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Detection of Monogenic Disorders Using Fuzzy Fractal Analysis with Grids and Triangular Dimension

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Abstract

Single abnormal gene structure of disorders, specifically the alpha (α) and beta (β) thalassemia recessive disorders are focused. From the NCBI website, the preferred DNA sequencing is downloaded. The objective is to study the structure of Single Abnormal Gene using modified Box counting principle and FFD-Fuzzy Fractal Dimension analysis. Initially the fractal dimension method is used and analyzed single abnormal gene structure with the help of box counting method where the grids are segmented into triangles. Further the analysis is enhanced through grid and triangular method of improved box counting methods named as Ruby Triangular dimension which is the novelty of the research. Comparison of Grid Dimension with Triangular Dimension based fractal and fuzzy fractal dimension in the severity of disease from its secondary structure of the disorder related genes structures are performed. Further the complexity of the Single Abnormal Gene structure evaluated to generate a unique Attractor for the prediction of the α-thalassemia and β-thalassemia disorder in earlier diagnosis, refer as bifurcation theory. The results shows that the triangular Ruby Dimension based improved box counting method facilitate quick with more exactitude. In grid method the size of the image should be 2n pixels and shrink to at most 2048 pixels, whereas the triangular pixels may be reduced to 23 times than grid method. Hence, this novel Fuzzy Fractal Ruby Triangular Dimension method shows better results and can be applied for image of higher dimensions with the same procedure.

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References

  1. Ataga, K.I., Cappellini, M.D., Rachmilewitz, E.A.: β-Thalassaemia and sickle cell anaemia as paradigms of hypercoagulability. Br. J. Haematol. 139(1), 3–13 (2007)

    Article  Google Scholar 

  2. Serindere, G., Belgin, C.: Evaluation of the effects of hemoglobinopathies on the mandible with fractal dimension analysis. Niger. J. Clin. Pract. 22(10), 1435–1440 (2019)

    Article  MATH  Google Scholar 

  3. Baird, D.C., Batten, S.H., Sparks, S.K.: Alpha-and beta-thalassemia: rapid evidence review. Am. Fam. Physician 105(3), 272–280 (2022)

    Google Scholar 

  4. Deschavanne, P.J., Giron, A., Vilain, J., et al.: Genomic signature: characterization and classification of species assessed by chaos game representation of sequences. Mol. Biol. Evol. 16, 1391–1399 (1999)

    Article  MATH  Google Scholar 

  5. Fiser, A., Tusnady, G.E., Simon, I.: Chaos game representation of protein structures. J. Mol. Graph. 12(302–304), 295 (1994)

    MATH  Google Scholar 

  6. Zhu, Y., Shen, N., Wang, X., Xiao, J., Lu, Y.: Alpha and beta-thalassemia mutations in Hubei area of China. BMC Med. Genet. 21, 1–5 (2020)

    Article  MATH  Google Scholar 

  7. Milošević, N.: The morphology of the brain neurons: box-counting method in quantitative analysis of 2D image. In: The fractal geometry of the brain, pp. 109–126. Springer, New York (2016)

    Chapter  MATH  Google Scholar 

  8. Yagmur, B., Tercanli-Alkis, H., Tayfun-Kupesiz, F., Karayilmaz, H., Kupesiz, O.A.: Alterations of panoramic radiomorphometric indices in children and adolescents with beta-thalassemia major: a fractal analysis study. Medicina Oral Patologia Oral y Cirugia Bucal 27(1), e10 (2022)

    Article  Google Scholar 

  9. Rubini, S., Jeyabharathi, Latha, Seethalakshmi: Estimation of fractal dimension in the analysis of single abnormal gene structure. TAGA J. Gr. Technol. 14(70), 775–781 (2018)

    MATH  Google Scholar 

  10. Vijian, D., Ab Rahman, W.S.W., Ponnuraj, K.T., Zulkafli, Z., Noor, N.H.M.: Molecular detection of alpha thalassemia: a review of prevalent techniques. Medeniyet Med. J. 36(3), 257 (2021)

    Google Scholar 

  11. Wirasati, I., Rustam, Z., Aurelia, J.E., Hartini, S., Saragih, G.S.: Comparison some of kernel functions with support vector machines classifier for thalassemia dataset. IAES Int. J. Artif. Intell. 10(2), 430 (2021)

    Google Scholar 

  12. Susanto, E., Syarif, A., Muludi, K., Perdani, R., & Wantoro, A.: Implementation of fuzzy-based model for prediction of thalassemia diseases. Paper presented at the Journal of Physics: conference series (2021)

  13. Aszhari, F., Rustam, Z., Subroto, F., & Semendawai, A.: Classification of thalassemia data using random forest algorithm. Paper presented at the Journal of Physics: Conference Series (2020)

  14. Liangpu, Xu., Mao, A., Liu, H., Gui, B., Choy, K.W., Huang, H., Qian, Yu., Zhang, X., Chen, M., Lin, Na., Chen, L., Han, J., Wang, Y., Zhang, M., Li, X., He, D., Lin, Y., Zhang, J., Cram, D.S., Cao, H.: Long-molecule sequencing: a new approach for identification of clinically significant DNA variants in α-thalassemia and β-thalassemia carriers. J. Mol. Diagn. 22(8), 1087–1095 (2020)

    Article  Google Scholar 

  15. Cesur, E., Bayrak, S., Kursun-Çakmak, E.Ş, Arslan, C., Köklü, A., Orhan, K.: Evaluating the effects of functional orthodontic treatment on mandibular osseous structure using fractal dimension analysis of dental panoramic radiographs. Angle Orthod. 90(6), 783–793 (2020)

    Article  Google Scholar 

  16. Elkington, L., Adhikari, P., Pradhan, P.: Fractal dimension analysis to detect the progress of cancer using transmission optical microscopy. Biophysica 2(1), 59–69 (2022)

    Article  MATH  Google Scholar 

  17. Panigrahy, C., Seal, A., Mahato, N.K.: Quantitative texture measurement of gray-scale images: fractal dimension using an improved differential box counting method. Measurement 147, 106859 (2019)

    Article  MATH  Google Scholar 

  18. Cimen, M.E., Boyraz, O.F., Yildiz, M.Z., Boz, A.F.: A new dorsal hand vein authentication system based on fractal dimension box counting method. Optik 226, 165438 (2021)

    Article  MATH  Google Scholar 

  19. Wu, M., Wang, W., Shi, D., Song, Z., Li, M., Luo, Y.: Improved box-counting methods to directly estimate the fractal dimension of a rough surface. Measurement 177, 109303 (2021)

    Article  MATH  Google Scholar 

  20. Yan, J., Sun, Y., Cai, S., Hu, X.: An improved box-counting method to estimate fractal dimension of images. J. Appl. Anal. Comput. 6(4), 1114–1125 (2016)

    MathSciNet  MATH  Google Scholar 

  21. Bisoi, A.K., Mishra, J.: On calculation of fractal dimension of images. Pattern Reconition Lett. 22(6–7), 631–637 (2001)

    Article  MATH  Google Scholar 

  22. Castillo, O., Melin, P.: A hybrid fuzzy-fractal approach for time series analysis and plant monitoring. Int. J. Intell. Syst. 17(8), 751–765 (2002)

    Article  MATH  Google Scholar 

  23. Castillo, O., Melin, P.: Hybrid intelligent systems for time series prediction using neural networks, fuzzy logic, and fractal theory. IEEE Trans. Neural Netw. 13(6), 1395–1408 (2002)

    Article  MATH  Google Scholar 

  24. Lopes, L., Betrouni, N.: Fractal and multifractal analysis: a review. Med. Image Anal. 13(4), 634–649 (2009)

    Article  MATH  Google Scholar 

  25. Melin, P., Castillo, O.: Intelligent control of aircraft dynamic systems with a new hybrid neuro–fuzzy–fractal approach. Inf. Sci. 142(1–4), 161–175 (2002)

    Article  MATH  Google Scholar 

  26. Yang, L., Tang, Y.Y., Lu, Y., Luo, H.: A fractal dimension and wavelet transform based method for protein sequence similarity analysis. IEEE/ACM Trans. Comput. Biol. Bioinf. 12(2), 348–359 (2014)

    Article  MATH  Google Scholar 

  27. Feng, J., Lin, W.-C., & Chen, C.-T.: Fractional box-counting approach to fractal dimension estimation. Paper presented at the proceedings of 13th international conference on Pattern recognition (1996)

  28. Harrar, K., Hamami, L.: The box counting method for evaluate the fractal dimension in radiographic images, 6th WSEAS international conference, Cairo, Egypt (2007)

  29. Mainieri, R.: On the equality of Hausdorff and box counting dimensions. Chaos Interdiscip. J. Nonlinear Sci. 3(2), 119–125 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  30. Skubalska-Rafajłowic, E.: A new method of estimation of the box-counting dimension of multivariate objects using space-filling curves, nonlinear. Analysis 63, e1281–e1287 (2005)

    MATH  Google Scholar 

  31. Chen, W., Chen, X.-x., & Zhou, L.: Box-counting dimension analysis of edge images detected with classical edge detector. Paper presented at the 2010 international conference on measuring technology and mechatronics automation (2010)

  32. Li, J., Qian, Du., Sun, C.: An improved box-counting method for image fractal dimension estimation. Pattern Recogn. 42, 2460–2469 (2009)

    Article  MATH  Google Scholar 

  33. Al-Saidi, N.M., Mohammed, A.J., Ahmed, A.M.: Fuzzy fractal dimension based on escape time algorithm. Appl. Math. Sci. 8(3), 117–129 (2014)

    MathSciNet  MATH  Google Scholar 

  34. Pedrycz, W., Bargiela, A.: Fuzzy fractal dimensions and fuzzy modeling. Inf. Sci. 153, 199–216 (2003)

    Article  MATH  Google Scholar 

  35. Chow, S.-N., Hale, J.K.: Methods of bifurcation theory, vol. 251. Springer Science & Business Media, Berlin (2012)

    MATH  Google Scholar 

  36. Sattinger, D.H.: Group theoretic methods in bifurcation theory, vol. 762. Springer, New York (2006)

    MATH  Google Scholar 

  37. Golubitsky, M., Stewart, I.: Hopf bifurcation in the presence of symmetry. Arch. Ration. Mech. Anal. 87, 107–165 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  38. Shang, X., Xu, X.: Update in the genetics of thalassemia: what clinicians need to know. Best Pract. Res. Clin. Obstet. Gynaecol. 39, 3–15 (2017)

    Article  MATH  Google Scholar 

  39. Farashi, S., Harteveld, C.L.: Molecular basis of α-beta thalassemia. Blood Cells Mol. Dis. (2018). https://doi.org/10.1016/j.bcmd.2017.09.004

    Article  Google Scholar 

  40. Sun, Y., Xue, B., Zhang, M., Yen, G.G., Lv, J.: Automatically designing CNN architectures using the genetic algorithm for image classification. IEEE Trans. Cybern. 50(9), 3840–3854 (2020)

    Article  MATH  Google Scholar 

  41. Sarkheil, H., Rahbari, S., Rayegani, B.: Conversion based fuzzy fractal dimension integrating self-similarity and porosity, via DFS and FIS (Mamdani and Sugeno systems). Chaos Solitons Fract. 140, 110183 (2020)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Thiagarajar College of Engineering, Madurai, Tamilnadu, India

    P. K. Sharon Rubini & S. Jeyabharathi

  2. Department of Zoology, The Madura College, Madurai, Tamilnadu, India

    B. Latha

Authors
  1. P. K. Sharon Rubini
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  2. S. Jeyabharathi
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  3. B. Latha
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Sharon Rubini, P.K., Jeyabharathi, S. & Latha, B. Detection of Monogenic Disorders Using Fuzzy Fractal Analysis with Grids and Triangular Dimension. Int. J. Fuzzy Syst. 26, 2209–2223 (2024). https://doi.org/10.1007/s40815-024-01730-2

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  • DOI: https://doi.org/10.1007/s40815-024-01730-2

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