Academic literature on the topic 'Social networks – Mathematical models'

Traditional Public Health decision-support can benefit from the Web and social media revolution. This dissertation presents approaches to mining social media benefiting public health epidemiology. Through discovery and analysis of trends in Influenza related blogs, a correlation to Centers for Disease Control and Prevention (CDC) influenza-like-illness patient reporting at sentinel health-care providers is verified. A second approach considers personal beliefs of vaccination in social media. A vaccine for human papillomavirus (HPV) was approved by the Food and Drug Administration in May 2006. The virus is present in nearly all cervical cancers and implicated in many throat and oral cancers. Results from automatic sentiment classification of HPV vaccination beliefs are presented which will enable more accurate prediction of the vaccine's population-level impact. Two epidemic models are introduced that embody the intimate social networks related to HPV transmission. Ultimately, aggregating these methodologies with epidemic and social network modeling facilitate effective development of strategies for targeted interventions.

Thesis (Ph.D.)--George Mason University, 2008.<br>Vita: p. 214-215. Thesis director: Edward J. Wegman, Yasmin H. Said Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computational Sciences and Informatics. Title from PDF t.p. (viewed Mar. 9, 2009). Includes bibliographical references (p. 209-213). Also issued in print.

Online social and information networks, like Facebook and Twitter, exploit the influence of neighbors to achieve effective information sharing and spreading. The process that information is spread via the connected nodes in social and information networks is referred to as diffusion. In the literature, a number of diffusion models have been proposed for different applications like influential user identification and personalized recommendation. However, comprehensive studies to discover the hidden diffusion mechanisms governing the information diffusion using the data-driven paradigm are still lacking. This thesis research aims to design novel diffusion models with the structural and behaviorable dependency of neighboring nodes for representing social networks, and to develop computational algorithms to infer the diffusion models as well as the underlying diffusion mechanisms based on information cascades observed in real social networks. By incorporating structural dependency and diversity of node neighborhood into a widely used diffusion model called Independent Cascade (IC) Model, we first propose a component-based diffusion model where the influence of parent nodes is exerted via connected components. Instead of estimating the node-based diffusion probabilities as in the IC Model, component-based diffusion probabilities are estimated using an expectation maximization (EM) algorithm derived under a Bayesian framework. Also, a newly derived structural diversity measure namely dynamic effective size is proposed for quantifying the dynamic information redundancy within each parent component. The component-based diffusion model suggests that node connectivity is a good proxy to quantify how a node's activation behavior is affected by its node neighborhood. To model directly the behavioral dependency of node neighborhood, we then propose a co-activation pattern based diffusion model by integrating the latent class model into the IC Model where the co-activation patterns of parent nodes form the latent classes for each node. Both the co-activation patterns and the corresponding pattern-based diffusion probabilities are inferred using a two-level EM algorithm. As compared to the component-based diffusion model, the inferred co-activation patterns can be interpreted as the soft parent components, providing insights on how each node is influenced by its neighbors as reflected by the observed cascade data. With the motivation to discover a common set of the over-represented temporal activation patterns (motifs) characterizing the overall diffusion in a social network, we further propose a motif-based diffusion model. By considering the temporal ordering of the parent activations and the social roles estimated for each node, each temporal activation motif is represented using a Markov chain with the social roles being its states. Again, a two-level EM algorithm is proposed to infer both the temporal activation motifs and the corresponding diffusion network simultaneously. The inferred activation motifs can be interpreted as the underlying diffusion mechanisms characterizing the diffusion happening in the social network. Extensive experiments have been carried out to evaluate the performance of all the proposed diffusion models using both synthetic and real data. The results obtained and presented in the thesis demonstrate the effectiveness of the proposed models. In addition, we discuss in detail how to interpret the inferred co-activation patterns and interaction motifs as the diffusion mechanisms under the context of different real social network data sets.

Thesis (MSc)--Stellenbosch University, 2011<br>ENGLISH ABSTRACT: With billions of current internet users interacting through social networks, the need has arisen to analyze the structure of these networks. Many authors have proposed random graph models for social networks in an attempt to understand and reproduce the dynamics that govern social network development. This thesis proposes a random graph model that generates social networks using a community-based approach, in which users’ affiliations to communities are explicitly modeled and then translated into a social network. Our approach explicitly models the tendency of communities to overlap, and also proposes a method for determining the probability of two users being connected based on their levels of commitment to the communities they both belong to. Previous community-based models do not incorporate community overlap, and assume mutual members of any community are automatically connected. We provide a method for fitting our model to real-world social networks and demonstrate the effectiveness of our approach in reproducing real-world social network characteristics by investigating its fit on two data sets of current online social networks. The results verify that our proposed model is promising: it is the first community-based model that can accurately reproduce a variety of important social network characteristics, namely average separation, clustering, degree distribution, transitivity and network densification, simultaneously.<br>AFRIKAANSE OPSOMMING: Met biljoene huidige internet-gebruikers wat deesdae met behulp van aanlyn sosiale netwerke kommunikeer, het die analise van hierdie netwerke in die navorsingsgemeenskap toegeneem. Navorsers het al verskeie toevalsgrafiekmodelle vir sosiale netwerke voorgestel in ’n poging om die dinamika van die ontwikkeling van dié netwerke beter te verstaan en te dupliseer. In hierdie tesis word ’n nuwe toevalsgrafiekmodel vir sosiale netwerke voorgestel wat ’n gemeenskapsgebaseerde benadering volg, deurdat gebruikers se verbintenisse aan gemeenskappe eksplisiet gemodelleer word, en dié gemeenskapsmodel dan in ’n sosiale netwerk omskep word. Ons metode modelleer uitdruklik die geneigdheid van gemeenskappe om te oorvleuel, en verskaf ’n metode waardeur die waarskynlikheid van vriendskap tussen twee gebruikers bepaal kan word, op grond van hulle toewyding aan hulle wedersydse gemeenskappe. Vorige modelle inkorporeer nie gemeenskapsoorvleueling nie, en aanvaar ook dat alle lede van dieselfde gemeenskap vriende sal wees. Ons verskaf ’n metode om ons model se parameters te pas op sosiale netwerk datastelle en vertoon die vermoë van ons model om eienskappe van sosiale netwerke te dupliseer. Die resultate van ons model lyk belowend: dit is die eerste gemeenskapsgebaseerde model wat gelyktydig ’n belangrike verskeidenheid van sosiale netwerk eienskappe, naamlik gemiddelde skeidingsafstand, samedromming, graadverdeling, transitiwiteit en netwerksverdigting, akkuraat kan weerspieël.

Epidemiologists rely on human interaction networks for determining states and dynamics of disease propagations in populations. However, such networks are empirical snapshots of the past. It will greatly benefit if human interaction networks are statistically predicted and dynamically created while an epidemic is in progress. We develop an application framework for the generation of human interaction networks and running epidemiological processes utilizing research on human mobility patterns and agent-based modeling. The interaction networks are dynamically constructed by incorporating different types of Random Walks and human rules of engagements. We explore the characteristics of the created network and compare them with the known theoretical and empirical graphs. The dependencies of epidemic dynamics and their outcomes on patterns and parameters of human motion and motives are encountered and presented through this research. This work specifically describes how the types and parameters of random walks define properties of generated graphs. We show that some configurations of the system of agents in random walk can produce network topologies with properties similar to small-world networks. Our goal is to find sets of mobility patterns that lead to empirical-like networks. The possibility of phase transitions in the graphs due to changes in the parameterization of agent walks is the focus of this research as this knowledge can lead to the possibility of disruptions to disease diffusions in populations. This research shall facilitate work of public health researchers to predict the magnitude of an epidemic and estimate resources required for mitigation.

The landscape of world migration involves multiple interacting movements of people at various geographic scales, posing significant challenges to the dyadic-independence assumption underlying standard migration models. To account for emerging patterns of multilateral migration relationships, we represent world migration as a time-evolving, spatial network. The nodes in the World Migration Network (WMN) are countries located in geographic space, and the edges represent migratory movements for each decade from 1960-2000. In the first part of the thesis, we characterise the spatial network structure of the WMN, with a particular focus on detecting and mapping mesoscopic structures called 'communities' (i.e., sets of countries with denser migration connections internally than to the rest of the WMN). We employ a method for community detection that simultaneously accounts for multilateral migration, spatial constraints, time-dependence, and directionality in the WMN. We then introduce an approach for characterising local (intracommunity) and global (intercommunity) connectivity in the WMN. On this basis, we define a threefold typology that distinguishes 'cave', 'bi-regional', and 'bridging' communities. These are characterised with distinct migration patterns, spatial network structures, and temporal dynamics: cave communities are tightly-knit enduring structures that channel local migration between contiguous countries; bi-regional communities merge migration between two distinct geographic regions; bridging communities have hub-and-spoke dynamic structures that emerge from globe-spanning movements. Our results suggest that the WMN is neither a globally interconnected network nor reproducing geographic boundaries but involves heterogeneous patterns of global and local ('glocal') migration connectivity. We examine a set of relational, homophily, and spatial mechanisms that could have possibly generated the 'glocal' structure we observe. We found that communities of different types arise from significantly different mechanisms. Our results suggest that migration communities can have important implications for world migration, as different types of community structure provide distinct opportunities and constraints, thereby distinctively shaping future migration patterns.

Multi Agent Systems (MAS) are computerised systems composed of autonomous software agents that interact to solve complex problems. Within a MAS, agents require some mechanism to coordinate their activities. In the MAS literature, norms have been widely used to coordinate agents’ activities. Thus, given a MAS, a major research challenge is how to synthesise a normative system, namely a collection of norms, which supports its agents’ coordination. This dissertation focuses on the automated synthesis of norms for open Multi- Agent Systems. In an open MAS, the agent population may change along time, agents may be developed by third parties and their behaviours are not known beforehand. These particular conditions make specially challenging to synthesise a normative system to govern an open MAS. The MAS literature has mainly investigated two general approaches to norm synthesis: off-line design, and on-line synthesis. The first approach aims at synthesising a normative system at design time. With this aim, it assumes that the MAS state space is known at design time and does not change at runtime. This goes against the nature of open MAS, and thus off-line design is not appropriate to synthesise their norms. Alternatively, on-line norm synthesis considers that norms are synthesised at runtime. Most on-line synthesis research has focused on norm emergence, which considers that agents synthesise their own norms, thus assuming that they have norm synthesis capabilities. Again, this cannot be assumed in open MAS. Against this background, this dissertation introduces a whole computational framework to perform on-line norm synthesis for open Multi-Agent Systems. Firstly, this framework provides a computational model to synthesise norms for a MAS at runtime. Such computational model requires neither knowledge about agents’ behaviours beforehand nor their participation in the norm synthesis pro- cess. Instead, it considers a regulatory entity that observes agents’ interactions at runtime, identifying situations that are undesirable for coordination to sub- sequently synthesise norms that regulate these situations. Our computational model has been conceived to be of general purpose so that it can be employed to synthesise norms in a wide range of application domains by providing little domain-dependent information. Secondly, our framework provides an abstract architecture to implement such regulatory entity (the so-called Norm Synthesis Machine), which observes a MAS and executes a synthesis strategy to synthe- sise norms. Thirdly, our framework encompasses a family of norm synthesis strategies intended to be executed by the Norm Synthesis Machine. Overall, this family of strategies supports multi-objective on-line norm synthesis Our first synthesis strategy, the so-called base, aims at synthesising effective normative systems that successfully avoid situations that are undesirable for a MAS’ coordination. Then, two further strategies (called iron and simon) go beyond effectiveness and also consider compactness as a norm synthesis goal. iron and simon take alternative approaches to synthesise compact normative systems that, in addition to effectively achieve coordination, are as synthetic as possible. This allows them to reduce agents’ computational efforts when reasoning about norms. A fourth strategy, the so-called lion, goes beyond effectiveness and compactness to also consider liberality as a synthesis goal. lion aims at synthesising normative systems that are effective and compact while preserving agents’ freedom to the greatest possible extent. Our final strategy is desmon, which is capable of synthesising norms by considering different degrees of reactivity. desmon allows to adjust the amount of information that is required to decide whether a norm must be included in a normative system or not. Thus, desmon can synthesise norms either by being reactive (i.e., by considering little information), or by being more deliberative (by employing more information). We provide empirical evaluations of our norm synthesis strategies in two application domains: a road traffic domain, and an on-line community domain. In this former domain, we employ these strategies to synthesise effective, compact and liberal normative systems that successfully avoid collisions between cars. In the latter domain, our strategies synthesise normative systems based on users’ complaints about inappropriate contents. In this way, our strategies implement a regulatory approach that synthesises norms when there is enough user consensus about the need for norms. Overall, this thesis advances in the state of the art in norm synthesis by providing a novel computational model, an abstract architecture and a family of strategies for on-line norm synthesis for open Multi-Agent Systems.<br>Els sistemes Multi-Agent (MAS) són sistemes computeritzats composats d’agents autònoms que interaccionen per resoldre problemes complexos. A un MAS, els agents requereixen algun mecanisme per a coordinar les seves activitats. A la literatura en Sistemes Multi-Agent, les normes han estat àmpliament utilitzades per coordinar les activitats dels agents. Per tant, donat un MAS, un dels majors reptes d’investigació és el de sintetizar el sistema normatiu, és a dir, la col·lecció de normes, que suporti la coordinació dels agents. Aquesta tesi es centra en la síntesi automàtica de normes per sistemes Multi-Agent oberts. A un MAS obert, la població d’agents pot canviar amb el temps, els agents poden ésser desenvolupats per terceres parts, i els comportaments dels agents són desconeguts per endavant. Aquestes condicions particulars fan especialment complicat sintetizar el sistema normatiu que reguli un sistema Multi-Agent obert. En general, la literatura en Sistemes Multi-Agent ha investigat dues aproximacions a la síntesi de normes: disseny off-line, i síntesi on-line. La primera aproximació consisteix a sintetizar un sistema normatiu en temps de disseny. Amb aquest propòsit, aquesta aproximació assumeix que l’espai d’estats d’un MAS és conegut en temps de disseny i no canvia en temps d’execució. Això va contra la natura dels sistemes Multi-Agent oberts, i per tant el disseny off-line no és apropiat per a sintetitzar les seves normes. Com a alternativa, la síntesi on-line considera que les normes són sintetizades en temps d’execució. La majoria de recerca en síntesi on-line s’ha centrat en la emergència de normes, que considera que els agents sintetizen les seves pròpies normes, per tant assumint que tenen la capacitat de sintetitzar-les. Aquestes condicions tampoc no es poden assumir en un MAS obert. Donat això, aquesta tesi introdueix un marc computacional per la síntesi on-line de normes en sistemes Multi-Agent oberts. Primer, aquest marc proveeix un model computacional per sintetizar normes per un MAS en temps d’execució. Aquest model computacional no requereix ni coneixement sobre els comportaments dels agents per endavant ni la seva participación en la síntesi de normes. En canvi, considera que una entitat reguladora observa les interaccions dels agents en temps d’execució, identificant situacions indesitjades per la coordinació i sintetizant normes que regulen aquestes situacions. El nostre model computacional ha estat dissenyat per a ésser de propòsit general per tal que pugui ser utilitzat a la síntesi de normes en un ampli ventall de dominis d’aplicació proporcionant només información clau sobre el domini. Segon, el nostre marc proveeix una arquitectura abstracta per implementar aquesta entitat reguladora, anomenada Màquina de Síntesi, que observa un MAS en temps d’execució i executa una estratègia de síntesi que s’encarrega de sintetizar normes. Tercer, el nostre marc incorpora una familia d’estratègies de síntesi destinades a ésser executades per una màquina de síntesi. En general, aquesta familia d’estratègies soporta la síntesi multi-objectiu i on-line de normes. La nostra primera estratègia, anomenada BASE, està dissenyada per sintetitzar sistemes normatius eficaços que evitin de manera satisfactòria situacions indesitjades per la coordinació d’un sistema Multi-Agent. Després, dues estratègies de síntesi, anomenades IRON i SIMON, van més enllà de la eficàcia i també consideren la compacitat com a objectiu de síntesi. IRON i SIMON prenen aproximacions alternatives a la síntesi de sistemes normatius compactes que, a més d’aconseguir la coordinació de manera efectiva, siguin tant sintètics com fos possible. Això permet a aquestes estratègies reduir els esforços computacionals dels agents a l’hora de raonar sobre les normes. Una quarta estratègia, anomenada LION, va més enllà de la eficàcia i la compacitat per considerar també la liberalitat com a objectiu de síntesi. Lion sintetitza sistemes normatius que són eficaços i compactes mentre preserven la llibertat dels agents tant com sigui possible. La nostra última estratègia és desmon, que és capaç de sintetizar normes considerant diferents graus de reactivitat. desmon permet ajustar la quantitat d’informació necessària per decidir si una norma cal que sigui o no inclosa a un sistema normatiu. DESMON pot sintetizar normes essent reactiu (considerant poca informació), o essent més deliberatiu (considerant més informació). En aquesta tesi presentem avaluacions empíriques de les nostres estratègies de síntesi en dos dominis d’aplicació: el domini del tràfic, i el domini de les comunitats on-line. En aquest primer domini, utilitzem les nostres estratègies per a sintetizar sistemes normatius eficaços, compactes i liberals que eviten colisions entre cotxes. Al segon domini, les nostres estratègies sintetizen sistemes normatius basant-se en les queixes dels usuaris de la comunitat sobre continguts inapropiats. D’aquesta manera, les nostres estratègies implementen un mecanisme de regulació que sintetiza normes quan hi ha suficient consens entre els usuaris sobre la necessitat de normes. Aquesta tesi avança en l’estat de l’art en síntesi de normes al proporcionar un novedós model computacional, una arquitectura abstracta i una familia d’estratègies per la síntesi on-line de normes per sistemes Multi-Agent oberts.