6,393 research outputs found
Fully Adaptive Gaussian Mixture Metropolis-Hastings Algorithm
Markov Chain Monte Carlo methods are widely used in signal processing and
communications for statistical inference and stochastic optimization. In this
work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw
samples from generic multi-modal and multi-dimensional target distributions.
The proposal density is a mixture of Gaussian densities with all parameters
(weights, mean vectors and covariance matrices) updated using all the
previously generated samples applying simple recursive rules. Numerical results
for the one and two-dimensional cases are provided
Improved Adaptive Rejection Metropolis Sampling Algorithms
Markov Chain Monte Carlo (MCMC) methods, such as the Metropolis-Hastings (MH)
algorithm, are widely used for Bayesian inference. One of the most important
issues for any MCMC method is the convergence of the Markov chain, which
depends crucially on a suitable choice of the proposal density. Adaptive
Rejection Metropolis Sampling (ARMS) is a well-known MH scheme that generates
samples from one-dimensional target densities making use of adaptive piecewise
proposals constructed using support points taken from rejected samples. In this
work we pinpoint a crucial drawback in the adaptive procedure in ARMS: support
points might never be added inside regions where the proposal is below the
target. When this happens in many regions it leads to a poor performance of
ARMS, with the proposal never converging to the target. In order to overcome
this limitation we propose two improved adaptive schemes for constructing the
proposal. The first one is a direct modification of the ARMS procedure that
incorporates support points inside regions where the proposal is below the
target, while satisfying the diminishing adaptation property, one of the
required conditions to assure the convergence of the Markov chain. The second
one is an adaptive independent MH algorithm with the ability to learn from all
previous samples except for the current state of the chain, thus also
guaranteeing the convergence to the invariant density. These two new schemes
improve the adaptive strategy of ARMS, thus simplifying the complexity in the
construction of the proposals. Numerical results show that the new techniques
provide better performance w.r.t. the standard ARMS.Comment: Matlab code provided in http://a2rms.sourceforge.net
Nonlocal Games and Quantum Permutation Groups
We present a strong connection between quantum information and quantum
permutation groups. Specifically, we define a notion of quantum isomorphisms of
graphs based on quantum automorphisms from the theory of quantum groups, and
then show that this is equivalent to the previously defined notion of quantum
isomorphism corresponding to perfect quantum strategies to the isomorphism
game. Moreover, we show that two connected graphs and are quantum
isomorphic if and only if there exists and that are
in the same orbit of the quantum automorphism group of the disjoint union of
and . This connection links quantum groups to the more concrete notion
of nonlocal games and physically observable quantum behaviours. We exploit this
link by using ideas and results from quantum information in order to prove new
results about quantum automorphism groups, and about quantum permutation groups
more generally. In particular, we show that asymptotically almost surely all
graphs have trivial quantum automorphism group. Furthermore, we use examples of
quantum isomorphic graphs from previous work to construct an infinite family of
graphs which are quantum vertex transitive but fail to be vertex transitive,
answering a question from the quantum group literature.
Our main tool for proving these results is the introduction of orbits and
orbitals (orbits on ordered pairs) of quantum permutation groups. We show that
the orbitals of a quantum permutation group form a coherent
configuration/algebra, a notion from the field of algebraic graph theory. We
then prove that the elements of this quantum orbital algebra are exactly the
matrices that commute with the magic unitary defining the quantum group. We
furthermore show that quantum isomorphic graphs admit an isomorphism of their
quantum orbital algebras which maps the adjacency matrix of one graph to that
of the other.Comment: 39 page
Left dorsolateral prefrontal cortex repetitive transcranial magnetic stimulation reduces the development of long-term muscle pain
The left dorsolateral prefrontal cortex (DLPFC) is involved in the experience and modulation of pain, and may be an important node linking pain and cognition. Repetitive transcranial magnetic stimulation (rTMS) to the left DLPFC can reduce chronic and experimental pain. However, whether left DLPFC rTMS can influence the development of chronic pain is unknown. Using repeated intramuscular injection of nerve growth factor to induce the development of sustained muscle pain (lasting weeks), 30 healthy individuals were randomized to receive 5 consecutive daily treatments of active or sham left DLPFC rTMS, starting before the first nerve growth factor injection on day 0. Muscle soreness and pain severity were collected daily for 14 days and disability on every alternate day. Before the first and 1 day after the last rTMS session, anxiety, depression, affect, pain catastrophizing, and cognitive performance on the attention network test were assessed. Left DLPFC rTMS treatment compared with sham was associated with reduced muscle soreness, pain intensity, and painful area (P < 0.05), and a similar trend was observed for disability. These effects were most evident during the days rTMS was applied lasting up to 3 days after intervention. Depression, anxiety, pain catastrophizing, and affect were unchanged. There was a trend toward improved cognitive function with rTMS compared with sham (P = 0.057). These data indicate that repeated left DLPFC rTMS reduces the pain severity in a model of prolonged muscle pain. The findings may have implications for the development of sustained pain in clinical populations
RANILLA GARCÍA, M. (coord.), Historia de una excavación horizontal. El hallazgo y la extracción de material lapidario de la muralla de León, León, 2016, 331 pp., ISBN: 978-84-941234-7-4. [RESEÑA]
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