Colliding spherical calcium waves in enzymatically isolated rat cardiac myocytes develop new wavefronts propagating perpendicular to the original direction. When investigated by confocal laser scanning microscopy (CLSM), using the fluorescent Ca2+ indicator fluo-3 AM, "cusp"-like structures become visible that are favorably approximated by double parabolae. The time-dependent position of the vertices is used to determine propagation velocity and negative curvature of the wavefront in the region of collision.
View Article and Find Full Text PDFThe median regression function is defined and demonstrated by examples. A lemma with sufficient conditions for continuity and differentiation of the median regression function is proved. Its estimation from a random sample is deduced firstly based on the empirical distribution function and secondly based on a kernel estimation with Gaussian kernels.
View Article and Find Full Text PDFMeasured time series with known basic periodicity may be modelfreely evaluated by procedures of local adjusted approximation. Examples of motility time series recorded in chronobiological experiments in the seasonal course of a year demonstrate aspects of choosing values of the smoothing parameter and the resulting effects for the quantitative description of the measured variations as well as for their interpretation.
View Article and Find Full Text PDFFor the discrete and for the continuous case, the problem of evaluating the derivatives of a function f(x) in a given interval of x is solved by local approximation method. Examples of application of the resulting numerical procedures are quoted relating the estimation of smooth function and its derivative for measured values (of a growth process), internal regression, trend elimination of time series, Bernstein polynomial, and kernel estimation of a density function.
View Article and Find Full Text PDFGegenbaurs Morphol Jahrb
February 1990
Measurements of endocrinological and pharmacological processes often yield courses of time series with exponentially saturated increasing first part followed by an exponentially decreasing part. Such measured courses may be mathematically modelled by the so-called BATEMAN function type, an expression consisting of 2 e-function terms. In this paper, the method of locally adjusted functional approximation for model-free quantitative evaluation of measured time series is sketched.
View Article and Find Full Text PDF