9,090 research outputs found
Learning Material-Aware Local Descriptors for 3D Shapes
Material understanding is critical for design, geometric modeling, and
analysis of functional objects. We enable material-aware 3D shape analysis by
employing a projective convolutional neural network architecture to learn
material- aware descriptors from view-based representations of 3D points for
point-wise material classification or material- aware retrieval. Unfortunately,
only a small fraction of shapes in 3D repositories are labeled with physical
mate- rials, posing a challenge for learning methods. To address this
challenge, we crowdsource a dataset of 3080 3D shapes with part-wise material
labels. We focus on furniture models which exhibit interesting structure and
material variabil- ity. In addition, we also contribute a high-quality expert-
labeled benchmark of 115 shapes from Herman-Miller and IKEA for evaluation. We
further apply a mesh-aware con- ditional random field, which incorporates
rotational and reflective symmetries, to smooth our local material predic-
tions across neighboring surface patches. We demonstrate the effectiveness of
our learned descriptors for automatic texturing, material-aware retrieval, and
physical simulation. The dataset and code will be publicly available.Comment: 3DV 201
Conformal correlators of mixed-symmetry tensors
We generalize the embedding formalism for conformal field theories to the
case of general operators with mixed symmetry. The index-free notation encoding
symmetric tensors as polynomials in an auxiliary polarization vector is
extended to mixed-symmetry tensors by introducing a new commuting or
anticommuting polarization vector for each row or column in the Young diagram
that describes the index symmetries of the tensor. We determine the tensor
structures that are allowed in n-point conformal correlation functions and give
an algorithm for counting them in terms of tensor product coefficients. A
simple derivation of the unitarity bound for arbitrary mixed-symmetry tensors
is obtained by considering the conservation condition in embedding space. We
show, with an example, how the new formalism can be used to compute conformal
blocks of arbitrary external fields for the exchange of any conformal primary
and its descendants. The matching between the number of tensor structures in
conformal field theory correlators of operators in d dimensions and massive
scattering amplitudes in d+1 dimensions is also seen to carry over to
mixed-symmetry tensors.Comment: 46 pages, many figures, v2: Reformulated the counting of tensor
structures, new section on conserved operators, v3: fixed typo
Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud
Despite the success of deep functional maps in non-rigid 3D shape matching,
there exists no learning framework that models both self-symmetry and shape
matching simultaneously. This is despite the fact that errors due to symmetry
mismatch are a major challenge in non-rigid shape matching. In this paper, we
propose a novel framework that simultaneously learns both self symmetry as well
as a pairwise map between a pair of shapes. Our key idea is to couple a self
symmetry map and a pairwise map through a regularization term that provides a
joint constraint on both of them, thereby, leading to more accurate maps. We
validate our method on several benchmarks where it outperforms many competitive
baselines on both tasks.Comment: Under Review. arXiv admin note: substantial text overlap with
arXiv:2110.0299
More CFTs and RG Flows from Deforming M2/M5-Brane Horizon
Near-horizon geometry of coincident M2-branes at a conical singularity is
related to M-theory on AdS4 times an appropriate seven-dimensional manifold X7.
For X_7=N^{0,1,0}, squashing deformation is known to lead to spontaneous
(super) symmetry breaking from N=(3, 0) to N=(0, 1) in gauged AdS4
supergravity. Via AdS/CFT correspondence, it is interpreted as renormalization
group flow of strongly coupled three-dimensional field theory with SU(3)*SU(2)
global symmetry. The flow interpolates between N=(0,1) fixed point in the UV to
N=(3,0)fixed point in the IR. Evidences for the interpretation are found both
from critical points of the supergravity scalar potential and from conformal
dimension of relevant chiral primary operators at each fixed point. We also
analyze cases with X7=SO(5)/SO(3)_{max}, V_{5,2}(R), M^{1,1,1}, Q^{1,1,1} and
find that there is no nontrivial renormalization group flows. We extend the
analysis to Englert type vacua of M-theory. By analyzing de Wit-Nicolai
potential, we find that deformation of S7 gives rise to renormalization group
flow from N=8, SO(8) invariant UV fixed point to N=1, G_2 invariant IR fixed
point. For AdS_7 supergravity relevant for near-horizon geometry of coincident
M5-branes, we also point out a nontrivial renormalization group flow from N=1
superconformal UV fixed point to non-supersymmetric IR fixed point.Comment: 21 pages, Latex, 3 figure
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