairament i dispersió dels adults. La probabilitat d'enlairament de R. ferrugineus és significativament major en mascles A més, aquesta probabilitat s'incrementa quan la temperatura i la radiació solar augmenten. Respecte a la dispersió de l'insecte mitjançant el vol, el nombre de recaptures es veu influenciat per la temperatura, augmentant significativament quan aquesta s'incrementa. De la mateixa manera, les distàncies de dispersió també s'incrementen significativament a mesura que ho fa la temperatura. L'insecte tendeix a volar distàncies <500m (77.1% dels adults recapturats), seguint la mateixa tendència observada en laboratori. No obstant, R. ferrugineus és capaç de recórrer fins a 7km, arribant-se a registrar vols potencials en laboratori de fins a 20km. Per últim, el temps de dispersió dels adults és molt curt (>90% es recapturaren en els 7 primers die / Ávalos Masó, JA. (2015). Factors influencing the mobility of Red Palm Weevil Rhynchophorus ferrugineus (Coleoptera: Dryophthoridae) adults [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/59394 / Compendio

After an intense period of concerts and projects that involved learning large quantities of new music I realized that I often got vocally tired when learning music. I have always been a quick learner but my method of learning has not always been beneficial for my vocal health. In this project I have explored new ways of learning music in which I prioritize vocal health. I have deepened my understanding of the vocal mechanism and experimented with vocal exercises as a part of learning repertoire. Making and listening to recordings of my repertoire and working sessions has helped me to hone my approach. I worked with two pieces of repertoire, spending three weeks on each piece, and focused on different parts of the learning process every week. After completing the work with each piece I chose a few of the recordings to show my singing teacher and a small group of my singing colleagues. This led to meaningful discussions that took my work further. This project has helped me to practice efficiently without becoming vocally tired, created a bridge between repertoire work and vocal technique, and increased the quality of my everyday work as a classical singer.

Cette thèse se concentre sur le sujet de la calibration de la camera interne et, en particulier, sur les aspects de haute précision. On suit et examine deux fils principaux: la correction d'une aberration chromatique de lentille et l'estimation des paramètres intrinsèques de la caméra. Pour la problème de l'aberration chromatique, on suit un chemin de post-traitement numérique de l'image, afin de se débarrasser des artefacts de couleur provoqués par le phénomène de dispersion du système d'objectif de la caméra, ce qui produit une désalignement perceptible des canaux couleur. Dans ce contexte, l'idée principale est de trouver un modèle de correction plus général pour réaligner les canaux de couleur que ce qui est couramment utilisé - différentes variantes du polynôme radial. Celui-ci ne peut pas être suffisamment général pour assurer la correction précise pour tous les types de caméras. En combinaison avec une détection précise des points clés, la correction la plus précise de l'aberration chromatique est obtenue en utilisant un modèle polynomial qui est capable de capter la nature physique du décalage des canaux couleur. Notre détection de points clés donne une précision allant jusqu'à 0,05 pixels, et nos expériences montrent sa grande résistance au bruit et au flou. Notre méthode de correction de l’aberration, par opposition aux logiciels existants, montre une géométrique résiduelle inférieure à 0,1 pixels, ce qui est la limite de la perception de la vision humaine. En ce qui concerne l'estimation des paramètres intrinsèques de la caméra, la question est de savoir comment éviter la compensation d'erreur résiduelle qui est inhérent aux méthodes globales d'étalonnage, dont le principe fondamental consiste à estimer tous les paramètres de la caméra ensemble - l'ajustement de faisceaux. Détacher les estimations de la distorsion de la caméra et des paramètres intrinsèques devient possible lorsque la distorsion est compensée séparément. Cela peut se faire au moyen de la harpe d'étalonnage, récemment développée, qui calcule le champ de distorsion en utilisant la mesure de la rectitude de cordes tendues dans différentes orientations. Une autre difficulté, étant donnée une image déjà corrigée de la distorsion, est de savoir comment éliminer un biais perspectif. Ce biais dû à la perspective est présent quand on utilise les centres de cibles circulaires comme points clés, et il s'amplifie avec l'augmentation de l'angle de vue. Afin d'éviter la modélisation de chaque cercle par une fonction conique, nous intégrons plutôt fonction de transformation affine conique dans la procédure de minimisation pour l'estimation de l'homographie. Nos expériences montrent que l'élimination séparée de la distorsion et la correction du biais perspectif sont efficaces et plus stables pour l'estimation des paramètres intrinsèques de la caméra que la méthode d'étalonnage globale / This dissertation focuses on internal camera calibration and, especially, on its high-precision aspects. Two main threads are followed and examined: lens chromatic aberration correction and estimation of camera intrinsic parameters. For the chromatic aberration problem, we follow a path of digital post-processing of the image in order to get rid from the color artefacts caused by dispersion phenomena of the camera lens system, leading to a noticeable color channels misalignment. In this context, the main idea is to search for a more general correction model to realign color channels than what is commonly used - different variations of radial polynomial. The latter may not be general enough to ensure stable correction for all types of cameras. Combined with an accurate detection of pattern keypoints, the most precise chromatic aberration correction is achieved by using a polynomial model, which is able to capture physical nature of color channels misalignment. Our keypoint detection yields an accuracy up to 0.05 pixels, and our experiments show its high resistance to noise and blur. Our aberration correction method, as opposed to existing software, demonstrates a final geometrical residual of less than 0.1 pixels, which is at the limit of perception by human vision. When referring to camera intrinsics calculation, the question is how to avoid residual error compensation which is inherent for global calibration methods, the main principle of which is to estimate all camera parameters simultaneously - the bundle adjustment. Detachment of the lens distortion from camera intrinsics becomes possible when the former is compensated separately, in advance. This can be done by means of the recently developed calibration harp, which captures distortion field by using the straightness measure of tightened strings in different orientations. Another difficulty, given a distortion-compensated calibration image, is how to eliminate a perspective bias. The perspective bias occurs when using centers of circular targets as keypoints, and it gets more amplified with increase of view angle. In order to avoid modelling each circle by a conic function, we rather incorporate conic affine transformation function into the minimization procedure for homography estimation. Our experiments show that separate elimination of distortion and perspective bias is effective and more stable for camera's intrinsics estimation than global calibration method

Les deux problèmes majeurs considérés dans cette thèse : le b-coloration problème et le graphe emballage problème. 1. Le b-coloration problème : Une coloration des sommets de G s'appelle une b-coloration si chaque classe de couleur contient au moins un sommet qui a un voisin dans toutes les autres classes de couleur. Le nombre b-chromatique b(G) de G est le plus grand entier k pour lequel G a une b-coloration avec k couleurs. EL Sahili et Kouider demandent s'il est vrai que chaque graphe d-régulier G avec le périmètre au moins 5 satisfait b(G) = d + 1. Blidia, Maffray et Zemir ont montré que la conjecture d'El Sahili et de Kouider est vraie pour d ≤ 6. En outre, la question a été résolue pour les graphes d-réguliers dans des conditions supplémentaires. Nous étudions la conjecture d'El Sahili et de Kouider en déterminant quand elle est possible et dans quelles conditions supplémentaires elle est vrai. Nous montrons que b(G) = d + 1 si G est un graphe d-régulier qui ne contient pas un cycle d'ordre 4 ni d'ordre 6. En outre, nous fournissons des conditions sur les sommets d'un graphe d-régulier G sans le cycle d'ordre 4 de sorte que b(G) = d + 1. Cabello et Jakovac ont prouvé si v(G) ≥ 2d3 - d2 + d, puis b(G) = d + 1, où G est un graphe d-régulier. Nous améliorons ce résultat en montrant que si v(G) ≥ 2d3 - 2d2 + 2d alors b(G) = d + 1 pour un graphe d-régulier G. 2. Emballage de graphe problème : Soit G un graphe d'ordre n. Considérer une permutation σ : V (G) → V (Kn), la fonction σ* : E(G) → E(Kn) telle que σ *(xy) = σ *(x) σ *(y) est la fonction induite par σ. Nous disons qu'il y a un emballage de k copies de G (dans le graphe complet Kn) s'il existe k permutations σi : V (G) → V (Kn), où i = 1, …, k, telles que σi*(E(G)) ∩ σj (E(G)) = ɸ pour i ≠ j. Un emballage de k copies d'un graphe G est appelé un k-placement de G. La puissance k d'un graphe G, noté par Gk, est un graphe avec le même ensemble de sommets que G et une arête entre deux sommets si et seulement si le distance entre ces deux sommets est au plus k. Kheddouci et al. ont prouvé que pour un arbre non-étoile T, il existe un 2-placement σ sur V (T). Nous introduisons pour la première fois le problème emballage marqué de graphe dans son graphe puissance / Two problems are considered in this thesis: the b-coloring problem and the graph packing problem. 1. The b-Coloring Problem : A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least a vertex in each other color class. The b-chromatic number of a graph G, denoted by b(G), is the maximum number t such that G admits a b-coloring with t colors. El Sahili and Kouider asked whether it is true that every d-regular graph G with girth at least 5 satisfies b(G) = d + 1. Blidia, Maffray and Zemir proved that the conjecture is true for d ≤ 6. Also, the question was solved for d-regular graphs with supplementary conditions. We study El Sahili and Kouider conjecture by determining when it is possible and under what supplementary conditions it is true. We prove that b(G) = d+1 if G is a d-regular graph containing neither a cycle of order 4 nor of order 6. Then, we provide specific conditions on the vertices of a d-regular graph G with no cycle of order 4 so that b(G) = d + 1. Cabello and Jakovac proved that if v(G) ≥ 2d3 - d2 + d, then b(G) = d + 1, where G is a d-regular graph. We improve this bound by proving that if v(G) ≥ 2d3 - 2d2 + 2d, then b(G) = d+1 for a d-regular graph G. 2. Graph Packing Problem : Graph packing problem is a classical problem in graph theory and has been extensively studied since the early 70's. Consider a permutation σ : V (G) → V (Kn), the function σ* : E(G) → E(Kn) such that σ *(xy) = σ *(x) σ *(y) is the function induced by σ. We say that there is a packing of k copies of G into the complete graph Kn if there exist k permutations σ i : V (G) → V (Kn), where i = 1,…, k, such that σ*i (E(G)) ∩ σ*j (E(G)) = ɸ for I ≠ j. A packing of k copies of a graph G will be called a k-placement of G. The kth power Gk of a graph G is the supergraph of G formed by adding an edge between all pairs of vertices of G with distance at most k. Kheddouci et al. proved that for any non-star tree T there exists a 2-placement σ on V (T). We introduce a new variant of graph packing problem, called the labeled packing of a graph into its power graph

Esta dissertação de mestrado investiga os formatos de modulação óptica alternativos ao tradicional formato binário de intensidade (NRZ - Non-return-to-zero), ditos avançados, como tecnologia chave para atender às exigências do mercado atual de telecomunicações por transporte de grande volume de dados e alta largura de banda, associados com a redução do custo da informação transmitida por bit. Os formatos avançados de modulação óptica fazem parte das tecnologias que estão sendo investigadas intensamente com o objetivo de superar os desafios impostos pela nova geração de sistemas ópticos com taxas a partir de 40 Gb/s. Este trabalho focaliza o estudo dessa tecnologia, apresentando uma visão geral dos formatos mais discutidos atualmente, suas características e tecnologias de implementação. Foram realizadas simulações utilizando o software comercial Optisystem versão 7.0 da empresa canadense Optiwave Systems Inc., para analisar o desempenho de alguns formatos de modulação de intensidade e de fase com respeito à sensibilidade do receptor, resistência ao cascateamento de filtragem óptica e a efeitos dispersivos e não-lineares. Procurou-se avaliar os formatos em enlaces reais, com características necessárias à sua possível utilização. Também é feita uma breve consideração dos custos associados aos formatos de modulação analisados neste trabalho. Dentre os formatos analisados, os RZ (Return-to zero) apresentaram maior sensibilidade do receptor e melhor tolerância aos efeitos não-lineares que os seus equivalentes NRZ, porém baixa tolerância aos efeitos dispersivos e ao cascateamento de filtragem óptica. O formato duobinário mostrou fraco desempenho de sensibilidade, mas provou ser o mais tolerante à dispersão cromática e à concatenação de filtragem óptica. Os formatos de modulação de fase mostraram ser bem resistentes aos efeitos não-lineares e aos efeitos dispersivos. / This MSc thesis investigates optical modulation formats as an alternative to the use of the traditional intensity binary format NRZ (Non-return-to-zero). Those formats, classified as advanced, represent one of the key technologies aimed to enable the high data volume and broadband, demanded by the present telecommunication market, with cost reduction of transmitted information per bit. Those technologies have been intensevely studied with purpose of overcoming the challenges imposed by the new generation of optical systems, with bit rates from 40 Gb/s. This work focuses on the study of modulation formats most discussed currently, presenting an overview of their main characteristics and implementation techniques. The performance of some intensity and phase formats, in terms of receiver sensitivity, optical filtering cascading, dispersion and nonlinear effects robustness, have been theoretically analyzed from simulations carried out with the commercial software Optisystem v. 7.0, of the Canadian company Optiwave Systems Inc. The analysis has been applied to real optical links, with characteristics that, potentially, demand their use. A cost analysis, based on estimated values associated to devices required for implementing the formats investigated in this work, is also presented. Among the formats studied, those based on RZ (Return-to zero) presented the highest receiver sensitivity and best tolerance to nonlinear effects, in comparison to their equivalent formats, based on NRZ. However, they are less tolerant to dispersive effects and optical filtering cascading. The duobinary format (DB) has shown a weak performance in terms of sensitivity, though has been proved to be the most tolerant to chromatic dispersion and filtering cascading effects. Among all formats, the phase modulation ones presented the highest resistance against nonlinear and dispersive effects.

Este trabalho investiga os pressupostos e fundamentos da Teoria das Cores de Goethe (Farbenlehre) como parte dos seus empenhos enquanto cientista da natureza. Apresenta a tradução de um texto seu sobre o método científico (Kautelen des Beobachters) e de um segundo texto sobre experimentos prismáticos (Beitrag zur Optik), no qual ele lança as bases do seu trabalho de mais de 30 anos sobre as cores. Estes textos, até então inexistentes em português, fornecem os subsídios para um entendimento mais amplo da Farbenlehre. E a pesquisa como um todo se orienta no sentido de contribuir para um resgate da fenomenologia goetheana para o ambiente cultural da atualidade. / This work investigates the principles and bases of Goethe\'s Theory of Colours (Farbenlehre\") as part of his studies as a Natures scientist. A translation of Goethe\'s essay on scientific methods (\"Kautelen des Beobachters\") and another on prismatic experiments (\"Beitrag zur Optik\"), where he sets the bases of his 30 years work on colours studies, are presented in this work too. The papers translated here were never before available in Portuguese, and they represent relevant subsidies for a comprehensive understanding of the \"Farbenlehre\". This research aims to contribute to the recovery of the Goethean\'s Phenomenology for the cultural enviroment of our days.