110,452 research outputs found
Simplicity of algebras associated to \'etale groupoids
We prove that the C*-algebra of a second-countable, \'etale, amenable
groupoid is simple if and only if the groupoid is topologically principal and
minimal. We also show that if G has totally disconnected unit space, then the
associated complex *-algebra introduced by Steinberg is simple if and only if
the interior of the isotropy subgroupoid of G is equal to the unit space and G
is minimal.Comment: The introduction has been updated and minor changes have been made
throughout. To appear in Semigroup Foru
Renormalization group equations in curved space-time with non-trivial Topology
Renormalization group equations for massless GUT's in curved space-time with
non-trivial topology are formulated. The asymptotics of the effective action
both at high and low energies are obtained. It is shown that the Casimir energy
contribution at high curvature (early Universe) becomes non-essential in the
effective action.Comment: 7 Page
Simplicity, primitivity and semiprimitivity of etale groupoid algebras with applications to inverse semigroup algebras
This paper studies simplicity, primitivity and semiprimitivity of algebras
associated to \'etale groupoids. Applications to inverse semigroup algebras are
presented. The results also recover the semiprimitivity of Leavitt path
algebras and can be used to recover the known primitivity criterion for Leavitt
path algebras.Comment: Updated after referee report and corrected misprint
An alternative marginal likelihood estimator for phylogenetic models
Bayesian phylogenetic methods are generating noticeable enthusiasm in the
field of molecular systematics. Many phylogenetic models are often at stake and
different approaches are used to compare them within a Bayesian framework. The
Bayes factor, defined as the ratio of the marginal likelihoods of two competing
models, plays a key role in Bayesian model selection. We focus on an
alternative estimator of the marginal likelihood whose computation is still a
challenging problem. Several computational solutions have been proposed none of
which can be considered outperforming the others simultaneously in terms of
simplicity of implementation, computational burden and precision of the
estimates. Practitioners and researchers, often led by available software, have
privileged so far the simplicity of the harmonic mean estimator (HM) and the
arithmetic mean estimator (AM). However it is known that the resulting
estimates of the Bayesian evidence in favor of one model are biased and often
inaccurate up to having an infinite variance so that the reliability of the
corresponding conclusions is doubtful. Our new implementation of the
generalized harmonic mean (GHM) idea recycles MCMC simulations from the
posterior, shares the computational simplicity of the original HM estimator,
but, unlike it, overcomes the infinite variance issue. The alternative
estimator is applied to simulated phylogenetic data and produces fully
satisfactory results outperforming those simple estimators currently provided
by most of the publicly available software
The microscopic dynamics of quantum space as a group field theory
We provide a rather extended introduction to the group field theory approach
to quantum gravity, and the main ideas behind it. We present in some detail the
GFT quantization of 3d Riemannian gravity, and discuss briefly the current
status of the 4-dimensional extensions of this construction. We also briefly
report on recent results obtained in this approach and related open issues,
concerning both the mathematical definition of GFT models, and possible avenues
towards extracting interesting physics from them.Comment: 60 pages. Extensively revised version of the contribution to
"Foundations of Space and Time: Reflections on Quantum Gravity", edited by G.
Ellis, J. Murugan, A. Weltman, published by Cambridge University Pres
- …