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By Moger T.A., Aalen O.O.

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Extra resources for Frailty modelling of testicular cancer incidence using Scandinavian data

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11 Actually, it is one of the candidates for membership in the (hypothetical) intermediate class N P I [53]. 1 UnQL UnQL is a language for querying data organized as a rooted directed graph with labeled edges [12]. According to the definition in [12], a rooted labeled graph is a tuple G = N, E, s, t, ν, , where N, E, s, t is a multi-graph, s, t : E → N denote the source and the target of each edge, respectively; ν ∈ N is the root of the graph, and : E → Label ∪ {⊥} is a labeling function for edges.

Let us study some more general properties of rule application for simple rules. We begin with the simple cases in which RGS consists only of edges. 1. For each G-Log rule R, if RGS consists only of one edge and no nodes, then [[ R ]]ξ is a function, for ξ in {∼, ∼, ≡}. Proof. We need to prove that for each G-Log graph G, there is exactly one G such that G, G ∈ [[ R ]]ξ . If R is not ξ-applicable, then the result holds by definition choosing G as G. Assume R is ξ-applicable in G, for any ξ in {∼, ∼, ≡}.

Consider a rule R ξ-applicable to G. The existence of a G fulfilling G such that Gi ξRRS (existing (1) and (2) is clearly ensured: for each Gi by hypothesis), consider Gi obtained by augmenting Gi with new nodes and edges ‘copying’ RGS . Consider G = G ∪ i Gi . 5) ensures that the process cannot enter into loop, thus ensuring the finiteness of the graph G . To get one (among the various possible) minimal graph it is sufficient to remove some of the new edges and nodes (possibly collapsing them) while the satisfiability property still holds.

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Frailty modelling of testicular cancer incidence using Scandinavian data by Moger T.A., Aalen O.O.

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