4 citations · 4 across the 5 of their papers we have counts for
7 papers
Rigorous mathematical analysis of the quasispecies model: From Manfred Eigen to the recent developments
Alexander S. Bratus, Artem S. Novozhilov, Yuri S. Semenov
We review the major progress in the rigorous analysis of the classical quasispecies model that usually comes in two related but different forms: the Eigen model and the Crow--Kimur…
Generalized Quasispecies Model on Finite Metric Spaces: Isometry Groups and Spectral Properties of Evolutionary Matrices
Yuri S. Semenov, Artem S. Novozhilov
The quasispecies model introduced by Eigen in 1971 has close connections with the isometry group of the space of binary sequences relative to the Hamming distance metric. Generaliz…
Adaptive Fitness Landscape for Replicator Systems: To Maximize or not to Maximize
Alexander S. Bratus, Artem S. Novozhilov, Yuri S. Semenov
Sewall Wright's adaptive landscape metaphor penetrates a significant part of evolutionary thinking. Supplemented with Fisher's fundamental theorem of natural selection and Kimura's…
On Eigen's quasispecies model, two-valued fitness landscapes, and isometry groups acting on finite metric spaces
Yuri S. Semenov, Artem S. Novozhilov
A two-valued fitness landscape is introduced for the classical Eigen's quasispecies model. This fitness landscape can be considered as a direct generalization of the so-called sing…
Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model
Yuri S. Semenov, Artem S. Novozhilov
We reformulate the eigenvalue problem for the selection--mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for a…
On the behavior of the leading eigenvalue of Eigen's evolutionary matrices
Yuri S. Semenov, Alexander S. Bratus, Artem S. Novozhilov
We study general properties of the leading eigenvalue of Eigen's evolutionary matrices depending on the probability of faithful reproduction. This is a linear…
Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution
Alexander S. Bratus, Artem S. Novozhilov, Yuri S. Semenov
A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix…