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, $\sigma_{MPP}$, is calculated analytically in the leading order. It is pointed out that for the center-of-mass energy range, $s \geq 5 m^{2}_{\mu}$, the cross section for $\sigma_{MPP}$ is less than $1 \mu$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

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

Measurement of Λ (1520) production in pp collisions at √s=7TeV and p–Pb collisions at √sNN=5.02TeV

The production of the Λ (1520) baryonic resonance has been measured at midrapidity in inelastic pp collisions at s=7TeV and in p–Pb collisions at sNN=5.02TeV for non-single diffractive events and in multiplicity classes. The resonance is reconstructed through its hadronic decay channel Λ (1520) → pK - and the charge conjugate with the ALICE detector. The integrated yields and mean transverse momenta are calculated from the measured transverse momentum distributions in pp and p–Pb collisions. The mean transverse momenta follow mass ordering as previously observed for other hyperons in the same collision systems. A Blast-Wave function constrained by other light hadrons (π, K, KS0, p, Λ) describes the shape of the Λ (1520) transverse momentum distribution up to 3.5GeV/c in p–Pb collisions. In the framework of this model, this observation suggests that the Λ (1520) resonance participates in the same collective radial flow as other light hadrons. The ratio of the yield of Λ (1520) to the yield of the ground state particle Λ remains constant as a function of charged-particle multiplicity, suggesting that there is no net effect of the hadronic phase in p–Pb collisions on the Λ (1520) yield

Measurement of prompt D0, D+, D*+, and DS+ production in p–Pb collisions at √sNN = 5.02 TeV

The measurement of the production of prompt D0, D+, D*+, and DS+ mesons in proton–lead (p–Pb) collisions at the centre-of-mass energy per nucleon pair of sNN = 5.02 TeV, with an integrated luminosity of 292 ± 11 μb−1, are reported. Differential production cross sections are measured at mid-rapidity (−0.96 < ycms< 0.04) as a function of transverse momentum (pT) in the intervals 0 < pT< 36 GeV/c for D0, 1 < pT< 36 GeV/c for D+ and D*+, and 2 < pT< 24 GeV/c for D+ mesons. For each species, the nuclear modification factor RpPb is calculated as a function of pT using a proton-proton (pp) ref- erence measured at the same collision energy. The results are compatible with unity in the whole pT range. The average of the non-strange D mesons RpPb is compared with theoretical model predictions that include initial-state effects and parton transport model predictions. The pT dependence of the D0, D+, and D*+ nuclear modification factors is also reported in the interval 1 < pT< 36 GeV/c as a function of the collision centrality, and the central-to-peripheral ratios are computed from the D-meson yields measured in different centrality classes. The results are further compared with charged-particle measurements and a similar trend is observed in all the centrality classes. The ratios of the pT-differential cross sections of D0, D+, D*+, and DS+ mesons are also reported. The DS+ and D+ yields are compared as a function of the charged-particle multiplicity for several pT intervals. No modification in the relative abundances of the four species is observed with respect to pp collisions within the statistical and systematic uncertainties. [Figure not available: see fulltext.]