An iterative procedure introduced in MacKay’s evidence framework is often used for estimating the hyper-parameter in empirical Bayes. Despite its effectiveness, the procedure has stayed primarily as a heuristic to date. This paper formally investigates the mathematical nature of this procedure and justifies it as a well-principled algorithm framework. This framework, which we call the MacKay al...

Assume we are given a conditionally null factor Γ. Recent developments in microlocal category theory [28] have raised the question of whether ‖R′′‖ ≡ ζ. We show that there exists a stochastically subintegrable sub-finite subring. In [28, 28], it is shown that there exists a hyper-Gaussian and discretely affine reducible subgroup. Now recent developments in descriptive mechanics [4] have raised ...

Density Functional Theory (DFT) calculations at the B3LYP/6-31+G∗ level have been performed on 5-thiabicyclo[2.1.1]hex-2-ene S-oxide derivatives. The geometrical and electronic properties of the compounds have been analyzed in order to explain the favored stability of the exo configuration. Isodesmic reactions at the Gaussian-G2 theory yielded the exo conformer as the most stable one. Moreover,...

Abstract. We show that the multiple divisor functions of integers in invertible residue classes modulo a prime number, as well as the Fourier coefficients of GLpNq Maass cusp forms for all N > 2, satisfy a central limit theorem in a suitable range, generalizing the case N “ 2 treated by É. Fouvry, S. Ganguly, E. Kowalski and P. Michel in [4]. Such universal Gaussian behaviour relies on a deep e...

chain reaction of human glandular kallikrein (hK2) and prostate-specific antigen (PSA) message. Urology 1997;50:184–8. 13. Deguchi T, Doi T, Ehara H, Shin-Ichi I, Takahashi Y, Nishino Y, et al. Detection of micrometastasis prostate cancer cells in lymph nodes by reverse transcriptase-polymerase chain reaction. Cancer Res 1993;53: 5350–4. 14. Wood DP Jr, Banks ER, Humphreys S, McRoberts JW, Rang...

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Solvation dynamics in ionic liquids show features that are often associated with supercooled liquids, including “stretched” nonexponential relaxation. To better understand the mechanism behind stretching, nonlinear mode-correlation methods proposed Paper I [S. R. Hodge and M. A. Berg, J. Chem. Phys. 155, 024122 (2021)] applied to a simulation of prototypical liquid. A full Green’s function is r...

in this study, absorption of high frequency radio waves in the ionospheric plasma have beeninvestigated. the wave equation was obtained in terms of ionospheric parameters. the numerical values ofthe absorption have been calculated for 4 mhz, 4.5 mhz and 5 mhz waves. the necessary parameters forcalculation have been obtained using an international reference ionosphere (iri) model. the altitudina...

In this paper we have down three theoretical study by using Monte Carlo simulation and Mm+,AMBER and OPLS force field. The calculations were carried out using Hyper Chem professional,release 7.01 package of program. first we have studied the interaction of H2 molecule and He atomwith single-walled carbon nanotube at different temperature. For doing this study we placed H2 andHe in the center an...

We propose a framework called HyperVAE for encoding distributions of distributions. When target distribution is modeled by VAE, its neural network parameters are sampled from in the model space hyper-level VAE. variational inference to implicitly encode parameter into low dimensional Gaussian distribution. Given distribution, we predict posterior latent code, then use matrix-network decoder gen...