The Transcriptome of Compatible and Incompatible Interactions of Potato (Solanum tuberosum) with Phytophthora infestans Revealed by DeepSAGE Analysis

Late blight, caused by the oomycete Phytophthora infestans, is the most important disease of potato (Solanum tuberosum). Understanding the molecular basis of resistance and susceptibility to late blight is therefore highly relevant for developing resistant cultivars, either by marker-assissted selection or by transgenic approaches. Specific P. infestans races having the Avr1 effector gene trigger a hypersensitive resistance response in potato plants carrying the R1 resistance gene (incompatible interaction) and cause disease in plants lacking R1 (compatible interaction). The transcriptomes of the compatible and incompatible interaction were captured by DeepSAGE analysis of 44 biological samples comprising five genotypes, differing only by the presence or absence of the R1 transgene, three infection time points and three biological replicates. 30.859 unique 21 base pair sequence tags were obtained, one third of which did not match any known potato transcript sequence. Two third of the tags were expressed at low frequency (<10 tag counts/million). 20.470 unitags matched to approximately twelve thousand potato transcribed genes. Tag frequencies were compared between compatible and incompatible interactions over the infection time course and between compatible and incompatible genotypes. Transcriptional changes were more numerous in compatible than in incompatible interactions. In contrast to incompatible interactions, transcriptional changes in the compatible interaction were observed predominantly for multigene families encoding defense response genes and genes functional in photosynthesis and CO2 fixation. Numerous transcriptional differences were also observed between near isogenic genotypes prior to infection with P. infestans. Our DeepSAGE transcriptome analysis uncovered novel candidate genes for plant host pathogen interactions, examples of which are discussed with respect to possible function

Minimum Fuel Control of the Planar Circular Restricted Three-Body Problem. Celestial Mechanics and Dynamical Astronomy

Abstract The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L 1 -minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point boundary value problem, it is difficult to use shooting methods to compute numerical solutions (even with multiple shooting, as many switchings on the control occur when low thrusts are considered). To overcome these difficulties, two homotopies are introduced: One connects the investigated problem to the minimization of the L 2 -norm of the control, while the other introduces an interior penalization in the form of a logarithmic barrier. The combination of shooting with these continuation procedures allows to compute fuel optimal transfers for medium or low thrusts in the Earth-Moon system from a geostationary orbit, either towards the L 1 Lagrange point or towards a circular orbit around the Moon. To ensure local optimality of the computed trajectories, second order conditions are evaluated using conjugate point tests

RIEMANNIAN METRIC OF THE AVERAGED CONTROLLED KEPLER EQUATION Metric of Kepler equation

A non-autonomous sub-Riemannian problem is considered: Since periodicity with respect to the independent variable is assumed, one can define the averaged problem. In the case of the minimization of the energy, the averaged Hamiltonian remains quadratic in the adjoint variable. When it is non-degenerate, a Riemannian problem and the corresponding metric can be uniquely associated to the averaged problem modulo the orthogonal group of the quadratic form. The analysis is applied to the controlled Kepler equation. Explicit computations provide the averaged Hamiltonian of the Kepler motion in the threedimensional case. The Riemannian metric is given, and the curvature of a special subsytem is evaluated

An algorithmic guide for finite-dimensional optimal control problems

We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an optimal control problem. We consider two classical examples, simple but significant enough to be enriched and generalized to other settings: Zermelo and Goddard problems. We provide sample of the codes used to solve them and make these codes available online. We discuss direct and indirect methods, Hamilton–Jacobi approach, ending with optimistic planning. The examples illustrate the pros and cons of each method, and we show how these approaches can be combined into powerful tools for the numerical solution of optimal control problems for ordinary differential equations