An output-sensitive algorithm for the minimization of 2-dimensional String Covers

String covers are a powerful tool for analyzing the quasi-periodicity of 1-dimensional data and find applications in automata theory, computational biology, coding and the analysis of transactional data. A \emph{cover} of a string $T$ is a string $C$ for which every letter of $T$ lies within some occurrence of $C$. String covers have been generalized in many ways, leading to \emph{k-covers}, \emph{$\lambda$-covers}, \emph{approximate covers} and were studied in different contexts such as \emph{indeterminate strings}. In this paper we generalize string covers to the context of 2-dimensional data, such as images. We show how they can be used for the extraction of textures from images and identification of primitive cells in lattice data. This has interesting applications in image compression, procedural terrain generation and crystallography

An international intercomparison of stable carbon isotope composition measurements of dissolved inorganic carbon in seawater

We report results of an intercomparison of stable carbon isotope ratio measurements in seawater dissolved inorganic carbon (δ 13C‐DIC) which involved 16 participating laboratories from various parts of the world. The intercomparison involved distribution of samples of a Certified Reference Material for seawater DIC concentration and alkalinity and a preserved sample of deep seawater collected at 4000 m in the northeastern Atlantic Ocean. The between‐lab standard deviation of reported uncorrected values measured with diverse analytical, detection, and calibration methods was 0.11‰ (1σ ). The multi‐lab average δ 13C‐DIC value reported for the deep seawater sample was consistent within 0.1‰ with historical measured values for the same water mass. Application of a correction procedure based on a consensus value for the distributed reference material, improved the between‐lab standard deviation to 0.06‰. The magnitude of the corrections were similar to those used to correct independent data sets using crossover comparisons, where deep water analyses from different cruises are compared at nearby locations. Our results demonstrate that the accuracy/uncertainty target proposed by the Global Ocean Observing System (±0.05‰) is attainable, but only if an aqueous phase reference material for δ 13C‐DIC is made available and used by the measurement community. Our results imply that existing Certified Reference Materials used for seawater DIC and alkalinity quality control are suitable for this purpose, if a “Certified” or internally consistent “consensus” value for δ 13C‐DIC can be assigned to various batches.publishedVersio

An international intercomparison of stable carbon isotope composition measurements of dissolved inorganic carbon in seawater

International audienceWe report results of an intercomparison of stable carbon isotope ratio measurements in seawater dissolved inorganic carbon (δ113C‐DIC) which involved 16 participating laboratories from various parts of the world. The intercomparison involved distribution of samples of a Certified Reference Material for seawater DIC concentration and alkalinity and a preserved sample of deep seawater collected at 4000 m in the northeastern Atlantic Ocean. The between‐lab standard deviation of reported uncorrected values measured with diverse analytical, detection, and calibration methods was 0.11‰ (1σ). The multi‐lab average δ13C‐DIC value reported for the deep seawater sample was consistent within 0.1‰ with historical measured values for the same water mass. Application of a correction procedure based on a consensus value for the distributed reference material, improved the between‐lab standard deviation to 0.06‰. The magnitude of the corrections were similar to those used to correct independent data sets using crossover comparisons, where deep water analyses from different cruises are compared at nearby locations. Our results demonstrate that the accuracy/uncertainty target proposed by the Global Ocean Observing System (±0.05‰) is attainable, but only if an aqueous phase reference material for δ13C‐DIC is made available and used by the measurement community. Our results imply that existing Certified Reference Materials used for seawater DIC and alkalinity quality control are suitable for this purpose, if a “Certified” or internally consistent “consensus” value for δ13C‐DIC can be assigned to various batches