Optimal control of linear bottleneck problems

International audienceThe regularity of Lagrange multipliers for state-constrained optimal control problems belongs to the basic questions of control theory. Here, we investigate bottleneck problems arising from optimal control problems for PDEs with certain mixed control-state inequality constraints. We show how to obtain Lagrange multipliers in Lp-spaces for linear problems and give an application to linear parabolic optimal control problems

Tomographic Reconstruction from a Few Views: A Multi-Marginal Optimal Transport Approach

19 pagesInternational audienceIn this article, we focus on tomographic reconstruction. The problem is to determine the shape of the interior interface using a tomographic approach while very few X-ray radiographs are performed. We use a multi-marginal optimal transport approach. Preliminary numerical results are presented

Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Analyse automatique des données scripturales prétraitées par des outils de visualization

RÉSUMÉ: Plusieurs méthodes pour analyser le processus d'écriture ont été utilisés afin de comprendre les stratégies des scripteurs. L'outil principal pour analyser le processus d'écriture est le fichier log, qui contient de façon exhaustive et détaillée l'ensemble des opérations effectuées par le scripteur lors de la rédaction d'un texte. Les données qui y sont emmagasinées sont de quantité considérable et lorsqu'elles ne sont pas préalablement traitées, elles sont hostiles à être analysées par l'humain. Parmi les outils d'analyse utilisés, les représentations du processus d'écriture permettent l'agrégation des données grâce à un pré-traitement. Les structures sous-jacentes des données ainsi représentées sont généralement plus propices à l'analyse que les données brutes. Cet article vise à démontrer différentes méthodes d'analyse automatique pouvant être appliquées à ces structures afin de trouver ou confirmer des structures et tendances à travers les données. ABSTRACT: Several methods to analyze the writing process were used in order to understand the strategies of the writers. The main tool to analyze the writing process is the log file which contains all the operations performed by the writer when writing a text, in a comprehensive and detailed way. The data stored in it is of considerable amount and when not previously treated, it is not made to be analyzed by humans. Among the analytical tools used, the representations of the writing process allow aggregation of data through a pre-treatment. The underlying data structures as shown by these tools are generally conducive to analyzing the raw data afterwards. This article aims to demonstrate various automatic analysis methods that can be applied to these structures to find or confirm the structures and trends through data

GCN5 modulates salicylic acid homeostasis by regulating H3K14ac levels at the 5ʹ and 3ʹ ends of its target genes

The modification of histones by acetyl groups has a key role in the regulation of chromatin structure and transcription. The Arabidopsis thaliana histone acetyltransferase GCN5 regulates histone modifications as part of the Spt-Ada-Gcn5 Acetyltransferase (SAGA) transcriptional coactivator complex. GCN5 was previously shown to acetylate lysine 14 of histone 3 (H3K14ac) in the promoter regions of its target genes even though GCN5 binding did not systematically correlate with gene activation. Here, we explored the mechanism through which GCN5 controls transcription. First, we fine-mapped its GCN5 binding sites genome-wide and then used several global methodologies (ATAC-seq, ChIP-seq and RNA-seq) to assess the effect of GCN5 loss-of-function on the expression and epigenetic regulation of its target genes. These analyses provided evidence that GCN5 has a dual role in the regulation of H3K14ac levels in their 5′ and 3′ ends of its target genes. While the gcn5 mutation led to a genome-wide decrease of H3K14ac in the 5′ end of the GCN5 down-regulated targets, it also led to an increase of H3K14ac in the 3′ ends of GCN5 up-regulated targets. Furthermore, genome-wide changes in H3K14ac levels in the gcn5 mutant correlated with changes in H3K9ac at both 5′ and 3′ ends, providing evidence for a molecular link between the depositions of these two histone modifications. To understand the biological relevance of these regulations, we showed that GCN5 participates in the responses to biotic stress by repressing salicylic acid (SA) accumulation and SA-mediated immunity, highlighting the role of this protein in the regulation of the crosstalk between diverse developmental and stress-responsive physiological programs. Hence, our results demonstrate that GCN5, through the modulation of H3K14ac levels on its targets, controls the balance between biotic and abiotic stress responses and is a master regulator of plant-environmental interactions