Global well-posedness of Kirchhoff systems

The aim of this paper is to establish the $H^1$ global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integrations for strictly hyperbolic systems with time-dependent coefficients. These integrations play an important role to setting the subsequent fixed point argument. The existence of solutions for less regular data is discussed, and several examples and applications are presented.Comment: 24 page

Mokobodzki's intervals: an approach to Dynkin games when value process is not a semimartingale

We study Dynkin games governed by a nonlinear $\mathbb E^f$-expectation on a finite interval $[0,T]$, with payoff c\`adl\`ag processes $L,U$ of class (D) which are not imposed to satisfy (weak) Mokobodzki's condition - the existence of a c\`adl\`ag semimartingale between the barriers. For that purpose we introduce the notion of Mokobodzki's stochastic intervals $\mathscr M(\theta)$ (roughly speaking, maximal stochastic interval on which Mokobodzki's condition is satisfied when starting from the stopping time $\theta$) and the notion of reflected BSDEs without Mokobodzki's condition (this is a generalization and modification of the notion introduced by Hamad\'ene and Hassani (2005)). We prove an existence and uniqueness result for RBSDEs with driver $f$ that is non-increasing with respect to the value variable (no restrictions on the growth) and Lipschitz continuous with respect to the control variable, and with data in $L^1$ spaces. Next, by using RBSDEs, we show numerous results on Dynkin games: existence of the value process, saddle points, and convergence of the penalty scheme. We also show that the game is not played beyond $\mathscr M(\theta)$, when starting from $\theta$

Global well-posedness of the Kirchhoff equation and Kirchhoff systems

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.Comment: arXiv admin note: text overlap with arXiv:1211.300

Enabling Smart Retrofitting and Performance Anomaly Detection for a Sensorized Vessel: A Maritime Industry Experience

The integration of sensorized vessels, enabling real-time data collection and machine learning-driven data analysis marks a pivotal advancement in the maritime industry. This transformative technology not only can enhance safety, efficiency, and sustainability but also usher in a new era of cost-effective and smart maritime transportation in our increasingly interconnected world. This study presents a deep learning-driven anomaly detection system augmented with interpretable machine learning models for identifying performance anomalies in an industrial sensorized vessel, called TUCANA. We Leverage a human-in-the-loop unsupervised process that involves utilizing standard and Long Short-Term Memory (LSTM) autoencoders augmented with interpretable surrogate models, i.e., random forest and decision tree, to add transparency and interpretability to the results provided by the deep learning models. The interpretable models also enable automated rule generation for translating the inference into human-readable rules. Additionally, the process also includes providing a projection of the results using t-distributed stochastic neighbor embedding (t-SNE), which helps with a better understanding of the structure and relationships within the data and assessment of the identified anomalies. We empirically evaluate the system using real data acquired from the vessel TUCANA and the results involve achieving over 80% precision and 90% recall with the LSTM model used in the process. The interpretable models also provide logical rules aligned with expert thinking, and the t-SNE-based projection enhances interpretability. Our system demonstrates that the proposed approach can be used effectively in real-world scenarios, offering transparency and precision in performance anomaly detection

Compact antenna for digital beamforming with software defined radios

An adaptive radio system combining compact switchless reconfigurable antenna with Software Defined Radio is proposed. The system allows control of the direction of the transmitted signal solely by adjusting the baseband I and Q components of the modulated signal, while maintaining small antenna size through the use of compact multiport antenna. The system is demonstrated in a line-of-sight configuration with QPSK modulation. Experimental results demonstrate good received power and low error vector magnitude of the demodulated signals