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This article discusses an application for classifying urban spaces using convolutional neural networks (CNNs). A seed dataset was initially generated composed of 630 photographs of urban spaces from the Adobe Stock repository. This dataset was topped up with images produced by two generative artificial intelligence (AI) engines, namely, Deep Dream Generator and Midjourney, making two additional augmented datasets, each composed of 2200 images. The training process was carried out using four well-known CNNs, namely, GoogLeNet, ResNet-18, ShuffleNet, and MobileNet-v2. The results show an increase of roughly 30% in the predicting capabilities in both augmented datasets when compared to the seed dataset. Furthermore, performance metrics are generally higher when using ResNet-18 which may suggest that this CNN architecture is more applicable to urban classification projects. Finally, although both generative AI engines have similar performance, Midjourney seems to slightly outperform Deep Dream Generator as a data augmentation engine for urban spaces. [ABSTRACT FROM AUTHOR]

In the Bondi-Sachs formulation of general relativity, the spacetime is foliated via a family of null cones. If these null cones are defined such that their vertices are traced by a regular world line, then the metric tensor has to obey regular boundary conditions at the vertices. We explore the general requirements of these regularity conditions when the world line is a time-like geodesic, and use axisymmetric vacuum spacetimes to demonstrate these requirements. We correct and complete vertex-boundary conditions that were used in the past. We derive nonlinear boundary conditions, which approximate locally a metric up to fourth order in normal coordinates, and linear boundary conditions of arbitrary order. It is shown that if the metric is represented by power series expansions of the metric variables, the coefficients of such series have a very rigid angular structure and a rigid hierarchical dependence of time derivatives of the expansion coefficients. [ABSTRACT FROM AUTHOR]