Некоторые полные сложностные дихотомии для задачи о доминирующем множестве

We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...

Added: October 1, 2026

Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence (IJCAI 2026)

International Joint Conferences on Artificial Intelligence, 2026.

Added: October 1, 2026

Asymptotics of Spectrum and Quantum Averages of the Hydrogen Atom in a Magnetic Field Near the Upper Boundaries of Spectral Clusters

A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545

We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using irreducible representations of the Karasev–Novikova algebra with quadratic commutation relations. We find the asymptotics of a series of eigenvalues and the corresponding asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...

Added: October 1, 2026

Ensemble-based Prototype-Augmented Multimodal Fusion for Ambivalence/Hesitancy Recognition

Ryumina E., Aksenov A., Сысоев Д. С. et al., IEEE Computer Society, 2026.

Ambivalence/hesitancy recognition in unconstrained videos is a challenging problem due to the subtle, multimodal, and context-dependent nature of this behavioral state. In this paper, a multimodal approach for video-level ambivalence/hesitancy recognition is presented for the 10th ABAW Competition. The proposed approach integrates four complementary modalities: scene, face, audio, and text. Scene dynamics are captured with ...

Added: September 30, 2026

Simultaneous approximation of the score function and its derivatives by deep neural networks

Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97

We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...

Added: September 30, 2026

Conservative Entropy and Energy Correct Difference Methods for One-Dimensional Quasi-Gasdynamic Systems of Equations

Zlotnik A., Mathematical notes 2026 Vol. 120 No. 6 P. 1005–1009

Numerical methods for solving systems of gas dynamic equations are the subject of a vast literature. A special family of spatially symmetric conservative difference methods based on preliminary kinetic, or quasi-gasdynamic (QGD), regularization of these equations was constructed and successfully tested. A pressing issue is the construction of numerical methods that are not only conservative ...

Added: September 30, 2026

О числе Пикара и размерности алгебраических однородных пространств

Beldiev I., Тимашёв Д. А., Алгебра и анализ 2026 Т. 38 № 5 С. 1–10

An algebraic variety X is called a homogeneous space if there exists a transitive regular action of an algebraic group on X. We prove inequalities between the dimension of a homogeneous space of a linear algebraic group and its Picard number. ...

Added: September 30, 2026

Decoding Algorithms for Binary U-UV Codes: A Unified Survey of Performance and Complexity

Ivanov F., Kotov F., IEEE Access 2026 Vol. 14 P. 104662–104679

U-UV codes, based on the Plotkin (U, U + V) construction, provide a unified framework that includes polar and Reed–Muller codes and enables flexible design through the choice of component codes. While modern capacity-approaching codes achieve excellent performance at large block lengths, their efficiency at short and moderate lengths remains limited, especially under low-latency constraints. ...

Added: September 30, 2026

An archaic reference-free method to jointly infer Neanderthal and Denisovan introgressed segments in modern human genomes,

Planche L., Ilina A., Jay F. et al., Molecular Biology and Evolution 2026 Article 235

Admixture between populations is a common feature of human history. Admixture events introduce new genetic variation that can fuel evolution. Characterizing the significance of admixture events on the evolution of populations across various species is of great interest to evolutionary geneticists. Local Ancestry Inference (LAI) methods infer genetic ancestry of an individual at a particular ...

Added: September 30, 2026

Uniqueness theorem for completely non-degenerate B-groups

Glutsyuk A., Ilyashenko Y., Izvestiya. Mathematics 2026 Vol. 90 No. 1 P. 73–89

We show that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar property is inherent to the quasi-Fuchsian groups but not to degenerate B-groups. We also study the factor of a B-group as a triple: the main factor, the marked characteristic complex, and a homotopy class of ...

Added: September 30, 2026

The EG-TD3 Machine Learning Architecture: Evolutionary-Guided Twin Delayed Deep Deterministic Policy Gradient

Djambong Tenkeu H., Institute for System Programming of the RAS, 2026.

Added: September 29, 2026

Серия инвариантных характеристик реальных сетей

Tuzhilin M., Автоматика и телемеханика 2026 № 11 С. 84–97

Предлагается обобщение двух известных инвариантов реальных сетей: степени и кси-центральности. Строится серия центральностей, основанная на матрице Лапласа сети и параметризованная параметром j со следующими свойствами: во-первых, при j = 0, 1 эти центральности совпадают со степенью и ксицентральностью; во-вторых, их распределение хорошо приближается распределением Вейбулла; в-третьих, для реальных сетей они имеют правостороннюю асимметрию, а для ...

Added: September 29, 2026

Нетривиальное поведение пирамидальных уединенных волн в обобщенном уравнении Гарднера

Melnikov I., Pelinovsky E., Доклады Российской академии наук. Физика, технические науки (ранее - Доклады Академии Наук. Физика) 2026 Т. 529 С. 29–36

Conditions for the emergence of pyramidal solitary waves (solitary waves possessing more than two inflection points) are presented for a family of generalized Korteweg – de Vries (KdV) equations. For the generalized Gardner equation, it is shown that pyramidal solitons are unstable. The decay of initial perturbations close to pyramidal solitary waves is demonstrated numerically. ...

Added: September 29, 2026

Pre-Calabi-Yau algebras and oriented gravity properad

Merkulov S., Journal of Pure and Applied Algebra 2026 Vol. 230 P. 1–19

We study the dual cyclic Hochschild complex $Cyc(A,\K)$ of a (possibly, infinite-dimensional) $A_\infty$-algebra $(A,\mu)$ and prove that any pre-Calabi-Yau extension $\pi$ of the given $A_\infty$ structure $\mu$ in $A$ induces on the cyclic cohomology of $(A,\mu)$ a representation of a new dg properad of {\em oriented}\, ribbon graphs. We compute the cohomology of that properad in terms of ...

Added: September 29, 2026

Нижние множества и свойства замкнутости классов функций подсчета

Ivanashev Y., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2026 Т. 529 С. 93–101

Язык L является нижним для релятивизируемого сложностного класса C, если CL=C. Для классов #P, GapP и SpanP известны точные нижние классы языков: Low(#P) = UP ∩ coUP, Low(GapP) = SPP и Low(SpanP) = NP ∩ coNP. В этой статье мы доказываем, что Low(TotP) = P, и приводим характеризации нижних классов функций для #P, GapP, TotP ...

Added: September 28, 2026

Combinatorics on finite words and the length of a finite-dimensional associative algebra

Хрыстик М. А., European Journal of Combinatorics 2026 Vol. 136 P. 104393–104393

Let 𝑓𝑊⁡(𝑛) be the number of different factors of length 𝑛 appearing in a word 𝑊. In a classical result by Morse and Hedlund, a characterization is given for infinite words satisfying the condition 𝑓𝑊⁡(𝑛)≤𝑛 for some 𝑛∈ℕ. In this paper, we describe the form of finite words that satisfy the condition 𝑓𝑊⁡(𝑛)≤𝑛. We study ...

Added: September 28, 2026

Role of dislocations in the mobility of pinned helium bubbles: Molecular dynamics simulations in aluminum

Piliugin L., Antropov A., Lobashev E. et al., Journal of Nuclear Materials 2026 Vol. 632 Article 156876

The effects of dislocations on the mobility of gas nanobubbles pinned to them are considered as novel unex- plored mechanisms of accelerated fission gas release and investigated using classical molecular dynamics of helium bubbles in FCC aluminum. Non-equilibrium methods are developed to calculate the mobility of a pinned bubble both along and across the dislocation ...

Added: September 28, 2026

MPI+OpenMP implementation of resolution-of-the-identity Hartree-Fock method exploiting permutational symmetry of three-center electron repulsion integrals

Kashpurovich I., Oleynichenko A., Stegailov V., Supercomputing Frontiers and Innovations 2026 Vol. 13 No. 1 P. 52–73

We report a high-performance implementation of the resolution-of-the-identity Hartree–Fock method that fully exploits the permutational symmetry of three-center electron repulsion integrals (ERI). The present implementation adopts a hybrid MPI+OpenMP parallelization strategy. Two different algorithmic approaches (with and without the pre-transformation of ERIs) are compared. A custom data layout introduced previously is employed. Designed to efficiently ...

Added: September 28, 2026

A Three-Party W-State Quantum Secret Sharing Protocol with X-Gate Encoding and Forbidden-Outcome Detection

Teregulov T., Loubenets E. R., / Series Quantum Physics "arXiv". 2026. No. 2609.31472.

We develop a new three-party quantum secret-sharing (QSS) protocol based on a three-qubit W state. This protocol encodes the secret-sequence bits using X gates and employs randomly selected Hadamard operations and measurement bases to generate information and security-test rounds. We evaluate the efficiency of the proposed protocol and analyze its security against an internal adversary ...

Added: September 28, 2026

Bytedance и Open Source - открытые проекты от разработчика TikTok

Silakov D., Системный администратор 2026 С. 84–89

Social media users rarely think about what lies behind the beautiful facade of activity feeds, teeming with photos and video stories. However, the widespread popularity of such platforms generates a huge amount of all sorts of content that needs to be stored, processed quickly, and displayed, and in the era of AI, it also needs ...

Added: September 28, 2026

Universal Comparison Methodology for Hough Transform Approaches

Kazimirov D., Vitalii Gulevskii, Kroshnin A. et al., Mathematics 2026 Article 1136

The Hough transform (HT) is widely used in computer vision, tomography, and neural networks. Numerous algorithms for HT computation have been proposed, making their systematic comparison essential. However, existing comparative methodologies are either non-universal and limited to certain HT formulations, or task-oriented, relying on application-specific criteria that do not fully capture algorithmic properties. This paper ...

Added: May 28, 2026

О СЛОЖНОСТИ ПРОБЛЕМЫ ТОТАЛЬНОЙ ВЫВОДИМОСТИ В НЕУКОРАЧИВАЮЩИХ И КОНТЕКСТНО-СВОБОДНЫХ ГРАММАТИКАХ

Dudakov S., Карлов Б. Н., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 524 № 1 С. 11–18

In this paper we study the problem of total derivability in context-free, noncontracting, and context-sensitive grammars. Given a grammar and a terminal word, one has to determine whether there exists a derivation of this word which uses each production no less than a given number of times. It is proved that the problem of total ...

Added: March 18, 2026

О схлопывании вероятностных иерархий. I

Speranski S. O., Алгебра и логика 2013 Т. 52 № 2 С. 236–254

Изучаются иерархии проблем общезначимости для префиксных фрагментов вероятностной логики с кванторами по пропозициональным формулам, обозначаемой QPL, и её вариантов. Доказывается: если подполе F вещественных чисел определимо в стандартной модели арифметики посредством формулы второго порядка, не содержащей кванторов по множествам, то проблема общезначимости над F-значными вероятностными структурами для $\Sigma_4$-QPL-предложений является $\Pi^1_1$-полной и, как следствие, соответствующая иерархия проблем общезначимости схлопывается. Более того, при ...

Added: December 27, 2025

Некоторые классификации сложности задачи о вершинной 3-раскраске

Дахно Г. С., Malyshev D., Математические заметки 2026 Т. 119 № 3 С. 360–376

Наследственный класс — множество графов, замкнутое относительно удаления вершин. Каждый такой класс имеет каноническое описание посредством минимальных запрещенных порожденных фрагментов. Задача о вершинной 3-раскраске (задача 3-ВР) для заданного графа состоит в том, чтобы определить, а можно ли множество его вершин разбить на три подмножества попарно несмежных вершин. Известна дихотомия сложности этой задачи для всех наследственных ...

Added: November 26, 2025