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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.
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
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
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
A. Omelchenko, Meshkov V., Petrov M. et al., Moscow Mathematical Journal 2010 Vol. 10 No. 3 P. 611–628
Exponential generating functions for the Dyck and Motzkin triangles are constructed for various assignments of multiplicities to the arrows of these triangles. The possibility to build such a function provided that the generating function for paths that end on the axis is a priori unknown is analyzed. Asymptotic estimates for the number of paths are ...
Added: August 30, 2018
Avdoshin S. M., Набебин А. А., М.: ДМК Пресс, 2019.
The book contains the necessary information from the algorithm theory, graph theory, combinatorics. It is considered partially recursive functions, Turing machines, some versions of the algorithms (associative calculus, the system of substitutions, grammars, Post's productions, Marcov's normal algorithms, operator algorithms). The main types of graphs are described (multigraphs, pseudographs, Eulerian graphs, Hamiltonian graphs, trees, bipartite ...
Added: August 24, 2018