2,910 research outputs found
Dedekind order completion of C(X) by Hausdorff continuous functions
The concept of Hausdorff continuous interval valued functions, developed
within the theory of Hausdorff approximations and originaly defined for
interval valued functions of one real variable is extended to interval valued
functions defined on a topological space X. The main result is that the set of
all finite Hausdorff continuous functions on any topological space X is
Dedekind order complete. Hence it contains the Dedekind order completion of the
set C(X) of all continuous real functions defined on X as well as the Dedekind
order completion of the set C_b(X) of all bounded continuous functions on X.
Under some general assumptions about the topological space X the Dedekind order
completions of both C(X) and C_b(X) are characterised as subsets of the set of
all Hausdorff continuous functions. This solves a long outstanding open problem
about the Dedekind order completion of C(X). In addition, it has major
applications to the regularity of solutions of large classes of nonlinear PDEs
Muon Pair Production by Electron-Photon Scatterings
The cross section for muon pair productions by electrons scattering over
photons, , is calculated analytically in the leading order. It is
pointed out that for the center-of-mass energy range, ,
the cross section for is less than b. The differential
energy spectrum for either of the resulting muons is given for the purpose of
high-energy neutrino astronomy. An implication of our result for a recent
suggestion concerning the high-energy cosmic neutrino generation through this
muon pair is discussed.Comment: a comment added, to appear in Phys. Rev. D, Rapid Communicatio
The output distribution of important LULU-operators
Two procedures to compute the output distribution phi_S of certain stack
filters S (so called erosion-dilation cascades) are given. One rests on the
disjunctive normal form of S and also yields the rank selection probabilities.
The other is based on inclusion-exclusion and e.g. yields phi_S for some
important LULU-operators S. Properties of phi_S can be used to characterize
smoothing properties of S. One of the methods discussed also allows for the
calculation of the reliability polynomial of any positive Boolean function
(e.g. one derived from a connected graph).Comment: 20 pages, up to trivial differences this is the final version to be
published in Quaestiones Mathematicae 201
Calculating the output distribution of stack filters that are erosion-dilation cascades, in particular LULU-filters
Original article available at http://arxiv.org/ENGLISH ABSTRACT: Two procedures to compute the output distribution 0S of certain stack filters S (so
called erosion-dilation cascades) are given. One rests on the disjunctive normal form of S
and also yields the rank selection probabilities. The other is based on inclusion-exclusion
and e.g. yields 0S for some important LULU-operators S. Properties of 0S can be used to
characterize smoothing properties.Preprin
Unsupervised 3D Perception with 2D Vision-Language Distillation for Autonomous Driving
Closed-set 3D perception models trained on only a pre-defined set of object
categories can be inadequate for safety critical applications such as
autonomous driving where new object types can be encountered after deployment.
In this paper, we present a multi-modal auto labeling pipeline capable of
generating amodal 3D bounding boxes and tracklets for training models on
open-set categories without 3D human labels. Our pipeline exploits motion cues
inherent in point cloud sequences in combination with the freely available 2D
image-text pairs to identify and track all traffic participants. Compared to
the recent studies in this domain, which can only provide class-agnostic auto
labels limited to moving objects, our method can handle both static and moving
objects in the unsupervised manner and is able to output open-vocabulary
semantic labels thanks to the proposed vision-language knowledge distillation.
Experiments on the Waymo Open Dataset show that our approach outperforms the
prior work by significant margins on various unsupervised 3D perception tasks.Comment: ICCV 202
GINA-3D: Learning to Generate Implicit Neural Assets in the Wild
Modeling the 3D world from sensor data for simulation is a scalable way of
developing testing and validation environments for robotic learning problems
such as autonomous driving. However, manually creating or re-creating
real-world-like environments is difficult, expensive, and not scalable. Recent
generative model techniques have shown promising progress to address such
challenges by learning 3D assets using only plentiful 2D images -- but still
suffer limitations as they leverage either human-curated image datasets or
renderings from manually-created synthetic 3D environments. In this paper, we
introduce GINA-3D, a generative model that uses real-world driving data from
camera and LiDAR sensors to create realistic 3D implicit neural assets of
diverse vehicles and pedestrians. Compared to the existing image datasets, the
real-world driving setting poses new challenges due to occlusions,
lighting-variations and long-tail distributions. GINA-3D tackles these
challenges by decoupling representation learning and generative modeling into
two stages with a learned tri-plane latent structure, inspired by recent
advances in generative modeling of images. To evaluate our approach, we
construct a large-scale object-centric dataset containing over 520K images of
vehicles and pedestrians from the Waymo Open Dataset, and a new set of 80K
images of long-tail instances such as construction equipment, garbage trucks,
and cable cars. We compare our model with existing approaches and demonstrate
that it achieves state-of-the-art performance in quality and diversity for both
generated images and geometries.Comment: Accepted by CVPR 202
Inner Space Preserving Generative Pose Machine
Image-based generative methods, such as generative adversarial networks
(GANs) have already been able to generate realistic images with much context
control, specially when they are conditioned. However, most successful
frameworks share a common procedure which performs an image-to-image
translation with pose of figures in the image untouched. When the objective is
reposing a figure in an image while preserving the rest of the image, the
state-of-the-art mainly assumes a single rigid body with simple background and
limited pose shift, which can hardly be extended to the images under normal
settings. In this paper, we introduce an image "inner space" preserving model
that assigns an interpretable low-dimensional pose descriptor (LDPD) to an
articulated figure in the image. Figure reposing is then generated by passing
the LDPD and the original image through multi-stage augmented hourglass
networks in a conditional GAN structure, called inner space preserving
generative pose machine (ISP-GPM). We evaluated ISP-GPM on reposing human
figures, which are highly articulated with versatile variations. Test of a
state-of-the-art pose estimator on our reposed dataset gave an accuracy over
80% on PCK0.5 metric. The results also elucidated that our ISP-GPM is able to
preserve the background with high accuracy while reasonably recovering the area
blocked by the figure to be reposed.Comment: http://www.northeastern.edu/ostadabbas/2018/07/23/inner-space-preserving-generative-pose-machine
Neutrinos produced by ultrahigh-energy photons at high red shift
Some of the proposed explanations for the origin of ultrahigh-energy cosmic
rays invoke new sources of energetic photons (e.g., topological defects, relic
particles, etc.). At high red shift, when the cosmic microwave background has a
higher temperature but the radio background is low, the ultrahigh-energy
photons can generate neutrinos through pair-production of muons and pions.
Neutrinos produced at high red shift by slowly evolving sources can be
detected. Rapidly evolving sources of photons can be ruled out based on the
existing upper limit on the neutrino flux.Comment: 4 pages, revtex; to appear in Phys. Rev. Let
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