Some differential equations for the Riemann θ\theta-function on Jacobians

We prove some differential equations for the Riemann theta function associated to the Jacobian of a Riemann surface. The proof is based on some variants of a formula by Fay for the theta function, which are motivated by their analogues in Arakelov theory of Riemann surfaces. Moreover, we give a generalization of Rosenhain's formula to hyperelliptic Riemann surfaces as conjectured by Gu\`ardia.Comment: Comments are welcom

On arithmetic intersection numbers on self-products of curves

We give a close formula for the N\'eron-Tate height of tautological integral cycles on Jacobians of curves over number fields as well as a new lower bound for the arithmetic self-intersection number $\hat{\omega}^2$ of the dualizing sheaf of a curve in terms of Zhang's invariant $\varphi$. As an application, we obtain an effective Bogomolov-type result for the tautological cycles. We deduce these results from a more general combinatorial computation of arithmetic intersection numbers of adelic line bundles on higher self-products of curves, which are linear combinations of pullbacks of line bundles on the curve and the diagonal bundle.Comment: 21 pages. Comments are welcome

Designing strategies to control grey mould in strawberry cultivation using decision support systems

Grey mould is one of the major diseases in strawberry cultivation. Fungicides to control Botrytis cinerea are applied frequently during flowering and sometimes at harvest. Reduction of pesticide use is one of the major aims of the Dutch government. Implementation of a Decision Support System (DSS) helps to achieve this goal. Pin point timing of fungicide application can possibly improve the efficacy of the treatment and reduce the number of spray applications. Predicted weather data to forecast infection risks are used by most DSS’s. However in strawberry cultivation irrigation is a daily practice. The effect of overhead irrigation on the Botrytis infection risk is unknown. This is one of the reasons that strawberry growers infrequently use DSS’s. Therefore adaptation of the model to agricultural management is necessary. Under low disease pressure DSS BoWaS controlled Botrytis fruit rot 62% better then routine applications of fungicides, with a 50% reduction of fungicide input. Adding an irrigation or a disease pressure sub-routine did not improve the model under low disease pressure. BoWaS based on disease pressure and weather resulted in better control of grey mould then the weather based BoWaS, under high disease pressure. Adding an irrigation rule did not improve the model further. Using the modified BoWaS reduced fungicide input with 36% compared to routine applications with the same efficacy

Robust Sparse Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal correlation. This paper discusses a method for Robust Sparse CCA. Sparse estimation produces canonical vectors with some of their elements estimated as exactly zero. As such, their interpretability is improved. We also robustify the method such that it can cope with outliers in the data. To estimate the canonical vectors, we convert the CCA problem into an alternating regression framework, and use the sparse Least Trimmed Squares estimator. We illustrate the good performance of the Robust Sparse CCA method in several simulation studies and two real data examples

An algorithm for the multivariate group lasso with covariance estimation

We study a group lasso estimator for the multivariate linear regression model that accounts for correlated error terms. A block coordinate descent algorithm is used to compute this estimator. We perform a simulation study with categorical data and multivariate time series data, typical settings with a natural grouping among the predictor variables. Our simulation studies show the good performance of the proposed group lasso estimator compared to alternative estimators. We illustrate the method on a time series data set of gene expressions

Commodity Dynamics: A Sparse Multi-class Approach

The correct understanding of commodity price dynamics can bring relevant improvements in terms of policy formulation both for developing and developed countries. Agricultural, metal and energy commodity prices might depend on each other: although we expect few important effects among the total number of possible ones, some price effects among different commodities might still be substantial. Moreover, the increasing integration of the world economy suggests that these effects should be comparable for different markets. This paper introduces a sparse estimator of the Multi-class Vector AutoRegressive model to detect common price effects between a large number of commodities, for different markets or investment portfolios. In a first application, we consider agricultural, metal and energy commodities for three different markets. We show a large prevalence of effects involving metal commodities in the Chinese and Indian markets, and the existence of asymmetric price effects. In a second application, we analyze commodity prices for five different investment portfolios, and highlight the existence of important effects from energy to agricultural commodities. The relevance of biofuels is hereby confirmed. Overall, we find stronger similarities in commodity price effects among portfolios than among markets

Sparse canonical correlation analysis from a predictive point of view

Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each data set. However, in high-dimensional settings where the number of variables exceeds the sample size or when the variables are highly correlated, traditional CCA is no longer appropriate. This paper proposes a method for sparse CCA. Sparse estimation produces linear combinations of only a subset of variables from each data set, thereby increasing the interpretability of the canonical variates. We consider the CCA problem from a predictive point of view and recast it into a regression framework. By combining an alternating regression approach together with a lasso penalty, we induce sparsity in the canonical vectors. We compare the performance with other sparse CCA techniques in different simulation settings and illustrate its usefulness on a genomic data set