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Mathematical models of growth have been developed a long period of time. Estimating the lag time in the growth process is a practically important problem. In this note we provide estimates for the one–sided Hausdorff approximation () of the shifted step–function by sigmoidal function arising from Box–Cox transformation. We present a software module (intellectual property) within the programming environment of CAS Mathematica for analysis of growth curves. Numerical examples, illustrating our results are given, too.
[1] O. Garcia, Unifying sigmoid univariate growth equations, Forest Biometry, Modelling and Information Sciences 1 (2005) 63–68
[2] O. Garcia, Visualization of a general family of growth functions and probability distributions - The Growth–curve Explorer, Environmental Modelling and Software 23 (2008) 1474–1475
[3] G. Box, D. Cox, An analysis of transformations, Journal of the Royal Statistical Society, B 26 (1964) 211–252
[4] G. Seber, C. Wild, Nonlinear Regression, Wiley–Interscience, New York (2003)
[5] S. Shoffner, S. Schnell, Estimation of the lag time in a subsequent monomer addition model for fibrill elongation, bioRxiv The preprint server for biology, (2015) 1–8, doi:10.1101/034900
[6] P. Arosio, T. P. J. Knowles, S. Linse, On the lag phase in amyloid fibril formation, Physical Chemistry Chemical Physics 17 (2015) 7606–7618, doi:10.1039/C4CP05563B
[7] R. Anguelov, S. Markov, Hausdorff Continuous Interval Functions and Approximations, In: M. Nehmeier et al. (Eds), Scientific Computing, Computer Arithmetic, and Validated Numerics, 16th International Symposium, Springer, SCAN 2014, LNCS 9553 (2016) 3–13, doi:10.1007/978-3-319-31769-4
[8] N. Kyurkchiev, A. Andreev, Approximation and antenna and filter synthesis: Some moduli in programming environment Mathematica, Saarbrucken, LAP LAMBERT Academic Publishing (2014), ISBN 978–3–659–53322–8.
[9] F. Hausdorff, Set Theory (2 ed.) (Chelsea Publ., New York, (1962 [1957]) (Republished by AMS-Chelsea 2005), ISBN: 978–0–821–83835–8.
[10] B. Sendov, Hausdorff Approximations (Kluwer, Boston, 1990), doi:10.1007/978-94-009-0673-0
[11] N. Kyurkchiev, A note on the new geometric representation for the parameters in the fibril elongation process, Compt. rend. Acad. bulg. Sci. (2016) (accepted).
[12] N. Kyurkchiev, On the Approximation of the step function by some cumulative distribution functions, Compt. rend. Acad. bulg. Sci. 68(12) (2015) 1475–1482.
[13] N. Kyurkchiev, S. Markov, On the Hausdorff distance between the Heaviside step function and Verhulst logistic function, J. Math. Chem. 54(1) (2016) 109–119, doi:10.1007/S10910-015-0552-0
[14] N. Kyurkchiev, S. Markov, Sigmoidal functions: some computational and modelling aspects, Biomath Communications 1(2) (2014) 30–48, doi:10.11145/j.bmc.2015.03.081
[15] A. Iliev, N. Kyurkchiev, S. Markov, On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions, BIOMATH 4(2) (2015) 1510101, doi:10.11145/j.biomath.2015.10.101
[16] A. Iliev, N. Kyurkchiev, S. Markov, On the Approximation of the step function by some sigmoid functions, Mathematics and Computers in Simulation (2015), doi:10.1016/j.matcom.2015.11.005
[17] N. Kyurkchiev, S. Markov, On the approximation of the generalized cut function of degree by smooth sigmoid functions, Serdica J. Computing 9(1) (2015) 101–112.
[18] N. Kyurkchiev, S. Markov, Sigmoid functions: Some Approximation and Modelling Aspects, Saarbrucken, LAP LAMBERT Academic Publishing (2015), ISBN 978–3–659–76045–7.
[19] V. Kyurkchiev, N. Kyurkchiev, On the Approximation of the Step function by Raised-Cosine and Laplace Cumulative Distribution Functions, European International Journal of Science and Technology 4(9) (2016) 75–84.
[20] N. Kyurkchiev, S. Markov, A. Iliev, A note on the Schnute growth model, International Journal of Engineering Research and Development 12 (6) (2016) 47–54.
[21] N. Kyurkchiev, A. Iliev, On some growth curve modeling: approximation theory and applications, International Journal of Trends in Research and Development 3 (3) (2016) 466–471.
