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The Exact Circuit Complexity of Boolean Functions in an Infinite Basis
Mathematical notes. 2025. Vol. 117. No. 4. P. 579–594.
V. V. Kochergin, A. V. Mikhailovich
The exact value of the complexity of the circuit implementation of an arbitrary Boolean function in a certain basis consisting of negation and all monotone Boolean functions is found. The complexity of a function is defined as the least number of basis elements sufficient to construct a circuit implementation of this function.
Yakovlev E., Maksimov D. A., Mathematical notes 2026 Vol. 120 No. 3 P. 483–496
Smooth principal bundles whose total spaces and bases are time oriented Lorentzian manifolds and whose projections are Lorentzian submersions preserving time orientations are studied. Previously, the authors showed that the chronologicity, causality, and stable causality always lift from the base to the space of a Lorentzian bundle. For strong causality and global hyperbolicity, this holds ...
Added: September 24, 2026
Sokolov V., Shabat G. B., Tsiganov A. V., Journal of Geometry and Physics 2026 Vol. 220
We consider Novikov equations for commutative ring generated by differential operators of
orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method
of compatible Poisson brackets, we find a separation of variables on a hyperelliptic curve
of genus 2 for the Novikov equations ...
Added: September 24, 2026
Marshakov A., Yung A., Ievlev E. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 No. 114 P. 1–22
We continue the study of non-Abelian vortex string in 4D N ¼ 2 supersymmetric QCD (SQCD) as critical superstring, and extend this analysis to UðNÞ gauge theory with arbitrary even N and Nf ¼ 2N number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by ...
Added: September 24, 2026
Demina M.V., Nechitailo V., Analysis and Mathematical Physics 2026 Vol. 16 No. 5 P. 1–25
We present a method of finding non-Liouvillian first integrals of rational two-dimensional differential systems. The method is based on the existence of two independent invariants that satisfy a linear second-order ordinary differential equation with respect to one of the variables. We call systems with this property R-integrable. These invariants are not necessarily polynomial; they can ...
Added: September 24, 2026
Bitter I., Konakov V., Mathematical notes 2026 Vol. 120 No. 4 P. 599–615
The paper provides a generalization of the local limit theorem on the convergence
of inhomogeneous Markov chains to the diffusion limit for the case in which the corresponding
coefficients of the process satisfy weak regularity conditions and coincide only asymptotically.
In particular, the drift coefficients under consideration can be unbounded with at most linear
growth, and the bounds reflect ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Ivan Bulychev, Savchenko A., AI 2026 Vol. 7 No. 9 Article 380
Recent advances in large language model (LLM) agents have shown promise for autonomous decision-making in recommender systems. However, existing approaches suffer from two fundamental limitations: flat agent memories that conflate different information modalities and prohibitive computational costs that prevent scaling beyond a few hundred users. We propose Hybrid-GraphRAG, a recommender system that integrates hierarchical agent ...
Added: September 24, 2026
Snegirev A., Sychev S., Futures 2026 Vol. 183 P. 1–22
This study addresses the systemic identification and categorization of risks associated with AI development, arising from tensions between technological evolution and institutional, infrastructural, and economic contexts. Drawing on a constructionist methodology, we interpret technological risks as constitutive elements of expert communities' images of the future. Through in-depth interviews with 100 AI experts, proportionally representing corporate, ...
Added: September 23, 2026
Parshakov P., Paklina S., International Journal of Human-Computer Interaction 2026 P. 1–17
This study examines how emotional tone shapes user preference in human–large language model (LLM) interaction. Drawing on the Computers as Social Actors framework, we treat conversational AI as a social communicator whose affective cues influence user judgments. Using large-scale pairwise preference data from LMSYS Chatbot Arena, we model emotional tone through the Valence–Arousal–Dominance framework and ...
Added: September 23, 2026
Andrabi U., Wadood E., Ojha S. K. et al., IEEE Access 2026 Vol. 14 P. 103358–103375
The emergence of 5G networks, aimed at accommodating diverse service requirements such as enhanced Mobile Broadband (eMBB), Ultra-Reliable Low-Latency Communication (URLLC), and massive Machine-Type Communication (mMTC), has presented significant challenges in radio resource management and network slicing. In dynamic heterogeneous network systems, traditional heuristics and mathematical programming methods find it challenging to attain scalable multi-objective ...
Added: September 23, 2026
Paklina S., Parshakov P., Elena Rapoport, Scientometrics 2026 P. 1–26
Generative artificial intelligence has become a routine part of academic writing. While much of the debate has focused on questions of integrity and authorship, less attention has been paid to how AI-assisted writing may affect research evaluation itself. This paper asks a straightforward but important question: does the use of LLMs in academic writing change ...
Added: September 23, 2026
Kertesz-Farkas A., Acquaye F. L., Journal of Proteome Research 2026 Vol. 25 P. 3764–3768
Ultimately, most tandem mass spectrometry (MS/MS) proteomics experiments aim to not just detect but also quantify the proteins in a given complex sample. Here, we describe an extension to the Crux MS/MS analysis toolkit to enable label-free quantification of peptides. We demonstrate that Crux’s new quantification command, which is modeled after the algorithms implemented in ...
Added: September 23, 2026
Maddalena L., Yildiz B., Del Vecchio Blanco F. et al., Risk Analysis 2026 Vol. 46 No. 4 P. 1–26
Heated tobacco products (HTPs) are marketed as alternatives to conventional cigarettes with a potential reduced risk profile. Yet, their actual impact on cancer and noncancer disease risk remains uncertain and requires rigorous quantitative assessment. In this study, we develop a unified and transparent computational framework for toxicological risk assessment of HTPs, integrating chemical emissions data ...
Added: September 22, 2026
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
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
Kochergin V., Mikhailovich A., Математические заметки 2025 Т. 117 № 4 С. 523–542
The exact value of the complexity of the circuit implementation of an arbitrary Boolean function in a certain basis consisting of negation and all monotone Boolean functions is found. The complexity of a function is defined as the least number of basis elements sufficient to construct a circuit implementation of this function. ...
Added: April 8, 2025
Mikhailovich A., Kochergin V., М.: Физматлит, 2024.
Added: March 10, 2025
Kochergin V., Mikhailovich A., Mathematical notes 2023 Vol. 113 No. 5 P. 794–803
The problem of determining the nonmonotone complexity of the implementation ofk-valued logic functions by logic circuits in bases consisting of all monotone (with respect to thestandard order) functions and finitely many nonmonotone functions is investigated. In calculatingthe complexity measure under examination only those elements of the circuit which are assignednonmonotone basis functions are taken into ...
Added: November 19, 2023