Salicylic acid (SA)-mediated innate immune responses are activated in plants perceiving volatile monoterpenes. Here, we show that monoterpene-associated responses are propagated in feed-forward loops involving the systemic acquired resistance (SAR) signaling components pipecolic acid, glycerol-3-phosphate, and LEGUME LECTIN-LIKE PROTEIN1 (LLP1). In this cascade, LLP1 forms a key regulatory unit in both within-plant and between-plant propagation of immunity. The data integrate molecular components of SAR into systemic signaling networks that are separate from conventional, SA-associated innate immune mechanisms. These networks are central to plant-to-plant propagation of immunity, potentially raising SAR to the population level. In this process, monoterpenes act as microbe-inducible plant volatiles, which as part of plant-derived volatile blends have the potential to promote the generation of a wave of innate immune signaling within canopies or plant stands. Hence, plant-to-plant propagation of SAR holds significant potential to fortify future durable crop protection strategies following a single volatile trigger.

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This contribution deals with nonlinear control systems. More precisely, we are interested in the formal computation of a so-called flat output, a particular generalized output whose property is, roughly speaking, that all the integral curves of the system may be expressed as smooth functions of the components of this flat output and their successive time derivatives up to a finite order (to be determined). Recently, a characterization of such flat output has been obtained in [14,15], in the framework of manifolds of jets of infinite order (see e.g. [18,9]), that yields an abstract algorithm for its computation. In this paper it is discussed how these conditions can be checked using computer algebra. All steps of the algorithm are discussed for the simple (but rich enough) example of a non holonomic car.

Hyper-regularity [7] is a property of matrices over skew polynomials. In this contribution we consider the skew polynomial ring K[d/dt], with K the field of meromorphic functions and with the multiplication rule d/dt · f = f · d/dt + df /dt for all f ∈ K-see e. g. [3, Chpt. 0.10]. A matrix M ∈ K[d/dt] n×m is hyper-regular if it can be transformed into a constant matrix of maximal rank in reduced echelon form, i. e., if there are unimodular matrices UIn [7], it has been proposed to check hyper-regularity by transformation into Smith-Jacobson form [3]. However, algorithms for the transformation into Smith-Jacobson form are rather computational costly. Therefore, we present an efficient algorithm for testing whether a matrix is hyper-regular, based on row-reduction (and the analogous column-reduction)-see [2, Def. 2.1 and Thm. 2.2]. The algorithm also provides the corresponding transformation matrices and is based on the following result:Theorem 1. If n ≥ m (n < m) then M is hyper-regular if and only if row-reduction (columnreduction) of M yields a matrix over K of rank m (rank n).The derived algorithm has an important application in control theory. It can be used to check, e.g., linear time varying control systems of the form84

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