Emission of volatile sesquiterpenes and monoterpenes in grapevine genotypes following Plasmopara viticola inoculation in vitro

The grapevine (Vitis vinifera) is one of the most widely cultivated fruit crops globally, and one of its most important diseases in terms of economic losses is downy mildew, caused by Plasmopara viticola. Several wild Vitis species have been found to be resistant to this pathogen and have been used in breeding programs to introduce resistance traits to susceptible cultivars. Plant defense is based on different mechanisms, and volatile organic compounds (VOCs) play a major role in the response to insects and pathogens. Although grapevine resistance mechanisms and the production of secondary metabolites have been widely characterized in resistant genotypes, the emission of VOCs has not yet been investigated following P. viticola inoculation. A Proton Transfer Reaction‐Time of Flight‐Mass Spectrometer (PTR‐ToF‐MS) was used to analyze the VOCs emitted by in vitro‐grown plants of grapevine genotypes with different levels of resistance. Downy mildew inoculation significantly increased the emission of monoterpenes and sesquiterpenes by the resistant SO4 and Kober 5BB genotypes, but not by the susceptible V. vinifera Pinot noir. Volatile terpenes were implicated in plant defense responses against pathogens, suggesting that they could play a major role in the resistance against downy mildew by direct toxicity or by inducing grapevine resistance. The grapevine genotypes differed in terms of the VOC emission pattern of both inoculated and uninoculated plants, indicating that PTR‐ToF‐MS could be used to screen hybrids with different levels of downy mildew resistance. Copyright © 2015 John Wiley & Sons, Ltd.     

Probabilistic interpretation of a coupled system of Hamilton–Jacobi–Bellman equations

In this paper, we give a probabilistic interpretation for a coupled system of Hamilton–Jacobi–Bellman equations using the value function of a stochastic control problem. First we introduce this stochastic control problem. Then we prove that the value function of this problem is deterministic and satisfies a (strong) dynamic programming principle. And finally, the value function is shown to be the unique viscosity solution of the coupled system of Hamilton–Jacobi–Bellman equations.     

Recurrence of Ancestral Lines and Offspring Trees in Time Stationary Branching Populations

For time stationary Galton- Watson-branching populations on a general type space, the structure of the “individually positive recurrent part” of the system is described: its building blocks consist of finitely many “clans” with positive recurrent trunks. Conditions are given when this nubsystem is void, and when it equals the full system. In addition, positive recurrence on the clan level is characterized. Whereas individual positive recurrence turns out to be a symmetric concept with respect to forward and backward time direction (i. e., with respect to anceatral lines and offspring trees), with individual null recurrence this symmetry can fail even in the absence of branching, i.e., for independently migrating particle systems (Example 13.1). For discrete type spaces a classification of types as to the various individual recurrence concepts (positive, null, forward and backward in time) is proposed and illustrated by a couple of results and examples. For finite type spaces conditiom on the branching dynamics and its mean matrix for the existence of nontrivial equilibria are given.     

Passivity and Microlocal Spectrum Condition

In the setting of vector-valued quantum fields obeying a linear wave-equation in a globally hyperbolic, stationary spacetime, it is shown that the two-point functions of passive quantum states (mixtures of ground- or KMS-states) fulfill the microlocal spectrum condition (which in the case of the canonically quantized scalar field is equivalent to saying that the two-pnt function is of Hadamard form). The fields can be of bosonic or fermionic character. We also give an abstract version of this result by showing that passive states of a topological *-dynamical system have an asymptotic pair correlation spectrum of a specific type. Received: 9 February 2000 / Accepted: 7 June 2000