Дисертації з теми "Vertexer"

A crista ou soleira de um vertedor, que é a parte superior e que está em contato com a água, tem em geral um desenvolvimento em planta linear, no sentido transversal ao do escoamento. Nos vertedores do tipo labirinto esse desenvolvimento em planta não é linear, é composto de um ou mais ciclos, os quais podem ter uma forma triangular ou trapezoidal. A vantagem do uso desse tipo de obra hidráulica é o aumento do comprimento total da soleira para uma mesma largura, o que se traduz em um aumento da capacidade de vazão da estrutura. A utilização de vertedores do tipo labirinto é particularmente vantajosa para cargas pequenas, pois sua eficiência se reduz com o aumento da carga. Um exemplo de aplicação é a utilização em locais nos quais a geologia ou a topografia impõe restrições de espaço para construção. Outro exemplo é o emprego em uma ampliação da capacidade de vazão de um vertedor existente, quando o vertedor labirinto seria construído sobre o mesmo. Foram apresentadas as principais metodologias de projeto publicadas desse tipo de vertedor . Para auxiliar na análise crítica das metodologias de projeto foram apresentados quatro estudos de casos de vertedores labirinto, cujas pesquisas foram realizadas em modelos físicos reduzidos, a saber: Barragem Prado (EUA), Vertedor Labirinto da Estação de Tratamento de Esgotos de Barueri (Brasil), Barragem Ute (EUA) e Barragem Dog River (EUA). Os resultados desses ensaios mostraram que as metodologias de projeto são capazes de predizer o desempenho dos vertedores dentro de uma faixa limitada de desvio, variável com a carga. Recomenda-se que projetos de maior responsabilidade, ou que tenham características diferentes das preconizadas pela bibliografia, sejam estudados em modelo físico reduzido.
The crest or weir of a spilway, that is the superior part and that it is in contact with the water, has usually a linear plan shape, in perpendicular to the flow direction. In the labyrinth spillways the plan shape is not linear, but varies using a triangular or trapezoidal planform. The advantage of the use of this water work is the increase of the total length of the weir for same width, what it is expressed as an increase of the capacity of discharge of the structure. The use of labyrinth spillways is particularly advantageous for small heads, therefore its efficiency reduces with the increase of the head. An application example is the use in sites in which geology or the topography impose restrictions of space for construction, another example is increase of the capacity of discharge of an existing spillway, where the labyrinth spillway would be constructed on it. The main design curves of this type of spillway had been presented. To assist in the critical analysis of the methodologies of design four case studies had been presented, whose research had been done in physical models: Prado Dam (U.S.A.), Labyrinth Spillway of the Wastewater Treatment Plant Barueri (Brazil), Ute Dam (U.S.A.) and Dog River Dam (U.S.A.). The results show that the design curves can predict the performance of the labyrinth spillways in a limited way. It is recommended that designs which have more responsibility (risks for human being) or that have different characteristics than the design methodologies should be studied in physical model.

Le fratture vertebrali sono tra le principali cause dell’incremento della mortalità. Queste sono dovute principalmente a traumi, tumori o particolari patologie metaboliche che colpiscono l’osso. Il tratto maggiormente interessato è quello toraco-lombare in quanto deve sopportare la maggior parte dei carichi. Risulta quindi necessario comprendere come la colonna vertebrale risponde ai carichi così da studiare e sviluppare nuovi protocolli e trattamenti per disordini del tratto spinale. Informazioni quantitative possono essere ottenute mediante test in vitro. Questi hanno alcune limitazioni dovute principalmente alla difficoltà di misurare le tensioni e le deformazioni in zone diverse dalla superficie, alla complessità e al costo delle prove. Un altro limite delle prove in vitro è rappresentato dal fatto che ciascun campione può essere testato a rottura una volta sola. Queste problematiche possono essere superate con l’utilizzo contemporaneo di modelli matematici e test in vitro. In particolare i test in vitro sono utilizzati in fase di validazione del modello matematico, ovvero nella determinazione di quanto il modello è una rappresentazione del comportamento reale che si sta simulando. Il presente lavoro di tesi si inserisce in un progetto di caratterizzazione di vertebre toraco-lombari utilizzate per la validazione di un modello agli elementi finiti. In particolare l’obiettivo dello studio è stata la realizzazione di prove meccaniche in modo da replicare l’anterior wedge fracture. Tali prove sono state effettuate presso il Laboratorio di Biomeccanica del Dipartimento di Ingegneria Industriale dell’Università di Bologna. Gli spostamenti registrati durante le prove sono stati utilizzati dal Laboratorio di Tecnologia Medica dell’Istituto Ortopedico Rizzoli come condizioni al contorno per la realizzazione di un modello FE. Una volta validato e messo a punto, il modello sarà utilizzato per valutare lo stato di salute della colonna vertebrale in vivo.

Metastasi ossee, osteoporosi e traumi sono le cause più comuni di fratture vertebrali che possono portare a conseguenze severe. In particolare, le fratture determinate da patologie e dall’invecchiamento colpiscono soprattutto il tratto toraco-lombare che è quello che sopporta la maggior parte dei carichi. Inoltre, le attività quotidiane inducono dei complessi scenari di carico sulla colonna vertebrale. Pertanto la misura di carichi in vivo ha un grande interesse clinico e biomeccanico dal momento che può essere necessaria per studiare il mal di schiena, le fratture vertebrali, il progetto di impianti, ecc. Tuttavia, le misure in vivo hanno il limite di essere invasive. Invece, le prove sperimentali hanno il vantaggio di essere non invasive, anche se presentano alcune limitazioni intrinseche quali la difficoltà di misurare le tensioni o le deformazioni che non siano sulla superficie delle vertebre e l’aumento della complessità e del costo delle prove nel momento in cui si vogliano fare misurazioni addizionali o sperimentare condizioni diverse. In alternativa, il comportamento meccanico delle strutture ossee può essere investigato con modelli numerici agli elementi finiti validati da prove sperimentali. È in questo contesto che va inserito il presente lavoro. Questa tesi ha lo scopo di cominciare un progetto sulla caratterizzazione biomeccanica di vertebre toraciche e lombari di soggetti affetti da osteoporosi da cui si ricaveranno i dati necessari per validare un modello agli elementi finiti. In particolare, durante i test meccanici si vuole riprodurre la tipica fattura vertebrale causata dall’osteoporosi, l’anterior wedge fracture. Le prove meccaniche sono state eseguite nel Laboratorio di Biomeccanica del Dipartimento di Ingegneria Industriale dell’Università di Bologna, mentre il modello agli elementi finiti sarà sviluppato dal Laboratorio di Tecnologia Medica dell’Istituto Ortopedico Rizzoli. Una volta validato, il modello sarà utilizzato per fare simulazioni di rottura in vivo.

Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to zero compared to the largest Fiedler coefficient of the graph. We propose a vertex-weighted spectral clustering algorithm which incorporates a vector of weights for each vertex of a given graph to form a vertex-weighted graph. The proposed algorithm predicts association of equidistant or nearly equidistant data points from both clusters while the unweighted clustering does not provide association. Finally, we implemented both the unweighted and the vertex-weighted spectral clustering algorithms on several data sets to show that the proposed algorithm works in general.

Os vertedores são estruturas hidráulicas construídas para controlar o nível d’água do reservatório, permitindo a passagem das vazões escoadas com a máxima eficiência possível sem provocar problemas à estrutura. Para atingir este objetivo, as condições de aproximação do escoamento à estrutura e a forma geométrica do perfil vertente são muito importantes. O controle da soleira por comportas provoca uma mudança significativa nas condições de escoamento sobre o perfil vertente. O posicionamento e a forma da comporta tem forte influência no comportamento do coeficiente de vazão e nas pressões sobre a soleira. A formação de vórtice é um fenômeno indesejável que pode ocorrer quando a operação da comporta é parcial, prejudicando a capacidade de vazão e provocando vibrações na estrutura. Este trabalho apresenta uma abordagem teórica sobre o assunto vertedor de superfície e escoamento sob comportas, apresentando resultados de diferentes estudos para melhor compreensão do funcionamento do vertedor.
Spillways are hydraulic structures constructed to control the water level of the reservoir, allowing the overflows with the maximum possible efficiency without provoking problems to the structure. The approach flow pattern to the structure and the geometric form of the spillway profile are basic importance. The control of the spillway by the floodgates modifies the draining conditions. The positioning and the form of the gate have strong influence in the behavior of the discharge coefficient and the pressures on the surface profile. A vortex formation is an undesirable phenomenon that it can occur when the operation of the floodgate is partial, reducing the discharge coefficient and produce vibrations in structure. This work presents a theoretical approach about flow over spillway and under of the partial opening of the floodgate, presenting results of different studies for better understanding the function of the spillway.

Diese Arbeit befaßt sich mit der Koppelung von Vertex-Modellen an die planaren $\phi^4$-Zufallsgraphen des Zugangs zur Quantengravitation über dynamische Polygonifizierungen. Das betrachtete System hat eine doppelte Bedeutung, einerseits als die Koppelung einer konformen Feldtheorie mit zentraler Ladung $C=1$ an zweidimensionale Euklidische Quantengravitation, andererseits als Anwendung von geometrischer, "annealed" Unordnung auf ein prototypisches Modell der statistischen Mechanik. Da das Modell mit Hilfe einer großangelegten Reihe von Monte Carlo Simulationen untersucht wird, müssen entsprechende Techniken für die Simulation von dynamischen Quadrangulierungen bzw. die dualen $\phi^4$-Graphen entwickelt werden. Hierzu werden verschiedene Algorithmen und die dazugehörigen Züge vorgeschlagen und hinsichtlich ihrer Ergodizität und Effizienz untersucht. Zum Vergleich mit exakten Ergebnissen werden die Verteilung der Koordinationszahlen bzw. bestimmte Analoga davon konstruiert. Für Simulationen des $F$-Modells auf $\phi^4$-Zufallsgraphen wird ein Ordnungsparameter für den antiferroelektrischen Phasenübergang mit Hilfe einer Plakettenspindarstellung formuliert. Ausführliche "finite-size scaling"-Analysen des Kosterlitz-Thouless-Phasenübergangs des $F$-Modells auf dem Quadratgitter und auf Zufallsgraphen werden vorgestellt und die Positionen der jeweiligen kritischen Punkte sowie die dazugehörigen kritischen Exponenten werden bestimmt. Die Rückreaktion des Vertex-Modells auf die Zufallsgraphen wird in Form der Koordinationszahlverteilung, der Verteilung der "Baby-Universen" und dem daraus resultierenden String-Suszeptibilitäts-Exponenten sowie durch die geometrische Zweipunktfunktion analysiert, die eine Schätzung der intrinsischen Hausdorff-Dimension des gekoppelten Systems liefert
In this thesis, the coupling of ice-type vertex models to the planar $\phi^4$ random graphs of the dynamical polygonifications approach to quantum gravity is considered. The investigated system has a double significance as a conformal field theory with central charge $C=1$ coupled to two-dimensional Euclidean quantum gravity and as the application of a special type of annealed connectivity disorder to a prototypic model of statistical mechanics. Since the model is analyzed by means of large-scale Monte Carlo simulations, suitable simulation techniques for the case of dynamical quadrangulations and the dual $\phi^4$ random graphs have to be developed. Different algorithms and the associated update moves are proposed and investigated with respect to their ergodicity and performance. For comparison to exact results, the co-ordination number distribution of the dynamical polygonifications model, or certain analogues of it, are constructed. For simulations of the 6-vertex $F$ model on $\phi^4$ random graphs, an order parameter for its anti-ferroelectric phase transitions is constructed in terms of a "plaquette spin" representation. Extensive finite-size scaling analyses of the Kosterlitz-Thouless point of the square-lattice and random graph $F$ models are presented and the locations of the critical points as well as the corresponding critical exponents are determined. The back-reaction of the coupled vertex model on the random graphs is investigated by an analysis of the co-ordination number distribution, the distribution of "baby universes" and the string susceptibility exponent as well as the geometric two-point function, yielding an estimate for the internal Hausdorff dimension of the coupled system

Switching on a vertex of a graph involves swapping the sets of neighbours and non-neighbours of the vertex. The resultant graph is called a switch card of the original graph. The switch deck of a graph is the collection of all of its switch cards. The vertex-switch reconstruction problem then asks which graphs (termed non-VSR graphs) cannot be uniquely determined from their switch decks. A review of the published knowledge about this problem is followed by an improved bound on the number of edges in a non-VSR graph, and a bound on the size of the automorphism group of a non-VSR graph. Finally, the results of a computer search are presented, showing that no non-VSR graphs of order 8 or 12 exist.

This work is an examination of various aspects of twisted vertex operator representations of Kac-Moody algebras. It starts with an introduction to Kac-Moody algebras and string theories, including a discussion of the propagation of strings on orbifolds. String interactions in a subclass of such models naturally involve twisted vertex operators. The centrally extended loop algebra realization of Kac-Moody algebras is used to explain why the inequivalent gradations of basic representations of Kac-Moody algebras g(^r) associated with g are in one-to-one correspondence with the conjugacy classes of the automorphism group of the root system, aut Ф(_g).The structure of the automorphism groups of the simple Lie algebra root systems are examined. A method of classifying the conjugacy classes of the Weyl groups is explained and then extended to cover the whole automorphism group in cases where there are additional Dynkin diagram symmetries. All possible automorphisms, a, that have the property that det (1 – σ(^r)) ≠ 0, r = 1, ….. , n - 1 where n is the order of a, are determined. Such automorphisms lead to interesting orbifold models in which some of the calculations are simplified. A thorough exposition of the twisted vertex operator representation is given including a detailed explanation of the zero-mode Hilbert space and the construction of the required cocycle operators. The relation of the vacuum degeneracy to the number of fixed subspace singularities in the orbifold construction is discussed. Explicit examples of twisted vertex operators and their associated cocycles are given. Finally it is shown how the twisted and an alternative shifted vertex operator representation of the same gradation may be identified. This is used to determine the invariant subalgebras of the gradations along with the vacuum degeneracies and conformal weights of the representations. The results of calculations for inequivalent gradations of the simply laced exceptional algebras are given.

Superstring theory posits that as complicated as nature may seem to the naive observer, the variety of observed phenomena may be explained by postulating that at the fundamental scale, matter is composed of lines of energy, namely strings. These oscillating lines would be elementary and would hence have no substructure. They are expected to be incredibly tiny, their line-like structure would become noticeable at scales close to the string scale (which may lie anywhere from the TeV scale all the way up to the Planck scale) and would appear to be point-like to the macroscopic observer. Internal consistency then also requires the presence of higher dimensional objects, namely D-branes, all of which conspire and combine in such a way so as to give rise to the observable Universe. Advances in cosmology suggest the early universe was much hotter and denser than is the Universe at present, that the Universe has expanded and continues to expand (exponentially in fact) at present. This in turn has led a number of theorists to point out the remarkable possibility that some of these strings or D-branes were also stretched with the expansion. The resulting macroscopic strings, the so-called cosmic strings, would potentially stretch across the entire Universe. Cosmic strings make their presence manifest by oscillating, scattering off other structures, by decaying, producing gravitational waves and so on, and this in turn hints at the available handles that may be used to observe them. Before we can hope to observe cosmic strings however, the first step is then clearly to understand these properties which determine their evolution. A number of approximate (classical) descriptions of cosmic strings have been constructed to date, but approximations break down, especially when potentially interesting things happen (e.g. close to cusps, i.e. points on the string that reach the speed of light) and can obscure the physics. Thankfully, one can go beyond these approximations: all properties of cosmic strings can be concisely and accurately contained or encoded in a single object, the so-called fundamental cosmic string vertex operator. In the present thesis I construct precisely this, covariant vertex operators for general cosmic strings and this is the first such construction. Cosmic strings, being macroscopic, are likely to exhibit classical behaviour in which case they would most accurately be described by a string theory analogue of the well known harmonic oscillator coherent states. By minimally extending the standard definition of coherent states, so as to include the string theory requirements, I go on to construct both open and closed covariant coherent state vertex operators. The naive construction of the latter requires the existence of a lightlike compactification of spacetime. When the lightlike winding states in the underlying Hilbert space are projected out, the resulting vertex operators have a classical interpretation and can consistently propagate in noncompact spacetime. Using the DDF map I identify explicitly the corresponding general lightcone gauge classical solutions around which the exact macroscopic quantum states are fluctuating. We go on to show that both the covariant gauge coherent vertex operators, the corresponding lightcone gauge coherent states and the classical solutions all share the same mass and angular momenta, which leads us to conjecture that the covariant and lightcone gauge states are different manifestations of the same state and share identical interactions. Apart from the coherent state vertices I also present a complete set of covariant mass eigenstate vertex operators and these may also be relevant in cosmic string evolution. Finally, I also present the first amplitude computation with the coherent states, the graviton emission amplitude (including the effects of gravitational backreaction) for a simple class of cosmic string loops. As a byproduct of the above, I find that the fundamental building blocks of arbitrarily massive covariant string states are given by elementary Schur polynomials (equivalently complete Bell polynomials). This construction enables one to address the aforementioned questions concerning the properties of cosmic strings, their cosmological signatures, and may lead to the first observations of such objects in the sky. This in turn would be a remarkable way of verifying Superstring theory as the framework underlying the structure of our Universe.

This thesis proposes the novel concept of Vertex Unique Labelled Subgraph (VULS) mining with respect to the field of graph-based knowledge discovery (or graph mining). The objective of the research is to investigate the benefits that the concept of VULS can offer in the context of vertex classification. A VULS is a subgraph with a particular structure and edge labelling that has a unique vertex labelling associated with it within a given (set of) host graph(s). VULS can describe highly discriminative and significant local geometries each with a particular associated vertex label pattern. This knowledge can then be used to predict vertex labels in 'unseen' graphs (graphs with edge labels, but without vertex labels). Thus this research is directed at identifying (mining) VULS, of various forms, that 'best' serve to both capture effectively graph information, while at the same time allowing for the generation of effective vertex label predictors (classifiers). To this end, four VULS classifiers are proposed, directed at mining four different kinds of VULS: (i) complete, (ii) minimal, (iii) frequent and (iv) minimal frequent. The thesis describes and discusses each of these in detail including, in each case, the theoretical definition and algorithms with respect to VULS identification and prediction. A full evaluation of each of the VULS categories is also presented. VULS has wide applicability in areas where the domain of interest can be represented in the form of some sort of a graph. The evaluation was primarily directed at predicting a form of deformation, known as springback, that occurs in the Asymmetric Incremental Sheet Forming (AISF) manufacturing process. For the evaluation two flat-topped, square-based, pyramid shapes were used. Each pyramid had been manufactured twice using Steel and twice using Titanium. The utilisation of VULS was also explored by applying the VULS concept to the field of satellite image interpretation. Satellite data describing two villages located in a rural part of the Ethiopian hinterland were used for this purpose. In each case the ground surface was represented in a similar manner to the way that AISF sheet metal surfaces were represented, with the $z$ dimension describing the grey scale value. The idea here was to predict vertex labels describing ground type. As will become apparent, from the work presented in this thesis, the VULS concept is well suited to the task of 3D surface classification with respect to AISF and satellite imagery. The thesis demonstrates that the use of frequent VULS (rather than the other forms of VULS considered) produces more efficient results in the AISF sheet metal forming application domain, whilst the use of minimal VULS provided promising results in the context of the satellite image interpretation domain. The reported evaluation also indicates that a sound foundation has been established for future work on more general VULS based vertex classification.

Nella tesi vengono presentate alcune relazioni fra gruppi quantici e modelli reticolari. In particolare si associa un modello vertex a una rappresentazione di un'algebra inviluppante quantizzata affine e si mostra che, specializzando il parametro quantistico ad una radice dell'unità, si manifestano speciali simmetrie.

Le Théorème des Quatre Couleurs, conjecturé en 1852 et prouvé en 1976, est à l'origine de l'étude des partitions des sommets de graphes peu denses. Il affirme que toute carte plane peut être coloriée avec au plus quatre couleurs différentes, de telle manière que deux régions qui partagent une frontière aient des couleurs différentes. Énoncé en terme de théorie des graphes, cela veut dire que tout graphe planaire, c'est à dire tout graphe qui peut être représenté dans le plan sans que deux arêtes ne se croisent, peut voir son ensemble de sommets partitionné en quatre ensembles tels que chacun de ces ensembles ne contient pas les deux extrémités d'une même arête. Une telle partition est appelée une coloration propre en quatre couleurs. Dans cette thèse, on s'intéresse à l'étude de la structure des graphes peu denses, selon différentes notions de densité. D'une part, on étudie les graphes planaires sans petits cycles, et d'autre part les graphes dont tous les sous-graphes ont un degré moyen peu élevé. Pour ces classes de graphes, on recherche tout d'abord le plus petit nombre de sommets à retirer pour obtenir une forêt, c'est à dire un graphe sans cycles. Cela peut être vu comme une partition des sommets du graphe en un ensemble induisant une forêt et un ensemble de sommets contenant au plus une fraction donnée des sommets du graphe. La motivation première de cette étude est une conjecture d'Albertson et Berman (1976) comme quoi tout graphe planaire admettrait une telle partition où la forêt contient au moins la moitié des sommets du graphe. Dans un second temps, on s'intéresse aux partitions des sommets de ces graphes en deux ensembles, tels que les sous-graphes induits par ces deux ensembles ont des propriétés particulières. Par exemple, ces sous-graphes peuvent être des graphes sans arêtes, des forêts, des graphes de degré borné, ou des graphes dont les composantes connexes ont un nombre borné de sommets. Ces partitions des sommets sont des extensions de la notion de coloration propre de graphe.On montre, pour différentes classes de graphes peu denses, que tous les graphes de ces classes admettent de telles partitions. On s'intéresse également aux aspect algorithmiques de la construction de telles partitions
The study of vertex partitions of planar graphs was initiated by the Four Colour Theorem, which was conjectured in 1852, and proven in 1976. According to that theorem, one can colour the regions of any planar map by using only four colours, in such a way that any two regions sharing a border have distinct colours. In terms of graph theory, it can be reformulated this way: the vertex set of every planar graph, i.e. every graph that can be represented in the plane such that edges do not cross, can be partitioned into four sets such that no edge has its two endpoints in the same set. Such a partition is called a proper colouring of the graph.In this thesis, we look into the structure of sparse graphs, according to several notions of sparsity. On the one hand, we consider planar graphs with no small cycles, and on the other hand, we consider the graphs where every subgraph has bounded average degree.For these classes of graphs, we first look for the smallest number of vertices that can be removed such that the remaining graph is a forest, that is a graph with no cycles. That can be seen as a partition of the vertices of the graph into a set inducing a forest and a set with a bounded fraction of the vertices of the graph. The main motivation for this study is a the Albertson and Berman Conjecture (1976), which states that every planar graph admits an induced forest containing at least one half of its vertices.We also look into vertex partition of sparse graphs into two sets both inducing a subgraph with some specific prescribed properties. Exemples of such properties can be that they have no edges, or no cycles, that they have bounded degree, or that they have bounded components. These vertex partitions generalise the notion of proper colouring. We show, for different classes of sparse graphs, that every graph in those classes have some specific vertex partition. We also look into algorithmic aspects of these partitions

Cette thèse tente d'aborder, avec quelques détours, deux questions centrales concernant le
centrosome des vertébrés : son rôle dans la motilité cellulaire et son rôle dans le cycle de
division cellulaire.
Après une introduction en trois parties (un tour d'horizon dans une optique historique, un
exposé détaillé des connaissances actuelles, puis une réflexion plus générale sur des bases
phylogénétiques), deux travaux sont présentés : une étude des rôles respectifs des deux
centrioles du centrosome des cellules de vertébrés, puis une étude du comportement
particulier du centrosome dans ces cellules en sortie de mitose.
L'ensemble de ce travail se fonde sur un outil précieux : l'établissement de lignées cellulaires
qui expriment de manière stable la centrine 1 humaine couplée à la GFP, ce qui constitue un
excellent marqueur des centrioles et de leur stade de maturation. En effet, le centrosome des
vertébrés contient deux structures microtubulaires appelée centrioles qui se reproduisent en
synchronie avec le cycle de division cellulaire par un mécanisme de duplication, un nouveau
centriole étant assemblé à proximité de chaque centriole présent. Il y a donc dans chaque
cellule, après une mitose, un nouveau et un ancien centriole aussi appelés centriole parental
ou centriole père et centriole fils.
La première étude, après avoir succinctement défini le comportement des centrioles dans les
différentes phases du cycle, se concentre plus précisément sur la phase G1 pendant laquelle il
a pu être observé que les deux centrioles peuvent transitoirement se séparer de plus de dix
microns. L'un des deux centrioles, qui a pu être identifié comme le centriole le plus jeune, a
une mobilité parfois importante, alors que le plus ancien, qui est associé à l'aster de
microtubules par des appendices qui sont caractéristiques de son ancienneté reste près du
centroïde de la cellule. La différence d'abondance des microtubules à proximité des deux
centrioles a pu être attribuée à une régulation différentielle de l'ancrage : le centriole le plus
ancien capture les microtubules qui sont nucléés dans un rayon de quelques microns autours
de lui, alors que le centriole fils, qui a une capacité de nucléation équivalente, a une capacité
d'ancrage des microtubules réduite. Ainsi, quand les deux centrioles sont éloignés l'un de
l'autre, de nombreux microtubules libres peuvent être observés dans la cellule, au contraire,
quand ils sont proches, la plupart des microtubules cellulaires sont ancrés sur le centrosome
(et en particulier sur le centriole père). Nous avons donc proposé que la cellule puisse
modifier son réseau microtubulaire en modulant la distance intercentriolaire.
La deuxième étude présentée porte sur un comportement particulier du centriole parental en
fin de mitose : après que les cellules se sont étalées, mais alors qu'elles sont encore reliées par
un pont cytoplasmique, les deux centrioles, dans chaque cellule fille, se séparent puis le
centriole parental quitte sa position centrale et stationne pendant 10 à 30 minutes à proximité
du pont cytoplasmique intercellulaire. Le pont se pince alors de chaque côté de la pièce
intermédiaire puis se rompt lorsque le centriole parental regagne sa position près du noyau.
Nous avons pu déterminer que le pincement du pont correspondait au détachement des
faisceaux de microtubules qu'il contient. Nous avons ensuite, à l'aide de drogue qui
dépolymérisent les microtubules, suggéré l'existence d'un contrôle de la présence du centriole
parental dans le pont. Nous avons étudié des cas de cellules acentriolaires et pu mettre en
évidence des défauts liés à la cytocinèse. Enfin, il nous est apparu, à la suite d'expériences sur
des substrats plus ou moins adhésifs que l'adhésion de la cellule à son substrat est un des
paramètres clé de la régulation de cet événement de fin de mitose.
Des interprétations plus spéculatives sont proposées dans les discussions qui suivent l'exposé
des résultats, ainsi que des expériences pour les tester.

For realistic nanostructures, there are inevitably some degree ofdisorder such as impurity atoms, imperfect lattices, surfaceroughness, etc.. For situations where disorder locate randomly inthe nanostructure, any calculated quantum transport results shouldbe averaged over disorder distributions. A brute force approach isto generate many disorder configurations, calculate each of them,and then average the results. For atomistic first principlesmodeling, such a brute force averaging is computationallyprohibitive - if not impossible, to perform. It is therefore veryimportant and useful to develop a theoretical framework where thedisorder averaging is done analytically before atomic firstprinciples analysis is carried out.In this thesis, we have developed such a first principlesnon-equilibrium quantum transport theory and its associated modelingsoftware for predicting disorder scattering in nano-electronicdevices. Our theoretical formalism is based on carrying out densityfunctional theory (DFT) within the Keldysh non-equilibrium Green'sfunction (NEGF) framework, and a non-equilibrium vertex correction(NVC) theory for handling disorder configurational average at thenon-equilibrium density matrix level. In our theory, we use thecoherent potential approximation to calculate disorder averaging ofthe device Hamiltonian and one particle Green's functions, and useNVC to calculate correlated multiple impurity scattering at thenon-equilibrium density matrix level. After the NEGF-DFT-NVCself-consistent calculation is converged, we calculate thetransmission coefficients by a second, unavoidable, vertexcorrection. The NEGF-DFT-NVC theory allows us to predictnon-equilibrium quantum transport properties of nanoelectronicdevices with atomistic disorder from first principles without anyphenomenological parameters. The theory and implementation detailsare presented.We have applied the NEGF-DFT-NVC method to investigate severalimportant problems associated with disorder scattering innano-electronic device systems. These include interface roughnessscattering in Fe/vacuum/Fe magnetic tunnel junctions; the diffusivescattering of carriers due to oxygen vacancies in Fe/MgO/Fe magnetictunnel junctions; the surface roughness scattering that enhancesresistivity of copper interconnect wires; and effects of barrierlayer coating for Cu interconnects. Our investigations reveal veryimportant role played by the atomic level defects and impurities toboth equilibrium and nonequilibrium quantum transport properties,and results compare favorably with the corresponding experimentaldata.
Dans le cas de nanostructures concrètes, un certain degré de désordre apparaît inévitable tel que la présence d'impuretés, de structures cristallines imparfaites, de surfaces rugueuses, etc. Dans les situations où le désordre se matérialise aléatoirement dans la nanostructure, tout calcul de transport quantique devrait être réalisé en tant que moyenne sur plusieurs distributions désordonnées. Une approche par force brute consiste à générer plusieurs configurations désordonnées, calculer les propriétés d'intérêt pour chacune d'entre elles, et ensuite effectuer la moyenne des résultats. Dans le cas de la modélisation atomique à partir des principes premiers, une telle moyenne par force brute est prohibitive en terme de temps de calcul - sinon impossible. Il est ainsi très important et utile de développer un cadre théorique où la moyenne de désordre est faite analytiquement avant que l'analyse par les principes premiers ne soit effectuée. Dans cette thèse, nous avons développé une telle théorie de transport quantique hors équilibre à partir des principes premiers et le logiciel de modélisation associé pour la prédiction de la diffusion par désordre dans des dispositifs nanoélectroniques. Notre formalisme théorique est basé sur l'utilisation de la théorie de la fonctionnelle de densité (DFT) dans le cadre de la fonction de Green hors équilibre de Keldysh(NEGF), et sur l'emploi d'une correction de sommet hors équilibre (NVC) pour le traitement des moyennes configurationnelles de désordre au niveau de la matrice de densité hors équilibre. Dans notre théorie, nous utilisons l'approximation du potentiel cohérent afin de calculer les moyennes de désordre de l'Hamiltonien du dispositif et les fonctions de Green à une particule, et nous utilisons la NVC pour calculer la diffusion par impuretés multiples corrélée au niveau de la matrice de densité hors équilibre. Après que le calcul auto-cohérent NEGF-DFT-NVC ait convergé, nous calculons les coefficients de transmission par le biais d'une seconde correction de sommet inévitable. La théorie NEGF-DFT-NVC nous permet de prédire les propriétés de transport quantique hors équilibre de dispositifs nanoélectroniques avec désordre au niveau atomique à partir des principes premiers sans aucun paramètre phénoménologique. La théorie et les détails d'implémentation sont présentés dans ce travail. Nous avons appliqué la méthode NEGF-DFT-NVC afin d'examiner plusieurs problèmes importants associés à la diffusion par désordre dans des systèmes de dispositif nanoélectronique. Cela inclut la diffusion par rugosité de surface dans des jonctions tunnel magnétiques Fe/vide/Fe; la diffusion due à des lacunes d'oxygène dans des jonctions tunnel magnétiques Fe/MgO/Fe; la diffusion par rugosité de surface qui décuple la resistivité de fils deconnexion en cuivre; et les effets des revêtements couche barrière pour des connexionsen Cu. Notre étude révèle le rôle très important joué par les défauts de niveau atomique et les impuretés vis-à-vis des propriétés de transport quantique à la fois en équilibre et hors équilibre, et les résultats se comparent favorablement aux données expérimentales correspondantes.

This work is principally concerned with the operator approach to the orbifold compactification of the bosonic string. Of particular importance to operator formalism is the con formal structure and the operator product expansion. These are introduced and discussed in detail. The Frenkel-Kac-Segal mechanism is then examined and is shown to be a consequence of the duality of dimension one operators of an analytic bosonic string compactified on a certain torus. Possible generalizations to higher dimension operators are discussed, this includes the cross-bracket algebra which plays a central role in the vertex operator representation of Griess's algebra, and hence the Fischer-Griess Monster Group. The mechanism of compactification is then extended to orbifolds. The exposition includes a detailed account of the twisted sectors, especially of the zero-modes and the twisted operator cocycles. The conformal structure, vertex operators and correlation functions for twisted strings are then introduced. This leads to a discussion of the vertex operators which represent the emission of untwisted states. It is shown how these operators generate Kac-Moody algebras in the twisted sectors. The vertex operators which insert twisted states are then constructed, and their role as intertwining operators is explained. Of particular importance in this discussion is the role of the operator cocycles, which are seen to be crucial for the correct working of the twisted string emission vertices. The previously established formalism is then applied in detail to the reflection twist. This includes an explicit representation of the twisted operator cocycles by elements of an appropriate Clifford algebra and the elucidation of the operator algebra of the twisted emission vertices, for the ground and first excited states in the twisted sector. This motivates the 'enhancement mechanism', a generalization of the Frenkel-Kac-Segal mechanism, involving twisted string emission vertices, in dimensions 8, 16 and 24. associated with rank 8 Lie algebras, rank 16 Lie algebras and the cross-bracket algebra for the Leech lattice, respectively. Some of the relevant characters of the 'enhanced" modules are determined, and the connection of the cross-bracket algebra to the phenomenon of 'Monstrous Moonshine' and the Monster Group is explained. Algebra enhancement is then discussed from the greatly simplified shifted picture and extensions to higher order twists are considered. Finally, a comparison of this work with other recent research is given. In particular, the connection with the path integral formalism and the extension to general asymmetric orbifolds is discussed. The possibility of reformulating the moonshine module in a 'covaxiant' twenty-six dimensional setting is also considered.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 133-134).
We generalize Zhu's theorem on modular invariance of characters of vertex operator algebras (VOAs) to the setting of vertex operator superalgebras (VOSAs) with rational, rather than integer, conformal weights. To recover SL₂ (Z)-invariance, it turns out to be necessary to consider characters of twisted modules. Initially we assume our VOSA to be rational, then we replace rationality with a different (weaker) condition. We regain SL₂(Z)-invariance by including certain 'logarithmic' characters. We apply these results to several examples. Next we define and study 'higher level twisted Zhu algebras' associated to a VOSA. Using a novel construction we compute these algebras for some well known VOAs.
by Jethro Van Ekeren.
Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
Includes bibliographical references (p. 149-151).
We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields. Given a strongly conformal SUSY vertex algebra V and a supercurve X, we construct a vector bundle [ ... ] on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle [ ... ] corresponding to a SUSY vertex algebra, carries the structure of a chiral algebra.
by Reimundo Heluani.
Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 125-129).
Suppose we are given a gigantic communication network, but are only interested in a small number of nodes (clients). There are many routing problems we could be asked to solve for our clients. Is there a much smaller network - that we could write down on a sheet of paper and put in our pocket - that approximately preserves all the relevant communication properties of the original network? As we will demonstrate, the answer to this question is YES, and we call this smaller network a vertex sparsifier. In fact, if we are asked to solve a sequence of optimization problems characterized by cuts or flows, we can compute a good vertex sparsifier ONCE and discard the original network. We can run our algorithms (or approximation algorithms) on the vertex sparsifier as a proxy - and still recover approximately optimal solutions in the original network. This novel pattern saves both space (because the network we store is much smaller) and time (because our algorithms run on a much smaller graph). Additionally, we apply these ideas to obtain a master theorem for graph partitioning problems - as long as the integrality gap of a standard linear programming relaxation is bounded on trees, then the integrality gap is at most a logarithmic factor larger for general networks. This result implies optimal bounds for many well studied graph partitioning problems as a special case, and even yields optimal bounds for more challenging problems that had not been studied before. Morally, these results are all based on the idea that even though the structure of optimal solutions can be quite complicated, these solution values can be approximated by crude (even linear) functions.
by Ankur Moitra.
Ph.D.

We investigate an alternative formulation of quantum field theory that elevates the Wilson- Zimmermann operator product expansion (OPE) to an axiom of the theory. We observe that the information contained in the OPE coefficients may be straightforwardly repackaged into "vertex operators". This way of formulating quantum field theory has quite obvious similarities to the theory of vertex algebras. As examples of this framework, we discuss the free massless boson in D dimensions and the massless Thirring model. We set up perturbation theory for vertex algebras. We discuss a general theory of perturbations of vertex algebras, which is similar to the Hochschild cohomology describing the deformation theory of ordinary algebras. We pass on to a more explicit discussion by looking at perturbations of the free massless boson in D dimensions. The perturbations we consider correspond to some interaction Lagrangian P(