Related papers: Semiconservative Replication in the Quasispecies M…
We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
We introduce a mathematical model in $\mathbb{R}^{n}$ for evolution equations with modified generalized Hartree nonlinearity given by $S_{\alpha,p,q}(u)=I_{\alpha}(|u|^{p+q}).$ One can see that this nonlinearity is not integrable due to the…
This paper develops a quasispecies model where cells can adopt a two-cell survival strategy. Within this strategy, pairs of cells join together, at which point one of the cells sacrifices its own replicative ability for the sake of the…
We investigate the error threshold for the emergence of quasispecies in the Eigen model. By mapping to to an effective Hamiltonian ruled by the "imaginary-time" Schr\"odinger equation, a variational ansatz is proposed and applied to…
The effects of error propagation in the reproduction of diploid organisms are studied within the populational genetics framework of the quasispecies model. The dependence of the error threshold on the dominance parameter is fully…
While the no-cloning theorem forbids the perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can take…
We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential…
We study the simple genetic algorithm with a ranking selection mechanism (linear ranking or tournament). We denote by $\ell$ the length of the chromosomes, by $m$ the population size, by $p_C$ the crossover probability and by $p_M$ the…
Using methods of statistical physics, we present rigorous theoretical calculations of Eigen's quasispecies theory with the truncated fitness landscape which dramatically limits the available sequence space of a reproducing quasispecies.…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
We investigate the evolutionary dynamics of a finite population of RNA sequences adapting to a neutral fitness landscape. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive…
We investigate the competition between two quasispecies residing on two disparate neutral networks. Under the assumption that the two neutral networks have different topologies and fitness levels, it is the mutation rate that determines…
We introduce a toy model for interacting populations connected by mutations and limited by a shared resource. We study the presence of Eigen's error threshold and mutational meltdown. The phase diagram of the system shows that the…
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent…
Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and complemented copy of a substring of length $k$ adjacent to its…
The problem of reconstructing a sequence from the set of its length-$k$ substrings has received considerable attention due to its various applications in genomics. We study an uncoded version of this problem where multiple random sources…
This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…
We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of quasispecies type equipped with a mesa shaped fitness landscape. We obtain…
Quantile-based randomized Kaczmarz (QRK) was recently introduced to efficiently solve sparsely corrupted linear systems $\mathbf{A} \mathbf{x}^*+\mathbf{\epsilon} = \mathbf{b}$ [SIAM J. Matrix Anal. Appl., 43(2), 605-637], where…