Telescopic actions

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements: (1) Aitchison's theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points; (2) Taubes' theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold.Comment: +higher dimension

Probabilistic classification of acute myocardial infarction from multiple cardiac markers

Logistic regression and Gaussian mixture model (GMM) classifiers have been trained to estimate the probability of acute myocardial infarction (AMI) in patients based upon the concentrations of a panel of cardiac markers. The panel consists of two new markers, fatty acid binding protein (FABP) and glycogen phosphorylase BB (GPBB), in addition to the traditional cardiac troponin I (cTnI), creatine kinase MB (CKMB) and myoglobin. The effect of using principal component analysis (PCA) and Fisher discriminant analysis (FDA) to preprocess the marker concentrations was also investigated. The need for classifiers to give an accurate estimate of the probability of AMI is argued and three categories of performance measure are described, namely discriminatory ability, sharpness, and reliability. Numerical performance measures for each category are given and applied. The optimum classifier, based solely upon the samples take on admission, was the logistic regression classifier using FDA preprocessing. This gave an accuracy of 0.85 (95% confidence interval: 0.78–0.91) and a normalised Brier score of 0.89. When samples at both admission and a further time, 1–6 h later, were included, the performance increased significantly, showing that logistic regression classifiers can indeed use the information from the five cardiac markers to accurately and reliably estimate the probability AMI

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.Comment: 17 pages, 5 figures; typo

A comparison between the homocyclic aromatic metabolic pathways from plant-derived compounds by bacteria and fungi

Aromatic compounds derived from lignin are of great interest for renewable biotechnical applications. They can serve in many industries e.g. as biochemical building blocks for bioplastics or biofuels, or as antioxidants, flavor agents or food preservatives. In nature, lignin is degraded by microorganisms, which results in the release of homocyclic aromatic compounds. Homocyclic aromatic compounds can also be linked to polysaccharides, tannins and even found freely in plant biomass. As these compounds are often toxic to microbes already at low concentrations, they need to be degraded or converted to less toxic forms. Prior to ring cleavage, the plant- and lignin-derived aromatic compounds are converted to seven central ring-fission intermediates, i.e. catechol, protocatechuic acid, hydroxyquinol, hydroquinone, gentisic acid, gallic acid and pyrogallol through complex aromatic metabolic pathways and used as energy source in the tricarboxylic acid cycle. Over the decades, bacterial aromatic metabolism has been described in great detail. However, the studies on fungal aromatic pathways are scattered over different pathways and species, complicating a comprehensive view of fungal aromatic metabolism. In this review, we depicted the similarities and differences of the reported aromatic metabolic pathways in fungi and bacteria. Although both microorganisms share the main conversion routes, many alternative pathways are observed in fungi. Understanding the microbial aromatic metabolic pathways could lead to metabolic engineering for strain improvement and promote valorization of lignin and related aromatic compounds.Peer reviewe

Inclusive J/psi production at mid-rapidity in pp collisions at root s=5.02 TeV

Inclusive J/psi production is studied in minimum-bias proton-proton collisions at a centre-of-mass energy of root s = 5.02 TeV by ALICE at the CERN LHC. The measurement is performed at mid-rapidity (vertical bar y vertical bar and are extracted and compared with results obtained at other collision energies.Peer reviewe

Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio