4,679 research outputs found
Point-wise Map Recovery and Refinement from Functional Correspondence
Since their introduction in the shape analysis community, functional maps
have met with considerable success due to their ability to compactly represent
dense correspondences between deformable shapes, with applications ranging from
shape matching and image segmentation, to exploration of large shape
collections. Despite the numerous advantages of such representation, however,
the problem of converting a given functional map back to a point-to-point map
has received a surprisingly limited interest. In this paper we analyze the
general problem of point-wise map recovery from arbitrary functional maps. In
doing so, we rule out many of the assumptions required by the currently
established approach -- most notably, the limiting requirement of the input
shapes being nearly-isometric. We devise an efficient recovery process based on
a simple probabilistic model. Experiments confirm that this approach achieves
remarkable accuracy improvements in very challenging cases
Variational Integrators for Reduced Magnetohydrodynamics
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics
equations with applications to both fusion and astrophysical plasmas,
possessing a noncanonical Hamiltonian structure and consequently a number of
conserved functionals. We propose a new discretisation strategy for these
equations based on a discrete variational principle applied to a formal
Lagrangian. The resulting integrator preserves important quantities like the
total energy, magnetic helicity and cross helicity exactly (up to machine
precision). As the integrator is free of numerical resistivity, spurious
reconnection along current sheets is absent in the ideal case. If effects of
electron inertia are added, reconnection of magnetic field lines is allowed,
although the resulting model still possesses a noncanonical Hamiltonian
structure. After reviewing the conservation laws of the model equations, the
adopted variational principle with the related conservation laws are described
both at the continuous and discrete level. We verify the favourable properties
of the variational integrator in particular with respect to the preservation of
the invariants of the models under consideration and compare with results from
the literature and those of a pseudo-spectral code.Comment: 35 page
NLO QCD corrections to SM-EFT dilepton and electroweak Higgs boson production, matched to parton shower in POWHEG
We discuss the Standard Model Effective Field Theory (SM-EFT) contributions
to neutral- and charge-current Drell-Yan production, associated production of
the Higgs and a vector boson, and Higgs boson production via vector boson
fusion. We consider all the dimension-six SM-EFT operators that contribute to
these processes at leading order, include next-to-leading order QCD
corrections, and interface them with parton showering and hadronization in
Pythia8 according to the POWHEG method. We discuss existing constraints on the
coefficients of dimension-six operators and identify differential and angular
distributions that can differentiate between different effective operators,
pointing to specific features of Beyond-the-Standard-Model physics.Comment: 42 pages, 8 Figure
Learning shape correspondence with anisotropic convolutional neural networks
Establishing correspondence between shapes is a fundamental problem in
geometry processing, arising in a wide variety of applications. The problem is
especially difficult in the setting of non-isometric deformations, as well as
in the presence of topological noise and missing parts, mainly due to the
limited capability to model such deformations axiomatically. Several recent
works showed that invariance to complex shape transformations can be learned
from examples. In this paper, we introduce an intrinsic convolutional neural
network architecture based on anisotropic diffusion kernels, which we term
Anisotropic Convolutional Neural Network (ACNN). In our construction, we
generalize convolutions to non-Euclidean domains by constructing a set of
oriented anisotropic diffusion kernels, creating in this way a local intrinsic
polar representation of the data (`patch'), which is then correlated with a
filter. Several cascades of such filters, linear, and non-linear operators are
stacked to form a deep neural network whose parameters are learned by
minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic
dense correspondences between deformable shapes in very challenging settings,
achieving state-of-the-art results on some of the most difficult recent
correspondence benchmarks
Numerical simulations of single and binary black holes in scalar-tensor theories: circumventing the no-hair theorem
Scalar-tensor theories are a compelling alternative to general relativity and
one of the most accepted extensions of Einstein's theory. Black holes in these
theories have no hair, but could grow "wigs" supported by time-dependent
boundary conditions or spatial gradients. Time-dependent or spatially varying
fields lead in general to nontrivial black hole dynamics, with potentially
interesting experimental consequences. We carry out a numerical investigation
of the dynamics of single and binary black holes in the presence of scalar
fields. In particular we study gravitational and scalar radiation from
black-hole binaries in a constant scalar-field gradient, and we compare our
numerical findings to analytical models. In the single black hole case we find
that, after a short transient, the scalar field relaxes to static
configurations, in agreement with perturbative calculations. Furthermore we
predict analytically (and verify numerically) that accelerated black holes in a
scalar-field gradient emit scalar radiation. For a quasicircular black-hole
binary, our analytical and numerical calculations show that the dominant
component of the scalar radiation is emitted at twice the binary's orbital
frequency.Comment: 21 pages, 6 figures, matches version accepted in Physical Review
Resonant-plane locking and spin alignment in stellar-mass black-hole binaries: a diagnostic of compact-binary formation
We study the influence of astrophysical formation scenarios on the
precessional dynamics of spinning black-hole binaries by the time they enter
the observational window of second- and third-generation gravitational-wave
detectors, such as Advanced LIGO/Virgo, LIGO-India, KAGRA and the Einstein
Telescope. Under the plausible assumption that tidal interactions are efficient
at aligning the spins of few-solar mass black-hole progenitors with the orbital
angular momentum, we find that black-hole spins should be expected to
preferentially lie in a plane when they become detectable by gravitational-wave
interferometers. This "resonant plane" is identified by the conditions
\Delta\Phi=0{\deg} or \Delta\Phi=+/-180{\deg}, where \Delta\Phi is the angle
between the components of the black-hole spins in the plane orthogonal to the
orbital angular momentum. If the angles \Delta \Phi can be accurately measured
for a large sample of gravitational-wave detections, their distribution will
constrain models of compact binary formation. In particular, it will tell us
whether tidal interactions are efficient and whether a mechanism such as mass
transfer, stellar winds, or supernovae can induce a mass-ratio reversal (so
that the heavier black hole is produced by the initially lighter stellar
progenitor). Therefore our model offers a concrete observational link between
gravitational-wave measurements and astrophysics. We also hope that it will
stimulate further studies of precessional dynamics, gravitational-wave template
placement and parameter estimation for binaries locked in the resonant plane.Comment: 26 pages, 11 figures, 3 tables, accepted in Physical Review D. 4
movies illustrating resonance locking are available online: for links, see
footnote 8 of the pape
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
We introduce a new framework for learning dense correspondence between
deformable 3D shapes. Existing learning based approaches model shape
correspondence as a labelling problem, where each point of a query shape
receives a label identifying a point on some reference domain; the
correspondence is then constructed a posteriori by composing the label
predictions of two input shapes. We propose a paradigm shift and design a
structured prediction model in the space of functional maps, linear operators
that provide a compact representation of the correspondence. We model the
learning process via a deep residual network which takes dense descriptor
fields defined on two shapes as input, and outputs a soft map between the two
given objects. The resulting correspondence is shown to be accurate on several
challenging benchmarks comprising multiple categories, synthetic models, real
scans with acquisition artifacts, topological noise, and partiality.Comment: Accepted for publication at ICCV 201
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