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Counting the Number of Perfect Matchings, and Generalized Decision Trees
Problems of Information Transmission. 2021. Vol. 57. No. 2. P. 143–160.
We consider a generalization of the Pólya–Kasteleyn approach to counting the number of perfect matchings in a graph based on computing the symbolic Pfaffian of a directed adjacency matrix of the graph. Complexity of algorithms based on this approach is related to the complexity of the sign function of a perfect matching in generalized decision tree models. We obtain lower bounds on the complexity of the sign of a perfect matching in terms of the deterministic communication complexity of the XOR sign function of a matching. These bounds demonstrate limitations of the symbolic Pfaffian method for both the general case and the case of sparse graphs.
Priority areas:
IT and mathematics
Language:
English
Publication based on the results of:
Ivanashev Y., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2026 Т. 529 С. 93–101
Язык L является нижним для релятивизируемого сложностного класса C, если CL=C. Для классов #P, GapP и SpanP известны точные нижние классы языков: Low(#P) = UP ∩ coUP, Low(GapP) = SPP и Low(SpanP) = NP ∩ coNP. В этой статье мы доказываем, что Low(TotP) = P, и приводим характеризации нижних классов функций для #P, GapP, TotP ...
Added: September 28, 2026
Piliugin L., Antropov A., Lobashev E. et al., Journal of Nuclear Materials 2026 Vol. 632 Article 156876
The effects of dislocations on the mobility of gas nanobubbles pinned to them are considered as novel unex- plored mechanisms of accelerated fission gas release and investigated using classical molecular dynamics of helium bubbles in FCC aluminum. Non-equilibrium methods are developed to calculate the mobility of a pinned bubble both along and across the dislocation ...
Added: September 28, 2026
Kashpurovich I., Oleynichenko A., Stegailov V., Supercomputing Frontiers and Innovations 2026 Vol. 13 No. 1 P. 52–73
We report a high-performance implementation of the resolution-of-the-identity Hartree–Fock method that fully exploits the permutational symmetry of three-center electron repulsion integrals (ERI). The present implementation adopts a hybrid MPI+OpenMP parallelization strategy. Two different algorithmic approaches (with and without the pre-transformation of ERIs) are compared. A custom data layout introduced previously is employed. Designed to efficiently ...
Added: September 28, 2026
Teregulov T., Loubenets E. R., / Series Quantum Physics "arXiv". 2026. No. 2609.31472.
We develop a new three-party quantum secret-sharing (QSS) protocol based on a three-qubit W state. This protocol encodes the secret-sequence bits using X gates and employs randomly selected Hadamard operations and measurement bases to generate information and security-test rounds. We evaluate the efficiency of the proposed protocol and analyze its security against an internal adversary ...
Added: September 28, 2026
Silakov D., Системный администратор 2026 С. 84–89
Social media users rarely think about what lies behind the beautiful facade of activity feeds, teeming with photos and video stories. However, the widespread popularity of such platforms generates a huge amount of all sorts of content that needs to be stored, processed quickly, and displayed, and in the era of AI, it also needs ...
Added: September 28, 2026
Prokhorov A., Wei Z., Sang H. et al., Journal of Productivity Analysis 2026 Vol. 65 P. 1–16
The stochastic frontier model (SFM) is widely employed in the analysis of productivity and efficiency, yet strict parametric forms, such as the Cobb-Douglas and Translog functions, are often assumed for modeling production, leading to potential misspecification issues. While semi- and nonparametric SFMs offer greater flexibility, they face challenges in imposing monotonicity and concavity to maintain ...
Added: September 28, 2026
Guterman A., Jonoska N., Kreines E. et al., Proceedings of the Edinburgh Mathematical Society 2026 Vol. 69 No. 3 P. 1041–1057
We provide four equivalent combinatorial conditions for a simple assembly graph (rigid vertex graph where all vertices are of degree 1 or 4) to have the largest number of Hamiltonian sets of polygonal paths relative to its size. These conditions serve to prove the conjecture that such a maximum, which is equal to 𝐹_(2𝑛+1) −1, ...
Added: September 27, 2026
Qian X., Guan X., Zhang B. et al., Journal of Global Optimization 2026
Inverse quickest path problem on networks ...
Added: September 27, 2026
Shishkina E., Современная математика. Фундаментальные направления 2026 Т. 72 № 1 С. 52–67
In this paper, we construct a weighted Sobolev space of fractional order based on the
generalized Bessel potential.We apply these results to the analysis of the singular fractional Schr¨odinger
equation. To solve the Cauchy problem for this equation, we prove an estimate that relates the norm of
the solution to the norm of the initial condition in the ...
Added: September 26, 2026
Shishkina E., Computational Mathematics and Mathematical Physics 2026 Vol. 66 No. 5 P. 804–815
This article demonstrates that the Laplace–Bessel operator generates a strongly continuous
semigroup on a weighted Lebesgue space. Using this semigroup, we define the fractional Laplace–
Bessel operator via Balakrishnan’s formula. Furthermore, we derive three distinct representations for
fractional powers of the negative Laplace–Bessel operator. ...
Added: September 26, 2026
Kolokoltsov V., Shishkina E., Journal of Theoretical Probability 2026 P. 39–83
In this paper, we introduce a new construction of fractional derivatives and integrals
with respect to a function, based on a matrix approach. We believe that this is a powerful
tool in both analytical and numerical calculations.We begin with the differential
operator with respect to a function that generates a semigroup. By discretizing this
operator, we obtain a matrix ...
Added: September 26, 2026
Switzerland: Springer Cham, 2026.
This volume gathers selected, peer-reviewed contributions presented at the 19th Conference of the International Federation of Classification Societies (IFCS 2026), held on 14–16 July 2026 in Milan, Italy. Reflecting the volume’s motto, Navigating Complexity – Statistical Methods, Data Analysis, and Machine Learning for Actionable Insights, the papers showcase modern methodologies and real-world applications designed to extract ...
Added: September 25, 2026
Petr Kucheriaviy, Bulletin of the Australian Mathematical Society 2026
We prove that an analogue of Rogers’ theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals. ...
Added: September 25, 2026
Kraevskiy A., Sokolovskiy E., Prokhorov A., Emerging Markets Review 2026 No. 74 P. 1–19
Financial markets of emerging economies are vulnerable to extreme and cascading information spillovers, surges, sudden stops and reversals. With this in mind, we develop a new online early warning system (EWS) to detect what is referred to as ‘concept drift’ in machine learning, as a ‘regime shift’ in economics and as a ‘change-point’ in statistics. ...
Added: September 25, 2026
Пелевин Ф. Е., Математические заметки 2026 Т. 120 № 1 С. 159–163
Две не равные тождественно нулю функции (последовательности элементов некоторого поля) будем называть эквивалентными, если они удовлетворяют функциональному уравнению типа теорем сложения тэта-функций. Основной результат работы состоит в том, что рассматриваемое отношение действительно является отношением эквивалентности. ...
Added: September 25, 2026
Shimanogov I. N., Vyalyi M., Siberian Mathematical Journal 2026 Vol. 67 No. 5 P. 1203–1212
We consider a class of Boolean algebras formed by intersections of regular languages with
a given language. In the case where such an algebra is isomorphic to the algebra of regular languages,
we prove the existence of an isomorphism that is computable using oracles for the regular realizability
problem and the infinite regular realizability problem. This result yields ...
Added: September 25, 2026
Дубич Е. В., Schagin D., Славянский форум 2026 № 2 (52) С. 560–565
The paper compares HTTP/2 and HTTP/3 for static resource transfer under software-simulated network degradation. The experiment shows that HTTP/3 is not universally faster, but it is more stable as latency and packet loss increase. ...
Added: September 25, 2026
Ramazanov I., Bukh A., Shepelev Igor A., Chaos 2026 No. 36 P. 083150–083150
We investigate how stochastic Poisson impulsive forcing influences the spatiotemporal dynamics of a two-dimensional network of Hindmarsh–Rose neurons. Unlike continuous noise, impulsive forcing introduces discrete, state-dependent perturbations, making the system response highly sensitive to both the statistics and the spatial structure of the input. In most of the parameter space, stochastic impulses destabilize the initial ...
Added: September 24, 2026
Shabanov N., Kuricheva O., Kurbatova J. et al., / Series Working Papers SSRN "Department of Economics Ca’ Foscari University of Venice". 2026.
The carbon balance of an ecosystem is the difference between Gross Primary Productivity (GPP) and Ecosystem Respiration (Reco) as expressed by Net Ecosystem Exchange (NEE). While remote sensing retrievals of GPP have reached maturity, Reco estimation remains underexplored and ultimately cast bias on NEE. Here we present an end-to-end multi-scale analysis of the mechanism of ...
Added: August 21, 2026
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
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
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
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