Biomedical subjects

Werner Ebeling

Publications and source records attributed to Werner Ebeling.

7 recordsLinked to original sources

PubMed2005

Noise-induced transition from translational to rotational motion of swarms.

We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition characterized by the breakdown of translational motion and the onset of swarm rotation as the noise intensity is increased. Statistical properties of swarm dynamics in the weak noise limit are further analytically investigated.

Animals↗

PubMed2004

Active and passive Brownian motion of charged particles in two-dimensional plasma models.

The dynamics of charged Coulomb grains in a plasma is numerically and analytically investigated. Analogous to recent experiments, it is assumed that the grains are trapped in an external parabolic field. Our simulations are based on a Langevin model, where the grain-plasma interaction is realized by a velocity-dependent friction coefficient and a velocity-independent diffusion coefficient. In addition to the ordinary case of positive (passive) friction between grains and plasma, we also discuss the effects of negative (active) friction. The latter case seems particularly interesting, since recent analytical calculations have shown that friction coefficients with negative parts may appear in some models of ion absorption by grains as well as in models of ion-grain scattering. Such negative friction may cause active Brownian motions of the grains. As our computer simulations show, the influence of negative friction leads to the formation of various stationary modes (rotations, oscillations), which, to some extent, can also be estimated analytically.

Journal Article↗

PubMed2004

Exact solutions for evolutionary strategies on harmonic landscapes.

In this paper two different evolutionary strategies are tested by means of harmonic landscapes. Both strategies are based on ensembles of searchers, spreading over the search space according to laws inspired by nature. The main difference between the two prototypes is given by the underlying selection mechanism, governing the increase or decrease of the local population of searchers in certain regions of the search space. More precisely, we compare a thermodynamic strategy, which is based on a physically motivated local selection criterion, with a biologically motivated strategy, which features a global selection scheme (i.e., global coupling of the searchers). Confining ourselves to a special class of initial conditions, we show that, in the simple case of harmonic test potentials, both strategies possess particular analytical solutions of the same type. By means of these special solutions, the velocities of the two strategies can be compared exactly. In the last part of the paper, we extend the scope of our discussion to a mixed strategy, combining local and global selection.

Biological Evolution↗

PubMed2002

Excitation of rotational modes in two-dimensional systems of driven Brownian particles.

Models of active Brownian motion in two-dimensional (2D) systems developed earlier are investigated with respect to the influence of linear attracting forces and external noise. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. In this case an analytical study of the bifurcations of the system is possible. We show that in the presence of external linear forces with only small deviations from radial symmetry, the system develops rotational excitations with left-right symmetry, corresponding to limit cycles in the 4D phase space, the corresponding distribution has the form of a hoop or a tire in the 4D space. In the last part we apply the theory to swarms of Brownian particles that are held together by weak and attracting forces, which lead to cluster formation. Since near the center the potential is at least approximately parabolic and near to the radial symmetry, the swarm develops rotational modes of motion with left-right symmetry.

Journal Article↗

PubMed2002

Bifurcations of a semiclassical atom in a periodic field.

The dynamics of an electron moving in the Coulomb field of a nucleus and a strong periodic field is studied in a semiclassical model. Hamiltonian equations of motion are derived using Gaussian wave functions, a variational principle, and an adiabatic approximation for the width of the wave packets. Predictions for the ionization probability are found to agree rather well with exact calculations in the barrier suppression regime. By introducing dissipation and fluctuation the model atom is considered as an open system. For the dissipative system we investigate the bifurcations in dependence on strength and frequency of the external field. A quite complex bifurcation scenario is obtained. The sensitivity with respect to noise is also studied.

Journal Article↗

PubMed2002

Ensemble-based control of evolutionary optimization algorithms.

This paper presents a study on how the intrinsic search parameters of an evolutionary optimization algorithm can be automatically controlled. It will be shown that only a small search parameter window ensures good optimization results. This evolutionary window, enclosing effective values for the mutation rate and temperature, can be adapted to by carefully steering the ensemble's fitness dispersion. A control sensor based on an entropy measure is introduced to achieve this goal. The efficiency of the proposed control method will be tested by optimizing artificial sequences such as the well-known low autocorrelated binary strings and natural sequences including RNA.

Algorithms↗

PubMed2002

Entropy and complexity of finite sequences as fluctuating quantities.

The paper is devoted to the analysis of digitized sequences of real numbers and discrete strings, by means of the concepts of entropy and complexity. Special attention is paid to the random character of these quantities and their fluctuation spectrum. As applications, we discuss neural spike-trains and DNA sequences. We consider a given sequence as one realization of finite length of certain random process. The other members of the ensemble are defined by appropriate surrogate sequences and surrogate processes. We show that n-gram entropies and the context-free grammatical complexity have to be considered as fluctuating quantities and study the corresponding distributions. Different complexity measures reveal different aspects of a sequence. Finally, we show that the diversity of the entropy (that takes small values for pseudorandom strings) and the context-free grammatical complexity (which takes large values for pseudorandom strings) give, nonetheless, consistent results by comparison of the ranking of sample sequences taken from molecular biology, neuroscience, and artificial control sequences.

Action Potentials↗