507 research outputs found
Contractibility of the Space of Opers for Classical Groups
The geometric Langlands program is an exciting direction of research,
although a lot of progress has been made there are still open questions and
gaps. One of the necessary steps for this program is the proof of the existence
and the cohomological triviality (more precisely, the O- contractibility) of
the space of rational opers. In this paper, we prove the homotopical
contractibility of the space of rational opers for classical groups
Deep Projective 3D Semantic Segmentation
Semantic segmentation of 3D point clouds is a challenging problem with
numerous real-world applications. While deep learning has revolutionized the
field of image semantic segmentation, its impact on point cloud data has been
limited so far. Recent attempts, based on 3D deep learning approaches
(3D-CNNs), have achieved below-expected results. Such methods require
voxelizations of the underlying point cloud data, leading to decreased spatial
resolution and increased memory consumption. Additionally, 3D-CNNs greatly
suffer from the limited availability of annotated datasets.
In this paper, we propose an alternative framework that avoids the
limitations of 3D-CNNs. Instead of directly solving the problem in 3D, we first
project the point cloud onto a set of synthetic 2D-images. These images are
then used as input to a 2D-CNN, designed for semantic segmentation. Finally,
the obtained prediction scores are re-projected to the point cloud to obtain
the segmentation results. We further investigate the impact of multiple
modalities, such as color, depth and surface normals, in a multi-stream network
architecture. Experiments are performed on the recent Semantic3D dataset. Our
approach sets a new state-of-the-art by achieving a relative gain of 7.9 %,
compared to the previous best approach.Comment: Submitted to CAIP 201
Monoids, Embedding Functors and Quantum Groups
We show that the left regular representation \pi_l of a discrete quantum
group (A,\Delta) has the absorbing property and forms a monoid
(\pi_l,\tilde{m},\tilde{\eta}) in the representation category Rep(A,\Delta).
Next we show that an absorbing monoid in an abstract tensor *-category C gives
rise to an embedding functor E:C->Vect_C, and we identify conditions on the
monoid, satisfied by (\pi_l,\tilde{m},\tilde{\eta}), implying that E is
*-preserving. As is well-known, from an embedding functor E: C->\mathrm{Hilb}
the generalized Tannaka theorem produces a discrete quantum group (A,\Delta)
such that C is equivalent to Rep_f(A,\Delta). Thus, for a C^*-tensor category C
with conjugates and irreducible unit the following are equivalent: (1) C is
equivalent to the representation category of a discrete quantum group
(A,\Delta), (2) C admits an absorbing monoid, (3) there exists a *-preserving
embedding functor E: C->\mathrm{Hilb}.Comment: Final version, to appear in Int. Journ. Math. (Added some references
and Subsection 1.2.) Latex2e, 21 page
Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase
We present results of molecular simulations that predict the phases formed by
the self-assembly of model nanospheres functionalized with a single polymer
"tether", including double gyroid, perforated lamella and crystalline bilayer
phases. We show that microphase separation of the immiscible tethers and
nanospheres causes confinement of the nanoparticles, which promotes local
icosahedral packing that stabilizes the gyroid and perforated lamella phases.
We present a new metric for determining the local arrangement of particles
based on spherical harmonic "fingerprints", which we use to quantify the extent
of icosahedral ordering.Comment: 8 pages, 4 figure
On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups
In this paper, we consider the relation between two nonabelian Fourier
transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig
parameters for unipotent elliptic representations of a split p-adic group and
the second is defined in terms of the pseudocoefficients of these
representations and Lusztig's nonabelian Fourier transform for characters of
finite groups of Lie type. We exemplify this relation in the case of the p-adic
group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3:
corrections in the table with unipotent discrete series of G
Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups
Let be a classical root system and be a field of sufficiently
large characteristic. Let be the classical group over with the root
system , be its maximal unipotent subgroup and be the
Lie algebra of . Let be an orthogonal subset of and be a
coadjoint orbit of associated with . We construct a polarization of
at the canonical form on . We also find the dimension of
in terms of the Weyl group of . As a corollary, we determine all
possible dimensions of irreducible complex represenations of the group for
the case of finite field .Comment: 11 page
The Impact of Non-Equipartition on Cosmological Parameter Estimation from Sunyaev-Zel'dovich Surveys
The collisionless accretion shock at the outer boundary of a galaxy cluster
should primarily heat the ions instead of electrons since they carry most of
the kinetic energy of the infalling gas. Near the accretion shock, the density
of the intracluster medium is very low and the Coulomb collisional timescale is
longer than the accretion timescale. Electrons and ions may not achieve
equipartition in these regions. Numerical simulations have shown that the
Sunyaev-Zel'dovich observables (e.g., the integrated Comptonization parameter
Y) for relaxed clusters can be biased by a few percent. The Y-mass relation can
be biased if non-equipartition effects are not properly taken into account.
Using a set of hydrodynamical simulations, we have calculated three potential
systematic biases in the Y-mass relations introduced by non-equipartition
effects during the cross-calibration or self-calibration when using the galaxy
cluster abundance technique to constraint cosmological parameters. We then use
a semi-analytic technique to estimate the non-equipartition effects on the
distribution functions of Y (Y functions) determined from the extended
Press-Schechter theory. Depending on the calibration method, we find that
non-equipartition effects can induce systematic biases on the Y functions, and
the values of the cosmological parameters Omega_8, sigma_8, and the dark energy
equation of state parameter w can be biased by a few percent. In particular,
non-equipartition effects can introduce an apparent evolution in w of a few
percent in all of the systematic cases we considered. Techniques are suggested
to take into account the non-equipartition effect empirically when using the
cluster abundance technique to study precision cosmology. We conclude that
systematic uncertainties in the Y-mass relation of even a few percent can
introduce a comparable level of biases in cosmological parameter measurements.Comment: 10 pages, 3 figures, accepted for publication in the Astrophysical
Journal, abstract abridged slightly. Typos corrected in version
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Now you see me (CME): Concept-based model extraction
Deep Neural Networks (DNNs) have achieved remarkable performance on a range
of tasks. A key step to further empowering DNN-based approaches is improving
their explainability. In this work we present CME: a concept-based model
extraction framework, used for analysing DNN models via concept-based extracted
models. Using two case studies (dSprites, and Caltech UCSD Birds), we
demonstrate how CME can be used to (i) analyse the concept information learned
by a DNN model (ii) analyse how a DNN uses this concept information when
predicting output labels (iii) identify key concept information that can
further improve DNN predictive performance (for one of the case studies, we
showed how model accuracy can be improved by over 14%, using only 30% of the
available concepts)
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