Walter Hoyer

The literature about Prediction Interval (PI) and Tolerance Interval (TI) in linear mixed models is usually developed for specific designs, which is a main limitation to their use. This paper proposes to reformulate the two‐sided PI to be generalizable under a wide variety of designs (one random factor, nested and crossed designs for multiple random factors, and balanced or unbalanced designs). This new methodology is based on the Hessian matrix, namely, the inverse of (observed) Fisher Information matrix, and is built with a cell mean model. The degrees of freedom for the total variance are calculated with the generalized Satterthwaite method and compared to the Kenward‐Roger's degrees of freedom for fixed effects. Construction of two‐sided TIs are also detailed with one random factor, and two nested and two crossed random variables. An extensive simulation study is carried out to compare the widths and coverage probabilities of Confidence Intervals (CI), PIs, and TIs to their nominal levels. It shows excellent coverage whatever the design and the sample size are. Finally, these CIs, PIs, and TIs are applied to two real data sets: one from orthopedic surgery study (intralesional resection risk) and the other from assay validation study during vaccine development.

Quality by design (ICH-Topic Q8) requires a prospective summary of the desired quality characteristics of a drug product. This is known as the Quality Target Product Profile (QTPP) which forms the basis for the design and development of the product. An analogous term has been established for analytical procedures called the Analytical Target Profile (ATP). The ATP, in a similar fashion to the QTPP, prospectively summarises the requirements associated with a measurement on a quality attribute which needs to be met by an analytical procedure. Criteria defined in the ATP relate to the maximum uncertainty associated with the reportable result that is required to maintain acceptable confidence in the quality decision made from the result. The ATP is used to assess the fitness of an analytical procedure in the development phase and during all changes across the analytical lifecycle. One or more analytical procedures can meet the requirements of an ATP. The ATP can be applied to any quality attribute across any pharmaceutical modality where an analytical procedure is used to generate a reportable result and this paper provides examples from three of these modalities: Small molecules, oligonucleotides and vaccines. Some key performance characteristics will be discussed for each ATP, namely specificity, accuracy and precision, taking into account the expected range of the analyte. The combination of accuracy and precision into a combined uncertainty characteristic will also be discussed as a more holistic approach. The use of the ATP concept will help focus attention on the properties of a method which impact quality decisions rather than method descriptions, and may enable greater regulatory flexibility across the lifecycle using established conditions based on method performance criteria as proposed in the Step 2 version of ICHQ12. The planned revision of ICHQ2 and development of a new guideline: ICHQ14 Analytical Procedure Development will provide a golden opportunity to harmonise the definition of new QbD concepts such as the ATP.

In this paper, we develop a classical electrodynamic theory to study the optical nonlinearities of metallic nanoparticles. The quasi free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the plasma equations. This theory is further tailored to study second-harmonic generation. Through detailed experiment-theory comparisons, we validate this classical theory as well as the associated numerical algorithm. It is demonstrated that our theory not only provides qualitative agreement with experiments but it also reproduces the overall strength of the experimentally observed second-harmonic signals.

Al – Bi – Cu phase equilibria were studied using dedicated thermal analysis and microstructural investigation of slowly solidified samples. Experimentation in the most decisive Cu-rich region was enabled by developing a BN insert in combination with Ta-encapsulation for these challenging samples. A consistent thermodynamic model of the Al – Bi – Cu system is developed for the first time and applied to calculations of the entire phase diagram. The liquid miscibility gap of Al – Bi alloys extends dramatically upon addition of Cu. The density difference of the two liquids was determined in dedicated experimentation on buoyancy forces. The useful composition and temperature range for these experiments in the ternary L′ + L′′ region was provided by the thermodynamic calculations. The density data can be well interpreted on the basis of presently calculated coexisting liquid phase compositions. Finally, distinct ternary monotectic features on solidification microstructures of Al – Bi – Cu alloys are revealed and inter-related with the phase formation from thermodynamic calculations.

We developed a classical electrodynamics theory to study the optical nonlinearities of metallic nanoparticles. Through a detailed comparison between existing experiments and numerical simulations, we validated this theory as well as the associated numerical algorithm.

We present experiments on second-harmonic generation from arrays of magnetic split-ring resonators and arrays of complementary split-ring resonators. In both cases, the fundamental resonance is excited by the incident femtosecond laser pulses under normal incidence, leading to comparably strong second-harmonic signals. These findings are discussed in terms of Babinet’s principle and in terms of a recently developed microscopic classical theory that leads to good agreement regarding the relative and the absolute nonlinear signal strengths. The hydrodynamic convective contribution is found to be the dominant source of second-harmonic generation—in contrast to a previous assignment [Science 313, 502 (2006) ].

A fully microscopical theory for the photoluminescence of a quantum-well in an arbitrary one-dimensional stack structure is presented. For strong-coupling configurations, the full semiconductor luminescence equations are solved. For the weak-coupling regime, a frequency-dependent filter function is directly derived from the semiconductor luminescence equations with the knowledge of the dielectric structure. Via that filter function, the detected luminescence can be related to the pure quantum-well emission in vacuum. The approach is generalized to include corrections to the emitted peak width due to the photonic-environment-dependent radiative decay, and the corrections are shown to be obtainable from the mode functions alone. The applicability of the method is thoroughly tested up to the onset of normal-mode coupling.