Related papers: Equilibrium state of molecular breeding
Contact inhibition refers to a reduction in the rate of cell migration and/or cell proliferation in regions of high cell density. Under normal conditions contact inhibition is associated with the proper functioning tissues, whereas abnormal…
We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution…
We introduce a simple theoretical approach for an equilibrium study of proteins with known native state structures. We test our approach with results on well-studied globular proteins, Chymotrypsin Inhibitor (2ci2), Barnase and the alpha…
Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…
The self-alignment concentrations, $c(x)$, as functions of the length, $x$, of the identically matching maximal segments in the genomes of a variety of species, typically present power-law tails extending to the largest scales, i.e., $c(x)…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
Solving the recombination equation has been a long-standing challenge of \emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two…
We introduce a model of DNA sequence evolution which can account for biases in mutation rates that depend on the identity of the neighboring bases. An analytic solution for this class of non-equilibrium models is developed by adopting…
Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene…
To learn about the past from a sample of genomic sequences, one needs to understand how evolutionary processes shape genetic diversity. Most population genetic inference is based on frameworks assuming adaptive evolution is rare. But if…
Many applications of machine learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, one data-driven approach…
We study the role of recombination, as practiced by genetically-competent bacteria, in speeding up Darwinian evolution. This is done by adding a new process to a previously-studied Markov model of evolution on a smooth fitness landscape;…
A popular current research trend deals with expanding the Monte-Carlo tree search sampling methodologies to the environments with uncertainty and incomplete information. Recently a finite population version of Geiringer theorem with…
We study the dynamics of a population subject to selective pressures, evolving either on RNA neutral networks or in toy fitness landscapes. We discuss the spread and the neutrality of the population in the steady state. Different limits…
Recent advances in deep learning optimization showed that, with some a-posteriori information on fully-trained models, it is possible to match the same performance by simply training a subset of their parameters. Such a discovery has a…
In this work, we discuss a cell-cell repulsion population dynamic model based on a hyperbolic Keller-Segel equation with two populations. This model can well describe the cell growth and dispersion in the cell co-culture experiment in the…
Sequence-to-Sequence models were introduced to tackle many real-life problems like machine translation, summarization, image captioning, etc. The standard optimization algorithms are mainly based on example-to-example matching like maximum…
We investigate a class of stochastic growth models involving competition between two phases in which one of the phases has a competitive advantage. The equilibrium populations of the competing phases are calculated using a mean field…