?
О некоторых перечислительных задачах лямбда-исчисления
Записки научных семинаров ПОМИ РАН. 2018. Т. 475. С. 99–121.
The article considers combinatorial problems associated with the enumeration of lambda-terms in a untyped lambda calculus, as well as in simply typed systems with a single atom in the style of Church. For the case of untyped lambda calculus a system of equations for generating functions is constructed which describes the number of lambda terms. In the case of typed lambda calculus, both the inhabited types and the simplest inhabitants in them are enumerated.
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
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
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 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
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
Taletskii D., Математический сборник 2023 Т. 214 № 11 С. 133–156
Сформулирована следующая гипотеза: если средняя степень вершин графа не превосходит натурального числа k ⩾ 1, то количество его k-доминирующих множеств не превосходит количества его независимых множеств, при этом равенство возможно, если и только если граф является k-регулярным. Эта гипотеза доказана для случая k ∈ {1,2}. ...
Added: November 2, 2023
Петренко А. А., Suvorov A., Шаякбаров Н. Ф., Пермь: Издательство Пермского национального исследовательского политехнического университета, 2022.
Рассмотрены вопросы, касающиеся языков функционального программирования: особенности применения, синтаксис, функции. Приведено большое количество содержательных примеров решения задач, демонстрирующих возможности языков функционального программирования.
Предназначено студентам образовательных учреждений высшего образования, обучающимся по специальностям направлений «Информатика и вычислительная техника», «Программная инженерия», а также лицам, самостоятельно изучающим функциональное программирование. ...
Added: October 25, 2022
Ignatov D. I., Yakovleva A., , in: Proceedings of the 9th International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI 2021)Vol. 2972.: CEUR-WS, 2021. P. 87–98.
In this paper we study certain properties of the GreConD algorithm for Boolean matrix factorisation, a popular technique in Data Mining with binary relational data. This greedy algorithm was inspired by the fact that the optimal number of factors for the Boolean matrix factorisation can be chosen among the formal concepts of the correspond- ing ...
Added: November 1, 2021
Gribanov D., Zolotykh N., Optimization Letters 2022 Vol. 16 No. 7 P. 1991–2018
Let a polyhedron $P$ be defined by one of the following ways:
\begin{enumerate}
\item[(i)] $P = \{x \in \RR^n \colon A x \leq b\}$, where $A \in \ZZ^{(n+k) \times n}$, $b \in \ZZ^{(n+k)}$ and $\rank A = n$,
\item[(ii)] $P = \{x \in \RR_+^n \colon A x = b\}$, where $A \in \ZZ^{k \times n}$, $b \in \ZZ^{k}$ ...
Added: October 29, 2021
Краско Е. С., Лабутин И. Н., Moskvin D. et al., Journal of Mathematical Sciences 2020 Vol. 247 P. 442–456
Combinatorial problems related to the enumeration of lambda terms in the untyped lambda calculus and in the Church-style simply typed lambda calculus with a single atom are considered. For the case of untyped lambda calculus, a system of equations for generating functions that enumerate lambda terms is derived. For the typed lambda calculus, the inhabited ...
Added: October 26, 2021
Harnad J., Runov B. A., Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions 2021 Vol. 8 No. 1 P. 119–158
Weighted constellations give graphical representations of weighted branched coverings of the Riemann sphere. They were introduced to provide a combinatorial inter-pretation of the 2D Toda τ-functions of hypergeometric type serving as generating functions for weighted Hurwitz numbers in the case of polynomial weight generating functions. The product over all vertex and edge weights of a ...
Added: October 21, 2021
Gravin N., Pasechnik D., Shapiro B. et al., Analysis and Mathematical Physics 2018 Vol. 8 No. 2 P. 255–287
We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P subset of R-d is a rational function. Its denominator is the product of linear forms dual to the vertices of P raised to the power equal to the degree of the ...
Added: February 25, 2021
Mazalov V. V., V. V. Gusev, Performance Evaluation 2020 Vol. 144 P. 102135
We consider a cooperative game based on a network in which nodes represent players
and the characteristic function is defined using a maximal covering by the pairs of
connected nodes. Problems of this form arise in many applications such as mobile
communications, patrolling, logistics and sociology. The Owen value, which describes
the significance of each node in the network, ...
Added: September 29, 2020
Zykov S. V., Шумский Л. Д., Тарасов И. Е., Cloud of Science 2018 Т. 5 С. 704–712
В работе исследуются типичные сценарии, при которых возникает потребность совместного использования ограниченных общесистемных ресурсов несколькими виртуальными машинами. Разработаны правила балансировки нагрузки в зависимости от информационных процессов, выполняемых виртуальными машинами. Вычисление производительности рассмотренных операций основано на типизированной модели, что дает возможность оценки общей производительности. ...
Added: November 3, 2019
Zykov S. V., Шумский Л. Д., Тарасов И. Е., Cloud of Science 2018 Т. 5 № 4 С. 711–720
This paper examines typical scenarios that require limited system resources shared by several virtual machines. Load balancing rules were developed; these are dependent on the information processes performed by the virtual machines. The productivity of these operations is based on types that allow assessment of the entire system productivity. ...
Added: January 30, 2019
Dolgorukov V., Kopylova A. O., Логические исследования 2018 Т. 24 № 2 С. 36–58
This paper focuses on the connection between “four-category ontologies” (which are based on Aristotle’s ontological square) and modern type-theoretical semantics. Four- category ontologies make a distinction between four types of entities: substantial universals, substantial particulars, accidental universals and accidental particulars. According to B. Smith, “fantology is a doctrine to the effect that the key to ...
Added: September 26, 2018