A virtualização de redes é um mecanismo que permite a coexistência de múltiplas redes virtuais sobre um mesmo substrato físico. Um dos desafios de pesquisa abordados na literatura é o mapeamento eficiente de recursos virtuais em infraestruturas físicas. Embora o referido desafio tenha recebido considerável atenção, as abordagens que constituem o estado-da-arte apresentam alta taxa de rejeição, i.e., a proporção de solicitações de redes virtuais negadas em relação ao total de solicitações efetuadas ao substrato é elevada. Nesta dissertação, caracteriza-se, inicialmente, a relação entre a qualidade dos mapeamentos de redes virtuais e as estruturas topológicas dos substratos subjacentes. Avalia-se as soluções exatas de um modelo de mapeamento online sob diferentes classes de topologias de rede. A partir do entendimento dos fatores topológicos que influenciam diretamente o processo de mapeamento de redes virtuais, propõe-se uma estratégia para planejar a expansão de redes de provedores de infraestrutura de forma a reduzir consistentemente a taxa de rejeição de requisições de redes virtuais e melhor aproveitar os recursos ociosos da mesma. Os resultados obtidos evidenciam que grande parte das rejeições de redes virtuais ocorre em situações em que há grande disponibilidade de recursos, mas alguns poucos já saturados acabam inviabilizando, em função de características de conectividade do substrato, o atendimento de novas requisições. Ademais, os resultados obtidos utilizando a estratégia proposta evidenciam que o fortalecimento de partes-chave da infraestrutura levam a uma ocupação muito mais satisfatória. Uma expansão de 10% a 20% dos recursos da infraestrutura contribui para um aumento sustentado de até 30% no número de redes virtuais aceitas e de até 45% no aproveitamento dos recursos em comparação com a rede original. / Network virtualization is a mechanism that allows the coexistence of multiple virtual networks on top of a single physical substrate. One of the research challenges addressed recently in the literature is the efficient mapping of virtual resources on physical infrastructures. Although this challenge has received considerable attention, state-of-the-art approaches present, in general, a high rejection rate, i.e., the ratio between the number of denied virtual network requests and the total amount of requests is considerably high. In this thesis, we characterize the relationship between the quality of virtual network mappings and the topological structures of the underlying substrates. Exact solutions of an online embedding model are evaluated under different classes of network topologies. From the understanding of the topological factors that directly influence the virtual network embedding process, we propose an expansion strategy of physical infrastructure in order to suggest adjustments that lead to higher virtual network acceptance and, in consequence, to improved physical resource utilization. The obtained results demonstrate that most of rejections occur in situations in which a significant amount of resource is available, but a few saturated devices and links, depending on connectivity features of the physical substrate, hinder the acceptance of new requests. Moreover, the obtained results using the proposed strategy evidence that an expansion of 10% to 20% of the infrastructure resources leads to a sustained increase of up to 30% in the number of accepted virtual networks and of up to 45% in resource usage compared to the original network.

The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.

Microblog has become a central platform where people express their thoughts and opinions toward public events in China. With the sudden outbreak of coronavirus, the posts related to coronavirus are usually followed by a burst immediately in microblog volume, which provides a great opportunity to explore public sentiment about the events. In this context, sentiment analysis is helpful to explore how coronavirus affects public opinions. Deep learning has become a very popular technique for sentiment analysis. This thesis uses Bidirectional Encoder Representations from Transformers (BERT), a pre-trained unsupervised language representation model based on deep learning, to generate initial token embeddings that are further tuned by a neural network model on a supervised corpus, a sentiment classifier is constructed. We utilize data recently made available by the government of Beijing which contains 1 million blog posts from January 1 to February 20, 2020. Also, the model developed in this thesis can be used to track the sentiment variation with Weibo microblog data in the future. At the final stage, the variation of public sentiment is analyzed and presented with visualization charts of preformed people sentiment variation with the development of coronavirus in China. Comparison of the results between labeled data and all data is performed in order to explore how thoughts and opinions evolve in time. The result shows a significant growth of the negative sentiment on January 20 when a lockdown started in Wuhan, and afterward the growth becomes slower. Around February 7 when doctor Wenliang Li died, the number of negative sentiments reached its peak.

Neste trabalho estudamos o problema relacionado à construção de uma teoria quântica para uma partícula, se movendo não relativisticamente num espaço curvo, tratado como uma subvariedade de outro Euclideano, talvez dando maior ênfase ao aspecto geométrico envolvido nesta abordagem, uma vez que os demais trabalhos relacionados ao mesmo tema não o fazem. Além de mostrarmos que o consequente uso de uma teoria de sistemas vinculados não contribui para remover as ambiguidades da formulação quântica, relacionados diretamente ao ordenamento de operadores, também apresentamos, através de uma quantização específica feita sob a prescrição de Dirac, elementos que permitem não apenas construir um formalismo quântico covariante, mas também liberto de qualquer correção quântica. Em adição, fazemos alguns comentários gerais no que se refere às outras abordagens clássicas possíveis para o mesmo problema, intentando construir teorias quânticas associadas ao sistema sob consideração. / In this work we study the problem related to the construction of a quantum theory for a particle, moving non-relativistically in a curved space, treated as submanifold of the other Euclidean, maybe putting more emphasis on the geometric aspect envolved in this approach, since the rest of the works related to the subject do not. Besides showing that the consequent use of a theory of constrained systems not contributes for remove the ambiguities in the quantum formulation, related directly to the ordering of operators, we also showing, through a specific quantization made in the prescription of Dirac, elements that offers resources not only to construct a covariant quantum formalism, but also free from any quantum correction. In addition, we make some general comments in relation to other classical approaches possible for the same problem, attempting to build quantum theories associated with the system under consideration.

Network virtualization is a technology that enables multiple virtual instances to coexist on a common physical network infrastructure. This paradigm fostered new business models, allowing infrastructure providers to lease or share their physical resources. Each virtual network is isolated and can be customized to support a new class of customers and applications. To this end, infrastructure providers need to embed virtual networks on their infrastructure. The virtual network embedding is the (NP-hard) problem of matching constrained virtual networks onto a physical network. Heuristics to solve the embedding problem have exploited several policies under different settings. For example, centralized solutions have been devised for small enterprise physical networks, while distributed solutions have been proposed over larger federated wide-area networks. In this thesis we present a policy-based architecture for the virtual network embedding problem. By policy, we mean a variant aspect of any of the three (invariant) embedding mechanisms: physical resource discovery, virtual network mapping, and allocation on the physical infrastructure. Our architecture adapts to different scenarios by instantiating appropriate policies, and has bounds on embedding efficiency, and on convergence embedding time, over a single provider, or across multiple federated providers. The performance of representative novel and existing policy configurations are compared via extensive simulations, and over a prototype implementation. We also present an object model as a foundation for a protocol specification, and we release a testbed to enable users to test their own embedding policies, and to run applications within their virtual networks. The testbed uses a Linux system architecture to reserve virtual node and link capacities.

Research on social networks and understanding the interactions of the users can be modeled as a task of graph mining, such as predicting nodes and edges in networks.Dealing with such unstructured data in large social networks has been a challenge for researchers in several years. Neural Networks have recently proven very successful in performing predictions on number of speech, image, and text data and have become the de facto method when dealing with such data in a large volume. Graph NeuralNetworks, however, have only recently become mature enough to be used in real large-scale graph prediction tasks, and require proper structure and data modeling to be viable and successful. In this research, we provide a new modeling of the social network which captures the attributes of the nodes from various dimensions. We also introduce the Neural Network architecture that is required for optimally utilizing the new data structure. Finally, in order to provide a hot-start for our model, we initialize the weights of the neural network using a pre-trained graph embedding method. We have also developed a new graph embedding algorithm. We will first explain how previous graph embedding methods are not optimal for all types of graphs, and then provide a solution on how to combat those limitations and come up with a new graph embedding method.

abstract: Hyperbolic geometry, which is a geometry which concerns itself with hyperbolic space, has caught the eye of certain circles in the machine learning community as of late. Lauded for its ability to encapsulate strong clustering as well as latent hierarchies in complex and social networks, hyperbolic geometry has proven itself to be an enduring presence in the network science community throughout the 2010s, with no signs of fading into obscurity anytime soon. Hyperbolic embeddings, which map a given graph to hyperbolic space, have particularly proven to be a powerful and dynamic tool for studying complex networks. Hyperbolic embeddings are exploited in this thesis to illustrate centrality in a graph. In network science, centrality quantifies the influence of individual nodes in a graph. Eigenvector centrality is one type of such measure, and assigns an influence weight to each node in a graph by solving for an eigenvector equation. A procedure is defined to embed a given network in a model of hyperbolic space, known as the Poincare disk, according to the influence weights computed by three eigenvector centrality measures: the PageRank algorithm, the Hyperlink-Induced Topic Search (HITS) algorithm, and the Pinski-Narin algorithm. The resulting embeddings are shown to accurately and meaningfully reflect each node's influence and proximity to influential nodes. / Dissertation/Thesis / Masters Thesis Computer Science 2020

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22574号 / 情博第711号 / 新制||情||122(附属図書館) / 京都大学大学院情報学研究科社会情報学専攻 / (主査)教授 吉川 正俊, 教授 鹿島 久嗣, 教授 田島 敬史, 特定准教授 JATOWT Adam Wladyslaw / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22807号 / 情博第737号 / 新制||情||126(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 下平 英寿, 教授 田中 利幸, 教授 鹿島 久嗣 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Une classe de graphes est close par mineurs si, pour tout graphe dans la classe et tout mineur de ce graphe, le mineur est ́egalement dans la classe. Par un fameux th ́eor`eme de Robertson et Seymour, nous savons que car- act ́eriser une telle classe peut ˆetre fait `a l’aide d’un nombre fini de mineurs exclus minimaux. Ceux-ci sont des graphes qui n’appartiennent pas `a la classe et qui sont minimaux dans le sens des mineurs pour cette propri ́et ́e.Dans cette thèse, nous étudions trois problèmes à propos de classes de graphes closes par mineurs. Les deux premiers sont reliés à la caractérisation de certaines classes de graphes, alors que le troisième étudie une relation de “packing-covering” dans des graphes excluant un mineur.Pour le premier problème, nous étudions des plongements isométriques de graphes dont les arêtes sont pondérées dans des espaces métriques. Principalement, nous nous intêressons aux espaces ell_2 et ell_∞. E ́tant donné un graphe pondéré, un plongement isométrique associe à chaque sommet du graphe un vecteur dans l’autre espace de sorte que pour chaque arête du graphe le poids de celle-ci est égal à la distance entre les vecteurs correspondant à ses sommets. Nous disons qu’une fonction de poids sur les arêtes est une fonction de distances réalisable s’il existe un tel plongement. Le paramètre f_p(G) détermine la dimension k minimale d’un espace ell_p telle que toute fonction de distances réalisable de G peut être plongée dans ell_p^k. Ce paramètre est monotone dans le sens des mineurs. Nous caractérisons les graphes tels que f_p(G) a une grande valeur en termes de mineurs inévitables pour p = 2 et p = ∞. Une famille de graphes donne des mineurs inévitables pour un invariant monotone pour les mineurs, si ces graphes “expliquent” pourquoi l’invariant est grand.Le deuxième problème étudie les mineurs exclus minimaux pour la classe de graphes avec φ(G) borné par une constante k, où φ(G) est un paramètre lié au dominant des coupes d’un graphe G. Ce polyèdre contient tous les points qui, composante par composante, sont plus grands ou égaux à une combination convexe des vecteurs d’incidence de coupes dans G. Le paramètre φ(G) est égal au membre de droite maximum d’une description linéaire du dominant des coupes de G en forme entière minimale. Nous étudions les mineurs exclus minimaux pour la propriété φ(G) <= 4 et montrons une nouvelle borne sur φ(G) en termes du “vertex cover number”.Le dernier problème est d’un autre type. Nous étudions une relation de “packing-covering” dans les classes de graphes excluant un mineur. Étant donné un graphe G, une boule de centre v et de rayon r est l’ensemble de tous les sommets de G qui sont à distance au plus r de v. Pour un graphe G et une collection de boules donnés nous pouvons définir un hypergraphe H dont les sommets sont ceux de G et les arêtes correspondent aux boules de la collection. Il est bien connu que dans l’hypergraphe H, le “transversal number” τ(H) vaut au moins le “packing number” ν(H). Nous montrons une borne supérieure sur ν(H) qui est linéaire en τ(H), résolvant ainsi un problème ouvert de Chepoi, Estellon et Vaxès. / A class of graphs is closed under taking minors if for each graph in the class and each minor of this graph, the minor is also in the class. By a famous result of Robertson and Seymour, we know that characterizing such a class can be done by identifying a finite set of minimal excluded minors, that is, graphs which do not belong to the class and are minor-minimal for this property.In this thesis, we study three problems in minor-closed classes of graphs. The first two are related to the characterization of some graph classes, while the third one studies a packing-covering relation for graphs excluding a minor.In the first problem, we study isometric embeddings of edge-weighted graphs into metric spaces. In particular, we consider ell_2- and ell_∞-spaces. Given a weighted graph, an isometric embedding maps the vertices of this graph to vectors such that for each edge of the graph the weight of the edge equals the distance between the vectors representing its ends. We say that a weight function on the edges of the graph is a realizable distance function if such an embedding exists. The minor-monotone parameter f_p(G) determines the minimum dimension k of an ell_p-space such that any realizable distance function of G is realizable in ell_p^k. We characterize graphs with large f_p(G) value in terms of unavoidable minors for p = 2 and p = ∞. Roughly speaking, a family of graphs gives unavoidable minors for a minor-monotone parameter if these graphs “explain” why the parameter is high.The second problem studies the minimal excluded minors of the class of graphs such that φ(G) is bounded by some constant k, where φ(G) is a parameter related to the cut dominant of a graph G. This unbounded polyhedron contains all points that are componentwise larger than or equal to a convex combination of incidence vectors of cuts in G. The parameter φ(G) is equal to the maximum right-hand side of a facet-defining inequality of the cut dominant of G in minimum integer form. We study minimal excluded graphs for the property φ(G) <= 4 and provide also a new bound of φ(G) in terms of the vertex cover number.The last problem has a different flavor as it studies a packing-covering relation in classes of graphs excluding a minor. Given a graph G, a ball of center v and radius r is the set of all vertices in G that are at distance at most r from v. Given a graph and a collection of balls, we can define a hypergraph H such that its vertices are the vertices of G and its edges correspond to the balls in the collection. It is well-known that, in the hypergraph H, the transversal number τ(H) is at least the packing number ν(H). We show that we can bound τ(H) from above by a linear function of ν(H) for every graphs G and ball collections H if the graph G excludes a minor, solving an open problem by Chepoi, Estellon et Vaxès. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished