We introduce the Padé-Z 2 (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determinants from the two ends of the Hybrid Monte Carlo trajectories with pseudofermions. Our results on the 8 3 × 12 lattice with Wilson action show that the statistical errors from the stochastic estimator can be reduced by more than an order of magnitude by employing an unbiased variational subtraction scheme which utilizes the off-diagonal matrices from the hopping expansion. Having been able to reduce the error of the determinant ratios to about 20 % with a relatively small number of noise vectors, this may become a feasible algorithm for simulating dynamical fermions in full QCD. We also discuss the application to the density of states in Hamiltonian systems.

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Predicting groundwater availability is important to water sustainability and drought mitigation. Machine-learning tools have the potential to improve groundwater prediction, thus enabling resource planners to: (1) anticipate water quality in unsampled areas or depth zones; (2) design targeted monitoring programs; (3) inform groundwater protection strategies; and (4) evaluate the sustainability of groundwater sources of drinking water. This paper proposes a machine-learning approach to groundwater prediction with the following characteristics: (i) the use of a regression-based approach to predict full groundwater images based on sequences of monthly groundwater maps; (ii) strategic automatic feature selection (both local and global features) using extreme gradient boosting; and (iii) the use of a multiplicity of machine-learning techniques (extreme gradient boosting, multivariate linear regression, random forests, multilayer perceptron and support vector regression). Of these techniques, support vector regression consistently performed best in terms of minimizing root mean square error and mean absolute error. Furthermore, including a global feature obtained from a Gaussian Mixture Model produced models with lower error than the best which could be obtained with local geographical features.

International audienceLarge applications of sensor networks, such as environmental risk monitoring, require the deployment of hundreds or even thousands of nodes. This study proposes and implements a novel stochastic physics-based optimisation algorithm that is both efficient (guarantees full target coverage with a reduced number of sensors) and scalable (meaning that it can be executed for very large-scale problems in a reasonable computation time). The algorithm employs ‘virtual sensors’ which move, merge, recombine, and ‘explode’ during the course of the algorithm, where the process of merging and recombining virtual sensors reduces the number of actual sensors while maintaining full coverage. The parameters which control sensor merging and explosion are varied during the algorithm to perform the same function as an annealing schedule in simulated annealing. Simulation results illustrate the rapidity and the effectiveness of the proposed method

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