27,768 research outputs found
The Holographic Life of the eta'
In the string holographic dual of large-N_c QCD with N_f flavours of
Kruczenski et al, the eta' meson is massless at infinite N_c and dual to a
collective fluctuation of N_f D6-brane probes in a supergravity background.
Here we identify the string diagrams responsible for the generation of a mass
of order N_f/N_c, consistent with the Witten-Veneziano formula, and show that
the supregravity limit of these diagrams corresponds to mixings with
pseudoscalar glueballs. We argue that the dependence on the theta-angle in the
supergravity description occurs only through the combination theta + 2
\sqrt{N_f} eta' / f_pi, as dictated by the U(1) anomaly. We provide a
quantitative test by computing the linear term in the eta' potential in two
independent ways, with perfect agreement.Comment: 1+26 pages, 8 figures; V4: Appendix added, version published in JHE
On the embedding of a (p-1)-dimensional non invertible map into a p-dimensional invertible map
This paper concerns the description of some properties of p-dimensional invertible real maps
Tb, turning into a (p - 1)-dimensional non invertible ones T0, p = 2, 3, when a parameter b of
the first map is equal to a critical value, say b=0. Then it is said that the noninvertible map is
embedded into the invertible one. More particularly properties of the stable, and the unstable
manifolds of a saddle fixed point are considered in relation with this embedding. This is made
by introducing the notion of folding as resulting from the crossing through a commutation curve
when p = 2, or a commutation surface when p = 3
Few-Shot Single-View 3-D Object Reconstruction with Compositional Priors
The impressive performance of deep convolutional neural networks in
single-view 3D reconstruction suggests that these models perform non-trivial
reasoning about the 3D structure of the output space. However, recent work has
challenged this belief, showing that complex encoder-decoder architectures
perform similarly to nearest-neighbor baselines or simple linear decoder models
that exploit large amounts of per category data in standard benchmarks. On the
other hand settings where 3D shape must be inferred for new categories with few
examples are more natural and require models that generalize about shapes. In
this work we demonstrate experimentally that naive baselines do not apply when
the goal is to learn to reconstruct novel objects using very few examples, and
that in a \emph{few-shot} learning setting, the network must learn concepts
that can be applied to new categories, avoiding rote memorization. To address
deficiencies in existing approaches to this problem, we propose three
approaches that efficiently integrate a class prior into a 3D reconstruction
model, allowing to account for intra-class variability and imposing an implicit
compositional structure that the model should learn. Experiments on the popular
ShapeNet database demonstrate that our method significantly outperform existing
baselines on this task in the few-shot setting
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