Tree-irreducible automorphisms of free groups

We introduce a new class of automorphisms $\varphi$ of the non-abelian free group $F_N$ of finite rank $N \geq 2$ which contains all iwips (= fully irreducible automorphisms), but also any automorphism induced by a pseudo-Anosov homeomorphism of a surface with arbitrary many boundary components. More generally, there may be subgroups of $F_N$ of rank $\geq 2$ on which $\varphi$ restricts to the identity. We prove some basic facts about such {\em tree-irreducible} automorphisms, and show that, together with Dehn twist automorphisms, they are the natural basic building blocks from which any automorphism of \FN can be constructed in a train track set-up. We then show: {\bf Theorem:} {\it Every tree-irreducible automorphism of $F_N$ has induced North-South dynamics on the Thurston compactification $\bar{\rm CV}_N$ of Outer space.} Finally, we define a "blow-up" construction on the vertices of a train track map, which, starting from iwips, produces tree-irreducible automorphisms which in general are not iwip

(k,q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior

Advanced diffusion magnetic resonance imaging (dMRI) techniques, like diffusion spectrum imaging (DSI) and high angular resolution diffusion imaging (HARDI), remain underutilized compared to diffusion tensor imaging because the scan times needed to produce accurate estimations of fiber orientation are significantly longer. To accelerate DSI and HARDI, recent methods from compressed sensing (CS) exploit a sparse underlying representation of the data in the spatial and angular domains to undersample in the respective k- and q-spaces. State-of-the-art frameworks, however, impose sparsity in the spatial and angular domains separately and involve the sum of the corresponding sparse regularizers. In contrast, we propose a unified (k,q)-CS formulation which imposes sparsity jointly in the spatial-angular domain to further increase sparsity of dMRI signals and reduce the required subsampling rate. To efficiently solve this large-scale global reconstruction problem, we introduce a novel adaptation of the FISTA algorithm that exploits dictionary separability. We show on phantom and real HARDI data that our approach achieves significantly more accurate signal reconstructions than the state of the art while sampling only 2-4% of the (k,q)-space, allowing for the potential of new levels of dMRI acceleration.Comment: To be published in the 2017 Computational Diffusion MRI Workshop of MICCA

Too-Systemic-To-Fail: What Option Markets Imply About Sector-Wide Government Guarantees

A conspicuous amount of aggregate tail risk is missing from the price of financial sector crash insurance during the 2007-2009 crisis. The difference in costs of out-of-the-money put options for individual banks, and puts on the financial sector index, increases fourfold from its pre-crisis level. At the same time, correlations among bank stocks surge, suggesting the high put spread cannot be attributed to a relative increase in idiosyncratic risk. We show that this phenomenon is unique to the financial sector, that it cannot be explained by observed risk dynamics (volatilities and correlations), and that illiquidity and no-arbitrage violations are unlikely culprits. Instead, we provide evidence that a collective government guarantee for the financial sector lowers index put prices far more than those of individual banks, explaining the divergence in the basket-index spread. By embedding a bailout in the standard one-factor option pricing model, we can closely replicate observed put spread dynamics. During the crisis, the spread responds acutely to government intervention announcements

Breaking up the band: European regulatory cooperation in a post-Brexit world

Since 1995, the European Medicines Agency (EMA) has progressed from harmonising regulation for human and veterinary medicines across the European Union Member State national competent authorities, to galvanising one of the most successful cooperative initiatives for regulation globally. Although the EMA is the focal point for stakeholders, regulation is delivered through the European medicines regulatory network, in which national authorities, like the UK’s Medicines & Healthcare products Regulatory Agency (MHRA), contribute. As with any collaboration, contributions by individual members vary, and the MHRA has been noted as an innovative and highly productive member of the network. Progress in regulation not only in Europe – but also around the world through convergence – can be attributed to this unique European cooperation. The decision by the UK to leave the European Union threatens to mark the end of this cooperation; we argue here that the best decision is to maintain regulatory cooperation under new structures

The application of compressive sampling to radio astronomy I: Deconvolution

Compressive sampling is a new paradigm for sampling, based on sparseness of signals or signal representations. It is much less restrictive than Nyquist-Shannon sampling theory and thus explains and systematises the widespread experience that methods such as the H\"ogbom CLEAN can violate the Nyquist-Shannon sampling requirements. In this paper, a CS-based deconvolution method for extended sources is introduced. This method can reconstruct both point sources and extended sources (using the isotropic undecimated wavelet transform as a basis function for the reconstruction step). We compare this CS-based deconvolution method with two CLEAN-based deconvolution methods: the H\"ogbom CLEAN and the multiscale CLEAN. This new method shows the best performance in deconvolving extended sources for both uniform and natural weighting of the sampled visibilities. Both visual and numerical results of the comparison are provided.Comment: Published by A&A, Matlab code can be found: http://code.google.com/p/csra/download

How well-proportioned are lens and prism spaces?

The CMB anisotropies in spherical 3-spaces with a non-trivial topology are analysed with a focus on lens and prism shaped fundamental cells. The conjecture is tested that well proportioned spaces lead to a suppression of large-scale anisotropies according to the observed cosmic microwave background (CMB). The focus is put on lens spaces L(p,q) which are supposed to be oddly proportioned. However, there are inhomogeneous lens spaces whose shape of the Voronoi domain depends on the position of the observer within the manifold. Such manifolds possess no fixed measure of well-proportioned and allow a predestined test of the well-proportioned conjecture. Topologies having the same Voronoi domain are shown to possess distinct CMB statistics which thus provide a counter-example to the well-proportioned conjecture. The CMB properties are analysed in terms of cyclic subgroups Z_p, and new point of view for the superior behaviour of the Poincar\'e dodecahedron is found

Determinants of methicillin-susceptible Staphylococcus aureus native bone and joint infection treatment failure: a retrospective cohort study.

BACKGROUND: Although methicillin-susceptible Staphylococcus aureus (MSSA) native bone and joint infection (BJI) constitutes the more frequent clinical entity of BJI, prognostic studies mostly focused on methicillin-resistant S. aureus prosthetic joint infection. We aimed to assess the determinants of native MSSA BJI outcomes. METHODS: Retrospective cohort study (2001-2011) of patients admitted in a reference hospital centre for native MSSA BJI. Treatment failure determinants were assessed using Kaplan-Meier curves and binary logistic regression. RESULTS: Sixty-six patients (42 males [63.6%]; median age 61.2 years; interquartile range [IQR] 45.9-71.9) presented an acute (n = 38; 57.6%) or chronic (n = 28; 42.4%) native MSSA arthritis (n = 15; 22.7%), osteomyelitis (n = 19; 28.8%) or spondylodiscitis (n = 32; 48.5%), considered as "difficult-to-treat" in 61 cases (92.4%). All received a prolonged (27.1 weeks; IQR, 16.9-36.1) combined antimicrobial therapy, after surgical management in 37 cases (56.1%). Sixteen treatment failures (24.2%) were observed during a median follow-up period of 63.3 weeks (IQR, 44.7-103.1), including 13 persisting infections, 1 relapse after treatment disruption, and 2 super-infections. Independent determinants of treatment failure were the existence of a sinus tract (odds ratio [OR], 5.300; 95% confidence interval [CI], 1.166-24.103) and a prolonged delay to infectious disease specialist referral (OR, 1.134; 95% CI 1.013-1.271). CONCLUSIONS: The important treatment failure rate pinpointed the difficulty of cure encountered in complicated native MSSA BJI. An early infectious disease specialist referral is essential, especially in debilitated patients or in presence of sinus tract

Is Acute High-Dose Secondhand Smoke Exposure Always Harmful to Microvascular Function in Healthy Adults?

Prev Cardiol.Long-term exposure to secondhand smoke (SHS) is associated with impaired vascular function. The authors investigated the vascular and blood pressure (BP) reactions to acute SHS exposure. Twenty-five healthy nonsmoking adults underwent a 1-hour exposure to SHS (mean fine particulate matter <2.5 μm level=315±116 μg/m 3 ). Microvascular endothelial-dependent vasodilatation (EDV) (EndoPAT, Itamar Medical, Caesarea, Israel) and aortic hemodynamics/compliance (SphygmoCor, AtCor Medical, West Ryde, Australia) were measured before and after the SHS exposure with BP measured every 15 minutes during and for a 24-hour period before and after the exposure. SHS exposure did not change EDV, aortic hemodynamics, arterial compliance, or 24-hour BP. However, diastolic BP significantly increased during the SHS exposure period by 3.4±5.6 mm Hg. Our brief SHS exposure did not impair microvascular endothelial function or arterial compliance in healthy nonsmoking adults, but brachial diastolic BP increased.Prev Cardiol. 2010;13:175–179. © 2010 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79199/1/j.1751-7141.2010.00074.x.pd