The Gauss map on a class of interval translation mappings

We study the dynamics of a class of interval translation map on three intervals. We show that in this class the typical ITM is of finite type (reduce to an interval exchange transformation) and that the complement contains a Cantor set. We relate our maps to substitution subshifts. Results on Hausdorff dimension of the attractor and on unique ergodicity are obtained

The arable farmer as the assessor of within-field soil variation

Feasible, fast and reliable methods of mapping within-field variation are required for precision agriculture. Within precision agriculture research much emphasis has been put on technology, whereas the knowledge that farmers have and ways to explore it have received little attention. This research characterizes and examines the spatial knowledge arable farmers have of their fields and explores whether it is a suitable starting point to map the within-field variation of soil properties. A case study was performed in the Hoeksche Waard, the Netherlands, at four arable farms. A combination of semi-structured interviews and fieldwork was used to map spatially explicit knowledge of within-field variation. At each farm, a field was divided into internally homogeneous units as directed by the farmer, the soil of the units was sampled and the data were analysed statistically. The results show that the farmers have considerable spatial knowledge of their fields. Furthermore, they apply this knowledge intuitively during various field management activities such as fertilizer application, soil tillage and herbicide application. The sample data on soil organic matter content, clay content and fertility show that in general the farmers’ knowledge formed a suitable starting point for mapping within-field variation in the soil. Therefore, it should also be considered as an important information source for highly automated precision agriculture systems

Representing uncertainty in continental-scale gridded precipitation fields for agrometeorological modeling

This work proposes a relatively simple methodology for creating ensembles of precipitation inputs that are consistent with the spatial and temporal scale necessary for regional crop modeling. A high-quality reference precipitation dataset [the European Land Data Assimilation System (ELDAS)] was used as a basis to define the uncertainty in an operational precipitation database [the Crop Growth Monitoring System (CGMS)]. The distributions of precipitation residuals (CGMS ¿ ELDAS) were determined for classes of CGMS precipitation and transformed to a Gaussian distribution using normal score transformations. In cases of zero CGMS precipitation, the occurrence of rainfall was controlled by an indicator variable. The resulting normal-score-transformed precipitation residuals appeared to be approximately multivariate Gaussian and exhibited strong spatial correlation; however, temporal correlation was very weak. An ensemble of 100 precipitation realizations was created based on back-transformed spatially correlated Gaussian residuals and indicator realizations. Quantile¿quantile plots of 100 realizations against the ELDAS reference data for selected sites revealed similar distributions (except for the 100th percentile, owing to some large residuals in the realizations). The semivariograms of realizations for sampled days showed considerable variability in the overall variance; the range of the spatial correlation was similar to that of the ELDAS reference dataset. The intermittency characteristics of wet and dry periods were reproduced well for most of the selected sites, but the method failed to reproduce the dry period statistics in semiarid areas (e.g., southern Spain). Finally, a case study demonstrates how rainfall ensembles can be used in operational crop modeling and crop yield forecasting

Chabauty-Coleman experiments for genus 3 hyperelliptic curves

We describe a computation of rational points on genus 3 hyperelliptic curves $C$ defined over $\mathbb{Q}$ whose Jacobians have Mordell-Weil rank 1. Using the method of Chabauty and Coleman, we present and implement an algorithm in Sage to compute the zero locus of two Coleman integrals and analyze the finite set of points cut out by the vanishing of these integrals. We run the algorithm on approximately 17,000 curves from a forthcoming database of genus 3 hyperelliptic curves and discuss some interesting examples where the zero set includes global points not found in $C(\mathbb{Q})$.Comment: 18 page

Multiphase sampling using expected value of information

This paper explores multiphase or infill sampling to reduce uncertainty after an initial sample has been taken and analysed to produce a map of the probability of some hazard. New observations are iteratively added by maximising the global expected value of information of the points. This is equivalent to minimisation of global misclassification costs. The method accounts for measurement error and different costs of type I and type II errors. Constraints imposed by a mobile sensor web can be accommodated using cost distances rather than Euclidean distances to decide which sensor moves to the next sample location. Calculations become demanding when multiple sensors move simultaneously. In that case, a genetic algorithm can be used to find sets of suitable new measurement locations. The method was implemented using R software for statistical computing and contributed libraries and it is demonstrated using a synthetic data set

Extending Elliptic Curve Chabauty to higher genus curves

We give a generalization of the method of "Elliptic Curve Chabauty" to higher genus curves and their Jacobians. This method can sometimes be used in conjunction with covering techniques and a modified version of the Mordell-Weil sieve to provide a complete solution to the problem of determining the set of rational points of an algebraic curve $Y$.Comment: 24 page