A note on the index bundle over the moduli space of monopoles

Donaldson has shown that the moduli space of monopoles $M_k$ is diffeomorphic to the space \Rat_k of based rational maps from the two-sphere to itself. We use this diffeomorphism to give an explicit description of the bundle on \Rat_k obtained by pushing out the index bundle from $M_k$. This gives an alternative and more explicit proof of some earlier results of Cohen and Jones.Comment: 9 page

S-duality and Topological Strings

In this paper we show how S-duality of type IIB superstrings leads to an S-duality relating A and B model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes. Moreover this confirms the existence of new branes in the two models. As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal.Comment: 13 page

On the geometrization of matter by exotic smoothness

In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein-Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. For sufficient complicated links and knots, there are "connecting tubes" (graph manifolds, torus bundles) which introduce an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components. We also discuss the gauge group of the theory to be U(1)xSU(2)xSU(3).Comment: 30 pages, 3 figures, svjour style, complete reworking now using Fintushel-Stern knot surgery of elliptic surfaces, discussion of Lorentz metric and global hyperbolicity for exotic 4-manifolds added, final version for publication in Gen. Rel. Grav, small typos errors fixe

Constructions of generalized complex structures in dimension four

Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven fashion, (twisted) generalized complex structures are constructed on a myriad of four-manifolds, both simply and non-simply connected, which are neither complex nor symplectic

Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons

We consider a complex vector bundle E endowed with a connection A over the eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A of the Spin(7)-instanton equations on R^2 x G/H and general solutions of non-Abelian coupled vortex equations on R^2. These vortices are BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over R^2, are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N=4 super Yang-Mills theory and show that they have the same feature.Comment: 14 pages; v2: typos fixed, published versio

Exotic Smooth Structures on Small 4-Manifolds

Let M be either CP^2#3CP^2bar or 3CP^2#5CP^2bar. We construct the first example of a simply-connected symplectic 4-manifold that is homeomorphic but not diffeomorphic to M.Comment: 11 page

Systematic Review of Medicine-Related Problems in Adult Patients with Atrial Fibrillation on Direct Oral Anticoagulants

New oral anticoagulant agents continue to emerge on the market and their safety requires assessment to provide evidence of their suitability for clinical use. There-fore, we searched standard databases to summarize the English language literature on medicine-related problems (MRPs) of direct oral anticoagulants DOACs (dabigtran, rivaroxban, apixban, and edoxban) in the treatment of adults with atri-al fibrillation. Electronic databases including Medline, Embase, International Pharmaceutical Abstract (IPA), Scopus, CINAHL, the Web of Science and Cochrane were searched from 2008 through 2016 for original articles. Studies pub-lished in English reporting MRPs of DOACs in adult patients with AF were in-cluded. Seventeen studies were identified using standardized protocols, and two reviewers serially abstracted data from each article. Most articles were inconclusive on major safety end points including major bleeding. Data on major safety end points were combined with efficacy. Most studies inconsistently reported adverse drug reactions and not adverse events or medication error, and no definitions were consistent across studies. Some harmful drug effects were not assessed in studies and may have been overlooked. Little evidence is provided on MRPs of DOACs in patients with AF and, therefore, further studies are needed to establish the safety of DOACs in real-life clinical practice

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease