Sparse optimization on measures with over-parameterized gradient descent

Mathematical Programming - Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks...     

Comments on Salem polynomials

Archiv der Mathematik - We strengthen a sufficient condition, due to R.S. Vieira, for a (reciprocal) polynomial $$R(x)=(x-\alpha _{1})(x-\alpha _{1}^{-1})\cdots (x-\alpha _{s})(x-\alpha...     

Hardware-in-the-loop simulation of wave energy converters based on dielectric elastomer generators

Dielectric elastomer generators (DEGs) are soft electrostatic generators based on low-cost electroactive polymer materials. These devices have attracted the attention of the marine energy community as a promising solution to implement economically viable wave energy converters (WECs). This paper introduces a hardware-in-the-loop (HIL) simulation framework for a class of WECs that combines the concept of the oscillating water columns (OWCs) with the DEGs. The proposed HIL system replicates in a laboratory environment the realistic operating conditions of an OWC/DEG plant, while drastically reducing the experimental burden compared to wave tank or sea tests. The HIL simulator is driven by a closed-loop real-time hydrodynamic model that is based on a novel coupling criterion which allows rendering a realistic dynamic response for a diversity of scenarios, including large scale DEG plants, whose dimensions and topologies are largely different from those available in the HIL setup. A case study is also introduced, which simulates the application of DEGs on an OWC plant installed in a mild real sea laboratory test-site. Comparisons with available real sea-test data demonstrated the ability of the HIL setup to effectively replicate a realistic operating scenario. The insights gathered on the promising performance of the analysed OWC/DEG systems pave the way to pursue further sea trials in the future.

     

Numerical differentiation on scattered data through multivariate polynomial interpolation

BIT Numerical Mathematics - We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja...     

A perimeter-based angle measure in Minkowski planes

Measuring angles in the Euclidean plane is a well-known topic, but for general normed planes there exists a variety of different concepts. These can be of a special kind, e.g. also preserving special orthogonality types. But these concepts are no angle measures in the sense of measure theory since they are not additive. This motivates us to define a new angle measure for normed planes that is in fact a measure in the sense of measure theory. Furthermore, we look at related types of rotation and reflection.     

Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

Parametrix for the localization of the Bergman metric on strictly pseudoconvex domains

We give the parameter version of a localization theorem for the Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of Graham-Kerzman is proved in the hereby paper, as well.