Related papers: Evolution patterns in Collatz problem
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
By analogue of [1,2] we define a cubic stochastic process and study evolution (dynamics) of a system $E$ which contains at least three elements.
Evolvability is the capacity to evolve. This paper introduces a simple computational model of evolvability and demonstrates that, under certain conditions, evolvability can increase indefinitely, even when there is no direct selection for…
Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models…
We introduce a new model for large scale evolution and extinction in which species are organized into food chains. The system evolves by two processes: origination/speciation and extinction. In the model, extinction of a given species can…
We introduce and study a general framework for modeling the evolution of crack networks. The evolution steps are triggered by exponential clocks corresponding to local micro-events, and thus reflect the state of the pattern. In an…
A series of results of evolution supervised by genetic algorithms with interest to agricultural and horticultural fields are reviewed. New obtained original results from the use of genetic algorithms on structure-activity relationships are…
We give a substitute to Feller property for semigroups of time-changed processes; under some conditions this leads to establish sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
Evolution by natural selection can be seen an algorithm for generating creative solutions to difficult problems. More precisely, evolution by natural selection is a class of algorithms that share a set of properties. The question we address…
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
The aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic properties of the particle and its characteristic…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is…
The theory of evolution equations has been applied in various ways in general relativity. Following some general considerations about this, some illustrative examples of the use of ordinary differential equations in general relativity are…
The evolution of a quantity, described by a function of space and time, relates the first derivative in time of this function to a spatial operator applied to the function. The initial value of the function at time $t=0$ is given. The…
An important question in biology is how the relative size of different organs is kept nearly constant during growth of an animal. This property, called proportionate growth, has received increased attention in recent years. We discuss our…
Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…