Write OK for the valuation ting, MK for the maximal ideal of K and kK for the residue field. Let us fix $ some uniformizer of K. We denote by acm : K → OK/(MK) the map sending some nonzero x ∈ K to x$−ord(x) mod MK , and sending zero to zero. This is a definable map. We denote by RV the union of K×/(1 +MK) and {0} and by rv : K → RV the quotient map. More generally, if m ∈ N∗, we set RVm = K×/(...

For the normal linear model regression setup, Zellner’s g-prior is extended for the case where the number of predictors p exceeds the number of observations n. Exact analytical calculation of the marginal density under this prior is seen to lead to a new closed form variable selection criterion. This results are also applicable to the multivariate regression setup. AMS subject classification: P...

Let G(V, E, W) be a graph n vertices and m edges, where each edge e is associated with a positive distance W(e). The traditional p-Center problem is to locate some kind of facilities at p vertices of G to minimize the maximum distance between any vertex and its nearest facility. This paper proposes a practical constraint: the subgraph induced by the p facility vertices must be connected and the...

We summarize the foundations and applications of the new semantics called p-stable and we show that it holds the important property of extending the WFS semantics.