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Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping
Discrete Mathematics and Applications. 2021. Vol. 31. No. 4. P. 259–269.
Mironkin V.
The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.
Medvedev V., Annals of Global Analysis and Geometry 2026 Vol. 70 No. 2 P. 8–23
This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 323–334
In this paper, an improved approach for automatic wildlife detection in natural environments based on the integration of a neural network architecture with a two-stream attention mechanism and a novel preclassification step based on infrared data has been presented. The proposed method addresses one of the key challenges in environmental monitoring: the need for scalable ...
Added: September 19, 2026
Aleksei Samarin, Nazarenko A., Kotenko E. et al., Proceedings of the ACM on Management of Data, USA 2026 Vol. 4 No. 1 P. 1–28
Modern knowledge and large volumes of data are increasingly encoded within neural networks, making the task of simplifying their structures and reducing the number of parameters especially relevant, both to improve efficiency and to facilitate deployment in resource-constrained environments. This paper presents a novel approach to neural network compression that addresses redundancy at both the ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2025 Vol. 35 No. 2 P. 148–158
This paper describes our research on creating classifiers for microbial images (micrococci microscopy images) obtained from pictures of unfixed microscopic scenes. In our work, we propose an AutoML approach based on the automatic generation and analysis of the feature space for constructing the most optimal descriptors of microorganism images for subsequent classification. This makes it ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 302–312
The lack of annotated microscopic datasets remains a major obstacle to training robust deep learning models for microbial classification. In this paper, a novel data augmentation pipeline that uses visual–linguistic large-scale models to generate synthetic microscopic images of six different bacterial and nonbacterial classes has been proposed. Synthetic samples have gradually been added to the ...
Added: September 19, 2026
Springer, Cham, 2026.
computer vision ...
Added: September 19, 2026
Springer, Cham, 2026.
Added: September 19, 2026
FRUCT Oy, 2024.
Added: September 19, 2026
FRUCT Oy, 2024.
Added: September 19, 2026
FRUCT Oy, 2025.
Added: September 19, 2026
FRUCT Oy, 2026.
Added: September 19, 2026
Aleksei Samarin, Nazarenko A., Kotenko E. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 8 P. 1–26
This paper presents a novel method for pruning deep neural networks based on the concept of flow, derived from the continuous modeling of signal propagation across layers. We derive flow functions for fully connected, convolutional, and self-attention architectures, and we propose a new iterative pruning algorithm, Iterative Flow-Aware Pruning (IFAP), that leverages these measures to ...
Added: September 19, 2026
Kuzyutin D., Smirnova N., Veselkov A., Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software 2026 Vol. 19 No. 3 P. 40–49
We consider spatial dynamic fishery management problem taking into account the resource migration process between an open-access fishing area and no-take marine protected area. The introduced extension of a standard single-criterion fish war game implies that each player aims to maximize simultaneously two performance criteria which present an economic benefit and an environmental conservation goal ...
Added: September 18, 2026
Ероховец Николай Юрьевич, Математический сборник 2026 Т. 217 № 5 С. 45–89
Toric topology assigns to each simple convex n-polytope P with m facets an n-dimensional real moment-angle manifold RZP with a canonical action of Zm2=(Z/2Z)m. We consider (not necessarily free) actions of subgroups H⊂Zm2 on RZP. The orbit space N(P,H)=RZP/H carries an action of Zm2/H. For general n we introduce the notion of Hamiltonian C(n,k)-subcomplex in the boundary of an ...
Added: September 17, 2026
Kuninets A., Malygina E., Cryptography and Communications 2026
In this paper, we determine explicit bases for Riemann–Roch spaces associated with various families of elliptic codes. We establish the feasibility and provide exact algorithms for constructing bases of Riemann–Roch spaces corresponding to arbitrary divisors on elliptic curves, including the non-effective case. These results are subsequently applied to derive bases for quasi-cyclic elliptic codes and ...
Added: September 17, 2026
Kazakov A., Koryakin V., Safonov K. et al., Journal of Differential Equations 2026 Vol. 480 Article 114626
We study a family of one-dimensional maps that models the dynamics of a system of differential equations with a Lorenz attractor near a bifurcation curve where the system has a pair of homoclinic loops with zero separatrix value. Of particular interest is the region of the parameter plane where the map has a robust chaotic ...
Added: September 16, 2026
Letellier C., Stankevich N., Houri S. et al., Chaos 2026 Vol. 36 No. 9 Article 093128
Toroidal chaos designates a chaotic solution that is structured in the neighborhood of a torus. For being chaotic, such a torus needs to be discontinuously fractalized to present a Cantor set, ensuring the great sensitivity to initial conditions required for chaos. A fractal is related to self-similarity and a non-integer dimension. In fact, although clearly ...
Added: September 16, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Смирнов С. В., Миллионщиков Д. В., Уфимский математический журнал 2021 Т. 13 № 2 С. 44–73
В данной работе изучаются характеристические алгебры для систем экспоненциального типа, соответствующих вырожденным матрицам Картана. Эти системы обобщают хорошо известные в теории интегрируемых систем гиперболические уравнения синус-Гордон и Цицейки. Для таких систем, соответствующих матрицам Картана ранга 2, характеристические алгебры описаны явно в терминах образующих и соотношений, и доказано, что они имеют линейный рост. Исследуется связь между ...
Added: September 11, 2026
Смирнов С. В., Glasgow Mathematical Journal 2026 Vol. 68 No. 2 P. 299–316
In the second half of the 19th century Darboux obtained determinant formulae that provide the general solution for a linear hyperbolic second order PDE with finite Laplace series. These formulae played an important role in his study of the theory of surfaces and, in particular, in the theory of conjugate nets. During the last three ...
Added: September 11, 2026
Mironkin V., Прикладная дискретная математика 2020 № 49 С. 5–17
We study the probability characteristics of the random mapping graph $ f_{\left[k\right]} $ --- the composition $k\in \mathbb{N}$ of independent equiprobable random mappings $ f_1, \ldots, f_k $, where $f_i\colon \left\{1,\ldots,n\right\}\to \left\{1,\ldots,n\right\}$, $n\in\mathbb{N}$, $i=1,\ldots,n$. The following results are obtained.
Let $k\in \mathbb{N}$ and random mappings $f_1,\ldots,f_k$ be independent with the equiprobable distribution on $\mathfrak{S}$. Then for ...
Added: September 20, 2020
Béal S., Deschamps M., Moulin H., Acta Astronautica 2020 Vol. 177 P. 313–319
Satellites launched by independent spacefaring agencies and firms create space congestion and collision risk. Taking as benchmark the cost of a marginal reduction of the congestion rate, we discuss tax mechanisms financing a debris removal effort. We compare the non-cooperative equilibrium traffic when there is a tax on each new launch to recover cleanup costs, ...
Added: August 25, 2020
Mironkin V., Математические вопросы криптографии 2020 Т. 11 № 1 С. 101–114
The probabilistic characteristics of graph corresponding to the
composition of independent uniform random mappings are studied. Exact expressions and estimates for the distribution
of distances from vertices to cycles are obtained. Formulas for expected
mean values of numbers of vertices lying on
at the given distance from cycles and
for the distribution function of the height of a random vertex ...
Added: May 31, 2020
Mironkin V., Дискретная математика 2019 Т. 31 № 4 С. 38–52
The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of a arbitrary vertex with some restrictions are calculated. Exact expressions for the probability of belonging of two arbitrary vertices to a single connected component, of hitting by a ...
Added: December 8, 2019