Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations

The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate convergence in MCMC and EM algorithms but are still not well studied for variational Bayes (VB) methods. As a fast deterministic approach to posterior approximation, VB is attracting increasing interest due to its suitability for large high-dimensional data. Use of different parametrizations for VB has not only computational but also statistical implications, as different parametrizations are associated with different factorized posterior approximations. We examine the use of partially noncentered parametrizations in VB for generalized linear mixed models (GLMMs). Our paper makes four contributions. First, we show how to implement an algorithm called nonconjugate variational message passing for GLMMs. Second, we show that the partially noncentered parametrization can adapt to the quantity of information in the data and determine a parametrization close to optimal. Third, we show that partial noncentering can accelerate convergence and produce more accurate posterior approximations than centering or noncentering. Finally, we demonstrate how the variational lower bound, produced as part of the computation, can be useful for model selection.Comment: Published in at http://dx.doi.org/10.1214/13-STS418 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Laser-induced forces between carbon nanotubes

Carbon nanotubes are the focus of intense research interest because of their unique properties and applications potential. We present a study based on quantum electrodynamics concerning the optical force between a pair of nanotubes under laser irradiance. To identify separate effects associated with the pair orientation and laser beam geometry, two different systems are analyzed, For each, an analytical expression for the laser-induced optical force is determined, and the corresponding magnitude is estimated. © 2005 Optical Society of America

Investigation of the 1+1 dimensional Thirring model using the method of matrix product states

We present preliminary results of a study on the non-thermal phase structure of the (1+1) dimensional massive Thirring model, employing the method of matrix product states. Through investigating the entanglement entropy, the fermion correlators and the chiral condensate, it is found that this approach enables us to observe numerical evidence of a Kosterlitz-Thouless phase transition in the model.Comment: 7 pages, 4 figures; contribution to the proceedings of Lattice 2018 conferenc

Splice Strength of Epoxy-Coated High Relative Rib Area Bars

The effect of epoxy coating on the splice strength of high relative rib area bars with and without confining transverse reinforcement is described. Test results for 47 beam splice specimens containing No. 5, No. 8, or No. 11 (16, 25 or 36 mm) bars with relative rib areas ranging from 0.101 to 0.141 and seven deformation patterns are included in the analysis. Twenty seven of the 47 beam splice tests are reported for the first time. Average coating thickness ranged from 7.1 to 16.8 mils (0.18 to 0.43 mm). Fortythree specimens were bottom-cast and four were top-cast. The test results for the high relative rib area bars are combined with 44 previous splice tests using conventional bars. Epoxy coating was found to have a much less detrimental effect on splice strength for high relative rib area bars than for conventional bars. The average splice strength ratio of coated to uncoated bars C/U is 0.89, compared to 0.74 for conventional reinforcement. C!U is approximately the same for splices with and without transverse reinforcement. The test results of the current study indicate that the development length modification factor required by the ACI Building Code (318-95) and the AASHTO Bridge Specifications (1992) can be reduced from 1.5 to 1.2 for epoxy-coated high relative rib bars

Plasmonic nanogap enhanced phase change devices with dual electrical-optical functionality

Modern-day computers use electrical signaling for processing and storing data which is bandwidth limited and power-hungry. These limitations are bypassed in the field of communications, where optical signaling is the norm. To exploit optical signaling in computing, however, new on-chip devices that work seamlessly in both electrical and optical domains are needed. Phase change devices can in principle provide such functionality, but doing so in a single device has proved elusive due to conflicting requirements of size-limited electrical switching and diffraction-limited photonic devices. Here, we combine plasmonics, photonics and electronics to deliver a novel integrated phase-change memory and computing cell that can be electrically or optically switched between binary or multilevel states, and read-out in either mode, thus merging computing and communications technologies

The Biermann Battery in Cosmological MHD Simulations of Population III Star Formation

We report the results of the first self-consistent three-dimensional adaptive mesh refinement magnetohydrodynamical simulations of Population III star formation including the Biermann Battery effect. We find that the Population III stars formed including this effect are both qualitatively and quantitatively similar to those from hydrodynamics-only (non-MHD) cosmological simulations. We observe peak magnetic fields of ~10^-9 G in the center of our star-forming halo at z ~ 17.55. The magnetic fields created by the Biermann Battery effect are predominantly formed early in the evolution of the primordial halo at low density and large spatial scales, and then grow through compression and by shear flows. The fields seen in this calculation are never large enough to be dynamically important (with beta >= 10^{15} at all times), and should be considered the minimum possible fields in existence during Population III star formation, and may be seed fields for the stellar dynamo or the magnetorotational instability at higher densities and smaller spatial scales.Comment: 4 pages, 3 figures; Submitted to the Astrophysical Journal Letters. Comments welcome. Typo found (and fixed) in equation