This is part of an ongoing program to classify maximal orders on surfaces via their ramification data. Del Pezzo orders and ruled orders have been classified in [6, 4] and [2]. In this paper, we classify numerically CalabiYau orders which are the noncommutative analogues of surfaces of Kodaira dimension zero. Throughout, all objects and maps are assumed to be defined over some algebraically clo...

Application of Hidden Markov Models to long observation sequences entails the computation of extremely small probabilities. These probabilities introduce numerical instability in the computations used to determine the probability of an observed sequence given a model, the most likely sequence of states, and the maximum likelihood model updates given an observation sequence. This paper explains ...