We show obstructions to the existence of a coclosed G 2 {\mathrm{G}_{2}} -structure on a Lie algebra 𝔤 {\mathfrak{g}} of dimension seven with non-trivial center. In particular, we prove that if there exists a Lie algebra epimorphism from 𝔤 {\mathfrak{g}} to a six-dimensional Lie algebra 𝔥 {\mathfrak{h}} , with the kernel contained in the center of 𝔤 {\mathfrak{g}} , then any coclosed G 2 {\mathrm{G}_{2}} -structure on 𝔤 {\mathfrak{g}} induces a closed and stable three form on 𝔥 {\mathfrak{h}} that defines an almost complex structure on 𝔥 {\mathfrak{h}} . As a consequence, we obtain a classification of the 2-step nilpotent Lie algebras which carry coclosed G 2 {\mathrm{G}_{2}} -structures. We also prove that each one of these Lie algebras has a coclosed G 2 {\mathrm{G}_{2}} -structure inducing a nilsoliton metric, but this is not true for 3-step nilpotent Lie algebras with coclosed G 2 {\mathrm{G}_{2}} -structures. The existence of contact metric structures is also studied.

We introduce an unsupervised learning method that aims to identify building anomalies using Interferometric Synthetic Aperture Radar (InSAR) time-series data. Specifically, we leverage data obtained from the European Ground Motion Service to develop our proposed approach, which employs a long short-term memory autoencoder model and a reconstruction loss function based on a soft variant of the dynamic time warping, namely “soft-DTW”. We deliberately utilize this loss function for its ability to compare time-series that are not aligned in time, unlike the other conventional reconstruction losses that do not account for time shifts. Moreover, we enhance the performance of anomaly detection by smoothing inputs with a Hann window and defining the learning objective to reconstruct the time order of randomly permuted input series. Our experimental findings, based on persistent scatterer data from Rome, Italy, reveal that our method outperforms several unsupervised machine learning and deep learning methods in detecting various types of building displacement, such as trend, noise, and step anomalies. Additionally, quantitative and qualitative evaluations validate the efficacy of our approach in identifying potentially anomalous buildings. Thus, our method offers a promising solution for detecting anomalies in PS-InSAR time-series, which could have substantial implications in the fields of urban monitoring and infrastructure management.

International Press of Boston - publishers of scholarly mathematical and scientific journals and books

Submesoscale eddies play an important role in the energy transfer from the mesoscale down to the dissipative range, as well as in tracer transport. They carry inorganic matter, nutrients and biomass; in addition, they may act as pollutant conveyors. However, synoptic observations of these features need high resolution sampling, in both time and space, making their identification challenging. Therefore, HF coastal radar were and are successfully used to accurately identify, track and describe them. In this paper we tested two already existing algorithms for the automated detection of submesoscale eddies. We applied these algorithms to HF radar velocity fields measured by a network of three radar systems operating in the Gulf of Naples. Both methods showed shortcomings, due to the high non-geostrophy of the observed currents. For this reason we developed a third, novel algorithm that proved to be able to detect highly asymmetrical eddies, often not properly identified by the previous ones. We used the results of the application of this algorithm to estimate the eddy boundary profiles and the eddy spatial distribution.