24,052 research outputs found
Laplace Approximation for Divisive Gaussian Processes for Nonstationary Regression
The standard Gaussian Process regression (GP) is usually formulated under stationary hypotheses: The noise power is considered constant throughout the input space and the covariance of the prior distribution is typically modeled as depending only on the difference between input samples. These assumptions can be too restrictive and unrealistic for many real-world problems. Although nonstationarity can be achieved using specific covariance functions, they require a prior knowledge of the kind of nonstationarity, not available for most applications. In this paper we propose to use the Laplace approximation to make inference in a divisive GP model to perform nonstationary regression, including heteroscedastic noise cases. The log-concavity of the likelihood ensures a unimodal posterior and makes that the Laplace approximation converges to a unique maximum. The characteristics of the likelihood also allow to obtain accurate posterior approximations when compared to the Expectation Propagation (EP) approximations and the asymptotically exact posterior provided by a Markov Chain Monte Carlo implementation with Elliptical Slice Sampling (ESS), but at a reduced computational load with respect to both, EP and ESS
Entanglement renormalization and gauge symmetry
A lattice gauge theory is described by a redundantly large vector space that
is subject to local constraints, and can be regarded as the low energy limit of
an extended lattice model with a local symmetry. We propose a numerical
coarse-graining scheme to produce low energy, effective descriptions of lattice
models with a local symmetry, such that the local symmetry is exactly preserved
during coarse-graining. Our approach results in a variational ansatz for the
ground state(s) and low energy excitations of such models and, by extension, of
lattice gauge theories. This ansatz incorporates the local symmetry in its
structure, and exploits it to obtain a significant reduction of computational
costs. We test the approach in the context of the toric code with a magnetic
field, equivalent to Z2 lattice gauge theory, for lattices with up to 16 x 16
sites (16^2 x 2 = 512 spins) on a torus. We reproduce the well-known ground
state phase diagram of the model, consisting of a deconfined and spin polarized
phases separated by a continuous quantum phase transition, and obtain accurate
estimates of energy gaps, ground state fidelities, Wilson loops, and several
other quantities.Comment: reviewed version as published in PRB; this version includes a new
section about the accuracy of the results several corrections and added
citation
Public-cooperative policy mechanisms for housing commons
Cooperative housing is experiencing a resurgence of interest worldwide. As a more democratic and affordable alternative to dominant housing provision, it is often heralded as a blueprint for ‘housing commons’. Despite its long history, however, cooperative housing has rarely gone beyond a ‘niche’ in the housing market. Recent critical housing scholarship is beginning to address this marginalisation and understand how a more widespread development of the sector can be supported. In times and places where cooperative housing has expanded beyond a ‘niche’ solution, the role of the state, through policy making at national, regional and municipal scale, stands out as an important enabling factor. Drawing on ten international cases, this study presents a framework for a rigorous and politically meaningful comparative approach to public-cooperative policy mechanisms for ‘housing commons’. Three key phases in the housing process (production, access and management, and maintenance of the model in time) are identified and discussed through concrete examples of policy areas and mechanisms. The article contributes to scholarship on cooperative housing policy making and ‘housing commons’ and argues for a shift in attention to questions of accessibility over time, and the thorny issue of permanent decommodification
Effects of critical temperature inhomogeneities on the voltage-current characteristics of a planar superconductor near the Berezinskii-Kosterlitz-Thouless transition
We analyze numerically how the voltage-current (V-I) characteristics near the
so-called Berezinskii-Kosterlitz-Thouless (BKT) transition of 2D
superconductors are affected by a random spatial Gaussian distribution of
critical temperature inhomogeneities with long characteristic lengths (much
larger than the in-plane superconducting coherence length amplitude). Our
simulations allow to quantify the broadening around the average BKT transition
temperature of both the exponent alpha in V I^alpha and of the resistance V/I.
These calculations reveal that strong spatial redistributions of the local
current will occur around the transition as either I or the temperature T are
varied. Our results also support that the condition alpha=3 provides a good
estimate for the location of the average BKT transition temperature, and that
extrapolating to alpha->1 the alpha(T) behaviour well below the transition
provides a good estimate for the average mean-field critical temperature.Comment: 18 pages; pdfLaTeX; 1 TeX file + 8 PDF files for figures
(figs.1,2,3a,3b,4,5a,5b,6
Classical simulation of quantum many-body systems with a tree tensor network
We show how to efficiently simulate a quantum many-body system with tree
structure when its entanglement is bounded for any bipartite split along an
edge of the tree. This is achieved by expanding the {\em time-evolving block
decimation} simulation algorithm for time evolution from a one dimensional
lattice to a tree graph, while replacing a {\em matrix product state} with a
{\em tree tensor network}. As an application, we show that any one-way quantum
computation on a tree graph can be efficiently simulated with a classical
computer.Comment: 4 pages,7 figure
Observation of enhanced transmission for s-polarized light through a subwavelength slit
Enhanced optical transmission (EOT) through subwavelength apertures is
usually obtained for p-polarized light. The present study experimentally
investigates EOT for s-polarized light. A subwavelength slit surrounded on each
side by periodic grooves has been fabricated in a gold film and covered by a
thin dielectric layer. The excitation of s-polarized dielectric waveguide modes
inside the dielectric film strongly increases the s-polarized transmission.
Transmission measurements are compared with a coupled mode model and show good
qualitative agreement. Adding a waveguide can improve light transmission
through subwavelength apertures, as both s and p-polarization can be
efficiently transmitted.Comment: 11 pages, 3 figures, submitted to Applied Physics Letter
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