2,768 research outputs found
On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain
The continuous and discrete symmetries of the Kuramoto-Sivashinsky system
restricted to a spatially periodic domain play a prominent role in shaping the
invariant sets of its chaotic dynamics. The continuous spatial translation
symmetry leads to relative equilibrium (traveling wave) and relative periodic
orbit (modulated traveling wave) solutions. The discrete symmetries lead to
existence of equilibrium and periodic orbit solutions, induce decomposition of
state space into invariant subspaces, and enforce certain structurally stable
heteroclinic connections between equilibria. We show, on the example of a
particular small-cell Kuramoto-Sivashinsky system, how the geometry of its
dynamical state space is organized by a rigid `cage' built by heteroclinic
connections between equilibria, and demonstrate the preponderance of unstable
relative periodic orbits and their likely role as the skeleton underpinning
spatiotemporal turbulence in systems with continuous symmetries. We also offer
novel visualizations of the high-dimensional Kuramoto-Sivashinsky state space
flow through projections onto low-dimensional, PDE representation independent,
dynamically invariant intrinsic coordinate frames, as well as in terms of the
physical, symmetry invariant energy transfer rates.Comment: 31 pages, 17 figures; added references, corrected typos. Due to file
size restrictions some figures in this preprint are of low quality. A high
quality copy may be obtained from
http://www.cns.gatech.edu/~predrag/papers/preprints.html#rp
PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models
In geometry processing, symmetry is a universal type of high-level structural
information of 3D models and benefits many geometry processing tasks including
shape segmentation, alignment, matching, and completion. Thus it is an
important problem to analyze various symmetry forms of 3D shapes. Planar
reflective symmetry is the most fundamental one. Traditional methods based on
spatial sampling can be time-consuming and may not be able to identify all the
symmetry planes. In this paper, we present a novel learning framework to
automatically discover global planar reflective symmetry of a 3D shape. Our
framework trains an unsupervised 3D convolutional neural network to extract
global model features and then outputs possible global symmetry parameters,
where input shapes are represented using voxels. We introduce a dedicated
symmetry distance loss along with a regularization loss to avoid generating
duplicated symmetry planes. Our network can also identify generalized cylinders
by predicting their rotation axes. We further provide a method to remove
invalid and duplicated planes and axes. We demonstrate that our method is able
to produce reliable and accurate results. Our neural network based method is
hundreds of times faster than the state-of-the-art methods, which are based on
sampling. Our method is also robust even with noisy or incomplete input
surfaces.Comment: Corrected typo
Broken symmetry in a two-qubit quantum control landscape
We analyze the physics of optimal protocols to prepare a target state with
high fidelity in a symmetrically coupled two-qubit system. By varying the
protocol duration, we find a discontinuous phase transition, which is
characterized by a spontaneous breaking of a symmetry in the
functional form of the optimal protocol, and occurs below the quantum speed
limit. We study in detail this phase and demonstrate that even though
high-fidelity protocols come degenerate with respect to their fidelity, they
lead to final states of different entanglement entropy shared between the
qubits. Consequently, while globally both optimal protocols are equally far
away from the target state, one is locally closer than the other. An
approximate variational mean-field theory which captures the physics of the
different phases is developed
PRS-Net: planar reflective symmetry detection net for 3D models
In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces
A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I
A new fast Bayesian approach is introduced for the detection of discrete
objects immersed in a diffuse background. This new method, called PowellSnakes,
speeds up traditional Bayesian techniques by: i) replacing the standard form of
the likelihood for the parameters characterizing the discrete objects by an
alternative exact form that is much quicker to evaluate; ii) using a
simultaneous multiple minimization code based on Powell's direction set
algorithm to locate rapidly the local maxima in the posterior; and iii)
deciding whether each located posterior peak corresponds to a real object by
performing a Bayesian model selection using an approximate evidence value based
on a local Gaussian approximation to the peak. The construction of this
Gaussian approximation also provides the covariance matrix of the uncertainties
in the derived parameter values for the object in question. This new approach
provides a speed up in performance by a factor of `hundreds' as compared to
existing Bayesian source extraction methods that use MCMC to explore the
parameter space, such as that presented by Hobson & McLachlan. We illustrate
the capabilities of the method by applying to some simplified toy models.
Furthermore PowellSnakes has the advantage of consistently defining the
threshold for acceptance/rejection based on priors which cannot be said of the
frequentist methods. We present here the first implementation of this technique
(Version-I). Further improvements to this implementation are currently under
investigation and will be published shortly. The application of the method to
realistic simulated Planck observations will be presented in a forthcoming
publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted
for publication in MNRA
Symmetry Detection in Geometric Models
PUNTIS (LO1506), SGS-2019-016Symmetry occurs very commonly in real world objects as well as in artificially created
geometric models. The knowledge about symmetry of a given object can be very useful in
many applications in computer graphics and geometry processing, such as compression,
object alignment, symmetric editing or completion of partial objects. In order to use
the symmetry of any object in any given application, it first needs to be found. In this
work, we provide some background about symmetry in general and about different types
of symmetry, mainly in 3D objects. Then we focus on the task of automatic symmetry
detection in 3D objects and we also describe the link between symmetry detection and the
problem of registration. Most importantly, we present our own contribution in these fields.
First, we show a new method of evaluating consensus in RANSAC surface registration
together with a thorough analysis of various distance metrics for rigid transformations
that can be used in this new approach. Afterwards, we provide an analysis of different
representations of the space of planes in context of symmetry plane detection. At last, we
propose a new, robust, fast and flexible method for symmetry plane detection based on a
novel differentiable symmetry measure
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