First, we compute off-line the shortest switching path which has the minimum discrete cost from an initial set to the given target set.
First, we compute off-line the shortest path, which has the minimum discrete cost, from an initial state to the given target set.
A mixed approach with a discrete cost function and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local subsystem problems and a coordinator within a hierarchical framework.
The proof of Lemma 1 appears in Appendix "Proofs to lemmas corresponding to the EDDC algorithm for discrete cost functions".
The proofs of the following lemmas appear in Appendix "Proofs to lemmas corresponding to the EDDC algorithm for discrete cost functions".
Furthermore, we performed exploratory analyses of the trajectory of costs for our linked cohort, which confirmed our hypothesis that aggregate cost per unit time was characterized by two discrete costing phases.
The time complexity of processing n letters in the input is O | Σ | n 3 log 2 n, where the base of the log function is determined by the range of cost values (Section "An online algorithm for EDDC using min-plus matrix-vector multiplication for discrete cost functions").
The mean 30-day cost curves confirmed the hypothesis of discrete cost phases with inflection points separating the post-discharge and stable phases, and the stable and pre-death phases estimated at 3 months post discharge and 6 months prior to death, respectively (Step 2).
In Section "An online algorithm for EDDC using min-plus matrix-vector multiplication for discrete cost functions", an efficient min-plus matrix-vector multiplication algorithm is described for matrices and vectors which differences between adjacent entries are taken from a finite integer interval.
Under some discreteness assumptions, this matrix-vector min-plus multiplication algorithm applies to several problems from the domains of context-free grammar parsing and RNA folding and, in particular, implies the asymptotically fastest O n 3 log 2 n time algorithm for single-strand RNA folding with discrete cost functions.
