Tails of random sums of a heavy-tailed number of light-tailed terms

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a portfolio is the sum of a random number of claims. If the tail of the claim number is heavier than the tail of the claim sizes, then under certain conditions the tail of the total claim size does not change asymptotically if the individual claim sizes are replaced by their expectations. The conditions allow the claim number distribution to be of consistent variation or to be in the domain of attraction of a Gumbel distribution with a mean excess function that grows to infinity sufficiently fast. Moreover, the claim number is not necessarily required to be independent of the claim sizes.Comment: Accepted for publication in Insurance: Mathematics and Economic

A Sliding Blocks Estimator for the Extremal Index

In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper we focus on the estimation of the extremal index which measures the degree of clustering of extremes. We consider disjoint and sliding blocks estimators and compare their asymptotic properties. In particular we show that the sliding blocks estimator is more efficient than the disjoint version and has a smaller asymptotic bias. Moreover we propose a method to reduce its bias when considering sufficiently large block sizes.Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Patient-specific image-based computer simulation for theprediction of valve morphology and calcium displacement after TAVI with the Medtronic CoreValve and the Edwards SAPIEN valve

AIMS: Our aim was to validate patient-specific software integrating baseline anatomy and biomechanical properties of both the aortic root and valve for the prediction of valve morphology and aortic leaflet calcium displacement after TAVI. METHODS AND RESULTS: Finite element computer modelling was performed in 39 patients treated with a Medtronic CoreValve System (MCS; n=33) or an Edwards SAPIEN XT (ESV; n=6). Quantitative axial frame morphology at inflow (MCS, ESV) and nadir, coaptation and commissures (MCS) was compared between multislice computed tomography (MSCT) post TAVI and a computer model as well as displacement of the aortic leaflet calcifications, quantified by the distance between the coronary ostium and the closest calcium nodule. Bland-Altman analysis revealed a strong correlation between the observed (MSCT) and predicted frame dimensions, although small differences were detected for, e.g., Dmin at the inflow (mean±SD MSCT vs. MODEL: 21.6±2.4 mm vs. 22.0±2.4 mm; difference±SD: -0.4±1.3 mm, p<0.05) and Dmax (25.6±2.7 mm vs. 26.2±2.7 mm; difference±SD: -0.6±1.0 mm, p<0.01). The observed and predicted calcium displacements were highly correlated for the left and right coronary ostia (R2=0.67 and R2=0.71, respectively p<0.001). CONCLUSIONS: Dedicated software allows accurate prediction of frame morphology and calcium displacement after valve implantation, which may help to improve outcome

Flow pumping system for physiological waveforms

A pulsatile flow pumping system is developed to replicate flow waveforms with reasonable accuracy for experiments simulating physiological blood flows at numerous points in the body. The system divides the task of flow waveform generation between two pumps: a gear pump generates the mean component and a piston pump generates the oscillatory component. The system is driven by two programmable servo controllers. The frequency response of the system is used to characterize its operation. The system has been successfully tested in vascular flow experiments where sinusoidal, carotid, and coronary flow waveforms are replicated

Major bleeding during negative pressure wound/V.A.C.® - therapy for postsurgical deep sternal wound infection - a critical appraisal

Negative-pressure wound therapy, commercially known as vacuum-assisted closure (V.A.C.®) therapy, has become one of the most popular (and efficacious) interim (prior to flap reconstruction) or definite methods of managing deep sternal wound infection. Complications such as profuse bleeding, which may occur during negative-pressure therapy but not necessarily due to it, are often attributed to a single factor and reported as such. However, despite the wealth of clinical experience internationally available, information regarding certain simple considerations is still lacking. Garnering information on all the factors that could possibly influence the outcome has become more difficult due to a (fortunate) decrease in the incidence of deep sternal wound infection. If more insight is to be gained from fewer clinical cases, then various potentially confounding factors should be fully disclosed before complications can be attributed to the technique itself or improvements to negative-pressure wound therapy for deep sternal wound infection can be accepted as evidence-based and the guidelines for its use adapted. The authors propose the adoption of a simple checklist in such cases

Detecting carotid stenosis from skin vibrations using Laser Doppler Vibrometry - An in vitro proof-of-concept.

Early detection of asymptomatic carotid stenosis may help identifying individuals at risk of stroke. We explore a new method based on laser Doppler vibrometry (LDV) which could allow the non-contact detection of stenosis from neck skin vibrations due to stenosis-induced flow disturbances. Experimental fluid dynamical tests were performed with water on a severely stenosed patient-specific carotid bifurcation model. Measurements were taken under various physiological flow regimes both in a compliant and stiff-walled version of the model, at 1 to 4 diameters downstream from the stenosis. An inter-arterial pressure catheter was positioned as reference. Increasing flow led to corresponding increase in power spectral density (PSD) of pressure and LDV recordings in the 0-500 Hz range. The stiff model lead to higher PSD. PSD of the LDV signal was less dependent on the downstream measurement location than pressure. The strength of the association between PSD and flow level, model material and measuring location was highest in the 0-50 Hz range, however useful information was found up to 200 Hz. This proof-of-concept suggests that LDV has the potential to detect stenosis-induced disturbed flow. Further computational and clinical validation studies are ongoing to assess the sensitivity and specificity of the technique for clinical screening.EU H2020 644798 gran