Data-Driven Extrapolation Via Feature Augmentation Based on Variably Scaled Thin Plate Splines

The data driven extrapolation requires the definition of a functional model depending on the available data and has the application scope of providing reliable predictions on the unknown dynamics. Since data might be scattered, we drive our attention towards kernel models that have the advantage of being meshfree. Precisely, the proposed numerical method makes use of the so-called Variably Scaled Kernels (VSKs), which are introduced to implement a feature augmentation-like strategy based on discrete data. Due to the possible uncertainty on the data and since we are interested in modelling the behaviour of the target functions, we seek for a regularized solution by ridge regression. Focusing on polyharmonic splines, we investigate their implementation in the VSK setting and we provide error bounds in Beppo–Levi spaces. The performances of the method are then tested on functions showing exponential or rational decay. Comparisons with Support Vector Regression (SVR) are also carried out and highlight that the proposed approach is effective, particularly since it does not require to train complex architecture constructions

How big is the image of the Galois representations attached to CM elliptic curves?

Using an analogue of Serre's open image theorem for elliptic curves with complex multiplication, one can associate to each CM elliptic curve $E$ defined over a number field $F$ a natural number $\mathcal{I}(E/F)$ which describes how big the image of the Galois representation associated to $E$ is. We show how one can compute $\mathcal{I}(E/F)$, using a closed formula that we obtain from the classical theory of complex multiplication

Reproduction capabilities of penalized hyperbolic-polynomial splines

This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-splines), were recently introduced by the authors as a generalization of P-splines. HB-splines are bell-shaped basis functions consisting of segments made of real exponentials $e^{\alpha x},\, e^{-\alpha x}$ and linear functions multiplied by these exponentials, $xe^{+\alpha x}$ and $xe^{-\alpha x}$. Here, we show that these type of penalized splines reproduce function in the space $\{e^{-\alpha x},\ x e^{-\alpha x}\}$, that is they fit exponential data exactly. Moreover, we show that they conserve the first and second 'exponential' moments.Comment: 11 pages, 2 figure

Application of a Multiphase Interleaved DC-DC Converter for Power-To-Hydrogen Systems

Power electronics plays a crucial role in the implementation of a clean hydrogen production system, whose last stage consists of a water electrolyzer requiring a DC power supply to be in operation. The most recent architectural solutions imply the use of an isolated DC-DC converter, collecting energy from medium voltage (MV) and delivering it to the electrolyzer. An equivalent electrical model of the electrolyzer is therefore needed, as well as an accurate design of the power converter stage, aiming at a high-efficiency operation of the electrolyzer's cells and at a low-ripple supply current, to avoid premature degradation. This work investigates a full-bridge step-down isolated DC-DC converter, focusing on the opportunity of a multiphase interleaved configuration, particularly convenient for the proposed application. The considered maximum power level is 400 kW, representing a small-scale example of an industrial water electrolyzer supplied by a maximum DC voltage of 700 V. Input DC voltage is 7 kV. Power electronics' simulation have been carried out, as well as model analysis of the proposed converter

Return to work of breast cancer survivors: Perspectives and challenges for occupational physicians

Breast cancer is one of the most common diseases worldwide, mainly affecting the female gender. Considering the increase of breast cancer incidence and the decrease of mortality due to news diagnostic and therapeutic tools, the return to work issue after treatment is going to be very common in the next years. Occupational physicians therefore need to face the return to work and the fitness for work of workers previously diagnosed with breast cancer with a sufficient cultural and technical background. In addition to individual characteristics preceding the diagnosis, clinical outcome, lifestyles and occupational variables are the most impactful factors on return to work that need to be taken into account. The aim of this work is to analyze these factors and discuss the central role of occupational physicians in the decision-making process of returning to work in breast cancer survivors

Regionalization of ports as a strategic leverage to improve competitiveness. A study on central italy ports and related hinterland

Nowadays, the success of a maritime port does not depend anymore on its traditional intrinsic points of strength, such as the internal capacity, but also on its ability to effectively integrate the development of its hinterland into business relations and supply chains. Mediterranean ports can get competitive, if specific "regionalization" processes are launched and supported. Key point for this strategy is the hinterland involvement: logistics and transports integration, railways, realization and development of dryports, terminals, distribution centres. All these are core elements for this purpose. The overall focus has changed from port performances to performance of the entire supply chain in the port-hinterland relationship. This is what it is going to do the Port of Civitavecchia, the most important port in Lazio Region, would like to become the central point into commercial, industrial and infrastructural development of central Italy. The development of railway terminal and of regional road network for the developing of intermodal logistics chain, of the industrial port activities (shipbuilding sector and oil bunkering), of trade relations with Fiumicino Airport and with the roman agroindustrial sector, of logistics relations with the dryport of Orte and with the intermodal terminal (road-railway) of Pomezia Santa Palomba, are some of the activities planned and undertaken by the port for improving the regionalization of Civitavecchia. Aim of this paper is to show and underline how these regionalization processes can increase the development, and so benefit the entire regional hinterland and the competitiveness and attraction of the entire port system. A model to estimate the regionalization effect has been designed by the authors and implemented to make a comparison analysis between Civitavecchia and competing ports. © 2021 Georg Thieme Verlag. All rights reserved

Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms

In this work we extend some ideas about greedy algorithms, which are well-established tools for, e.g., kernel bases, and exponential-polynomial splines whose main drawback consists in possible overfitting and consequent oscillations of the approximant. To partially overcome this issue, we develop some results on theoretically optimal interpolation points. Moreover, we introduce two algorithms which perform an adaptive selection of the spline interpolation points based on the minimization either of the sample residuals (f-greedy), or of an upper bound for the approximation error based on the spline Lebesgue function (λ-greedy). Both methods allow us to obtain an adaptive selection of the sampling points, i.e., the spline nodes. While the f-greedy selection is tailored to one specific target function, the λ-greedy algorithm enables us to define target-data-independent interpolation nodes