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Background: More than 500,000 new cases of squamous cell carcinoma of the head and neck (SCCHN) are registered annually in the world. 7,036 new cases of the disease were registered in Ukraine during 2018, about 35% of patients did not live even a year from the date of diagnosis as a modern standard for the treatment of patients with inoperable locally advanced SCCHN, chemoradiation treatment in the classical dose fractionation mode with chemo modification with cisplatin is used by specialists. Objective: The objective of this study is to analyze the effectiveness of chemoradiation treatment with cisplatin and 5-fluorouracil in the treatment of patients with SCCHN using modern mathematical models. Methods: During the investigation we assessed the effectiveness of treatment in 108 patients with locally advanced SCCHN (stages III, IVa, IVb). The results of calculating the probabilities of complications were obtained using the method of multivariate classification based on the radial basis ANN. Results: Analyzing the groups with different methods of chemo modification, we can conclude that the method of chrono-modulated radiochemotherapy with 5-fluorouracil and the chemoradiation therapy with cisplatin were almost equal in efficiency, namely 77% and 73.5%, respectively (p=0.35). Conclusion: Using the chemoradiation therapy with 5-fluorouracil in the treatment of patients with low somatic status and elderly patients is more expedient in contrast to the methods using cisplatin. The advantage of selection of mentioned treatment method is also confirmed by the results of calculating the average complication risks using the method of multivariate classification based on a radial-basis neural network.

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This paper analyses the definition of inverse and direct problems in engineering dimensional chains calculation based on discrete analogue data and the methodologies for solving these problems. It is shown that the direct dimensional chains calculation, which belongs to the class of inverse boundary value problems in a stochastic formulation, can be transformed into multi-criteria problems of stochastic optimization with mixed conditions. The new multi-step solutions search methodology for these problems is based on non-linear robust estimation methods. It can be achieved through hierarchical two-level decisions synthesis scheme development. At the first step, this scheme includes identification of surrogate models (in the form of regression equations). At the second step, the effective robust estimates are computed to determine unknown values; estimations of unknown quantities are carried out under a priori and parametric data uncertainties. Results of calculations of inverse and direct problems in engineering dimensional chains for two-stage axial compressors are presented. They were obtained using interactive computer systems for decision-making support “ROD&IDS”.