39,422 research outputs found
Relative fixed-width stopping rules for Markov chain Monte Carlo simulations
Markov chain Monte Carlo (MCMC) simulations are commonly employed for
estimating features of a target distribution, particularly for Bayesian
inference. A fundamental challenge is determining when these simulations should
stop. We consider a sequential stopping rule that terminates the simulation
when the width of a confidence interval is sufficiently small relative to the
size of the target parameter. Specifically, we propose relative magnitude and
relative standard deviation stopping rules in the context of MCMC. In each
setting, we develop sufficient conditions for asymptotic validity, that is
conditions to ensure the simulation will terminate with probability one and the
resulting confidence intervals will have the proper coverage probability. Our
results are applicable in a wide variety of MCMC estimation settings, such as
expectation, quantile, or simultaneous multivariate estimation. Finally, we
investigate the finite sample properties through a variety of examples and
provide some recommendations to practitioners.Comment: 24 page
Regularity in the local CR embedding problem
We consider a formally integrable, strictly pseudoconvex CR manifold of
hypersurface type, of dimension . Local CR, i.e. holomorphic,
embeddings of are known to exist from the works of Kuranishi and Akahori.
We address the problem of regularity of the embedding in standard H\"older
spaces , . If the structure of is of class
, , , we construct a local CR
embedding near each point of . This embedding is of class , for every
, . Our method is based on Henkin's local homotopy
formula for the embedded case, some very precise estimates for the solution
operators in it, and a substantial modification of a previous Nash-Moser
argument due to the second author
Unified covariant treatment of hyperfine splitting for heavy and light mesons
This paper aims at proving the fundamental role of a relativistic formulation
for quarkonia models.
We present a completely covariant description of a two-quark system
interacting by the Cornell potential with a Breit term describing the hyperfine
splitting. Using an appropriate procedure to calculate the Breit correction, we
find heavy meson masses in excellent agreement with experimental data.
Moreover, also when applied to light quarks and even taking average values of
the running coupling constant, we prove that covariance properties and
hyperfine splitting are sufficient to explain the light mesons spectrum and to
give a very good agreement with the data.Comment: 4 page
Functional PCA for Remotely Sensed Lake Surface Water Temperature Data
Functional principal component analysis is used to investigate a high-dimensional surface water temperature data set of Lake Victoria, which has been produced in the ARC-Lake project. Two different perspectives are adopted in the analysis: modelling temperature curves (univariate functions) and temperature surfaces (bivariate functions). The latter proves to be a better approach in the sense of both dimension reduction and pattern detection. Computational details and some results from an application to Lake Victoria data are presented
Single-Particle Tunneling in Doped Graphene-Insulator-Graphene Junctions
The characteristics of tunnel junctions formed between n- and p-doped
graphene are investigated theoretically. The single-particle tunnel current
that flows between the two-dimensional electronic states of the graphene (2D-2D
tunneling) is evaluated. At a voltage bias such that the Dirac points of the
two electrodes are aligned, a large resonant current peak is produced. The
magnitude and width of this peak is computed, and its use for devices is
discussed. The influence of both rotational alignment of the graphene
electrodes and structural perfection of the graphene is discussed.Comment: 23 pages, 9 figures; added Section II(E) and associated figures, and
made other minor typographical correction
Improving Facial Attribute Prediction using Semantic Segmentation
Attributes are semantically meaningful characteristics whose applicability
widely crosses category boundaries. They are particularly important in
describing and recognizing concepts where no explicit training example is
given, \textit{e.g., zero-shot learning}. Additionally, since attributes are
human describable, they can be used for efficient human-computer interaction.
In this paper, we propose to employ semantic segmentation to improve facial
attribute prediction. The core idea lies in the fact that many facial
attributes describe local properties. In other words, the probability of an
attribute to appear in a face image is far from being uniform in the spatial
domain. We build our facial attribute prediction model jointly with a deep
semantic segmentation network. This harnesses the localization cues learned by
the semantic segmentation to guide the attention of the attribute prediction to
the regions where different attributes naturally show up. As a result of this
approach, in addition to recognition, we are able to localize the attributes,
despite merely having access to image level labels (weak supervision) during
training. We evaluate our proposed method on CelebA and LFWA datasets and
achieve superior results to the prior arts. Furthermore, we show that in the
reverse problem, semantic face parsing improves when facial attributes are
available. That reaffirms the need to jointly model these two interconnected
tasks
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