Decision tree-based context clustering based on cross validation and hierarchical priors

The standard, ad-hoc stopping criteria used in decision tree-based context clustering are known to be sub-optimal and require parameters to be tuned. This paper proposes a new approach for decision tree-based context clustering based on cross validation and hierarchical priors. Combination of cross validation and hierarchical priors within decision tree-based context clustering offers better model selection and more robust parameter estimation than conventional approaches, with no tuning parameters. Experimental results on HMM-based speech synthesis show that the proposed approach achieved significant improvements in naturalness of synthesized speech over the conventional approaches. © 2011 IEEE.

Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

Hierarchical electrohydrodynamic structures for surface-enhanced Raman scattering.

Surface enhanced Raman scattering (SERS) is a well-established spectroscopic technique that requires nanoscale metal structures to achieve high signal sensitivity. While most SERS substrates are manufactured by conventional lithographic methods, the development of a cost-effective approach to create nanostructured surfaces is a much sought-after goal in the SERS community. Here, a method is established to create controlled, self-organized, hierarchical nanostructures using electrohydrodynamic (HEHD) instabilities. The created structures are readily fine-tuned, which is an important requirement for optimizing SERS to obtain the highest enhancements. HEHD pattern formation enables the fabrication of multiscale 3D structured arrays as SERS-active platforms. Importantly, each of the HEHD-patterned individual structural units yield a considerable SERS enhancement. This enables each single unit to function as an isolated sensor. Each of the formed structures can be effectively tuned and tailored to provide high SERS enhancement, while arising from different HEHD morphologies. The HEHD fabrication of sub-micrometer architectures is straightforward and robust, providing an elegant route for high-throughput biological and chemical sensing.

Hierarchical electrohydrodynamic structures for surface-enhanced Raman scattering (adv. Mater. 23/2012).

On page OP 175, U. Steiner and co-workers destabilise polymer trilayer films using an electric field to generate separated micrometre-sized core-shell pillars, which are further modified by selective polymer dissolution to yield polymer core columns surrounded by a rim and micro-volcano rim structures. When coated with gold and decorated with Raman active probes, all three structure types give rise to substantial enhancement in surface-enhanced Raman scattering (SERS). Since this SERS enhancement arises from each of the isolated structures in the array, these surface patterns are an ideal platform for multiplexed SERS detection.

A subdivision-based implementation of the hierarchical b-spline finite element method

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. © 2012 Elsevier B.V.