Stochastic Approximation to Understand Simple Simulation Models

This paper illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyse the dynamics of many simple simulation models. To demonstrate the type of results that can be obtained using this approximation, we present two illustrative examples which are meant to serve as methodological references for researchers exploring this area. Finally, we prove some convergence results for simulations of a family of evolutionary games, namely, intra-population imitation models in n-player games with arbitrary payoffs.Ministerio de Educación (JC2009- 00263), Ministerio de Ciencia e Innovación (CONSOLIDER-INGENIO 2010: CSD2010-00034, DPI2010-16920

Massive binary black holes in galactic nuclei and their path to coalescence

Massive binary black holes form at the centre of galaxies that experience a merger episode. They are expected to coalesce into a larger black hole, following the emission of gravitational waves. Coalescing massive binary black holes are among the loudest sources of gravitational waves in the Universe, and the detection of these events is at the frontier of contemporary astrophysics. Understanding the black hole binary formation path and dynamics in galaxy mergers is therefore mandatory. A key question poses: during a merger, will the black holes descend over time on closer orbits, form a Keplerian binary and coalesce shortly after? Here we review progress on the fate of black holes in both major and minor mergers of galaxies, either gas-free or gas-rich, in smooth and clumpy circum-nuclear discs after a galactic merger, and in circum-binary discs present on the smallest scales inside the relic nucleus.Comment: Accepted for publication in Space Science Reviews. To appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher

ADAMTS13 regulation of VWF multimer distribution in severe COVID‐19

Background Consistent with fulminant endothelial cell activation, elevated plasma von Willebrand factor (VWF) antigen levels have been reported in patients with COVID-19. The multimeric size and function of VWF are normally regulated through A Disintegrin And Metalloprotease with ThrombSpondin Motif type 1 motif, member 13 (ADAMTS-13)--mediated proteolysis. Objectives This study investigated the hypothesis that ADAMTS-13 regulation of VWF multimer distribution may be impaired in severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) infection contributing to the observed microvascular thrombosis. Patients and Methods Patients with COVID-19 (n = 23) were recruited from the Beaumont Hospital Intensive Care Unit (ICU) in Dublin. Plasma VWF antigen, multimer distribution, ADAMTS-13 activity, and known inhibitors thereof were assessed. Results We observed markedly increased VWF collagen-binding activity in patients with severe COVID-19 compared to controls (median 509.1 versus 94.3 IU/dl). Conversely, plasma ADAMTS-13 activity was significantly reduced (median 68.2 IU/dl). In keeping with an increase in VWF:ADAMTS-13 ratio, abnormalities in VWF multimer distribution were common in patients with COVID-19, with reductions in high molecular weight VWF multimers. Terminal sialylation regulates VWF susceptibility to proteolysis by ADAMTS-13 and other proteases. We observed that both N- and O-linked sialylation were altered in severe COVID-19. Furthermore, plasma levels of the ADAMTS-13 inhibitors interleukin-6, thrombospondin-1, and platelet factor 4 were significantly elevated. Conclusions These findings support the hypothesis that SARS-CoV-2 is associated with profound quantitative and qualitative increases in plasma VWF levels, and a multifactorial down-regulation in ADAMTS-13 function. Further studies will be required to determine whether therapeutic interventions to correct ADAMTS-13-VWF multimer dysfunction may be useful in COVID-microvascular thrombosis and angiopathy

Galaxy bulges and their massive black holes: a review

With references to both key and oft-forgotten pioneering works, this article starts by presenting a review into how we came to believe in the existence of massive black holes at the centres of galaxies. It then presents the historical development of the near-linear (black hole)-(host spheroid) mass relation, before explaining why this has recently been dramatically revised. Past disagreement over the slope of the (black hole)-(velocity dispersion) relation is also explained, and the discovery of sub-structure within the (black hole)-(velocity dispersion) diagram is discussed. As the search for the fundamental connection between massive black holes and their host galaxies continues, the competing array of additional black hole mass scaling relations for samples of predominantly inactive galaxies are presented.Comment: Invited (15 Feb. 2014) review article (submitted 16 Nov. 2014). 590 references, 9 figures, 25 pages in emulateApJ format. To appear in "Galactic Bulges", E. Laurikainen, R.F. Peletier, and D.A. Gadotti (eds.), Springer Publishin

Supplementary Material for: Short-Term Effects of Phenobarbitone on Electrographic Seizures in Neonates

<br><strong><em>Background:</em></strong> Phenobarbitone is the most common first-line anti-seizure drug and is effective in approximately 50% of all neonatal seizures. <b><i>Objective:</i></b> To describe the response of electrographic seizures to the administration of intravenous phenobarbitone in neonates using seizure burden analysis techniques. <b><i>Methods:</i></b> Multi-channel conventional EEG, reviewed by experts, was used to determine the electrographic seizure burden in hourly epochs. The maximum seizure burden evaluated 1 h before each phenobarbitone dose (T_-1) was compared to seizure burden in periods of increasing duration after each phenobarbitone dose had been administered (T₊₁, T₊₂ to seizure offset). Differences were analysed using linear mixed models and summarized as means and 95% CI. <b><i>Results:</i></b> Nineteen neonates had electrographic seizures and met the inclusion criteria for the study. Thirty-one doses were studied. The maximum seizure burden was significantly reduced 1 h after the administration of phenobarbitone (T₊₁) [-14.0 min/h (95% CI: -19.6, -8.5); p < 0.001]. The percentage reduction was 74% (IQR: 36-100). This reduction was temporary and not significant within 4 h of administrating phenobarbitone. Subgroup analysis showed that only phenobarbitone doses at 20 mg/kg resulted in a significant reduction in the maximum seizure burden from T_-1 to T₊₁ (p = 0.002). <b><i>Conclusions:</i></b> Phenobarbitone significantly reduced seizures within 1 h of administration as assessed with continuous multi-channel EEG monitoring in neonates. The reduction was not permanent and seizures were likely to return within 4 h of treatment