Direct and secondary nuclear excitation with x-ray free-electron lasers

The direct and secondary nuclear excitation produced by an x-ray free electron laser when interacting with a solid-state nuclear target is investigated theoretically. When driven at the resonance energy, the x-ray free electron laser can produce direct photoexcitation. However, the dominant process in that interaction is the photoelectric effect producing a cold and very dense plasma in which also secondary processes such as nuclear excitation by electron capture may occur. We develop a realistic theoretical model to quantify the temporal dynamics of the plasma and the magnitude of the secondary excitation therein. Numerical results show that depending on the nuclear transition energy and the temperature and charge states reached in the plasma, secondary nuclear excitation by electron capture may dominate the direct photoexcitation by several orders of magnitude, as it is the case for the 4.8 keV transition from the isomeric state of $^{93}$Mo, or it can be negligible, as it is the case for the 14.4 keV M\"ossbauer transition in $^{57}\mathrm{Fe}$. These findings are most relevant for future nuclear quantum optics experiments at x-ray free electron laser facilities.Comment: 17 pages, 7 figures; minor corrections made; accepted by Physics of Plasma

A non-Markovian model for cell population growth: speed of convergence and central limit theorem

In De Gunst (1989) a stochastic model was developed for the growth of a batch culture of plant cells. In this paper the mathematical properties of the model are considered. We investigate the asymptotic behaviour of the population growth as predicted by the model when the initial cell number of population members tends to infinity. In particular it is shown that the total cell number, which is a non-Markovian counting process, converges almost surely, uniformly on the real line to a non-random function and the rate of convergence is established. Moreover, a central limit theorem is proved. Computer simulations illustrate the behaviour of the process. The model is graphically compared with experimental data

Wild Bootstrap for Counting Process-Based Statistics

The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to justify the accuracy of inference procedures such as hypothesis tests or time-simultaneous confidence bands. This paper consists of two parts: in Part~I, a general framework is developed in which the large sample properties are established in a unified way by using martingale structures. The framework includes most of the well-known non- and semiparametric statistical methods in time-to-event analysis and parametric approaches. In Part II, the Fine-Gray proportional sub-hazards model exemplifies the theory for inference on cumulative incidence functions given the covariates. The model falls within the framework if the data are censoring-complete. A simulation study demonstrates the reliability of the method and an application to a data set about hospital-acquired infections illustrates the statistical procedure.Comment: 2 parts, 115 pages, 2 figures, 13 table

Inference via Wild Bootstrap and Multiple Imputation under Fine-Gray Models with Incomplete Data

Fine-Gray models specify the subdistribution hazards for one out of multiple competing risks to be proportional. The estimators of parameters and cumulative incidence functions under Fine-Gray models have a simpler structure when data are censoring-complete than when they are more generally incomplete. This paper considers the case of incomplete data but it exploits the above-mentioned simpler estimator structure for which there exists a wild bootstrap approach for inferential purposes. The present idea is to link the methodology under censoring-completeness with the more general right-censoring regime with the help of multiple imputation. In a simulation study, this approach is compared to the estimation procedure proposed in the original paper by Fine and Gray when it is combined with a bootstrap approach. An application to a data set about hospital-acquired infections illustrates the method.Comment: 32 pages, 2 figures, 1 tabl

Critical illness-induced bone loss is related to deficient autophagy and histone hypomethylation

BACKGROUND Survivors of critical illness are at increased risk of fractures. This may be due to increased osteoclast formation during critical illness, leading to trabecular bone loss. Such bone loss has also been observed in Paget's disease, and has been related to deficient autophagy. Deficient autophagy has also been documented in vital organs and skeletal muscle of critically ill patients. The objective of this study was to investigate whether deficient autophagy can be linked to critical illness-induced bone loss. METHODS Osteoclasts grown in vitro and their precursor cells isolated from peripheral blood of critically ill patients and from matched healthy volunteers were analysed for the expression of autophagy genes (SQSTM1, Atg3 and Atg7), and proteins (p62, Atg-5, and microtubule-associated protein light chain 3-II (LC3-II)) and for autophagy and epigenetic signalling factors via PCR arrays and were treated with the autophagy inducer rapamycin. The effect of rapamycin was also investigated at the tissue level in an in vivo rabbit model of critical illness. RESULTS Many more osteoclasts formed in vitro from the blood precursor cells isolated from critically ill patients, which accumulated p62, and displayed reduced expression of Atg5, Atg7, and LC3-II compared to healthy controls, suggesting deficient autophagy, whilst addition of rapamycin reduced osteoclast formation. PCR arrays revealed a down-regulation of histone methyltransferases coupled with an up-regulation of negative regulators of autophagy. Critically ill rabbits displayed a reduction in trabecular and cortical bone, which was rescued with rapamycin. CONCLUSIONS Deficient autophagy in osteoclasts and their blood precursor cells at least partially explained aberrant osteoclast formation during critical illness and was linked to global histone hypomethylation. Treatment with the autophagy activator Rapamycin reduced patient osteoclast formation in vitro and reduced the amount of bone loss in critically ill rabbits in vivo. These findings may help to develop novel therapeutic targets to prevent critical illness-induced bone loss