Programming With Models: Writing Statistical Algorithms for General Model Structures With NIMBLE

We describe NIMBLE, a system for programming statistical algorithms for general model structures within R. NIMBLE is designed to meet three challenges: flexible model specification, a language for programming algorithms that can use different models, and a balance between high-level programmability and execution efficiency. For model specification, NIMBLE extends the BUGS language and creates model objects, which can manipulate variables, calculate log probability values, generate simulations, and query the relationships among variables. For algorithm programming, NIMBLE provides functions that operate with model objects using two stages of evaluation. The first stage allows specialization of a function to a particular model and/or nodes, such as creating a Metropolis-Hastings sampler for a particular block of nodes. The second stage allows repeated execution of computations using the results of the first stage. To achieve efficient second-stage computation, NIMBLE compiles models and functions via C++, using the Eigen library for linear algebra, and provides the user with an interface to compiled objects. The NIMBLE language represents a compilable domain-specific language (DSL) embedded within R. This article provides an overview of the design and rationale for NIMBLE along with illustrative examples including importance sampling, Markov chain Monte Carlo (MCMC) and Monte Carlo expectation maximization (MCEM). Supplementary materials for this article are available online.     

Some static problems for elastic bodies with a crust

Summary This paper studies the diffusion of stresses in a linear isotropic elastic body coated with a thin elastic shell called the ?crust?. Two static problems are considered. The first is that of the semi-infinite half-space covered by a thin plate subject to a point load at the origin. In the second problem a solid elastic sphere enveloped by a thin spherical elastic shell with two opposite point loads at the poles is investigated. Solutions for the displacement within the thin crust are obtained in the two problems by means of the Hankel transform and the Legendre polynomial respectively.

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Sommario Questo lavoro studia la diffusione degli sforzi in un corpo elastico, lineare, isotropo rivestito da un guscio elastico sottile denominato la ?crosta?. Sono considerati due problemi elastostatici. Il primo è quello di un semispazio coperto da una piastra sottile soggetta and un carico concentrato nell'origine. Nel secondo problema si studia una sfera solida elastica avvolta da un guscio sottile elastico con due carichi concentrati opposti nei poli. Nei due problemi le soluzioni in termini di spostamenti entro la crosta si ottengono rispettivamente mediante la trasformata di Hankel e i polinomi di Legendre.

     

Conformations of diester triphenylphosphonium ylides with an ylidic ester or keto and ester ylidic groups

The structures of three related keto diester and diester ylides, namely diethyl 3‐oxo‐2‐(triphenylphosphoranylidene)glutarate, C₂₇H₂₇O₅P, (I), diethyl 3‐oxo‐2‐(triphenylphosphoranylidene)glutarate acetic acid monosolvate, C₂₇H₂₇O₅P·C₂H₄O₂, (II), and diethyl 2‐(triphenylphosphoranylidene)succinate, C₂₆H₂₇O₄P, (III), are presented. The syn‐keto anti‐ester conformations in the crystalline keto diesters are governed by electronic delocalization between the P—C and ylidic bonds and an acyl group, and by intra‐ and intermolecular interactions. There are also intramolecular attractive and repulsive interactions of different types (C—H...O and C—H...π) controlling the molecular conformations. The mono‐ylidic diester (III) has an anti‐ester conformation, while those for (I) and (II) are related to pyrolytic formation of acetylene derivatives. The terminal nonylidic ester group in (I) was disordered over two sets of almost equally populated positions.     

Zur Bestimmung des Kalis und Natrons in Pflanzenaschen und ?hnlichen Substanzen

Ohne Zusammenfassung     

Die Wiedergewinnung des Jods

Ohne Zusammenfassung     

Use of xenon as a mobile phase for on–line capillary supercritical fluid chromatography–fourier transform infrared spectrometry

Xenon is investigated as a mobile phase for on-line capillary supercritical fluid chromatography-Fourier transform infrared spectrometry (SFC-FTIR). Polycyclic aromatic hydrocarbons, aromatic isocyanates, and epoxy acrylate oligomers are analyzed as examples to show that xenon has similar selectivities and solvating powe to CO₂. Its optical transparency makes it ideal for IR detection. A stop flow system is constructed to increase the sensitivity of spectra measured from compounds which are weak IR absorbers.     

Anisotropy of electromagnetically induced left-handedness in atomic three-level media based upon bianisotropic polarizabilities and tensor character

A three-level atomic system, configured as either a gaseous medium or a solid state material, with a driving field establishing a Rabi frequency of control, is tested by a probe field. The medium has bianisotropic microscopic polarizability and magnetizability, from which the permittivity and permeability tensors are derived. Non-isotropy and polarization dependence for left-handedness (negative index of refraction) is demonstrated through examination of tensor components in the detuning frequency spectrum. These results have important implications for use in optical or electronic devices.