In this paper, we introduce the concept of the independence graph of a directed 2-complex. We show that the class of diagram groups is closed under graph products over independence graphs of rooted 2-trees. This allows us to show that a diagram group containing all countable diagram groups is a semi-direct product of a partially commutative group and R. Thompson's group F. As a result, we prove...

Judicial independence is an idea that has both internal (or normative) and external (or institutional) aspects. From a normative viewpoint, judges should be autonomous moral agents, who can be relied on to carry out their public duties independent of venal or ideological considerations. Independence, or impartiality, in this sense is a desirable aspect of a judge’s character. But judges are hum...

The theory of causal independence is frequently used to facilitate the assessment of the probabilistic parameters of discrete probability distributions of complex Bayesian networks. Although it is possible to include continuous parameters in Bayesian networks as well, such parameters could not, so far, be modeled by means of causal-independence theory, as a theory of continuous causal independe...