Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

Hierarchical Partial Planarity

In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to construct layouts of these graphs in which the readability of an edge is proportional to its importance, that is, more important edges have fewer crossings. We formalize this problem and study the case in which there exist three different degrees of importance. We give a polynomial-time testing algorithm when the graph induced by the two most important sets of edges is biconnected. We also discuss interesting relationships with other constrained-planarity problems.Comment: Conference version appeared in WG201

Centerpoints: a link between optimization and convex geometry

We introduce a concept that generalizes several different notions of a “centerpoint” in the literature. We develop an oracle-based algorithm for convex mixed-integer optimization based on centerpoints. Further, we show that algorithms based on centerpoints are “best possible” in a certain sense. Motivated by this, we establish several structural results about this concept and provide efficient algorithms for computing these points

Access technique and its problems in parenteral nutrition – Guidelines on Parenteral Nutrition, Chapter 9

Catheter type, access technique, and the catheter position should be selected considering to the anticipated duration of PN aiming at the lowest complication risks (infectious and non-infectious). Long-term (>7–10 days) parenteral nutrition (PN) requires central venous access whereas for PN <3 weeks percutaneously inserted catheters and for PN >3 weeks subcutaneous tunnelled catheters or port systems are appropriate. CVC (central venous catheter) should be flushed with isotonic NaCl solution before and after PN application and during CVC occlusions. Strict indications are required for central venous access placement and the catheter should be removed as soon as possible if not required any more. Blood samples should not to be taken from the CVC. If catheter infection is suspected, peripheral blood-culture samples and culture samples from each catheter lumen should be taken simultaneously. Removal of the CVC should be carried out immediately if there are pronounced signs of local infection at the insertion site and/or clinical suspicion of catheter-induced sepsis. In case PN is indicated for a short period (max. 7–10 days), a peripheral venous access can be used if no hyperosmolar solutions (>800 mosm/L) or solutions with a high titration acidity or alkalinity are used. A peripheral venous catheter (PVC) can remain in situ for as long as it is clinically required unless there are signs of inflammation at the insertion site

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ collinear points or an empty pentagon. As an application, we settle the next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]

High-resolution and low-background 163^{163}Ho spectrum: interpretation of the resonance tails

The determination of the effective electron neutrino mass via kinematic analysis of beta and electron capture spectra is considered to be model-independent since it relies on energy and momentum conservation. At the same time the precise description of the expected spectrum goes beyond the simple phase space term. In particular for electron capture processes, many-body electron-electron interactions lead to additional structures besides the main resonances in calorimetrically measured spectra. A precise description of the $^{163}$Ho spectrum is fundamental for understanding the impact of low intensity structures at the endpoint region where a finite neutrino mass affects the shape most strongly. We present a low-background and high-energy resolution measurement of the $^{163}$Ho spectrum obtained in the framework of the ECHo experiment. We study the line shape of the main resonances and multiplets with intensities spanning three orders of magnitude. We discuss the need to introduce an asymmetric line shape contribution due to Auger–Meitner decay of states above the auto-ionisation threshold. With this we determine an enhancement of count rate at the endpoint region of about a factor of 2, which in turn leads to an equal reduction in the required exposure of the experiment to achieve a given sensitivity on the effective electron neutrino mass

Extracellular NAD and ATP: Partners in immune cell modulation

Extracellular NAD and ATP exert multiple, partially overlapping effects on immune cells. Catabolism of both nucleotides by extracellular enzymes keeps extracellular concentrations low under steady-state conditions and generates metabolites that are themselves signal transducers. ATP and its metabolites signal through purinergic P2 and P1 receptors, whereas extracellular NAD exerts its effects by serving as a substrate for ADP-ribosyltransferases (ARTs) and NAD glycohydrolases/ADPR cyclases like CD38 and CD157. Both nucleotides activate the P2X7 purinoceptor, although by different mechanisms and with different characteristics. While ATP activates P2X7 directly as a soluble ligand, activation via NAD occurs by ART-dependent ADP-ribosylation of cell surface proteins, providing an immobilised ligand. P2X7 activation by either route leads to phosphatidylserine exposure, shedding of CD62L, and ultimately to cell death. Activation by ATP requires high micromolar concentrations of nucleotide and is readily reversible, whereas NAD-dependent stimulation begins at low micromolar concentrations and is more stable. Under conditions of cell stress or inflammation, ATP and NAD are released into the extracellular space from intracellular stores by lytic and non-lytic mechanisms, and may serve as ‘danger signals–to alert the immune response to tissue damage. Since ART expression is limited to naïve/resting T cells, P2X7-mediated NAD-induced cell death (NICD) specifically targets this cell population. In inflamed tissue, NICD may inhibit bystander activation of unprimed T cells, reducing the risk of autoimmunity. In draining lymph nodes, NICD may eliminate regulatory T cells or provide space for the preferential expansion of primed cells, and thus help to augment an immune response