Objective. The primary purpose of this work is to analyze the ability of N-BEATS architecture for the problem of prediction and classification of electrocardiogram (ECG) signals. To achieve this, performance comparison with various types of other SotA (state-of-the-art) recurrent neural network architectures commonly used for such problems is conducted. Approach. Four architectures (N-BEATS, LSTM, LSTM with peepholes, GRU) were tested for performance and dimension reduction problems for different number of leads (2, 3, 4, 6, 12), both in variants consisting of blended branches, allowing retaining accuracy while reducing the computational capacity needed. The analysis was performed on datasets and using metrics from Challenges in Cardiology (CinC) 2021 competition. Main results. Best results were achieved for LSTM with peepholes, then LSTM, GRU and the worst for N-BEATS (challenge metrics respectively: 0.42, 0.40, 0.39, 0.35; for times: 0.0395 s, 0.0036 s, 0.0027 s, 0.0002 s). Commonly used LSTM outperforms N-BEATS in terms of multi-label classification, data set resilience, and obtained challenge metrics. Still, N-BEATS can obtain acceptable results for 2 lead classification (metric of 0.35 for N-BEATS and 0.38 for other networks) and outperforms other solutions in terms of complexity and speed. Significance. This paper features a novel approach of using the N-BEATS, which was previously used only for forecasting, to classify ECG signals with success. While N-BEATS multi-label classification capacity is lower than LSTM, its speed obtaining results with a reduced number of leads (faster by one to two degrees of magnitude) allows for arrhythmias detection and classification while using off-the-shelf wearable devices (Holter monitors, sport bands, etc).

In this paper, the new method of the determination of entries of the state matrices of the positive two-dimensional systems described by the second Fornasini-Marchesini model (IIF-M) using digraphs theory D ⁽²⁾ has been presented. For the proposed method parallel computing algorithm was constructed. Algorithm is based on GPGPU (General- Purpose Computing on Graphics Processing Units) computing method to gain needed speed and computational power for such solution. The proposed method was discussed and illustrated with numerical examples. Proposed solution allows digraphs construction for any positive two-dimensional system, regardless of its complexity.

This work compared the multi-element analysis of human hair and nails using inductively coupled plasma mass spectrometry (ICP MS) with an easy, fast, cheap, non-destructive method using energy-dispersive x-ray fluorescence (ED XRF). The ICP MS-based method was more sensitive (over 30 elements could be quantified) and costly (requiring more time, samples, and chemicals). The EDX-based method required laboratory and certified reference materials made of hair for instrument calibration. It was less sensitive (16 elements could be quantified: S, Si, Ca, Br, Fe, Cu, Cr, Mg, Si, K, Mn, Ni, Zn, Se, Sr, Pb), but it allowed us to replace troublesome grinding with the dissolution of keratin-based material with an alkalic agent (tetramethylammonium hydroxide, TMAH) and the formation of stable-for-days pellets. This method is simple, enables automation, and, due to the modification of wells in the autosampler of the EDX system via the immersion of home-designed inserts, it requires smaller amounts of biological material and binder (down to 70 mg instead of 500 mg required by commercially available instrument) to perform analysis. It was concluded that the EDX-based method offers complementary selectivity and sensitivity to ICP MS with the possibility of sample reuse for further analysis.

This paper presents a series of further modifications to the parallel algorithm used for finding digraphs realisations of the characteristic polynomial. What distinguishes the mentioned algorithm from other state-of-the-art solutions is the ability to find a complete set of existing solutions, not just a few of them. Moreover, solutions found tend to be minimal in terms of a rank of matrices created. Due to a of large number of solutions tested and an NP-hard complexity of the problem, the parallel algorithm is incapable of finding solutions for more complicated problems in reasonable time. To address this problem additional modifications of the algorithm structure are proposed and explained. Modifications presented in this paper contribute to a reduction of a number of improper solutions that are created, and later tested and rejected, by the algorithm making it work in all cases, except the most trivial ones, at least by an order of magnitude faster.

In this paper the alternative method for determination of all possible lower reachability indices has been proposed. Method is based on the extension of parallel digraphs creation algorithm presented previously. As a solution of problem of determination of lower reachability index, method finds all possible finite paths in the digraphs - each of them representing one of the indices. By performing complete traversal of the digraphs we are able to reach all the possible lower reachability indices for any number of variables at once. Proposed method is illustrated by a numerical example.