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Two meta-evolutionary optimization strategies described in this paper accelerate the convergence of evolutionary programming algorithms while still retaining much of their ability to deal with multi-modal problems. The strategies, called…
A punctuated equilibrium model of biological evolution with relative fitness between different species being the fundamental driving force of evolution is introduced. Mutation is modeled as a fitness updating cellular automaton process…
Because of the finiteness of the life span and boundedness of the physical space, the more reasonable or physical choice is the tempered power-law instead of pure power-law for the CTRW model in characterizing the waiting time and jump…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of…
This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a…
The EPDiff equation governs geodesic flow on the diffeomorphisms with respect to a chosen metric, which is typically a Sobolev norm on the tangent space of vector fields. EPDiff admits a remarkable ansatz for its singular solutions, called…
The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
The performance of evolutionary algorithms can be heavily undermined when constraints limit the feasible areas of the search space. For instance, while Covariance Matrix Adaptation Evolution Strategy is one of the most efficient algorithms…
Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature.…
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…
The electromagnetic self-force equation of motion is known to be afflicted by the so-called runaway problem. A similar problem arises in the semiclassical Einstein's field equation and plagues the self-consistent semiclassical evolution of…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…
In this article, we first investigate the kinematics of specific geodesic flows on two dimensional media with constant curvature, by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation along the…
We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
In the paper, a linear differential equation with variable coefficients and a Caputo fractional derivative is considered. For this equation, a Cauchy problem is studied, when an initial condition is given at an intermediate point that does…