Solution to the Henckell--Rhodes problem: finite FF-inverse covers do exist

For a finite connected graph $\mathcal{E}$ with set of edges $E$, a finite $E$-generated group $G$ is constructed such that the set of relations $p=1$ satisfied by $G$ (with $p$ a word over $E\cup E^{-1}$) is closed under deletion of generators (i.e.~edges). As a consequence, every element $g\in G$ admits a unique minimal set $\mathrm{C}(g)$ of edges (the \emph{content} of $g$) needed to represent $g$ as a word over $\mathrm{C}(g)\cup\mathrm{C}(g)^{-1}$. The crucial property of the group $G$ is that connectivity in the graph $\mathcal{E}$ is encoded in $G$ in the following sense: if a word $p$ forms a path $u\longrightarrow v$ in $\mathcal{E}$ then there exists a $G$-equivalent word $q$ which also forms a path $u\longrightarrow v$ and uses only edges from their content; in particular, the content of the corresponding group element $[p]_G=[q]_G$ spans a connected subgraph of $\mathcal{E}$ containing the vertices $u$ and $v$. As an application it is shown that every finite inverse monoid admits a finite $F$-inverse cover. This solves a long-standing problem of Henckell and Rhodes.Comment: 46 pages, 14 figures, new result Cor. 2.7 included, several inaccuracies removed, more details include

Growth Hormone (GH)-Releasing Peptide Stimulation of GH Release from Human Somatotroph Adenoma Cells: Interaction with GH-Releasing Hormone, Thyrotropin- Releasing Hormone, and Octreotide.

The synthetic hexapeptide GH-releasing peptide (GHRP; His-D-Trp-Ala-Trp-D-Phe-Lys-NH2) specifically stimulates GH secretion in humans in vivo and in animals in vitro and in vivo via a still unknown receptor and mechanism. To determine the effect of GHRP on human somatotroph cells in vitro, we stimulated cell cultures derived from 12 different human somatotroph adenomas with GHRP alone and in combination with GH-releasing hormone (GHRH), TRH, and the somatostatin analog octreotide. GH secretion of all 12 adenoma cultures could be stimulated with GHRP, whereas GHRH was active only in 6 adenoma cultures. In GHRH-responsive cell cultures, simultaneous application of GHRH and GHRP had an additive effect on GH secretion. TRH stimulated GH release in 4 of 7 adenoma cultures; in TRH-responsive cell cultures there was also an additive effect of GHRP and TRH on GH secretion. In 5 of 9 adenoma cultures investigated, octreotide inhibited basal GH secretion. In these cell cultures, GHRP-induced GH release was suppressed by octreotide. In 5 of 5 cases, the protein kinase-C inhibitor phloretin partly inhibited GHRP-stimulated GH release, but not basal GH secretion. In summary, GH secretion was stimulated by GHRP in all somatotroph adenomas investigated, indicating that its unknown receptor and signaling pathway are expressed more consistently in somatotroph adenoma cells than those for GHRH, TRH, and somatostatin. Our data give further evidence that GHRP-stimulated GH secretion is mediated by a receptor different from that for GHRH or TRH, respectively, and that protein kinase-C is involved in the signal transduction pathway. Because human somatotroph adenoma cell cultures respond differently to various neuropeptides (GHRH, TRH, somatostatin, and others), they provide a model for further investigation of the mechanism of action of GHRP-induced GH secretion

Submicron silicon powder production in an aerosol reactor

Powder synthesis by thermally induced vapor phase reactions is described. The powder generated by this technique consists of spherical, nonagglomerated particles of high purity. The particles are uniform in size, in the 0.1–0.2 µm size range. Most of the particles are crystalline spheres. A small fraction of the spheres are amorphous. Chain agglomerates account for less than 1% of the spherules

Ultra high temperature particle bed reactor design

A direct nuclear propulsion engine which could be used for a mission to Mars is designed. The main features of this reactor design are high values for I(sub sp) and very efficient cooling. This particle bed reactor consists of 37 cylindrical fuel elements embedded in a cylinder of beryllium which acts as a moderator and reflector. The fuel consists of a packed bed of spherical fissionable fuel particles. Gaseous H2 passes over the fuel bed, removes the heat, and is exhausted out of the rocket. The design was found to be neutronically critical and to have tolerable heating rates. Therefore, this particle bed reactor design is suitable as a propulsion unit for this mission

Quantum phase transition in the dioptase magnetic lattice

The study of quantum phase transitions, which are zero-temperature phase transitions between distinct states of matter, is of current interest in research since it allows for a description of low-temperature properties based on universal relations. Here we show that the crystal green dioptase Cu_6Si_6O_18 . 6H_2O, known to the ancient Roman as the gem of Venus, has a magnetic crystal structure, formed by the Cu(II) ions, which allows for a quantum phase transition between an antiferromagnetically ordered state and a quantum spin liquid.Comment: 6 pages, 5 figures, EPL, in pres

Fabrication of High-Conductivity, Transparent Electrodes with Trenched Metal Bus Lines

A novel transparent electrode system has been developed for thin film electroluminescent displays in which the poor conductivity of the indium-tin-oxide (ITO) electrodes has been augmented by high-conductivity buses of thick aluminum or silver. The augmented electrode system consists of patterned ITO electrodes, 200 Fm wide, centered over narrow aluminum or silver lines 40 ~m wide and separated by an intermediate diffusion barrier film of titanium to promote adhesion to the ITO and prevent blackening of the main ITO electrode by interfacial reactions. The sheet resistances of the augmented ITO electrodes (A1-Ti-ITO and Ti-Ag-Ti-ITO) were lowered by two orders of magnitude relative to the unaugmented ITO electrodes, yielding absolute values on the order of 0.1 ~/s

How can a 22-pole ion trap exhibit 10 local minima in the effective potential?

The column density distribution of trapped OH$^-$ ions in a 22-pole ion trap is measured for different trap parameters. The density is obtained from position-dependent photodetachment rate measurements. Overall, agreement is found with the effective potential of an ideal 22-pole. However, in addition we observe 10 distinct minima in the trapping potential, which indicate a breaking of the 22-fold symmetry. Numerical simulations show that a displacement of a subset of the radiofrequency electrodes can serve as an explanation for this symmetry breaking

Topological interactions in systems of mutually interlinked polymer rings

The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of which is part of a different ring is kept constant. The topology conservation is imposed by the Gauss invariant. A previous approach (M.Otto, T.A. Vilgis, Phys.Rev.Lett. {\bf 80}, 881 (1998)) to the problem is refined in several ways. It is confirmed, that asymptotically, i.e. for large $R\gg R_G$ where $R_G$ is average size of single random walk ring, the effective topological interaction (free energy) scales $\propto R^4$.Comment: 16 pages, 3 figur

DNA methylation profiling of the human major histocompatibility complex: A pilot study for the Human Epigenome Project

The Human Epigenome Project aims to identify, catalogue, and interpret genome-wide DNA methylation phenomena. Occurring naturally on cytosine bases at cytosine-guanine dinucleotides, DNA methylation is intimately involved in diverse biological processes and the aetiology of many diseases. Differentially methylated cytosines give rise to distinct profiles, thought to be specific for gene activity, tissue type, and disease state. The identification of such methylation variable positions will significantly improve our understanding of genome biology and our ability to diagnose disease. Here, we report the results of the pilot study for the Human Epigenome Project entailing the methylation analysis of the human major histocompatibility complex. This study involved the development of an integrated pipeline for high-throughput methylation analysis using bisulphite DNA sequencing, discovery of methylation variable positions, epigenotyping by matrix-assisted laser desorption/ionisation mass spectrometry, and development of an integrated public database available at http://www.epigenome.org. Our analysis of DNA methylation levels within the major histocompatibility complex, including regulatory exonic and intronic regions associated with 90 genes in multiple tissues and individuals, reveals a bimodal distribution of methylation profiles (i.e., the vast majority of the analysed regions were either hypo- or hypermethylated), tissue specificity, inter-individual variation, and correlation with independent gene expression data

Cluster Observations of a Cusp Diamagnetic Cavity: Structure, Size, and Dynamics

We have analyzed Cluster magnetic field and plasma data during high‐altitude cusp crossing and compared them with high‐resolution MHD simulations. Cluster encountered a diamagnetic cavity (DMC) during northward interplanetary magnetic field (IMF) conditions, and as the IMF rotated southward, the spacecraft reencountered the cavity more at the sunward side of the cusp because the reconnection site had changed location. We found evidence of magnetic reconnection both during northward and southward IMF conditions. The Cluster separation was ∼5000 km, enabling for the first time measurements both inside the DMC and surrounding boundaries that allowed us to construct the structure of the DMC and put the observations of ion pitch angle distributions in context of local reconnection topology and gradients of the boundaries. The cavity is characterized by strong magnetic field fluctuations and high‐energy particles. At the magnetosheath boundary the high‐energy particle fluxes reduced by several orders of magnitude. Throughout the magnetosheath, the high‐energy proton fluxes remained low except during brief intervals when sc4 and sc1 dropped back into the cavity due to changes in solar wind dynamic pressure. However, the high‐energy O+ fluxes did not drop as much in the magnetosheath and were mostly at 60°–120° pitch angles, indicative of a trapped population in the DMC which is observed in the magnetosheath due to a large gyroradius. Significant fluxes of protons and ionized oxygen were also observed escaping from the diamagnetic cavity antiparallel to the magnetic field in a time scale more consistent with the local DMC source than with a reflected bow shock source