Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ

The paper considers a new method of interpolation of nonlinear functions on a segment, the so-called 𝑝-factor interpolation method. It is shown using the example of Newton’s interpolation polynomial that in the case of degeneration of the approximated function 𝑓(𝑥) in the solution, classical interpolation does not provide the necessary accuracy for finding an approximate solution to the equation 𝑓(𝑥) = 0, in contrast to the non-degenerate regular case. In turn, the use of 𝑝-factor interpolation polynomials for approximating functions in order to obtain the desired approximate solution to the equation provides the necessary order of accuracy in the argument during calculations. The obtained results are based on the constructions of the theory of 𝑝-regularity and the apparatus of 𝑝-factor operators, effectively used in the study of degenerate mappings.

It is shown that the multiple non-constant relaxation time lattice Boltzmann equation for five discrete velocities is equivalent to the nonlinear anisotropic diffusion equation. The application of the proposed model to speckle and gaussian noise removal problem is considered.

We propose a novel method for rapid pattern analysis in high-dimensional numerical data, termed “tunnel clustering”. The main advantages of this method are its relatively low computational complexity, endogenous determination of cluster composition and number, and a high degree of interpretability of the final results. We present descriptions of three different variations: one with fixed hyperparameters, an adaptive version, and a combined approach. Three fundamental properties of tunnel clustering are examined. Practical applications are demonstrated on both synthetic datasets containing 100,000 objects and on classical benchmark datasets.

Here we present a formula counting the countable spectrum of an arbitrary weakly o-minimal theory of finite convexity rank having less than 2ω pairwise non-isomorphic countable models.

The problem of approximating a continuous real function of one real variable, defined on a segment, using a band-limited function based on A. N. Tikhonov’s regularization method is considered. Numerical estimates of the accuracy of such approximations are calculated for a model trigonometric function. The reasons why a theoretical estimate of the approximation accuracy of a continuous function by band-limited functions is difficult to achieve numerically are analyzed. The problem of estimating the spectrum of a signal defined on a finite interval is discussed.

Measuring a company’s ethics is an important element in the mechanism of regulating the behavior of market participants, as it allows consumers and regulators to make better decisions, which has a disciplining effect on companies. We tested various methods of machine analysis of consumer feedback from Russian banks and developed an Ethics Index that allows us to calculate a quantitative assessment of the ethics of three hundred Russian banks based on consumer feedback for different time periods from 2005 to 2022. We used a bag-of-words method based on the Moral Foundations Dictionary (MFD) and BERT model training based on a 3,000- and 10,000-sentence sample marked up by experts. The resulting index was validated based on the number of arbitration cases from 2005 to 2022 (more ethical companies are involved in fewer arbitration cases as a defendant), with only the BERT model validated and the MFD-based model not. The ethicality index will be useful as an alternative metric to the popular ESG ratings both for theoretical research on company behavior and for practical tasks of managing company reputation and forming policies to regulate the behavior of market participants.