Modeling of Cognitive Process Using Complexity Theory Methods Vladimir Soloviev[0000-0002-4945-202X], Natalia Moiseienko[0000-0002-3559-6081] and Olena Tarasova [0000-0002-6001-5672] Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine {vnsoloviev2016, n.v.moiseenko, e.ju.tarasova}@gmail.com Abstract. The features of modeling of the cognitive component of social and humanitarian systems have been considered. An example of using multiscale, multifractal and network complexity measures has shown that these and other synergetic models and methods allow us to correctly describe the quantitative differences of cognitive systems. The cognitive process is proposed to be regarded as a separate implementation of an individual cognitive trajectory, which can be represented as a time series and to investigate its static and dynamic features by the methods of complexity theory. Prognostic possibilities of the complex systems theory will allow to correct the corresponding pedagogical technologies. Keywords: cognitive systems, complex systems, complex networks, synergetics, degree of complexity, new pedagogical technologies. 1 Introduction Recently, it has become clear that pedagogical science operates on the transmission of a kind of structured information that is knowledge. Information, as the main concept of cybernetics, is characterized by a metric function and, thus, the search for optimal management of educational processes is translated into a plane of mathematical modeling [1-3]. In science, starting with R. Descartes, I. Newton and P.-S. Laplace determinism and strict conditional constructions had been predominant for a long time. Initially, these views were developed in science and mathematics, and then moved into the humanitarian field, in particular, in pedagogy. As a result, many attempts have been made to organize education as a perfectly functioning machine. According to the dominant ideas then, for the education of a person the only need was to learn how to manage such a “machine”, that is to turn education into a kind of production and technological process. The emphasis was on standardized training procedures and fixed patterns of learning. Thus appeared the beginning of the technological approach in teaching and, consequently, the predominance of teaching the reproductive activity of students. For many complex systems, the phenomenon of self-organization is characteristic [4]. It leads to the fact that very often a few variables, the so-called order parameters, are detected very often for the description of an object, which is described by a large or even infinite number of variables [5]. These parameters “subordinate” other variables, defining their values. The researchers are aware of the mechanisms of self- organization, which lead to the allocation of parameters of order, methods of their description as well as the corresponding mathematical models. However, it is likely, our brain has a brilliant ability to find these parameters, to “simplify reality”, finding more effective algorithms for their selection. The process of learning and education allows one to find successful combinations that can be the order parameter in certain situations or the mechanisms of searching for such parameters (“learn to study”, “learn to solve non-standard tasks”). It is also advisable to use the ideas of a soft (or fuzzy) simulation. All said by V.I. Arnold, in the case of hard and soft models [6], takes place in pedagogical science. Since in humanitarian systems the results of their interaction and development can not be predicted in detail, by analogy with complex quantum systems one can speak the principle of uncertainty for humanitarian systems. In the process of learning unplanned small changes always occur as well as fluctuations in the various pedagogical systems (and the individual, and the team of students, and knowledge systems). Therefore, the basis of modern educational models should lie in the principle of uncertainty in a number of managerial and educational parameters. Network education refers to a new educational paradigm [7], which is called “networking”. Its distinctive features are learning based on the synthesis of the objective world and virtual reality by activating both the sphere of rational consciousness and the sphere of intuitive, unconscious. The networking of a student and a computer is characterized as an intellectual partnership representing the so- called “distributed intelligence”. Unlike the traditional, network education strategy is focused not on the systematization of knowledge and the assimilation of the next main core of information, but on the development of abilities and motivation to generate their own ideas [8]. Within the framework of recent research in the Davos forum, 10 skills were identified, most demanded by 2022 [9]: (1) Analytical thinking and innovation; (2) Active learning and learning strategies; (3) Creativity, originality and initiative; (4) Technology design and programming; (5) Critical thinking and analysis; (6) Complex problem-solving; (7) Leadership and social influence; (8) Emotional intelligence; (9) Reasoning, problem-solving and ideation; (10) Systems analysis and evaluation. Obviously, the cognitive component in the transformation processes of Industry 4.0 is dominant, which actualizes attention to the study of cognitive processes. The complexities here are reduced to the fact that cognitive processes are poorly formalized. Therefore, the field of theoretical works until recently was virtually empty. The picture has fundamentally changed with the use of recent synergetic studies. The fact is that the doctrine of the unity of the scientific method asserts: for the study of events in the social-humanitarian systems, the same methods and criteria apply to the study of natural phenomena. Significant success was achieved within the framework of interdisciplinary approaches and the theory of self-organization – synergetics [4, 5]. The process of intellection is a cognitive process characterized by an individual cognitive trajectory whose complexity is an integro-differential characteristic of an individual. The task is to quantify cognitive trajectories and present them in the form of a time series that can be analyzed quantitatively. The theory of complexity introducing various measures of complexity, allows us to classify cognitive trajectories by complexity and choose more complex, as more efficient ones. The analysis procedure can be done dynamically, by correcting the trajectories by means of progressive pedagogical technologies. Previously, we introduced various quantitative measures of complexity for particular time series, in particular: algorithmic, fractal, chaos-dynamic, recurrent, nonreversible, network, and others [10]. Significant advantage of the introduced measures is their dynamism, that is, the ability to monitor the time of change in the chosen measure and compare with the corresponding dynamics of the output time series. This allowed us to compare the changes in the dynamics of the system, which is described by the time series, with characteristic changes in concrete measures of complexity and draw conclusions about the properties of the cognitive trajectory. Objects of research are cognitive processes that control neurophysiological and other cognitive characteristics of a person: ─ the length of the full step of different age children [11], a healthy young person and the elderly, or those with neurodegeneration (Alzheimer’s, Parkinson’s, Huntington’s, etc. [12]); ─ human recalls of words [13]; ─ objects of cognitive linguistics – the works of various authors, different genres, written in different languages [14]; ─ discretized multi-genre musical compositions [15]. The corresponding databases in the form of time series are in open access [16]. In this paper, we consider some of the informative measures of complexity and adapt them in order to study the cognitive processes. The paper is structured as follows. Section 2 describes previous studies in these fields. Section 3 presents information mono- and multiscale measures of complexity. Section 4 describes the technique of fractal and multifractal. Network measures of complexity and their effectiveness in the study of cognitive processes are presented in Section 5. 2 Analysis of previous studies Researchers interested in human cognitive processes have long used computer simulations to try to identify the principles of cognition [17]. Existing theoretical developments in this scientific field describe complex, dynamic, and emergent processes that shape intra- (e.g., cognition, motivation and emotion) and inter- (e.g., teacher-student, student-student, parent-child interactions, collaborative teams) person phenomena at multiple levels. These processes are fundamental characteristics of complex systems but the research methods that are used sometimes do not match the complexity of processes that need to be described. From the set of methods of the theory of complex systems we consider only those related to information, fractal, and network complexity measures. Entropic measures in general are relevant for a wide variety of linguistic and computational subfields. In the context of quantitative linguistics, entropic measures are used to understand laws in natural languages, such as the relationship between word frequency, predictability and the length of words, or the trade-off between word structure and sentence structure [18]. Together with Shannon’s entropy, more complex versions are used: the Approximate entropy, Sample entropy [19]. In order to demonstrate the scale-invariant properties of cognitive processes, these types of entropy were used in a multiscale version in the study of cognitive processes of cerebral activity [20], human locomotion functions [21], in linguistics [19]. Cognitive processes like most complex systems [22] exhibit fractal properties [23, 24], analysis and the use of results requires careful research. In recent years, the complex networks methods [25] have become widespread. They not only allow the construction and exploration of networks with obvious (as in linguistics) nodes and links [26], but also those reproduced from the time series by actively developing methods [27, 28]. In our recent works, we have used some of the modern methods of the theory of complex systems for the analysis of such a complex system as cryptocurrency [29, 30]. In this paper, we adapt them to cognitive signals. 3 Information mono- and multiscale measures of complexity Based on the different nature of the methods laid down in the basis of the formation of the measure of complexity, they pay particular demands to the time series that serve the input. For example, information requires stationarity of input data. At the same time they have different sensitivity to such characteristics as determinism, stochasticity, causality and correlation. In this paper, we do not use classical information measures (for example, the complexity behind Kolmogorov, entropy measures), since complex signals manifest complexity inherent to them on various spatial and temporal scales, that is, they have scale-invariant properties. They, in particular, are manifested through the power laws of distribution. Obviously, the classic indicators of algorithmic complexity are unacceptable and lead to erroneous conclusions. To overcome such difficulties, multiscale methods are used. The idea of this group of methods includes two consecutive procedures: 1) coarse graining (“granulation”) of the initial time series – the averaging of data on non- intersecting segments, the size of which (the window of averaging) increased by one when switching to the next largest scale; 2) computing at each of the scales a definite (still mono scale) complexity indicator. The process of “rough splitting” consists in the averaging of series sequences in a series of non-intersecting windows, and the size of which – increases in the transition from scale to scale [31]. Each element of the “granular” time series is in accordance with the expression: j yj  1 /   x , 1 j  N /, i ( j 1) 1 i (1) where τ characterizes the scale factor. The length of each “granular” row depends on the size of the window and is even N/τ. For a scale equal to 1, the “granular” series is exactly identical to the original one. We demonstrate the work of multi-scale measures of complexity on examples of Approximate Entropy and Sample Entropy [19]. Approximate Entropy (ApEn) is a “regularity statistic”, which determines the possibility of predicting fluctuations in time series. Intuitively, it means that the presence of repetitive patterns (sequences of a certain length constructed from successive numbers of sequences) fluctuations in the time series leads to a greater predictability of the time series than those in which there are no repetitions of the templates. The comparatively large value of ApEn shows the likelihood that similar observation patterns will not follow one another. In other words, a time series containing a large number of repetitive patterns has a relatively small ApEn, and the ApEn value for a less predictable (more complex) process is greater. When calculating ApEn for a given time series SN consisting of N values t(1), t(2), t(3), ..., t(N) two parameters are chosen, m and r. The first of these parameters, m, indicates the length of the template, and the second – r – defines the similarity criterion. The sequences of time series elements SN consisting of m numbers taken starting from the number i are called, and are called vectors pm(i). The two vectors (patterns), pm(i) and pm(j), will be similar if all the difference pairs of their respective coordinates are less than the values of r, that is, if |t(i+k)–t(j+k)|