Related papers: Non-Archimedean Replicator Dynamics and Eigen's Pa…
Biological actuators -- from myosin motors to muscles -- follow Hill's model where a dimensionless parameter $\alpha$ captures the nonlinear coupling between contraction rate and force generation. Our prior work identified a characteristic…
Recent research on the non-stationary nature of the dynamics of complex systems is reviewed through three specific models. The long time dynamics consists of a slow, decelerating but spasmodic release of generalized intrinsic strain. These…
A dynamical version of the Widom-Rowlinsom model in the continuum is considered. The dynamics is modelled by a spatial two-component birth-and-death Glauber process where particles, in addition, are allowed to change their type with density…
The objects of our interest are the so-called $A$-permutations, which are permutations whose cycle length lie in a fixed set $A$. They have been extensively studied with respect to the uniform or the Ewens measure. In this paper, we extend…
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
We study a class of non-reversible, continuous-time random walks in random environments on $\mathbb{Z}^d$ that admit a cycle representation with finite cycle length. The law of the transition rates, taking values in $[0, \infty)$, is…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model…
We present an analysis of well-posedness of constrained evolution of 3+1 formulations of GR. In this analysis we explicitly take into account the energy and momentum constraints as well as possible algebraic constraints on the evolution of…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the…
We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the…
The advent of modern genome sequencing techniques allows for a more stringent test of the neutrality hypothesis of Darwinian evolution, where all individuals have the same fitness. Using the individual based model of Wright and Fisher, we…
At the fundamental conceptual level, two alternatives have traditionally been considered for how mutations arise and how evolution happens: 1) random mutation and natural selection, and 2) Lamarckism. Recently, the theory of…
In this study, we construct an evolutionary model of a population of DNA sequences interacting with the surrounding environment on the topological monoid A* of strings on the alphabet A = { a, c, g, t }. A partial differential equation…
A self-consistent quadratic theory is presented to account for nonlinear contributions in quantum dynamics. Evolution equations are shown to depend on higher-order gradients of the Hamiltonian, which are incorporated via their equations of…
In ecology and population dynamics, gene-flow refers to the transfer of a trait from one population to another. This phenomenon appears in studying the evolution of social features, such as languages. From the mathematical point of view,…
Since Newton, all classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. The boundary conditions creating the phase space of all possible values of the variables are…
In this work, we investigate the non-Markovian dynamical evolution of a ${\Lambda}$-type atom interacting with a semi-infinite one-dimensional photonic waveguide via two atomic transitions. The waveguide terminates at a perfect mirror,…