This work proposes a new algorithm to classify high impedance faults (HIFs) in distribution systems. HIFs can be represented by small current magnitudes with non-linear variations, which complicate their detection in distribution grids. The proposed method uses the Hermite transform (HT) as a signal processing technique that offers several advantages, one of the more important being the ability to analyze the signal at multiple resolution levels and at different frequency bands thanks to their filter functions based on Gaussian derivatives. The Hermite coefficients are used to extract signal features that allow efficient identification of the transient behaviour related to HIFs and other typical faults. In this sense, a multichannel approach based on the Hermite transform is proposed to classify different types of faults and HIFs. This analysis is carried out in a distribution network considering photovoltaic (PV) systems considering three different classifiers, which are also used to compare our results with the discrete wavelet transform (DWT) as signal decomposition model; the comparison suggests that our proposal presents better performance discriminating HIFs from typical faults.

Heart diseases are the most important causes of death in the world and over the years, the study of cardiac movement has been carried out mainly in two dimensions, however, it is important to consider that the deformations due to the movement of the heart occur in a three-dimensional space. The $3D+t$ analysis allows to describe most of the motions of the heart, for example, the twisting motion that takes place on every beat cycle that allows us identifying abnormalities of the heart walls. Therefore, it is necessary to develop algorithms that help specialists understand the cardiac movement. In this work, we developed a new approach to determine the cardiac movement in three dimensions using a differential optical flow approach in which we use the steered Hermite transform (SHT) which allows us to decompose cardiac volumes taking advantage of it as a model of the human vision system (HVS). Our proposal was tested in complete cardiac computed tomography (CT) volumes ( $3D+t$ ), as well as its respective left ventricular segmentation. The robustness to noise was tested with good results. The evaluation of the results was carried out through errors in forwarding reconstruction, from the volume at time t to time $t+1$ using the optical flow obtained (interpolation errors). The parameters were tuned extensively. In the case of the 2D algorithm, the interpolation errors and normalized interpolation errors are very close and below the values reported in ground truth flows. In the case of the 3D algorithm, the results were compared with another similar method in 3D and the interpolation errors remained below 0.1. These results of interpolation errors for complete cardiac volumes and the left ventricle are shown graphically for clarity. Finally, a series of graphs are observed where the characteristic of contraction and dilation of the left ventricle is evident through the representation of the 3D optical flow.

The flagellar movement of the mammalian sperm plays a crucial role in fertilization. In the female reproductive tract, human spermatozoa undergo a process called capacitation which promotes changes in their motility. Only capacitated spermatozoa may be hyperactivated and only those that transition to hyperactivated motility are capable of fertilizing the egg. Hyperactivated motility is characterized by asymmetric flagellar bends of greater amplitude and lower frequency. Historically, clinical fertilization studies have used two-dimensional analysis to classify sperm motility, despite the inherently three-dimensional (3D) nature of sperm motion. Recent research has described several 3D beating features of sperm flagella. However, the 3D motility pattern of hyperactivated spermatozoa has not yet been characterized. One of the main challenges in classifying these patterns in 3D is the lack of a ground-truth reference, as it can be difficult to visually assess differences in flagellar beat patterns. Additionally, it is worth noting that only a relatively small proportion, approximately 10-20% of sperm incubated under capacitating conditions exhibit hyperactivated motility. In this work, we used a multifocal image acquisition system that can acquire, segment, and track sperm flagella in 3D+t. We developed a feature-based vector that describes the spatio-temporal flagellar sperm motility patterns by an envelope of ellipses. The classification results obtained using our 3D feature-based descriptors can serve as potential label for future work involving deep neural networks. By using the classification results as labels, it will be possible to train a deep neural network to automatically classify spermatozoa based on their 3D flagellar beating patterns. We demonstrated the effectiveness of the descriptors by applying them to a dataset of human sperm cells and showing that they can accurately differentiate between non-hyperactivated and hyperactivated 3D motility patterns of the sperm cells. This work contributes to the understanding of 3D flagellar hyperactive motility patterns and provides a framework for research in the fields of human and animal fertility.