On The Geometry of Field Theoretic Gerstenhaber Structures

Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for arbitrary fibre bundles. Special emphasis has been put on naturality of the constructions. Further, the treatment of symmetries is explained. Finally, the canonical field theoretical 2-form is obtained by pull back and integration of the polysymplectic form over space like hypersurfaces

Selective advantage of topological disorder in biological evolution

We examine a model of biological evolution of Eigen's quasispecies in a holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). So, the evolution dynamics is determined by the topology of the genome space. It is modeled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria, under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call ``topological''. A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested.Comment: 6 pages, 5 figures, svjour class, accepted in EPJ

Reaction Path Averaging: Characterizing the Structural Response of the DNA Double Helix to Electron Transfer

A polarizable environment, prominently the solvent, responds to electronic changes in biomolecules rapidly. The knowledge of conformational relaxation of the biomolecule itself, however, may be scarce or missing. In this work, we describe in detail the structural changes in DNA undergoing electron transfer between two adjacent nucleobases. We employ an approach based on averaging of tens to hundreds of thousands of nonequilibrium trajectories generated with molecular dynamics simulation, and a reduction of dimensionality suitable for DNA. We show that the conformational response of the DNA proceeds along a single collective coordinate that represents the relative orientation of two consecutive base pairs, namely, a combination of helical parameters shift and tilt. The structure of DNA relaxes on time scales reaching nanoseconds, contributing marginally to the relaxation of energies, which is dominated by the modes of motion of the aqueous solvent. The concept of reaction path averaging (RPA), conveniently exploited in this context, makes it possible to filter out any undesirable noise from the nonequilibrium data, and is applicable to any chemical process in general.Comment: 45 pages, 20 figures, published, added Supplementary informatio

Limiting the influence of regulated electrical drainage on track circuits

For the past two years, the authors of this paper have been working on the development of a new regulated electrical drainage system for tram tracks, which may also be used on railways in the future. When this drainage is used on train tracks equipped with track circuits, it is necessary to make sure that the drainage does not generate current harmonics which may be dangerous for the correct functioning of the circuits. In the Czech Republic, requirements regarding the operation of track circuits are stated by Standard CSN 342613. When the drainage was tested on tram tracks, where there are no track circuits, it was found out that in certain operation modes, the drainage generates frequencies which collide with the frequencies of track circuits. Therefore, a passive filter was designed to solve this problem. With the use of computer simulation and measurements on a laboratory model, it was verified that this filter is able to suppress unwanted current harmonics, so that they are in agreement with the above mentioned Standard. These measurements and simulations are described in this paper.Web of Science245565

Functorial prolongations of some functional bundles

We discuss two kinds of functorial prolongations of the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. We study the prolongation of vector fields in both cases and we prove that the bracket is preserved. Our proof is based on several new results concerning the finite dimensional Weil bundles