Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.     

Adaptive Neuro-Fuzzy Inference System and a Multilayer Perceptron Model Trained with Grey Wolf Optimizer for Predicting Solar Diffuse Fraction

The accurate prediction of the solar diffuse fraction (DF), sometimes called the diffuse ratio, is an important topic for solar energy research. In the present study, the current state of Diffuse irradiance research is discussed and then three robust, machine learning (ML) models are examined using a large dataset (almost eight years) of hourly readings from Almeria, Spain. The ML models used herein, are a hybrid adaptive network-based fuzzy inference system (ANFIS), a single multi-layer perceptron (MLP) and a hybrid multi-layer perceptron grey wolf optimizer (MLP-GWO). These models were evaluated for their predictive precision, using various solar and DF irradiance data, from Spain. The results were then evaluated using frequently used evaluation criteria, the mean absolute error (MAE), mean error (ME) and the root mean square error (RMSE). The results showed that the MLP-GWO model, followed by the ANFIS model, provided a higher performance in both the training and the testing procedures.     

A framework to perform high-order deconvolution for finite-volume method on simplicial meshes

In this article, a new framework to design high-order approximations in the context of node-centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High-performance computing context. This method is based on deconvolution between nodal and volume-average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh-to-mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high-rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third-order expansion. This method, although tightly connected to the k-exact schemes theory, does not rely on successive corrections: the high-order property is obtained in a single operation, which makes them more attractive in terms of performances.     

Flume testing of passively adaptive composite tidal turbine blades under combined wave and current loading

The tidal energy industry is progressing rapidly, but there are still barriers to overcome to realise the commercial potential of this sector. Large magnitude and highly variable loads caused by waves acting on the turbine are of particular concern. Composite blades with in-built bend-twist elastic response may reduce these peak loads, by passively feathering with increasing thrust. This could decrease capital costs by lowering the design loads, and improve robustness through the mitigation of pitch mechanisms. In this study, the previous research is extended to examine the performance of bend-twist blades in combined wave–current flow, which will frequently be encountered in the field. A scaled 3 bladed turbine was tested in the flume at IFREMER with bend-twist composite blades and equivalent rigid blades, sequentially under current and co-directional wave–current cases. In agreement with previous research, when the turbine was operating in current alone at higher tip speed ratios the bend-twist blades reduced the mean thrust and power compared to the rigid blades. Under the specific wave–current condition tested the average loads were similar on both blade sets. Nevertheless, the bend-twist blades substantially reduced the magnitudes of the average thrust and torque fluctuations per wave cycle, by up to 10% and 14% respectively.     

The Szegö kernel on a class of non-compact CR manifolds of high codimension

We generalize Nagel’s formula for the Szegö kernel and use it to compute the Szegö kernel on a class of non-compact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also discuss the control metric on these manifolds and relate it to the size of the Szegö kernel.