Old and recent theoretical works by Andrzej Pekalski (APE) are recalled as possible sources of interest for describing network formation and clustering in complex (scientific) communities, through self-organisation and percolation processes. Emphasis
is placed on APE self-citation network over four decades. The method is that used for detecting scientists field mobility by focusing on authors self-citation, co-authorships and article topics networks as in [1,2]. It is shown that APEs self-citation patterns reveal important information on APE interest for research topics over time as well as APE engagement on different scientific topics and in different networks of collaboration. Its interesting complexity results from degrees of freedom and external fields leading to so called internal shock resistance. It is found that APE network of scientific interests belongs to independent clusters and occurs through rare or drastic events as in irreversible preferential attachment processes, similar to those found in usual mechanics and thermodynamics phase transitions.
We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words frequencies, the empirical analysis is performed by studying classes of frequently-equivalent words, i.e. by
grouping words depending on their frequencies. Two limiting cases are considered: the dilute limit, i.e. for those words that are used less than once a day, and the dense limit for frequent words. In both cases, extreme events occur more frequently than expected from the Poisson hypothesis. These deviations from Poisson statistics reveal non-trivial time correlations between events that are associated with bursts of activities. The distribution of waiting times is shown to behave like a stretched exponential and to have the same shape for different sets of words sharing a common frequency, thereby revealing universal features.
