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

Extreme State Aggregation Beyond MDPs

We consider a Reinforcement Learning setup where an agent interacts with an environment in observation-reward-action cycles without any (esp.\ MDP) assumptions on the environment. State aggregation and more generally feature reinforcement learning is concerned with mapping histories/raw-states to reduced/aggregated states. The idea behind both is that the resulting reduced process (approximately) forms a small stationary finite-state MDP, which can then be efficiently solved or learnt. We considerably generalize existing aggregation results by showing that even if the reduced process is not an MDP, the (q-)value functions and (optimal) policies of an associated MDP with same state-space size solve the original problem, as long as the solution can approximately be represented as a function of the reduced states. This implies an upper bound on the required state space size that holds uniformly for all RL problems. It may also explain why RL algorithms designed for MDPs sometimes perform well beyond MDPs.Comment: 28 LaTeX pages. 8 Theorem

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

Consistent alpha-cluster description of the 12C (0^+_2) resonance

The near-threshold 12C (0^+_2) resonance provides unique possibility for fast helium burning in stars, as predicted by Hoyle to explain the observed abundance of elements in the Universe. Properties of this resonance are calculated within the framework of the alpha-cluster model whose two-body and three-body effective potentials are tuned to describe the alpha - alpha scattering data, the energies of the 0^+_1 and 0^+_2 states, and the 0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2 state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition radius are found in remarkable agreement with the experimental data. The 0^+_2-state structure is described as a system of three alpha-particles oscillating between the ground-state-like configuration and the elongated chain configuration whose probability exceeds 0.9

Getting into the water with the Ecosystem Services Approach: The DESSIN ESS evaluation framework

Driven by Europe's pressing need to overcome its water quality and water scarcity challenges, the speed of innovation in the water sector is outpacing that of science. The methodologies available to assess the impact of innovative solutions to water-related challenges remain limited and highly theoretical, which sets boundaries on their application and usefulness to water practitioners. This hampers the uptake of new technologies and innovative management practices, thus foregoing potential gains in resource efficiency and nature protection, as well as wider benefits to society and the economy. To address this gap, the DESSIN project developed a framework to evaluate the changes in ecosystem services (ESS) associated with technical or management solutions implemented at the water body, sub-catchment or catchment level. The framework was developed with a specific focus on freshwater ecosystems to allow for a more detailed exploration of practical implementation issues. Its development, testing and validation was carried out by conducting ESS evaluations in three different urban case study settings. The framework builds upon existing classification systems for ESS (CICES and FEGS-CS) and incorporates the DPSIR adaptive management scheme as its main structural element. This enables compatibility with other international initiatives on ESS assessments and establishes a direct link to the EU Water Framework Directive, respectively. This work furthers research on practical implementation of the Ecosystem Services Approach, while pushing the discussion on how to promote more informed decision-making and support innovation uptake to address Europe's current water-related challenges

Hospital use of systemic antifungal drugs

BACKGROUND: Sales data indicate a major increase in the prescription of antifungal drugs in the last two decades. Many new agents for systemic use that only recently have become available are likely to be prescribed intensively in acute care hospitals. Sales data do not adequately describe the developments of drug use density. Given the concerns about the potential emergence of antifungal drug resistance, data on drug use density, however, may be valuable and are needed for analyses of the relationship between drug use and antifungal resistance. METHODS: Hospital pharmacy records for the years 2001 to 2003 were evaluated, and the number of prescribed daily doses (PDD, defined according to locally used doses) per 100 patient days were calculated to compare systemic antifungal drug use density in different medical and surgical service areas between five state university hospitals. RESULTS: The 3-year averages in recent antifungal drug use for the five hospitals ranged between 8.6 and 29.3 PDD/100 patient days in the medical services (including subspecialties and intensive care), and between 1.1 and 4.0 PDD/100 patient days in the surgical services, respectively. In all five hospitals, systemic antifungal drug use was higher in the hematology-oncology service areas (mean, 48.4, range, 24 to 101 PDD/100 patient days, data for the year 2003) than in the medical intensive care units (mean, 18.3, range, 10 to 33 PDD/100) or in the surgical intensive care units (mean, 10.7, range, 6 to 18 PDD/100). Fluconazole was the most prescribed antifungal drug in all areas. In 2003, amphotericin B consumption had declined to 3 PDD/100 in the hematology-oncology areas while voriconazole use had increased to 10 PDD/100 in 2003. CONCLUSION: Hematology-oncology services are intense antifungal drug prescribing areas. Fluconazole and other azol antifungal drugs are the most prescribed drugs in all patient care areas while amphotericin B use has considerably decreased. The data may be useful as a benchmark for focused interventions to improve prescribing quality