Weak Invariants of Actions of the Automorphism Group of a Graph

Automorphism groups of graphs may lead to multiple equivalent solutions of graph-clustering algorithms and to a certain degree of arbitrariness in selecting one or more solution(s) as well as to problems with partition comparison measures. Knowledge of the automorphism group is crucial for stability analysis, for evaluating the degree of arbitrariness involved in selecting a solution, as well as for a further classification as congruent solutions or structurally equivalent solutions. For this purpose we identify three weak invariants of group actions of the automorphism group of a graph, namely modularity, partition type, and the Kolmogorov-Sinai entropy. In particular, we extend the Kolmogorov-Sinai entropy for measuring the uncertainty in finite permutation groups and we apply the underlying construction for testing if multiple structurally equivalent solutions exist for a given graph partition

Ultra-thin insulating layers of hexagonal boron nitride for high-resolution scanning tunneling spectroscopy

Scanning tunneling spectroscopy (STS) allows for probing the local density of states of surfaces and adsorbates with atomic spatial resolution. When molecules or other nanostructures are electronically decoupled from the surface, STS can be interpreted in terms of the electronic structure of the isolated adsorbate. Ultra-thin insulating layers of metal oxides or alkali halides are commonly used to decouple single molecules and atoms. This thesis explores the possibilities of an alternative decoupling material: hexagonal boron nitride (h-BN).  We start by investigating the atomic-scale structure and electronic properties of an h-BN monolayer on Ir(111) and find that it is characterized by a moiré superstructure with a work function modulation of approx. 0.5 eV. Subsequent STS experiments on molecules deposited onto the h-BN/Ir(111) system indicate their efficient decoupling from the metallic substrate and local charging through the h-BN work function modulation. Comparing molecules in different charge states, we go beyond the prevalent single-particle picture when interpreting STS on molecules and explain the observed resonances as a series of many-body excited states. Finally, we utilize h-BN covalently attached to graphene (G) islands to decouple the G edges from the metallic substrate. This gives rise to an electronic state at the h-BN/G interface, which closely resembles the edge state theoretically predicted for pristine graphene edges.  The work presented in this thesis opens new avenues for high-resolution STS on molecular systems using h-BN as an ultra-thin insulating layer

Benchmarking van der Waals-treated DFT: The case of hexagonal boron nitride and graphene on Ir(111)

There is enormous recent interest in weak, van der Waals-type (vdW) interactions due to their fundamental relevance for two-dimensional materials and the so-called vdW heterostructures. Tackling this problem using computer simulation is very challenging due to the non-trivial, non-local nature of these interactions. We benchmark different treatments of London dispersion forces within the density functional theory (DFT) framework on hexagonal boron nitride or graphene monolayers on Ir(111) by comparing the calculated geometries to a comprehensive set of experimental data. The geometry of these systems crucially depends on the interplay between vdW interactions and wave function hybridisation, making them excellent test cases for vdW-treated DFT. Our results show strong variations in the calculated atomic geometry. While some of the approximations reproduce the experimental structure, this is rather based on \textit{a posteriori} comparison with the ``target results''. General predictive power in vdW-treated DFT is not achieved yet and might require new approaches.Comment: More or less published version, with Supporting Materia

A Chandra survey of fluorescence Fe lines in X-ray Binaries at high resolution

In this paper we present a comprehensive survey of 41 X-ray binaries (10 HMXBs and 31 LMXBs) with Chandra, with specific emphasis on the Fe K region and the narrow Fe Kalpha line, at the highest resolution possible. We find that: a) The Fe Kalpha line is always centered at 1.9387 +- 0.0016 Angstroms, compatible with Fe I up to Fe X; we detect no shifts to higher ionization states nor any difference between HMXBs and LMXBs. b) The line is very narrow, with FWHM < 5 mAngstroms, which means that the reprocessing material is not rotating at high speeds. c) Fe Kalpha fluorescence is present in all the HMXB in the survey while such emissions are very rare (~ 10% ) among LMXBs. d) The lack of Fe line emission is always accompanied by the lack of any detectable K edge. e) We obtain the empirical curve of growth of the equivalent width of the Fe Kalpha line versus the density column of the reprocessing material, i.e. EW_{Kalpha} vs N_{H}, and show that it is consistent with a reprocessing region spherically distributed around the compact object. f) We show that fluorescence in X-ray binaries follows the X-ray Baldwin effect. We interpret this finding as evidence of decreasing neutral Fe abundance with increasing X-ray illumination and use it to explain some spectral states of Cyg X-1 and as a possible cause of the lack of narrow Fe line emission in LMXBs. g) Finally, we study anomalous morphologies. We present the first evidence of a Compton shoulder in the HMXB X1908+075. Also the Fe Kalpha lines of 4U1700-37 and LMC X-4 present asymmetric wings suggesting the presence of highly structured stellar winds in these systems.Comment: 12 pages, 11 figures, accepted for publication in Ap

Armirani beton s mineraliziranim česticama drva kao element za ukrućenje smanjene gustoće

The aim of the cooperative research project was the development of a wood-cement in-situ concrete used as local fi ller and stiffening element in wooden ceiling elements. For further processing, only water should be added to the mineralized particles, whereby the amount of added water is relevant to the adjustment of the consistence and flowing characteristics. Portland cement was used as binding component. Particle residues of Scots Pine (Pinus sylvestris L.) and spruce (Picea abies (L.) Karst.) from sanding with 60 grit paper, as filling components, were supplied by Lignotrend GmbH, an industrial manufacturer of solid wood structural elements (cross laminated timber) and project partner. The mineralization of these wood particles has also been studied. Three different ways to accelerate the hydration of the cement and therefore to counteract the effect of the so called cement poisons were examined. Moreover, the compressive strength of hardened concrete had to be set to not less than 3.2 N/mm2, which was also examined.Cilj zajedničkog istraživanja bio je proizvesti beton od drva i cementa koji će se upotrebljavati kao punilo i kao element za ukrućivanje drvnih stropnih elemenata. Za daljnju obradu mineraliziranim česticama drva treba samo dodati vodu, pri čemu je količina dodane vode relevantna za prilagodbu konzistencije i svojstva tečljivosti betona. Kao vezivna komponenta upotrijebljen je portlandski cement, a kao punilo drvne čestice nastale brušenjem drva običnog bora (Pinus sylvestris L.) i smreke (Picea abies (L.) Karst.), i to brusnim papirom granulacije 60. Drvne čestice dobavljene su od tvrtke Lignotrend GmbH, industrijskog proizvođača strukturnih elemenata od masivnog drva (unakrsnoga lameliranog drva), koja je ujedno i partner u projektu. Mineralizacija čestica drva također je dio istraživanja. Istražena su tri različita načina ubrzavanja hidratacije cementa, a istraženi su i tim procesima suprotni učinci, tzv. otrovi cementa, kao i tlačna čvrstoća otvrdnutog betona, koja ne smije biti manja od 3,2 N / mm2

The role of nicotinic acetylcholine receptor alpha 7 in intensive care unit acquired weakness (ICUAW) in an experimental rat model

Im Rattenmodell wurde überprüft, ob durch extraartikuläres Pinning induzierte Immobilisation bzw. durch intravenöse Applikation von Corynebacterium parvum ausgelöste Infektion zu einer verstärkten Expression postsynaptischer nikotinischer Acetylcholinrezeptoren alpha7 führen. Zudem wurde untersucht, ob eine Therapie mittels GTS-21 die Zunahme der Rezeptorexpression abschwächt. Während alleinige Immobilisation die Rezeptorexpression nicht signifikant erhöhte, war sie infolge von Infektion um das 11-fache erhöht. Therapie reduzierte die Rezeptorexpression signifikant.This study examines in an experimental rat model whether immobilization due to extraarticular pinning and infection due to intravenous injection of Corynebacterium parvum may cause an upregulation of postsynaptic nicotinic acetylcholine receptors alpha7. In addition, it was hypothesized that treatment with GTS-21 can attenuate the elevation of receptor expression. Whereas immobilization alone had no significant effect, receptor expression was increased 11-fold by infection. Therapy resulted in a significantly reduced receptor expression

A two-phase model for the Narrow Line Region of NGC 4151

NGC 4151 is one of the brightest and best-studied Seyfert galaxies. Here, we present a two-phase model of the narrow-line region (NLR) of NGC 4151. This study is motivated by (i) the fact that the X-ray spectrum of NGC 4151 is among the flattest known for Seyferts, and (ii) the recent Chandra detection of an X-ray narrow-line region in this galaxy. X-ray spectra as flat as that of NGC 4151 (Gamma_x = -1.5) are expected to favor the presence of two gas phases in pressure equilibrium (Krolik, McKee & Tarter 1981). In the present study, we show that a pronounced two-phase equilibrium develops in the extended emission-line region if we use the observed multi-wavelength spectrum of NGC 4151 to ionize the clouds. The material is stable to isobaric perturbations over a wide range of temperatures. We therefore propose that such a condition has arisen in the NLR of NGC 4151, and that it explains the detection of hot, extended X-ray gas which we identify as the NLR-cloud confining medium.Comment: 5 pages, A&A in press (scheduled for June/July issue). Preprint and related papers also available at http://www.xray.mpe.mpg.de/~skomossa