Optimization of sample clean-up for the determination of small amounts of MOSH and MOAH in edible oils - method DGF C-VI 22 (20).

Methods for determining MOSH and MOAH in edible oils showed major problems with interlaboratory comparability of analytical results, especially in the lower concentration range below 10 mg/kg. However, a method with improved sensitivity and reproducibility is urgently needed to obtain a valid data basis for minimization efforts. To cope this problem a new method was created in 2020. The method was established as the standard method DGF C-VI 22 (20) of the German Society for Fat Science e.V. (DGF). For the development of this method different sample epoxidation approaches have been performed, evaluated and improved. Additionally, a saponification, a decision tree for sample preparation, an upstream clean-up column and a system suitability test were introduced. The focus was on reliability and interlaboratory comparability over all edible oil matrices up to a LOQ of 1 mg/kg. The optimized method was validated in terms of trueness and precision in a collaborative trail with 11 laboratories. The achieved recovery rates of 89-105% MOSH and 70-105% MOAH met the JRC requirements. Method and validation results were obtained with HorRat values between 1.3 and 1.8 for MOSH and MOAH.

Determining MOSH and MOAH with High Sensitivity in Vegetable Oil─A New, Reliable, and Comparable Approach Using Online LC-GC-FID─Evaluation of Method Precision Data.

A method for the analysis of saturated mineral oil hydrocarbons (MOSH) and aromatic mineral oil hydrocarbons (MOAH) has been developed to improve interlaboratory precisions especially for amounts below 10 mg/kg. This approach was adopted as the standard method DGF C-VI 22 (20) of the German Society of Fat Sciences. Therefore, this method was evaluated on different edible oils containing a variety of interfering biogenic substances. The precision data were determined in an interlaboratory trial with an international group of 14 laboratories from Germany, Austria, and Italy. Good reproducible relative standard deviations for total MOSH (12.5-20.7%) and total MOAH (12.4-39.5%) as well as HorRat values ranging between 1.1 and 2.3 for total MOSH and between 0.9 and 2.6 for total MOAH have been achieved. As some matrices showed residual interferences in the MOAH fraction, these substances were further analyzed by online high-performance liquid chromatography-comprehensive two dimensional gas chromatography with time of flight mass detection.

A Bayesian Approach to the Estimation of Parameters and Their Interdependencies in Environmental Modeling.

We present a case study for Bayesian analysis and proper representation of distributions and dependence among parameters when calibrating process-oriented environmental models. A simple water quality model for the Elbe River (Germany) is referred to as an example, but the approach is applicable to a wide range of environmental models with time-series output. Model parameters are estimated by Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling. While the best-fit solution matches usual least-squares model calibration (with a penalty term for excessive parameter values), the Bayesian approach has the advantage of yielding a joint probability distribution for parameters. This posterior distribution encompasses all possible parameter combinations that produce a simulation output that fits observed data within measurement and modeling uncertainty. Bayesian inference further permits the introduction of prior knowledge, e.g., positivity of certain parameters. The estimated distribution shows to which extent model parameters are controlled by observations through the process of inference, highlighting issues that cannot be settled unless more information becomes available. An interactive interface enables tracking for how ranges of parameter values that are consistent with observations change during the process of a step-by-step assignment of fixed parameter values. Based on an initial analysis of the posterior via an undirected Gaussian graphical model, a directed Bayesian network (BN) is constructed. The BN transparently conveys information on the interdependence of parameters after calibration. Finally, a strategy to reduce the number of expensive model runs in MCMC sampling for the presented purpose is introduced based on a newly developed variant of delayed acceptance sampling with a Gaussian process surrogate and linear dimensionality reduction to support function-valued outputs.

Symplectic Gaussian process regression of maps in Hamiltonian systems.

We present an approach to construct structure-preserving emulators for Hamiltonian flow maps and Poincaré maps based directly on orbit data. Intended applications are in moderate-dimensional systems, in particular, long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations. The method is based on multi-output Gaussian process (GP) regression on scattered training data. To obtain long-term stability, the symplectic property is enforced via the choice of the matrix-valued covariance function. Based on earlier work on spline interpolation, we observe derivatives of the generating function of a canonical transformation. A product kernel produces an accurate implicit method, whereas a sum kernel results in a fast explicit method from this approach. Both are related to symplectic Euler methods in terms of numerical integration but fulfill a complementary purpose. The developed methods are first tested on the pendulum and the Hénon-Heiles system and results compared to spectral regression of the flow map with orthogonal polynomials. Chaotic behavior is studied on the standard map. Finally, the application to magnetic field line tracing in a perturbed tokamak configuration is demonstrated. As an additional feature, in the limit of small mapping times, the Hamiltonian function can be identified with a part of the generating function and thereby learned from observed time-series data of the system's evolution. For implicit GP methods, we demonstrate regression performance comparable to spectral bases and artificial neural networks for symplectic flow maps, applicability to Poincaré maps, and correct representation of chaotic diffusion as well as a substantial increase in performance for learning the Hamiltonian function compared to existing approaches.

Gaussian Process Regression for Data Fulfilling Linear Differential Equations with Localized Sources.

Specialized Gaussian process regression is presented for data that are known to fulfill a given linear differential equation with vanishing or localized sources. The method allows estimation of system parameters as well as strength and location of point sources. It is applicable to a wide range of data from measurement and simulation. The underlying principle is the well-known invariance of the Gaussian probability distribution under linear operators, in particular differentiation. In contrast to approaches with a generic covariance function/kernel, we restrict the Gaussian process to generate only solutions of the homogeneous part of the differential equation. This requires specialized kernels with a direct correspondence of certain kernel hyperparameters to parameters in the underlying equation and leads to more reliable regression results with less training data. Inhomogeneous contributions from linear superposition of point sources are treated via a linear model over fundamental solutions. Maximum likelihood estimates for hyperparameters and source positions are obtained by nonlinear optimization. For differential equations representing laws of physics the present approach generates only physically possible solutions, and estimated hyperparameters represent physical properties. After a general derivation, modeling of source-free data and parameter estimation is demonstrated for Laplace's equation and the heat/diffusion equation. Finally, the Helmholtz equation with point sources is treated, representing scalar wave data such as acoustic pressure in the frequency domain.

Fracture Resistance of Various Thickness e.max CAD Lithium Disilicate Crowns Cemented on Different Supporting Substrates: An In Vitro Study.

PURPOSE: To investigate the influence of abutment material properties on the fracture resistance and failure mode of lithium disilicate (IPS e.max) CAD/CAM (computer-aided design/manufacturing) crowns on traditionally and minimally prepared simulated tooth substrates. MATERIALS AND METHODS: Thirty lithium disilicate (IPS e.max) CAD/CAM crowns were divided into three groups (n = 10): TD: traditional thickness crowns cemented on Paradigm MZ100 abutments; MD: minimal thickness crowns cemented on Paradigm MZ100 abutments; ME: minimal thickness crowns cemented on e.max abutments. The 3Shape system was used to scan, design and mill all abutments and crowns with a die space set to 40 µm. Traditional thickness crowns were designed based on manufacturer guidelines with 1.5 mm occlusal thickness and 1.0 mm margins. Minimal thickness crowns were designed with 0.7 mm occlusal thickness and 0.5 mm margins. MZ100 composite and e.max abutments were selected to simulate dentin and enamel substrates, respectively, based on their elastic-modulus. Variolink Esthetic was used to cement all samples following manufacturer's instructions. A universal testing machine was used to load all specimens to fracture with a 3 mm radius stainless steel hemispherical tip at a crosshead speed 0.5 mm/minute along the longitudinal axis of the abutment with a 1 mm thermoplastic film placed between the loading tip and crown surface. Data was analyzed using ANOVA and Bonferroni post hoc assessment. Fractographic analysis was performed with scanning electron microscopy (SEM). RESULTS: The mean fracture load (standard deviation) was 1499 (241) N for TD; 1228 (287) N for MD; and 1377 (96) N for ME. Statistically significant difference between groups did not exist (p = 0.157, F = 1.995). In groups TD and MD with low e-modulus abutments, the dispersion of a probability distribution (coefficient of variation: CV) was statistically higher than that of group ME with high e-modulus abutments. SEM illustrated larger micro-fracture dimensions in Group MD than Group ME. CONCLUSION: Minimal thickness e.max crowns did not demonstrate statistical difference in fracture resistance from traditional thickness crowns. Fracture mechanisms of minimal thickness e.max crowns may be affected by the e-modulus of the substrate. Minimal thickness e.max crowns may be a viable restorative option when supported by high e-modulus materials.