Preferential attachment networks with power law degree sequence undergo a phase transition when the power law exponent τ changes. For τ > 3 typical distances in the network are logarithmic in the size of the network and for 2 < τ < 3 they are doubly logarithmic. In this thesis, we identify the correct scaling constant for τ ∈ (2, 3) and discover a surprising dichotomy between preferential attachment networks and networks without preferential attachment. This contradicts previous conjectures of universality. Moreover, using a model recently introduced by Dereich and Mörters, we study the critical behaviour at τ = 3, and establish novel results for the scale of the typical distances under lower order perturbations of the attachment function.

Complex networks are composed of a large number of interacting nodes. Examples of complex networks include the topology of the Internet, connections between websites or web pages in the World Wide Web (WWW), and connections between participants in social networks.Due to their ubiquity, modeling complex networks is importantfor answering many research questions that cannot be answered without a mathematical model. For example, mathematical models of complex networks can be used to find the most vulnerable nodes to protect during a virus attack in theInternet, to predict connections between websites in the WWW, or to find members of different communities insocial networks. Researchers have analyzed complex networksand concluded that they are distinguished from other networks by four specific statistical properties. These four statistical properties are commonly known in this field as: (i) thesmall world effect,(ii) high average clustering coefficient, (iii) scale-free power law degree distribution, and (iv) emergence of community structure. These four statistical properties are further described later in this dissertation. Mostmodels used to generate complex networks attempt to produce networks with these statistical properties. Additionally, most of these network models generate homogeneous complex networks where all the networknodes are considered to have the same properties. Homogenous complex networks neglect the heterogeneous nature ofthe nodes in many complexnetworks. Moreover, somemodels proposed for generating heterogeneous complexnetworks are not general as they make specific assumptions about the properties of the network.Including heterogeneity in the connection algorithm of a modelwould makeitmore suitable for generating the subset of complex networks that exhibit selective linking.Additionally, all modelsproposed, to date, for generating heterogeneous complex networks do not preserve all four of the statistical properties of complexnetworks stated above. Thus, formulation of a model for the generation of general heterogeneous complex networkswith characteristics that resemble as much as possible the statistical properties common to the real-world networks that have received attention from the research community is still an open research question. In this work, we propose two new types of models to generate heterogeneous complex networks. First, we introduce the Integrated Attribute Similarity Model (IASM). IASM uses preferential attachment(PA) to connect nodes based on a similarity measure for node attributes combined with a node's structural popularity measure. IASM integrates the attribute similarity measure and a structural popularity measure in the computation of the connection function used to determine connectionsbetween each arriving (newly created) node and the existing(previously created or old) network nodes. IASM is also the first model known to assign an attribute vector having more than one element to each node, thus allowing different attributes per node in the generated complex network. Networks generated using IASM have a power law degree distribution and preserve the small world phenomenon. IASM models are enhanced to increase their clustering coefficient using a triad formation step (TFS). In a TFS, a node connects to the neighbor of the node to which it was previously connected through preferential attachment, thus forming a triad. The TFS increases the number of triads that are formed in the generated network which increases the network's average clustering coefficient. We also introduce a second novel model,the Settling Node Adaptive Model (SNAM). SNAM reflects the heterogeneous nature of connectionstandard requirements for nodes. The connectionstandard requirements for a noderefers to the values of attribute similarity and/or structural popularityof old node ythat node new xwould find acceptable in order to connect to node y.SNAM is novel in that such a node connection criterion is not included in any previous model for the generation of complex networks. SNAM is shown to be successful in preserving the power law degree distribution, the small world phenomenon, and the high clustering coefficient of complex networks. Next,we implement a modification to the IASM and SNAM models that results in the emergence of community structure.Nodes are classified into classes according to their attribute values. The connection algorithm is modified to include the class similarity values between network nodes. This community structure model preservesthe PL degree distribution, small world property, and does not affect average clustering coefficient values expected from both IASM and SNAM. Additionally, the model exhibits the presence of community structure having most of the connections made between nodes belonging to the same class with only a small percent of the connections made between nodes of different classes. We perform a mathematical analysis of IASM and SNAM to study the degree distribution for networks generated by both models. This mathematical analysis shows that networks generated by both models have a power law degree distribution. Finally, we completed a case study to illustrate the potential value of our research on the modeling of heterogeneous complex networks. This case study was performed on a Facebook dataset. The case study shows that SNAM, with some modifications to the connection algorithm, is capable of generating a network with almost the same characteristics as found for the original dataset. The case study providesinsight on how the flexibility of SNAM's connection algorithm can be an advantagethat makes SNAM capable of generating networks with different statistical properties. Ideas for future research areas includestudyingthe effect of using eigenvector centrality, instead of degree centrality, on the emergence of community structure in IASM; usingthe nodeindex as an indication for its order of arrival to the network and distributing added connections fairly among networknodes along the life of the generated network; experimenting with the nature of attributesto generatea more comprehensive model; and usingtime sensitive attributes in the models, where the attribute can change its value with time, / Ph. D.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24039号 / 情博第795号 / 新制||情||134(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 加納 学 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Um dos objetivos das próximas gerações dos sistemas de comunicação é permitir que os usuários acessem e distribuam um ou mais serviços a qualquer hora, em qualquer lugar, independentemente do tipo de terminal (telefone convencional, telefone celular, assistentes pessoais digitais, notebooks, dentre outros) ou da tecnologia da rede de acesso utilizados. Esse cenário é denominado convergência de serviços utilizando-se redes heterogêneas, e em tal realidade, as arquiteturas de qualidade de serviço existentes em cada uma das tecnologias dos sistemas de comunicação não oferecem mecanismos de interoperabilidade e em diversos casos não há controle sob os fluxos de dados uma vez admitido na infraestrutura do sistema de comunicação, assim como questões de handover heterogêneo não são tratadas. A tese propõe uma arquitetura para controle de Qualidade de Serviço para um ambiente heterogêneo composto de backbones IP e redes de acesso de diversas tecnologias, sendo tal arquitetura composta de agentes autônomos e distribuídos nos equipamentos de um sistema de comunicação; assim como.controles baseados no comportamento de uma região de um sistema de comunicação e apoiados na teoria e princípios de sistemas complexos. Os agentes da arquitetura proposta utilizando o princípio de preferential attachment mostraram-se eficientes na determinação do caminho de melhor condição de qualidade de serviços. Os componentes da arquitetura proposta estão localizados em cada equipamento de comunicação, desde o dispositivo do usuário até o provedor de serviços. As medições realizadas pelos agentes e utilizando um algoritmo baseado no conceito de preferential attachment permitiram ao agente alterar o caminho de um fluxo de dados durante sua transmissão para outros caminhos que apresentaram condições mais adequadas de acordo com os parâmetros de QoS. A decisão é baseada no contrato de qualidade de serviço especificado entre usuário e provedor de serviço e, considerando sob controle todos os elementos envolvidos na comunicação; tem-se controle distribuído de qualidade de serviço fim a fim. / One of the targets of the next generation communication systems is to provide access to any service, to any user, anytime, anywhere, regardless the access network technology or type of user device (mobile phone, PDA, personal computer, and so on). This scenario is called convergence of services by heterogeneous networks, and in such scenario quality of service mechanisms presented in legacy communication systems do not provide mechanisms for interoperability between communication systems nor control data flows after control admission in the border of the communication systems. The heterogeneous handover is also not handled by such QoS architectures. This thesis proposes a QoS control architecture for an heterogeneous communication systems composed by IP backbones and several access networks for several kind of technologies. This architecture is composed by a multiagent system and has controls based on the local behavior of the communication system and supported by complex systems theory. The agent decision algorithm is based on preferential attachment concept and the experimentation results indicate that agents could identify a better path to handle a data flow according to QoS parameters. The agents decided to change the path used to transmit the flow data autonomously and according to quality of service contract between user and service provider. The measurements in the test based on preferential attachment algorithm was useful in order agent change flow data path during data flow transmission to other paths with better conditions according to QoS requisites. The agent decision is based on the parameter values defined between end user and service provider. Considering the control elements from proposed architecture it was achieved end-to-end distributed control.

Um dos objetivos das próximas gerações dos sistemas de comunicação é permitir que os usuários acessem e distribuam um ou mais serviços a qualquer hora, em qualquer lugar, independentemente do tipo de terminal (telefone convencional, telefone celular, assistentes pessoais digitais, notebooks, dentre outros) ou da tecnologia da rede de acesso utilizados. Esse cenário é denominado convergência de serviços utilizando-se redes heterogêneas, e em tal realidade, as arquiteturas de qualidade de serviço existentes em cada uma das tecnologias dos sistemas de comunicação não oferecem mecanismos de interoperabilidade e em diversos casos não há controle sob os fluxos de dados uma vez admitido na infraestrutura do sistema de comunicação, assim como questões de handover heterogêneo não são tratadas. A tese propõe uma arquitetura para controle de Qualidade de Serviço para um ambiente heterogêneo composto de backbones IP e redes de acesso de diversas tecnologias, sendo tal arquitetura composta de agentes autônomos e distribuídos nos equipamentos de um sistema de comunicação; assim como.controles baseados no comportamento de uma região de um sistema de comunicação e apoiados na teoria e princípios de sistemas complexos. Os agentes da arquitetura proposta utilizando o princípio de preferential attachment mostraram-se eficientes na determinação do caminho de melhor condição de qualidade de serviços. Os componentes da arquitetura proposta estão localizados em cada equipamento de comunicação, desde o dispositivo do usuário até o provedor de serviços. As medições realizadas pelos agentes e utilizando um algoritmo baseado no conceito de preferential attachment permitiram ao agente alterar o caminho de um fluxo de dados durante sua transmissão para outros caminhos que apresentaram condições mais adequadas de acordo com os parâmetros de QoS. A decisão é baseada no contrato de qualidade de serviço especificado entre usuário e provedor de serviço e, considerando sob controle todos os elementos envolvidos na comunicação; tem-se controle distribuído de qualidade de serviço fim a fim. / One of the targets of the next generation communication systems is to provide access to any service, to any user, anytime, anywhere, regardless the access network technology or type of user device (mobile phone, PDA, personal computer, and so on). This scenario is called convergence of services by heterogeneous networks, and in such scenario quality of service mechanisms presented in legacy communication systems do not provide mechanisms for interoperability between communication systems nor control data flows after control admission in the border of the communication systems. The heterogeneous handover is also not handled by such QoS architectures. This thesis proposes a QoS control architecture for an heterogeneous communication systems composed by IP backbones and several access networks for several kind of technologies. This architecture is composed by a multiagent system and has controls based on the local behavior of the communication system and supported by complex systems theory. The agent decision algorithm is based on preferential attachment concept and the experimentation results indicate that agents could identify a better path to handle a data flow according to QoS parameters. The agents decided to change the path used to transmit the flow data autonomously and according to quality of service contract between user and service provider. The measurements in the test based on preferential attachment algorithm was useful in order agent change flow data path during data flow transmission to other paths with better conditions according to QoS requisites. The agent decision is based on the parameter values defined between end user and service provider. Considering the control elements from proposed architecture it was achieved end-to-end distributed control.

Between 1997 and 2009, 47 major defense acquisition programs experienced cost overruns of at least 15% or 30% over their current or original baseline estimates, respectively (GAO, 2011, p. 1). Known formally as a Nunn-McCurdy breach (GAO, 2011, p. 1), the reasons for this excessive growth are myriad, although nearly 70% of the cases identified engineering and design issues as a contributing factor (GAO, 2011, p. 5). Accordingly, Congress legislatively acknowledged the need for change in 2009 with the passage of the Weapon Systems Acquisition Reform Act (WSARA, 2009), which mandated additional rigor and accountability in early life cycle (or Pre-Milestone A) cost estimation. Consistent with this effort, the Department of Defense has recently required more system specification earlier in the life cycle, notably the submission of detailed architectural models, and this has created opportunities for new approaches. In this dissertation, I describe my effort to transform one such model (or view), namely the SV-3, into computational knowledge that can be leveraged in Pre-Milestone A cost estimation and risk analysis. The principal contribution of my work is Algorithm 3-a novel, network science-based method for estimating the cost of unforeseen architectural growth in defense programs. Specifically, using number theory, network science, simulation, and statistical analysis, I simultaneously find the best fitting probability mass functions and strengths of preferential attachment for an incoming subsystem's interfaces, and I apply blockmodeling to find the SV-3's globally optimal macrostructure. Leveraging these inputs, I use Monte Carlo simulation and the Constructive Systems Engineering Cost Model to estimate the systems engineering effort required to connect a new subsystem to the existing architecture. This effort is chronicled by the five articles given in Appendices A through C, and it is summarized in Chapter 2.In addition to Algorithm 3, there are several important, tangential outcomes of this work, including: an explicit connection between Model Based System Engineering and parametric cost modeling, a general procedure for organizations to improve the measurement reliability of their early life cycle cost estimates, and several exact and heuristic methods for the blockmodeling of one-, two-, and mixed-mode networks. More generally, this research highlights the benefits of applying network science to systems engineering, and it reinforces the value of viewing architectural models as computational objects.

YouTube is the second largest social media platform in the world, with a multitude of popularchannels which combine politicised commentary with news reporting. The platform providesdirect accessibility to data which makes it possible for the commentators to adjust theircontent to reach wider audiences, however done to an extreme could mean that the creatorspick topics which are the most financially beneficial or lead to fame. If this were the case itwould highlight populist newsmaking and the mechanisms behind it. To investigate theproduction-consumption interaction, data from the 10 most popular channels for 2021 wascollected. Using latent Dirichlet allocation and preferential attachment analysis, the effect ofcumulative advantage, and whether topic choice was driven by views were measured. Apositive feedback loop, where prevalent topics become more prevalent, was found in all buttwo channels, but picking topics which generated more views was only present for onechannel. The findings imply that the top political news commentators over a year have a set oftopics which they return to at a high degree, but choosing the topics which simply are themost popular for the time is not a general feature.

Entendimento de processos que levem ao surgimento de opiniões extremas é valioso na prevenção de atos de violência. Os modelos são ferramentas úteis para identificar possíveis padrões relacionados a estes processos. No entanto, modelos discretos ou contínuos com confiança limitada não se mostram adequados para estudar dinâmicas caracterizadas pela divergência de opiniões. É proposta uma extensão cultural do modelo de Opiniões Contínuas e Ações Discretas (CODA) com múltiplos assuntos alternados por um mecanismo de ligação preferencial. Os agentes são influenciados não só em suas opiniões, mas também nas importâncias que atribuem aos diferentes assuntos. As principais características do modelo são o surgimento de preferências e consensos locais, aos quais estão associadas as opiniões mais extremas. Há, em contrapartida, persistência de opiniões brandas nos temas menos preferidos. O estudo do espaço paramétrico do modelo revelou que modificações diminuindo a localidade das interações aumentam maiorias e amenizam opiniões. Duas estratégias distintas de debate foram testadas. Zelotes têm poder de conversão aumentado quando dispersos. Evitadores minimizam o número de interações indesejável se agrupados. Foram esboçadas abordagens para inserção de efeitos da mídia na dinâmica / Understanding processes leading to extremism is invaluable to prevent violence outbursts. Models are useful tools that allow for identifying patterns related to those processes. Nevertheless, discrete models and bounded-confidence continuous models are unfit for studying diversion-based dynamics. We present a cultural extension of CODA model, with multiple subjects selected through a preferential attachment rule. Agents are influenced in their opinions and relevance attributed to different subjects. The most notable results of the dynamics are the establishment of local subject preferences and consensus, associated with more extreme opinions. On the other hand, there is persistence of immature undeveloped opinion in the locally less regarded subjects. The study of parametric space has shown that settings reducing the locality of interactions both increase the majority size and make opinions less extreme. Two distinct debate strategies were simulated. Zealots increase conversions when spread throughout the network. In contrast, subject avoiders decrease the number of unwanted interactions by grouping together. Some ideas for introducing media influence to the model were outlined

Entendimento de processos que levem ao surgimento de opiniões extremas é valioso na prevenção de atos de violência. Os modelos são ferramentas úteis para identificar possíveis padrões relacionados a estes processos. No entanto, modelos discretos ou contínuos com confiança limitada não se mostram adequados para estudar dinâmicas caracterizadas pela divergência de opiniões. É proposta uma extensão cultural do modelo de Opiniões Contínuas e Ações Discretas (CODA) com múltiplos assuntos alternados por um mecanismo de ligação preferencial. Os agentes são influenciados não só em suas opiniões, mas também nas importâncias que atribuem aos diferentes assuntos. As principais características do modelo são o surgimento de preferências e consensos locais, aos quais estão associadas as opiniões mais extremas. Há, em contrapartida, persistência de opiniões brandas nos temas menos preferidos. O estudo do espaço paramétrico do modelo revelou que modificações diminuindo a localidade das interações aumentam maiorias e amenizam opiniões. Duas estratégias distintas de debate foram testadas. Zelotes têm poder de conversão aumentado quando dispersos. Evitadores minimizam o número de interações indesejável se agrupados. Foram esboçadas abordagens para inserção de efeitos da mídia na dinâmica / Understanding processes leading to extremism is invaluable to prevent violence outbursts. Models are useful tools that allow for identifying patterns related to those processes. Nevertheless, discrete models and bounded-confidence continuous models are unfit for studying diversion-based dynamics. We present a cultural extension of CODA model, with multiple subjects selected through a preferential attachment rule. Agents are influenced in their opinions and relevance attributed to different subjects. The most notable results of the dynamics are the establishment of local subject preferences and consensus, associated with more extreme opinions. On the other hand, there is persistence of immature undeveloped opinion in the locally less regarded subjects. The study of parametric space has shown that settings reducing the locality of interactions both increase the majority size and make opinions less extreme. Two distinct debate strategies were simulated. Zealots increase conversions when spread throughout the network. In contrast, subject avoiders decrease the number of unwanted interactions by grouping together. Some ideas for introducing media influence to the model were outlined

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a (sub-)linear function of the indegree of the older vertex at that time. We provide a limit theorem with rates of convergence for the distribution of a vertex, chosen uniformly at random, as the number of vertices tends to infinity. To do so, we develop Stein's method for a new class of limting distributions including power-laws. Similar, but slightly weaker results are shown to be deducible using coupling techniques. Concentrating on a specific preferential attachment model we also show that the outdegree distribution asymptotically follows a Poisson law. In addition, we deduce a central limit theorem for the number of isolated vertices. We thereto construct a size-bias coupling which in combination with Stein’s method also yields bounds on the distributional distance.