A measure of majorisation emerging from single-shot statistical mechanics

The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorisation determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorisation governs which evolutions can be realized via thermal interactions, whereas the nondecrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation, same main results / added minor result on pure bipartite state entanglement (appendix G) / near to published versio

Left ventricular systolic series elastic properties in aortic stenosis before and after valve replacement

In seven patients with aortic valve disease the time course of an auxotonic beat was compared with that of an isovolumetric beat produced by aortic cross clamping during open heart surgery. The rate of systolic stress rise (dS/dt; g·cm−2) of the isovolumetric beat at peak meridional wall stress (Sp; g·cm−2) of the auxotonic beat was determined by tipmanometry and simultaneous sonomicrometry and was found to be 87% of maximum dS/dt. In the second part of the study the stiffness index (k) was calculated in patients undergoing cardiac catheterisation according to: k = 0.87·(max·dS/dt)/Sp·Vcf, where Vcf = normalised midwall circumferential fibre shortening velocity (circ·s−1). In 22 patients, 10 controls and 12 patients with aortic stenosis before (pre) and after (post) valve replacement the systolic stiffness index k (circ−1) was determined using tipmanometry and frame by frame angiocardiography. Muscle fibre diameter and interstitial fibrosis were assessed from left ventricular endomyocardial biopsies. The systolic stiffness index k was 15 circ−1 in controls, 14 in preoperative patients with aortic stenosis and 12 (p<0.01 v controls) in postoperative patients. There was a significant correlation between k and muscle fibre diameter (r = 0.55; p<0.01) but not between k and interstitial fibrosis or ejection fraction. We conclude that systolic stiffness index k is normal despite marked left ventricular hypertrophy in preoperative patients with aortic stenosis. Following successful valve replacement systolic stiffness index decreased and was significantly lower than in controls. Series elasticity appears to be determined by structures related to the muscle cell rather than to interstitial fibrosi

Early results after mitral valvuloplasty for pure mitral regurgitation

In this study we present the results of 105 consecutive patients with pure mitral regurgitation who underwent surgical treatment. In all patients mitral regurgitation was associated with mitral valve prolapse: 54 patients underwent mitral valvuloplasty and 51 patients mitral valve replacement. Clinical assessment and echocardiography were used as follow-up criteria at one year after surgery. After mitral valvuloplasty, NYH A decreased from 2.7±0.8 to 1.1±0.7 (P<0.01) and workload capacity increased from 65±28% to 96±25% (P<0.001); left endsystolic atrial dimension and enddiastolic dimension decreased from 6.2±0.8 to 4.8±1.2 cm (P<0.001) and from 7.2±1.3 to 5.9±0.8 cm (P<0.01); ventricular contraction fraction did not change significantly. After mitral valve replacement, clinical and echocardiographic improvement was significant but less remarkable than after valvuloplasty; ventricular contraction fraction fell from 39±7% to 29±8% in contrast to patients undergoing mitral valvuloplasty in whom no significant change occurred. Complications were rare in both groups though only a minority of patients undergoing mitral valvuloplasty received anticoagulants. We conclude that mitral valvuloplasty in patients with pure mitral regurgitation associated with mitral valve prolapse gives excellent results, particularly regarding left ventricular function when compared with the patients after mitral valve replacemen

Derivatives and Credit Contagion in Interconnected Networks

The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, {\em but also} by directly triggering each other through contagion. Although credit default swaps have radically altered the dynamics of contagion for more than a decade, models quantifying their impact on systemic risk are still missing. Here, we examine contagion through credit default swaps in a stylized economic network of corporates and financial institutions. We analyse such a system using a stochastic setting, which allows us to exploit limit theorems to exactly solve the contagion dynamics for the entire system. Our analysis shows that, by creating additional contagion channels, CDS can actually lead to greater instability of the entire network in times of economic stress. This is particularly pronounced when CDS are used by banks to expand their loan books (arguing that CDS would offload the additional risks from their balance sheets). Thus, even with complete hedging through CDS, a significant loan book expansion can lead to considerably enhanced probabilities for the occurrence of very large losses and very high default rates in the system. Our approach adds a new dimension to research on credit contagion, and could feed into a rational underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure

Fetal body MRI and its application to fetal and neonatal treatment: an illustrative review

This Review depicts the evolving role of MRI in the diagnosis and prognostication of anomalies of the fetal body, here including head and neck, thorax, abdomen and spine. A review of the current literature on the latest developments in antenatal imaging for diagnosis and prognostication of congenital anomalies is coupled with illustrative cases in true radiological planes with viewable three-dimensional video models that show the potential of post-acquisition reconstruction protocols. We discuss the benefits and limitations of fetal MRI, from anomaly detection, to classification and prognostication, and defines the role of imaging in the decision to proceed to fetal intervention, across the breadth of included conditions. We also consider the current capabilities of ultrasound and explore how MRI and ultrasound can complement each other in the future of fetal imaging

A mechanism for the Double-Spin Asymmetry in Electromagnetic ρ\rho Production at HERMES

We calculate the contribution of meson and pomeron exchanges to the double-spin asymmetry in $\rho$-meson electromagnetic production at HERMES energies. We show that the observed double-spin asymmetries, which are large, can be explained by the interference between the natural parity $f_2$-secondary Reggeon and the unnatural parity anomalous $f_1$ exchanges.Comment: 7 pages, 3 figures, Late

Exclusive diffractive processes and the quark substructure of mesons

Exclusive diffractive processes on the nucleon are investigated within a model in which the quark-nucleon interaction is mediated by Pomeron exchange and the quark substructure of mesons is described within a framework based on the Dyson-Schwinger equations of QCD. The model quark-nucleon interaction has four parameters which are completely determined by high-energy $\pi N$ and $K N$ elastic scattering data. The model is then used to predict vector-meson electroproduction observables. The obtained $\rho$- and $\phi$-meson electroproduction cross sections are in excellent agreement with experimental data. The predicted $q^2$ dependence of $J/\psi$-meson electroproduction also agrees with experimental data. It is shown that confined-quark dynamics play a central role in determining the behavior of the diffractive, vector-meson electroproduction cross section. In particular, the onset of the asymptotic $1/q^4$ behavior of the cross section is determined by a momentum scale that is set by the current-quark masses of the quark and antiquark inside the vector meson. This is the origin of the striking differences between the $q^2$ dependence of $\rho$-, $\phi$- and $J/\psi$-meson electroproduction cross sections observed in recent experiments.Comment: 53 pages, 23 figures, revtex and epsfig. Minor additions to tex