A Characterization of Uniquely Representable Graphs

The betweenness structure of a finite metric space $M = (X, d)$ is a pair $\mathcal{B}(M) = (X,\beta_M)$ where $\beta_M$ is the so-called betweenness relation of $M$ that consists of point triplets $(x, y, z)$ such that $d(x, z) = d(x, y) + d(y, z)$. The underlying graph of a betweenness structure $\mathcal{B} = (X,\beta)$ is the simple graph $G(\mathcal{B}) = (X, E)$ where the edges are pairs of distinct points with no third point between them. A connected graph $G$ is uniquely representable if there exists a unique metric betweenness structure with underlying graph $G$. It was implied by previous works that trees are uniquely representable. In this paper, we give a characterization of uniquely representable graphs by showing that they are exactly the block graphs. Further, we prove that two related classes of graphs coincide with the class of block graphs and the class of distance-hereditary graphs, respectively. We show that our results hold not only for metric but also for almost-metric betweenness structures.Comment: 16 pages (without references); 3 figures; major changes: simplified proofs, improved notations and namings, short overview of metric graph theor

Underlying Event Studies for LHC Energies

Underlying event was originally defined by the CDF collaboration decades ago. Here we improve the original definition to extend our analysis for events with multiple-jets. We introduce a definition for surrounding rings/belts and based on this definition the jet- and surrounding-belt-excluded areas will provide a good underlying event definition. We inverstigate our definition via the multiplicity in the defined geometry. In parallel, mean transverse momenta of these areas also studied in proton-proton collisions at $\sqrt{s}=7$ TeV LHC energy.Comment: 6 pages and 4 figure

Shape of an elastica under growth restricted by friction

We investigate the quasi-static growth of elastic fibers in the presence of dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of stability against infinitesimal perturbations over finite time intervals is proposed and a semi-analytical method for the determination of the critical length is developed. The post-critical behavior of the system is studied by using an appropriate numerical scheme based on variational methods. We find post-critical shapes for uniformly distributed as well as for concentrated growth and demonstrate convergence to a figure-8 shape for large lengths when self-crossing is allowed. Comparison with simple physical experiments yields reasonable accuracy of the theoretical predictions

Black hole horizons can hide positive heat capacity

Regarding the volume as independent thermodynamic variable we point out that black hole horizons can hide positive heat capacity and specific heat. Such horizons are mechanically marginal, but thermally stable. In the absence of a canonical volume definition, we consider various suggestions scaling differently with the horizon radius. Assuming Euler-homogeneity of the entropy, besides the Hawking temperature, a pressure and a corresponding work term render the equation of state at the horizon thermally stable for any meaningful volume concept that scales larger than the horizon area. When considering also a Stefan--Boltzmann radiation like equation of state at the horizon, only one possible solution emerges: the Christodoulou--Rovelli volume, scaling as $V\sim R^5$, with an entropy $S = \frac{8}{3}S_{BH}$.Comment: 5 pages, no figures, to be published in Phys. Lett.

Utility of serological markers in inflammatory bowel diseases: Gadget or magic?

The panel of serologic markers for inflammatory bowel diseases (IBD) is rapidly expanding. Although anti-Saccharomyces cerevisiae antibodies (ASCA) and atypical perinuclear antineutrophil cytoplasmic antibodies (P-ANCA) remain the most widely investigated, an increasing amount of experimental data is available on newly discovered antibodies directed against various microbial antigens. The role of the assessment of various antibodies in the current IBD diagnostic algorithm is often questionable due to their limited sensitivity. In contrast, the association of serologic markers with disease behavior and phenotype is becoming increasingly well-established. An increasing number of observations confirms that patients with Crohn's disease expressing multiple serologic markers at high titers are more likely to have complicated small bowel disease (e.g. stricture and/or perforation) and are at higher risk for surgery than those without, or with low titers of antibodies. Creating homogenous disease sub-groups based on serologic response may help develop more standardized therapeutic approaches and may help in a better understanding of the pathomechanism of IBD. Further prospective clinical studies are needed to establish the clinical role of serologic tests in IBD