Potential Response of Soil-Borne Fungal Pathogens Affecting Crops to a Scenario of Climate Change in Europe

A study was carried out on the potential response of soil-borne pathogens causing crop yield losses under a climate change scenario in Europe. A controlled chamber set of experiments was carried out to quantify pathogen response to temperature using pure colonies of three soil-borne fungi, representative of low (Fusarium nivale), medium-high (Athelia rolfsii) and high (Macrophomina phaseolina) temperature requirements. A generic model to simulate fungal growth response to temperature based on these experiments was developed and linked to a soil temperature model component, and to components to simulate soil water content accounting for crop water uptake of potential hosts. Pathogens relative growth was simulated over Europe using the IPCC A1B emission scenario as realization of the Hadley-CM3 global climate model, available from the European Commission and processed for use with biophysical models. The simulations resulting from using the time span centred on 2030 were compared to the baseline, centred on the year 2000, using a sample of 30 years of daily weather. The general trend of soil-borne pathogens response to the scenario of climate change is a relative increase in growth in colder areas of Europe, as a function of their temperature requirements. Projections of F. nivale in the future indicate a relative increase of this winter pathogen of wheat in Northern European countries. A. rolfsii and M. phaseolina, two soil-borne pathogens typical of warmer agricultural areas, could find more favourable conditions in areas of the Central Europe, but they differentiated in Southern Europe where A. rolfsii resulted affected by summer soil temperatures above optimum

On the regularizing power of multigrid-type algorithms

We consider the deblurring problem of noisy and blurred images in the case of known space invariant point spread functions with four choices of boundary conditions. We combine an algebraic multigrid previously defined ad hoc for structured matrices related to space invariant operators (Toeplitz, circulants, trigonometric matrix algebras, etc.) and the classical geometric multigrid studied in the partial differential equations context. The resulting technique is parameterized in order to have more degrees of freedom: a simple choice of the parameters allows us to devise a quite powerful regularizing method. It defines an iterative regularizing method where the smoother itself has to be an iterative regularizing method (e.g., conjugate gradient, Landweber, conjugate gradient for normal equations, etc.). More precisely, with respect to the smoother, the regularization properties are improved and the total complexity is lower. Furthermore, in several cases, when it is directly applied to the system $A{\bf f}={\bf g}$, the quality of the restored image is comparable with that of all the best known techniques for the normal equations $A^TA{\bf f}=A^T{\bf g}$, but the related convergence is substantially faster. Finally, the associated curves of the relative errors versus the iteration numbers are ``flatter'' with respect to the smoother (the estimation of the stop iteration is less crucial). Therefore, we can choose multigrid procedures which are much more efficient than classical techniques without losing accuracy in the restored image (as often occurs when using preconditioning). Several numerical experiments show the effectiveness of our proposals

Fractional graph Laplacian for image reconstruction

Image reconstruction problems, like image deblurring and computer tomography, are usually ill-posed and require regularization. A popular approach to regularization is to substitute the original problem with an optimization problem that minimizes the sum of two terms, an term and an term with . The first penalizes the distance between the measured data and the reconstructed one, the latter imposes sparsity on some features of the computed solution. In this work, we propose to use the fractional Laplacian of a properly constructed graph in the term to compute extremely accurate reconstructions of the desired images. A simple model with a fully automatic method, i.e., that does not require the tuning of any parameter, is used to construct the graph and enhanced diffusion on the graph is achieved with the use of a fractional exponent in the Laplacian operator. Since the fractional Laplacian is a global operator, i.e., its matrix representation is completely full, it cannot be formed and stored. We propose to replace it with an approximation in an appropriate Krylov subspace. We show that the algorithm is a regularization method under some reasonable assumptions. Some selected numerical examples in image deblurring and computer tomography show the performance of our proposal

Analysis of Multigrid Preconditioning for Implicit PDE Solvers for Degenerate Parabolic Equations

Abstract. In this paper an implicit numerical method designed for nonlinear degenerate parabolic equations is proposed. A convergence analysis and the study of the related computa-tional cost are provided. In fact, due to the nonlinear nature of the underlying mathematical model, the use of a fixed point scheme is required. The chosen scheme is the Newton method and its con-vergence is proven under mild assumptions. Every step of the Newton method implies the solution of large, locally structured, linear systems. A special effort is devoted to the spectral analysis of the relevant matrices and to the design of appropriate multigrid preconditioned Krylov methods. Numerical experiments for the validation of our analysis complement this contribution