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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.
Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2026 № 6 С. 132–138
In schemes S for placing r particles in n distinguishable cells, their placement in selected m cells – schemes S∗ is studied, for which the analysis is carried out by a new enumerative method (EM) in extended areas of enumerative combinatorics: finding the number of outcomes and, based on the construction of a model of ...
Added: September 11, 2026
Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2026 № 6 С. 139–147
The class of particle cell arrangements under consideration is characterized by the introduction of an upper limit on the filling levels of the cells, which must be achieved in at least one cell of each outcome of each arrangement. The circuits are distinguished by the paired qualities of their constituent elements (cells and particles) according ...
Added: September 11, 2026
Савченко В. В., Savchenko L., Измерительная техника 2026 Т. 75 № 3 С. 105–113
Within the framework of a current area of research in the field of speech acoustics – non-invasive analysis of speech
production processes – the acute problem of insufficient accuracy of parametric methods for coding a turbulent (noise) type voice source is considered. In order to overcome this problem, a method for coding a sound source with increased ...
Added: September 11, 2026
Фирсанова В. И., Journal of Mathematical Sciences 2024 Vol. 285 No. 1 P. 112–125
Text-to-image models use user-generated prompts to produce images. Such text-to-image models as DALL-E 2, Imagen, Stable Diffusion, and Midjourney can generate photorealistic or similar to human-drawn images. Apart from imitating human art, large text-to-image models have learned to produce combinations of pixels reminiscent of captions in natural languages. For example, a generated image might contain ...
Added: September 9, 2026
Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 8 С. 110–123
Для многокритериальных задач принятия решений по аналогии с качественной вероятностью введены понятия полной и частичной качественной важности как бинарных отношений, обладающих постулируемыми
свойствами. Предложено новое определение отношения нестрогого предпочтения на множестве вариантов решений, порождаемое качественной
важностью. Исследованы его свойства. Указаны аналитические правила,
позволяющие попарно сравнивать варианты по предпочтительности. Проведено сравнение новых отношений предпочтения с разработанными ранее для задач, ...
Added: September 9, 2026
Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 7 С. 113–126
Рассматриваются задачи принятия решений, когда предпочтения оцениваются в порядковой шкале, а возможности реализации значений
неопределенного фактора описываются качественной вероятностью (полной или только частичной). Вводятся определения отношений предпочтения и безразличий на множестве стратегий. Предлагаются простые
решающие правила, позволяющие сравнивать стратегии по предпочтительности, и приводятся иллюстративные примеры. ...
Added: September 9, 2026
Фирсанова В. И., Человек: образ и сущность. Гуманитарные аспекты 2025 Vol. 2 No. 62 P. 203–214
Abstract. The paper highlights prompt engineering in academic setting to reduce plagiarism and increase students' interest. The research problem is the lack of a unified methodology for using artificial intelligence in education. The paper aims to create a generative artificial intelligence user interface, the Virtual Teaching Assistant. Teachers were interviewed, the first collection of presets ...
Added: September 9, 2026
Chemical Papers 2026
Benzenoid hydrocarbons are structurally regular aromatic compounds, which makes them well suited for quantitative structure–property relationship (QSPR) studies. This study presents a QSPR analysis of nineteen benzenoid hydrocarbon species using degree-based topological co-indices. We developed a Python program to compute eleven degree-based topological co-indices from molecular graphs and evaluated their ability to explain variations in ...
Added: September 8, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Glutsyuk A., / Series arXiv "math". 2026.
A planar dual billiard is a planar curve γ equipped with a family (σP)|P∈γ of projective involutions of the projective lines LP tangent to γ at P that fix P. A dual billiard is called rationally integrable, if there exists a rational function R(x,y) of two variables (called first integral) whose restriction to each tangent ...
Added: September 8, 2026
Alexandrov A., Glutsyuk A., Journal of Differential Equations 2026 Vol. 465 Article 114178
The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order differential equations: special double confluent Heun equations. In the present paper, we construct two new families of dynamical systems on ...
Added: September 8, 2026
Glutsyuk A., Inventiones Mathematicae 2026 Vol. 245 P. 977–1058
A caustic of a strictly convex planar bounded billiard is a smooth curve whose tangent lines are reflected from the billiard boundary to its tangent lines. The famous Birkhoff Conjecture, studied by many mathematicians, states that if the billiard boundary has an inner neighborhood foliated by closed caustics, then it is an ellipse. In the paper we study ...
Added: September 8, 2026
Вохминцев И. В., Вестник международных организаций: образование, наука, новая экономика 2026 Т. 21 № 2
The EAEU and the CSTO are Russia’s principal regional international organisations. Understanding, assessing, and analysing the foreign-policy positions of the countries that belong to them is a matter of the state’s national interests. This determines the purpose of the study: to identify the level and the form of cohesion in the voting of EAEU and ...
Added: September 7, 2026
Prikhodko Artem, Kubrak D., Compositio Mathematica 2026 Vol. 162 No. 6 P. 1377–1438
In this follow-up paper we show that smooth Hodge-proper stacks over O𝐾 are ℚ𝑝-locally acyclic: namely the natural map between étale ℚ𝑝-cohomology of the algebraic and Raynaud generic fibers is an equivalence. This establishes the ℚ𝑝-case of general conjectures made in D. Kubrak and A. Prikhodko [p-adic Hodge theory for Artin stacks, Mem. Amer. Math. ...
Added: September 7, 2026
Ismailov A., Constructive Approximation 2026
The measure of the positivity set {x ∈ [0; 2π] | f (x) > 0} of a trigonometric polynomial f is bounded from below by the Motzkin density.
We generalize the bound to polynomials in several variables and almost periodic functions.
We then use these generalizations to extend known results on Taikov’s problem. ...
Added: September 7, 2026
Alshanskaia E., Portnova G., Liaukovich K. et al., Frontiers in Neuroscience 2024 Vol. 18
Added: September 7, 2026
Зуенко Д. О., Trofimova E., Хайдарова И., IEEE Access 2026 Vol. 14 P. 121339–121357
Oil spill segmentation in Synthetic Aperture Radar (SAR) images is limited by noisy annotations in publicly available datasets and by architectural choices that interact with label quality in opposing directions. First, we introduce a manually refined version of the Deep-SAR Oil Spill (SOS) dataset, in which 36.25% of masks are corrected for false positives, missed ...
Added: September 7, 2026
Kelbert M., Statistics 2026 Vol. 60
We present variational representations for the weighted divergencies
and exponential error function, and discuss implications for the
statistical inference and entropic optimal transport. ...
Added: September 7, 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