BackgroundE-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.Methodology/Principal FindingsHere, 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.Conclusions/SignificanceOverall, 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 present an empirical study of user activity in online BBC discussion forums, measured by the number of posts written by individual debaters and the average sentiment of these posts. Nearly 2.5 million posts from over 18 thousand users were investigated. Scale free distributions were observed for activity in individual discussion threads as well as for overall activity.The number of unique users in a thread normalized by the thread length decays with thread length, suggesting that thread life is sustained by mutual discussions rather than by independent comments. Automatic sentiment analysis shows that most posts contain negative emotions and the most active users in individual threads express predominantly negative sentiments. It follows that the average emotion of longer threads is more negative and that threads can be sustained by negative comments. An agent based computer simulation model has been used to reproduce several essential characteristics of the analyzed system. The model stresses the role of discussions between users, especially emotionally laden quarrels between supporters of opposite *

We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q ≥ 3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T * , which linearly increases with q. Moreover, we show that for q = 3 the phase transition is continuous and discontinuous for larger values of q. For q > 3 the hysteresis exhibits oscillatory behavior -expanding for even values of q and shrinking for odd values of q. If only simulation results were taken into account, this phenomenon could be mistakenly interpreted as switching from discontinuous to continuous phase transitions or even as evidence of the so-called mixed phase transitions. Due to the mean-field like nature of the model we are able to calculate analytically not only the stationary value of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable and metastable steady states. The main message is that in case of non-equilibrium systems the hysteresis can behave in an odd way and computer simulations alone may mistakenly lead to incorrect conclusions.

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 multi-levelness 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 a behavior is observed for q = 6. Interestingly, only this rule admits construction of realistic variants of the model, in line with recent social experiments.

The state of health of patients is typically not characterized by a single disease alone but by multiple (comorbid) medical conditions. These comorbidities may depend strongly on age and gender. We propose a specific phenomenological comorbidity network of human diseases that is based on medical claims data of the entire population of Austria. The network is constructed from a two-layer multiplex network, where in one layer the links represent the conditional probability for a comorbidity, and in the other the links contain the respective statistical significance. We show that the network undergoes dramatic structural changes across the lifetime of patients. Disease networks for children consist of a single, strongly interconnected cluster. During adolescence and adulthood further disease clusters emerge that are related to specific classes of diseases, such as circulatory, mental, or genitourinary disorders. For people over 65 these clusters start to merge, and highly connected hubs dominate the network. These hubs are related to hypertension, chronic ischemic heart diseases, and chronic obstructive pulmonary diseases. We introduce a simple diffusion model to understand the spreading of diseases on the disease network at the population level. For the first time we are able to show that patients predominantly develop diseases that are in close network proximity to disorders that they already suffer. The model explains more than 85% of the variance of all disease incidents in the Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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 investigated flows of visitors migrating between different portal subpages. Two various portals were studied as weighted networks where nodes are portal subpages and edge weights are numbers of user transitions. Such networks differ from networks of portal subpages connected by hyperlinks prepared by portal designers. Distributions of link weights, node strengths, and times spent by visitors at one subpage follow power laws over several decades for data collected during two different days and for weekly data. The distribution of numbers P(z) of unique subpages visited during one session is exponential and there is a square-root dependence between the total number of transitions n during a single visit and the average z . A model of portal surfing is developed where the browsing process corresponds to a self-attracting walk on the weighted network with a short memory. Results of numerical simulation are in agreement with weekly and daily portal data, and our analytical approach fits empirical data in the center part of scaling regime.

We investigate a kinetic Ising model with several single-spin flip dynamics (including Metropolis and heat-bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs situation is far less clear -the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms are more resistant to the annealed disorder, which causes only small quantitative changes in the model behavior. On the other hand, there are dynamics for which the influence of annealing on the system is significant, and qualitative changes arise like switching the type of phase transition from continuous to discontinuous one. We try to identify features of the proposed dynamics which are responsible for the above phenomenon.