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Optimal monomial quadratization for ODE systems: extended abstract
ACM Communications in Computer Algebra. 2021. Vol. 54. No. 3. P. 119–123.
Bychkov A., Pogudin G.
Transformation of a polynomial ODE system to a special quadratic form has been successfully used recently as a preprocessing step for model order reduction methods. However, to the best of our knowledge, there has been no practical algorithm for performing this step automatically with any optimality guarantees.
We present an algorithm that, given a system of polynomial ODEs, finds a transformation into a quadratic ODE system by introducing new variables which are monomials of the original variables. The algorithm is guaranteed to produce an optimal transformation of this form. The algorithm is implemented, and we demonstrate it on examples from the literature.
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Stepanyants V., Andrey V. Fizulin, Chibirov A. et al., FUTURE TRANSPORTATION 2026 Vol. 6 No. 5 Article 225
Reliable Vehicle-to-Everything (V2X) evaluation requires propagation models that represent terrain and multilevel infrastructure. Most integrated vehicular simulators still rely on planar models, but the magnitude of the resulting bias is unclear. This study quantitatively compares flattened two-dimensional (2D) and terrain-aware three-dimensional (3D) variants of three scenarios using identical Sionna RT settings. The pipeline combines OpenStreetMap ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Groshev Maksim, Rybakov Petr, Teterin N. et al., Sensors 2026 Article 6171
Manual assessment of soybean yield components, such as pod number, is laborious, time-consuming, and subjective. Existing computer-vision approaches based on object detection or instance segmentation perform poorly on close-range RGB imagery of soybean canopies due to severe occlusions, ambiguous plant boundaries, and the high cost of bounding-box annotation. To address these challenges, we propose a ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Томск: Издательство Томского государственного университета, 2026.
Материалы сборника Шестнадцатой Международной конференции «Новые информационные
технологии в исследовании сложных структур» (Москва, 21–25 сентября 2026 г.) ориентированы на
широкий круг специалистов, работающих на стыке теории информации, системного анализа и
прикладных предметных областей. В издание вошли результаты исследований, посвящённые
моделированию дискретных и стохастических структур управления и связи, разработке
высокопроизводительных вычислительных и телекоммуникационных систем, а также вопросам
цифровой трансформации образования, архитектурно-градостроительного проектирования,
экологического ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Серебренников Д. А., Belov A. V., Информационные технологии и вычислительные системы 2026 № 3 С. 157–169
В условиях роста стоимости энергоресурсов и необходимости повышения энергоэффективности производственных процессов особую актуальность приобретает задача оптимизации энергопотребления промышленных предприятий. В данной работе рассматривается подход к управлению энергозатратами машиностроительного предприятия на основе методов многокритериальной оптимизации. Постановка задачи включает несколько целевых функций: минимизацию энергопотребления, минимизацию стоимости электроэнергии с учётом тарифных ограничений и максимизацию производственной эффективности. Для решения ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Zykov S. V., Уфимцев Г. А., Моделирование, оптимизация и информационные технологии 2026 Т. 14 № 8 С. 1–13
Информационные системы формируют большие объёмы событийных журналов, которые используются для анализа работы приложений и сервисов. При этом события могут поступать в аналитический контур позже момента их фактического возникновения и не в исходном порядке. Такая рассинхронизация приводит к ошибкам при построении агрегированных временных показателей, а регулярный полный пересчёт многомерного аналитического куба требует значительных вычислительных затрат. Целью ...
Added: October 2, 2026
Belova T., Dementiev Y., Fomin F. et al., , in: 27th European Conference on Artificial Intelligence, 19–24 October 2024, Santiago de Compostela, Spain – Including 13th Conference on Prestigious Applications of Intelligent Systems (PAIS 2024)Vol. 392.: IOS Press, 2024. P. 3461–3468.
Added: October 24, 2024
Vladlena D. Markvirer, Ekaterina A. Karnaukhova, , in: 023 International Conference on Quality Management, Transport and Information Security, Information Technologies (IT&QM&IS).: Petrozavodsk: IEEE, 2023. P. 152–155.
This article presents an overview of the main algorithms used in resource distribution problems. The description, input and output data, as well as peculiarities and complexity of these algorithms are considered. The paper proposes a modified algorithm for finding vapor combinations in a graph, which allows solving the problem of optimal load distribution between the ...
Added: December 25, 2023
Anoshin V. I., Beketova A., Parusnikova A. et al., Computational Mathematics and Mathematical Physics 2023 Vol. 63 No. 1 P. 86–95
The second member of the fourth Painlevé hierarchy is considered. Convergence of certain power asymptotic expansions in a neighborhood of zero is proved. New families of power asymptotic expansions are found. Computations are carried out using a computer algebra system. Reference to a code that can be used for computing the Gevrey order of the ...
Added: March 30, 2023
Association for Computing Machinery (ACM), 2021.
The International Symposium on Symbolic and Algebraic Computation (ISSAC) is the premier conference for research in symbolic computation and computer algebra. ISSAC is the continuation of conferences with the names SYMSAC, EUROCAL, EUROSAM, and EUROCAM, which have alternated between North America and Europe before merging into ISSAC. The whole series started in 1966 with the ...
Added: September 27, 2021
Open Publishing Association, 2021.
This volume contains papers presented at the Ninth International Symposium on Symbolic Computation in Software Science, SCSS 2021.
Symbolic Computation is the science of computing with symbolic objects (terms, formulae, programs, representations of algebraic objects, etc.). Powerful algorithms have been developed during the past decades for the major subareas of symbolic computation: computer algebra and computational ...
Added: September 23, 2021
Maslov V. P., Mathematical notes 2021 Vol. 109 No. 2 P. 241–246
In this article, the notions of tropical mathematics and subtropical mathematics are studied. The main principles of tropical analysis and examples of their application to various problems are considered. ...
Added: February 7, 2021
Springer, 2020.
This book constitutes the proceedings of the 15th International Computer Science Symposium in Russia, CSR 2020, held in Yekaterinburg, Russia, in June 2020.
The 25 full papers and 6 invited papers were carefully reviewed and selected from 49 submissions. The papers cover a broad range of topics, such as: algorithms and data structures; computational complexity, including ...
Added: September 4, 2020
NY: ACM, 2018.
The International Symposium on Symbolic and Algebraic Computation (ISSAC) is the premier conference for research in symbolic computation and computer algebra. ISSAC 2018, to be held at the City University of New York, New York City, USA, is the 43rd meeting in this series. The series has been held annually since 1981. ISSAC is sponsored ...
Added: November 1, 2019
Springer, 2019.
Added: August 4, 2019
Anna Presnova, Valery Afanas'ev, , in: IFAC-PapersOnLineVol. 51. Issue 32.: Editions Elsevier, 2018. Ch. 45 P. 428–433.
The problem of optimal control is formulated for a class of nonlinear objects that can be represented as objects with a linear structure and parameters that depend on the state. The linear structure of the transformed nonlinear system and the quadratic functional of quality allow for the synthesis of optimal control, i.e. parameters of the ...
Added: November 4, 2018
Springer, 2018.
This book constitutes the refereed post-conference proceedings of the 29th International Workshop on Combinatorial Algorithms, IWOCA 2018, held in Singapore, Singapore, in July 2018. The 31 regular papers presented in this volume were carefully reviewed and selected from 69 submissions. They cover diverse areas of combinatorical algorithms, complexity theory, graph theory and combinatorics, combinatorial optimization, ...
Added: October 23, 2018