1. Proofs In this section we derive the proofs of all propositions in the main paper. Proposition 1. The AD entropy of the generalized distribution of y can be written as the sum of the negative log-likelihood of y and the AD entropy of the conditional distribution of the hidden variable given the output, Hα,β(Q y x ;w) = − logP (y|x,w) +Hα,β(P y x ;w). (1) Proof. The AD entropy of the generali...

We analyze optical spectra of a sample of 502 galaxies in close pairs and n-tuples, separated by ≤ 50h−1kpc. We extracted the sample objectively from the CfA2 redshift survey, without regard to the surroundings of the tight systems; we re-measure the spectra with longer exposures, to explore the spectral characteristics of the galaxies. We use the new spectra to probe the relationship between s...

The extraplanar diffuse ionized gas (eDIG) in 17 nearby, edge-on disk galaxies is studied using deep Taurus Tunable Filter Hα and [N II] λ6583 images and conventional interference filter Hα + [N II] λ6548, 6583 images which reach flux levels generally below ∼ 1 × 10−17 erg s−1 cm−2 arcsec−2. [N II] λ6583/Hα excitation maps are available for 10 of these objects. All but one galaxy in the sample ...

this paper aims to investigate the presence of quantifier phrase and classifier phrase in the dp of sarhadi dialect of the baluchi language. to reach this goal, pseudo partitive constructions and their characteristics in different languages are introduced and then it is shown that determiner phrases containing a classifier in baluchi are examples of juxtaposed pseudo partitive constructions in ...