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Two characterisations of a random mean from a Dirichlet process, as a limit of finite sums of a simple symmetric form and as a solution of a certain stochastic equation, are developed and investigated. These are used to reach results on and new insights into the distributions of such random means. In particular, identities involving functional transforms and recursive moment formulae are established. Furthermore, characterisations for several choices of the Dirichlet process parameter (leading to symmetric, unimodal, stable, and finite mixture distributions) are provided. Our methods lead to exact simulation recipes for prior and posterior random means, an approximation algorithm for the exact densities of these means, and limiting normality theorems for posterior distributions. The theory also extends to mixtures of Dirichlet processes and to the case of several random means simultaneously.

A unifying framework for Bayesian analysis in discrete nonparametric settings is proposed. To this aim, a general class of nonparametric discrete prior distributions on an arbitrary sample space is introduced. The general structure of the posterior and predictive distributions and an explicit updating mechanism for the posterior are developed. [Copyright &y& Elsevier]

The use of DNA to template the assembly of nanoscale wires and protein-functionalized nanogap contacts is described: Specifically, the use of DNA to template the assembly of gold nanowires between conventionally patterned gold contacts on a silicon wafer substrate. Also described is the use of DNA to template the assembly of protein-functionalized nanogap gold contacts on a silicon wafer substrate. Of particular significance is the finding that suitably modified gold nanoparticles recognize and bind selectively the protein-functionalized nanogap and are localized there.

Branched oligonucleotides with symmetric arms 6–15, which may contain biotin as a second recognition code, were prepared. These molecules are designed to be used for the directed assembly of nanomaterials. The branched structure of the desired oligonucleotides was confirmed by mass spectrometry on small branched oliognucleotides, by gel electrophoresis, and by hybridization with complementary oligonucleotide&bond;nanoparticle conjugates, followed by visualization of the complexes by transmission electron microscopy.

Oligodeoxynucleotide conjugates 1–15 carrying anchoring groups such as amino, thiol, pyrrole, and carboxy groups were prepared. A post-synthetic modification protocol was developed. In this method 2'-deoxy-O⁴-(p-nitrophenyl)uridine-3-phosphoramidite was prepared and incorporated in oligonucleotides. After assembly, the modified nucleoside was made to react with different amines carrying the anchoring groups. At the same time, protecting groups were removed to yield the desired oligonucleotide conjugates. In a second approach, amino, thiol, and carboxylic groups were introduced into the 3'-end of the oligonucleotides by preparing solid supports loaded with the appropriate amino acids. Oligonucleotide&bond;gold conjugates were prepared and their binding properties were examined.

Silver and silica nanoparticles stabilised by long chain alkanes have been prepared and characterised using 1H-NMR, transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS). Upon solvent evaporation, the alkane stabilised silica and silver nanoparticles self-assemble into close-packed two- and three-dimensional structures. Furthermore, it is shown that a mixture of large silica (90 Å) and small silver (48 Å) nanoparticles self-assemble into mixed well-defined close-packed structures. It has been demonstrated that particle size, core material and solvent composition can be employed to control the forces between individual nanoparticles and, consequently, the structure of the self-assembled arrays. These mixed structures have also been studied using UV-visible spectroscopy and their collective optical properties are shown to depend on their overall composition.

A time series is a commonly observed type of data, and it is analyzed in several ways in real applications. Within the possible analysis, change point detection is one of the crucial inferential targets for studying the behavior of a time series. We consider a multiple change point detection model for a multivariate time series. Among the possible approaches to perform multiple change point detection, we propose an extension to the multivariate case of one of the main state-of-the-art approaches, working in a Bayesian nonparametric framework. We combine a combinatorial prior distribution, which relies on a model-based clustering approach to detect the change points, with a multivariate kernel for time-dependent realizations in a general fashion. We further extend the model to the case of missing observations and derive opportune quantities to perform data imputation. Thereafter, we investigate the properties of the multivariate model with an extensive simulation study, and we apply the model to perform change point detection in two real data applications. [ABSTRACT FROM AUTHOR]