Institute of Mathematics and Informatics

We define and study in-depth the so-called completely inert and uniformly completely inert subgroups of Abelian groups. We curiously show that a subgroup is completely inert exactly when it is characteristically inert. Moreover, we prove that a subgroup is uniformly completely inert precisely when it is uniformly characteristically inert. These two statements somewhat strengthen recent results due to Goldsmith-Salce established for totally inert subgroups in J. Commut. Algebra (2025). Some other closely relevant things are obtained as well.

The classical Benjamini–Hochberg (B-H) method, widely used across various disciplines such as genetics, epidemiology, and social sciences, serves as an established procedure for controlling the false discovery rate (FDR) in multiple comparison scenarios. The B-H method assumes independence among tests, which often does not hold in large-scale dependent datasets. The Benjamini–Yekutieli (B-Y) adjustment controls the FDR under arbitrary dependence but is often very conservative and can lead to a reduction in statistical power. This paper investigates the performance of the B-H and B-Y procedures under specific positive block dependence structures. Two parametric forms of block dependence are considered to model the correlation among paired t -test statistics. Estimation algorithms induced by different matrix norms are developed for approximating the value of the unknown parameter. Modifications of existing multiple testing approaches are proposed by incorporating test dependence and enhancing their power through integration of Kolmogorov-Smirnov tests. Simulation studies are performed to demonstrate that the recommended methods preserve FDR control while improving power compared to traditional techniques.

Generative AI (GenAI) systems are increasingly deployed across high-impact sectors, introducing security risks that fundamentally differ from those of traditional software. Their probabilistic behavior, emergent failure modes, and expanded attack surface, particularly through retrieval and tool integration, complicate threat modeling and control assurance. This paper presents a threat-centric analysis that maps adversarial techniques to the core architectural layers of generative AI systems, including training pipelines, model behavior, retrieval mechanisms, orchestration, and runtime interaction. Using established taxonomies such as the OWASP LLM Top 10 and MITRE ATLAS alongside empirical research, we show that many GenAI security risks are structural rather than configurable, limiting the effectiveness of perimeter-based and policy-only controls. We additionally analyze the impact of regulatory divergence on GenAI security architecture and find that EU frameworks serve in practice as the highest common technical baseline for transatlantic deployments.

Efficient retrieval of mathematical and structural similarities in System Dynamics models remains a significant challenge for traditional lexical systems, which often fail to capture the contextual dependencies of simulation processes. This paper presents an architectural approach and implementation of a semantic search module integrated into an existing cloud-based modeling and simulation system. The proposed method employs a strategy for serializing graph structures into textual descriptions, followed by the generation of vector embeddings via local ONNX inference and indexing within a vector database (Qdrant). Experimental validation performed on a diverse corpus of complex dynamic models, compares the proposed approach against traditional information retrieval methods (Full-Text Search, Keyword Search in PostgreSQL, and Apache Lucene with Standard and BM25 scoring). The results demonstrate the distinct advantage of semantic search, achieving high precision (over 90%) within the scope of the evaluated corpus and effectively eliminating information noise. In comparison, keyword search exhibited only 24.8% precision with a significant rate of false positives, while standard full-text analysis failed to identify relevant models for complex conceptual queries (0 results). Despite a recorded increase in latency (~2 s), the study proves that the vector-based approach is a significantly more robust solution for detecting hidden semantic connections in mathematical model databases, providing a foundation for future developments toward multi-vector indexing strategies.

Fractional calculus, the study of derivatives and integrals of arbitrary order [...]

This paper aims to present the efforts to design and develop the analytical services of the CultIS - a web-based platform for intelligent cultural content management. The CultIS Analytical Module’s purpose is to provide advanced statistical data and analysis for the content usage and user interests in digital libraries powered by CultIS. Based on some of the top rated open-source solutions, the module provides both flexibility and high performance in data loading, report management and visualization. The paper discusses the motivation for the development of the CultIS Analytical Module, the selection of relevant technologies for the development, some specifics of the design and the implementation and some legal issues of data analytics. The proposed solution aims to face the problems and fill the gaps which exist in the current area of analytical solutions and platforms.

Histograms summarize distributions of numerical data into densities per ranges of values and are typically used for fast approximation of selectivities of range predicates. This paper introduces an approach for intuitionistic fuzzy selectivity estimation from histograms when predicates are expressed in fuzzy terms with membership functions on the numeric values, where the degree of indefiniteness corresponds to the level of uncertainty resulting from the accuracy loss due to approximation. In the case of bidimensional histograms, a method for estimating the joint selectivity of conjunctive predicates over the two dimensions is proposed in a way that the joint selectivity can be considered as a measure of correlation. The approach is validated through the use of SQL queries against a synthetically generated dataset and its corresponding bidimensional histogram.

The target of this work is to give a new insight in the theory of strongly weakly nil-clean rings, recently defined by Kosan and Zhou [On weakly nil-clean rings, Front. Math. China 11(4) (2016) 949–955] and further explored in detail by Chen–Sheibani [Strongly weakly nil-clean rings, J. Algebra Appl. 16 (2017)]. Indeed, we consider those rings whose non-units are strongly weakly nil-clean and succeed to establish that this class of rings is strongly [Formula: see text]-regular and, even something more, that it possesses a complete characterization in terms of the Jacobson radical and sections of the [Formula: see text] full matrix ring. Additionally, some extensions like Morita context rings and groups rings are also studied in this directory.

A powerful and convenient model for any process workflows, including clinical pathways in medical practice, is the Partially Observable Markov Decision Process model (POMDP). However, the algorithms for computing the optimal policy in such models are approximate and require a significant number of data samples for convergence. In addition, there aren’t easy-to-use software products that can be used by the medical staff. This article presents a software that can be used as a digital second opinion assistant for assessing the clinical risks and optimization of the clinical pathways using only data from the patient’s medical history and basic statistics. Based on an original methodology that combines deterministic modeling of the workflows with stochastic optimization, it implements efficient algorithms for assessing the risks of recurring conditions and developing complications in clinical practice. The software combines an intuitive and convenient interactive model editor with completely automatic calculation of the risks and the strategy for treatment. Initially developed for security by design of cyber systems, it can be used for optimization of sequential processes in many medical areas, such as diagnostics, monitoring, and control.