A Hierarchical Model for Ordinal Matrix Factorization

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based on Gibbs sampling and one based on variational Bayes. Importantly, these algorithms may be implemented in the factorization of very large matrices with missing entries. The model is evaluated on a collaborative filtering task, where users have rated a collection of movies and the system is asked to predict their ratings for other movies. The Netflix data set is used for evaluation, which consists of around 100 million ratings. Using root mean-squared error (RMSE) as an evaluation metric, results show that the suggested model outperforms alternative factorization techniques. Results also show how Gibbs sampling outperforms variational Bayes on this task, despite the large number of ratings and model parameters. Matlab implementations of the proposed algorithms are available from cogsys.imm.dtu.dk/ordinalmatrixfactorization.

Hierarchical orientation of crystallinity by block-copolymer patterning and alignment in an electric field

Electron and hole conducting 10-nm-wide polymer morphologies hold great promise for organic electro-optical devices such as solar cells and light emitting diodes. The self-assembly of block-copolymers (BCPs) is often viewed as an efficient way to generate such materials. Here, a functional block copolymer that contains perylene bismide (PBI) side chains which can crystallize via π-π stacking to form an electron conducting microphase is patterned harnessing hierarchical electrohydrodynamic lithography (HEHL). HEHL film destabilization creates a hierarchical structure with three distinct length scales: (1) micrometer-sized polymer pillars, containing (2) a 10-nm BCP microphase morphology that is aligned perpendicular to the substrate surface and (3) on a molecular length scale (0.35-3 nm) PBI π-π-stacks traverse the HEHL-generated plugs in a continuous fashion. The good control over BCP and PBI alignment inside the generated vertical microstructures gives rise to liquid-crystal-like optical dichroism of the HEHL patterned films, and improves the electron conductivity across the film by 3 orders of magnitude. © 2013 American Chemical Society.

Engineering hierarchical nanostructures by elastocapillary self-assembly

Surfaces coated with nanoscale filaments such as silicon nanowires and carbon nanotubes are potentially compelling for high-performance battery and capacitor electrodes, photovoltaics, electrical interconnects, substrates for engineered cell growth, dry adhesives, and other smart materials. However, many of these applications require a wet environment or involve wet processing during their synthesis. The capillary forces introduced by these wet environments can lead to undesirable aggregation of nanoscale filaments, but control of capillary forces can enable manipulation of the filaments into discrete aggregates and novel hierarchical structures. Recent studies suggest that the elastocapillary self-assembly of nanofilaments can be a versatile and scalable means to build complex and robust surface architectures. To enable a wider understanding and use of elastocapillary self-assembly as a fabrication technology, we give an overview of the underlying fundamentals and classify typical implementations and surface designs for nanowires, nanotubes, and nanopillars made from a wide variety of materials. Finally, we discuss exemplary applications and future opportunities to realize new engineered surfaces by the elastocapillary self-assembly of nanofilaments. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Hierarchical carbon nanowire microarchitectures made by plasma-assisted pyrolysis of photoresist

We present a new approach for the fabrication and integration of vertically aligned forests of amorphous carbon nanowires (CNWs), using only standard lithography, oxygen plasma treatment, and thermal processing. The simplicity and scalability of this process, as well as the hierarchical organization of CNWs, provides a potential alternative to the use of carbon nanotubes and graphene for applications in microsystems and high surface area materials. The CNWs are highly branched at the nanoscale, and novel hierarchical microstructures with CNWs connected to a solid amorphous core are made by controlling the plasma treatment time. By multilayer processing we demonstrate deterministic joining of CNW micropillars into 3D sensing networks. Finally we show that these networks can be chemically functionalized and used for measurement of DNA binding with increased sensitivity. © 2011 American Chemical Society.

Fabrication of high-aspect-ratio polymer microstructures and hierarchical textures using carbon nanotube composite master molds

Scalable and cost effective patterning of polymer structures and their surface textures is essential to engineer material properties such as liquid wetting and dry adhesion, and to design artificial biological interfaces. Further, fabrication of high-aspect-ratio microstructures often requires controlled deep-etching methods or high-intensity exposure. We demonstrate that carbon nanotube (CNT) composites can be used as master molds for fabrication of high-aspect-ratio polymer microstructures having anisotropic nanoscale textures. The master molds are made by growth of vertically aligned CNT patterns, capillary densification of the CNTs using organic solvents, and capillary-driven infiltration of the CNT structures with SU-8. The composite master structures are then replicated in SU-8 using standard PDMS transfer molding methods. By this process, we fabricated a library of replicas including vertical micro-pillars, honeycomb lattices with sub-micron wall thickness and aspect ratios exceeding 50:1, and microwells with sloped sidewalls. This process enables batch manufacturing of polymer features that capture complex nanoscale shapes and textures, while requiring only optical lithography and conventional thermal processing. © 2011 The Royal Society of Chemistry.

Mechanical properties of hierarchical lattices

This paper focuses on the stiffness and strength of lattices with multiple hierarchical levels. We examine two-dimensional and three-dimensional lattices with up to three levels of structural hierarchy. At each level, the topology and the orientation of the lattice are prescribed, while the relative density is varied over a defined range. The properties of selected hierarchical lattices are obtained via a multiscale approach applied iteratively at each hierarchical level. The results help to quantify the effect that multiple orders of structural hierarchy produces on stretching and bending dominated lattices. Material charts for the macroscopic stiffness and strength illustrate how the property range of the lattices can expand as subsequent levels of hierarchy are added. The charts help to gain insight into the structural benefit that multiple hierarchies can impart to the macroscopic performance of a lattice. © 2013 Elsevier Ltd. All rights reserved.

Approximate Bayesian Computation for Smoothing

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate Bayesian Computation (ABC) and it involves the introduction of auxiliary variables valued in the same space as the observations. The quality of the approximation may be controlled to arbitrary precision through a parameter ε > 0. We provide theoretical results which quantify, in terms of ε, the ABC error in approximation of expectations of additive functionals with respect to the smoothing distributions. Under regularity assumptions, this error is, where n is the number of time steps over which smoothing is performed. For numerical implementation, we adopt the forward-only sequential Monte Carlo (SMC) scheme of [14] and quantify the combined error from the ABC and SMC approximations. This forms some of the first quantitative results for ABC methods which jointly treat the ABC and simulation errors, with a finite number of data and simulated samples. © Taylor & Francis Group, LLC.

Active learning of model evidence using Bayesian quadrature

Numerical integration is a key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a modelbased method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.

A Bayesian framework to predict deformations during supported excavations based on a semi-empirical method

The ground movements induced by the construction of supported excavation systems are generally predicted by empirical/semi-empirical methods in the design stage. However, these methods cannot account for the site-specific conditions and for information that becomes available as an excavation proceeds. A Bayesian updating methodology is proposed to update the predictions of ground movements in the later stages of excavation based on recorded deformation measurements. As an application, the proposed framework is used to predict the three-dimensional deformation shapes at four incremental excavation stages of an actual supported excavation project. © 2011 Taylor & Francis Group, London.

A Bayesian framework to predict deformations during supported excavations based on a semi-empirical method

The ground movements induced by the construction of supported excavation systems are generally predicted in the design stage by empirical/semi-empirical methods. However, these methods cannot account for the site-specific conditions and for information that become available as an excavation proceeds. A Bayesian updating methodology is proposed to update the predictions of ground movements in the later stages of excavation based on recorded deformation measurements. As an application, the proposed framework is used to predict the three-dimensional deformation shapes at four incremental excavation stages of an actual supported excavation project. Copyright © ASCE 2011.

Bayesian updating of a unified soil compression model

Some amount of differential settlement occurs even in the most uniform soil deposit, but it is extremely difficult to estimate because of the natural heterogeneity of the soil. The compression response of the soil and its variability must be characterised in order to estimate the probability of the differential settlement exceeding a certain threshold value. The work presented in this paper introduces a probabilistic framework to address this issue in a rigorous manner, while preserving the format of a typical geotechnical settlement analysis. In order to avoid dealing with different approaches for each category of soil, a simplified unified compression model is used to characterise the nonlinear compression behavior of soils of varying gradation through a single constitutive law. The Bayesian updating rule is used to incorporate information from three different laboratory datasets in the computation of the statistics (estimates of the means and covariance matrix) of the compression model parameters, as well as of the uncertainty inherent in the model.