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A new class of parametric models, referred to as sample parametric models, is developed for random elements that match sample rather than the first two moments and/or other global properties of these elements. The models can be used to characterize, e.g., material properties at small scale in which case their samples represent microstructures of material specimens selected at random from a population. The samples of the proposed models are elements of finite-dimensional vector spaces spanned by samples, eigenfunctions of Karhunen–Loève (KL) representations, or modes of singular value decompositions (SVDs). The implementation of sample parametric models requires knowledge of the probability laws of target random elements. Numerical examples including stochastic processes and random fields are used to demonstrate the construction of sample parametric models, assess their accuracy, and illustrate how these models can be used to solve efficiently stochastic equations. [ABSTRACT FROM AUTHOR]

Data driven decision making is a key element of today's pharmaceutical research, including early drug discovery. It comprises questions like which target to pursue, which chemical series to pursue, which compound to make next, or which compound to select for advanced profiling and promotion to pre-clinical development. In the following paper we will exemplify how data integrity, i.e. the context data is generated in and auxiliary information that is provided for individual result records, can influence decision making in early lead discovery programs. In addition we will describe some approaches which we pursue at Boehringer Ingelheim to reduce the risk for getting misguided. [ABSTRACT FROM AUTHOR]

Conditions under which samples of continuous stochastic processes X (t) on bounded time intervals [ 0 , τ ] can be represented by samples of finite dimensional (FD) processes X d (t) are augmented such that samples of Slepian models S d , a (t) of X d (t) can be used as surrogates for samples of Slepian models S a (t) of X (t). FD processes are deterministic functions of time and d < ∞ random variables. The discrepancy between target and FD samples is quantified by the metric of the space C [ 0 , τ ] of continuous functions. The numerical illustrations, which include Gaussian/non-Gaussian FD processes and solutions of linear/nonlinear random vibration problems, are consistent with the theoretical findings in the paper. [ABSTRACT FROM AUTHOR]

Abstract: The influence of sample properties and composition on the size and concentration of aerosol particles generated by nanosecond Nd:YAG laser ablation at 213nm was investigated for three sets of different materials, each containing five specimens with a similar matrix (Co-cemented carbides with a variable content of W and Co, steel samples with minor differences in elemental content and silica glasses with various colors). The concentration of ablated particles (particle number concentration, PNC) was measured in two size ranges (10–250nm and 0.25–17µm) using an optical aerosol spectrometer. The shapes and volumes of the ablation craters were obtained by Scanning Electron Microscopy (SEM) and by an optical profilometer, respectively. Additionally, the structure of the laser-generated particles was studied after their collection on a filter using SEM. The results of particle concentration measurements showed a significant dominance of particles smaller than 250nm in comparison with larger particles, irrespective of the kind of material. Even if the number of particles larger than 0.25µm is negligible (up to 0.1%), the volume of large particles that left the ablation cell can reach 50% of the whole particle volume depending on the material. Study of the ablation craters and the laser-generated particles showed a various number of particles produced by different ablation mechanisms (particle splashing or condensation), but the similar character of released particles for all materials was observed by SEM after particle collection on the membrane filter. The created aerosol always consisted of two main structures — spherical particles with diameters from tenths to units of micrometers originally ejected from the molten surface layer and µm-sized “fibres” composed of primary agglomerates with diameters in the range between tens and hundreds of nanometers. The shape and structure of ablation craters were in good agreement with particle concentration measurements. Samples with a high crater rim and melted bottom produced the highest number of large spherical particles. The mass values of all produced aerosols were calculated from the measured ablation crater volumes and sample densities. [Copyright &y& Elsevier]

In this paper, we study a new type of stochastic functional differential equations which are called hybrid pantograph stochastic functional differential equations (HPSFDEs). We investigate moment properties and sample properties of the solutions such as the moment exponential stability, almost sure exponential stability and almost sure polynomial stability. Moreover, several theoretical examples and one practical example are given to illustrate our theory. [ABSTRACT FROM AUTHOR]