Signature, positive Hopf plumbing and the Coxeter transformation

By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds of them lie on the unit circle. In contrast, we show that for divide links, the signature cannot be linearly bounded from below by the genus.

Prometheus Framework for Fuzzy Information Retrieval in Semantic Spaces

This paper introduces a novel vision for further enhanced Internet of Things services. Based on a variety of data (such as location data, ontology-backed search queries, in- and outdoor conditions) the Prometheus framework is intended to support users with helpful recommendations and information preceding a search for context-aware data. Adapted from artificial intelligence concepts, Prometheus proposes user-readjusted answers on umpteen conditions. A number of potential Prometheus framework applications are illustrated. Added value and possible future studies are discussed in the conclusion.

Clinical Course of acute-on-chronic liver failure syndrome and effects on prognosis

Acute-on-chronic liver failure (ACLF) is characterized by acute decompensation (AD) of cirrhosis, organ failure(s), and high 28-day mortality. We investigated whether assessments of patients at specific time points predicted their need for liver transplantation (LT) or the potential futility of their care. We assessed clinical courses of 388 patients who had ACLF at enrollment, from February through September 2011, or during early (28-day) follow-up of the prospective multicenter European Chronic Liver Failure (CLIF) ACLF in Cirrhosis study. We assessed ACLF grades at different time points to define disease resolution, improvement, worsening, or steady or fluctuating course. ACLF resolved or improved in 49.2%, had a steady or fluctuating course in 30.4%, and worsened in 20.4%. The 28-day transplant-free mortality was low-to-moderate (6%-18%) in patients with nonsevere early course (final no ACLF or ACLF-1) and high-to-very high (42%-92%) in those with severe early course (final ACLF-2 or -3) independently of initial grades. Independent predictors of course severity were CLIF Consortium ACLF score (CLIF-C ACLFs) and presence of liver failure (total bilirubin ≥12 mg/dL) at ACLF diagnosis. Eighty-one percent had their final ACLF grade at 1 week, resulting in accurate prediction of short- (28-day) and mid-term (90-day) mortality by ACLF grade at 3-7 days. Among patients that underwent early LT, 75% survived for at least 1 year. Among patients with ≥4 organ failures, or CLIF-C ACLFs >64 at days 3-7 days, and did not undergo LT, mortality was 100% by 28 days. CONCLUSIONS Assessment of ACLF patients at 3-7 days of the syndrome provides a tool to define the emergency of LT and a rational basis for intensive care discontinuation owing to futility.

Horizon shells and BMS-like soldering transformations

We revisit the theory of null shells in general relativity, with a particular emphasis on null shells placed at horizons of black holes. We study in detail the considerable freedom that is available in the case that one solders two metrics together across null hypersurfaces (such as Killing horizons) for which the induced metric is invariant under translations along the null generators. In this case the group of soldering transformations turns out to be infinite dimensional, and these solderings create non-trivial horizon shells containing both massless matter and impulsive gravitational wave components. We also rephrase this result in the language of Carrollian symmetry groups. To illustrate this phenomenon we discuss in detail the example of shells on the horizon of the Schwarzschild black hole (with equal interior and exterior mass), uncovering a rich classical structure at the horizon and deriving an explicit expression for the general horizon shell energy-momentum tensor. In the special case of BMS-like soldering supertranslations we find a conserved shell-energy that is strikingly similar to the standard expression for asymptotic BMS supertranslation charges, suggesting a direct relation between the physical properties of these horizon shells and the recently proposed BMS supertranslation hair of a black hole.

Cutting Arcs For Torus Links And Trees

Among all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., An , Dn , E6 , E7 and E8 ) among all positive tree-like Hopf plumbings.

A note on the stable equivalence problem

We provide counterexamples to the stable equivalence problem in every dimension d ≥ 2. That means that we construct hypersurfaces H₁ , H₂ ⊂ C d+1 whose cylinders H₁ × C and H₂ × C are equivalent hypersurfaces in C d+2 , although H₁ and H₂ themselves are not equivalent by an automorphism of C d+1 . We also give, for every d ≥ 2, examples of two non-isomorphic algebraic varieties of dimension d which are biholomorphic.