?
Chaotic time series prediction with employment of ant colony optimization
Expert Systems with Applications. 2012. Vol. 39. No. 9. P. 8474–8478.
Gromov V., Shulga A.
In this study, the novel method to predict chaotic time series is proposed. The method employs the ant colony optimization paradigm to analyze topological structure of the attractor behind the given time series and to single out the typical sequences corresponding to the different part of the attractor. The typical sequences are used to predict the time series values. The method was applied to time series generated by the Lorenz system, the Mackey–Glass equation, and weather time series as well. The method is able to provide robust prognosis to the periods comparable with the horizon of prediction.
Highlights
► Novel method based on ant colony optimization to predict chaotic series is proposed. ► The method allows forecast series for periods comparable with horizon of prognosis. ► The method was tested by standard benchmarks (Lorenz system, Mackey–Glass equation). ► The method allows extract parts of series bad and good for prognosis.
Language:
English
Springer Singapore (Singapore), 2024.
Included in the following conference series:
INdAM: INdAM Meeting: Kolmogorov Operators and their Applications Workshop
Conference proceedings info: INdAM 2022
Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields.
This volume collects a selection of the talks given at the Cortona meeting by ...
Added: July 17, 2026
Veretennikov A., Pascucci A., Rondelli A., Stochastic Processes and their Applications 2026 Vol. 199 Article 104978
We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural conditions, we also establish results concerning both weak and strong well-posedness. ...
Added: July 17, 2026
Veretennikov A., Ляппиева А. А., Теория вероятностей и ее применения 2026 Т. 71 № 2 С. 295–304
Установлен новый результат о сильной единственности для многомерного СДУ с невырожденной диффузией и частично нерегулярным сносом. Его можно рассматривать как комбинированный вариант на темы Ямада и Ватанабэ (1971), Звонкина (1974) и первого автора настоящей статьи (1980). ...
Added: July 17, 2026
Veretennikov A., Нуриева А. И., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 525 С. 24–30
Предложено новое достаточное условие в задаче о центральной предельной теореме в схеме серий для неоднородных цепей Маркова, с возможностью того, что минимум эргодического коэффициента Маркова–Добрушина может быть ближе к нулю, чем в основном условии Добрушина. ...
Added: July 17, 2026
О частных производных модифицированных полиномов Бернштейна–Станку для функций нескольких переменных
Veretennikov A., Мазутский Н. М., Математический сборник 2025 Т. 216 № 7 С. 3–27
Целью работы является доказательство аппроксимации смешанных производных второго порядка для функции нескольких переменных в норме L1 такими же производными модифицированных полиномов Бернштейна–Станку при минимальной возможной регулярности. ...
Added: July 17, 2026
Ахмярова А. Т., Veretennikov A., Теория вероятностей и ее применения 2025 Т. 70 № 2 С. 211–227
В работе предложены новые версии слабого закона больших чисел (ЗБЧ) для слабо зависимых слагаемых (вообще говоря, разнораспределенных) как при наличии математического ожидания каждого из них, так и без такового. Одним из основных условий в первом из трех рассматриваемых случаев, в котором развиваются идеи из статьи Ю. Ш. Чау 1971 г., является равномерная интегрируемость слагаемых по Чезаро в духе работ по ЗБЧ для ...
Added: July 17, 2026
Veretennikov A., Stochastics and Dynamics 2024
A new weak existence result for degenerate multi-dimensional stochastic McKean–Vlasov equation is established under relaxed regularity conditions. ...
Added: July 17, 2026
Ахмярова А. Т., Veretennikov A., Теория вероятностей и ее применения 2024 Т. 69 № 3 С. 427–438
Предложен новый вариант усиленного закона больших чисел для попарно независимых случайных величин. Основная цель — ослабить требование существования математического ожидания каждого из слагаемых. Предположение о попарной независимости также ослаблено. ...
Added: July 17, 2026
Veretennikov A., Moscow Mathematical Journal 2024 Vol. 24 No. 1 P. 107–124
Second order recurrence are established for a d-dimensional diffusion with an additive Wiener process, with switching, and with one recurrent and one transient regime and constant switching intensities, under suitable conditions. As a corollary, the rate of convergence towards the invariant regime of order t^{−2} is claimed. The approach is based on embedded Markov chains ...
Added: July 16, 2026
Veretennikov A., Mathematics 2023 Vol. 11 No. 21 Article 4514
Positive recurrence for a single-server queueing system is established under generalized service intensity conditions, without the assumption of the existence of a service density distribution function, but with a certain integral type lower bound as a sufficient condition. Positive recurrence implies the existence of the invariant distribution and a guaranteed slow convergence to it in ...
Added: July 16, 2026
Veretennikov A., Markov Processes and Related Fields 2023 Vol. 23 No. 2 P. 259–294
The ergodic Bellman's (HJB) equation is proved for a one-dimensional controlled diffusion with switching with variable diffusion and drift coefficients both depending on control; the intensities of transitions of the discrete component are constant. Its existence and uniqueness is established. Also, the convergence of the reward iteration improvement algorithm is established to the cost constant ...
Added: July 16, 2026
Михайлов И. А., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 1 Article 8
Whole-slide histology images (WSIs) can exceed 100 k × 100 k pixels, making direct pixel-level segmentation infeasible and requiring patch-level classification as a practical alternative for downstream WSI segmentation. However, most approaches either treat patches independently, ignoring spatial and biological context, or rely on deep graph models prone to oversmoothing and loss of local tissue ...
Added: July 16, 2026
On recurrence, convergence and mixing rate for generalised Wright - Fisher's diffusion with mutation
Veretennikov A., Sineokiy R., Markov Processes and Related Fields 2023 Vol. 23 No. 2 P. 241–258
Generalised one-dimensional Fisher -- Wright diffusion process with mutations is consiedered. This is a well-known model in populational genetics. The goal of the paper is an exponential recurrence of the process, which also implies exponential rate of convergence towards the invariant measure. ...
Added: July 16, 2026
Veretennikov A., Mathematics 2023 Vol. 11 No. 14 Article 3096
Polynomial recurrence bounds for a class of stochastic differential equations with a rotational symmetric gradient type drift and an additive Wiener process are established, as well as certain a priori moment inequalities for solutions. The key feature of this paper is that the approach does not use Lyapunov functions because it is not clear how ...
Added: July 16, 2026
Kuninets A., Malygina E., Leevik A. G. et al., Journal of Computer Virology and Hacking Techniques 2026 No. 22 Article 62
In this work, we investigate the application of Barnes–Wall lattices in post-quantum cryptographic schemes. We survey and analyze several constructions of Barnes–Wall lattices, including subgroup chains, the generalized k-ing construction, and connections with Reed-Muller codes, highlighting their equivalence over both Z[i] and Z. Building on these structural insights, we introduce a new algorithm for efficient ...
Added: July 16, 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
Zapryagaev A., Pahomov F., Logic Journal of the IGPL 2026 Vol. 34 No. 4 Article 12
We prove the linear orders first-order definable in the standard model (Z;<,+) of Presburger arithmetic are exactly those that are (Z;<,+)-definably embeddable into the lexicographic ordering on Z^n for some n. ...
Added: July 16, 2026
Veretennikov A., Veretennikova M., Reliability: Theory & Applications 2022 Vol. 17 No. 3(69) P. 273–291
A simple model of the new notion of ``Markov up'' processes is proposed; its positive recurrence and ergodic properties are shown under the appropriate conditions. ...
Added: July 16, 2026
Veretennikov A., Stochastics and Partial Differential Equations: Analysis and Computations 2022 Vol. 10 P. 1165–1179
Positive recurrence of a $d$-dimensional diffusion with an additive Wiener process, with switching and with one recurrent and one transient regimes and variable switching intensities is established under suitable conditions. The approach is based on embedded Markov chains. ...
Added: July 15, 2026
Veretennikov A., Queueing Systems 2022 Vol. 100 No. 3-4 P. 357–359
B.A. Sevastyanov's result about Erlang telephone station problem has been extended in several publications. In this short note one open question about this model has been discussed. The whole volume was devoted mainly to open problems related to the name of Erlang. ...
Added: July 15, 2026
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 No. 1 P. 014217–014217
This study investigates the dynamical origins and statistical properties of extreme events (EEs) in a diffusively coupled theoretical Brusselator system, extending from pairwise interactions to globally coupled networks. Statistically, the emergence of EEs is characterized by heavy-tailed probability density functions and exponential interevent interval distributions, alongside an analysis of the complementary cumulative distribution function and ...
Added: July 15, 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