E-communities, social groups interacting online, have recently become an object of interdisciplinary research. As with face-to-face meetings, Internet exchanges may not only include factual information but also emotional information – how participants feel about the subject discussed or other group members. Emotions in turn are known to be important in affecting interaction partners in offline communication in many ways. Could emotions in Internet exchanges affect others and systematically influence quantitative and qualitative aspects of the trajectory of e-communities? The development of automatic sentiment analysis has made large scale emotion detection and analysis possible using text messages collected from the web. However, it is not clear if emotions in e-communities primarily derive from individual group members' personalities or if they result from intra-group interactions, and whether they influence group activities. Here, for the first time, we show the collective character of affective phenomena on a large scale as observed in four million posts downloaded from Blogs, Digg and BBC forums. To test whether the emotions of a community member may influence the emotions of others, posts were grouped into clusters of messages with similar emotional valences. The frequency of long clusters was much higher than it would be if emotions occurred at random. Distributions for cluster lengths can be explained by preferential processes because conditional probabilities for consecutive messages grow as a power law with cluster length. For BBC forum threads, average discussion lengths were higher for larger values of absolute average emotional valence in the first ten comments and the average amount of emotion in messages fell during discussions. Overall, our results prove that collective emotional states can be created and modulated via Internet communication and that emotional expressiveness is the fuel that sustains some e-communities.

We study a nonlinear $q$-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. To study the role of the multilevelness in this model we propose three methods of transferring the model from a mono- to a multiplex network. They take into account two criteria: one related to the status of independence (LOCAL vs GLOBAL) and one related to peer pressure (AND vs OR). In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex: a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior. However, qualitative changes in the phase transitions can be observed for only one of the considered rules: LOCAL&AND. For this rule the phase transition becomes discontinuous for $q=5$, whereas for a monoplex such behavior is observed for $q=6$. Interestingly, only this rule admits construction of realistic variants of the model, in line with recent social experiments.

Computing layer similarities is an important way of characterizing multiplex networks because various static properties and dynamic processes depend on the relationships between layers. We provide a taxonomy and experimental evaluation of approaches to compare layers in multiplex networks. Our taxonomy includes, systematizes and extends existing approaches, and is complemented by a set of practical guidelines on how to apply them.

Despite substantial progress in the study of diabetes, important questions remain about its comorbidities and clinical heterogeneity. To explore these issues, we develop a framework allowing for the first time to quantify nation-wide risks and their age- and sex-dependence for each diabetic comorbidity, and whether the association may be consequential or causal, in a sample of almost two million patients. This study is equivalent to nearly 40,000 single clinical measurements. We confirm the highly controversial relation of increased risk for Parkinson’s disease in diabetics, using a 10 times larger cohort than previous studies on this relation. Detection of type 1 diabetes leads detection of depressions, whereas there is a strong comorbidity relation between type 2 diabetes and schizophrenia, suggesting similar pathogenic or medication-related mechanisms. We find significant sex differences in the progression of, for instance, sleep disorders and congestive heart failure in diabetic patients. Hypertension is a highly sex-sensitive comorbidity with females being at lower risk during fertile age, but at higher risk otherwise. These results may be useful to improve screening practices in the general population. Clinical management of diabetes must address age- and sex-dependence of multiple comorbid conditions. We quantify for the first time age- and gender-dependent relative risks for each possible comorbidity of type 1 and 2 diabetes in a nation-wide claims dataset containing almost two million patients, and test whether the association may be consequential or causal. This study therefore contains almost 40,000 single clinical measurements, all with the maximum patient number available in an entire country. We confirm the relation between diabetes and Parkinson's disease, and find different progression routes of mental disorders in type 1 and type 2 diabetics. Among many other results, we also report significant gender differences in the progression of congestive heart failure, sleep disorders, hypertension, and hyperlipidemia. This work provides the first complete statistical description of all diabetic comorbidities and their dependence on patient age and sex. These results may be of immediate use to improve screening practices and therapy of diabetic patients due to more accurate diagnosis and treatment of important comorbidities.