Use of robust methods to determine quadratic surfaces: application to heritage

3D surveys of archaeological elements and the construction of virtual models enable us to reconstruct historical sites. They provide useful data to select specific building processes.Photogrammetry and Terrestrial Laser Scanning (TLS) are the most common techniques to obtain synthetically heritage models. These techniques provide massive data which can only be managed by replacing them by primitive shapes, thereby obtaining more simple models and the explicit geometry of the element. Statistical and robust methods are used for this substitution, thereby avoiding the common errors due to measuring. Of these methods, the most widely used are the least-median-of-squares (LMedS) and the RANSAC method.Another computation method consists in recursive processes based on evolutive-type algorithms to adjust the model to the data captured.This paper describes two surface computation methodologies to determine the modelling of a column shaft located in temple G of the archaeological park of Selinunte (Sicily).     

High precision isotopic analyses of lead ores from New Mexico by MC-ICP-MS: implications for tracing the production and exchange of Pueblo IV glaze-decorated pottery

Between ca. 1275 and 1700 CE, Pueblo groups in the northern Southwest United States produced and exchanged ceramic bowls decorated with lead-based glaze paints. Previous studies of these glaze-decorated bowls have used lead isotopic analysis by ICP-MS to identify the sources of lead used by Pueblo potters, and investigate how social or economic factors may have influenced resource use among different Pueblo communities (e.g. 13 and 14; Huntley et al., 2007; Huntley, 2008). However, interpretations of much of this isotopic data have remained provisional because of overlap among the isotopic ratios of potential sources and because the isotopic composition of many glaze paints do not clearly match any known source. Here, we use multi-collector ICP-MS to re-measure the lead isotopic composition of 48 samples of lead sulfide (galena) and lead carbonate (cerussite) from sources in New Mexico that were potentially utilized by Pueblo potters, including mines within the Cerrillos Hills, Magdalena, Hansonburg, and Joyita Hills mining districts. These results define the isotopic composition of lead ores from these districts with greater precision and accuracy than achieved in previous studies and better distinguish among these mining districts in lead isotope space. Most significantly, we find that galena mineralization within the Cerrillos Hills only has a modest degree of isotopic variation, with ²⁰⁶Pb/²⁰⁴Pb ratios from 18.508 to 18.753, ²⁰⁷Pb/²⁰⁴Pb ratios from 15.580 to 15.607, and ²⁰⁸Pb/²⁰⁴Pb ratios from 38.388 to 38.560. These ranges are far narrower than previously reported, and should supersede previously published values for this district. In total, we conclude that isotopic measurements of both ores and glaze paints made by MC-ICP-MS will provide new information about the provenance of lead in glaze paints and allow for more detailed interpretations about resource procurement and exchange in the Pueblo world.     

A Comparison of Spatial and Nonspatial Methods in Statistical Modeling of NO2: Prediction Accuracy,Uncertainty Quantification,and Model Interpretation

${\text{NO}}_2$ is a traffic-related air pollutant. Ground ${\text{NO}}_2$ monitoring stations measure ${\text{NO}}_2$ concentrations at certain locations and statistical predictive methods have been developed to predict ${\text{NO}}_2$ as a continuous surface. Among them, ensemble tree-based methods have shown to be powerful in capturing nonlinear relationships between ${\text{NO}}_2$ measurements and geospatial predictors but it is unclear if the spatial structure of ${\text{NO}}_2$ is also captured in the response-covariates relationships. We dive into the comparison between spatial and nonspatial data models accounting for prediction accuracy, model interpretation and uncertainty quantification. Moreover, we implement two new spatial and a nonspatial methods that have not been applied to air pollution mapping. We implemented our study using national ground station measurements of ${\text{NO}}_2$ in Germany and the Netherlands of 2017. Our results indicate heterogeneous levels of importance of modeling the spatial process in different areas. The prediction intervals predicted with ensemble tree-based methods are more satisfactory than the geostatistical methods. The two new methods implemented each obtained better prediction accuracy compared to the original ensemble tree-based and stacking methods. The probabilistic distribution of the spatial random field estimated by the geostatistical methods could provide useful information for analyzing emission sources and the spatial process of observations.