Proof of two conjectures of Z.-W. Sun on congruences for Franel numbers

For all nonnegative integers n, the Franel numbers are defined as $$f_n=\sum_{k=0}^n {n\choose k}^3.$$ We confirm two conjectures of Z.-W. Sun on congruences for Franel numbers: \sum_{k=0}^{n-1}(3k+2)(-1)^k f_k &\equiv 0 \pmod{2n^2}, \sum_{k=0}^{p-1}(3k+2)(-1)^k f_k &\equiv 2p^2 (2^p-1)^2 \pmod{p^5}, where n is a positive integer and p>3 is a prime.Comment: 8 pages, minor changes, to appear in Integral Transforms Spec. Func

A study of blow-ups in the Keller-Segel model of chemotaxis

We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions. The numerical findings (in two dimensions) are then compared with analytical predictions regarding formation and interaction of singularities obtained via analysis of the stochastic differential equations associated with the Keller-Segel model

Not All Children with Cystic Fibrosis Have Abnormal Esophageal Neutralization during Chemical Clearance of Acid Reflux.

PurposeAcid neutralization during chemical clearance is significantly prolonged in children with cystic fibrosis, compared to symptomatic children without cystic fibrosis. The absence of available reference values impeded identification of abnormal findings within individual patients with and without cystic fibrosis. The present study aimed to test the hypothesis that significantly more children with cystic fibrosis have acid neutralization durations during chemical clearance that fall outside the physiological range.MethodsPublished reference value for acid neutralization duration during chemical clearance (determined using combined impedance/pH monitoring) was used to assess esophageal acid neutralization efficiency during chemical clearance in 16 children with cystic fibrosis (3 to <18 years) and 16 age-matched children without cystic fibrosis.ResultsDuration of acid neutralization during chemical clearance exceeded the upper end of the physiological range in 9 of 16 (56.3%) children with and in 3 of 16 (18.8%) children without cystic fibrosis (p=0.0412). The likelihood ratio for duration indicated that children with cystic fibrosis are 2.1-times more likely to have abnormal acid neutralization during chemical clearance, and children with abnormal acid neutralization during chemical clearance are 1.5-times more likely to have cystic fibrosis.ConclusionSignificantly more (but not all) children with cystic fibrosis have abnormally prolonged esophageal clearance of acid. Children with cystic fibrosis are more likely to have abnormal acid neutralization during chemical clearance. Additional studies involving larger sample sizes are needed to address the importance of genotype, esophageal motility, composition and volume of saliva, and gastric acidity on acid neutralization efficiency in cystic fibrosis children

The Influence of Specimen Thickness on the High Temperature Corrosion Behavior of CMSX-4 during Thermal-Cycling Exposure

CMSX-4 is a single-crystalline Ni-base superalloy designed to be used at very high temperatures and high mechanical loadings. Its excellent corrosion resistance is due to external alumina-scale formation, which however can become less protective under thermal-cycling conditions. The metallic substrate in combination with its superficial oxide scale has to be considered as a composite suffering high stresses. Factors like different coefficients of thermal expansion between oxide and substrate during temperature changes or growing stresses affect the integrity of the oxide scale. This must also be strongly influenced by the thickness of the oxide scale and the substrate as well as the ability to relief such stresses, e.g., by creep deformation. In order to quantify these effects, thin-walled specimens of different thickness (t = 100500 lm) were prepared. Discontinuous measurements of their mass changes were carried out under thermal-cycling conditions at a hot dwell temperature of 1100 C up to 300 thermal cycles. Thin-walled specimens revealed a much lower oxide-spallation rate compared to thick-walled specimens, while thinwalled specimens might show a premature depletion of scale-forming elements. In order to determine which of these competetive factor is more detrimental in terms of a component’s lifetime, the degradation by internal precipitation was studied using scanning electron microscopy (SEM) in combination with energy-dispersive X-ray spectroscopy (EDS). Additionally, a recently developed statistical spallation model was applied to experimental data [D. Poquillon and D. Monceau, Oxidation of Metals, 59, 409–431 (2003)]. The model describes the overall mass change by oxide scale spallation during thermal cycling exposure and is a useful simulation tool for oxide scale spallation processes accounting for variations in the specimen geometry. The evolution of the net-mass change vs. the number of thermal cycles seems to be strongly dependent on the sample thickness

Assessment of the effectiveness of a risk-reduction measure on pluvial flooding and economic loss in Eindhoven, the Netherlands

Open Access journalCopyright © 2013 The Authors. Published by Elsevier Ltd.12th International Conference on Computing and Control for the Water Industry, CCWI2013Cities are increasingly assessing and reducing pluvial flood risk. Quantitative assessment of the effectiveness of risk-reduction measures is required. We use hydraulic simulation with GIS-based financial analysis to assess the pluvial flood risk for Eindhoven, The Netherlands. Analysis is carried out for four scenarios: two rainfall events, with and without separation of the combined sewer-stormwater network. Flooding statistics show how the risk-reduction measure impacts local flooding. Financial analysis demonstrates the saving resulting from the risk-reduction measure. Expected annual damage is reduced by c.€130,500. City authorities are better equipped in making cost-benefit decisions regarding implementation of pluvial flood risk-reduction measures.EC FP7 project PREPARED: Enabling Chang

Assessing Financial Loss due to Pluvial Flooding and the Efficacy of Risk-Reduction Measures in the Residential Property Sector

The final publication is available at Springer via http://dx.doi.org/10.1007/s11269-014-0833-6A novel quantitative risk assessment for residential properties at risk of pluvial flooding in Eindhoven, The Netherlands, is presented. A hydraulic model belonging to Eindhoven was forced with low return period rainfall events (2, 5 and 10-year design rainfalls). Three scenarios were analysed for each event: a baseline and two risk-reduction scenarios. GIS analysis identified areas where risk-reduction measures had the greatest impact. Financial loss calculations were carried out using fixed-threshold and probabilistic approaches. Under fixed-threshold assessment, per-event Expected Annual Damage (EAD) reached €38.2 m, with reductions of up to €454,000 resulting from risk-reduction measures. Present costs of flooding reach €1.43bn when calculated over a 50-year period. All net-present value figures for the risk-reduction measures are negative. Probabilistic assessment yielded EAD values up to more than double those of the fixed-threshold analysis which suggested positive net-present value. To the best of our knowledge, the probabilistic method based on the distribution of doorstep heights has never before been introduced for pluvial flood risk assessment. Although this work suggests poor net-present value of risk-reduction measures, indirect impacts of flooding, damage to infrastructure and the potential impacts of climate change were omitted. This work represents a useful first step in helping Eindhoven prepare for future pluvial flooding. The analysis is based on software and tools already available at the municipality, eliminating the need for software upgrading or training. The approach is generally applicable to similar cities.European Commission Seventh Framework Program (EC FP7

Planning with Information-Processing Constraints and Model Uncertainty in Markov Decision Processes

Information-theoretic principles for learning and acting have been proposed to solve particular classes of Markov Decision Problems. Mathematically, such approaches are governed by a variational free energy principle and allow solving MDP planning problems with information-processing constraints expressed in terms of a Kullback-Leibler divergence with respect to a reference distribution. Here we consider a generalization of such MDP planners by taking model uncertainty into account. As model uncertainty can also be formalized as an information-processing constraint, we can derive a unified solution from a single generalized variational principle. We provide a generalized value iteration scheme together with a convergence proof. As limit cases, this generalized scheme includes standard value iteration with a known model, Bayesian MDP planning, and robust planning. We demonstrate the benefits of this approach in a grid world simulation.Comment: 16 pages, 3 figure

Teratoma formation of human embryonic stem cells in three-dimensional perfusion culture bioreactors

Teratoma formation in mice is today the most stringent test for pluripotency that is available for human pluripotent cells, as chimera formation and tetraploid complementation cannot be performed with human cells. The teratoma assay could also be applied for assessing the safety of human pluripotent cell-derived cell populations intended for therapeutic applications. In our study we examined the spontaneous differentiation behaviour of human embryonic stem cells (hESCs) in a perfused 3D multi-compartment bioreactor system and compared it with differentiation of hESCs and human induced pluripotent cells (hiPSCs) cultured in vitro as embryoid bodies and in vivo in an experimental mouse model of teratoma formation. Results from biochemical, histological/immunohistological and ultrastuctural analyses revealed that hESCs cultured in bioreactors formed tissue-like structures containing derivatives of all three germ layers. Comparison with embryoid bodies and the teratomas revealed a high degree of similarity of the tissues formed in the bioreactor to these in the teratomas at the histological as well as transcriptional level, as detected by comparative whole-genome RNA expression profiling. The 3D culture system represents a novel in vitro model that permits stable long-term cultivation, spontaneous multi-lineage differentiation and tissue formation of pluripotent cells that is comparable to in vivo differentiation. Such a model is of interest, e.g. for the development of novel cell differentiation strategies. In addition, the 3D in vitro model could be used for teratoma studies and pluripotency assays in a fully defined, controlled environment, alternatively to in vivo mouse models. Copyright (c) 2012 John Wiley & Sons, Ltd