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Recently, many researchers studied the degenerate multi-special polynomials as degenerate versions of the multi-special polynomials and obtained some identities and properties of the those polynomials. The aim of this paper was to introduce the degenerate multi-poly-Changhee polynomials arising from multiple logarithms and investigate some interesting identities and properties of these polynomials that determine the relationship between multi-poly-Changhee polynomials, the Stirling numbers of the second kind, degenerate Stirling numbers of the first kind and falling factorial sequences. In addition, we investigated the phenomenon of scattering the zeros of these polynomials.

In this paper, a distributed machine-learning strategy, i.e., federated learning (FL), is used to enable the artificial intelligence (AI) model to be trained on dispersed data sources. The paper is specifically meant to forecast cryptocurrency prices, where a long short-term memory (LSTM)-based FL network is used. The proposed framework, i.e., F-LSTM utilizes FL, due to which different devices are trained on distributed databases that protect the user privacy. Sensitive data is protected by staying private and secure by sharing only model parameters (weights) with the central server. To assess the effectiveness of F-LSTM, we ran different empirical simulations. Our findings demonstrate that F-LSTM outperforms conventional approaches and machine learning techniques by achieving a loss minimal of $ 2.3 times 10^{-4} $. Furthermore, the F-LSTM uses substantially less memory and roughly half the CPU compared to a solely centralized approach. In comparison to a centralized model, the F-LSTM requires significantly less time for training and computing. The use of both FL and LSTM networks is responsible for the higher performance of our suggested model (F-LSTM). In terms of data privacy and accuracy, F-LSTM addresses the shortcomings of conventional approaches and machine learning models, and it has the potential to transform the field of cryptocurrency price prediction.

Decision-making in a railway station regarding the compatibility of the positions of the switches of the turnouts and the indications (proceed/stop) of the railway colour light signals is a safety-critical issue that is considered very labor-intensive. Different authors have proposed alternative solutions to automate its supervision, which is performed by the so-called railway interlocking systems. The classic railway interlocking systems are route-based and their compatibility is predetermined (usually by human experts): only some chosen routes are simultaneously allowed. Some modern railway interlocking systems are geographical and make decisions on the fly, but are unsuitable if the station is very large and the number of trains is high. In this paper, we present a completely new algebraic model for decision-making in railway interlocking systems, based on other computer algebra techniques, that bypasses the disadvantages of the approaches mentioned above (its performance does not depend on the number of trains in the railway station and can be used in large railway stations). The main goal of this work is to provide a mathematical solution to the interlocking problems. We prove that our approach solves it in linear time. Although our approach is interesting from a theoretical perspective, it has a significant limitation: it can hardly be adopted in an actual interlocking implementation, mainly due to the heavy certification requirements for this kind of safety-critical application. Nevertheless, the results may be useful for simulations that do not require certification credit.