We extend the existing framework of semiimplicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference in models where the prior and the posterior can be expressed as an intractable infinite mixture of some analytic density with a highly flexible implicit mixing distribution. We provide a sandwich bound on the evidence lower bound (ELBO) objective that can be made arbitrarily tight. Unlike discriminator-based and kernel-based approaches to implicit variational inference, DSIVI optimizes a proper lower bound on ELBO that is asymptotically exact. We evaluate DSIVI on a set of problems that benefit from implicit priors. In particular, we show that DSIVI gives rise to a simple modification of VampPrior, the current state-of-theart prior for variational autoencoders, which improves its performance.

TOLOADS UDC 622.235Rock bursts occur when blasting is carried out in deep horizons of Donbass collieries in sandstones with a Protod'yakonov hardness f= 6-10. It is assumed that this is largely due to the stressed state of the rock mass induced by the pressure of the overlying rocks, tectonic processes, and saturation of the rock with gas at a pressure of 30-100 atm.Before a working is driven, the rock mass is in a state of volumetric stress. When the working is driven by blasting, the explosions cause additional stresses in the rock mass, which reach 35-280 kg/cm z, depending on the properties of the rocks and the properties of the explosives at the contact of the charge with the rock. At a distance of up to 15 charge radii from the explosion center, the shock waves are propagated at ultrasonic speeds; at a distance of 15-500 radii, the stress waves are propagated at the speed of sound, the stresses retaining fairly high values.Under the conditions of hydrostatic load, at a distance of 10-20 charge radii from the explosion center we observe plastic deformations -a zone of overcrushing of the rock at concentric circumferences. There are no radial fissures in the walls of the cavity. During the explosion, at a distance of 20-400 charge radii a wave of reversible deformation of the rock is formed. It is due to the potential energy of an elastically compressed medium; hence its effect is manifested after part of the rock mass has been detached. The reversible deformation wave is a tension wave and is displaced only toward the free surface. On these grounds we may infer that the stresses induced by firing shothole charges are an additional pulse which leads to the ejection of rock.Methods which control the stress field parameters enable one to reduce the probability of occurrence of bursts. The value of the stresses being propagated into the heart of the rock mass depends on the pressure at the shock front. The pressure at the shock front may be greatly reduced by using linings of materials with an acoustic impedance markedly different from that of the rock being blasted, the: ~. linings being located between the charge and the wall of the blast hole. The pressure (stress) transmitted to the rock mass in absence of a gap is determined by the equation oma x = k Pay N/m2'where k is the refractive index 2 p, C,where Pl is the density of the medium, in kg/m s, C, is the velocity of the longitudinal wave, in m/sec, Pex is the density of the explosive charge, in kg/m s, and Dex is the detonation velocity of the explosives, in m/see.As the shock wave passes through the lining, the stress is reduced by refraction of the wave at the chargelining and lining-rock interfaces.The stress transmitted to the rock mass through the lining in the forward elastic wave is calculated by the equationInstitute of Geotechnical Mechanics, Academy of Sciences of the URrSSR, Dnepropetrovsk.

Yur T. V., Dubrovin V. I., Kharitonov V. N. ANALYSIS OF WAVELET TRANSFORM FILTERING PROPERTIESFiltering properties of continuous wavelet transform are investigated in the paper. The method that decreases the influence of edge effects on wavelet analysis results is described. The choice of wavelet for non-stationary signals analysis is grounded. The method of construction of a filter bank with required analyzing properties is proposed. The given method is applied to the problem of rolling bearing diagnostics by vibration signals.

No abstract

No abstract