To the question of restoring symbol sequences encoding noisy periodic functions

In business informatics, one of the research subjects is the analysis of data on processes in applied subject areas; here problems of qualitative analysis arise. Such problems arise, for example, in the qualitative study of log files of business processes, in the analysis and prediction of time series and other processes of a different nature. Quite often, to represent information about the processes under study, the methods of qualitative analysis use symbolic coding, which makes it possible to remove unnecessary detailing of numerical descriptions. The relevance of this study is due to the fact that when working with the raw data, researchers often face the presence of noise and distortions of the data, which significantly complicates the solution of the problems of qualitative analysis. When working with symbolic representations of the processes under study, which quite often have a periodic nature, we observe noise of deletion, insertion and replacement of symbols, which complicate the solution of the problem of revealing and analyzing the periodicity. This article deals with the problem of recovering periodic symbolic sequences obtained by coding from samples of continuous periodic functions and distorted by noise of insertion, replacement and deletion of symbols. Trigonometric functions are considered as a specific example of synthetic time series data. To encode trigonometric functions, alphabets of various cardinalities are used. The article presents an experimental study of the dependence of the quality characteristics of the method of period and a periodically repeating fragment recovery, previously proposed by the authors and improved in this study. For alphabets of different cardinalities at fixed sampling intervals, the fraction of sequences with a satisfactorily reconstructed period and the relative error in determining the period are given. The quality of reconstruction of a periodically repeating fragment is estimated by the edit distance from the reconstructed periodic sequence to the original sequence distorted by noise.

Permutation Entropy of Weakly Noise-Affected Signals

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.

Conceptual Framework of Sustainable Management of the Process of Forming a Project Team with Functional Redundancy

The paper examines the impact of the COVID-19 pandemic on human resource management processes in project-oriented companies. It is proposed to use formal transformations on groups of performers. The use of formal transformations will reduce the influence of the subjective factor and improve the quality of sustainability management decisions made when forming a project team. The formalization of the selection process of applicants and the distribution of work among the performers have been considered. The existing methods of forming a project team with functional redundancy are approximate. Methodological support for the process of forming a project team with functional redundancy, based on a logical-combinatorial approach, and allowing to form project teams under given constraints, is proposed. A method of forming a functionally redundant project team based on formal transformations of groups of performers has been developed. The use of the apparatus of symbolic sequences for the formation of a project team with functional redundancy is proposed. An example of using the proposed method when forming a command with functional redundancy is considered. It is shown that the use of this methodological support makes it possible to select the composition of the project team with the minimum number and the minimum value of the characteristic.

Analysis of Fluctuation Patterns in Emotional States Using Electrodermal Activity Signals and Improved Symbolic Aggregate Approximation

Analysis of fluctuations in electrodermal activity (EDA) signals is widely preferred for emotion recognition. In this work, an attempt has been made to determine the patterns of fluctuations in EDA signals for various emotional states using improved symbolic aggregate approximation. For this, the EDA is obtained from a publicly available online database. The EDA is decomposed into phasic components and divided into equal segments. Each segment is transformed into a piecewise aggregate approximation (PAA). These approximations are discretized using 11 time-domain features to obtain symbolic sequences. Shannon entropy is extracted from each PAA-based symbolic sequence using varied symbol size [Formula: see text] and window length [Formula: see text]. Three machine-learning algorithms, namely Naive Bayes, support vector machine and rotation forest, are used for the classification. The results show that the proposed approach is able to determine the patterns of fluctuations for various emotional states in EDA signals. PAA features, namely maximum amplitude and chaos, significantly identify the subtle fluctuations in EDA and transforms them in symbolic sequences. The optimal values of [Formula: see text] and [Formula: see text] yield the highest performance. The rotation forest is accurate (F-[Formula: see text] and 60.02% for arousal and valence dimensions) in classifying various emotional states. The proposed approach can capture the patterns of fluctuations for varied-length signals. Particularly, the support vector machine yields the highest performance for a lower length of signals. Thus, it appears that the proposed method might be utilized to analyze various emotional states in both normal and clinical settings.

Statistical Complexity Analysis of Turing Machine tapes with Fixed Algorithmic Complexity Using the Best-Order Markov Model

Sources that generate symbolic sequences with algorithmic nature may differ in statistical complexity because they create structures that follow algorithmic schemes, rather than generating symbols from a probabilistic function assuming independence. In the case of Turing machines, this means that machines with the same algorithmic complexity can create tapes with different statistical complexity. In this paper, we use a compression-based approach to measure global and local statistical complexity of specific Turing machine tapes with the same number of states and alphabet. Both measures are estimated using the best-order Markov model. For the global measure, we use the Normalized Compression (NC), while, for the local measures, we define and use normal and dynamic complexity profiles to quantify and localize lower and higher regions of statistical complexity. We assessed the validity of our methodology on synthetic and real genomic data showing that it is tolerant to increasing rates of editions and block permutations. Regarding the analysis of the tapes, we localize patterns of higher statistical complexity in two regions, for a different number of machine states. We show that these patterns are generated by a decrease of the tape’s amplitude, given the setting of small rule cycles. Additionally, we performed a comparison with a measure that uses both algorithmic and statistical approaches (BDM) for analysis of the tapes. Naturally, BDM is efficient given the algorithmic nature of the tapes. However, for a higher number of states, BDM is progressively approximated by our methodology. Finally, we provide a simple algorithm to increase the statistical complexity of a Turing machine tape while retaining the same algorithmic complexity. We supply a publicly available implementation of the algorithm in C++ language under the GPLv3 license. All results can be reproduced in full with scripts provided at the repository.

A Matrix-Based Regularity Measure for Symbolic Sequences

A set of statistics is developed for defining and determining the regularity of symbolic sequences. This is achieved by testing a given sequence against a template set with fixed asymptotic symbol proportions $p_i$, $\sum_i p_i = 1$. The process centers on casting the sequence into matrix product form, and defining a parametrized probability distribution via the entrywise norms. The parameter allows varying the weighting between strict adherence to the template sequences, and a generalized Bernoulli randomness. Numerical methods for estimating the entropy of the resulting probability distributions are also developed. The logarithms of the norms of the sequences under test are further shown to satisfy a central limit theorem. This allows the assignment of z-scores, and rigorous comparison of the regularity between sequences of different types. Potential applications are explored, including time series and ergodic systems.