Molecular effects of resistance elicitors from biological origin and their potential for crop protection

Plants contain a sophisticated innate immune network to prevent pathogenic microbes from gaining access to nutrients and from colonising internal structures. The first layer of inducible response is governed by the plant following the perception of microbe- or modified plant-derived molecules. As the perception of these molecules results in a plant response that can provide efficient resistance towards non-adapted pathogens they can also be described as ‘defence elicitors’. In compatible plant/microbe interactions, adapted microorganisms have means to avoid or disable this resistance response and promote virulence. However, this requires a detailed spatial and temporal response from the invading pathogens. In agricultural practice, treating plants with isolated defence elicitors in the absence of pathogens can promote plant resistance by uncoupling defence activation from the effects of pathogen virulence determinants. The plant responses to plant, bacterial, oomycete or fungal-derived elicitors are not, in all cases, universal and need elucidating prior to the application in agriculture. This review provides an overview of currently known elicitors of biological rather than synthetic origin and places their activity into a molecular context

Stochastic Galerkin Method for Optimal Control Problem Governed by Random Elliptic PDE with State Constraints

In this paper, we investigate a stochastic Galerkin approximation scheme for an optimal control problem governed by an elliptic PDE with random field in its coefficients. The optimal control minimizes the expectation of a cost functional with mean-state constraints. We first represent the stochastic elliptic PDE in terms of the generalized polynomial chaos expansion and obtain the parameterized optimal control problems. By applying the Slater condition in the subdifferential calculus, we obtain the necessary and sufficient optimality conditions for the state-constrained stochastic optimal control problem for the first time in the literature. We then establish a stochastic Galerkin scheme to approximate the optimality system in the spatial space and the probability space. Then the a priori error estimates are derived for the state, the co-state and the control variables. A projection algorithm is proposed and analyzed. Numerical examples are presented to illustrate our theoretical results