A Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods

In this work, we propose a multigrid preconditioner for Jacobian-free Newton-Krylov (JFNK) methods. Our multigrid method does not require knowledge of the Jacobian at any level of the multigrid hierarchy. As it is common in standard multigrid methods, the proposed method also relies on three building blocks: transfer operators, smoothers, and a coarse level solver. In addition to the restriction and prolongation operator, we also use a projection operator to transfer the current Newton iterate to a coarser level. The three-level Chebyshev semi-iterative method is employed as a smoother, as it has good smoothing properties and does not require the representation of the Jacobian matrix. We replace the direct solver on the coarsest level with a matrix-free Krylov subspace method, thus giving rise to a truly Jacobian-free multigrid preconditioner. We will discuss all building blocks of our multigrid preconditioner in detail and demonstrate the robustness and the efficiency of the proposed method using several numerical examples

Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints

We propose a nonlinear additive Schwarz method for solving nonlinear optimization problems with bound constraints. Our method is used as a "right-preconditioner" for solving the first-order optimality system arising within the sequential quadratic programming (SQP) framework using Newton's method. The algorithmic scalability of this preconditioner is enhanced by incorporating a solution-dependent coarse space, which takes into account the restricted constraints from the fine level. By means of numerical examples, we demonstrate that the proposed preconditioned Newton methods outperform standard active-set methods considered in the literature

Multilevel Minimization for Deep Residual Networks

We present a new multilevel minimization framework for the training of deep residual networks (ResNets), which has the potential to significantly reduce training time and effort. Our framework is based on the dynamical system's viewpoint, which formulates a ResNet as the discretization of an initial value problem. The training process is then formulated as a time-dependent optimal control problem, which we discretize using different time-discretization parameters, eventually generating multilevel-hierarchy of auxiliary networks with different resolutions. The training of the original ResNet is then enhanced by training the auxiliary networks with reduced resolutions. By design, our framework is conveniently independent of the choice of the training strategy chosen on each level of the multilevel hierarchy. By means of numerical examples, we analyze the convergence behavior of the proposed method and demonstrate its robustness. For our examples we employ a multilevel gradient-based methods. Comparisons with standard single level methods show a speedup of more than factor three while achieving the same validation accuracy

Multilevel minimization for deep residual networks

We present a new multilevel minimization framework for the training of deep residual networks (ResNets), which has the potential to significantly reduce training time and effort. Our framework is based on the dynamical system’s viewpoint, which formulates a ResNet as the discretization of an initial value problem. The training process is then formulated as a time-dependent optimal control problem, which we discretize using different time-discretization parameters, eventually generating multilevel-hierarchy of auxiliary networks with different resolutions. The training of the original ResNet is then enhanced by training the auxiliary networks with reduced resolutions. By design, our framework is conveniently independent of the choice of the training strategy chosen on each level of the multilevel hierarchy. By means of numerical examples, we analyze the convergence behavior of the proposed method and demonstrate its robustness. For our examples we employ a multilevel gradient-based methods. Comparisons with standard single level methods show a speedup of more than factor three while achieving the same validation accuracy

Parasitic plant small RNA analyses unveil parasite-specific signatures of microRNA retention, loss, and gain

Parasitism is a successful life strategy that has evolved independently in several families of vascular plants. The genera Cuscuta and Orobanche represent examples of the two profoundly different groups of parasites: one parasitizing host shoots and the other infecting host roots. In this study, we sequenced and described the overall repertoire of small RNAs from Cuscuta campestris and Orobanche aegyptiaca. We showed that C. campestris contains a number of novel microRNAs (miRNAs) in addition to a conspicuous retention of miRNAs that are typically lacking in other Solanales, while several typically conserved miRNAs seem to have become obsolete in the parasite. One new miRNA appears to be derived from a horizontal gene transfer event. The exploratory analysis of the miRNA population (exploratory due to the absence of a full genomic sequence for reference) from the root parasitic O. aegyptiaca also revealed a loss of a number of miRNAs compared to photosynthetic species from the same order. In summary, our study shows partly similar evolutionary signatures in the RNA silencing machinery in both parasites. Our data bear proof for the dynamism of this regulatory mechanism in parasitic plants.MicroRNAs in parasitic plants reflect their lifestyle

Why we need more collaboration in Europe to enhance post-marketing surveillance of vaccines.

The influenza A/H1N1 pandemic in 2009 taught us that the monitoring of vaccine benefits and risks in Europe had potential for improvement if different public and private stakeholders would collaborate better (public health institutes (PHIs), regulatory authorities, research institutes, vaccine manufacturers). The Innovative Medicines Initiative (IMI) subsequently issued a competitive call to establish a public-private partnership to build and test a novel system for monitoring vaccine benefits and risks in Europe. The ADVANCE project (Accelerated Development of Vaccine benefit-risk Collaboration in Europe) was created as a result. The objective of this paper is to describe the perspectives of key stakeholder groups of the ADVANCE consortium for vaccine benefit-risk monitoring and their views on how to build a European system addressing the needs and challenges of such monitoring. These perspectives and needs were assessed at the start of the ADVANCE project by the European Medicines Agency together with representatives of the main stakeholders in the field of vaccines within and outside the ADVANCE consortium (i.e. research institutes, public health institutes, medicines regulatory authorities, vaccine manufacturers, patient associations). Although all stakeholder representatives stated they conduct vaccine benefit-risk monitoring according to their own remit, needs and obligations, they are faced with similar challenges and needs for improved collaboration. A robust, rapid system yielding high-quality information on the benefits and risks of vaccines would therefore support their decision making. ADVANCE has developed such a system and has tested its performance in a series of proof of concept (POC) studies. The system, how it was used and the results from the POC studies are described in the papers in this supplementary issue

Mycobacterium leprae diversity and population dynamics in medieval Europe from novel ancient genomes.

Funder: Max-Planck SocietyFunder: St John’s College, CambridgeFunder: Fondation Raoul FollereauFunder: University of Zurich’s University Research Priority Program “Evolution in Action: From Genomes to Ecosystems”Funder: the Senckenberg Centre for Human Evolution and Palaeoenvironment (S-HEP) at the University of TübingenBackgroundHansen's disease (leprosy), widespread in medieval Europe, is today mainly prevalent in tropical and subtropical regions with around 200,000 new cases reported annually. Despite its long history and appearance in historical records, its origins and past dissemination patterns are still widely unknown. Applying ancient DNA approaches to its major causative agent, Mycobacterium leprae, can significantly improve our understanding of the disease's complex history. Previous studies have identified a high genetic continuity of the pathogen over the last 1500 years and the existence of at least four M. leprae lineages in some parts of Europe since the Early Medieval period.ResultsHere, we reconstructed 19 ancient M. leprae genomes to further investigate M. leprae's genetic variation in Europe, with a dedicated focus on bacterial genomes from previously unstudied regions (Belarus, Iberia, Russia, Scotland), from multiple sites in a single region (Cambridgeshire, England), and from two Iberian leprosaria. Overall, our data confirm the existence of similar phylogeographic patterns across Europe, including high diversity in leprosaria. Further, we identified a new genotype in Belarus. By doubling the number of complete ancient M. leprae genomes, our results improve our knowledge of the past phylogeography of M. leprae and reveal a particularly high M. leprae diversity in European medieval leprosaria.ConclusionsOur findings allow us to detect similar patterns of strain diversity across Europe with branch 3 as the most common branch and the leprosaria as centers for high diversity. The higher resolution of our phylogeny tree also refined our understanding of the interspecies transfer between red squirrels and humans pointing to a late antique/early medieval transmission. Furthermore, with our new estimates on the past population diversity of M. leprae, we gained first insights into the disease's global history in relation to major historic events such as the Roman expansion or the beginning of the regular transatlantic long distance trade. In summary, our findings highlight how studying ancient M. leprae genomes worldwide improves our understanding of leprosy's global history and can contribute to current models of M. leprae's worldwide dissemination, including interspecies transmissions