Local and global error models to improve uncertainty quantification

In groundwater applications, Monte Carlo methods are employed to model the uncertainty on geological parameters. However, their brute-force application becomes computationally prohibitive for highly detailed geological descriptions, complex physical processes, and a large number of realizations. The Distance Kernel Method (DKM) overcomes this issue by clustering the realizations in a multidimensional space based on the flow responses obtained by means of an approximate (computationally cheaper) model; then, the uncertainty is estimated from the exact responses that are computed only for one representative realization per cluster (the medoid). Usually, DKM is employed to decrease the size of the sample of realizations that are considered to estimate the uncertainty. We propose to use the information from the approximate responses for uncertainty quantification. The subset of exact solutions provided by DKM is then employed to construct an error model and correct the potential bias of the approximate model. Two error models are devised that both employ the difference between approximate and exact medoid solutions, but differ in the way medoid errors are interpolated to correct the whole set of realizations. The Local Error Model rests upon the clustering defined by DKM and can be seen as a natural way to account for intra-cluster variability; the Global Error Model employs a linear interpolation of all medoid errors regardless of the cluster to which the single realization belongs. These error models are evaluated for an idealized pollution problem in which the uncertainty of the breakthrough curve needs to be estimated. For this numerical test case, we demonstrate that the error models improve the uncertainty quantification provided by the DKM algorithm and are effective in correcting the bias of the estimate computed solely from the MsFV results. The framework presented here is not specific to the methods considered and can be applied to other combinations of approximate models and techniques to select a subset of realizations

The functions of DNA methylation by CcrM in Caulobacter crescentus: a global approach.

DNA methylation is involved in a diversity of processes in bacteria, including maintenance of genome integrity and regulation of gene expression. Here, using Caulobacter crescentus as a model, we exploit genome-wide experimental methods to uncover the functions of CcrM, a DNA methyltransferase conserved in most Alphaproteobacteria. Using single molecule sequencing, we provide evidence that most CcrM target motifs (GANTC) switch from a fully methylated to a hemi-methylated state when they are replicated, and back to a fully methylated state at the onset of cell division. We show that DNA methylation by CcrM is not required for the control of the initiation of chromosome replication or for DNA mismatch repair. By contrast, our transcriptome analysis shows that >10% of the genes are misexpressed in cells lacking or constitutively over-expressing CcrM. Strikingly, GANTC methylation is needed for the efficient transcription of dozens of genes that are essential for cell cycle progression, in particular for DNA metabolism and cell division. Many of them are controlled by promoters methylated by CcrM and co-regulated by other global cell cycle regulators, demonstrating an extensive cross talk between DNA methylation and the complex regulatory network that controls the cell cycle of C. crescentus and, presumably, of many other Alphaproteobacteria.