Related papers: A Growth model for DNA evolution
We introduce a simple model for DNA evolution. Using the method of Peng et al.$^1$, we investigate the fractal properties of the system. For small chains and chains of intermediate size we find a fractal exponent that indicates the…
In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…
Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random…
We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations…
We study theoretically the in vitro evolution of a DNA sequence by binding to a transcription factor. Using a simple model of protein-DNA binding and available binding constants for the Mnt protein, we perform large-scale, realistic…
The explosive growth of large language models (LLMs) has created a vast but opaque landscape: millions of models exist, yet their evolutionary relationships through fine-tuning, distillation, or adaptation are often undocumented or unclear,…
Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
A model of genome evolution is proposed. Based on three assumptions the evolutionary theory of a genome is formulated. The general law on the direction of genome evolution is given. Both the deterministic classical equation and the…
The modeling of time series is becoming increasingly critical in a wide variety of applications. Overall, data evolves by following different patterns, which are generally caused by different user behaviors. Given a time series, we define…
In this paper we present a novel tool to evaluate problem solving systems. Instead of using a system to solve a problem, we suggest using the problem to evaluate the system. By finding a numerical representation of a problem's complexity,…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
In this paper, we introduce an alternative approach, namely GEN (Genetic Evolution Network) Model, to the deep learning models. Instead of building one single deep model, GEN adopts a genetic-evolutionary learning strategy to build a group…
In molecular phylogeny, relationships among organisms are reconstructed using DNA or protein sequences and are displayed as trees. A linear increase in the number of sequences results in an exponential increase of possible trees. Thus,…
A general theoretical framework is put forth to organize and understand various observed phenomena and mathematical relationships in the field of molecular biology. By modeling each cell in eukaryotic organisms as a processor having a…
We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the…
A simple model of species origin resulted from dynamic features of a population, solely, is developed. The model is based on the evolution optimality in space distribution, and the selection is gone over the mobility. Some biological issues…
A simple model of macroevolution is proposed exhibiting both the property of punctuated equilibrium and the dynamics of potentialities for different species to evolve towards increasingly higher complexity. It is based on the phenomenon of…
The evolution model with parallel mutation-selection scheme is solved for the case when selection is accompanied by base substitutions, insertions, and deletions. The fitness is assumed to be either a single-peak function (i.e., having one…
Solvable structures are exploited in order to find families of explicit solutions to evolution PDEs admitting suitable differential constraints. The effectiveness of the method is verified on several explicit examples.