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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>October</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Mining of PubMed Publications for Neurophysiological Tests Assessing the Cognitive Reserves</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Maxim Bakaev</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Olga Razumnikova</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Novosibirsk State Technical University</institution>
          ,
          <addr-line>Novosibirsk</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2020</year>
      </pub-date>
      <volume>1</volume>
      <fpage>0</fpage>
      <lpage>16</lpage>
      <abstract>
        <p>Our paper is dedicated to the selection of neuropsychological tests effective for experimental assessment of cognitive reserves, which are increasingly studied as the world population ages. In this, we separately consider the systems of attention, memory and intelligence and use the list of 36 candidate tests composed by domain expert relying on OntoNeuroLOG - Mental State Assessment ontology, which we extend in OWL format. The names of the tests are employed in extracting the publications from PubMed (MEDLINE) bio-medical database with the tools provided by E-utilities (EDirect). To assess the application context, represented as the subject group and the studied pathology, we perform word frequency analysis for the publications' titles and itemize the most prominent journals. Ultimately we select in total 5 tests that are most popularly used by the research community and whose application context is relevant for the cognitive reserves studies. These neuropsychological instruments include Stroop task, Fluency test, Divided attention tasks, Dual task, and Rey complex figure . We believe that both the mining method that we used and the resulting test battery can be of interest to experimental researchers in Neuropsychology.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Just as Mathematics has come to be “the language of science”, information technologies (IT)
are becoming “the toolbox of science”, as the volume of research publications is growing
exponentially. Moreover, the power of the growth is itself accelerating: from 2-3% annual increase
in the mid-XX century to 8-9% in 2010 [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], leaving little hope for the purely expert knowledge.
Organized collections of publications that are accessible online do so far cope with this tide
quantitatively, but the functionality they provide with respect to search and analysis often lags
behind the actual needs of the scientific community. Meanwhile, many fields of research would
benefit from the ability to use flexible literature mining tools tailored to the research goals. This
is particularly true for emerging and shifting areas of science, without the established concepts,
the universally accepted methodologies, or the contexts of their application. A vivid example
of such a dynamic field is Neuropsychology, which in addition deals with such complex and
multi-aspect subjects as human brain, mind and behavior.
      </p>
      <p>
        Particularly, the issues related to the formation and activation of cognitive resources gain
in importance lately. This concept is used to explain individual differences in the changes of
cognitive functions that accompany brain ageing or damage, and the terms “cognitive reserves”,
“compensatory reserves”, etc. are used as close synonyms in various contexts and schools. The
increasing interest is due to the growing life expectancy of the population and longer professional
careers in the elder age, which require preservation of mental and physical health [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. However,
the atrophy of nerve cells that steadily intensifies with age and the increasing probability of
pathologies in other physiological systems, whose treatment requires surgical intervention with
the use of general anesthesia, increase the risk of cognitive dysfunctions and a decline in the
quality of life for elder people. Correspondingly, every year there’s a gain in the interest towards
identification of informative indicators of cognitive functions and brain activity, which could
predict the dynamics of the development of the brain’s pathological state and the resources of its
adaptive functions.
      </p>
      <p>
        Our previous review of research results in mechanisms of the brain’s ageing suggested that
despite the seemingly existing consensus with respect to decreasing speed of mental operations,
worsening cognitive flexibility and short-term memory [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], it remains unclear whether the
observed diversity of these effects is explicitly due to the compensatory functions of the brain, or
due to the wide range of experimental conditions that are used when testing the cognitive
status. The indicators of attention, memory and intelligence can be considered the most universal
representation of functional status of the brain and its potential resources. So, we ran the
preliminary set of the related keywords through the online search interface of PubMed1, the website
serving as the gateway to biomedical publications – it contains more than 30 million of them,
mostly from MEDLINE database. The changes in the number of PubMed publications that
relfect the research results of this field (with various combinations of keywords attention, memory,
intelligence, and compensatory resources/reserves) are presented in Table 1.
These data suggest that the use of PubMed online search interface to manually combine the
1 https://www.ncbi.nlm.nih.gov/pubmed/
concepts of interest to reflect the research goal involves relatively high e ffort. The potential
predictors of cognitive reserves (CR) include so many indicators of various cognitive processes
including effectiveness of functions in attention and memory systems or components of
intelligence (e.g. [
        <xref ref-type="bibr" rid="ref3 ref4 ref5">3-5</xref>
        ]). Moreover, if these concepts are combined with the terms “cognitive reserves”
or “cognitive resources” that interest us, the search interval further narrows (see in Table 1) and
it no longer fully reflects the observed research interest towards adaptive potential of the brain
in ageing and the related pathological conditions. The total number of all possible combinations
for the 8 elementary keywords shown as the example in Table 1 would be equal to 28-1 = 63
search queries. At the same time, in our previous study of PubMed publications [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] we found
increasing interest towards understanding the role of Processing speed, Inhibition and Emotional
regulation, with most works in 2010-2019 being dedicated to memory (11102) and attention
(6390). Clearly such numbers of publications are beyond an expert’s capability for thorough
reviewing, and call for automation of the analysis, which can be provided by data and text mining
technologies.
      </p>
      <p>To assess the effectiveness of functions of attention, memory and intelligence systems, a wide
diversity of experimental conditions and test batteries are utilized, ranging between
different countries and various pathological conditions. For instance, the relatively unsophisticated
Mini–Mental State Examination is certified in the Russian healthcare system, but it is mostly
useful for screening obvious dementia. As for the CR assessment, the number of test batteries
proposed in the literature is rather high, which impedes their selection in practice and makes
cross-publication meta-analysis troublesome [7; 8]. So, the goal of the current research is the
development of test battery for CR based on the identification of the experimental tests and
subject groups that are most common in the studies of the systems’ functions with respect to the
cognitive reserves. Particularly, we perform: 1) the extraction of the test-related publications
from PubMed and their counting per the time periods, 2) the identification of the most common
subject groups and the experimental contexts (particularly, the studied pathologies) from the
word frequency analysis in the extracted publication, 3) the itemization of the most prominent
publication venues (journals) for each of the tests.</p>
      <p>The remaining of the paper is organized as follows. In Section 2, we describe the use of tools
for PubMed mining and the domain ontology that we employed. In Section 3, we present the
software implementation and the results of the analysis. Finally, we discuss the findings and
their limitations and provide the conclusions.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Method and Tools</title>
      <p>Our mining method is based upon the analysis of the tests’ popularity in the publications related
to CR, so its main assumption is the wisdom of the research community. In the next sub-chapter
we detail the method and overview some related work.</p>
      <sec id="sec-2-1">
        <title>2.1. PubMed Mining</title>
        <p>Quantitative mining of existing publications in Neuroscience nowadays often has the form of
meta-analysis – the study of several aggregated datasets, usually using statistical methods. A
certain disadvantage of this method is that it requires access to the publications’ full texts or the
openly available datasets. Also, it has poor capabilities for automation, particularly if it seeks to
cover relatively dated, pre-standardization research works. Another popular kind of secondary
research is bibliometrics: even though it primarily deals with impact, citations and ranking
of publications, there are also applications for the development of thesauri (bibliomining) and
studying the relative “impact” of concepts. In [9], the top-10 terms with the highest relative
citation scores were identified based on the publications’ titles and abstracts extracted from Web
of Science’s “Neuroscience” category and on the Journal Citation Reports (JCR).</p>
        <p>Still, PubMed appears to be a more appropriate source for biomedical data and text mining,
both due to the focus of the underlying MEDLINE database, the great number and temporal
range of publications, and the robust API access tools. In the last decade, the emphasis on
developing custom software for biomedical mining (such as [10] or [11]) has gradually diminished,
as Entrez (E-utilities) become the de-facto standard [12], save possibly for Qinsight (Quertle),
which however is a commercial product. E-utilities are 9 server-based programs that provide
interface into the Entrez query and database system at the National Center for Biotechnology
Information (NCBI). In our current research we mostly relied on the following utilities and
functions2:
• ESearch – responds to a text query, returning the list of matching publications identifiers
(UIDs) in a given database, for later use in ESummary, EFetch or ELink.
• ESummary – responds to a list of UIDs from a given database with the corresponding
document summaries (DocSum). It functions for all Entrez databases, and a text search in
web Entrez is equivalent to ESearch-ESummary .
• ELink – responds to a list of UIDs in a given database with either a list of related UIDs and
relevancy scores in the same database or a list of linked UIDs in another Entrez database.
• EFetch – responds to a list of UIDs in a given database with the corresponding data
records in a specified format. Currently, it does not support all the 38 Entrez databases;
• efilter – navigation function that filters or restricts the results of a previous query within
the Entrez databases;
• xtract – Entrez direct function that converts EDirect XML output into a table of data
values.</p>
        <p>While the above utilities and functions allow extraction of publications and their specific fields
from the Entrez databases, our goals also included the analysis of word frequency. The Entrez
Direct (EDirect) software extends E-utilities and allows access to the interconnected NCBI’s
databases from UNIX Command Line. Particularly, it already includes the function that is
capable of performing straightforward counting of the words in the provided textual corpus:
WordAtATime() {
2 See the documentation at https://www.ncbi.nlm.nih.gov/books/NBK179288/
sed ’s/[^a-zA-Z0-9]/ /g; s/^ *//’ |
tr ’A-Z’ ’a-z’ |
fmt -w 1
}
alias word-at-a-time=’WordAtATime’</p>
        <p>Another function included as a script with the EDirect software allows sorting the words’
frequencies:</p>
        <p>SortUniqCountRank() {
sort -f |
uniq -i -c |
perl -pe ’s/\s*(\d+)\s(.+)/$1\t$2/’ |
sort -t $’\t’ -k 1,1nr -k 2f
}
alias sort-uniq-count-rank=’SortUniqCountRank’</p>
        <p>As we mentioned above, our third goal involves the per-test analysis of the frequency of
journals that publish the papers. Conveniently, the output for the Document Summary provided
by the E-utilities in XML format contains the property FullJournalName. Since the journals’
names are standardized, we felt there was no need for a sophisticated analysis, so we relied on
MS Excel’s Pivot Tables functionality to count the most frequent journals for the publications
extracted for each of the tests.</p>
        <p>So, after the mining tools fit for our purposes were selected and configured, the next challenge
was to obtain the list of candidate tests for the assessment of CR, per the systems of attention,
memory and intelligence.</p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. The Neurophysiological Tests Ontology</title>
        <p>
          It should be noted that the term “cognitive resources” is more frequent and had emerged earlier
than “cognitive reserves” in English-language publications. The analysis of literature containing
these keywords suggests that in the study of cognitive reserves much more attention is paid to the
brain’s structures and functions, as well as their re-organizations that activates due to traumatic
or pathological damage of the nervous system, while in the study of cognitive resources it is
paid mostly to emotional and / or motivational regulation of cognitive activity. For more detailed
review of CR in Neuroscience, the reader can kindly refer e.g. to our previous publication on the
subject [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ]. Suffice to say that for the purposes of our research we are going to treat publications
containing either of the keywords “cognitive functions”, “cognitive resources” and “cognitive
reserves” as relevant.
        </p>
        <p>The analysis for the selection of the tests needs to be performed independently per the systems
of attention, memory and intelligence, as each of them has unique context with respect to the
tests application. Since this implied the need for thesaurus (query keywords) combined with
domain knowledge (the classification of the tests per the systems), we turned to the use of ontology.
In biomedicine, neuroscience, neuropsychology, and etc. ontologies are seen as an effective tool
for organization of concepts, theories, and models related to the brain, cognitive functions and
behavior, psychological metrics and so on [13]. A remarkable number of ontologies was
created and made available [14], particularly since the wide introduction of the infamous Protégé
ontology editor, developed by the Stanford Center for Biomedical Informatics Research.</p>
        <p>The results of our review of existing ontologies suggested that OntoNeuroLOG [15]
apparently contains the most extensive list of instruments for subject data acquisition (i.e. tests). It is
also conveniently available in OWL format and represented online at BioPortal within the
Mental State Assessment ontology3. A certain disadvantage was the respectable age of the project,
nearly 10 years, which suggested the need for updating, given the high dynamics in the domain
of Neuropsychology. Another trouble was that the names of the tests (see in Fig. 1) were by and
large not appropriate for direct usage as keywords in search queries.</p>
        <p>The representation of the systems-related classes in OntoNeuroLOG (see in Fig. 2) was not
satisfactory for our purposes: 1) the structure does not reflect domain knowledge (they concepts
are just direct subclasses of the domain class) and 2) they have no relations to the tests (no links
to subclasses of the Subject data acquisition instrument class).</p>
        <p>The up-to-date list with the names of the tests relevant for CR was composed by a
Neuropsychology domain expert, who also specified their relations to the systems. All of these were
implemented in Protégé 4.3.0 OWL editor as the extensions of the Subject data acquisition
instrument class, as shown in Fig. 3-5 (visualized with OntoGraph plug-in). The names of classes
at the bottom level correspond to the keywords as they will be used in the search queries for the
3 https://bioportal.bioontology.org/ontologies/ONL-MSA/</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Results</title>
      <sec id="sec-3-1">
        <title>3.1. Software Implementation</title>
        <p>The E-utilities (EDirect) PubMed mining tools accept natural language-based queries as the
input and output matching publications, while one of the configuration options is Automated Term
Mapping (ATM). Enabled by default, it extends the initial query with the supposedly relevant
keywords selected from a list of pre-indexed terms. The somehow unpredictable helpfulness of
ATM has long been the source for complains in the PubMed mining research [16]. However, in
our informal tryouts we found that its current implementation increases the number of extracted
publications by the relatively consistent 8%. Since we were mostly interested in the relative
numbers between the tests, we decided that this overhead, even if its relevance is uncertain, will
not significantly bias the results and kept the ATM defaults.</p>
        <p>We installed the previously described EDirect software on a virtual server under Debian
operating system and used the UNIX terminal queries in the following format to perform the
publications search and filtering:
esearch -db pubmed -query "cognitive AND (functions OR resources OR reserves)" |
efilter -query "Attention AND Network AND Test" | efetch -format docsum |
xtract -pattern DocumentSummary -element Id SortFirstAuthor Title
FullJournalName PubDate &gt; AttentionNetworkTest.txt</p>
        <p>This example query extracts the specified fields (UID, first author’s name, publication title,
journal name, publication date) for the Attention Network Test and saves the output as delimited
values to the AttentionNetworkTest.txt file for further analysis. So, we ran 36 such queries
– for every test’s name specified in the ontology (as illustrated in Fig. 3-5).</p>
        <p>In analyzing the word frequency, we considered several options. Searching in the
publications’ titles only is by far the fastest, but it is limited in the corpus volume. Full text search, even
though the slowest, is potentially the most robust, but in turned out that full texts are not
accessible for most publications, particularly the ones preceding the proliferation of the Open Access.
PubMed also provides the -related key for ELink, which at some higher computational costs
extends the search results so that they supposedly better represent the field, similarly to the ATM
mechanism that we described previously. We informally tested the correspondence of the words
distribution for one of the tests to Zipf’s law using Kolmogorov-Smirnov’s test implemented in
plpva library for R (http://www.santafe.edu/aaronc/powerlaws/), and found that the hypothesis
had to be rejected, unlike for the simple title search. Since some of the related results suggest
that natural language texts that make sense abide by Zipf’s law in contrast to random ones [17],
we ultimately decided to rely on the simple title search in our analysis of the words frequencies.</p>
        <p>So, it resulted in the following query that uses the previously described UNIX alias commands
word-at-a-time and sort-uniq-count-rank :
esearch -db pubmed -query "cognitive AND (functions OR resources OR reserves)" |
efilter -query " Attention AND Network AND test " | efetch -format docsum |
xtract -pattern DocumentSummary -element Title | word-at-a-time
| sort-uniq-count-rank &gt; frequencyANT.txt</p>
        <p>This example query generates a table of word occurrence counts for the Attention Network
Test, sorted by frequency, and saves it to the frequencyANT.txt file.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. The PubMed Mining Results</title>
        <p>The mining was performed in April 2020, so the results are current for that date. In Tables
2-4 we present the results of the analysis per the systems: the dynamics of various tests, the
most common subject groups, the pathologies and the most prominent journals, if any. The
ifgures are the absolute numbers of relevant publications found, while the subject groups and the
pathologies are based on the word frequency analysis in the whole body of publications’ titles
for a test. The tests are sorted by the total number of publications retrieved, and the names of the
most popular tests that are the candidates for the test battery are highlighted in bold. In Table
3, the Alternate Category test is not shown, as the total number of extracted publications for it
was 0. In Table 4, the Travelling Salesman, Amthauer’s Structures, Mayer-Solovey Emotional
Intelligence, Guilford-Sulliven tests are not shown for the same reason, so the group of
socialemotional intelligence test is not represented. Blank cells in the tables mean there were too few
publications for a conclusive analysis.</p>
        <p>The results of the analysis suggest that Fluency test and Stroop task are the most common
in studies of executive attention functions. The working memory with respect to the cognitive
resources is studied much more often that the other types of memory; and the most common
working memory tests are Dual task and Wisconsin card sorting test. The relatively smaller
number of publications dedicated to the testing of intelligence as a cognitive resource is probably
due to the organizational complexity and high work effort needed for such studies, which require
more time compared to the performance of separate tests of attention and memory. The most
common is IQ analysis based on Wechsler Adult Intelligence Scale for patients with diagnosed
schizophrenia. In Fig. 6 and Fig. 7 we show the dynamics (logarithmic scale and exponential
trends are used) for the numbers of publications for the selected most popular tests related to
attention and memory respectively.</p>
        <p>The expert analysis of the publications’ titles filtered from PubMed with the concepts of the
ontology that we created, has further limited the set of the publications. For instance, out of the
196 articles combining CR and Attention Network Test, the expert recognized 42 (21.4%) to be
indeed relevant. About the same share (22.3%) was maintained for the publications combining
CR and Color Word Interference: 25 truly relevant ones out of 112 found. So, for further
facilitation of the information search and analysis, we studied the frequencies of the words encountered
in the titles.</p>
        <p>The analysis of the obtained lists has confirmed the appropriateness of the classification of
tests based on the expert’s opinion. E.g., for the Attention Network Test the top positions in the
list were held by attention 52, cognitive (47) and network (35). For the Fluency test, the most
frequent were cognitive (480), functions (171) and executive (159). Besides, the analysis allowed
identification of the most common subject groups, and the pathologies, as shown in Tables 2-4.</p>
        <p>According to Tables 2-4, the vast majority of studies with the functions of attention, memory
and intelligence being tested, are dedicated lately to researching mechanisms of Alzheimer’s
decease and schizophrenia. Cognitive resources with respect to attention in children are most
commonly studied with Ongoing task, while age-related memory changes are studied with Dual
task and Logical Memory Test.</p>
        <p>If the cognitive reserves are considered in the traditional way, as the neural networks of
complex organization obtained during the education process and the subsequent professional
cognitive activities [18], then the volume and organization of the created networks are capable of
compensating their partial loss due to atrophy of the neurons and nerve fibers caused by aging
and the related Alzheimer’s disease processes. According to our findings, Design Fluency Test,
Divided attention tasks, and Rey complex figure are the most commonly used instruments for the
neuropsychological measuring of attention and memory as the indices of cognitive reserves.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Discussion and Conclusions</title>
      <p>Unlike the studies focused on the search and review of socio-psychological or
neurophysiological instruments for identification of cognitive reserves [19; 4] (and, accordingly the surveys and
questionnaires for the education level, professional activities and lifestyle, as well as the
particulars of architecture and functional activity of various brain structures measured with fMRI),
our work was aimed towards classification, search and analysis of neuropsychological tools for
testing the functions of attention and memory systems, whose indicators are seen as the primal
psychometric predictors for cognitive reserves both in normal and pathological ageing [3; 20;
21; 18]. The multitude of approaches towards the assessment of CRs subsequently defines the
diversity of the functions tested. In our work we sought to identify the psychometric methods
that are most frequently used or discussed, as we did not evaluate the con-text in which the
test-related terms were mentioned, and it might as well have been negative ones. Still, our
informal verification of the extracted publications reveals that the works in which where the tests are
utilized are quite more common than reviews or critiques.</p>
      <p>As the results suggest, various versions of the Fluency test and Divided attention tasks and the
Dual task are used more often than the others in studying of ageing-related cognitive reserves.
This does not come as a surprise, since the universal processes in the ageing brain are decrease in
the information transfer speed (which is reflected in the generation of ideas in the Fluency test)
and the decline in effectiveness of coordination of the different neural systems when the volume
of the information being processed grows (hence the diminishing performances in the Divided
attention tasks and the Dual task). It seems that the relative scarcity of using the Rey complex
ifgure for testing spatial memory in patients with Alzheimer’s disease in literature is due to the
fact that the structure the most sensitive to age-related atrophy of nerve cells is hippocampus,
which ensures the formation of new traces of memory and especially spatial memory (see review
in [3; 22]).</p>
      <p>The relatively infrequent joint mentioning of the compensatory resources/reserves &amp;
memory or compensatory resources/reserves &amp; attention (see PubMed search results in Table 1) but
the greater number of publications returned in our mining with E-utilities is seemingly due to
the fact that most research works dedicated to studying the mechanisms of age-related memory
weakening (10659 publications mentioning aging AND memory and 5190 for aging AND
attention in PubMed during the last 5 years only) use the concept of “cognitive reserves” when
discussing the discovered effects, but not as important keywords.</p>
      <p>It remains unclear why despite the education being recognized as one of the most
important indicators of cognitive reserves preventing the development of age-related dementia [23;
24], relatively little attention is given to testing intelligence. Perhaps it is due to the
organizational difficulties in applying the well-known techniques (Wechsler Adult Intelligence Scale and
Stanford-Binet test) in fairly large samples.</p>
      <p>Correspondingly, the described technology for mining the literature based on the keywords of
interest and the frequency analysis of concepts allows effective planning of research by selecting
the most informative experimental conditions. With respect to our goals related to the search for
predictors of cognitive reserves, these include such instruments as Stroop task, Fluency test,
Divided attention tasks, Dual task, and Rey complex figure .</p>
      <p>An important limitation of our study is that the list of tests’ names to be used as the keywords
in the literature mining process was composed based on an expert’s subjective opinion. It is
very much likely incomplete, due to the expert’s limited memory and the range of interests,
which mostly covers normal, but not pathological brain ageing processes. So while the current
work is focused on the most common experimental conditions for testing attention, memory and
intelligence, it is possible that some more rare testing instruments may be no less informative
in assessing the cognitive functions. Further, the word frequency analysis, which we used to
identify the tests’ application context, was performed only for the publication titles, not the full
texts. However, it is unclear whether this is indeed a disadvantage, as mining of full texts is
much more complex, and may be biased by the terms not related to the paper contents, e.g. from
the literature review.</p>
      <p>Another notable limitation is that no verification of the test battery’s e ffectiveness was
performed, even though our research plans include this as an important priority. Among other
research prospects we see the exploration of sustainability of the effect found with each of the
methods, based on the analysis of the citations (impact) of publications that mention them. We
also plan to consider the efficiency of tests related to emotional regulation of behavior that is
known to be an important factor in formation and usage of cognitive resources. The method
based on the popularity of the publications and the mining technology that we developed lay
within the mainstream computational Neuroscience [25; 26]. We believe that they, as well as the
proposed test battery, can be of practical use for researchers working in experimental
Neuropsychology.</p>
    </sec>
    <sec id="sec-5">
      <title>Acknowledgments</title>
      <p>The reported study was funded by RFBR according to the research project No. 19-29-01017. We
also thank our Master student, Alexander Lukichev, for his assistance in EDirect programming.
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