=Paper=
{{Paper
|id=Vol-2393/paper_356
|storemode=property
|title=Modeling of Cognitive Process Using Complexity Theory Methods
|pdfUrl=https://ceur-ws.org/Vol-2393/paper_356.pdf
|volume=Vol-2393
|authors=Vladimir Soloviev,Natalia Moiseenko,Olena Tarasova
|dblpUrl=https://dblp.org/rec/conf/icteri/SolovievMT19
}}
==Modeling of Cognitive Process Using Complexity Theory Methods==
<pdf width="1500px">https://ceur-ws.org/Vol-2393/paper_356.pdf</pdf>
<pre>
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)|<r, 0 ≤ k ≤ m.
    For the considered set of all vectors pm of the length m of the time series SN,
values:

                                                       nim r 
                                     Cim r                                           (2)
                                                      N  m 1
can be calculated. Where nim(r) – the number of vectors in pm, similar to the vector
pm(i) (taking into account the chosen similarity criterion r). The value Cim(r) is the
fraction of vectors of length m, which are similar to the vector of the same length,
whose elements begin with the number i. For a given time series, the values Cim(r) for
each vector in pm are calculated, after which there is an average value Cm(r) that
expresses the prevalence of similar vectors of length m in a row SN. Directly the ApEn
for the time series SN using the vectors of length m and the similarity criterion r is
determined by the formula:

                        ApEn(S N , m, r )  lnCm r  / Cm1 r                      (3)
that is, as a natural logarithm of the ratio of the repetition of vectors of length m to the
repetition of vectors in length m+1+1.
    Thus, if there are similar vectors in the time series, ApEn will estimate the
logarithmic probability that the subsequent intervals after each of the vectors will be
different. The smaller ApEn values correspond to the greater likelihood that vectors
follow similar ones. If the time series is very irregular, the presence of such vectors
can not be predictable and the value of ApEn is relatively large.
    Sample Entropy (SampEn) is similar to the ApEn, but when calculating the
SampEn, two conditions are added:
─ does not take into account the similarity of the vector to itself;
─ when calculating the probabilistic values of SampEn, the length of the vectors is
  not used.

In Ошибка! Источник ссылки не найден.a shows the ApEn dependence of the
scale to the test signals – flicker (1/f) white noise (wnoise) and electrocardiogram
(ECG) signal compared to the shuffled signal (ECG shuffled).




  Fig. 1. (a) ApEn of artificial and natural signals, depending on the scale; (b) autocorrelation
      functions for control the stride intervals fluctuations and Alzheimer’s disease (als),
                            Huntington’s (hunt) and Parkinson’s (park)

From Fig. 1a it is evident that, as expected, a flicker signal was a scale-invariant one.
The ECG signal is complex on a large scale. Its complexity is lost when shuffled and
becomes very close to a random signal.
   Cognitive signals differ in the functions of autocorrelation: the more complex ones
have a longer “memory”, which is manifested in the slowdown of the function of
autocorrelation with the lag (Fig. 1b).
   Accordingly, the signal of a healthy person and a multiscale entropy measure is
more complicated (Fig. 2a). We also investigated multiscale complexity measures for
time series of stride intervals in children from 40 to 163 months (Fig. 2b).
   Obviously, the complexity of the signal for an older child is increasing.
Fig. 2. Multiscale entropy of stride intervals time series templates for healthy and Alzheimer’s
                            disease (a) and children of all ages (b)

The next study cognitive signal is the time series of time intervals between human-to-
word responses (human recalls of words). Recall in memory refers to the mental
process of retrieval of information from the past and is a way to study the memory
processes of humans and animals [13]. Recall describes the process in which a person
is given a list of items to remember and then is tested by being asked to recall. For the
autocorrelation function and the multiscale SampEn we obtain the results presented in
Fig. 3.




Fig. 3. Autocorrelation functions (a) and MSE measures of complexity (b) signals 1-3 series of
                                            recalls

Unfortunately, due to insufficient statistics and short-term time series, identification
of differences in these methods is not possible.
   Similar studies for musical works of various genres (aria, blues, brazilian samba)
and literary works by famous authors (L. Tolstoy’s “War and Peace”, L. Carroll
“Alice in Wonderland”, C. Dickens “Cricket on the Hearth”) gave the results shown
in Fig. 4.
Fig. 4. Autocorrelation of musical (a) and literary (b) works; (c) and (d) are the corresponding
                          multiscale entropy measures of complexity

Obviously, MSE allows classification of the analyzed cognitive signals in terms of
complexity.


4      Multifractal measures of complexity

In the general case, the procedure of popular Multifractal Detrended Fluctuation
Analysis (MF-DFA) is implemented by the following algorithm. Let be a sequence of
length N. Then determine the accumulation Y i                x  x , i  1..N . We
                                                                  i
                                                                  k 1   k

divide it into Ns=int(N/s) segments of the same length s that do not overlap. For each
of the Ns sequences, we calculate the local trend by the least squares method,
determine the deviations F 2 v, s   1/ s      Y (( 1)s  i   y (i)))
                                                   s                              2
                                                                                      for each
                                                   k 1                      v

segment ν,   1..N and for each   N s  1..2 N s . There yν(i) is an interpolating
polynomial on the segment ν. Find the mean for all subsequences to obtain the
                                                                                         1/ q
function of q-order fluctuations F  s   
                                                                      q /2 
                                                  v 1 
                                                         F 2  s,   
                                              1
                                                
                                                  2 Ns
                                  q                                                            . The
                                            2N                            
standard DFA method corresponds to the case q=2. Determine the scaling behavior of
the fluctuation function by analyzing the double logarithmic scale of the dependence
Fq(s) on q. If the sequence xi has long-term correlations, Fq(s) increases with
increasing s according to the power law Fq s   s
                                                              h (q )
                                                                       . For stationary time series,
h(2) identical to the Hurst exponent. Thus, the function h(q) can be called the
generalized Hurst exponent.




Fig. 5. Spectra of multifractality (a) reaching the stage of healthy and sick patients; (b) children
              of all ages; (c) musical works of different genres; (d) literary works

Together with the generalized Hurst exponent, a spectrum of generalized fractal
dimensions Dq is introduced that characterize the distribution of points in a given
domain and is determined by the relation Dq=τ(q)/(q–1), where the function τ(q) has
the form  (q)  lim ln z q, s  / ln s  , and Z(q, s) is a generalized statistical sum
                     s 0
which is characterized by an index of degree q.
    To characterize the multifractal set, the so-called multifractal spectrum function
f(α) (the spectrum of singularities of a multifractal) is used, which is actually equal to
the Hausdorff dimension of a homogeneous fractal subset of the initial set, giving a
dominant contribution to the statistical sum for a given q value. The connection
between the values f(α) and τ(q) is determined by the relationship τ(q)=qα–f(α).
    The extremum of the function f(α) determines some average value of the Hurst
exponent, and the value Δα=αmax–αmin – the width of the spectrum of the
multifractality – characterizes the degree of complexity of the system.
    In Fig. 5 shows the spectra of multifractality of some of the cognitive systems
described above.
    We see that more complex signals have wider spectra of multifractality.
Consequently, the multifractal measure of complexity can be used to analyze
cognitive signals. We have implemented a dynamic procedure for calculating
multifractal parameters, which allows you to follow the change in the complexity of
the signal in time.


5      Complex network methods for studying cognitive
       processes

One of the most important areas of cognitive science is cognitive linguistics.
Cognitive linguistics is a trend in linguistics that studies and describes the language in
terms of cognitive mechanisms that underlie human mental activity. Thus,
cognitology is, so to speak, a computer that characterizes a person by analyzing his
psyche, mental activity, and on the first place among the tasks put forward research
language that is inextricably linked with human.
   The significance of language for cognition is extremely great, because it is through
language that one can objectivize the mental activity, that is, verbalize it. On the other
hand, learning a language is an indirect way of studying cognition, because cognitive
and language structures are in certain proportions. One of the tools of the study of
cognitive linguistics is the theory of complex networks. The nodes in such networks
are elements of these complex systems, and the links between nodes – the interaction
between the elements.
   In the last decade, the structural properties of language, the texts of literary works
and texts related to religious consciousness, as well as the organization of musical
works and painting began to be studied and analyzed from the point of view of the
application of methods of the complex networks theory. Relevant networks form a
special, little-known category, which is called cognitive networks [25].
   The term “cognitive networks” was proposed in studies on the research of the
network structure of the natural language. Of particular interest is the study of
cognitive networks for understanding the principles of brain function. To date,
research using the theory of complex networks in the study of the brain contributed to
a deeper understanding of the general patterns of interconnection of different levels of
its structural organization, and the involvement in these studies of the concept of
cognitive networks will take into account some of the features of the human creative
functions.
   Let us consider the peculiarities of the application of the theory of complex
systems in the problems of cognitive linguistics. The first step in applying the theory
of complex networks to the analysis of the text is the presentation of this text as a set
of nodes and links, the construction of a language network. There are different ways
of interpreting nodes and connections, which leads, accordingly, to different
representations of the network of languages. Along with the sequential, “linear”
analysis of texts, the construction of networks, whose nodes are their elements -
words or phrases, fragments of natural language, can reveal structural elements of the
text, without which he loses his connectivity. In this case, the task of determining
which of the important structural elements are also important information, such as
determining the information structure of the text, is relevant. Such elements can also
be used to identify still poorly defined components of the text, such as collocation,
paraphrase unity, for example, when searching for similar snippets in different texts.
   We know several approaches to constructing networks of texts, so-called word
networks, and different ways of interpreting nodes and relationships, which leads,
accordingly, to different types of representation of such networks. The nodes can be
connected to each other, if the corresponding words are next to the text, belong to the
same sentence or paragraph, connected syntactically or semantically. Preserving
syntactic relationships between words leads to the image of a text in the form of a
directed network, where the direction of link corresponds to the subordination of the
word.
   Thus, if from a certain text (or another linguistic unit) a complex cognitive network
(for example, a semantic graph) is created by a certain algorithm, then it is expedient
to use the topological and spectral measures [10] of such complex cognitive networks
and even trace their dynamics within the framework of the algorithm of the moving
window [29, 30].
   We will conduct a preliminary study of the frequency distribution of words in
some well-known English-language literary works. The software developed by us
analyzes the text of the work, creates a dictionary, each word of which has a unique
code, in the process of analysis, the number of each of the words of the work is
calculated, and also exports a text file of word codes that can be subjected to further
analysis (frequency analysis, graph construction, its analysis).
    Detailed results of the analysis of the spectral and topological properties of
cognitive networks will be presented in a separate paper. At the same time, we will
show only the fact that the constructed cognitive warnings convey the individual
properties of complex networks in general.
   In Fig. 6 on the logarithmic scale, the frequencies of words in the works are given.
The linear trend corresponds to the distribution of α from the Zipf law [26]: P(k)∼ck-α.
   It is known that in order to comply with the Zipf law, the index should be
approximately equal to units. Execution on this linguistic unit (text) of a rank
distribution of the type of the Zipf law may be a sign of “correctness” (a good
organization) of this text taken as a whole. In this case, Twain’s novel is better
organized, although this usually requires a wider and more profound analysis.
    Fig. 6. The distribution of the frequency of words in the in novels of L. Tolstoy’s “War and
            Peace”, α=1.37 and of Mark Twain “The Prince and the Pauper” by, α=1.00


6        Conclusions

Thus, the modeling of social and humanitarian systems, the core of which is a
cognitive component, can be carried out within the framework of a synergetic
paradigm, the modern point of which is the theory of complex networks. The
considered separate methods of the theory of complex systems demonstrate the
possibility of quantitative analysis of cognitive functions. In particular, the results
obtained in this paper suggest that informational (mono and multiscale), fractal and
multifractal, as well as network measures of complexity can be used to quantify
cognitive processes. This allows us to classify normal and anomalous phenomena, to
offer a method for analyzing the cognitive trajectory over time, to model possible
methods for its correction, taking into account external conditions.
    In addition to the fundamental scientific significance – the understanding of the
work of the human brain – work in this direction aims to overcome the general crisis
of the educational system, the essence of which is the inadequacy of the goals,
content, forms and methods of education new conditions.


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