4,250 research outputs found
Learning SO(3) Equivariant Representations with Spherical CNNs
We address the problem of 3D rotation equivariance in convolutional neural
networks. 3D rotations have been a challenging nuisance in 3D classification
tasks requiring higher capacity and extended data augmentation in order to
tackle it. We model 3D data with multi-valued spherical functions and we
propose a novel spherical convolutional network that implements exact
convolutions on the sphere by realizing them in the spherical harmonic domain.
Resulting filters have local symmetry and are localized by enforcing smooth
spectra. We apply a novel pooling on the spectral domain and our operations are
independent of the underlying spherical resolution throughout the network. We
show that networks with much lower capacity and without requiring data
augmentation can exhibit performance comparable to the state of the art in
standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio
Coexistence of Magneto-Rotational and Jeans Instabilities in an Axisymmetric Nebula
We analyze the magneto-rotational instability (MRI) effects on gravitational
collapse and its influence on the instability critical scale. In particular, we
study an axisymmetric nonstratified differentially rotating cloud, embedded in
a small magnetic field, and we perform a local linear stability analysis,
including the self gravity of the system. We demonstrate that the linear
evolution of the perturbations is characterized by the emergence of an
anisotropy degree of the perturbed mass densities. Starting with spherical
growing overdensities, we see that they naturally acquire an anisotropy of
order unity in their shape. Despite the linear character of our analysis, we
infer that such a seed of anisotropy can rapidly grow in a nonlinear regime,
leading to the formation of filament-like structures. However, we show how such
an anisotropy is essentially an intrinsic feature of the Jean instability, and
how MRI only plays a significant role in fixing the critical scale of the mode
spectrum. We then provide a characterization of the present analysis in terms
of the cosmological setting, in order to provide an outlook of how the present
results could concern the formation of large-scale structures across the
Universe.Comment: 8 pages, 4 figure
The Skeleton: Connecting Large Scale Structures to Galaxy Formation
We report on two quantitative, morphological estimators of the filamentary
structure of the Cosmic Web, the so-called global and local skeletons. The
first, based on a global study of the matter density gradient flow, allows us
to study the connectivity between a density peak and its surroundings, with
direct relevance to the anisotropic accretion via cold flows on galactic halos.
From the second, based on a local constraint equation involving the
derivatives of the field, we can derive predictions for powerful statistics,
such as the differential length and the relative saddle to extrema counts of
the Cosmic web as a function of density threshold (with application to
percolation of structures and connectivity), as well as a theoretical framework
to study their cosmic evolution through the onset of gravity-induced
non-linearities.Comment: 10 pages, 8 figures; proceedings of the "Invisible Universe" 200
Minkowski Tensors in Two Dimensions - Probing the Morphology and Isotropy of the Matter and Galaxy Density Fields
We apply the Minkowski Tensor statistics to two dimensional slices of the
three dimensional density field. The Minkowski Tensors are a set of functions
that are sensitive to directionally dependent signals in the data, and
furthermore can be used to quantify the mean shape of density peaks. We begin
by introducing our algorithm for constructing bounding perimeters around
subsets of a two dimensional field, and reviewing the definition of Minkowski
Tensors. Focusing on the translational invariant statistic - a matrix - we calculate its eigenvalues for both the entire excursion
set () and for individual connected regions and holes
within the set (). The ratio of eigenvalues
informs us of the presence of global anisotropies in
the data, and is a measure of the
mean shape of peaks and troughs in the density field. We study these quantities
for a Gaussian field, then consider how they are modified by the effect of
gravitational collapse using the latest Horizon Run 4 cosmological simulation.
We find are essentially independent of gravitational collapse,
as the process maintains statistical isotropy. However, the mean shape of peaks
is modified significantly - overdensities become relatively more circular
compared to underdensities of the same area. When applying the statistic to a
redshift space distorted density field, we find a significant signal in the
eigenvalues , suggesting that they can be used to probe the
large-scale velocity field.Comment: 17 pages, accepted for publication in AP
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
3D + t Morphological Processing: Applications to Embryogenesis Image Analysis
We propose to directly process 3D + t image sequences with mathematical morphology operators, using a new classi?cation of the 3D+t structuring elements. Several methods (?ltering, tracking, segmentation) dedicated to the analysis of 3D + t datasets of zebra?sh embryogenesis are introduced and validated through a synthetic dataset. Then, we illustrate the application of these methods to the analysis of datasets of zebra?sh early development acquired with various microscopy techniques. This processing paradigm produces spatio-temporal coherent results as it bene?ts from the intrinsic redundancy of the temporal dimension, and minimizes the needs for human intervention in semi-automatic algorithms
Mark correlations: relating physical properties to spatial distributions
Mark correlations provide a systematic approach to look at objects both
distributed in space and bearing intrinsic information, for instance on
physical properties. The interplay of the objects' properties (marks) with the
spatial clustering is of vivid interest for many applications; are, e.g.,
galaxies with high luminosities more strongly clustered than dim ones? Do
neighbored pores in a sandstone have similar sizes? How does the shape of
impact craters on a planet depend on the geological surface properties? In this
article, we give an introduction into the appropriate mathematical framework to
deal with such questions, i.e. the theory of marked point processes. After
having clarified the notion of segregation effects, we define universal test
quantities applicable to realizations of a marked point processes. We show
their power using concrete data sets in analyzing the luminosity-dependence of
the galaxy clustering, the alignment of dark matter halos in gravitational
-body simulations, the morphology- and diameter-dependence of the Martian
crater distribution and the size correlations of pores in sandstone. In order
to understand our data in more detail, we discuss the Boolean depletion model,
the random field model and the Cox random field model. The first model
describes depletion effects in the distribution of Martian craters and pores in
sandstone, whereas the last one accounts at least qualitatively for the
observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics,
second Wuppertal conference "Spatial statistics and statistical physics
Lumpy Structures in Self-Gravitating Disks
Following Toomre & Kalnajs (1991), local models of slightly dissipative
self-gravitating disks show how inhomogeneous structures can be maintained over
several galaxy rotations. Their basic physical ingredients are self-gravity,
dissipation and differential rotation. In order to explore the structures
resulting from these processes on the kpc scale, local simulation of
self-gravitating disks are performed in this paper in 2D as well as in 3D. The
third dimension becomes a priori important as soon as matter clumping causes a
tight coupling of the 3D equations of motion. The physically simple and general
framework of the model permits to make conclusions beyond the here considered
scales. A time dependent affine coordinate system is used, allowing to
calculate the gravitational forces via a particle-mesh FFT-method, increasing
the performance with respect to previous direct force calculations. Persistent
patterns, formed by transient structures, whose intensity and morphological
characteristic depend on the dissipation rate are obtained and described. Some
of our simulations reveal first signs of mass-size and velocity dispersion-size
power-law relations, but a clear scale invariant behavior will require more
powerful computer techniques.Comment: 28 pages, 32 figures. Accepted for publication in A&A. Full
resolution paper available at http://obswww.unige.ch/Preprints/dyn_art.htm
Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics
We study the statics and the dynamics of domain patterns in proper
hexagonal-orthorhombic ferroelastics; these patterns are of particular interest
because they provide a rare physical realization of disclinations in crystals.
Both our static and dynamical theories are based entirely on classical,
nonlinear elasticity theory; we use the minimal theory consistent with
stability, symmetry and ability to explain qualitatively the observed patterns.
After scaling, the only parameters of the static theory are a temperature
variable and a stiffness variable. For moderate to large stiffness, our static
results show nested stars, unnested stars, fans and other nodes, triangular and
trapezoidal regions of trapped hexagonal phase, etc observed in electron
microscopy of Ta4N and Mg-Cd alloys, and also in lead orthovanadate (which is
trigonal-monoclinic); we even find imperfections in some nodes, like those
observed. For small stiffness, we find patterns like those observed in the
mineral Mg-cordierite. Our dynamical studies of growth and relaxation show the
formation of these static patterns, and also transitory structures such as
12-armed bursts, streamers and striations which are also seen experimentally.
The major aspects of the growth-relaxation process are quite unlike those in
systems with conventional order parameters, for it is inherently nonlocal; for
example, the changes from one snapshot to the next are not predictable by
inspection.Comment: 9 pages, 3 figures (1 b&w, 2 colour); animations may be viewed at
http://huron.physics.utoronto.ca/~curnoe/sim.htm
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