Age Dependence of the Menstrual Cycle Correlation Dimension

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References

[1] H. G. Burger, G. E. Hale, L. Dennerstein, and D. M. Robertson, “Cycle and Hormone Changes during the Perimenopause: The Key Role of Ovarian Function,” Menopause, Vol. 15, No. 4, 2008, pp. 603-612.
doi:10.1097/gme.0b013e318174ea4d

[2] P. S. Derry and G. N. Derry, “Menstruation, Perimenopause, and Chaos Theory,” Perspectives in Biology and Medicine, Vol. 55, No. 1, 2012, pp. 26-42.
doi:10.1353/pbm.2012.0003

[3] A. Treloar, R. Boynton, B. Behn, and B. Brown, “Variation of the Human Menstrual Cycle through Reproductive Life,” International Journal of Fertility, Vol. 12, No. 1, 1967, pp. 77-126.

[4] L. D. Lisabeth, S. D. Harlow, B. Gillespie, X. Lin. and M. Sowers, “Staging Reproductive Aging: a Comparison of Proposed Bleeding Criteria for the Menopausal Transition,” Menopause, Vol. 11, No. 2, 2004, pp. 186-197.
doi:10.1097/01.GME.0000082146.01218.86

[5] R. J. Ferrell and M. Sowers, “Longitudinal, Epidemiologic Studies of Female Reproductive Aging,” Annals of the New York Academy of Sciences, Vol. 1204, No. 1, 2010, pp. 188-197.
doi:10.1111/j.1749-6632.2010.05525.x

[6] S. D. Harlow and P. Paramsothy, “Menstruation and the Menopausal Transition,” Obstetrics & Gynecology Clinics of North America, Vol. 38, No. 3, 2011, pp. 595-607.
doi:10.1016/j.ogc.2011.05.010

[7] G. N. Derry and P. S. Derry, “Characterization of Chaotic Dynamics in the Human Menstrual Cycle,” Nonlinear Biomedical Physics, Vol. 4, No. 1, 2010, Article # 5.
doi:10.1186/1753-4631-4-5

[8] J. B. Bassingthwaighte, L. S. Liebovitch, and B. J. West, “Fractal Physiology,” Oxford University Press, Oxford, 1994.

[9] K. Prank, H. Harms, G. Brabant, R. Hesch, M. Dammig, and F. Mitschke, “Nonlinear Dynamics in Pulsatile Secretion of Parathyroid Hormone in Normal Human Subjects,” Chaos, Vol. 5, No. 1, 1995, pp. 76-81.
doi:10.1063/1.166089

[10] T. Noguchi, N. Yamada, M. Sadamatsu, and N. Kato, “Evaluation of Self-similar Features in Time Series of Serum Growth Hormone and Prolactin Levels by Fractal Analysis: Effects of Delayed Sleep and Complexity of Diurnal Variation,” Journal of Biomedical Science, Vol. 5, No. 3, 1998, pp. 221-225. doi:10.1007/BF02253472

[11] I. Ilias, A. N. Vgontzas, A. Provata, and G. Mastorakos, “Complexity and Non-linear Description of Diurnal Cortisol and Growth Hormone Secretory Patterns Before and After Sleep Deprivation,” Endocrine Regulations, Vol. 36, No. 2, 2002, pp. 63-72.

[12] P. Mansfield and S. Bracken, “Tremin: A History of the World’s Oldest Ongoing Study of Menstruation and Women’s Health,” East Rim Publishers, Lemont, 2003.

[13] R. Castro and T. D. Sauer, “Forecasting and Dimension Calculations from Event Timing Data,” Nonlinear Phenomena in Complex Systems, Vol. 2, No. 3, 1999, pp. 42-51.

[14] F. Takens, “On the Numerical Determination of the Dimension of an Attractor,” In: B. Braaksma, H. Braer, and F. Takens, Eds., Dynamical Systems and Bifurcations, Springer-Verlag, Berlin, 1985, pp. 99-106.
doi:10.1007/BFb0075637

[15] P. Grassberger and I. Procaccia, “Characterization of Strange Attractors,” Physical Review Letters, Vol. 50, No. 5, 1983, pp. 346-349. doi:10.1103/PhysRevLett.50.346

[16] K. Judd, “An Improved Estimator of Dimension and Some Comments on Providing Confidence Intervals,” Physica D, Vol. 56, No. 2-3, 1992, 216-228.
doi:10.1016/0167-2789(92)90025-I

[17] K. Judd, “Estimating Dimension From Small Samples,” Physica D, Vol. 71, No. 4, 1994, pp. 421-429.
doi:10.1016/0167-2789(94)90008-6

[18] L. H. Clark, P. M. Schlosser, and J. F. Selgrade, “Multiple Stable Periodic Solutions in a Model for Hormonal Control of the Menstrual Cycle,” Bulletin of Mathematical Biology, Vol. 65, No. 1, 2003, pp. 157-173.
doi:10.1006/bulm.2002.0326

[19] I. Reinecke and P. Deuflhard, “A Complex Mathematical Model of the Human Menstrual Cycle,” Journal of Theoretical Biology, Vol. 247, No. 2, 2007, pp. 303-330.
doi:10.1016/j.jtbi.2007.03.011

[20] R. J. Bogumil, M. Ferin, J. Rootenberg, L. Speroff, and R. L. Vande Wiele, “Mathematical Studies of the Human Menstrual Cycle. I. Formulation of a Mathematical Model,” Journal of Clinical Endocrinology & Metabolism, Vol. 35, No. 1, 1972, pp. 126-142.
doi:10.1210/jcem-35-1-126