Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied. Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips. Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime. Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature. Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences. / QC 20100811

Interactions are what gives us the knowledge of the world around us. Interactions on all levels may fundamentally be seen as an exchange of information and a possible response of the same. Whether it is an electron in an electrical field or a handsome dude in a bar responding to a flirtation---interactions make things happen. In this sense we can see that objects without the capability of interacting with each other also are invisible to each other. Chains of pairwise interacting entities can serve as mediators of indirect interactions between objects. Nonetheless, in the limit of no interactions, we get into a philosophical debate whether we actually may consider anything to exist since it can not be detected in any way. Interactions between matter tend to be organized and show a hierarchical structure in which smaller sub-systems can be seen as parts of a bigger system, which in turn might be a smaller part of an even bigger system. This is reflected by the fact that we have sciences that successfully study specific interactions between objects or matter---physics, chemistry, biology, ecology, sociology,... What happens in a situation where all length scales are important? How does the structure of the underlying network of interactions affect the dynamical properties of a system? What network structures do we find and how are they created? This thesis is a physicist's view of collective dynamics, from superconductors to social systems and navigation in city street networks.

<p>Understanding the structure of a network is an essential part in understanding the behavior of the system it represents, but as the system becomes really large, a visualization of the full network looses its potential to reveal important structural relationships. Then we need ways to simplify and highlight the important structures of the network while the details are filtered out, just like good maps do. We have developed an interactive application that utilizes mathematical methods based on network and information theory to reveal the important patterns hidden in huge amount of interaction data. The application gives the professional as well as the nonprofessional user the ability to load his or hers own file containing the network data, from mobile phone networks and social online networks to transport networks and financial networks and lets you explore the data and generate a customized map which highlights the influential patterns in your data. A demo application is also developed to demonstrate the mathematical and information-theoretical principles behind the map generation.</p> / <p>För att koppla form till funktion är nätverk ett oumbärligt verktyg, men när systemen blir riktigt stora förlorar nätverken sin förmåga att avslöja viktiga strukturella samband. Då behövs det kraftfulla metoder för att förenkla och framhäva de viktiga strukturerna i nätverken samtidigt som detaljerna filtreras bort, precis som bra kartor gör. Vi har utvecklat en interaktiv applikation som utnyttjar matematiska metoder baserat på nätverks- och in- formationsteori för att avslöja viktiga mönster som ligger dolt i myllret av interaktionsdata. Du kan läsa in din egen fil med nätverksdata, från telekommunikationsnätverk och sociala online-nätverk till transportnärverk och finansiella nätverk, och få tillbaka en skräddarsydd karta som låter dig upptäcka de inflytelserika mönstren i nätverket. En demo-applikation är också utvecklad för att demonstrera de matematiska och informationsteoretiska principerna bakom kartgenereringen.</p>

Understanding the structure of a network is an essential part in understanding the behavior of the system it represents, but as the system becomes really large, a visualization of the full network looses its potential to reveal important structural relationships. Then we need ways to simplify and highlight the important structures of the network while the details are filtered out, just like good maps do. We have developed an interactive application that utilizes mathematical methods based on network and information theory to reveal the important patterns hidden in huge amount of interaction data. The application gives the professional as well as the nonprofessional user the ability to load his or hers own file containing the network data, from mobile phone networks and social online networks to transport networks and financial networks and lets you explore the data and generate a customized map which highlights the influential patterns in your data. A demo application is also developed to demonstrate the mathematical and information-theoretical principles behind the map generation. / För att koppla form till funktion är nätverk ett oumbärligt verktyg, men när systemen blir riktigt stora förlorar nätverken sin förmåga att avslöja viktiga strukturella samband. Då behövs det kraftfulla metoder för att förenkla och framhäva de viktiga strukturerna i nätverken samtidigt som detaljerna filtreras bort, precis som bra kartor gör. Vi har utvecklat en interaktiv applikation som utnyttjar matematiska metoder baserat på nätverks- och in- formationsteori för att avslöja viktiga mönster som ligger dolt i myllret av interaktionsdata. Du kan läsa in din egen fil med nätverksdata, från telekommunikationsnätverk och sociala online-nätverk till transportnärverk och finansiella nätverk, och få tillbaka en skräddarsydd karta som låter dig upptäcka de inflytelserika mönstren i nätverket. En demo-applikation är också utvecklad för att demonstrera de matematiska och informationsteoretiska principerna bakom kartgenereringen.

Community detection in networks is an important area of current research with many applications. Finding community structures is a challenging task and despite significant effort no satisfactory method has been found. Different methods find different communities in the same network and with different computational requirements. To counter this problem, several different methods are often used and the results compared manually. In this thesis, we present three different methods to instead merge the results from different methods (or several runs from the same algorithm) to find better estimates of the community structure. Another problem in practical applications is noisy and imperfect networks with missing and false edges. These imperfections are natural results from the methods used to map the network structure and are often difficult to eliminate. In this thesis, we apply a Monte Carlo-sampling method in combination with the introduced methods for merging community detection results to find community structures in such networks. The method is tested by simulation studies on both real-world networks and synthetic networks with generated uncertainties and imperfections. We finally demonstrate how it is possible to generate confidence levels of the obtained community structure from the merging methods. This allows for a qualitative comparison of the robustness and significance of the network clustering. / Identifikation av grupperingar i nätverk är ett viktigt område inom aktuell forskning med många olika tillämpningsområden. Att finna grupperingar är ofta svårt och trots betydande ansträngningar har ingen tillfredsställande metod hittats. Olika metoder finner ofta olika grupperingar i samma nätverk och kräver varierande beräkningskraft. För att hantera dessa problem används ofta flera metoder vartefter resultaten jämförs manuellt. I detta examensarbete presenterar vi tre olika metoder att istället slå samman resultat från olika metoder (eller fler körningar från samma algoritm) för att hitta bättre uppskattningar av grupperingarna. Ett annat problem i praktiska tillämpningar är brus och ofullständiga nätverk med saknade och falska kanter. Dessa brister är naturliga resultat från de metoder som används för att kartlägga nätverketstrukturen och det är ofta svåra att eliminera dessa. I detta examensarbete använder vi Monte Carlo-metoder i kombination med de introducerade metoderna för att slå samman funna grupperingar för att hitta grupperingar i det osäkra nätverket. Vi testar metoden genom simuleringstudier på både verkliga och syntetiska nätverk med genererade osäkerheter och brister. Slutligen demostrerar vi hur det är möjligt att skapa konfidensnivåer för noder i grupperingar med hjälp av metoderna för sammanslagning. Detta möjliggör en kvalitativ jämförelse av stabilitet och signifikans av identifierade nätverksgrupperingar.

We are constantly struggling to understand how nature works, trying to identify recurrent events and looking for analogies and relations between objects or individuals. Knowing patterns of behavior is powerful and fundamental for survival of any species. In this thesis, datasets of diverse systems related to transportation, economics, sexual and social contacts, are characterized by using the formalisms of time series and network theory. Part of the results consists on the collection and analyzes of original network data, the rest focuses on the simulation of dynamical processes on these networks and to study how they are affected by the particular structures. The majority of the thesis is about temporal networks, i.e. networks whose structure changes in time. The new temporal dimension reveals structural dynamical properties that help to understand the feedback mechanisms responsible to make the network structure to adapt and to understand the emergence and inhibition of diverse phenomena in dynamic systems, as epidemics in sexual and contact networks. / Vi är ständigt kämpar för att förstå hur naturen fungerar, försöker identifier återkommande evenemang och söker analogier och relationer mellan objekt eller individer. Veta beteendemönster är kraftfull och grundläggande för överlevnad av arter. I denna avhandling, dataset av olika system i samband med transporter är ekonomi, sexuella och sociala kontakter, som kännetecknas av att använda formalismer av tidsserier och nätverk teori. En del av resultatet utgörs av insamling och analys av ursprungliga nätdata, fokuserar resten på simulering av dynamiska processer i dessa nätverk och att studera hur de påverkas av de särskilda strukturer. Huvuddelen av avhandlingen handlar om tidsmässiga nät, i.e. nät vars struktur förändringar i tid. Den nya tidsdimensionen avslöjar strukturella dynamiska egenskaper som hjälper till att förstå den feedback mekanismer som ansvarar för att göra nätverksstruktur att anpassa sig och förstå uppkomsten och hämning av olika företeelser i dynamiska system, epidemier i sexuella och kontaktnät. / Constantemente nos esforçamos para entender como a natureza funciona, tentando identificar eventos recorrentes e procurando por analogias e relações entre objetos ou indivíduos. Conhecer padrões de comportamento é algo poderoso e fundamental para a sobrevivência de qualquer espécie. Nesta tese, dados de sistemas diversos, relacionados a transporte, economia, contatos sexuais e sociais, são caracterizados usando o formalismo de séries temporais e teoria de redes. Uma parte dos resultados consiste na coleta e análise de dados de redes originais, a outra parte concentra-se na simulação de processos dinâmicos nessas redes e no estudo de como esses processos são afetados por determinadas estruturas. A maior parte da tese é sobre redes temporais, ou seja, redes cuja estrutura varia no tempo. A nova dimensão temporal revela propriedades estruturais dinâmicas que contribuem para o entendimento dos mecanismos de resposta responsáveis pela adaptação da rede, e para o entendimento da emergência e inibição de fenômenos diversos em sistemas dinâmicos, como epidemias em redes sexuais e de contato pessoal.