Weblog patterns and human dynamics with decreasing interest

Weblog is the fourth way of network exchange after Email, BBS and MSN. Most bloggers begin to write blogs with great interest, and then their interests gradually achieve a balance with the passage of time. In order to describe the phenomenon that people's interest in something gradually decreases until it reaches a balance, we first propose the model that describes the attenuation of interest and reflects the fact that people's interest becomes more stable after a long time. We give a rigorous analysis on this model by non-homogeneous Poisson processes. Our analysis indicates that the interval distribution of arrival-time is a mixed distribution with exponential and power-law feature, that is, it is a power law with an exponential cutoff. Second, we collect blogs in ScienceNet.cn and carry on empirical studies on the interarrival time distribution. The empirical results agree well with the analytical result, obeying a special power law with the exponential cutoff, that is, a special kind of Gamma distribution. These empirical results verify the model, providing an evidence for a new class of phenomena in human dynamics. In human dynamics there are other distributions, besides power-law distributions. These findings demonstrate the variety of human behavior dynamics.Comment: 8 pages, 1 figure

Timing interactions in social simulations: The voter model

The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.Comment: Book Chapter, 23 pages, 9 figures, 5 table

Emotional persistence in online chatting communities

How do users behave in online chatrooms, where they instantaneously read and write posts? We analyzed about 2.5 million posts covering various topics in Internet relay channels, and found that user activity patterns follow known power-law and stretched exponential distributions, indicating that online chat activity is not different from other forms of communication. Analysing the emotional expressions (positive, negative, neutral) of users, we revealed a remarkable persistence both for individual users and channels. I.e. despite their anonymity, users tend to follow social norms in repeated interactions in online chats, which results in a specific emotional "tone" of the channels. We provide an agent-based model of emotional interaction, which recovers qualitatively both the activity patterns in chatrooms and the emotional persistence of users and channels. While our assumptions about agent's emotional expressions are rooted in psychology, the model allows to test different hypothesis regarding their emotional impact in online communication.Comment: 34 pages, 4 main and 12 supplementary figure

Universal features of correlated bursty behaviour

Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution in a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems

Local variation of hashtag spike trains and popularity in Twitter

We draw a parallel between hashtag time series and neuron spike trains. In each case, the process presents complex dynamic patterns including temporal correlations, burstiness, and all other types of nonstationarity. We propose the adoption of the so-called local variation in order to uncover salient dynamics, while properly detrending for the time-dependent features of a signal. The methodology is tested on both real and randomized hashtag spike trains, and identifies that popular hashtags present regular and so less bursty behavior, suggesting its potential use for predicting online popularity in social media.Comment: 7 pages, 7 figure

Random Walks on Stochastic Temporal Networks

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.Comment: Chapter in Temporal Networks (Petter Holme and Jari Saramaki editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor corrections and modifications. This chapter is based on arXiv:1112.3324, which contains additional calculations and numerical simulation

The Atlantic Ocean at the last glacial maximum: 1. Objective mapping of the GLAMAP sea-surface conditions

Recent efforts of the German paleoceanographic community have resulted in a unique data set of reconstructed sea-surface temperature for the Atlantic Ocean during the Last Glacial Maximum, plus estimates for the extents of glacial sea ice. Unlike prior attempts, the contributing research groups based their data on a common definition of the Last Glacial Maximum chronozone and used the same modern reference data for calibrating the different transfer techniques. Furthermore, the number of processed sediment cores was vastly increased. Thus the new data is a significant advance not only with respect to quality, but also to quantity. We integrate these new data and provide monthly data sets of global sea-surface temperature and ice cover, objectively interpolated onto a regular 1°x1° grid, suitable for forcing or validating numerical ocean and atmosphere models. This set is compared to an existing subjective interpolation of the same base data, in part by employing an ocean circulation model. For the latter purpose, we reconstruct sea surface salinity from the new temperature data and the available oxygen isotope measurements