Interactive Probability Models: Inverse Problems on the Sphere

We expose a class of probabilistic models withonly two outcomes that we call interactive probabilitymodels for the analysis of data that arise in situationswhere there is influence of the measurer on the measured. We reconstruct a Borel measurecorresponding to possible sets of probabilities that arerelated to outcomes of experiments. We give threeexamples: one that corresponds to the quantum mechanical case, one to a deterministic measurement, andone to a situation where the outcome of the measurementis determined by the measurement apparatusonly.     

Three-site model for hydrogen adsorption on supported platinum particles: influence of support ionicity and particle size on the hydrogen coverage

Pt L(3) X-ray absorption edge data on small supported Pt particles (N < 6.5) reveals that at very low H(2) pressure or high temperature the strongest bonded H is chemisorbed in an atop position. With decreasing temperature or at higher H(2) pressure only n-fold (n = 2 or 3) sites are occupied. At high H(2) pressure or low temperature, the weakest bonded H is positioned in an "ontop" site, with the chemisorbing Pt already having a stronger bond to a H atom in an n-fold site. DFT calculations show that the adsorption energy of hydrogen increases for Pt particles on ionic (basic) supports. The combination of the DFT calculations with hydrogen chemisorption data and the analysis of the Pt L(3) X-ray absorption spectra implies that both the H coverage and/or the type of active Pt surface sites, which are present at high temperature catalytic reaction conditions, strongly depend on the ionicity of the support. The consequences for Pt catalyzed hydrogenolysis and hydrogenation reactions will be discussed.     

Zener tunneling of light waves in an optical superlattice

We report on the observation of Zener tunneling of light waves in spectral and time-resolved transmission measurements, performed on an optical superlattice made of porous silicon. The structure was designed to have two photonic minibands, spaced by a narrow frequency gap. A gradient in the refractive index was introduced to create two optical Wannier-Stark ladders and, at a critical value of the optical gradient, tunneling between energy bands was observed in the form of an enhanced transmission peak and a characteristic time dependence of the transmission.     

Optical necklace states in Anderson localized 1D systems

We report on the observation of nonlocalized modes or necklace states of light waves in disordered systems in the Anderson localized regime. The samples consist of positional-disordered binary multilayer systems. Anderson localized modes manifest themselves as narrow high-transmission peaks in the transmission spectrum, whereas the average of the logarithm of the transmission coefficient decreases linearly with thickness. Optical necklace states are observed as modes with a characteristic multiresonance time response and relatively fast decay time.     

The internal-state distribution of sodium dimers in a free jet expansion

The internal-state distribution of sodium dimers (Na₂) is studied experimentally in the first part of a low-pressure free jet expansion of sodium vapour, using the method of laser-induced fluorescence. The measured distribution is of a Boltzmann type at the nozzle exit but deviates strongly from it thereafter.     

The role of the modular pairs in the category of complete orthomodular lattice

We study the modular pairs of a complete orthomodular lattice i.e. a CROC. We propose the concept ofm-morphism as a mapping which preserves the lattice structure, the orthogonality and the property to be a modular pair. We give a characterization of them-morphisms in the case of the complex Hilbert space to justify this concept.     

Amplified extended modes in random lasers

We report on a new random laser phenomenon that gives rise to narrow emission modes without requiring optical cavities. Sharp emission peaks are observed experimentally over a broad range of scattering strengths and analyzed in numerical calculations. We find that the introduction of exponential gain in a multiple light scattering process strongly increases the importance of very long light paths. Such long paths are rare and often neglected in passive disordered materials but we show that they can dominate the emission spectrum from an amplifying disordered system.     

Non-uniform polonium distribution in lead–bismuth eutectic revealed by evaporation experiments

Understanding polonium evaporation from lead-bismuth eutectic (LBE) is required for the design of nuclear installations that use liquid LBE as coolant or spallation target. In the present study we measured the time-dependent release of polonium from LBE samples in Ar/5 %H₂ and Ar between room temperature and 500 °C. Our experiments revealed that the majority of polonium in the samples evaporated according to established temperature correlations for the Henry constant of polonium in LBE. However a small fraction of polonium in the LBE behaved differently, causing a relatively large but transient polonium release at the start of evaporation experiments. We showed that this volatile fraction of polonium was located near the sample surface and was formed after prolonged exposure of the samples to air at room temperature. We speculate that the peculiar evaporation behavior of this surface polonium is caused by enrichment and association with an oxide layer.     

Assessing the statistical validity of proteomics based biomarkers

A strategy is presented for the statistical validation of discrimination models in proteomics studies. Several existing tools are combined to form a solid statistical basis for biomarker discovery that should precede a biochemical validation of any biomarker. These tools consist of permutation tests, single and double cross-validation. The cross-validation steps can simply be combined with a new variable selection method, called rank products. The strategy is especially suited for the low-samples-to-variables-ratio (undersampling) case, as is often encountered in proteomics and metabolomics studies. As a classification method, principal component discriminant analysis is used; however, the methodology can be used with any classifier. A dataset containing serum samples from Gaucher patients and healthy controls serves as a test case. Double cross-validation shows that the sensitivity of the model is 89% and the specificity 90%. Potential putative biomarkers are identified using the novel variable selection method. Results from permutation tests support the choice of double cross-validation as the tool for determining error rates when the modelling procedure involves a tuneable parameter. This shows that even cross-validation does not guarantee unbiased results. The validation of discrimination models with a combination of permutation tests and double cross-validation helps to avoid erroneous results which may result from the undersampling.