The application of the theory of fractals for studying the regularities of forming the infosphere of training applicants for nursing specialities

The research stems from challenges which are characteristic of contemporary post-industrial. With respect to the initiation of training Masters of nursing in Ukraine a great importance is attributed to the research component the professional competence.

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The application of the theory of fractals for studying the regularities of forming the infosphere of training applicants for nursing specialities

О.V. Voznyuk, E.F. Malinovsky, V.V. Svyrydiuk

The research stems from challenges which are characteristic of contemporary post-industrial, information and technological stage of development of human civilization. With respect to the initiation of training Masters of nursing in Ukraine a great importance is attributed to the research component of the professional competence of nurses with higher education, i.e. Masters of nursing. Taking into account the insufficient theoretical and methodical status of the problem, the researchers aim their study at developing a new approach to forming the infosphere of nursing as a research speciality on the basis of the theory of fractals. To achieve the goal the authors have used the content analysis of Master's theses of 150 Masters in accordance with 112 indices, Hurst index calculation included. The calculated Hurst index values testify to a high level of structural organization of Master's theses, as well as to certain regularities in using information sources in contrast with chaos and the absence of prevailing tendencies. The use of information sources which were referred to by the students of Master's course for conducting research and writing Master's theses, as well as the application of the techniques of content-analysis and scientific prognostication have made it possible to determine a number of tendencies in forming the infosphere of nursing as a research speciality. One can observe a pronounced tendency to decreasing the use of paper media as information sources, as well as the tendency to increasing the part of electronic media and the part of information sources in foreign languages. Among the information sources in foreign languages, in comparison with Russian English sources, prevail considerably. The study does not cover all aspects of the mentioned pedagogical problem since the further prospects for studying relates to the analysis of the quantity and quality of intellectual property objects created by the

Key words: information sources, electronic media, nursing, Master of nursing, scientometrics technologies, Hurst indext, infosphere, fractality (self-similarity).

ВИКОРИСТАННЯ ТЕОРІЇ ФРАКТАЛІВ ДЛЯ ВИВЧЕННЯ ЗАКОНОМІРНОСТЕЙ ФОРМУВАННЯ ІНФОРМАЦІЙНОГО ПРОСТОРУ ПІДГОТОВКИ ЗДОБУВАЧІВ МЕДСЕСТРИНСЬКИХ СПЕЦІАЛЬНОСТЕЙ

О.В. Вознюк, Е.Ф. Маліновський, В.В. Свиридюк

Дослідження випливає із викликів, характерних для сучасного постіндустріального, інформаційно-технологічного етапу розвитку людської цивілізації. Щодо започаткування підготовки магістрів сестринської справи в Україні велике значення надається дослідницькій складовій професійної компетентності медичних сестер з вищою освітою, тобто магістрів сестринської справи. Враховуючи недостатній теоретико-методичний статус проблеми, дослідження спрямоване на розробку нового підходу до формування інфосфери медсестринства як наукової спеціальності на основі теорії фракталів. Для досягнення поставленої мети автори використали контент-аналіз магістерських дисертацій 150 магістрів за 112 індексами, включаючи розрахунок індексу Херста. Розраховані значення індексу Херста свідчать про високий рівень структурної організації магістерських дисертацій, а також про певні закономірності використання джерел інформації на відміну від хаосу та відсутності переважаючих тенденцій. Використання інформаційних джерел, на які посилалися студенти магістратури для проведення досліджень та написання магістерських дисертацій, а також застосування прийомів змістовного аналізу та наукового прогнозування дозволили визначити низку тенденцій формування інфосфери медсестринства як наукової спеціальності. Спостерігається яскраво виражена тенденція до зменшення використання паперових носіїв інформації як джерела інформації, а також тенденція до збільшення частки електронних ЗМІ та частини джерел інформації іноземними мовами. Серед інформаційних джерел іноземними мовами в порівнянні з російською значно переважають англійські джерела. Дослідження не охоплює всіх аспектів зазначеної педагогічної проблеми, оскільки подальші перспективи вивчення пов'язані з аналізом кількості та якості створених магістрами об'єктів інтелектуальної власності, що дає змогу сформулювати наукометричні критерії оцінки значущості наукових досліджень наукової галузі студентів магістратури, виявляючи тим самим свою здатність створювати об'єкти інтелектуальної власності.

Ключові слова: джерела інформації, електронні засоби масової інформації, сестринська справа, магістр медсестринства, наукометричні технології, індекс Херста, інфосфера, фрактальність (самоподібність).

Introduction of the issue

At the beginning of the 21st century, Ukraine found itself in the period of trial. A rapid advance in science and engineering, the introduction of newest computer technologies into production, education and everyday life, as well as urbanization, economic cataclysms, international terrorism, geopolitical instability, manifestations of regional separatism, a high level of population migration - this is just a brief list of challenges which are characteristic of contemporary post-industrial, information and technological stage of development of human civilization. The above challenges are very hard to cope with in a separate country. Hence, as an answer to these global challenges, the progressive part of the Ukrainian society proclaimed the mainstreaming policy towards the European integration. Hence the researchers' attention is to be focused on fundamental universal human values which are based on competence, intellectual property, research potentials of the country and training of a competitive personality [10].

Current state of the issue

Beginning from 2008, and as far as the training of masters of nursing in Ukraine is concerned, a great importance is attached to substantiating the process of forming the information environment of Nursing as a scientific speciality. The entire process is based on the information and communicative competence of Masters which is closely connected with the information and computer technologies and scientometrics that deal with studying the communicativeness of researchers and the quantitative evaluation of validity of research results according to citation indices. theory fractals nursing specialities

At large, the scientific research while dealing with various aspects of communication in science and technology, deals also with the quantitative measurement of scientific results thus developing new approaches to quantitative assessment of the value of a scientific component, specifically in higher professional education. In this respect, Derek John de Solla Price believes, that evaluating scientific productivity, one cannot measure what one would like, but only that which is probable and possible [5; 6].

So, one of the main problems of the Masters' professional training in the higher educational establishments is connected with forming the scientific communicative competence in the Masters due to the quality of their scientific research. And this can be achieved by means of innovative scientometrics technologies [1; 2; 9; 5-7], particularly in the sphere of quantitative measurement [6] made on the basis of the theory of fractals [2].

Outline of unresolved issues brought up in the article. Taking into account the insufficient theoretical and methodical status of the problem, we can state that some questions concerning the quantitative measurement by means of scientometrics of the results of the conducted research presented in the Master's theses still remain unsolved. Specifically, we aim our study at developing a new approach to forming the infosphere of nursing as a research speciality on the basis of the theory of fractals being the newest perspective of scientific research.

Aim of the research

The analysis of the research and practical activities of higher educational establishments where Masters of nursing are trained testifies to the insufficient investigation into training Masters in this speciality. Hence, the research under study is aimed at elaborating new approaches to studying the regularities of shaping Nursing as a research speciality.

Results and discussion

In order to succeed, we use the method of contentanalysis of Master's theses of 150 Zhytomyr medical institute graduates that were written and defended within 10 years beginning with 2010. With this in view, 150 theses were formalized (digitalized) according to 112 indices.

The formalized indices were put into the table of Excel for Windows Professional table which made them available for the correlation and contentanalysis using the Excel and statisticl programs of statistical data processing.

At present, the majority of researchers consider the information infosphere to be a stochastic one possessing all characteristic features of fractality [3; 4; 8].

The fractality (self-similarity) of the infosphere lies in the fact that under the avalanche-like increase in the information amount, the distribution of its media according to such characteristics as sources, authors, subjects do not practically change its form. The application of the theory of fractals for analyzing the infosphere of research publications makes it possible to reveal some regularities.

At present, the issue-related information volumes are actually considered as self-similar formations capable of self-development. They are typical stochastic fractals, since their self-similarity, for instance the distribution of information clusters by their dimensions, coincides with the mathematically calculated expectations and is used for revealing the regularities from among the multiplicity of empirical data. Chaos postulation as an integral creative dynamic moment of the reality which can be self-organized (order and disorder are inseparable from each other) can be manifested at the present stage of the theory of fractals for analyzing chaos with the aim of looking for regularities, and Hurst index is used for calculating the probability of various trends which describe and prognosticate the dynamics of processes in time [9].

We suggest using the research strategy of the content-analysis of fractality of the dynamics rows through equalizing them according to the least square method with the aim of assessing the extrapolation indices for the next 2 or 3 years.

Table 1 suggests the list and specific weight of the information sources used by Masters of Nursing of Zhytomyr Medical institute for writing their Master's theses.

Table1

The structure of information sources which were used by Masters of Nursing when writing their Master's theses

Sequence No.

Name of Source

Absol.

M±m, %

1

Electronic internet resources

3611

21,5±0,3

2

Periodical research publications (journals)

3044

18,1±0,3

3

Collections of writings(abstracts and articles) of scientific and practical conferences, congresses, meetings, symposia and other scientific forums

2690

16,0±0,3

4

Monographs

1310

7,8±0,2

5

Reference books, encyclopedias, defining dictionaries

956

5,7±0,2

6

Regulatory acts of legislation (Laws of Ukraine, Resolutions of the Cabinet of Ministers, Orders of sectoral ministries

743

4,4±0,2

7

Master's theses

566

3,4±0,1

8

Standards (sectoral educational and industrial standards in rendering services

531

3,2±0,1

9

Dissertations

431

2,6±0,1

10

Textbooks

425

2,5±0,1

11

Dissertation extended abstracts

390

2,3±0,1

12

Reports on research practice

389

2,3±0,1

13

Instructional guidelines with visas of sectoral ministries

354

2,1±0,1

14

Domestic and foreign statistic publications

319

1,9±0,1

15

Manuals

248

1,5±0,1

16

Archival records

177

1,1±0,1

17

Patents for inventions and utility models and other patent and information documents and publications

142

0,8±0,1

18

Diploma papers

110

0,7±0,1

19

Abstract periodicals

107

0,6±0,1

20

Government reports

106

0,6±0,1

21

Mass media (newspapers, magazines, brochures etc.)

71

0,5±0,1

22

Commercial and business information (sale sheets etc.)

70

0,5±0,1

23

Resolutions of scientific and practical conferences, congresses, symposia, and other scientific forums.

35

0,2±0,1

24

Total

16825

100,0±0,0

In total, when writing their Master's referred to 16825 various information theses 150 Masters of nursing have sources which in average amounts to 112,1±1,8 sources per Master's paper. Most often Masters have referred to internet resources, articles in scientific journals, abstracts and articles in the proceedings of scientific and practical conferences, meetings, congresses, symposia and other scientific forums. The part of these three basic information sources totals 55,6±0,4% as compared to all sources used. Along with it, the prospective Masters have used 12147 (72,2±0,3%) of references in the Ukrainian language and 4678 (27,8±0,3%) in foreign languages. In its turn, among 4678 foreign language sources, those written in Cyrillic script (mostly Russian) amounted to 2540 (15,1±0,5%) and 2138 (12,7±0,5%) - in Latin (mostly English).

Table 2 presents the main indices of using information sources by Masters.

Table 2

The dynamics of using information sources by Masters

Index title

Years

2010

2011

2012

2013

2014

2015

2016

2017

2018

Quantity of Master's theses defended

19

14

24

13

14

23

12

16

15

Average quantity of information sources used

115,1

102,4

116,2

98,5

110,6

112,3

115,9

103,4

117,6

Share of sources in Ukrainian, %

90,4

73,9

76,7

80,4

75,9

87,5

71,6

80,3

70,6

Share of sources in foreign language, %

9,6

26,1

23,3

19,6

24,1

12,5

28,4

19,7

29,4

Share of foreign sources in Cyrillic script, %

5,6

15,9

11,0

9,5

9,8

5,3

8,2

6,4

5,8

Share of foreign sources in Latin, %

4,0

10,2

13,3

10,1

14,3

17,2

20,2

13,3

23,6

Share of electronic information sources, %

15, 4

18, 6

16,8

22,6

20,3

23,1

19,9

26,7

22,2

According to the data of table 2 it appears difficult to determine the regularity of using various research information sources by Masters of nursing.

The traditional illustration method, the graphic presentation of the dynamics of indices, also makes it impossible to see a distinct regularity or tendency (Fig.1)

When using the content-analysis of fractality of dynamics rows, one can determine the prevailing tendency (trend), carry out the extrapolation; and applying Hurst index calculation one can assess the probability of using research information sources by Masters of nursing prognosticated for 2019, 2020 and 2021. Table 3 presents the distribution of Master's works according to the average quantity of information sources used depending on the year of defence.

According to table 3 data we have constructed a graph related to the dynamics of the average quantity of the information sources used in Master's theses depending on the defence year (fig.2).

Fig. 1. The dynamics of using various research information sources by Masters of nursing

Table 3

The distribution of the quantity of the information sources used in Master's theses depending on the defence year

Defence year

Quantity of theses defended

Average quantity of the information sources used depending on the defence year, M±m

Absolute quantity of master's theses defended

Part M±m, %

2010

19

12,7±3,0

115,1

2011

14

9,3±2,6

102,4

2012

24

16,0±3,3

116,2

2013

13

8,7±2,5

98,5

2014

14

9,3±2,6

110,6

2015

23

15,3±3,2

112,3

2016

12

8,0±2,4

115,9

2017

16

10,7±2,9

103,4

2018

15

10,0±2,8

117,6

With the aim of determining the prevailing tendency we have used the technique of equalizing the rows of the dynamics according to the least square method. Table 4 presents the initial data for using the above technique. We have according to the algorithm presented below.

Fig. 2. The graph of the dynamics of the average quantity of the information

Table 4

The initial data for trending with the average quantity of the information sources used in Master's theses with the interval of 9 years and the prediction for 3

consecut

ive years

Years

Average value of the number of pages, У

Conditional time, Х

ХУ

Х2

Equalized data, Ух

2010

115,1

-4

-460,4

16

108,4

2011

102,4

-3

-307,2

9

108,9

2012

116,2

-2

-232,4

4

109,3

2013

98,5

-1

-98,5

1

109,8

2014

110,6

0

0

0

110,2

2015

112,3

1

112,3

1

110,6

2016

115,9

2

231,8

4

111,1

2017

103,4

3

310,2

9

111,5

2018

117,6

4

470,4

16

112,0

n =9

Ey = 991,8

Eyx = 26,2

ЕХ2 = 60

2019

5

112,4

2020

6

112,8

2021

7

113,3

Fig. 3. Actual and equalized dynamics of the average quantity of the information sources within 9 years

The value of Hurst index which equals % proves marginal. All values which are less than % testify to the low prognostication probability. Hurst index which is approaching to zero testifies to the absence of the prevailing tendency (trend), and the quantities analyzed take on random values. The values of H which are bigger than % are focused on a certain direction of the dynamics of the process in the past and have a high probability of extending the dynamics in the same direction in future. The larger the value of Hurst index exceeding % is, the higher the prognosticating probability.

The technique of equalizing the dynamics graphs makes it possible to use other time intervals as well. Table 5 presents the value of Hurst index and prognosticated values of the quantity of the information sources used depending on the duration of the interval (3, 5, 7 and 9 years), according to which the equalizing of the dynamics rows and the calculations of the prognostication probability were made. Among the four intervals analyzed the value of Hurst index for the 3-year-long interval proves most probable. Consequently, in 2019, 2020 and 2021 the average quantity of the information sources per Master's thesis will amount to 113,6, 114,3, and 114,9 respectively.

Table 5

The value of Hurst index and prognosticated values of the average quantity of the information sources depending on the interval according to which the equalizing of the rows of the dynamics and the prognostications were made

Name of index

Intervals according to which the equalizing of the rows of the dynamics were made, years

3

5

7

9

Hurst index

1,490

1,026

0,800

0,670

Prognosticated values of the average quantity of the information sources used

2019

113,6

113,5

113,4

112,4

2020

114,3

114,0

114,1

112,8

2021

114,9

114,5

114,7

113,3

The use of the information sources referred to by students of the Master's course, when writing Master's theses, the technique of the content-analysis have made it possible to determine a series of tendencies in forming the infosphere of the research speciality of "Nursing".

It has been established that the calculated Hurst index values testify to a high level of structuredness of Master's theses, as well as to the availability of certain regularities of using the information sources by Masters of nursing as opposed to chaos and the absence of prevailing tendencies.

In particular, there exists a regular tendency towards the decrease in the use of paper media as information sources by Masters of nursing, as well as the corresponding increase in the part of electronic information sources.

One can also observe the tendency towards increasing the part of information sources in foreign languages used by Masters of nursing. Among the information sources used in foreign languages the part of references in English is increasing rapidly, whereas the part of Russian references used is decreasing.

The study does not highlight all aspects of forming the infosphere of nursing as a research speciality. The further aspect for studying relates to the analysis of the quantity and quality of intellectual property objects created by the Masters that enables to formulate scientometric criteria for assessing the significance of scientific research of the Masters, thus revealing their ability not only to create the objects of intellectual property, but also to present these objects to the international scientific community by means of scientometric web-network, to promote them on the market of intellectual property.

REFERENCES (TRANSLATED & TRANSLITERATED)

1. Vozniuk, O.V. (2002). Terminolohiia skladnykh informatsiinykh system [Terminology of complex information systems]. Tezy dopovidei XIII viiskovo-naukovoi konferentsii ZhVIRE. Ch. 3. / za red. O.V. Vozniuka. Zhytomyr: ZhVIRE [in Ukrainian].

2. Svyrydiuk, V.Z., Svyrydiuk, V.V. (2018). Naukovi skladova vyshchoi medsestrynskoi osvity ta yii otsinka za naukometrychnymy kryteriiamy [Scientific component of higher nursing education and its estimation according to scientometric criteria]. Vyshcha osvita v medsestrynstvi: problemy i perspektyvy - Higer education in nursing: problems and prospects: materialy nauk. prak. konf. z mizhnarodnoiu uchastiu, Zhytomyr 25-26 zhovtnia 2018 r. / za red V.I. Shatyla. Zhytomyr: Polissia, 172-181 [in Ukrainian].

3. Albert, R., & Barabasi, A.-L. (2002). Statistical mechanics of complex networks. Rev. Mod. Phys, 74, 47-97 [in English].

4. Bunde, A., & Havlin, S., ed. (1996). Fractals and Disordered Systems. 2nd edition. Springer-Verlag, Heidelberg [in English].

5. De Solla Price, D.J. (1967). A guide to graduate study and research in the history of science and medicine. Isis; an international review devoted to the history of science and its cultural influences, 3, 385-395. DOI:10.1086/350271 [in English].

6. De Solla Price, D.J. (1970). Smiles at the Unobtrusive. Nature, 226, 52-49. DOI:10.1038/226985a0 [in English].

7. Garfield, E (2006). The history and meaning of the journal impact factor. Journal of the American Medical Association, 295 (1), 9-30. DOI:10.1001/jama.295.1.90 [in English].

8. Song, C., Havlin, S. & Makse, H.A. (2005). Self-similarity of Complex Networks. Nature, 433, 7024, 392-395. DOI: 10.1038/nature03248 [in English].

9. Voznyuk, Q.V., & Svyrydyuk, V.V. (2019). Efficiency estimation of scientific research conducted by masters' of nursing by means of modern scientometric technologies. Zhytomyr Ivan Franko State University Journal. Pedagogical Sciences, 2 (97). DOI: 10.35433/pedagogy.2(97).2019.89-102 [in English].

10. Voznyuk, A., & Zdanevych, L. (2019). Application of System and Synergetic Paradigm of Management of Social-Economic, Educational Processes in Ukraine. Pedagogical Discourse, 26, 19-26. DOI: 10.31475/ped.dys.2019.26.03 [in English].

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