2,164 research outputs found
One Particle Hilbertspace of 2+1 dimensional Gravity using Non commuting Coordinates
After a review of multi particle solutions in classical 2+1 dimensional
gravity we will construct a one particle Hilbert space. As we will use a curved
momentum space, the coordinates are represented as non commuting
Hermitian operators on this Hilbertspace. Finally we will indicate how to
construct a Schrodinger equation.Comment: 4 pages Latex, 2 eps figures, uses espcr.sty; Talk given at the
Second Meeting on Constrained Dynamics and Quantum Gravity, Santa Margherita
Ligure, Italy, 17-21 september 199
VAE with a VampPrior
Many different methods to train deep generative models have been introduced
in the past. In this paper, we propose to extend the variational auto-encoder
(VAE) framework with a new type of prior which we call "Variational Mixture of
Posteriors" prior, or VampPrior for short. The VampPrior consists of a mixture
distribution (e.g., a mixture of Gaussians) with components given by
variational posteriors conditioned on learnable pseudo-inputs. We further
extend this prior to a two layer hierarchical model and show that this
architecture with a coupled prior and posterior, learns significantly better
models. The model also avoids the usual local optima issues related to useless
latent dimensions that plague VAEs. We provide empirical studies on six
datasets, namely, static and binary MNIST, OMNIGLOT, Caltech 101 Silhouettes,
Frey Faces and Histopathology patches, and show that applying the hierarchical
VampPrior delivers state-of-the-art results on all datasets in the unsupervised
permutation invariant setting and the best results or comparable to SOTA
methods for the approach with convolutional networks.Comment: 16 pages, final version, AISTATS 201
Dynamic roughening of the magnetic flux landscape in YBaCuO
We study the magnetic flux landscape in YBaCuO thin films as
a two dimensional rough surface. The vortex density in the superconductor forms
a self-affine structure in both space and time. This is characterized by a
roughness exponent and a growth exponent .
This is due to the structure and distribution of flux avalanches in the
self-organized critical state, which is formed in the superconductor. We also
discuss our results in the context of other roughening systems in the presence
of quenched disorder.Comment: 13 pages, 7 figures, accepted for publication in Physica
The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity
In this paper we describe the matter-free toroidal spacetime in 't Hooft's
polygon approach to 2+1-dimensional gravity (i.e. we consider the case without
any particles present). Contrary to earlier results in the literature we find
that it is not possible to describe the torus by just one polygon but we need
at least two polygons. We also show that the constraint algebra of the polygons
closes.Comment: 18 pages Latex, 13 eps-figure
The 2+1 Kepler Problem and Its Quantization
We study a system of two pointlike particles coupled to three dimensional
Einstein gravity. The reduced phase space can be considered as a deformed
version of the phase space of two special-relativistic point particles in the
centre of mass frame. When the system is quantized, we find some possibly
general effects of quantum gravity, such as a minimal distances and a foaminess
of the spacetime at the order of the Planck length. We also obtain a
quantization of geometry, which restricts the possible asymptotic geometries of
the universe.Comment: 59 pages, LaTeX2e, 9 eps figure
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