A numerical study of stretched smectic-A elastomer sheets

We present a numerical study of stretching monodomain smectic-A elastomer sheets, computed using the finite element method. When stretched parallel to the layer normal the microscopic layers in smectic elastomers are unstable to a transition to a buckled state. We account for the layer buckling by replacing the microscopic energy with a coarse grained effective free energy that accounts for the fine scale deformation of the layers. We augment this model with a term to describe the energy of deforming buckled layers, which is necessary to reproduce the experimentally observed Poisson's ratios post-buckling. We examine the spatial distribution of the microstructure phases for various stretching angles relative to the layer normal, and for different length-to-width aspect ratios. When stretching parallel to the layer normal the majority of the sample forms a bi-directionally buckled microstructure, except at the clamps where uni-directional microstructure is predicted. When stretching at small inclinations to the layer normal the phase of the sample is sensitive to the aspect ratio of the sample, with the bi-directionally buckled phase persistent to large angles only for small aspect ratios. We relate these theoretical results to experiments on smectic-A elastomers.Comment: 14 pages, 17 figure

Uniform convergence of Vapnik--Chervonenkis classes under ergodic sampling

We show that if $\mathcal{X}$ is a complete separable metric space and $\mathcal{C}$ is a countable family of Borel subsets of $\mathcal{X}$ with finite VC dimension, then, for every stationary ergodic process with values in $\mathcal{X}$, the relative frequencies of sets $C\in\mathcal{C}$ converge uniformly to their limiting probabilities. Beyond ergodicity, no assumptions are imposed on the sampling process, and no regularity conditions are imposed on the elements of $\mathcal{C}$. The result extends existing work of Vapnik and Chervonenkis, among others, who have studied uniform convergence for i.i.d. and strongly mixing processes. Our method of proof is new and direct: it does not rely on symmetrization techniques, probability inequalities or mixing conditions. The uniform convergence of relative frequencies for VC-major and VC-graph classes of functions under ergodic sampling is established as a corollary of the basic result for sets.Comment: Published in at http://dx.doi.org/10.1214/09-AOP511 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

AMENITIES IN AN URBAN EQUILIBRIUM MODEL: RESIDENTIAL DEVELOPMENT IN PORTLAND, OREGON

This paper analyzes the effect of open space and other amenities on housing prices and development density within the framework of an urban equilibrium model. The model is estimated as a system of equations that includes households' residential choice decisions and developers' development decisions and emphasizes the importance of amenities in the formation of development patterns and property values. The model is applied to Portland, Oregon, where ambitious open space programs have been implemented. The results suggest that amenities are important: households are willing to pay more for newer houses located in areas of less dense development, with more open space, better views, less traffic congestion, and near amenity locations. For the developer, increases in housing prices result in an attempt to provide more and larger houses. The attempt to provide more houses, however, results in higher density, which will ultimately reduce prices. A simulation analysis evaluates the policy implications of the model results and indicates substantial benefits from alterations in housing patternsCommunity/Rural/Urban Development, R11, R21, R31,

Reducing Reparameterization Gradient Variance

Optimization with noisy gradients has become ubiquitous in statistics and machine learning. Reparameterization gradients, or gradient estimates computed via the "reparameterization trick," represent a class of noisy gradients often used in Monte Carlo variational inference (MCVI). However, when these gradient estimators are too noisy, the optimization procedure can be slow or fail to converge. One way to reduce noise is to use more samples for the gradient estimate, but this can be computationally expensive. Instead, we view the noisy gradient as a random variable, and form an inexpensive approximation of the generating procedure for the gradient sample. This approximation has high correlation with the noisy gradient by construction, making it a useful control variate for variance reduction. We demonstrate our approach on non-conjugate multi-level hierarchical models and a Bayesian neural net where we observed gradient variance reductions of multiple orders of magnitude (20-2,000x)

Approximate Inference for Constructing Astronomical Catalogs from Images

We present a new, fully generative model for constructing astronomical catalogs from optical telescope image sets. Each pixel intensity is treated as a random variable with parameters that depend on the latent properties of stars and galaxies. These latent properties are themselves modeled as random. We compare two procedures for posterior inference. One procedure is based on Markov chain Monte Carlo (MCMC) while the other is based on variational inference (VI). The MCMC procedure excels at quantifying uncertainty, while the VI procedure is 1000 times faster. On a supercomputer, the VI procedure efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50 terabytes of images in 14.6 minutes, demonstrating the scaling characteristics necessary to construct catalogs for upcoming astronomical surveys.Comment: accepted to the Annals of Applied Statistic

Simultaneous laser vibrometry on multiple surfaces with a single beam system using range-resolved interferometry

A novel range-resolved interferometric signal processing technique that uses sinusoidal optical frequency modulation is applied to multi-surface vibrometry, demonstrating simultaneous optical measurements of vibrations on two surfaces using a single, collimated laser beam, with a minimum permissible distance of 3.5 cm between surfaces. The current system, using a cost-effective laser diode and a fibre-coupled, downlead insensitive setup, allows an interferometric fringe rate of up to 180 kHz to be resolved with typical displacement noise levels of 8 pm Hz-0.5. In this paper, the system is applied to vibrometry measurements of a table-top cryostat, with concurrent measurements of the optical widow and the sample holder inside. This allows the separation of common-mode vibrations of the whole cryostat from differential vibrations between the window and the sample holder.EPSR