Nonholonomic systems with symmetry allowing a conformally symplectic reduction

Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a nondegenerate almost-Poisson structure on a ``compressed'' space. Here we show, in the simplest non-holonomic systems, that in favorable circumnstances the compressed system is conformally symplectic, although the ``non-compressed'' constrained system never admits a Jacobi structure (in the sense of Marle et al.).Comment: 8 pages. A slight edition of the version to appear in Proceedings of HAMSYS 200

Assessment of RNAi-induced silencing in banana (Musa spp.)

In plants, RNA- based gene silencing mediated by small RNAs functions at the transcriptional or post-transcriptional level to negatively regulate target genes, repetitive sequences, viral RNAs and/or transposon elements. Post-transcriptional gene silencing (PTGS) or the RNA interference (RNAi) approach has been achieved in a wide range of plant species for inhibiting the expression of target genes by generating double-stranded RNA (dsRNA). However, to our knowledge, successful RNAi-application to knock-down endogenous genes has not been reported in the important staple food crop banana

Geodesic Warps by Conformal Mappings

In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g.\ in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary biologist D'Arcy Wentworth Thompson, who demonstrated warps to deform images of one species into another. However, unlike the deformations in modern methods, which are drawn from the full set of diffeomorphism, he deliberately chose lower-dimensional sets of transformations, such as planar conformal mappings. In this paper we study warps of such conformal mappings. The approach is to equip the infinite dimensional manifold of conformal embeddings with a Riemannian metric, and then use the corresponding geodesic equation in order to obtain diffeomorphic warps. After deriving the geodesic equation, a numerical discretisation method is developed. Several examples of geodesic warps are then given. We also show that the equation admits totally geodesic solutions corresponding to scaling and translation, but not to affine transformations

Continuous Blooming of Convex Polyhedra

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.Comment: 13 pages, 6 figure

Classical Signal Model for Quantum Channels

Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, so called prequantum classical statistical field theory (PCSFT). This model provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system (e.g., entangled systems), as averages with respect to fluctuations of classical (Gaussian) random fields. In this note we consider some consequences of PCSFT for quantum information theory. They are based on the observation \cite{W} of two authors of this paper that classical Gaussian channels (important in classical signal theory) can be represented as quantum channels. Now we show that quantum channels can be represented as classical linear transformations of classical Gaussian signa

The origin of defects induced in ultra-pure germanium by Electron Beam Deposition

The creation of point defects in the crystal lattices of various semiconductors by subthreshold events has been reported on by a number of groups. These observations have been made in great detail using sensitive electrical techniques but there is still much that needs to be clarified. Experiments using Ge and Si were performed that demonstrate that energetic particles, the products of collisions in the electron beam, were responsible for the majority of electron-beam deposition (EBD) induced defects in a two-step energy transfer process. Lowering the number of collisions of these energetic particles with the semiconductor during metal deposition was accomplished using a combination of static shields and superior vacuum resulting in devices with defect concentrations lower than $10^{11}\,$cm$^{-3}$, the measurement limit of our deep level transient spectroscopy (DLTS) system. High energy electrons and photons that samples are typically exposed to were not influenced by the shields as most of these particles originate at the metal target thus eliminating these particles as possible damage causing agents. It remains unclear how packets of energy that can sometimes be as small of 2eV travel up to a $\mu$m into the material while still retaining enough energy, that is, in the order of 1eV, to cause changes in the crystal. The manipulation of this defect causing phenomenon may hold the key to developing defect free material for future applications.Comment: 18 pages, 9 figure

Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

Ordering and finite-size effects in the dynamics of one-dimensional transient patterns

We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Freedericksz transition in nematic liquid crystals.The dynamics leads to the emergence of finite domains which are locally periodic and independent of each other. This picture is substantiated by a finite-size scaling law for the structure factor. The mechanism of evolution towards the final homogeneous state is by local roll destruction and associated reduction of local wavenumber. The scaling law breaks down for systems of size comparable to the size of the locally periodic domains. For systems of this size or smaller, an apparent nonlinear selection of a global wavelength holds, giving rise to long lived periodic configurations which do not occur for large systems. We also make explicit the unsuitability of a description of transient pattern dynamics in terms of a few Fourier mode amplitudes, even for small systems with a few linearly unstable modes.Comment: 18 pages (REVTEX) + 10 postscript figures appende