The centre's main objectives are:
1
developing and advancing interpretable machine learning and data mining methods for NLP and recommender systems
2
developing models that enhance the functionality of existing large language models by leveraging additional resources: linguistic models, knowledge models, search models, and planning algorithms
3
developing models and methods for automatic knowledge acquisition using large language models (LLM), including methods for transfer learning between different languages and different tasks
4
developing models and methods for research, modelling, and analysis within the framework of complex systems theory
5
developing semantic analysis tools based on mathematical methods in formal concept theory
Structure
International Laboratory of Intelligent Systems and Structural Analysis
We conduct research that enables the integration of structural and neural network representations in applied data analysis tasks
Laboratory of Models and Methods of Computational Pragmatics
We work on natural language processing (NLP), interpretable machine learning, and data mining, develop recommender systems and services, and advance multimodal clustering and classification methods that enable the creation of user interest profiles across multiple modalities
Laboratory of Complex Systems Modelling and Control
We conduct fundamental and applied scientific research in the mathematical modelling of complex systems, studying synchronisation phenomena, sudden regime changes, quasi-regularities, self-organisation, evaluating the effectiveness of rare event forecasting algorithms, and managing complex systems
Semantics Analysis Laboratory (in Russian)
Study of natural language as a whole within the natural science paradigm using methods of computer science and applied mathematics
Management
Director of the Centre, Doctor of Sciences, Professor
Deputy Director of the Centre, Candidate of Sciences
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Publications
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Book
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Article
Немарковская семантическая диффузия в многомерных пространствах: подход на основе уравнений Маккина–Власова–Фоккера–Планка
Information diffusion models traditionally focus on event propagation, user activity and network interactions, providing limited mathematical insight into the evolution of semantic content itself. In this paper, narrative evolution is formulated as the evolution of probability measures in a multidimensional semantic space. We construct a mathematical bridge from event cascades to empirical semantic measures and subsequently to nonlinear density dynamics. The resulting framework is described by a non-Markovian McKean--Vlasov--Fokker--Planck equation incorporating semantic drift, collective interaction and memory effects. Within this setting, stable narrative configurations are characterized as stationary density solutions, while structural semantic transitions are associated with changes in their stability properties. The proposed model provides a unified probabilistic description of semantic diffusion and establishes a theoretical foundation for the analysis of long-term narrative evolution, semantic stabilization and regime transitions in complex information environments.
Вестник Южно-Уральского государственного университета. Серия: Вычислительная математика и информатика. 2026.
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Book chapter
Complexity of reasoning in Kleene algebra with sum-of-letters hypotheses
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. One of such classes of hypotheses is formed by sum-of-letters hypotheses, of the form $a \leq b_1 + \ldots + b_k$, where $a, b_1, \ldots, b_k$ are letters. In the present paper, we strengthen the undecidability result proved for this class of hypotheses by Doumane et al. (2019) and establish the exact complexity—$\Sigma^0_1$-completeness. Moreover, we strengthen our result and show the same complexity bounds for one fixed set of sum-of-letters hypotheses. We also accompany this result with a decidability one, for comparison.
In bk.: 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.
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Working paper
Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image segmentation, but their development depends on well-annotated training datasets. However, there is a notable lack of publicly available MRA datasets with detailed brain vessel annotations. To address this gap, we propose a novel semi-supervised learning lightweight neural network with Hessian matrices on board for 3D segmentation of complex structures such as tubular structures, which we named HessNet. The solution is a Hessian-based neural network with only 6000 parameters. HessNet can run on the CPU and significantly reduces the resource requirements for training neural networks. The accuracy of vessel segmentation on a minimal training dataset reaches state-of-the-art results. It helps us create a large, semi-manually annotated brain vessel dataset of brain MRA images based on the IXI dataset (annotated 200 images). Annotation was performed by three experts under the supervision of three neurovascular surgeons after applying HessNet. It provides high accuracy of vessel segmentation and allows experts to focus only on the most complex important cases. The dataset is available at https://git.scinalytics.com/terilat/VesselDatasetPartly.Statistical mechanics. arXie. arXive, 2025