On the Telegraph Equation with a Small Parameter

This work is an edited translation, by A. Bobrowski and W. Chojnacki, of the original Polish text entitled O rownaniu telegrafistow z malym parametrem which appeared in Prace Naukowe Politechniki Lubelskiej 212, Matematyka (Research Bulletin of the Lublin University of Technology 212, Mathematics), 1991, vol. 12, pp. 17-40.This work is an edited translation, by A. Bobrowski and W. Chojnacki, of the original Polish text entitled O rownaniu telegrafistow z malym parametrem which appeared in Prace Naukowe Politechniki Lubelskiej 212, Matematyka (Research Bulletin of the Lublin University of Technology 212, Mathematics), 1991, vol. 12, pp. 17-40

On the Favard classes of semigroups associated with pseudo-resolvents

A pseudo-resolvent on a Banach space, indexed by positive numbers and tempered at infinity, gives rise to a bounded strongly continuous one-parameter semigroup S on a closed subspace of the ambient Banach space. We prove that the range space of the pseudo-resolvent contains the domain of the generator of S, and is contained in the Favard class of S, which consists of all uniformly Lipschitz vectors for S. We explore when some or all of these three spaces coincide.Wojciech Chojnacki and Jan Kisyńsk

Nonparametric Bayesian Logic

The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation. This paper extends BLOG by adopting generative processes over function spaces - known as nonparametrics in the Bayesian literature. We introduce syntax for reasoning about arbitrary collections of objects, and their properties, in an intuitive manner. By exploiting exchangeability, distributions over unknown objects and their attributes are cast as Dirichlet processes, which resolve difficulties in model selection and inference caused by varying numbers of objects. We demonstrate these concepts with application to citation matching