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Abstract Localization of faults in a large power system is one of the most important and difficult tasks of power systems monitoring. A fault, typically a shorted line, can be seen almost instantaneously by all measurement devices throughout the system, but determining its location in a geographically vast and topologically complex system is difficult. The task becomes even more difficult if measurements devices are placed only at some network nodes. We show that regression graph neural networks we construct, combined with a suitable statistical methodology, can solve this task very well. A chief advance of our methods is that we construct networks that produce localization without having being trained on data that contain fault localization information. We show that a synergy of statistics and deep learning can produce results that none of these approaches applied separately can achieve. 

Summary The paper is concerned with testing normality in samples of curves and error curves estimated from functional regression models. We propose a general paradigm based on the application of multivariate normality tests to vectors of functional principal components scores. We examine finite sample performance of a number of such tests and select the best performing tests. We apply them to several extensively used functional data sets and determine which can be treated as normal, possibly after a suitable transformation. We also offer practical guidance on software implementations of all tests we study and develop large sample justification for tests based on sample skewness and kurtosis of functional principal component scores. 

Modern heavy vehicles rely on insecure protocols (CAN and SAE-J1939) to facilitate communication between the embedded devices that control their various subsys- tems. Due to the growing integration of wireless-enabled embedded devices, vehicles are becoming increasingly vulnerable to remote cyberattacks against their embedded networks. We propose an efficient deep-learning-based approach for mitigating such attacks through real-time J1939 signal reconstruction. Our approach uses random feature masking during training to build a generalized model of a vehicle’s network. To reduce the computa- tional and storage burden of the model, we employ 8-bit Quantization-Aware Training (QAT), enabling its deploy- ment on resource-constrained embedded devices while maintaining high performance. We evaluate Transformer and LSTM-based architectures, demonstrating that both effectively reconstruct signals with minimal computa- tional and storage overhead. Our approach achieves sig- nal reconstruction with error levels below 1% of their operating range while maintaining a very low storage footprint of under 1 MB, demonstrating that lightweight deep-learning models can enhance resiliency against real- time attacks in heavy vehicles. 

The concepts of physical dependence and approximability have been extensively used over the past two decades to quantify nonlinear dependence in time series. We show that most stochastic volatility models satisfy both dependence conditions, even if their realizations take values in abstract Hilbert spaces, thus covering univariate, multi‐variate and functional models. Our results can be used to apply to general stochastic volatility models a multitude of inferential procedures established for Bernoulli shifts.