Related papers: Error Thresholds in Presence of Epistatic Interact…
Material training is a method to endow materials with specific responses through external driving. We study the complexity of attainable responses, as expressed in the number of sites that are simultaneously controlled. With increased…
A four-state mutation-selection model for the evolution of populations of DNA-sequences is investigated with particular interest in the phenomenon of error thresholds. The mutation model considered is the Kimura 3ST mutation scheme, fitness…
Deep learning has been immensely successful at a variety of tasks, ranging from classification to AI. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understanding…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation. Biologically motivated by the influence of seasons or the variation of drug concentration during medical treatment,…
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…
The quasispecies theory is studied for dynamic replication landscapes. A meaningful asymptotic quasispecies is defined for periodic time dependencies. The quasispecies' composition is constantly changing over the oscillation period. The…
Recombination is introduced into Eigen's theory of quasispecies evolution. Comparing numerical simulations of the rate equations in the non-recombining and recombining cases show that recombination has a strong effect on the error threshold…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
On rugged fitness landscapes where sign epistasis is common, adaptation can often involve either individually beneficial "uphill" mutations or more complex mutational trajectories involving fitness valleys or plateaus. The dynamics of the…
Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the…
Growing efforts to measure fitness landscapes in molecular and microbial systems are premised on a tight relationship between landscape topography and evolutionary trajectories. This relationship, however, is far from being straightforward:…
We study an ideal-gas-like model where the particles exchange energy stochastically, through energy conserving scattering processes, which take place if and only if at least one of the two particles has energy below a certain energy…
We introduce a model of molecular evolution in which the fitness of an individual depends both on its own and on the parent's genotype. The model can be solved by means of a nonlinear mapping onto the standard quasispecies model. The…
This paper extends the semiconservative quasispecies equations to account for arbitrary post-replication lesion repair efficiency. Such an extension could be an important tool for understanding processes such as cancer development and stem…
The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a…
Gradual changes in exploitation, nutrient loading, etc. produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts…
The drift-barrier hypothesis states that random genetic drift constrains the refinement of a phenotype under natural selection. The influence of effective population size and the genome-wide deleterious mutation rate were studied…
Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over…
In epistatic fitness landscapes, the fitness effect of a mutation depends on the genetic background and may even switch between deleterious and beneficial depending on the presence of another mutation. Epistatic interactions may cause both…
Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not…