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Research presented in this paper was initiated by the publication [A. D. Agaltsov and R. G. Novikov, Examples of solving the inverse scattering problem and the equations of the Veselov–Novikov hierarchy from the scattering data of point potentials, Russian Math. Surveys74 (2019), 3, 373–386] and is based on its results. Two sets of the complex monopole scattering coefficients are distinguished among the possible values of these coefficients for nonabsorbing inhomogeneities. These sets differ in phases of the scattering coefficients. In order to analyze the features and possibilities of reconstructing the inhomogeneities of both sets, on the one hand, the inverse problem is solved for each given value of the monopole scattering coefficient using the Novikov functional algorithm. On the other hand, the scatterer is selected in the form of a homogeneous cylinder with the monopole scattering coefficient that coincides with the given one. The results obtained for the monopole inhomogeneity and for the corresponding cylindrical scatterer are compared in the coordinate and spatial-spectral spaces. The physical reasons for the similarities and differences in these results are discussed when the amplitude of the scattering coefficient changes, as well as when passing from one set to another. [ABSTRACT FROM AUTHOR]

Indirect methods for the indirect estimation of reference intervals are increasingly being used, especially for validation of reference intervals, as they can be applied to routine patient data. In this study, we compare three statistically different indirect methods for the verification and validation of reference intervals in eight laboratories distributed throughout Europe. The RefLim method is a fast and simple approach which calculates the reference intervals by extrapolating the theoretical 95 % of non-pathological values from the central linear part of a quantile-quantile plot. The Truncated Maximum Likelihood (TML) method estimates a smoothed kernel density function for the distribution of the mixed data, for which it is assumed that the "central" part of the distribution represents the healthy population. The refineR utilizes an inverse modelling approach. This algorithm identifies a model that best explains the observed data before transforming the data with the Box-Cox transformation. We show that the different indirect methods each have their advantages but can also lead to inaccurate or ambiguous results depending on the approximation of the mathematical model to real-world data. A combination of different methodologies can improve the informative value and thus the reliability of results. Based on routine measurements of four enzymes alkaline phosphatase (ALP), total amylase (AMY), cholinesterase (CHE) and gamma-glutamyl transferase (GGT) in adult women and men, we demonstrate that some reference limits taken from the literature need to be adapted to the laboratory's particular local and population characteristics. [ABSTRACT FROM AUTHOR]