Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator

We consider the problem of recovering the initial data (or initial state) of infinite-dimensional linear systems with unitary semigroups. It is well-known that this inverse problem is well posed if the system is exactly observable, but this assumption may be very restrictive in some applications. In this paper we are interested in systems which are not exactly observable, and in particular, where we cannot expect a full reconstruction. We propose to use the algorithm studied by Ramdani et al. in (Automatica 46:1616–1625, 2010) and prove that it always converges towards the observable part of the initial state. We give necessary and sufficient condition to have an exponential rate of convergence. Numerical simulations are presented to illustratethe theoretical results

Origin error in estimation of analysis error covariances in variational data assimilation

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The optimal solution (analysis) error arises due to the errors of the input data (background and observation errors). For random and normally distributed input data errors, the optimal solution error covariance operator is approximated by the inverse Hessian of the auxiliary (linearized) data assimilation problem, which involves the tangent linear model constraints. The so-called 'origin error' occurs [5] in estimating the analysis error covariance. An exact equation is derived for the origin error, and algorithms to estimate this error for computing the variances are presented

Adjoint to the Hessian derivative and error covariances in variational data assimilation

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The optimal solution error is considered through the errors of input data (background and observation errors). The optimal solution error covariance operator is approximated by the inverse Hessian of the auxiliary (linearized) data assimilation problem, which involves the tangent linear model constraints. We show that the derivative of the inverse Hessian with respect to the exact solution may be treated as the measure of nonlinearity for analysis error covariances in variational data assimilation problems

On error sensitivity analysis in variational data assimilation

Theme 4 - Simulation et optimisation de systemes complexes - Projet IdoptSIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.2001 n.4220 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

275 years of forestry meets genomics in Pinus sylvestris

Abstract Pinus sylvestris has a long history of basic and applied research that is relevant for both forestry and evolutionary studies. Its patterns of adaptive variation and role in forest economic and ecological systems have been studied extensively for nearly 275 years, detailed demography for a 100 years and mating system more than 50 years. However, its reference genome sequence is not yet available and genomic studies have been lagging compared to, for example, Pinus taeda and Picea abies, two other economically important conifers. Despite the lack of reference genome, many modern genomic methods are applicable for a more detailed look at its biological characteristics. For example, RNA‐seq has revealed a complex transcriptional landscape and targeted DNA sequencing displays an excess of rare variants and geographically homogenously distributed molecular genetic diversity. Current DNA and RNA resources can be used as a reference for gene expression studies, SNP discovery, and further targeted sequencing. In the future, specific consequences of the large genome size, such as functional effects of regulatory open chromatin regions and transposable elements, should be investigated more carefully. For forest breeding and long‐term management purposes, genomic data can help in assessing the genetic basis of inbreeding depression and the application of genomic tools for genomic prediction and relatedness estimates. Given the challenges of breeding (long generation time, no easy vegetative propagation) and the economic importance, application of genomic tools has a potential to have a considerable impact. Here, we explore how genomic characteristics of P. sylvestris, such as rare alleles and the low extent of linkage disequilibrium, impact the applicability and power of the tools

Potential for evolutionary responses to climate change – evidence from tree populations

Evolutionary responses are required for tree populations to be able to track climate change. Results of 250 years of common garden experiments show that most forest trees have evolved local adaptation, as evidenced by the adaptive differentiation of populations in quantitative traits, reflecting environmental conditions of population origins. On the basis of the patterns of quantitative variation for 19 adaptation-related traits studied in 59 tree species (mostly temperate and boreal species from the Northern hemisphere), we found that genetic differentiation between populations and clinal variation along environmental gradients were very common (respectively, 90% and 78% of cases). Thus, responding to climate change will likely require that the quantitative traits of populations again match their environments. We examine what kind of information is needed for evaluating the potential to respond, and what information is already available. We review the genetic models related to selection responses, and what is known currently about the genetic basis of the traits. We address special problems to be found at the range margins, and highlight the need for more modeling to understand specific issues at southern and northern margins. We need new common garden experiments for less known species. For extensively studied species, new experiments are needed outside the current ranges. Improving genomic information will allow better prediction of responses. Competitive and other interactions within species and interactions between species deserve more consideration. Despite the long generation times, the strong background in quantitative genetics and growing genomic resources make forest trees useful species for climate change research. The greatest adaptive response is expected when populations are large, have high genetic variability, selection is strong, and there is ecological opportunity for establishment of better adapted genotypes