Влияние аксиомы связности на сложность модальной логики.

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Влияние аксиомы связности на сложность модальной логики.

Математика и теоретические компьютерные науки. 2025. Т. 3. № 2. С. 58–84.

Kudinov A., Мясников К. М.

The paper proves that for weakly transitive logics with the universal modality, whose formula satisfiability problem is in PSPACE, adding the connectedness axiom does not increase the complexity. Furthermore, an explicit algorithm solving this problem is presented.

Research target: Mathematics

Publication based on the results of:

Development of a system of models for scenario forecasting of economic growth and key macro-parameters of the Russian economy, including the use of expert survey data (2025)

Обобщение пространства Фока

Дильмухаметова Алия Мидхатовна, Напалков В. В., Муллабаева А. У., Уфимский математический журнал 2010 Т. 2 № 1 С. 52–58

В данной статье введены обобщённые пространства Фока и рассмотрены основные свойства этих пространств. Найдена операция, сопряженная к операции умножения на переменную в обобщенном пространстве Фока. Также определены собственные функции сопряженного оператора. Изучены обобщенное преобразование Лапласа и задача построения базиса для введенных пространств. ...

Added: September 21, 2026

Segmentation of the Iris and Pupil of the Human Eye in Images from an Infrared Camera

Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 855–862

Tasks related to the automation of medical data processing are becoming more urgent. Particular attention is paid to systems for monitoring and analyzing human physiological parameters. Such systems often use specialized sensors to capture biomedical images, such as infrared cameras. This article describes our study of the problem of segmenting the eye pupil and iris ...

Added: September 21, 2026

A Model Based on Universal Filters for Image Color Correction

Aleksei Samarin, Nazarenko A., Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 844–854

Improving image quality is becoming an increasingly popular task, especially when working with mobile devices. One common approach to image enhancement is the use of convolutional neural networks. However, to achieve good results, such networks must be large enough, otherwise there is a risk of unwanted artifacts. In addition, large convolutional neural networks require significant ...

Added: September 21, 2026

Streptococci Recognition in Microscope Images Using Taxonomy-based Visual Features

Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Optical Memory and Neural Networks (Information Optics) 2024 Vol. 33 P. 424–434

This study explores the development of classifiers for microbial images, specifically focusing on streptococci captured via microscopy of live samples. Our approach uses AutoML-based techniques and automates the creation and analysis of feature spaces to produce optimal descriptors for classifying these microscopic images. This technique leverages interpretable taxonomic features based on the external geometric attributes ...

Added: September 21, 2026

Specialized Image Descriptors Adaptation for Polyp Recognition over Endoscopic Images

Aleksei Samarin, Aleksei Toropov, Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1053–1060

This paper presents a novel approach to classification in biomedical imaging, specifically targeting polyp recognition in video endoscopy snapshots. Our method leverages specialized image descriptors to enhance the accuracy and robustness of polyp recognition. By employing these specialized descriptors, we address the challenges inherent in analyzing biomedical images from open datasets. Our approach not only ...

Added: September 21, 2026

Lightweight Image Preprocessing Model for Improving Microorganism Detection in Microscopic Scenes

Самарин А. В., Торопов А. Г., Савельев А. Г. et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1044–1052

This paper presents a study aimed at improving the detection quality of small-sized microorganisms under challenging microscopic conditions through the application of a lightweight combined image preprocessing model. We focused on the task of detecting diplococci in images obtained through dynamic sample microscopy. The proposed approach employs predefined filters for image preprocessing, combined with the ...

Added: September 21, 2026

Advancements in Signal, Image and Video Processing

Singapore: Springer Singapore, 2025.

Added: September 21, 2026

IDAP++: Advancing Divergence-Based Pruning via Filter-Level and Layer-Level Optimization

Aleksei Samarin, Nazarenko A., Kotenko E. et al., / Series arXiv "math". 2025. No. 2511.20141.

This paper presents a novel approach to neural network compression that addresses redundancy at both the filter and architectural levels through a unified framework grounded in information flow analysis. Building on the concept of tensor flow divergence, which quantifies how information is transformed across network layers, we develop a two-stage optimization process. The first stage ...

Added: September 21, 2026

Об одном классе дифференциальных уравнений с переменными коэффициентами

Дильмухаметова Алия Мидхатовна, Напалков В. В., «Doklady Mathematics» 2009 Т. 424 № 5 С. 591–593

В данной статье вводится определенный класс дифференциальных уравнений с переменными коэффициентами, который тесно связан с операцией умножения Адамара и операторами Данкла имеющими применение в математической физике. Показано, что уравнения этого класса могут быть сведены к уранвениям в обобщенных производных с постоянными коэффициентами. ...

Added: September 21, 2026

Modernized Nonlocal Blocks for Infrared Camera Image Segmentation of the Human Eye

Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2025 Vol. 35 No. 2 P. 169–178

This study explores the incorporation of specialized self-attention mechanisms into deep learning architectures, with a particular emphasis on segmenting human iris and pupil regions in infrared images. In this work, we present some modified versions of nonlocal blocks designed to enhance self-attentive properties while addressing the distinct characteristics of infrared imaging data. By applying these customized ...

Added: September 21, 2026

Non-Contrast Brain CT Images Segmentation Enhancement: Lightweight Pre-Processing Model for Ultra-Early Ischemic Lesion Recognition and Segmentation

Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Journal of Imaging 2025 Vol. 11 No. 10 Article 359

Timely identification and accurate delineation of ultra-early ischemic stroke lesions in non-contrast computed tomography (CT) scans of the human brain are of paramount importance for prompt medical intervention and improved patient outcomes. In this study, we propose a deep learning-driven methodology specifically designed for segmenting ultra-early ischemic regions, with a particular emphasis on both the ...

Added: September 21, 2026

ФУНДАМЕНТАЛЬНЫЙ ПРИНЦИП ЭЙЛЕРА ДЛЯ ОДНОГО КЛАССА ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ В ЧАСТНЫХ ПРОИЗВОДНЫХ С ПЕРЕМЕННЫМИ КОЭФФИЦИЕНТАМИ

Дильмухаметова Алия Мидхатовна, Напалков В. В., «Doklady Mathematics» 2012 Т. 443 № 3 С. 293–295

В данной работе введены обобщенные частные производные, изучены дифференциальные уравнения в обобщенных частных производных с постоянными коэффициентами и доказан фундаментальный принцип Эйлера для таких уравнений. Устанавливлена связь с классом уравнений в обычных частных производных с переменными коэффициентами. ...

Added: September 21, 2026

Pattern Recognition. ICPR 2024 International Workshops and Challenges

Springer, Cham, 2025.

Added: September 21, 2026

Automation of Multi-Class Microscopy Image Classification Based on the Microorganisms Taxonomic Features Extraction

Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Journal of Imaging 2025 Vol. 11 No. 6 P. 1–20

This study presents a unified low-parameter approach to multi-class classification of microorganisms (micrococci, diplococci, streptococci, and bacilli) based on automated machine learning. The method is designed to produce interpretable taxonomic descriptors through analysis of the external geometric characteristics of microorganisms, including cell shape, colony organization, and dynamic behavior in unfixed microscopic scenes. A key advantage ...

Added: September 21, 2026

Some rigidity results for static three-manifolds with boundary and positive scalar curvature

Medvedev V., Annals of Global Analysis and Geometry 2026 Vol. 70 No. 2 P. 8–23

This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect ...

Added: September 19, 2026

Improving the Accuracy of Automatic Wildlife Detection in Nature Reserves Using Infrared Imaging

Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 323–334

In this paper, an improved approach for automatic wildlife detection in natural environments based on the integration of a neural network architecture with a two-stream attention mechanism and a novel preclassification step based on infrared data has been presented. The proposed method addresses one of the key challenges in environmental monitoring: the need for scalable ...

Added: September 19, 2026

IDAP++: Advancing Divergence-Aware Pruning with Joint Filter and Layer Optimization

Aleksei Samarin, Nazarenko A., Kotenko E. et al., Proceedings of the ACM on Management of Data, USA 2026 Vol. 4 No. 1 P. 1–28

Modern knowledge and large volumes of data are increasingly encoded within neural networks, making the task of simplifying their structures and reducing the number of parameters especially relevant, both to improve efficiency and to facilitate deployment in resource-constrained environments. This paper presents a novel approach to neural network compression that addresses redundancy at both the ...

Added: September 19, 2026

Automated Feature Engineering-Based Approach for Micrococci Microscopic Image Classification and Taxonomic Characteristics Determination

Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2025 Vol. 35 No. 2 P. 148–158

This paper describes our research on creating classifiers for microbial images (micrococci microscopy images) obtained from pictures of unfixed microscopic scenes. In our work, we propose an AutoML approach based on the automatic generation and analysis of the feature space for constructing the most optimal descriptors of microorganism images for subsequent classification. This makes it ...

Added: September 19, 2026

Improvement in Microbial Classification Quality Using Synthetic Microscopic Images Generated by Large Visual-Language Models

Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 302–312

The lack of annotated microscopic datasets remains a major obstacle to training robust deep learning models for microbial classification. In this paper, a novel data augmentation pipeline that uses visual–linguistic large-scale models to generate synthetic microscopic images of six different bacterial and nonbacterial classes has been proposed. Synthetic samples have gradually been added to the ...

Added: September 19, 2026

Complexity of reasoning in Kleene algebra with sum-of-letters hypotheses

Stepan L. Kuznetsov, , in: Automated Reasoning: 13th International Joint Conference, IJCAR 2026, Lisbon, Portugal, July 26–29, 2026, Proceedings, Part II. (LNCS, volume 16689)Vol. 16689.: Cham: Springer, 2026. P. 161–177.

Kleene algebras are an algebraic abstraction of regular expressions, one of the central notions in computer science. While the equational theory of Kleene algebras is known to be decidable, reasoning from finite sets of hypotheses (Horn theory) quickly becomes undecidable. This happens even for simple classes of hypotheses which themselves do not involve Kleene star. ...

Added: July 26, 2026

Modal Products and Around

Shehtman V. B., Gagarin A., , in: Graph Games and Logic Design. Recent Developments and Further Directions. (TREN, volume 66)Vol. 66.: Springer, 2026. Ch. 17 P. 419–450.

The chapter contains an overview of results on products of propositional modal logics and related constructions: semiproducts, Segerberg squares, and others. We focus mainly on axiomatizations, finite model property, and decidability; we also sketch connections with classical and modal predicate logics. In some cases we give ideas of proofs, especially of those using games. ...

Added: June 30, 2026

Алгоритмическая сложность теорий с итерацией Клини

Kuznetsov S., Успехи математических наук 2026 Т. 81 № 1(487) С. 137–204

Итерация (звёздочка) Клини – это одна из наиболее интересных алгебраических операций, встречающихся в теоретической информатике. Исследования структур с этой операцией – алгебр Клини и их расширений – начинаются с классического понятия регулярных выражений, задающих формальные языки. Впоследствии были введены так называемые алгебры действий (В. Пратт, 1991 г.; Д. Козен, 1994 г.), или алгебры Клини с делениями. В этих структурах звёздочка Клини сочетается с делениями, согласованными с частичным порядком (такие ...

Added: February 4, 2026

О кванторной версии модальной логики Белнапа–Данна

Грефенштейн А. В., Speranski S. O., Математический сборник 2024 Т. 215 № 3 С. 37–69

Разрабатывается кванторная версия пропозициональной модальной логики BK из статьи С. П. Одинцова и Х. Вансинга, в основе которой лежит (немодальная) система Белнапа–Данна; мы будем обозначать эту версию через QBK. Сначала с помощью метода канонических моделей будет доказано, что QBK — как и некоторые важные её расширения — сильно полна относительно подходящей семантики возможных миров. Затем мы ...

Added: December 26, 2025

Two Types of Filtrations for wK4 and Its Relatives

Kudinov A., Shapirovsky I., Studia Logica 2025 P. 1–25

We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For m > 0, let Lm be the logic defined by axiom ♦^{m+1}p → ♦p ∨ p. We construct quotient filtrations for the logics Lm, which implies that these logics and their tense counterparts have the finite model property. Then, we construct selective filtrations ...

Added: October 14, 2025