Entwicklung und Darstellung von Strategieoptionen zur Behandlung von Saatgut im ökologischen Landbau

Zur Erzeugung gesunden Saatgutes steht im Öko-Landbau neben präventiven Maßnahmen eine Reihe verschiedener Saatgutbehandlungsverfahren zur Verfügung (physikalische Methoden, Pflanzenextrakte, Naturstoffe und Mikroorganismenpräparate), die jedoch für die zahlreichen, wichtigen Wirt/Pathogen-Kombinationen nicht hinreichend untersucht waren. Inhalt und Ziel dieses Verbundvorhabens war es, Erfolg versprechende, aber hinsichtlich Handhabbarkeit und Wirksamkeit bislang nicht ausreichend untersuchte Varianten zu überprüfen sowie Schwellenwerte zu ermitteln, die eine Saatgutbehandlung indizieren. Um eine schnelle Übertragbarkeit wirksamer Verfahren in die Praxis zu ermöglichen, wurden neben den physikalischen Verfahren überwiegend gelistete Pflanzenstärkungsmittel untersucht. Im ersten Untersuchungsschritt wurden Klimakammer- und Gewächshausversuche angelegt. Ansätze, die sich unter diesen Modellbedingungen für die Praxistestung als geeignet erwiesen, wurden in Feldversuchen (Projekt 03OE127/2) überprüft. Für wichtige Wirt/Pathogen-Kombinationen konnten unter Modellbedingungen Behandlungsvarianten mit guten Wirkungen ausgewählt werden, die keine bis geringe negative Auswirkungen auf die Keimfähigkeit hatten. Bei Sommergerste mit Netzflecken oder Streifenkrankheit sowie bei Haferflugbrand konnten nach Behandlung mit Heißwasser, LEBERMOOSER, Ethanol, Milsana flüssig, Serenade und/oder Cedomon gute bis sehr gute Wirkungen erreicht werden. An Winterweizen mit Fusarium spp., Stagonospora nodorum bzw. Schneeschimmel sowie Winterroggen mit Schneeschimmel wurde eine Wirkung vor allem durch FZB 53, Warm- oder Heißwasserbehandlung und LEBERMOOSER erreicht. Von den besonders schwer zu bekämpfenden Krankheiten wurden Anthraknose an Lupine und Ascochyta pisi an Erbse mit Feuchtheißluft reduziert, jedoch war die Wirkung nicht ausreichend

Computing domains of attraction for planar dynamics

In this note we investigate the problem of computing the domain of attraction of a ow on R2 for a given attractor. We consider an operator that takes two inputs, the description of the ow and a cover of the attractors, and outputs the domain of attraction for the given attractor. We show that: (i) if we consider only (structurally) stable systems, the operator is (strictly semi-)computable; (ii) if we allow all systems de ned by C1-functions, the operator is not (semi-)computable. We also address the problem of computing limit cycles on these systems

A CDCL-style calculus for solving non-linear constraints

In this paper we propose a novel approach for checking satisfiability of non-linear constraints over the reals, called ksmt. The procedure is based on conflict resolution in CDCL style calculus, using a composition of symbolical and numerical methods. To deal with the non-linear components in case of conflicts we use numerically constructed restricted linearisations. This approach covers a large number of computable non-linear real functions such as polynomials, rational or trigonometrical functions and beyond. A prototypical implementation has been evaluated on several non-linear SMT-LIB examples and the results have been compared with state-of-the-art SMT solvers.Comment: 17 pages, 3 figures; accepted at FroCoS 2019; software available at <http://informatik.uni-trier.de/~brausse/ksmt/

Solving analytic differential equations in polynomial time over unbounded domains

In this paper we consider the computational complexity of solving initial-value problems de ned with analytic ordinary diferential equations (ODEs) over unbounded domains of Rn and Cn, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of de nition, provided it satis es a very generous bound on its growth, and that the function admits an analytic extension to the complex plane

The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

In this paper we revisit one of the rst models of analog computation, Shannon's General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPACcomputability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Moreover, since GPACs are equivalent to systems of polynomial di erential equations then we show that all real computable functions can be de ned by such models

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Robust computations with dynamical systems

In this paper we discuss the computational power of Lipschitz dynamical systems which are robust to in nitesimal perturbations. Whereas the study in [1] was done only for not-so-natural systems from a classical mathematical point of view (discontinuous di erential equation systems, discontinuous piecewise a ne maps, or perturbed Turing machines), we prove that the results presented there can be generalized to Lipschitz and computable dynamical systems. In other words, we prove that the perturbed reachability problem (i.e. the reachability problem for systems which are subjected to in nitesimal perturbations) is co-recursively enumerable for this kind of systems. Using this result we show that if robustness to in nitesimal perturbations is also required, the reachability problem becomes decidable. This result can be interpreted in the following manner: undecidability of veri cation doesn't hold for Lipschitz, computable and robust systems. We also show that the perturbed reachability problem is co-r.e. complete even for C1-systems

The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result

We construct a self-affine sponge in R 3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, implying that sponges with a dimension gap represent a nonempty open subset of the parameter space

Computability and dynamical systems

In this paper we explore results that establish a link between dynamical systems and computability theory (not numerical analysis). In the last few decades, computers have increasingly been used as simulation tools for gaining insight into dynamical behavior. However, due to the presence of errors inherent in such numerical simulations, with few exceptions, computers have not been used for the nobler task of proving mathematical results. Nevertheless, there have been some recent developments in the latter direction. Here we introduce some of the ideas and techniques used so far, and suggest some lines of research for further work on this fascinating topic