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Development of the Semantic Space ‘‘Mathematics’’ by Integrating a Subspace of Its Applied Area

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Abstract

The article focus on problem of developing a semantic library by adding a new applied scientific field. The addition to the main content of the library is built using publications of a journal on applied issues of composite materials. The description of the original subject area is expanded. Universal Decimal Classification and Mathematics Subject Classification articles are detailed by corresponding to the local subject area. At the same time, the tasks of adding terms to the thesaurus, building a reference corpus of the applied subject area of mathematics, and creating a custom interface are solved. Formulas and equations of the local subject area are semantically linked to the main content of the library. The main advantage of using semantic libraries for this kind of tasks is to enrich the existing knowledge base of the library and identify relationships in the data. To study these problems, it is necessary to interact with subject matter experts and use modern tools and methods for natural language processing, machine learning, and approaches to knowledge representation. Representation of knowledge in the form of ontologies and thesauri connects the definitions of key concepts of the subject area not only within the same scientific school, but also allows experts and users to ‘‘communicate’’ in the same language. As a global thesaurus of the subject area, terminologically delineating its boundaries, the data of the Mathematical Encyclopedia, a Soviet encyclopedic edition integrated into the library, are used. Integration of data within the library allows expanding the description of subject areas related to the applications of mathematics in interdisciplinary research and technology. On the example of one of the applied sections of problems of mathematical physics, the procedure is shown for including arrays of publications of a specialized journal into the ontology of a semantic library. The ontology is based on available data sources, library content, and specific dictionaries and thesauri. The proposed approach will allow using the content of the semantic library ‘‘Mathematics’’ for scientific research, minimizing the process of searching for information in the local subject area, without losing more general results contained outside this area.

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Notes

  1. https://udcsummary.info/php/index.php?lang=ru&pr=Y

  2. https://zbmath.org/classification/

  3. http://minidml.mathdoc.fr/

  4. http://www.bdim.eu/

  5. http://www.cedram.org/,  http://portail.mathdoc.fr/PMO/,  https://hal.archives-ouvertes.fr/, http://www.numdam.org/, https://tel.archives-ouvertes.fr/

  6. https://dml.cz/

  7. https://www.digizeitschriften.de/

  8. https://projecteuclid.org/, https://arxiv.org/

  9. http://pldml.icm.edu.pl/

  10. https://ems.press/journals/pm

  11. https://www.emis.de/

  12. https://mathshistory.st-andrews.ac.uk/

  13. http://mathdiss.mathguide.de/

  14. http://www.prometeus.nsc.ru/sciguide/

  15. https://dlmf.nist.gov/

  16. https://zbmath.org/

  17. https://www.researchgate.net/

  18. http://www.wolfram.com/

  19. http://www.mathnet.ru/

  20. http://eqworld.ipmnet.ru/indexr.htm

  21. http://ontomathpro.org/ontology/

  22. https://encyclopediaofmath.org/

  23. http://libmeta.ru/

  24. https://mkmk.ras.ru/en/

  25. https://grnti.ru/

REFERENCES

  1. J. Blechschmidt and O. G. Ernst, ‘‘Three ways to solve partial differential equations with neural networks. A review,’’ GAMM-Mitteilungen 44, e202100,006 (2021). https://doi.org/10.1002/gamm.202100006

  2. S. Cuomo et al., ‘‘Scientific machine learning through physics-informed neural networks: Where we are and what’s next,’’ J. Sci. Comput. 92 (3), 88 (2022). https://doi.org/10.1007/s10915-022-01939-z

    Article  MathSciNet  MATH  Google Scholar 

  3. N. F. Noy, ‘‘Semantic integration: A survey of ontology-based approaches,’’ ACM SIGMOD Record 33 (4), 65–70 (2004).

    Article  Google Scholar 

  4. C. Klaussner and D. Zhekova, ‘‘Lexico-syntactic patterns for automatic ontology building,’’ in Proceedings of the 2nd Student Research Workshop associated with RANLP (2011), pp. 109–114.

  5. K. Hornik, M. Stinchcombe, and H. White, ‘‘Multilayer feedforward networks are universal approximators,’’ Neural Networks 2, 359–366 (1989).

    Article  MATH  Google Scholar 

  6. T. Bouche, ‘‘Digital mathematics libraries: The good, the bad, the ugly,’’ Math. Comput. Sci. 3, 227–241 (2010). https://doi.org/10.1007/s11786-010-0029-2

    Article  MATH  Google Scholar 

  7. N. P. Tuchkova and O. M. Ataeva, ‘‘Approaches to knowledge extraction in scientific subject domains,’’ Inform. Math. Technol. Sci. Manage. 2 (18), 5–18 (2020). http://doi.org/10.38028/ESI.2020.18.2.00

    Article  Google Scholar 

  8. P. D. F. Ion and S. M. Watt, ‘‘The global digital mathematics library and the international mathematical knowledge trust,’’ Lect. Notes Comput. Sci. 10383, 1 (2017). https://doi.org/10.1007/978-3-319-62075-6_5

    Article  MATH  Google Scholar 

  9. Zentralblatt MATH. https://zbmath.org/about/, https://zbmath.org/?q=review/. Accessed 2022.

  10. K. Hulek and O. Teschke, ‘‘The transition of zbMATH towards an open information platform for mathematics,’’ EMS Newsl. 116, 44–47 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Elizarov, A. Kirillovich, E. Lipachev, and O. Nevzorova, ‘‘Digital Ecosystem OntoMath: Mathematical Knowledge Analytics and Management,’’ Commun. Computer Inform. Sci. 706, 33–46 (2017). https://doi.org/10.1007/978-3-319-57135-5_3.

    Article  Google Scholar 

  12. I. M. Vinogradov, Mathematical Encyclopedia, Ed. by I. M. Vinogradov (Sov. Encyclopedia, Moscow, 1982), Vols. 1–5 [in Russian].

    MATH  Google Scholar 

  13. O. Ataeva, V. Serebryakov, and E. Sinelnikova, ‘‘Thesaurus and ontology building for semantic library based on mathematical encyclopedia,’’ in Proceedings of the DAMDID/RCDL 2019, Kazan, Russia, October 15–18, 2019, CEUR Workshop Proc. 2523, 148–157 (2019).

    Google Scholar 

  14. F. Muller and O. Teschke, ‘‘Will all mathematics be on the arXiv (soon)?,’’ EMS Newslett. 99, 55–57 (2016).

    MATH  Google Scholar 

  15. M. M. K. Hlava, ‘‘The taxobook: History, theories, and concepts of knowledge organization, Part 1 of a 3-part series,’’ Synth. Lect. Inform. Concepts, Retrieval, Services 6 (3), 1–80 (2014).

    Google Scholar 

  16. A. M. Elizarov, A. V. Kirillovich, E. K. Lipachev, O. A. Nevzorova, V. D. Solovyev, and N. G. Zhiltsov, ‘‘Mathematical knowledge representation: Semantic models and formalisms,’’ Lobachevskii J. Math. 35, 348–354 (2014). https://doi.org/10.1134/S1995080214040143

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Kohlhase, ‘‘Mathematical knowledge management: Transcending the one-brain barrier with theory graphs,’’ EMS Newslett., 22–27 (2014).

  18. M. Bravo, L. F. Hoyos Reyes, and J. A. Reyes Ortiz, ‘‘Methodology for ontology design and construction,’’ Contadurra Administr. 64 (4), 1–24 (2019).

    Google Scholar 

  19. O. M. Ataeva and V. A. Serebryakov, ‘‘Ontology of digital semantic library LibMeta,’’ Inform. Primen. 12, 2–10 (2018). https://doi.org/10.14357/19922264180101

    Article  Google Scholar 

  20. V. Serebryakov and O. Ataeva, ‘‘Ontology based approach to modeling of the subject domain ’mathematics’ in the digital library,’’ Lobachevskii J. Math. 42, 1920–1934 (2021). https://doi.org/10.1134/S199508022108028X

    Article  MATH  Google Scholar 

  21. A. M. Elizarov, A. B. Zhizhchenko, N. G. Zhiltsov, A. V. Kirillovich, and E. K. Lipachev, ‘‘Mathematical knowledge ontologies and recommender systems for collections of documents in physics and mathematics,’’ Dokl. Math. 93, 231–233 (2016). https://doi.org/10.1134/S1064562416020174

    Article  MathSciNet  MATH  Google Scholar 

  22. S. Grimm et al., ‘‘Ontologies and the semantic web,’’ in Handbook of Semantic Web Technologies, Ed. by J. Domingue, D. Fensel, and J. A. Hendler (Springer, Berlin, 2011).

    Google Scholar 

  23. O. M. Ataeva, V. A. Serebryakov, and N. P. Tuchkova, ‘‘Mathematical physics branches: Identifying mixed type equations,’’ Lobachevskii J. Math. 40, 876–886 (2019). https://doi.org/10.1134/S1995080219070047

    Article  MATH  Google Scholar 

  24. M. M. K. Hlava, ‘‘The Taxobook: Principles and practices of building taxonomies, part 2 of a 3-part series,’’ Synth. Lect. Inform. Concepts, Retriev. Services 6 (4), 1–164 (2014).

    Google Scholar 

  25. M. M. K. Hlava, ‘‘The Taxobook: Applications, implementation, and integration in search: Part 3 of a 3-part series,’’ Synth. Lect. Inform. Concepts, Retriev. Services 6 (4), 1–156 (2014).

    Google Scholar 

  26. O. M. Ataeva, V. A. Serebryakov, and N. P. Tuchkova, ‘‘Creating the applied subject area ontology by means of the content of the digital semantic library,’’ Lobachevskii J. Math. 43, 1557–1566 (2022). https://doi.org/10.1134/S1995080222100043

    Article  MATH  Google Scholar 

  27. L. Zhao and R. Ichise, ‘‘Ontology integration for linked data,’’ J. Data Semant. 3, 237–254 (2014).

    Article  Google Scholar 

  28. A. M. Elizarov, E. K. Lipachev, and M. A. Malahal’cev, Principles of MathML Representation of Mathematical Texts in Internet (Kazan. Mat. Ob-vo, Kazan, 2008) [in Russian].

    Google Scholar 

  29. M. Kohlhase et al., ‘‘Mathematical formula search,’’ EMS Newsl. 89, 56–58 (2013).

    MATH  Google Scholar 

  30. B. R. Miller and A. Youssef, ‘‘Technical aspects of the digital library of mathematical functions,’’ Ann. Math. Artif. Intell. 38, 121–136 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  31. C. D. Manning, P. Raghavan, and H. Schütze, Introduction to Information Retrieval (Cambridge Univ. Press, Cambridge, 2008).

    Book  MATH  Google Scholar 

  32. D. Allemang and J. Hendler, Semantic Web for the Working Ontologist: Effective Modeling in RDFS and OWL (Elsevier, Amsterdam, 2011).

    Google Scholar 

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Funding

This work was supported by budget topics of the Ministry of Science and Higher Education of the Russian Federation ‘‘Mathematical methods for data analysis and forecasting.’’

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Correspondence to O. M. Ataeva, V. A. Serebryakov or N. P. Tuchkova.

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(Submitted by A. M. Elizarov)

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Ataeva, O.M., Serebryakov, V.A. & Tuchkova, N.P. Development of the Semantic Space ‘‘Mathematics’’ by Integrating a Subspace of Its Applied Area. Lobachevskii J Math 43, 3435–3446 (2022). https://doi.org/10.1134/S1995080222150069

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