We study conformations of the Gaussian polymer chains in d-dimensional space in the presence of an external field with the harmonic potential. We apply a path integral approach to derive an explicit expression for the probability distribution function of the gyration radius. We calculate this function using Monte Carlo simulations and show that our numerical and theoretical results are in a good agreement for different values of the external field.

Age‐period‐cohort (APC) models are frequently used in a variety of health and demographic‐related outcomes. Fitting and interpreting APC models to data in equal intervals (equal age and period widths) is nontrivial due to the structural link between the three temporal effects (given two, the third can always be found) causing the well‐known identification problem. The usual method for resolving the structural link identification problem is to base a model on identifiable quantities. It is common to find health and demographic data in unequal intervals, this creates further identification problems on top of the structural link. We highlight the new issues by showing that curvatures which were identifiable for equal intervals are no longer identifiable for unequal data. Furthermore, through extensive simulation studies, we show how previous methods for unequal APC models are not always appropriate due to their sensitivity to the choice of functions used to approximate the true temporal functions. We propose a new method for modeling unequal APC data using penalized smoothing splines. Our proposal effectively resolves the curvature identification issue that arises and is robust to the choice of the approximating function. To demonstrate the effectiveness of our proposal, we conclude with an application to UK all‐cause mortality data from the Human mortality database.

Transurethral resection of the prostate (TURP) continues to be an effective intervention for certain indications; and this procedure is still one of the most commonly performed in urology. The use of a 3-way catheter with continuous bladder irrigation (CBI) post-TURP is widely practiced in a bid to prevent clot retention. We report our unique experience with the use of 2-way urethral catheters post-TURP surgery.   Methodology Data was prospectively collected for 143 consecutive patients who underwent a bipolar TURP between July 2015 and October 2017. The following outcomes where measured and compared against the literature: resection time, resected weight, haemoglobin level, hospital stay, catheterization days, transfusion rate and complications. Results Two-way 18-French catheters were used in 132/143 (91.7%) patients. The remaining 11/143 (8.3%) patients had a 3-way 22-French catheter and CBI immediately post-TURP. There were no incidences of clot retention requiring a return to theatre. There were 2/132 (1.5%) patients requiring transfusion who received 2-way catheterization. The average resection time was 44.8 (10-100) minutes, with a mean resected weight of 22.8 (2.0-70.0) grams. Post-operatively, we found minimal drop in haemoglobin levels, with a fall of 0.7 g/dL on average, with a range of 0.1-3.4 g/dL. Mean length of stay following TURP was 1.45 days (1-18), and 101/132 (76.5%) of patients had a successful trial without catheter on the first post-operative day. Conclusion Our outcomes compare favorably with the published data. This study suggests it may be possible to reduce the cost and resources associated with the use of 3-way catheters and CBI post-TURP surgery by using a 2-way catheter instead. Despite this, appropriate patient selection for this novel technique needs to be adopted. Our results would suggest that patients with smaller prostates or limited resections might be suitable for a 2-way urethral catheter post-TURP.

Age-period-cohort (APC) models are frequently used in a variety of health and demographic related outcomes. Fitting and interpreting APC models to data in equal intervals (equal age and period widths) is non-trivial due to the structural link between the three temporal effects (given two, the third can always be found) causing the wellknown identification problem. The usual method for resolving the structural link identification problem is to base a model off identifiable quantities. It is common to find health and demographic data in unequal intervals, this encounters further identification problems on top of the structural link. We highlight the new issues by showing quantities that were identifiable for equal intervals are no longer identifiable for unequal data. Furthermore, through extensive simulation studies, we show how previous methods for unequal APC models are not always appropriate due to their sensitivity to the choice of functions used to approximate the true temporal functions. We propose a new method for modelling unequal APC data using penalised smoothing splines. Our proposal effectively resolves any additional issues that arise and is robust to the choice of the approximating function. To demonstrate the effectiveness of our proposal, we conclude with an application to UK all-cause mortality data from the Human mortality database (HMD).