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The Nonnegative Rank of a Matrix: Hard Problems, Easy Solutions
SIAM Review. 2017. Vol. 59. No. 4. P. 794–800.
Shitov Y.
Using elementary linear algebra, we develop a technique that leads to solutions of two widely known problems on nonnegative matrices. First, we give a short proof of the result by Vavasis stating that the nonnegative rank of a matrix is NP-hard to compute. This proof is essentially contained in the paper by Jiang and Ravikumar, who discussed this topic in different terms fifteen years before the work of Vavasis. Second, we present a solution of the Cohen-Rothblum problem on rational nonnegative factorizations, which was posed in 1993 and remained open until now.
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Kudinov A., Мясников К. М., Математика и теоретические компьютерные науки 2025 Т. 3 № 2 С. 58–84
The paper proves that for weakly transitive logics with the universal modality, whose formula satisfiability problem is in PSPACE, adding the connectedness axiom does not increase the complexity. Furthermore, an explicit algorithm solving this problem is presented. ...
Added: October 14, 2025
Blank M., Discrete and Continuous Dynamical Systems 2025 Vol. 45 No. 11 P. 4186–4201
Appeals to randomness in various number-theoretic constructions appear regularly in modern scientific publications. Such famous names as V.I. Arnold, M. Katz, Ya.G. Sinai, and T. Tao are just a few examples. Unfortunately, all of these approaches rely on various, although often very non-trivial and elegant, heuristics. A new analytical approach is proposed to address the ...
Added: May 23, 2025
Смирнов И. А., Разумов П. В., Сафарьян О. А. et al., Изд-во ВлГУ, 2019.
В данной статье представлен проект модификации и оптимизации ρ – метода факторизации Полларда с помощью рекурсивного метода подсчета факторизации чисел, работающий быстрее стандартного алгоритма на 27%, что сможет значительно облегчить работу по расшифрованию и криптографическому анализу различных шифров типа RSA. Были рассмотрены и использованы алгоритм факторизации, алгоритм Эвклида для нахождения НОД, подсчитана алгоритмическая сложность, матрица ...
Added: May 11, 2023
Смирнов И. А., Разумов П. В., Болдырихин Н. В. et al., IEEE, 2019.
Investigations of cryptographic algorithms for
today are very actually in connection with cybernetic attacks
threat and necessity of information protection at the
enterprises of various levels including the strategic
appointment. The project implementation of John Pollard’s
factorization ρ–method in the programming language C ++ is
presented, which works faster than the standard algorithm by
27%. It can facilitate greatly the deciphering operation ...
Added: May 10, 2023
Черкесова Л. В., Сафарьян О. А., Смирнов И. А., Молодой исследователь Дона 2018 Т. 3 (12) С. 111–121
The paper presents the project implementation of ρ-factor Pollard factorization in C ++, which works faster than the standard algorithm by 27%, which can significantly facilitate the work in deciphering and cryptanalysis of various ciphers such as RSA ...
Added: May 9, 2023
Stepan L. Kuznetsov, Journal of Logic and Computation 2023 Vol. 33 No. 6 P. 1437–1462
We prove undecidability and pinpoint the place in the arithmetical hierarchy for commutative action logic, i.e. the equational theory of commutative residuated Kleene lattices (action lattices), and infinitary commutative action logic, the equational theory of *-continuous commutative action lattices. Namely, we prove that the former is Σ01�10-complete and the latter is Π01�10-complete. Thus, the situation is the ...
Added: March 7, 2023
Faliszewski P., Karpov A., Obraztsova S., Autonomous Agents and Multi-Agent Systems 2022 Vol. 36 Article 18
We analyze the complexity of several NP-hard election-related problems under the assumptions that the voters have group-separable preferences. We show that under this assumption our problems typically remain NP-hard, but we provide more efficient algorithms if additionally the clone decomposition tree is of moderate height. We also show a polynomial-time algorithm for sampling group-separable elections uniformly at ...
Added: March 14, 2022
Sergei Valentinovich Fedorenko, IEEE Access 2021 Vol. 9 P. 38673–38686
A novel method for finding roots of polynomials over finite fields has been proposed.
This method is based on the cyclotomic discrete Fourier transform algorithm.
The improvement is achieved by using the normalized cyclic convolutions,
which have a small complexity and allow matrix decomposition,
as well as methods of adapting the truncated normalized cyclic convolutions calculation.
For small values of ...
Added: April 15, 2021
Kuznetsov S., , in: Logic, Language, and Security. Essays Dedicated to Andre Scedrov on the Occasion of His 65th BirthdayIssue 12300.: Cham: Springer, 2020. P. 3–16.
Infinitary action logic is an extension of the multiplicative-additive Lambek calculus with Kleene iteration, axiomatized by an 𝜔-rule. Buszkowski and Palka (2007) show that this logic is \(\Pi^0_1\)-complete. As shown recently by Kuznetsov and Speranski, the extension of infinitary action logic with the exponential modality is much harder: \(\Pi^1_1\)-complete. The raise of complexity is of ...
Added: November 25, 2020
Shitov Y., Fuzzy Sets and Systems 2020 Vol. 382 P. 165–171
Matrix factorization problems over various semirings naturally arise in different contexts of modern pure and applied mathematics. These problems are very hard in general and cause computational difficulties in applications. We give a survey of what is known on the algorithmic complexity of Boolean, tropical, nonnegative, and positive semidefinite factorizations, and we examine the behavior ...
Added: November 11, 2020
Maksaev A., Записки научных семинаров ПОМИ РАН 2019 Т. 482 С. 231–243
В настоящей работе доказано, что при λ > 1 аддитивное отображение, строго сохраняющее множество λ-скрамблинг матриц над полукольцом B, является биекцией. Охарактеризован общий вид такого отображения над любым антинегативным коммутативным полукольцом с единицей и без делителей нуля. ...
Added: October 30, 2020
Maksaev A., Journal of Mathematical Sciences 2020 Vol. 249 No. 2 P. 263–270
In this paper, it is proved that for λ > 1, an additive map that strongly preserves the set of λ-scrambling matrices over the Boolean semiring B is a bijection. The general form of such a map over any antinegative commutative semiring with identity and without zero divisors is characterized. ...
Added: October 30, 2020
Guterman A., Maksaev A., Fundamenta Informaticae 2018 Vol. 162 No. 2-3 P. 119–141
The notion of scrambling index was firstly introduced by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every pair of vertices u and v of D there exist two directed paths of lengths k to a common vertex w. This notion ...
Added: October 30, 2020