AUTHORS: Radoslav Mavrevski, Metodi Traykov, Ivan Trenchev, Miglena Trencheva
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ABSTRACT: Mathematical models are commonly used in biological sciences. To understand complex biological systems such as cells, tissues, or others, it is not enough to identify and characterize only individual molecules in the system. It also is necessary to obtain a thorough understanding of the interaction between molecules and different pathways. Computational models help investigators to analyze systems, develop hypotheses to guide the design of new experimental tests. Known are mathematical methods referring to different categories of biological processes. Now, modeling approaches are essential for biologists, enabling them to analyze complex physiological processes. The aim of this study is to presents a step-by-step applying non-linear regression analysis for fast and effective data analysis in the biology. To achieve this aim is used non-linear regression analysis method by GraphPad Prism software and the modeling of specific experimental data taken from available literature. Nonlinear regression is an extremely useful tool in analyzing data, but choosing a model is a scientific decision based on biology, chemistry or physiology and etc. and not be based solely on the shape of the graph.
KEYWORDS: Mathematical models, fitting, model selection criteria, biological data
REFERENCES:
[1] H. Acquah, Comparison of Akaike information criterion (AIC) and Bayesian information criterion (BIC) in selection of an asymmetric price relationship, J. Dev. Agric. Econ., 2, 2010, 1-6.
[2] SJ. Ahn, Geometric Fitting of Parametric Curves and Surfaces, JIPS 4, 2008, 153-158.
[3] H. Akaike, A new look at the statistical model identification, IEEE Trans. Autom. Control, 19, 1974, 716–772.
[4] P. Burnham and D. Anderson, Model Selection and Multimodel Inference 2 ed., SpringerVerlag, New York, 2002.
[5] ID. Coope, Circle fitting by linear and nonlinear least squares, J. Optim. Theory. Appl. 76, 1993, 381-388.
[6] S. Konishi, G. Kitagawa, Information criteria and statistical modeling, New York: Springer Science and Business media, 2008.
[7] R. Mavrevski, Selection and comparison of regression models: estimation of torque-angle relationships, C. R. Acad. Bulg. Sci. 67, 2014, 1345-1354.
[8] C.M Hurvich, C. Tsai, Regression and time series model selection in small samples, Biometrika, 76, 1989, 297-307.
[9] C.M. Hurvich, J.S. Simonoff, C-L. Tsa, Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion, Journal of the Royal Statistical Society, 60, 1998, 271-293.
[10] K. G. Ashton, R. L. Burke, J. N. Layne, Geographic variation in body and clutch size of gopher tortoises, Copcia, 49, 2007, 355-363.
[11] N. Stoeva. The Right of the Personal Data Protection - Nature and Guarantees. Proceedings of the International Scientific Seminar “Intellectual Property in Bulgaria - Perception, Awareness and Behavior” Trencheva, T. (compl.), Za bukvite-O Pismeneh, Sofia, 2018, pp. 89-104.