Large deviations of a modified Jackson network: stability and rough asymptotics

Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion of time spent on the boundary, where server 2 is idle, may be zero. This is in sharp contrast to the unmodified Jackson network which spends a nonzero proportion of time on this boundary.Comment: Published at http://dx.doi.org/10.1214/105051604000000666 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A novel system for classifying tooth root phenotypes.

Human root and canal number and morphology are highly variable, and internal root canal form and count does not necessarily co-vary directly with external morphology. While several typologies and classifications have been developed to address individual components of teeth, there is a need for a comprehensive system, that captures internal and external root features across all teeth. Using CT scans, the external and internal root morphologies of a global sample of humans are analysed (n = 945). From this analysis a method of classification that captures external and internal root morphology in a way that is intuitive, reproducible, and defines the human phenotypic set is developed. Results provide a robust definition of modern human tooth root phenotypic diversity. The method is modular in nature, allowing for incorporation of past and future classification systems. Additionally, it provides a basis for analysing hominin root morphology in evolutionary, ecological, genetic, and developmental contexts

Cardiovascular Magnetic Resonance Imaging for the Investigation of Ischaemic Heart Disease

Introduction: Coronary artery disease (CAD) remains the number one cause of mortality worldwide; improving diagnosis and treatment is a priority. Multi- parametric cardiovascular magnetic resonance (CMR) offers quantitative assessment of the cardiovascular system with a variety of techniques allowing assessment of anatomy, function, myocardial composition and perfusion during a single scan. Aims: To assess 1.) diagnostic accuracy of visual and quantitative perfusion CMR to single-photon emission computed tomography (MPS-SPECT) in patients with left main stem CAD. 2.) the hypothesis that patients with ischaemic (ICM) and non-ischaemic cardiomyopathy (NICM) have different torsion and strain parameters 3.) development and validation of a contemporary multivariable risk model of CAD from a large population undergoing X-ray angiography. 4.) a rapid 3D mDIXON pulse sequence for image quality and quantitation of MI. 5.) T1 rho prepared (T1ρ) dark blood sequence and compare to blood nulled PSIR (BN) and standard myocardium nulled PSIR (MN) for detection and quantification of scar. Methods: Patients were recruited between 2008 and 2017. Patients in chapters 3,4,6,7 underwent multi-parametric CMR including late gadolinium enhancement (LGE) imaging at 1.5 or 3.0T. Patients in chapter 5 underwent angiography. Results: 1.) CMR demonstrated significantly higher area under the curve for detection of LMS or equivalent disease over MPS-SPECT(P=0.0001). 2.) Despite no difference in LV dimensions, EF and strain between ICM and NICM, NICM patients had significantly lower LV twist(P=0.023) and torsion(P=0.017) compared to ICM. 3.) The developed model discriminated well and was well-calibrated. Diamond and Forrester and Duke scores substantially over-predicted CAD risk, whilst CAD Consortium risk models slightly under-estimated risk. 4.) Image quality was comparable between 3D and 2D LGE(P=0.162). Time for 3D image acquisition was only 5% of the time required for a standard 2D acquisition. 5.) CNRscar-blood was significantly increased for BN and T1ρ compared to MN LGE. BN LGE demonstrated significantly higher reader confidence scores

Early and Late-Time Observations of SN 2008ha: Additional Constraints for the Progenitor and Explosion

We present a new maximum-light optical spectrum of the the extremely low luminosity and exceptionally low energy Type Ia supernova (SN Ia) 2008ha, obtained one week before the earliest published spectrum. Previous observations of SN 2008ha were unable to distinguish between a massive star and white dwarf origin for the SN. The new maximum-light spectrum, obtained one week before the earliest previously published spectrum, unambiguously shows features corresponding to intermediate mass elements, including silicon, sulfur, and carbon. Although strong silicon features are seen in some core-collapse SNe, sulfur features, which are a signature of carbon/oxygen burning, have always been observed to be weak in such events. It is therefore likely that SN 2008ha was the result of a thermonuclear explosion of a carbon-oxygen white dwarf. Carbon features at maximum light show that unburned material is present to significant depths in the SN ejecta, strengthening the case that SN 2008ha was a failed deflagration. We also present late-time imaging and spectroscopy that are consistent with this scenario.Comment: ApJL, accepted. 5 pages, 3 figure