Subharmonic variation of Azukawa pseudometrics for balanced domains

Behavioural Pseudometrics for Nondeterministic Probabilistic Systems

For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on Hennessy-Milner logic. The logic for characterising ...

Extensions of totally bounded pseudometrics

Clusters, Concepts, and Pseudometrics

The fields of cluster analysis and concept analysis are both used to identify patterns in data. Concept analysis identifies similarities between sets of objects based on their attributes. Cluster analysis groups objects with related characteristics based on some notion of distance. In this paper, we investigate connections between these two approaches. In particular, for each binary relation de...

Modal Characterisations of Behavioural Pseudometrics

For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on the Hennessy-Milner logic. The logic for characteris...

Fluctuation bounds for subharmonic functions

We obtain bounds for the angular fluctuations of a subharmonic function f(z) = R log |z− w| dμ(w) in terms of the distribution of the angular mean. This can be applied to study the regularity of subharmonic functions.