.
Ensuring the safety of systems that incorporate electrical, electronic, and programmable electronic safety-related functions requires quantitative evaluation of risk control and/or reduction performance, typically expressed as the Safety Integrity Level (SIL) defined in IEC 61508. However, existing probabilistic approaches have limited capability to represent modern safety architectures in which Safety Functions (SFs) consist of interdependent elements arranged in series, parallel, or heterogeneous redundant structures. Such configurations are increasingly common in contemporary safety-critical applications, including autonomous driving systems and humanoid robotics. This paper proposes a unified analytical framework for evaluating the dependability characteristics of SFs and the risk metric of Hazardous Event Rate (HER) through two key abstractions: the Component Function Set (CS) and the Critical Functional Element (CFE). These concepts allow complex safety-related systems to be represented using consistent failure and restoration characteristics across structural variations. The framework derives dangerous failure rates, effective restoration rates, and unavailabilities for series, parallel, and mixed configurations. HER is formulated by combining Markov modeling of demand and failure dynamics with transformation into an equivalent fault tree using irreversible Priority-AND (PAND) logic, avoiding exponential growth in state-space size. The proposed method provides exact or tight upper bounds for HER and clarifies how architecture, diagnostic capability, and demand characteristics influence hazard occurrence. An illustrative example demonstrates applicability to systems with non-uniform redundancy and diagnostic coverage. The framework offers a practical analytical tool for architecture-aware functional safety evaluation in modern safety-critical systems.
During the article a hybrid named-entity recognition (NER) algorithm for Uzbek is presented. It combines rule-based modules (transliteration, dialect normalization, morphological analysis) with modern neural network models. The study is motivated by Uzbek’s agglutinative morphology, dialect diversity and the lack of specialized resources, which hinder the direct application of named entity recognition methods developed for English or other high-resource languages. As part of the work, an annotated corpus of more than three thousand sentences in the Uzbek language was formed, including legal documents, scientific articles, news materials and informal texts from social networks. The corpus is marked up according to the BIOES scheme taking into account the specific morphological and lexical features of the Uzbek language. The developed rule-oriented algorithms (transliteration, dialect standardization, morphological analysis) are integrated into a single post-processing system that complements neural network models. As a result of experiments aimed at assessing the effectiveness of the proposed approach, it was found that the hybrid approach significantly improves the accuracy and completeness metrics of named entity recognition in different thematic domains. The practical value of the study is that the proposed system can serve as a basis for automatic processing of Uzbek texts in the tasks of searching and extracting information, dialect normalization, annotating large text data and digitalization of document flow. The theoretical significance is that the work expands approaches to named entity recognition for low-resource languages, offering methods that take into account morphological-syntactic and dialectal features.
This article analyses definite integral area problems as a specific type of graphical problems in school mathematics. The study proposes an extended classification of graphical problems in which solution process involves graphical construction followed by analytical reasoning. Based on definitions of visual thinking developed by some researchers, the theoretical analysis of the extended classification of graphical problems demonstrates the integration of visual and logical thinking. Definite integral area problems are explored as A(GA)A-type graphical problems of an extended classification. A sequence of A(GA)A-type graphical problems involving linear functions are formulated, general formulas for calculating areas are derived through both geometric methods and the definite integral. The article also demonstrates how A(GA)A-type problems can be constructed as a sequence of problems from particular cases to general cases using ChatGPT-5.2. In addition, different methods for solving such problems are presented by ChatGPT-5.2. The capabilities of GeoGebra for visualizing the bounded area are also analyzed.
modern 3D assets increasingly travel together with audio-video (A/V) recordings: inspection meshes with synchronized video, reconstructed scenes linked to narration, and CAD-derived models packaged with capture logs. In practice, the most valuable metadata-session identifiers, timecodes and segment boundaries, frequency fingerprints, calibration parameters, and integrity statements-are stored out-of-band (sidecar JSON, database rows, container headers). During routine processing (NURBS-to-mesh tessellation, remeshing, decimation for level-of-detail, smoothing/fairing, and reduced-precision export), this external binding can silently break, causing metadata loss or enabling malicious transplant of provenance from one asset to another. This paper frames the dissertation problem of geometrically robust encoding and synchronization of A/V metadata inside parametric 3D surfaces (NURBS) and triangle meshes. We systematize the design space via a taxonomy that separates carrier (NURBS vs. mesh), embedding domain (spatial, invariant/differential, spectral, multiresolution), and synchronization strategy (intrinsic anchors, patch replication, parametric anchors). We formalize threat models that include both benign pipeline transformations (noise, quantization, smoothing, decimation) and adversarial actions (erasure, desynchronization, transplant). From these, we derive design requirements: bounded distortion (RMS/Hausdorff), anchor repeatability under topology change, redundancy with error-correcting codes, quantization-aware modulation, and cryptographic verification tying the decoded token to an A/V fingerprint and signed manifest. Finally, we report benchmark evidence using Bit Error Rate (BER) together with normalized RMS and approximate Hausdorff distance under representative attacks, supported by figures and tables to enable reproducibility.
In the era of interconnected systems, System of Systems (SoS) environments present increasingly complex risks that challenge traditional safety management methods. These environments amplify risks through dynamic interactions among components, necessitating advanced methodologies to ensure safety and reliability. This study proposes an enhanced Losses and Hazards Identification Process (LHIP) framework, incorporating a hazard prioritization mechanism to systematically identify, analyze, and manage hazards when integrating additional systems. The framework addresses both traditional and emergent hazards, providing a structured approach to prioritizing hazards based on the severity of their associated losses. Applied to a nuclear power plant integrating a hydrogen production system, the framework effectively identifies and mitigates losses and hazards. By evaluating hazards through a scoring system that quantifies potential impacts, the prioritization mechanism facilitates efficient resource allocation to high-priority risks, supporting proactive mitigation strategies. Furthermore, the framework enhances traceability between hazards and their associated losses, ensuring timely feedback to development processes and enabling iterative safety improvements. Aligning with regulatory requirements and industry trends in risk-informed safety management, LHIP framework offers a robust and practical solution for enhancing safety in complex SoS environments. Its structured approach addresses the growing need for systematic risk management as system integration becomes increasingly prevalent. This study represents a significant advancement in hazard analysis, offering broad applicability to other high-risk, complex systems. Future research will focus on dynamic risk assessments, leveraging real-time data and predictive analytics to support continuous hazard evaluation and prioritization, facilitating adaptive safety management in rapidly evolving systems.
