The Invariant Fields of the Sylow groups of Classical Groups in the natural characteristic

Let X be any finite classical group defined over a finite field of characteristic p>0. In this paper we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.Comment: 33 page

Nonlinear Dynamics of Composite Fermions in Nanostructures

We outline a theory describing the quasi-classical dynamics of composite fermions in the fractional quantum Hall regime in the potentials of arbitrary nanostructures. By an appropriate parametrization of time we show that their trajectories are independent of their mass and dispersion. This allows to study the dynamics in terms of an effective Hamiltonian although the actual dispersion is as yet unknown. The applicability of the theory is verified in the case of antidot arrays where it explains details of magnetoresistance measurements and thus confirms the existence of these quasiparticles.Comment: submitted to Europhys. Lett., 4 pages, postscrip

The learning walks of ants (Hymenoptera: Formicidae)

When transitioning from in-nest duties to their foraging life outside the nest, ants perform a series of highly choreographed learning walks around the nest entrance, before leaving to forage for the first time. These learning walks have been described in detail only for a few species of ants, but a pattern of similarities and differences is emerging that we review here with an emphasis on understanding the functional significance of this learning process for efficient homing in ants. We compare the organization of learning walks in ants with that of the learning flights in bees and wasps and provide a list of key research questions that would need to be tackled if we are to understand the role of learning walks in the acquisition of nest-location information, the evolution of this highly conserved learning process, and how it is controlled.We acknowledge financial support to JZ from the Australian Research Council’s Discovery Program (DP150101172 and DP150102699) and to PNF from a Scientia-Scholarship, University of Würzburg, and the Deutsche Forschungsgemeinschaft (project FL1060/1-1)

The invariant fields of the Sylow groups of classical groups in the natural characteristic

Let X be any finite classical group defined over a finite field of characteristic p > 0. In this article, we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular, we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.info:eu-repo/semantics/publishedVersio

The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic

Let G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.info:eu-repo/semantics/publishedVersio

A repulsive trap for two electrons in a magnetic field

We study numerically and analytically the dynamics of two classical electrons with Coulomb interaction in a two dimensional antidot superlattice potential in the presence of crossed electric and magnetic fields. It is found that near one antidot the electron pair can be trapped for a long time and the escape rate from such a trap is proportional to the square of a weak electric field. This is qualitatively different from the case of noninteracting electrons which are trapped forever by the antidot. For the pair propagation in the antidot superlattice we found a broad parameter regime for which the pair is stable and where two repulsive electrons propagate together on an enormously large distance.Comment: revtex, 5 pages, 6 figure

Cluster formation in a stepping stone model with continuous, hierarchically structured sites

A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" L'evy processes. This model can be understood as a continuum limit of discrete state-space, two allele, genetics models with hierarchically structured resampling and migration. The existence of a process rescaling limit on suitable large space and time scales is established and interpreted in terms of the dynamics of cluster formation. This paper was inspired by recent work of Klenke

High quality protein microarray using in situ protein purification

<p>Abstract</p> <p>Background</p> <p>In the postgenomic era, high throughput protein expression and protein microarray technologies have progressed markedly permitting screening of therapeutic reagents and discovery of novel protein functions. Hexa-histidine is one of the most commonly used fusion tags for protein expression due to its small size and convenient purification via immobilized metal ion affinity chromatography (IMAC). This purification process has been adapted to the protein microarray format, but the quality of <it>in situ </it>His-tagged protein purification on slides has not been systematically evaluated. We established methods to determine the level of purification of such proteins on metal chelate-modified slide surfaces. Optimized <it>in situ </it>purification of His-tagged recombinant proteins has the potential to become the new gold standard for cost-effective generation of high-quality and high-density protein microarrays.</p> <p>Results</p> <p>Two slide surfaces were examined, chelated Cu²⁺slides suspended on a polyethylene glycol (PEG) coating and chelated Ni²⁺slides immobilized on a support without PEG coating. Using PEG-coated chelated Cu²⁺slides, consistently higher purities of recombinant proteins were measured. An optimized wash buffer (PBST) composed of 10 mM phosphate buffer, 2.7 mM KCl, 140 mM NaCl and 0.05% Tween 20, pH 7.4, further improved protein purity levels. Using <it>Escherichia coli </it>cell lysates expressing 90 recombinant <it>Streptococcus pneumoniae </it>proteins, 73 proteins were successfully immobilized, and 66 proteins were <it>in situ </it>purified with greater than 90% purity. We identified several antigens among the <it>in situ</it>-purified proteins via assays with anti-<it>S. pneumoniae </it>rabbit antibodies and a human patient antiserum, as a demonstration project of large scale microarray-based immunoproteomics profiling. The methodology is compatible with higher throughput formats of <it>in vivo </it>protein expression, eliminates the need for resin-based purification and circumvents protein solubility and denaturation problems caused by buffer exchange steps and freeze-thaw cycles, which are associated with resin-based purification, intermittent protein storage and deposition on microarrays.</p> <p>Conclusion</p> <p>An optimized platform for <it>in situ </it>protein purification on microarray slides using His-tagged recombinant proteins is a desirable tool for the screening of novel protein functions and protein-protein interactions. In the context of immunoproteomics, such protein microarrays are complimentary to approaches using non-recombinant methods to discover and characterize bacterial antigens.</p

Dynamical Instabilities and Deterministic Chaos in Ballistic Electron Motion in Semiconductor Superlattices

We consider the motion of ballistic electrons within a superlattice miniband under the influence of an alternating electric field. We show that the interaction of electrons with the self-consistent electromagnetic field generated by the electron current may lead to the transition from regular to chaotic dynamics. We estimate the conditions for the experimental observation of this deterministic chaos and discuss the similarities of the superlattice system with the other condensed matter and quantum optical systems.Comment: 6 pages, RevTEX; 4 fig