In this paper, we study Copy Number Variation (CNV) data. The underlying process generating CNV segments is generally assumed to be memory-less, giving rise to an exponential distribution of segment lengths. In this paper, we provide evidence from cancer patient data, which suggests that this generative model is too simplistic, and that segment lengths follow a power-law distribution instead. We conjecture a simple preferential attachment generative model that provides the basis for the observed power-law distribution. We then show how an existing statistical method for detecting cancer driver genes can be improved by incorporating the power-law distribution in the null model.

We review the notion of perfect recall in the literature on interpreted systems, game theory and epistemic logic. In the context of Epistemic Temporal Logic (ETL), we give a (to our knowledge) novel frame condition for perfect recall. In contrast to existing characterizations, it is local in a sense which allows it to straightforwardly be translated into a defining formula in a language that only has next-step temporal operators. This frame condition also gives rise to a complete axiomatization of perfect recall in S5 ETL.

In a recent paper, van Benthem, Gerbrandy, Hoshi and Pacuit gave a natural translation of dynamic epistemic logic (DEL) into epistemic temporal logic (ETL) and proved a representation theorem, characterizing those ETL models that are translations of some DEL protocol; among the characterizing properties we also find synchronicity. In this paper, we argue that synchronicity is not an inherent property of DEL, but rather of the translation that van Benthem et al. used. We provide a different translation that produces asynchronous ETL models and discuss a minimal temporal extension of DEL that removes the ambiguities between the possible translations. This allows us a first attempt at assessing which of the epistemic-temporal properties are intrinsic to DEL and which are properties of the translation.

Perfect recall, intuitively the ability to remember all past mental states, has been predominantly studied in the context of interpreted systems and game theory, which mostly consider S5 systems (of "correct" knowledge). More recently, the notion has become of interest to the epistemic logic community, where weaker systems are not unusual. Building upon recent work where we studied different definitions of perfect recall in Epistemic Temporal Logic (ETL), we argue that the intuitive motivations given there are still valid in such sub-S5 settings. However, definitions that were equivalent in S5 cease to be so without S5, so that these less restrictive settings allow for a more fine-grained comparison of the different definitions and their underlying intuitions.

We consider two simple variants of a framework for reasoning about knowledge amongst communicating groups of players. Our goal is to clarify the resulting epistemic issues. In particular, we investigate what is the impact of common knowledge of the underlying hypergraph connecting the players, and under what conditions common knowledge distributes over disjunction. We also obtain two versions of the classic result that common knowledge cannot be achieved in the absence of a simultaneous event (here a message sent to the whole group).