Redes complexas têm sido cada vez mais utilizadas para a modelagem e análise dos mais diversos sistemas da natureza. Um dos tópicos mais estudados na área de redes está relacionado com a identificação e caracterização de grupos de nós mais conectados entre si do que com o restante da rede, chamados de comunidades. Neste trabalho, mostramos que comunidades podem ser caracterizadas por quatro classes gerais de propriedades, relacionadas com a topologia interna, dinâmica interna, fronteira topológica, e fronteira dinâmica das comunidades. Verificamos como estas diferentes características influenciam em dinâmicas ocorrendo sobre a rede. Em especial, estudamos o inter-relacionamento entre a topologia e a dinâmica das comunidades para cada uma dessas quatro classes de atributos. Mostramos que certas propriedades provocam a alteração desse inter-relacionamento, dando origem ao que chamamos de comportamento específico de comunidades. De forma a apresentarmos e analisarmos este conceito nos quatro casos considerados, estudamos as seguintes combinações topológicas e dinâmicas. Na primeira, investigamos o passeio aleatório tradicional ocorrendo sobre redes direcionadas, onde mostramos que a direção das conexões entre comunidades é o principal fator de alteração no relacionamento topologia-dinâmica. Aplicamos a metodologia proposta em uma rede real, definida por módulos corticais de animais do gênero Macaca. O segundo caso estudado aborda o passeio aleatório enviesado ocorrendo sobre redes não direcionadas. Mostramos que o viés associado às transições da dinâmica se tornam cada vez mais relevantes com o aumento da modularidade da rede. Verificamos também que a descrição da dinâmica a nível de comunidades possibilita modelarmos com boa acurácia o fluxo de passageiros em aeroportos. A terceira análise realizada envolve a dinâmica neuronal integra-e-dispara ocorrendo sobre comunidades geradas segundo o modelo Watts-Strogatz. Mostramos que as comunidades podem possuir não apenas diferentes níveis de ativação dinâmica, como também apresentar diferentes regularidades de sinal dependendo do parâmetro de reconexão utilizado na criação das comunidades. Por último, estudamos a influência das posições de conexões inibitórias na dinâmica integra-e-dispara, onde mostramos que a inibição entre comunidades dá origem a interessantes variações na ativação global da rede. As análises realizadas revelam a importância de, ao modelarmos sistemas reais utilizando redes complexas, considerarmos alterações de parâmetros do modelo na escala de comunidades. / There has been a growing interest in modeling diverse types of real-world systems through the tools provided by complex network theory. One of the main topics of research in this area is related to the identification and characterization of groups, or communities, of nodes more densely connected between themselves than with the rest of the network. We show that communities can be characterized by four general classes of features, associated with the internal topology, internal dynamics, topological border, and dynamical border of the communities. We verify that these characteristics have direct influence on the dynamics taking place over the network. Particularly, for each considered class we study the interdependence between the topology and the dynamics associated with each network community. We show that some of the studied properties can influence the topology-dynamics interdependence, inducing what we call the communities specific behavior. In order to present and characterize this concept on the four considered classes, we study the following combinations of network topology and dynamics. We first investigate traditional random walks taking place on a directed network. We demonstrate that, for this dynamics, the direction of the edges between communities represents the main method for the modification of the topology-dynamics relationship. We apply the developed approach on a real-world network, defined by the connectivity between cortical regions in primates of the Macaca genus. The second studied case considers the biased random walk on undirected networks. We demonstrate that the transition bias of this dynamics becomes more relevant for higher network modularity. In addition, we show that the biased random walk can be used to model with good accuracy the passenger flow inside the communities of two airport networks. The third analysis is done on a neuronal dynamics, called integrate-and-fire, applied to networks composed of communities generated by the Watts-Strogatz model. We show that the considered communities can not only posses distinct dynamical activation levels, but also yield different signal regularity. Lastly, we study the influence of the positions of inhibitory connections on the integrate-and-fire dynamics. We show that inhibitory connections placed between communities can have a non-trivial influence on the global behavior of the dynamics. The current study reveals the importance of considering parameter variations of network models at the scale of communities.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-19T14:12:35Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Pablo dos Santos Borges - 2014.pdf: 2427043 bytes, checksum: 437e002ed7ce19054628b4d9d4be9a92 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-19T14:12:50Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Pablo dos Santos Borges - 2014.pdf: 2427043 bytes, checksum: 437e002ed7ce19054628b4d9d4be9a92 (MD5) / Made available in DSpace on 2015-01-19T14:12:50Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Pablo dos Santos Borges - 2014.pdf: 2427043 bytes, checksum: 437e002ed7ce19054628b4d9d4be9a92 (MD5) Previous issue date: 2014-07-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The following work was carried out over the game of odd or even. By exploring this game, we analyze a dispute between two players, one being a strategist and another layman. In the rst part were successive bets, in which the strategist had advantage over the layman. Then play until someone stay without money. The methodology is investigative and directed by activities that seek to show the importance of this knowledge in cognitive training of the student, giving it a theoretical re ection on the practice experienced and stimulating logical reasoning mathematical experiences. The work was divided into parts. Before starting the detail work, we use a theoretical basis directed to Game Theory and Probability. In the course of this, we present the relevant problems of work results. Shortly following section, we have four draft classes using the game of odd or even. One of which was performed at the High School students. / O trabalho a seguir, foi realizado em cima do Jogo do Par ou Ímpar. Ao explorar esse jogo, analisamos uma disputa entre dois jogadores, sendo um deles estrategista e o outro leigo. Na primeira parte consideramos sucessivas apostas, nais quais, o estrategista tem vantagem probabilística sobre o leigo. Depois, consideramos o caso onde os jogadores jogam até que alguém que sem dinheiro. A metodologia é investigativa e direcionada por atividade que buscam mostrar a importância desse conhecimento na formação cognitiva do aluno, propiciando-lhe uma re exão teórico-prática acerca das experiências vivenciadas e estimulando o raciocínio lógico matemático. O trabalho foi dividido em partes. Antes de iniciar o detalhamento do trabalho, usamos um embasamento teórico direcionado a Teoria dos Jogos e a Probabilidade. No desenrolar deste, apresentamos resultados pertinentes a problemática do trabalho. Logo em seguida, temos quatro propostas de aulas utilizando o jogo do Par ou Ímpar. Sendo que uma delas foi executada aos alunos do Ensino Médio.

Orientador: Lee Luan Ling / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-20T02:24:35Z (GMT). No. of bitstreams: 1 YakovNae_M.pdf: 7990917 bytes, checksum: 122c511d9ba839a2f1464fbe7fca09b4 (MD5) Previous issue date: 2011 / Resumo: Gerência de armazenamento em Redes de Sensores Sem Fio (RSSF) é uma questão muito crítica. Além da RSSFs conter uma vasta quantidade de armazenamento agregada, ela não pode ser usada inteiramente. Portanto, o sistema inteiro falha quando o primeiro sensor tem sua capacidade de armazenamento esgotada, deixando uma grande capacidade de armazenamento inutilizada. Sugere-se que os sensores devem-se ser capazes de detectar as capacidades de armazenamentos inutilizadas, para prolongar as suas funcionalidades. Entretanto, em RSSF de larga escala isso pode ser muito difícil uma vez que os sensores podem não ter conhecimento da existência dos outros. Neste trabalho apresenta-se duas principais contribuições: otimização da capacidade total de armazenamento para RSSF em grande escala e uma nova abordagem de roteamento - Deterministic "Random" Walk (Passeio "Aleatório" Determinístico). Apresenta-se um novo modelo de armazenamento via construção "sob demanda" de Cadeias de Armazenamento Distribuídas ( Distributed Storage Chains (DSC). Estas cadeias representam parcerias entrem os sensores que podem compartilhar suas capacidades de armazenamento. Resultando, os sensores não estão sujeitos às suas limitações de armazenamento, mas para à capacidade total de armazenamento disponível no sistema. Constrói-se estas cadeia via passeio determinístico sobre a topologia sugerida. Todavia, mostra-se que estes passeios apresentam um comportamento aleatório que é muito eficiente em termos de localização de capacidade de armazenamento disponível / Abstract: Storage management of Wireless Sensor Networks (WSN) is a very critical issue in terms of system's lifetime. While WSNs host a vast storage capacity on the aggregate, that capacity cannot be used entirely. Eventually, the entire network may fail when the first sensor has its own storage capacity depleted, leaving behind a large amount of unutilized storage capacity. We suggest that sensors should be able to detect unutilized storage capacity in order to prolong their functionality. However, for large scale WSNs this can be a difficult task, since sensors may not be aware of the existence of others. This work has two main contributions: an optimization of the overall storage capacity for large scale WSNs and a novel routing approach of deterministic "random" walk. We present a new storage model by building "on - demand" Distributed Storage Chains (DSC). These chains represent partnership between sensors that share their storage capacity. As a result, sensors are no longer subjected to their own storage limitations but to the total amount of available storage in the WSN. We construct these chains via deterministic walks over our suggested topology. However, we show that these walks resemble the behavior of random walks and are therefore highly efficient in terms of locating available storage / Mestrado / Telecomunicações e Telemática / Mestre em Engenharia Elétrica

This diploma thesis deals with the market-making strategy's profitability analysis, tested on simulation of central order book. The theoretical part describes how the market maker quotes the price of supply and demand and mathematically proves under which circumstances this strategy is profitable. The practical part introduces a simulation of the central order book. The advantage of simulating the entire order book is that we have information about the number of market participants and quotes at any given time. It also introduces a fictitious market maker quoting the price of supply and demand at any given moment, the price being determined by the price of the previous time step. The order book is simulated in three different settings - random walk, mean-reversion and leptokurtic distribution, and it is shown that the expected profitability of the market-maker strategy is positive in all three cases.

Större företag finner det ofta svårt att sprida information om innovation och innovativa projekt. Projektet ska underlätta för företag att föra vidare och sammla in information om innovation och innovativa projekt. Detta uppnås genom utveckling av en webbsajt som kan hantera projekt. Webbsajtens funktionalitet är likt en aktiemarknad där alla användare(de anställda på företaget) kan investera i projekt som de tror har hög innovationspotential. Med hjälp av eget konstruerade algorithmer så kommer detta bli möjligt. Analyser och uträkningar utförs samt deras resultat redovisas på webbsidan. Det är en krav att varje användare registrerar sig först innan de får tillgång till webbsidan. Databasen är gjord i mySQL. Utvecklingen av algoritmen och serversidan är programmerad i PHP och SQL. Clientsidan är programmerad i HTML, CSS och JavaScrip.

On considère une marche aléatoire réelle dont les accroissements sont construits à partir d’une chaîne de Markov définie sur un espace abstrait. Sous des hypothèses de centrage de la marche et de décroissance rapide de la dépendance de la chaîne de Markov par rapport à son passé (de type trou spectral), on se propose d’étudier le premier instant pour lequel une telle marche markovienne passe dans les négatifs. Plus précisément, on établit que le comportement asymptotique de la probabilité de survie est inversement proportionnel à la racine carrée du temps. On étend également à nos modèles markoviens le résultat des marches aléatoires aux accroissements indépendants suivant : la loi asymptotique de la marche aléatoire renormalisée et conditionnée à rester positive est la loi de Rayleigh. Dans un deuxième temps, on restreint notre modèle aux cas où la chaîne de Markov définissant les accroissements de la marche aléatoire est à valeurs dans un espace d’états fini. Sous cette hypothèse et lorsque que la marche est dite non-lattice, on complète nos résultats par des théorèmes locaux pour la marche aléatoire conjointement avec le fait qu’elle soit restée positive. Enfin on applique ces développements aux processus de branchement soumis à un environnement aléatoire, lui-même défini à partir d’une chaîne de Markov à valeurs dans un espace d’états fini. On établit le comportement asymptotique de la probabilité de survie du processus dans le cas critique et les trois cas sous-critiques (fort, intermédiaire et faible) / We consider a real random walk whose increments are constructed by a Markov chain definedon an abstract space. We suppose that the random walk is centred and that the dependence of the Markov walk in its past decreases exponentially fast (due to the spectral gap property). We study the first time when the random walk exits the positive half-line and prove that the asymptotic behaviour of the survey probability is inversely proportional to the square root of the time. We extend also to our Markovian model the following result of random walks with independent increments: the asymptotic law of the random walk renormalized and conditioned to stay positive is the Rayleigh law. Subsequently, we restrict our model to the cases when the Markov chain defining the increments of the random walk takes its values on a finite state space. Under this assumption and the condition that the walk is non-lattice, we complete our results giving local theorems for the random walk conditioned to stay positive. Finally, we apply these developments to branching processes under a random environment defined by a Markov chain taking its values on a finite state space. We give the asymptotic behaviour of the survey probability of the process in the critical case and the three subcritical cases (strongly, intermediate and weakly).

Stock Prices have been modeled using a variety of techniques such as neural networks, simple regression based models and so on with limited accuracy. We attempt to use Random Walk method to model movements of stock prices with modifications to account for market sentiment. A simulator has been developed as part of the work to experiment with actual NASDAQ100 stock data and check how the actual stock values compare with the predictions. In cases of short and medium term prediction (1-3 months), the predicted prices are close to the actual values, while for longer term (1 year), the predictions begin to diverge. The Random Walk method has been compared with linear regression, average and last known value across four periods and has that the Random Walk method is no better that the conventional methods as at 95% confidence there is no significant difference between the conventional methods and Random Walk model. / Prediction of stock markets has been the research interest of many scientists around the world. Speculators who wish to make a “quick buck” as well as economists who wish to predict crashes, anyone in the financial industry has an interest in predicting what stock prices are likely to be. Clearly, there is no model which can accurately predict stock prices; else markets would be absolutely perfect! However, the problem is pertinent and any improvement in the accuracy of prediction improves the state of financial markets today. This forms the broad motivation of our study.

Nowadays, the use of mobile phones and other wireless devices has become an indispensable part of daily life. However, the focus of wireless communication is on infrastructure-based networks, making them prone to service outage if for any reason the infrastructure is overloaded or there is no network coverage. This is the case in a disaster area, where the infrastructure that supports the communication may be destroyed or could become useless. Different approaches to complement the exchange of information in these scenarios are emerging as research results. This thesis concerns Random-Walk Gossip (RWG), which is a protocol to disseminate information in disaster areas. RWG is a many-cast protocol for intermittently connected mobile ad hoc networks. The more people can communicate, the more chances of success there are. Therefore, it is useful to investigate the possibility of implementing such protocols on commodity devices. Since Symbian is currently the most widespread mobile phone operating system, this master's thesis presents the implementation of the protocol in that platform. The protocol is also implemented in Linux and Mac OS X in order to provide heterogeneity. Finally, some aspects of the performance of the protocol in different devices are analyzed, studying the CPU load, memory consumption, radio range, energy consumption and response time of different devices using the protocol. The studies show that the use of the RWG protocol in both laptops and handheld devices is viable.

The main objects of interest in this thesis are relatively hyperbolic groups. We will study some of their geometric properties, and we will be especially concerned with geometric properties of their boundaries, like linear connectedness, avoidability of parabolic points, etc. Exploiting such properties will allow us to construct, under suitable hypotheses, quasi-isometric embeddings of hyperbolic planes into relatively hyperbolic groups and quasi-isometric embeddings of relatively hyperbolic groups into products of trees. Both results have applications to fundamental groups of 3-manifolds. We will also study probabilistic properties of relatively hyperbolic groups and of groups containing ``hyperbolic directions'' despite not being relatively hyperbolic, like mapping class groups, Out(F<sub>n</sub>), CAT(0) groups and subgroups of the above. In particular, we will show that the elements that generate the ``hyperbolic directions'' (hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in mapping class groups, fully irreducible elements in Out(F_n) and rank one elements in CAT(0) groups) are generic in the corresponding groups (provided at least one exists, in the case of CAT(0) groups, or of proper subgroups). We also study how far a random path can stray from a geodesic in the context of relatively hyperbolic groups and mapping class groups, but also of groups acting on a relatively hyperbolic space. We will apply this, for example, to show properties of random triangles.

This thesis proposes a new chroma keying method that can automatically detect background, foreground, and unknown regions. For background color detection, we use K-means clustering in color space to calculate the limited number of clusters of background colors. We use spatial information to clean the background regions and minimize the unknown regions. Our method only needs minimum inputs from user. For unknown regions, we implement the alpha matte based on Wang's robust matting algorithm, which is considered one of the best algorithms in the literature, if not the best. Wang's algorithm is based on modified random walk. We proposed a better color selection method, which improves matting results in the experiments. In the thesis, a detailed implementation of robust matting is provided. The experimental results demonstrate that our proposed method can handle images with one background color, images with gridded background, and images with difficult regions such as complex hair stripes and semi-transparent clothes.