Re-investigating Dempster's idea on evidence combination.

In this paper, we investigate the problem encountered by Dempster's combination rule in view of Dempster's original combination framework. We first show that the root of Dempster's combination rule (defined and named by Shafer) is Dempster's original idea on evidence combination. We then argue that Dempster's original idea on evidence combination is, in fact, richer than what has been formulated in the rule. We conclude that, by strictly following what Dempster has suggested, there should be no counterintuitive results when combining evidence.

The outflow ranking method for weighted directed graphs

A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms. Besides the well-known axioms of anonymity and positive responsiveness we introduce outflow monotonicity – meaning that in pairwise comparison between two nodes, a node is not doing worse in case its own outflow does not decrease and the other node’s outflow does not increase – and order preservation – meaning that adding two weighted digraphs such that the pairwise ranking between two nodes is the same in both weighted digraphs, then this is also their pairwise ranking in the ‘sum’ weighted digraph. The outflow ranking method generalizes the ranking by outdegree for directed graphs, and therefore also generalizes the ranking by Copeland score for tournaments.

Re-treatment profiles during long-term maintenance therapy in a periodontal practice in Norway

Background: Periodontal therapy coupled with active maintenance has been shown to be effective in maintaining periodontal health, however, the question of re-treatment is rarely alluded to in the literature.