402 research outputs found
Capacity estimation of two-dimensional channels using Sequential Monte Carlo
We derive a new Sequential-Monte-Carlo-based algorithm to estimate the
capacity of two-dimensional channel models. The focus is on computing the
noiseless capacity of the 2-D one-infinity run-length limited constrained
channel, but the underlying idea is generally applicable. The proposed
algorithm is profiled against a state-of-the-art method, yielding more than an
order of magnitude improvement in estimation accuracy for a given computation
time
Nested Sequential Monte Carlo Methods
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from
sequences of probability distributions, even where the random variables are
high-dimensional. NSMC generalises the SMC framework by requiring only
approximate, properly weighted, samples from the SMC proposal distribution,
while still resulting in a correct SMC algorithm. Furthermore, NSMC can in
itself be used to produce such properly weighted samples. Consequently, one
NSMC sampler can be used to construct an efficient high-dimensional proposal
distribution for another NSMC sampler, and this nesting of the algorithm can be
done to an arbitrary degree. This allows us to consider complex and
high-dimensional models using SMC. We show results that motivate the efficacy
of our approach on several filtering problems with dimensions in the order of
100 to 1 000.Comment: Extended version of paper published in Proceedings of the 32nd
International Conference on Machine Learning (ICML), Lille, France, 201
Sequential Monte Carlo for Graphical Models
We propose a new framework for how to use sequential Monte Carlo (SMC)
algorithms for inference in probabilistic graphical models (PGM). Via a
sequential decomposition of the PGM we find a sequence of auxiliary
distributions defined on a monotonically increasing sequence of probability
spaces. By targeting these auxiliary distributions using SMC we are able to
approximate the full joint distribution defined by the PGM. One of the key
merits of the SMC sampler is that it provides an unbiased estimate of the
partition function of the model. We also show how it can be used within a
particle Markov chain Monte Carlo framework in order to construct
high-dimensional block-sampling algorithms for general PGMs
Tricritical behavior of the massive chiral Gross-Neveu model
The phase diagram of the massive chiral Gross-Neveu model (the
1+1-dimensional Nambu-Jona-Lasinio model at large N) is investigated in the
vicinity of the tricritical point. Using the derivative expansion, the grand
canonical potential is cast into the form of a Ginzburg-Landau effective
action. Minimization of this action by variational and numerical methods
reveals both 1st and 2nd order phase transitions to a chiral crystal phase,
separated by a tricritical line. These findings are contrasted to the massive
Gross-Neveu model with discrete chiral symmetry where only 2nd order
transitions have been observed.Comment: 10 pages, 10 figures; v2: More details about perturbation theory
given, cf Eqs. (46-48
Surface reconstruction induced anisotropic energy landscape of bismuth monomers and dimers on the Si(001) surface
Spin qubits have attracted tremendous attention in the effort of building
quantum computers over the years. Natural atomic scale candidates are group-V
dopants in silicon, not only showing ultra-long lifetimes but also being
compatible with current semiconductor technology. Nevertheless, bulk dopants
are difficult to move with atomic precision, impeding the realization of
desired structures for quantum computing. A solution is to place the atom on
the surface which opens possibilities for atom level manipulations using
scanning tunneling microscopy (STM). For this purpose, bismuth appears to be a
good candidate. Here, we use ab-initio methods to study theoretically the
adsorption of bismuth atoms on the Si(001) surface and investigate the
adsorption sites and the transitions between them. We demonstrate the complex
influence of the dimer row surface reconstruction on the energy landscape seen
by a bismuth monomer and a dimer on the surface, and find anisotropic
transition paths for movement on the surface. From a deposition simulation we
obtain the expected occupation of adsorption sites. Our work lays the
foundation for further application of bismuth atoms as qubits on silicon
surfaces.Comment: 12 pages, 8 figure
The lid method for exhaustive exploration of metastable states of complex systems
The `lid' algorithm performs an exhaustive exploration of neighborhoods of
local energy minima of energy landscapes. This paper describes an
implementation of the algorithm, including issues of parallel performance and
scalability. To illustrate the versatility of the approach and to stress the
common features present in landscapes of quite different systems, we present
selected results for 1) a spin glass, 2) a ferromagnet, 3) a covalent network
model for glassy systems, and 4) a polymer. The exponential nature of the local
density of states found in these systems and its relation to the ordering
transition is briefly commented upon.Comment: RevTeX, 11 pages, 1 figur
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