Related papers: Diffusion on a hypercubic lattice with pinning pot…
As mathematical model for the evolutionary equations of species the masterequation is choiced. Two formulations will be demonstrated to include the changes of parameters into the masterequation - that is, on the one hand, the formation of a…
This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of…
Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time…
The dispute on whether the three-dimensional (3D) incompressible Euler equations develop an infinitely large vorticity in a finite time (blowup) keeps increasing due to ambiguous results from state-of-the-art direct numerical simulations…
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…
Our planet is experiencing an accelerated process of change associated to a variety of anthropogenic phenomena. The future of this transformation is uncertain, but there is general agreement about its negative unfolding that might threaten…
According to the "hard-steps" model, the origin of humanity required "successful passage through a number of intermediate steps" (so-called "hard" or "critical" steps) that were intrinsically improbable with respect to the total time…
Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…
In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion…
Environmental science almost invariably proposes problems of extreme complexity, typically characterized by strongly nonlinear evolution dynamics. The systems under investigation have many degrees of freedom - which makes them complicated -…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
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 study the defocusing energy-critical nonlinear wave equation in four dimensions. Our main result proves the stability of the scattering mechanism under random pertubations of the initial data. The random pertubation is defined through a…
Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…
We consider numerically dynamics of a flat anisotropic Universe in Einstein-Gauss-Bonnet gravity with positive $\Lambda$ in dimensionalities 5+1 and 6+1. We identify three possible outcomes of the evolution, one singular and two…
Possibility to establish macroscopic phenomenological theory for biological systems, akin to the akin to the well-established framework of thermodynamics, is briefly reviewed. We introduce the concept of an evolutionary fluctuation-response…
We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these…
Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources…
In this work, we characterize the solution of a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection and migration between two habitats. Assuming that the effects…
Time evolution of a black hole lattice universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of opposite faces. Defining…