2,707 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
On the numerical analysis of triplet pair production cross-sections and the mean energy of produced particles for modelling electron-photon cascade in a soft photon field
The double and single differential cross-sections with respect to positron
and electron energies as well as the total cross-section of triplet production
in the laboratory frame are calculated numerically in order to develop a Monte
Carlo code for modelling electron-photon cascades in a soft photon field. To
avoid numerical integration irregularities of the integrands, which are
inherent to problems of this type, we have used suitable substitutions in
combination with a modern powerful program code Mathematica allowing one to
achieve reliable higher-precission results. The results obtained for the total
cross-section closely agree with others estimated analytically or by a
different numerical approach. The results for the double and single
differential cross-sections turn out to be somewhat different from some
reported recently. The mean energy of the produced particles, as a function of
the characteristic collisional parameter (the electron rest frame photon
energy), is calculated and approximated by an analytical expression that
revises other known approximations over a wide range of values of the argument.
The primary-electron energy loss rate due to triplet pair production is shown
to prevail over the inverse Compton scattering loss rate at several (2)
orders of magnitude higher interaction energy than that predicted formerly.Comment: 18 pages, 8 figures, 2 tables, LaTex2e, Iopart.cls, Iopart12.clo,
Iopams.st
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
Electromagnetic showers in a strong magnetic field
We present the results concerning the main shower characteristics in a strong
magnetic field obtained through shower simulation. The processes of magnetic
bremsstrahlung and pair production were taken into account for values of the
parameter . We compare our simulation results with a recently
developed cascade theory in a strong magnetic field.Comment: 11 pages, 9 eps figures, LaTex2e, Iopart.cls, Iopart12.clo,
Iopams.st
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
Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image
We describe the first method to automatically estimate the 3D pose of the
human body as well as its 3D shape from a single unconstrained image. We
estimate a full 3D mesh and show that 2D joints alone carry a surprising amount
of information about body shape. The problem is challenging because of the
complexity of the human body, articulation, occlusion, clothing, lighting, and
the inherent ambiguity in inferring 3D from 2D. To solve this, we first use a
recently published CNN-based method, DeepCut, to predict (bottom-up) the 2D
body joint locations. We then fit (top-down) a recently published statistical
body shape model, called SMPL, to the 2D joints. We do so by minimizing an
objective function that penalizes the error between the projected 3D model
joints and detected 2D joints. Because SMPL captures correlations in human
shape across the population, we are able to robustly fit it to very little
data. We further leverage the 3D model to prevent solutions that cause
interpenetration. We evaluate our method, SMPLify, on the Leeds Sports,
HumanEva, and Human3.6M datasets, showing superior pose accuracy with respect
to the state of the art.Comment: To appear in ECCV 201
Multiwavelength observations of Mkn 501 during the 1997 high state
During the observation period 1997, the nearby Blazar Mkn 501 showed
extremely strong emission and high variability. We examine multiwavelength
aspects of this event using radio, optical, soft and hard X-ray and TeV data.
We concentrate on the medium-timescale variability of the broadband spectra,
averaged over weekly intervals.
We confirm the previously found correlation between soft and hard X-ray
emission and the emission at TeV energies, while the source shows only minor
variability at radio and optical wavelengths. The non-linear correlation
between hard X-ray and TeV fluxes is consistent with a simple analytic estimate
based on an SSC model in which Klein-Nishina effects are important for the
highest-energy electrons in the jet, and flux variations are caused by
variations of the electron density and/or the spectral index of the electron
injection spectrum.
The time-averaged spectra are fitted with a Synchrotron Self-Compton (SSC)
dominated leptonic jet model, using the full Klein-Nishina cross section and
following the self-consistent evolution of relativistic particles along the
jet, accounting for gamma-gamma absorption and pair production within the
source as well as due to the intergalactic infrared background radiation. The
contribution from external inverse-Compton scattering is tightly constrained by
the low maximum EGRET flux and found to be negligible at TeV energies. We find
that high levels of the X-ray and TeV fluxes can be explained by a hardening of
the energy spectra of electrons injected at the base of the jet, in remarkable
contrast to the trend found for gamma-ray flares of the flat-spectrum radio
quasar PKS 0528+134.Comment: accepted for publication in ApJ, 31 pages, 11 figure
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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