Local Derivative-Free Approximation of Computationally Expensive Posterior Densities

Bayesian inference using Markov chain Monte Carlo (MCMC) is computationally prohibitive when the posterior density of interest, π, is computationally expensive to evaluate. We develop a derivative-free algorithm GRIMA to accurately approximate π by interpolation over its high-probability density (HPD) region, which is initially unknown. Our local approach reduces the waste of computational budget on approximation of π in the low-probability region, which is inherent in global experimental designs. However, estimation of the HPD region is nontrivial when derivatives of π are not available or are not informative about the shape of the HPD region. Without relying on derivatives, GRIMA iterates (a) sequential knot selection over the estimated HPD region of π to refine the surrogate posterior and (b) re-estimation of the HPD region using an MCMC sample from the updated surrogate density, which is inexpensive to obtain. GRIMA is applicable to approximation of general unnormalized posterior densities. To determine the range of tractable problem dimensions, we conduct simulation experiments on test densities with linear and nonlinear component-wise dependence, skewness, kurtosis and multimodality. Subsequently, we use GRIMA in a case study to calibrate a computationally intensive nonlinear regression model to real data from the Town Brook watershed. Supplemental materials for this article are available online.     

Synthesis and characterization of A4[Re6Q8L6]@SiO2 red-emitting silica nanoparticles based on Re6 metal atom clusters (A = Cs or K, Q = S or Se, and L = OH or CN)

Metal atom clusters constitute very promising candidates as luminophores for applications in biotechnology because they are nanosized entities offering robust luminescence in the near-infrared field (NIR). However, they cannot be used as prepared for biological applications because of potential toxic effects and quenching of the clusters' luminescence in aqueous media, and they therefore need to be dispersed in a biocompatible matrix. We describe herein the encapsulation of octahedral rhenium clusters, denoted as A(4)[Re(6)Q(8)L(6)] (A = Cs or K, Q = S or Se, and L = OH or CN), in silica nanoparticles by a water-in-oil microemulsion process, paying particular attention to the clusters' stability. The obtained A(4)[Re(6)Q(8)L(6)]@SiO(2) nanoparticles are 30 nm in size with good monodispersity and a perfectly spherical shape, as shown by scanning electron microscopy (SEM). The presence of cluster units inside the silica matrix was evidenced by scanning transmission electron microscopy in annular dark-field mode (ADF-STEM). From the point of view of their optical properties, the A(4)[Re(6)Q(8)L(6)]@SiO(2) nanoparticles show red and NIR emission under UV excitation, even when dispersed in water. The evolution of the structural and luminescence properties of clusters before and after encapsulation was followed by Raman and photoluminescence spectroscopy.     

Spherical CR-manifolds of dimension 3

A sphericalCR-structure on a smooth (2n–1)-manifoldM is a maximal collection of distinguished charts modeled on the boundary H ⁿ of the complex hyperbolic space, where coordinate changes are restrictions of transformations from PU(n, 1). There exists a development map , where is the universal covering ofM, which is a local diffeomorphism. We study properties of the development maps and holonomy groups of sphericalCR-structures on compact 3-dimensional manifolds. We also give constructions of fundamental domains for some discrete subgroups of PU(2, 1).     

Analysis of Decomposition Algorithms with Benders Cuts for p-Median Problem

In this paper the algorithms for solving the p-median problem based on the Benders decomposition are investigated. A family of problems hard for solving with such algorithms is constructed and then generalized to a special NP-hard case of the p-median problem. It is shown that the effectiveness of the considered algorithms depends on the choice of the optimal values of the dual variables used in Benders cuts. In particular, the depth of the cuts can be equal to one.     

The triple pyrophosphate Cs3CaFe(P2O7)2

The complex phosphate tricaesium calcium iron bis(diphosphate), Cs₃CaFe(P₂O₇)₂, has been prepared by the flux method. Isolated [FeO₅] and [CaO₆] polyhedra are linked by two types of P₂O₇ groups into a three‐dimensional framework. The latter is penetrated by hexagonal channels along the a axis where three Cs atoms are located. Calculations of caesium Voronoi–Dirichlet polyhedra give coordination schemes for the three Cs atoms as [8 + 3], [9 + 1] and [9 + 4]. The structure includes features of both two‐ and three‐dimensional frameworks of caesium double pyrophosphates.     

Incorporation of hafnium (IV) into KTP framework from phosphate‐fluoride fluxes

Solid solutions KTi_1‐XHf_XOPO₄ (х = 0.008 – 0.107) possessing the KTiOPO₄ structure, have been synthesized in molten system K₂O‐P₂O₅‐TiO₂‐HfF₄. The crystal growth experiment of Hf‐doped KTP crystal has been reported. The X‐ray powder diffraction data and chemical analysis are also presented. It has been shown that KTiOPO₄ crystal structure slightly changes when Hf incorporates into the framework. Transmission/absorption spectra of KTi_0.974Hf_0.026OPO₄ crystals have been recorded. The incorporation of Hf ions shifts the optical absorption edge in the UV‐visible spectrum towards the long‐wavelength region with absorption near 387 nm.     

QCM based sensor for detecting volumetric properties of liquids

We introduce a microacoustic sensor, which combines the quartz crystal microbalance, a liquid-filled cavity and an intermediate artificial layer with effective acoustic properties. Each of the three components fulfils a specific task. The quartz vibrates in its thickness shear mode and acts as source and detector of shear waves, which penetrate the intermediate artificial layer and excite a resonance in the liquid-filled cavity. Both the piezoelectric transducer and the liquid-filled cavity are high-Q resonators with well-adjusted resonance frequencies very close to each other. The intermediate artificial layer couples the two resonators in a distinct manner via control of the propagation of acoustic waves between the quartz crystal and the liquid-filled cavity layer. The origin of the sensor signal is a change of the resonance frequency of the liquid-filled cavity caused by variations of acoustic properties of the liquid analyte inside the cavity, first of all speed of sound. This resonance appears as second resonance peak in the admittance spectrum of the quartz crystal.