?
The exact solution of the mutator model with directed mutations, linear fitness function, and finite genome length
Chinese Journal of Physics. 2018. Vol. 56. No. 5. P. 2235–2240.
Yakushkina T., Saakian D.
In this study, we considered the model by Beckman and Loeb [Proc. Natl. Acad. Sci. U.S.A. 103 (2006) 14140] for the mutator phenomena. We construct an infinite population Crow-Kimura model with a mutator gene, directed mutations, a linear fitness function, and a finite genome length. We solved analytically the dynamics of the model using the generating function method. Such models provide realistic predictions for finite population sizes and have been widely discussed recently. The analytical formulas provided can be used to calculate the advantage of the mutator mechanism for the accumulation of mutations in cancer biology.
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
ООО "Издательство Юрайт ", 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
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
Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
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
Anfisa V. Popova, Bykova D., Fedonin G. et al., Molecular Biology and Evolution 2025 Vol. 42 No. 11 Article msaf264
Many Mycobacterium tuberculosis (MTB) genome sites experience different selective forces depending on whether a patient is treated with antibiotics. Here, we searched for pairs of such sites that evolve interdependently. We reconstructed the phylogeny of more than 11,000 MTB clinical isolates with known phenotypes for at least one of 13 antitubercular drugs. By analyzing the ...
Added: November 18, 2025
Popova A., Neverov A. D., Nature Communications 2020 Vol. 11 Article 4603
Amino acid propensities at a site change in the course of protein evolution. This may happen for two reasons. Changes may be triggered by substitutions at epistatically interacting sites elsewhere in the genome. Alternatively, they may arise due to environmental changes that are external to the genome. Here, we design a framework for distinguishing between ...
Added: June 9, 2025
Popova A., Neverov A. D., Proceedings of the National Academy of Sciences of the United States of America 2019 Vol. 116 No. 42 P. 21104–21112
Influenza A virus (IAV) is a major public health problem and a pandemic threat. Its evolution is largely driven by diversifying positive selection so that relative fitness of different amino acid variants changes with time due to changes in herd immunity or genomic context, and novel amino acid variants attain fitness advantage. Here, we hypothesize ...
Added: June 9, 2025
Klink G. V., Kalinina O. V., Bazykin G. A., PLoS Computational Biology 2022 Vol. 18 No. 2 Article e1009878
Fitness conferred by the same allele may differ between genotypes and environments, and these differences shape variation and evolution. Changes in amino acid propensities at protein sites over the course of evolution have been inferred from sequence alignments statistically, but the existing methods are data-intensive and aggregate multiple sites. Here, we develop an approach to ...
Added: June 26, 2024
Klink G. V., Kalinina O., Bazykin G., Virus Evolution 2024 Vol. 10 No. 1 Article veae036
Amino acid preferences at a protein site depend on the role of this site in protein function and structure as well as on external constraints. All these factors can change in the course of evolution, making amino acid propensities of a site time-dependent. When viral subtypes divergently evolve in different host subpopulations, such changes may ...
Added: June 26, 2024
Samokhin I., Yakushkina T., Bratus A., Chinese Journal of Physics 2021 P. 1–27
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We assume that evolutionary parameters of mutation and selection processes vary in a way to maximize the mean fitness ...
Added: February 4, 2022
Drozhzhin S., Yakushkina T., Bratus A., Journal of Mathematical Biology 2021 Vol. 82 No. 3 Article 15
In this paper, we discuss fitness landscape evolution of permanent replicator systems applying the hypothesis that the specific time of evolutionary adaptation of system parameters is much slower than the time of internal evolutionary dynamics. In other words, we suppose that the extremal principle of Darwinian evolution based on Fisher’s fundamental theorem of natural selection ...
Added: February 26, 2021
Saakian D., Yakushkina T., Journal of the Physical Society of Japan 2020 Vol. 89 Article 044801
The mutator gene model is one of the fundamental models of modern evolutionary dynamics. Usually, one considers a transition between two evolutionary regimes: the wild-type and mutator type. In this study, we introduce a hierarchy of three types with the transitions between them, considering an extra allele for the mutator gene. We examine both the ...
Added: May 14, 2020
Yakushkina T., Saakian D., Chinese Journal of Physics 2019 Vol. 57 P. 309–313
We consider the two-habitat quasispecies model, which describes evolutionary process with migration on the basis of the Eigen model. In the first habitat there is only one genotype, and here is an influx of the replicators from the first habitat to the second one with the rate h. We solve exactly the case of a single-peak ...
Added: February 18, 2020
Saakian D., Chinese Journal of Physics 2019
We consider the two-habitat quasispecies model, which describes evolutionary process with migration on the basis of the Eigen model. In the first habitat there is only one genotype, and here is an influx of the replicators from the first habitat to the second one with the rate h. We solve exactly the case of a single-peak ...
Added: December 10, 2019
Saakian D., Vardanyan E., Yakushkina T., Physica A: Statistical Mechanics and its Applications 2020 Vol. 541 Article 123091
We investigate the evolutionary model with recombination and random switches in the fitness function due to change in a special gene. The dynamical behaviour of the fitness landscape induced by the specific mutations is closely related to the mutator phenomenon, which, together with recombination, plays an important role in modern evolutionary studies. It is of ...
Added: December 10, 2019