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Funding: This work was supported by the European Research Council (Consolidator Grant 101002326 to J.K.). Ribosomally synthesized and post-translationally modified peptide natural products have provided many highly unusual scaffolds. This includes the intriguing alkaloids crocagins, which possess a tetracyclic core structure and whose biosynthesis has remained enigmatic. Here we use in vitro experiments to demonstrate that three proteins, CgnB, CgnC and CgnE, are sufficient for the production of the hallmark tetracyclic crocagin core from the precursor peptide CgnA. The crystal structures of the homologues CgnB and CgnE reveal them to be the founding members of a peptide-binding protein family and allow us to rationalize their distinct functions. We further show that the hydrolase CgnD liberates the crocagin core scaffold, which is subsequently N-methylated by CgnL. These insights allow us to propose a biosynthetic scheme for crocagins. Bioinformatic analyses based on these data led to the discovery of related biosynthetic pathways that may provide access to a structurally diverse family of peptide-derived pyrroloindoline alkaloids. Publisher PDF

A method for solving an inventory control problem, of which input data are described by triangular fuzzy numbers will be presented here. The continuous review model of the inventory control problem with fuzzy input data will be focused in, and a new solution method will be presented. For the reason that the result should be a fuzzy number because of fuzzy input data, and the certain number about order quantity is prefered in the real-world, it is necessary to transform the fuzzy result to crisp one. The interval mean value concept is used here to help to solve this problem. Under the condition of total cost minimum, the interval order quantity maximum can be obtained.

Goal programming (GP) is one of powerful techniques for solving multi-objective optimization and has been applied to various real-life problems. This paper presents an evolution program for solving nonlinear goal programming problems.

Idempotent semifield is a fundamental algebraic structure in max-plus algebra. It differs from field in that the addition is idempotent and there is no inverse of addition. We discuss the completeness and complete extension of idempotent semifields, which is achieved through a max-plus version of Dedekind cuts. Subsequently, we use our results to obtain a generalization of the linear extension theorem, an important result in max-plus algebra and systems theory. This theorem had been proved valid for finitely generated semimodules, and we generalize it to countably generated semimodules.