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A novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.

First, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.

AAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.

AAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.

The authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

Sarcasm is a linguistic expression that usually carries the opposite meaning of what is being said by words, thus making it difficult for machines to discover the actual meaning. It is mainly distinguished by the inflection with which it is spoken, with an undercurrent of irony, and is largely dependent on context, which makes it a difficult task for computational analysis. Moreover, sarcasm expresses negative sentiments using positive words, allowing it to easily confuse sentiment analysis models. This paper aims to demonstrate the task of sarcasm detection using the approach of machine and deep learning.

For the purpose of sarcasm detection, machine and deep learning models were used on a data set consisting of 1.3 million social media comments, including both sarcastic and non-sarcastic comments. The data set was pre-processed using natural language processing methods, and additional features were extracted and analysed. Several machine learning models, including logistic regression, ridge regression, linear support vector and support vector machines, along with two deep learning models based on bidirectional long short-term memory and one bidirectional encoder representations from transformers (BERT)-based model, were implemented, evaluated and compared.

The performance of machine and deep learning models was compared in the task of sarcasm detection, and possible ways of improvement were discussed. Deep learning models showed more promise, performance-wise, for this type of task. Specifically, a state-of-the-art model in natural language processing, namely, BERT-based model, outperformed other machine and deep learning models.

This study compared the performance of the various machine and deep learning models in the task of sarcasm detection using the data set of 1.3 million comments from social media.