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On a Construction of Easily Decodable Sub-de Bruijn Arrays
Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций"). 2019. Vol. 13. No. 2. P. 280–289.
Makarov D., Yashunsky A.
We consider the two-dimensional generalizations of de Bruijn sequences; i.e., the integer-valued arrays whose all fragments of a fixed size (windows) are different. For these arrays, dubbed sub-de Bruijn, we consider the complexity of decoding; i.e., the determination of a position of a window with given content in an array. We propose a construction of arrays of arbitrary size with arbitrary windows where the number of different elements in the array is of an optimal order and the complexity of decoding a window is linear.
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 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
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
Yerbolova A. S., Tomashchuk K., Kogan A. et al., Complexity 2026 Vol. 2026 No. 1 Article 5519690
Tis paper presents a novel approach to analyzing and grouping natural languages based on the degree of their chaoticity. It clusters 52 languages from 18 language families, according to the value of the entropy–complexity pair, to reveal the chaotic properties of semantic trajectories. Te obtained clusters appear to be closely correlated with the family of ...
Added: February 16, 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
Speranski S. O., Journal of Logic and Computation 2013 Vol. 23 No. 5 P. 1035–1055
In the present article, the quantifiers over propositions are first introduced into the language for reasoning about probability, then the complexity issues for validity problems dealing with the corresponding hierarchy of probabilistic sentences are investigated. We prove, among other things, the $\Pi^1_1$-completeness for the general validity and also indicate the least level in the hierarchy ...
Added: December 27, 2025
Speranski S. O., Computability 2015 Vol. 4 No. 2 P. 159–174
Added: December 27, 2025
Speranski S. O., Studia Logica 2017 Vol. 105 No. 2 P. 407–429
The paper contains a survey on the complexity of various truth hierarchies arising in Kripke’s theory. I present some new arguments, and use them to obtain a number of interesting generalisations of known results. These arguments are both relatively simple, involving only the basic machinery of constructive ordinals, and very general. ...
Added: December 26, 2025
Kuznetsov S., Speranski S. O., Annals of Pure and Applied Logic 2022 Vol. 173 No. 2 Article 103057
We introduce infinitary action logic with exponentiation — that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allow some of the structural rules (contraction, weakening, permutation). The logic is presented in the form of an infinitary sequent calculus. We prove cut elimination and, in the case ...
Added: December 26, 2025
Kuznetsov S., Speranski S. O., Studia Logica 2023 Vol. 111 No. 2 P. 251–280
Infinitary action logic can be naturally expanded by adding exponential and subexponential modalities from linear logic. In this article we shall develop infinitary action logic with a subexponential that allows multiplexing (instead of contraction). Both non-commutative and commutative versions of this logic will be considered, presented as infinitary sequent calculi. We shall prove cut admissibility ...
Added: December 26, 2025
Speranski S. O., Logic Journal of the IGPL 2025 Vol. 33 No. 2 Article jzae042
This paper is concerned with a two-sorted probabilistic language, denoted by QPL, which contains quantifiers over events and over reals, and can be viewed as an elementary language for reasoning about probability spaces. The fragment of QPL containing only quantifiers over reals is a variant of the well-known ‘polynomial’ language from [Fagin et al. 1990, Section 6]. ...
Added: December 26, 2025
Speranski S. O., Logic Journal of the IGPL 2025 Vol. 33 No. 3 Article jzae114
We shall be concerned with two natural expansions of the quantifier-free ‘polynomial’ probability logic of [Fagin et al. 1990]. One of these, denoted by QPL-e, is obtained by adding quantifiers over arbitrary events, and the other, denoted by p-QPL-e, uses quantifiers over propositional formulas — or equivalently, over events expressible by such formulas. The earlier proofs ...
Added: December 26, 2025
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Логвиненко Т. И., Стрельцова А. В., Otstavnov N. et al., Вопросы образования 2025 № 2 С. 101–141
The aim of this article is to review empirical studies, meta-analyses and systematicreviews on educational interventions for developing and improving reading compre-hension in adolescents, including both typically developing readers and those ex-periencing reading difficulties. We distinguish seven intervention types aimed at im-proving reading comprehension, each targeting different components as the basisfor intervention: decoding and reading ...
Added: December 11, 2025