Related papers: Numerical solution of the nonlinear evolution equa…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…
We construct an anomalous dimension for small x evolution which goes beyond standard fixed order perturbative evolution by including resummed small x logarithms deduced from the leading order BFKL equation with running coupling.…
Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution…
We study the limit of a kinetic evolution equation involving a small parameter and perturbed by a smooth random term which also involves the small parameter. Generalizing the classical method of perturbed test functions, we show the…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the solutions. We study the corner…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
Dynamical systems, for instance in model predictive control, often contain unknown parameters, which must be determined during system operation. Online or on-the-fly parameter identification methods are therefore necessary. The challenge of…
We calculate the effect of the less singular terms at small x on the evolution of the coefficient function in \phi^3 theory in six dimensions, which result from a complete solution of the ladder equation. Scale-invariant next-to-leading…
We solve the CCFM equation numerically in the presence of a boundary condition which effectively incorporates the non-linear dynamics. We retain the full dependence of the unintegrated gluon distribution on the coherence scale, and extract…
A key challenge to make effective use of evolutionary algorithms is to choose appropriate settings for their parameters. However, the appropriate parameter setting generally depends on the structure of the optimisation problem, which is…
The purpose of this research was to compare the robustness and performance of a local and global optimization algorithm when given the task of fitting the parameters of a common non-linear dose-response model utilized in the field of…
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…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
We consider adaptive control problem in presence of nonlinear parametrization of uncertainties in the model. It is shown that despite traditional approaches require for domination in the control loop during adaptation, it is not often…
Deep inelastic scattering at small x can be described very effectively using saturation inspired dipole models. We investigate whether such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is…
This paper studies the limit of a kinetic evolution equation involving a small parameter and driven by a random process which also scales with the small parameter. In order to prove the convergence in distribution to the solution of a…
The numerical solutions of the non-linear evolution equation are shown to display the ``geometric'' scaling recently discovered in the experimental data. The phenomena hold both for proton and nucleus targets for all $x$ below $10^{-2}$ and…
A modification of the collinear evolution equations as an appropriate approach to improve the behavior of parton distribution functions in the region of small longitudinal momentum fractions, and to find more theoretical arguments to…