Identification of roughness with optimal contact response with respect to real contact area and normal stiffness

Additive manufacturing technologies are a key point of the current era of Industry 4.0, promoting the production of mechanical components via the addition of subsequent layers of material. Then, they may be also used to produce surfaces tailored to achieve a desired mechanical contact response. In this work, we develop a method to prototype profiles optimizing a suitable trade-off between two different target mechanical responses. The mechanical design problem is solved relying on both physical assumptions and optimization methods. An algorithm is proposed, exploiting an analogy between genetics and the multiscale characterization of roughness, where various length-scales are described in terms of rough profiles, named chromosomes. Finally, the proposed algorithm is tested on a representative example, and the topological and spectral features of roughness of the optimized profiles are discussed

Generalized vec trick for fast learning of pairwise kernel models

Pairwise learning corresponds to the supervised learning setting where the goal is to make predictions for pairs of objects. Prominent applications include predicting drug-target or protein-protein interactions, or customer-product preferences. In this work, we present a comprehensive review of pairwise kernels, that have been proposed for incorporating prior knowledge about the relationship between the objects. Specifically, we consider the standard, symmetric and anti-symmetric Kronecker product kernels, metric-learning, Cartesian, ranking, as well as linear, polynomial and Gaussian kernels. Recently, a O(nm + nq) time generalized vec trick algorithm, where n, m, and q denote the number of pairs, drugs and targets, was introduced for training kernel methods with the Kronecker product kernel. This was a significant improvement over previous O(n(2)) training methods, since in most real-world applications m, q << n. In this work we show how all the reviewed kernels can be expressed as sums of Kronecker products, allowing the use of generalized vec trick for speeding up their computation. In the experiments, we demonstrate how the introduced approach allows scaling pairwise kernels to much larger data sets than previously feasible, and provide an extensive comparison of the kernels on a number of biological interaction prediction tasks