THE PRACTICAL INTERGRATION OF LINEAR ALGEBRA IN GENETICS, CUBIC SPLINE INTERPOLATION, ELECTRIC CIRCUITS AND TRAFFIC FLOW

Abstract

A fundamental mathematical field with many applications in science and engineering is linear algebra. This paper investigates the various applications of linear algebra in the fields of traffic flow analysis, electric circuits, cubic spline interpolation, and genetics. This research delves into individual applications while emphasizing cross-disciplinary insights, fostering innovative solutions through the convergence of genetics, cubic spline interpolation, circuits, and traffic flow analysis. The research employs specific methodologies in each application area to demonstrate the practical integration of linear algebra in genetics, cubic spline interpolation, electric circuits, and traffic flow analysis. In genetics, linear algebra techniques are utilized to represent genetic data using matrices, analyze genotype distributions across generations, and identify genotype-phenotype associations. For cubic spline interpolation, linear algebra is employed to construct smooth interpolating curves, involving the derivation of equations for spline functions and the determination of coefficients using boundary conditions and continuity requirements. In electric circuit analysis, linear algebra is crucial for modeling circuit elements, formulating systems of linear equations based on Kirchhoff's laws, and solving for voltage and current distributions in circuits. In traffic flow analysis, linear algebra techniques are used to represent traffic movement in networks, formulate systems of linear equations representing traffic flow dynamics, and solve for traffic flow solutions to optimize transportation networks. By addressing contemporary challenges, emerging research frontiers, and future trajectories at the intersection of linear algebra and diverse domains, this study underscores the profound impact of mathematical tools in advancing understanding and resolving complex real-world problems across multiple fields.

Keywords

• Linear algebra
• Genetics
• Cubic spline
• Traffic flow
• Electric circuits

References

1. H. A. Abdulmohsin, H. B. Abdul Wahab, and A. M. Jaber Abdul Hossen, "A Novel Classification Method with Cubic Spline Interpolation", Intelligent Automation & Soft Computing, vol. 31, no. 1, pp. 780-863, 2022.
2. K. M. M. Aburaas, "Matrices and their Applications in Electrical Circuits", African Journal of Advanced Pure and Applied Sciences (AJAPAS), pp. 364- 370, 2023.
3. S. Andrilli and D. Hecker, Elementary linear algebra. Academic Press, Elsevier, Netherlands, 2022.
4. M. Ashraf, V. De Filippis, and M. A. Siddeeque, Advanced Linear Algebra with Applications. Springer Nature Singapore, Gateway East, Singapore, 2022.
5. M. L. De Klerk and A. K. Saha, "A review of the methods used to model traffic flow in a substation communication network", IEEE Access, vol. 8, pp. 204545-204562, 2020.
6. W. Hao, D. Rui, L. Song, Y. Ruixiang, Z. Jinhai, and C. Juan, “Data processing method of noise logging based on cubic spline interpolation”, Applied Mathematics and Nonlinear Sciences, vol. 6, no. 1, pp. 93–102, 2021.
7. A. D. Madhuri, P. V. N. Sagar, P. G. Raju, and A. A. Tanuja, "A Study on Applications of Linear Algebra", Mathematical Statistician and Engineering Applications, vol. 71, no. 4, pp. 2463-2473, 2022.
8. C. D. Meyer and I. Stewart, “Matrix analysis and Applied linear algebra”, Society for Industrial and Applied Mathematics (SIAM), 2023.

9. M. M. Moghaddama, "11th Seminar on Linear Algebra and its Applications", arXiv preprint arXiv:2206.05494, 2022.
10. T. T. Moh, "Linear Algebra and its Applications", Monatshefte für Mathematik, vol. 199, pp. 929-931, 2022.