On the computation of zone and double zone diagrams

Classical objects in computational geometry are defined by explicit relations. Several years ago the pioneering works of T. Asano, J. Matousek and T. Tokuyama introduced "implicit computational geometry", in which the geometric objects are defined by implicit relations involving sets. An important member in this family is called "a zone diagram". The implicit nature of zone diagrams implies, as already observed in the original works, that their computation is a challenging task. In a continuous setting this task has been addressed (briefly) only by these authors in the Euclidean plane with point sites. We discuss the possibility to compute zone diagrams in a wide class of spaces and also shed new light on their computation in the original setting. The class of spaces, which is introduced here, includes, in particular, Euclidean spheres and finite dimensional strictly convex normed spaces. Sites of a general form are allowed and it is shown that a generalization of the iterative method suggested by Asano, Matousek and Tokuyama converges to a double zone diagram, another implicit geometric object whose existence is known in general. Occasionally a zone diagram can be obtained from this procedure. The actual (approximate) computation of the iterations is based on a simple algorithm which enables the approximate computation of Voronoi diagrams in a general setting. Our analysis also yields a few byproducts of independent interest, such as certain topological properties of Voronoi cells (e.g., that in the considered setting their boundaries cannot be "fat").Comment: Very slight improvements (mainly correction of a few typos); add DOI; Ref [51] points to a freely available computer application which implements the algorithms; to appear in Discrete & Computational Geometry (available online

Quality of Vitamin K Antagonist Control and 1-Year Outcomes in Patients with Atrial Fibrillation: A Global Perspective from the GARFIELD-AF Registry

AimsVitamin K antagonists (VKAs) need to be individually dosed. International guidelines recommend a target range of international normalised ratio (INR) of 2.0–3.0 for stroke prevention in atrial fibrillation (AF). We analysed the time in this therapeutic range (TTR) of VKA-treated patients with newly diagnosed AF in the ongoing, global, observational registry GARFIELD-AF. Taking TTR as a measure of the quality of patient management, we analysed its relationship with 1-year outcomes, including stroke/systemic embolism (SE), major bleeding, and all-cause mortality.Methods and ResultsTTR was calculated for 9934 patients using 136,082 INR measurements during 1-year follow-up. The mean TTR was 55.0%; values were similar for different VKAs. 5851 (58.9%) patients had TTRConclusionA large proportion of patients with AF had poor VKA control and these patients had higher risks of stroke/SE, major bleeding, and all-cause mortality. Our data suggest that there is room for improvement of VKA control in routine clinical practice and that this could substantially reduce adverse outcomes.</div

One-way membrane trafficking of SOS in receptor-triggered Ras activation

SOS is a key activator of the small GTPase Ras. In cells, SOS-Ras signaling is thought to be initiated predominantly by membrane-recruitment of SOS via the adaptor Grb2 and balanced by rapidly reversible Grb2:SOS binding kinetics. However, SOS has multiple protein and lipid interactions that provide linkage to the membrane. In reconstituted membrane experiments, these Grb2-independent interactions are sufficient to retain SOS on the membrane for many minutes, during which a single SOS molecule can processively activate thousands of Ras molecules. These observations raise questions concerning how receptors maintain control of SOS in cells and how membrane-recruited SOS is ultimately released. We addressed these questions in quantitative reconstituted SOS-deficient chicken B cell signaling systems combined with single molecule measurements in supported membranes. These studies reveal an essentially one-way trafficking process in which membrane-recruited SOS remains trapped on the membrane and continuously activates Ras until it is actively removed via endocytosis

The <i>Aspergillus fumigatus pkcA</i>^G579R Mutant Is Defective in the Activation of the Cell Wall Integrity Pathway but Is Dispensable for Virulence in a Neutropenic Mouse Infection Model

<div><p><i>Aspergillus fumigatus</i> is an opportunistic human pathogen, which causes the life-threatening disease, invasive pulmonary aspergillosis. In fungi, cell wall homeostasis is controlled by the conserved <u>C</u>ell <u>W</u>all <u>I</u>ntegrity (CWI) pathway. In <i>A</i>. <i>fumigatus</i> this signaling cascade is partially characterized, but the mechanisms by which it is activated are not fully elucidated. In this study we investigated the role of protein kinase C (PkcA) in this signaling cascade. Our results suggest that <i>pkcA</i> is an essential gene and is activated in response to cell wall stress. Subsequently, we constructed and analyzed a non-essential <i>A</i>. <i>fumigatus pkcA</i>^G579R mutant, carrying a Gly579Arg substitution in the PkcA C1B regulatory domain. The <i>pkcA</i>^G579R mutation has a reduced activation of the downstream <u>M</u>itogen-<u>A</u>ctivated <u>P</u>rotein <u>K</u>inase, MpkA, resulting in the altered expression of genes encoding cell wall-related proteins, markers of endoplasmic reticulum stress and the unfolded protein response. Furthermore, PkcA^G579R is involved in the formation of proper conidial architecture and protection to oxidative damage. The <i>pkcA</i>^G579R mutant elicits increased production of TNF-α and phagocytosis but it has no impact on virulence in a murine model of invasive pulmonary aspergillosis. These results highlight the importance of PkcA to the CWI pathway but also indicated that additional regulatory circuits may be involved in the biosynthesis and/or reinforcement of the <i>A</i>. <i>fumigatus</i> cell wall during infection.</p></div