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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.
Vlasenko D., Saranskaia I., Zakharov D., European Physical Journal: Special Topics 2026 P. 1–16
Hypergraphs provide a natural framework for representing neurophysiological interactions distributed across sets of sensors. A key methodological question is how hyperedges should be defined from frequency-resolved electroencephalography/magnetoencephalography (EEG/MEG) data. We demonstrate a construction strategy in which hyperedges are obtained from canonical coherence (caCOH), an extension of coherence that estimates coupling between multidimensional signal spaces. To ...
Added: August 18, 2026
Borisov D., Katzarkov Ludmil, Sheshmani A. et al., American Journal of Mathematics 2026 Vol. 148 No. 4 P. 1075–1101
It is shown that there are globally defined Lagrangian distributions on the stable loci of derived \mathrm{Quot}-stacks of coherent sheaves on Calabi--Yau four-folds. Dividing by these distributions produces perfectly obstructed smooth stacks with globally defined -1-shifted potentials, whose derived critical loci give back the stable loci of smooth stacks of sheaves in global Darboux form. ...
Added: August 18, 2026
Moshkin A., Fedorov M., Arlazarov V. et al., Algorithms 2026 Vol. 19 No. 7 Article 523
Artificial intelligence (AI) technologies, which are being actively developed in modern medicine today, increase the speed and quality of patient care. This article mainly seeks to demonstrate the use of various options of computer analysis of clinical images to solve practical problems of increasing the efficiency of routine diagnostics using retrospective analysis, as well as ...
Added: August 17, 2026
CHEN Y., Howlett R. J., Tanaka S. et al., Springer, 2026.
The Smart Innovation, Systems and Technologies book series encompasses the topics of knowledge, intelligence, innovation and sustainability. The aim of the series is to make available a platform for the publication of books on all aspects of single and multi-disciplinary research on these themes in order to make the latest results available in a readily-accessible ...
Added: August 16, 2026
Богатырев А. Б., Математический сборник 2023 Т. 214 № 3 С. 106–119
Рассматривается клеточное разбиение пространства модулей вещественных кривых рода 2 с отмеченной точкой на единственном вещественном овале. Клетки перечисляются определенными графами, веса которых описывают комплексную структуру на кривой. Показано, что стягивание ребра графа приводит к корневой особенности естественного отображения из весов графа в пространство модулей кривых. ...
Added: August 14, 2026
Богатырев А. Б., Gendron Q., Успехи математических наук 2023 Т. 78 № 1 С. 209–210
Уравнение Пелля-Абеля — это функциональное уравнение вида P²-DQ² = 1, с заданным многочленом D, свободным от квадратов, и неизвестными многочленами P и Q. Мы показываем, что пространство уравнений Пелля-Абеля с фиксированными степенями D и примитивным решением P является комплексным многообразием. Мы описываем его связные компоненты с помощью эффективно вычислимого инварианта. ...
Added: August 14, 2026
Богатырев А. Б., Transactions of the Moscow Mathematical Society 2024 Vol. 85 No. 2 P. 323–337
The best uniform rational approximation of the Sign function on two intervals separated by zero was explicitly found by E. I. Zolotarëv in 1877. The natural extension of this problem to three bands was solved by E. Stiefel in 1961. We indicate the solutions overlooked by the prominent geometer and study their properties. ...
Added: August 14, 2026
Богатырев А. Б., Успехи математических наук 2026 Т. 81 № 3(489) С. 159–160
Предложена простая и эффективно реализуемая формула для изменения абелевых интегралов (включая их периоды) при вариации образующих классической группы Шоттки, представляющей риманову поврехность. ...
Added: August 14, 2026
Gendron Q., Compositio Mathematica 2025 Vol. 161 No. 7 P. 1483–1511
A Pell–Abel equation is a functional equation of the form P^2-DQ^2=1 , with a given polynomial D free of squares and unknown polynomials P and Q. We show that the space of Pell–Abel equations with the degrees of D and of the primitive solution P fixed is a complex manifold. We describe its connected components ...
Added: August 14, 2026
Yu Z., Wang J., Wang Z. et al., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2026 Vol. 384 P. 1–16
The integration of data-driven and knowledge-driven approaches in generative geospatial modelling (GGM) is often hindered by their mathematical incompatibilities. Here, we propose a geometric algebra (GA)-based framework that employs a unified multi-vector representation to fuse heterogeneous data and diverse knowledge. The framework facilitates structured reasoning and hypothesis generation through a task-adaptable, five-stage cycle: representation, reasoning, ...
Added: August 13, 2026
Cham: Springer, 2026.
This book constitutes the proceedings of the 10th International Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2025, held in conjunction with Computer Graphics International conference, CGI 2025, in Hong Kong, China, on July 14, 2025.
The 14 full papers included in this volume were carefully reviewed and selected from 16 submissions. The papers ...
Added: August 13, 2026
Ratnikov F., European Physical Journal: Special Topics 2026 P. 1–10
EEG recordings are often affected by the loss or corruption of individual channels due to electrode detachment, poor scalp contact, or external interference. Such channels must be accurately reconstructed before further analysis. In this study, we investigate Next-Generation Reservoir Computing (NG-RC) as a data-driven approach for reconstructing corrupted EEG channels and compare its performance with ...
Added: August 12, 2026
Speranski S. O., Математические заметки 2026 Т. 120 № 3 С. 470–483
We show that, in terms of closure ordinals, many infinitary calculi for ‘first-order’ logics of probability (i.e., for languages similar to those in [Abadi & Halpern 1994]) are as hard as possible: the corresponding closure ordinals coincide with the least non-constructive ordinal, denoted by $\omega_1^{\mathrm{CK}}$. ...
Added: August 12, 2026
Minets M., Krasnozhenov G., Trofimova E. et al., PeerJ Computer Science 2026 Vol. 12 Article e4063
This article presents CAD2TechSpec, a novel framework for automating design processes within computer-aided design (CAD) systems by leveraging multimodal large language models (LLMs). The framework enables the analysis and generation of detailed design specifications, including the automated creation of machining process plans. Our system architecture combines 3D model rendering, dimensionality reduction techniques, and the capabilities ...
Added: August 12, 2026
Мизинов П. В., Journal of Computer Virology and Hacking Techniques 2023 No. 20 P. 383–396
Biometric vein recognition systems are vulnerable to presentation attacks. Traditionally, researchers have used a near-infrared (NIR) drawing of the user’s vascular bed to create a presentation attack instrument (PAI). This paper investigates the feasibility of using free software to capture a venous pattern of the hand without NIR under normal lighting conditions and to create ...
Added: August 11, 2026
Ali S., Bocharnikov V., Ratnikov F. et al., Sensors 2026 Vol. 26 No. 16 Article 5024
Large distributed sensor arrays require repeated recalibration as radiation damage, material aging, gain variation, and readout drift alter channel responses. We studied a high-granularity calorimeter as a large sensor array and addressed unsupervised recalibration from two unpaired datasets: a nominal reference response and an aged response with attenuated cell-wise signals. Aging was modeled by a ...
Added: August 11, 2026
Trubochkina N. K., М.: Издательство «Юрайт», 2026.
This textbook is designed to develop students' holistic understanding of modern production processes and methods for their analysis and management using machine learning technologies. In the context of the fourth industrial revolution, where traditional engineering disciplines are inextricably intertwined with intelligent data processing methods, there is a growing need for specialists capable of integrating knowledge ...
Added: August 8, 2026
Kulev Y., Maksaev A., Promyslov V., Linear Algebra and its Applications 2026 Vol. 730 P. 51–72
The notion of λ-th upper scrambling index was introduced by Huang and Liu in 2010, as a generalization of a notion considered by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every λ vertices of D there exist directed paths of lengths k from these vertices to a common vertex. This ...
Added: August 7, 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