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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 3

An Application of the Bipolar Metric Space Structure for Missing Data Imputation in Ligand–Target Interactions

Utku Gürdal(BURDUR MEHMET AKİF ERSOY ÜNİVERSİTESİ)0000-0003-2887-2188
Selim Çetin(BURDUR MEHMET AKİF ERSOY ÜNİVERSİTESİ)0000-0002-9017-1465
Reha Yapalı(MUŞ ALPARSLAN ÜNİVERSİTESİ)0000-0003-0665-9087
Pages
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Publication Date
2026-10-13
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

By emphasizing that the proposed method can be tested under various topics in both the natural sciences and the humanities, the study thus presents a pioneering example in this direction.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the bipolar metric space structure is tested on a real dataset for the first time.
📊
Key Findings & Data:In this context, ligand–target interaction scores are examined and transformed into a form compatible with the bipolar metric function, an incomplete-data scenario is evaluated, and in addition, the closest pairs of the same type are identified and the resulting findings are analyzed.
💡
Conclusion & Impact:By emphasizing that the proposed method can be tested under various topics in both the natural sciences and the humanities, the study thus presents a pioneering example in this direction.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:bipolar metric space · missing data imputation · ligand target interaction

Abstract

In this study, the bipolar metric space structure is tested on a real dataset for the first time. In this context, ligand–target interaction scores are examined and transformed into a form compatible with the bipolar metric function, an incomplete-data scenario is evaluated, and in addition, the closest pairs of the same type are identified and the resulting findings are analyzed. The model is also applied to provide theoretical estimations for some missing entries in the dataset. By emphasizing that the proposed method can be tested under various topics in both the natural sciences and the humanities, the study thus presents a pioneering example in this direction.

🔖

Cite This Article

Gürdal, U., Çetin, S., Yapalı, R. (2026). An Application of the Bipolar Metric Space Structure for Missing Data Imputation in Ligand–Target Interactions. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 3. https://doi.org/10.47000/tjmcs.1834256

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References (45)

  1. Åqvist, J., Luzhkov, V.B., Brandsdal, B.O., Ligand binding affinities from MD simulations, Accounts of Chemical Research, 35(6)(2002), 358–365.
  2. Atchley, W., Wingenbach, G., Akers, C., Comparison of course completion and student performance through online and traditional courses, International Review of Research in Open and Distributed Learning, 14(4)(2013), 104–116,
  3. Batista-Foguet, J.M., Fortiana, J., Currie, C., Villalb´ı, J.R., Socio-economic indexes in surveys for comparisons between countries, Social Indicators Research, 67(3)(2004), 315–332.
  4. Bell, R.P., The rates of simple acid–base reactions, Quarterly Reviews, Chemical Society, 13(3)(1959), 169–182.
  5. Bhardwaj, R., Existence and uniqueness of solutions of nonlinear integral equations through results in fuzzy bipolar metric spaces, Journal of Nonlinear Modeling and Analysis, 7(2025)(2), 399–413.
  6. Bhavani, C.U., Naresh, P., Rao, B.S., Reddy, G.U., Innovative approaches to (A, B)-contraction and T-coupling fixed points in bipolar parametric metric spaces, Adv. Fixed Point Theory, 15(1)(2025), 16.
  7. Bretz, S.L., Linenberger, K.J., Development of the enzyme–substrate interactions concept inventory, Biochemistry and Molecular Biology Education, 40(4)(2012), 229–233.
  8. Çetin, S., Gürdal, U., Characterization of bipolar ultrametric spaces and fixed point theorems, Hacettepe Journal of Mathematics and Statistics, 52(1)(2023), 185–196.
  9. Copeland, R.A., The dynamics of drug-target interactions: drug-target residence time and its impact on efficacy and safety, Expert Opinion on Drug Discovery, 5(4)(2010), 305–310.
  10. Costello, R., Toshkov, D., Bos, B., Krouwel, A., Congruence between voters and parties: the role of party-level issue salience, European Journal of Political Research, 60(1)(2021), 92–113.
  11. Ghasab, E.L., De la Sen, M., Solving damped harmonic oscillator as a second-order differential equations and Caputo fractional differential equation in bipolar Menger probabilistic b-metric spaces, International Journal of Analysis and Applications, 23(1)(2025), 133.
  12. Grant, P.R., Ecological compatibility of bird species on islands, The American Naturalist, 100(914)(1966), 451–462.
  13. Gupta, V., Anju, A., Thakur, D., Sehgal, I., Existence of fixed points in neutrosophic bipolar fuzzy metric spaces with application, Journal of the Indonesian Mathematical Society, 31(3)(2025), 1601.
  14. Gürdal, U., Mutlu, A., Özkan, K., Fixed point results for α-ψ-contractive mappings in bipolar metric spaces, J. Inequal. Spec. Funct., 11(1)(2020), 64–75.
  15. Gürdal, U., Yapalı, R., Mutlu, A., Generalized Kuratowski closure operators in the bipolar metric setting, Proceedings of International Mathematical Sciences, 6(1)(2024), 1–17.
  16. Hirschenhauser, K., Meichel, Y., Schmalzer, S., Beetz, A.M., Children love their pets: do relationships between children and pets co-vary with taxonomic order, gender, and age?, Anthrozo¨os, 30(3)(2017), 441–456.
  17. Hussaina, N., Alharbib, N., Basendwaha, G., Solving multi-order fractional differential equations using covariant contraction principle, J. Math. Computer Sci., 39(1)(2025), 71–89.
  18. Jeevanandam, U.M., Kathavarayan, D., Raveendran, S.B., Azmi, F., Mlaiki, N., Fixed point theorems on ℵ-extended fuzzy bipolar b-metric spaces, International Journal of Analysis and Applications, 22(1)(2024), 223–223.
  19. Kishore, G.N.V., Rao, B.S., Prasad, D.R., Radenovi´c, S., Multivalued Δ-symmetric covariant results in bipolar metric spaces, Zhurnal Sibirskogo federal’nogo universiteta. Matematika i fizika, 17(5)(2024), 575–585.
  20. Konwar, N., Debnath, P., Fixed-point results of F-contractions in bipolar p-metric spaces, Axioms, 13(11)(2024), 773–773.
  21. Limprayoon, J., Bunpatcharacharoen, P., Mungkala, C., Common interpolative rational type contractions in bipolar metric spaces, Bangmod International Journal of Mathematical and Computational Science, 11(1)(2025), 305–327.
  22. Mani, G., Ramaswamy, R., Gnanaprakasam, A.J., Elsonbaty, A., Abdelnaby, O.A.A., Radenovi´c, S., Application of fixed points in bipolar controlled metric space to solve fractional differential equation, Fractal and Fractional, 7(3)(2023), 242–242.
  23. Mebarki, K., Boudaoui, A., Belhenniche, A., Bota, M.F., Fixed-point theorems for covariant and contravariant multivalued mappings in bipolar b-metric spaces, Mathematics, 13(18)(2025), 2983–2983.
  24. Murthy, P.P., Dhuri, C.P., Patel, U.D., Common fixed point for w-compatible maps in a bipolar metric space, Facta Universitatis, Series: Mathematics and Informatics, 1(1)(2025), 421–438.
  25. Mutlu, A., Gürdal, U., Bipolar metric spaces and some fixed point theorems, Journal of Nonlinear Science and Applications, 9(9)(2016), 1–1.
  26. Mutlu, A., Özkan, K., Gürdal, U., Fixed point theorems for multivalued mappings on bipolar metric spaces, Fixed Point Theory, 21(1)(2020), 271–280.
  27. Mutlu, A., Özkan, K., Gürdal, U., Locally and weakly contractive principle in bipolar metric spaces, TWMS Journal of Applied and Engineering Mathematics, 10(2)(2020), 379–388.
  28. Neri, D., Montigiani, S., Kirkham, P.M., Biophysical methods for the determination of antibody-antigen affinities, Trends in Biotechnology, 14(12)(1996), 465–470.
  29. Olaleru, J.O., Apanpa, K.I., Mogbademu, A.A., Fixed point results of Hardy and Rogers mappings in bipolar metric spaces with application to integral equations, Open Journal of Mathematical Sciences (OMS), 9(1)(2025), 233–244.
  30. Özkan, K., Gürdal, U.,Mutlu, A., Caristi’s and Downing-Kirk’s fixed point theorems on bipolar metric spaces, Fixed Point Theory, 22(2)(2021), 785–785.
  31. Rajitha, V., Reddy, G.U., On some quadruple fixed points of covariant mappings in bipolar metric spaces with applications, Adv. Fixed Point Theory, 14(1)(2024), 34.
  32. Ramaswamy, R., Fixed point theorems on multiplicative cone bipolar metric space and their applications, European Journal of Pure and Applied Mathematics, 18(4)(2025), 1.
  33. Rani, J., Prakasam, A., Fixed points of operators with multiplicative closed graphs on bipolar b-multiplicative metric spaces, Adv. Fixed Point Theory, 14(1)(2024), 57.
  34. Rao, S., Tarani, K.C.N., Murthy, N.V.E.S., Srinuvasa Rao, B., Certain applications of JS-quasi-contraction fixed point theorems in bipolar metric spaces, Adv. Fixed Point Theory, 14(1)(2024), 31.
  35. Sarwar, M., Ali, N., Abodayeh, K., Promsakon, C., Sitthiwirattham, T., Contravariant Reich type F-contraction in F-bipolar metric spaces with application, Results in Nonlinear Analysis, 8(2)(2025), 328–336.
  36. Schumaker, B.L., Apparent brightness of stars and lasers, TDA Progress Report, 1988, 42–93.
  37. Sedghi, S., Sımkha, M., G¨urdal, U., Mutlu, A., Fixed point theorems for contravariant maps in bipolar b-metric spaces with integration application, Proceedings of International Mathematical Sciences, 6(1)(2024), 29–43.
  38. Stanford, G., DeMent, J.D., A method for measuring short-term nutrient absorption by plants: I. Phosphorus, Soil Science Society of America Journal, 21(6)(1957), 612–617.
  39. Taleb, M.M., Borkar, V.C., Fixed point theorems in triple-composed bipolar metric spaces and its application to solving coupled ordinary differential equations, Palestine Journal of Mathematics, 14(1)(2025), 1.
  40. Tang, J., Szwajda, A., Shakyawar, S., Xu, T., Hintsanen, P., Wennerberg, K., Aittokallio, T., Making sense of large-scale kinase inhibitor bioactivity data sets: a comparative and integrative analysis, Journal of Chemical Information and Modeling, 54(3)(2014), 735–743.
  41. Varalakshmi, K., Reddy, G.U., On some applications of P-contraction fixed point theorems in bipolar metric spaces, International Journal of Analysis and Applications, 22(1)(2024), 159.
  42. Wang, A., Zhang, Q., Shuangyao, Z., Xiaonong, L., Zhanglin, P., A review-driven customer preference measurement model for product improvement: sentiment-based importance–performance analysis, Information Systems and eBusiness Management, 18(1)(2020), 61–88.
  43. Wong, K.S., Salleh, Z., Akhadkulov, H., Kuljanov, U.N., Exploring Proinov-type and Banach-type contractions in fuzzy bipolar metric spaces, Journal of Inequalities and Applications, 2025(1)(2025), 94.
  44. Yadav, S., Ughade, M., Shukla, M.K., Fixed-points of interpolative Kannan type contractions in bipolar metric spaces, Adv. Fixed Point Theory, 13(1)(2023), 24.
  45. Younis, M., Mutlu, A., Ahmad, H., C´ iric´ contraction with graphical structure of bipolar metric spaces and related fixed point theorems, Hacettepe Journal of Mathematics and Statistics, 1(1)(2024), 1–19.