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We studied the dynamic network of relationships among avatars in the massively multiplayer online game Planetside 2. In the spring of 2014, two separate servers of this game were merged, and as a result, two previously distinct networks were combined into one. We observed the evolution of this network in the seven month period following the merger. We found that some structures of original networks...
The mathematical analysis of the second-order phase transitions that occur in α-asynchronous cellular automata field is a highly challenging task. From the experimental side, these phenomena appear as a qualitative change of behaviour which separates a behaviour with an active phase, where the system evolves in a stationary state with fluctuations, from a passive state, where the system is absorbed...
The paper includes English translations (together with original Latin versions) of three papers of Adam Adamandy Kochański (1631-1700), originally published in Acta Eruditorum in 1682 (“Solutio theorematum”), 1685 (“Observationes cyclometricae”), and 1686 (“Considerationes quaedam”). The translation is as faithful as possible, often literal, and it is mainly intended to be of help to those who wish...
Problem of giving the overall expression pattern within on the basis of his first few elements is well known to every mathematician. Puzzles of this type have something probably very appealing for anyone professionally involved in mathematics. If, however, we are dealing with during the initial elements that comes from a study published over three hundred years ago, the problem becomes even repeatedly...
We investigate inflection structure of a synthetic language using Latin as an example. We construct a bipartite graph in which one group of vertices correspond to dictionary headwords and the other group to inflected forms encountered in a given text. Each inflected form is connected to its corresponding headword, which in some cases in non-unique. The resulting sparse graph decomposes into a large...
A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function I A on the interval [0, 1]. It is shown that any cellular automaton rule can be represented by a (nonunique) rule formulated in terms of a pair (p, I A ). This new class of automata networks contains discrete systems...
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