Secondary Characteristic Classes of Surface Bundles

The Miller-Morita-Mumford classes associate to an oriented surface bundle $E\to B$ a class $\kappa_i(E) \in H^{2i}(B;\Z)$. In this note we define for each prime $p$ and each integer $i\geq 1$ a secondary characteristic class $\lambda_i(E) \in H^{2i(p-1)-2}(B;\Z)/\Z\kappa_{i(p-1)-1}$. The mod $p$ reduction \lambda_i(E) \in H^*(B; \F_p) has zero indeterminacy and satisfies $p\lambda_i(E) = \kappa_{i(p-1)-1}(E) \in H^*(B;\Z/p^2)$.Comment: 6 page

The Equivariant Cobordism Category

For a finite group $G$, we define an equivariant cobordism category $\mathcal{C}_d^G$. Objects of the category are $(d-1)$-dimensional closed smooth $G$-manifolds and morphisms are smooth $d$-dimensional equivariant cobordisms. We identify the homotopy type of its classifying space (i.e. geometric realization of its simplicial nerve) as the fixed points of the infinite loop space of an equivariant spectrum.Comment: 44 pages; v2 has more details and many improvement

Operations on stable moduli spaces.

We construct certain operations on stable moduli spaces and use them to compare cohomology of moduli spaces of closed manifolds with tangential structure. We obtain isomorphisms in a stable range provided the p-adic valuation of the Euler characteristics agree, for all primes p not invertible in the coefficients for cohomology.EPSRC grant EP/M027783/1, the ERC under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 756444), and a Philip Leverhulme Prize from the Leverhulme Trust

Monoids of moduli spaces of manifolds

We study categories of d-dimensional cobordisms from the perspective of Tillmann and Galatius-Madsen-Tillmann-Weiss. There is a category $C_\theta$ of closed smooth (d-1)-manifolds and smooth d-dimensional cobordisms, equipped with generalised orientations specified by a fibration $\theta : X \to BO(d)$. The main result of GMTW is a determination of the homotopy type of the classifying space $BC_\theta$. The goal of the present paper is a systematic investigation of subcategories $D$ of $C_\theta$ having classifying space homotopy equivalent to that of $C_\theta$, the smaller such $D$ the better. We prove that in most cases of interest, $D$ can be chosen to be a homotopy commutative monoid. As a consequence we prove that the stable cohomology of many moduli spaces of surfaces with $\theta$-structure is the cohomology of the infinite loop space of a certain Thom spectrum. This was known for certain special $\theta$, using homological stability results; our work is independent of such results and covers many more cases.Comment: 52 pages, 5 figures; v2: extended discussion of application

Madsen-Weiss for geometrically minded topologists

We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the argument is a geometric version of Harer stability, which we formulate as a theorem about folded maps.Comment: 67 pages, 15 figure

The Optimal Route of Administration of the Glycoprotein IIb/IIIa Receptor Antagonist Abciximab During Percutaneous Coronary Intervention; Intravenous Versus Intracoronary

The use of the glycoprotein (GP) IIb/IIIa receptor antagonist Abciximab has over the years become an important part of the anticoagulant regimen in patients with acute coronary syndrome undergoing percutaneous coronary intervention. Abciximab is a potent inhibitor of platelet aggregation and thrombus formation, but other mechanisms, such as suppression of the inflammatory pathways, have also been proposed to contribute to the benefits of Abciximab

Mod p homology of the stable mapping class group

We calculate the homology of the mapping class group in the stable range. The calculation is based on Madsen and Weiss' proof of the "Generalised Mumford Conjecture".Comment: 29 page

Applied mediation analyses:a review and tutorial

In recent years, mediation analysis has emerged as a powerful tool to disentangle causal pathways from an exposure/treatment to clinically relevant outcomes. Mediation analysis has been applied in scientific fields as diverse as labour market relations and randomized clinical trials of heart disease treatments. In parallel to these applications, the underlying mathematical theory and computer tools have been refined. This combined review and tutorial will introduce the reader to modern mediation analysis including: the mathematical framework; required assumptions; and software implementation in the R package medflex. All results are illustrated using a recent study on the causal pathways stemming from the early invasive treatment of acute coronary syndrome, for which the rich Danish population registers allow us to follow patients’ medication use and more after being discharged from hospital

Cardiac Time Intervals by Tissue Doppler Imaging M-Mode:Normal Values and Association with Established Echocardiographic and Invasive Measures of Systolic and Diastolic Function

PURPOSE:To define normal values of the cardiac time intervals obtained by tissue Doppler imaging (TDI) M-mode through the mitral valve (MV). Furthermore, to evaluate the association of the myocardial performance index (MPI) obtained by TDI M-mode (MPITDI) and the conventional method of obtaining MPI (MPIConv), with established echocardiographic and invasive measures of systolic and diastolic function. METHODS:In a large community based population study (n = 974), where all are free of any cardiovascular disease and cardiovascular risk factors, cardiac time intervals, including isovolumic relaxation time (IVRT), isovolumic contraction time (IVCT), and ejection time (ET) were obtained by TDI M-mode through the MV. IVCT/ET, IVRT/ET and the MPI ((IVRT+IVCT)/ET) were calculated. We also included a validation population (n = 44) of patients who underwent left heart catheterization and had the MPITDI and MPIConv measured. RESULTS:IVRT, IVRT/ET and MPI all increased significantly with increasing age in both genders (p<0.001 for all). IVCT, ET, IVRT/ET, and MPI differed significantly between males and females, displaying that women, in general exhibit better cardiac function. MPITDI was significantly associated with invasive (dP/dt max) and echocardiographic measures of systolic (LVEF, global longitudinal strain and global strainrate s) and diastolic function (e', global strainrate e)(p<0.05 for all), whereas MPIConv was significantly associated with LVEF, e' and global strainrate e (p<0.05 for all). CONCLUSION:Normal values of cardiac time intervals differed between genders and deteriorated with increasing age. The MPITDI (but not MPIConv) is associated with most invasive and established echocardiographic measures of systolic and diastolic function