Doklady Mathematics最新文献

This paper presents a study on the effectiveness of discriminative methods for abbreviation lemmatization in Russian texts. Unlike generative approaches, discriminative models select an optimal lemma from a fixed set of candidates, eliminating the risk of generating grammatically incorrect word forms. For the first time in Russian language processing, we have conducted a comprehensive analysis of four context-aware approaches: (1) masked language model ranking, (2) binary classification, (3) multi-class classification, and (4) prompt-based learning. Special attention is given to cases of contextual ambiguity, where the same abbreviation within a single text fragment corresponds to different lemmas. The results demonstrate that fine-tuned multi-class classification achieves the highest quality (macro-averaged F-score of 97.75–99.92% depending on the abbreviation). However, with limited training data, both prompt-based learning and masked language model ranking show promising results. Moreover, the effectiveness of these approaches increases in cases of contextual ambiguity. The study contributes to the development of Russian text processing methods by providing practical recommendations for selecting architectures for abbreviation lemmatization tasks.

Predicting customer churn requires considering multiple reasons for customer leave, including financial difficulties, dissatisfaction with service quality, and switching to competitors. Survival analysis methods allow us to estimate the probability of an event occurring over time, but have limited functionality in the case of competing risks. The paper proposes adapting classical survival analysis methods to competing risks by constructing a set of individual models using the One-vs-Rest scheme, with different approaches for incorporating censored events. The proposed method for aggregating forecasts using a multi-class classification meta-model will simplify the process of making expert decisions. According to the results of an experimental study using Freddie Mac mortgage lending data, the proposed methods surpassed existing solutions in quality and can be applied to mortgage lending problems.

The paper proposes a system of definitions for basic concepts of computability theory that underlie the mathematics of the digital world: algorithm, computability, calculus, and object complexity close to modern understanding. Hierarchies of the finite and the problem of consistency are considered.

This paper investigates a novel approach for detecting trees in high-resolution satellite imagery by leveraging synthetic canopy height model (CHM) data. We demonstrate that integrating fine-scale CHM maps significantly enhances both the quality and accuracy of tree detection. Additionally, the study conducts a comparative evaluation of several neural network architectures for delineating tree crowns in imagery. Experimental results confirm the effectiveness of the proposed method, underscoring its potential to streamline satellite data processing workflows and strengthen the reliability of automated vegetation monitoring systems.

Determining the spatial resolution (GSD) of remote sensing images is in demand in various fields, from environmental monitoring to urban planning and agriculture, which makes it relevant to analyze both urban and natural landscapes. This study focuses on deep learning methods for evaluating the GSD of still images, and its purpose is to study the impact exerted on the quality of GSD assessment by approaches, such as autoencoder pre-training on still images (SSL) and taking into account features from different levels of the model. All the models under consideration were trained on images of landscapes of different types. Scaling augmentations were also used to train them to expand the range of GSD in data samples. ResNet18 was used as a baseline model, which, based on available data, demonstrates MAPE values ranging from 2.73 to 15.6%. Using the relative loss function directly in training allows one to improve performance on data with low spatial resolution from 15.6 to 14.7%. At the same time, using the SSL approach slightly improves performance at high GSD values. A combination of SSL with FPN reaches 3.61% on a set with a mixed landscape type. The results make it possible to use the trained models to solve applied problems. However, it is necessary to choose the most appropriate method for each specific case.

Classical inversion formulas for the integral Radon transform assume that the integrand is smooth. However, this restriction does not fully correspond to application of results in probing theory, which is the main area of application of the Radon transform. It would be more natural to assume that jump discontinuities are admissible for integrands. The paper presents several inversion formulas proved by the authors for piecewise continuous functions. The formulas are compared, and preliminary recommendations on their use for numerical algorithms are given.

The problem of interpolation in the mean of a function by an integro quadratic spline given integrally averaged function values is considered. It is shown that an integro quadratic spline can be defined via a cubic interpolation spline. Since cubic interpolation splines have been studied quite well, well-known error bounds for them and some of their properties can be transferred to integro quadratic splines. Points of superconvergence of integro splines are found, i.e., points at which a spline or its derivatives provide a higher order of approximation.

An alternative definition of Weyl fractional derivatives is given, and their effect on functions from Gevrey classes is studied. For a partial differential equation with Weyl derivatives, conditions for the solvability of the Cauchy problem in Gevrey classes are found.

An improvement of Riordan’s result on the threshold probability of the occurrence of a spanning subgraph in a random graph is obtained for some classes of subgraphs. In particular, this result implies an improved bound for the maximum power of a Hamiltonian cycle in a random graph. Moreover, a sharp asymptotic threshold probability for a random graph to contain spanning subgraphs from a wide class of (k)-degenerate graphs is found.