Derivative based global sensitivity measures

The method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol' sensitivity indices and has several advantages over them. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that for estimation of Sobol' sensitivity indices. This paper presents a survey of recent advances in DGSM concerning lower and upper bounds on the values of Sobol' total sensitivity indices $S\_{i}^{tot}$. Using these bounds it is possible in most cases to get a good practical estimation of the values of $S\_{i}^{tot}$. Several examples are used to illustrate an application of DGSM

Influence of backreaction of electric fields and Schwinger effect on inflationary magnetogenesis

We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling $f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ of the electromagnetic field to the inflaton field $\phi$. We consider the case where the coupling function $f(\phi)$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter $\epsilon$ and inflaton energy density, $\rho_{E}\sim \epsilon \rho_{\rm inf}$. It affects the inflaton field evolution and leads to the scale-invariant electric power spectrum and the magnetic one which is blue with the spectral index $n_{B}=2$ for any decreasing coupling function. This gives an upper limit on the present-day value of observed magnetic fields below $10^{-22}\,{\rm G}$. It is worth emphasizing that since the effective electric charge of particles $e_{\rm eff}=e/f$ is suppressed by the coupling function, the Schwinger effect becomes important only at the late stages of inflation when the inflaton field is close to the minimum of its potential. The Schwinger effect abruptly decreases the value of the electric field, helping to finish the inflation stage and enter the stage of preheating. It effectively produces the charged particles, implementing the Schwinger reheating scenario even before the fast oscillations of the inflaton. The numerical analysis is carried out in the Starobinsky model of inflation for the powerlike $f\propto a^{\alpha}$ and Ratra-type $f=\exp(\beta\phi/M_{p})$ coupling functions.Comment: 21 pages, 8 figure

Comptomization and radiation spectra of X-ray sources. Calculation of the Monte Carlo method

The results of computations of the Comptomization of low frequency radiation in weakly relativistic plasma are presented. The influence of photoabsorption by iron ions on a hard X-ray spectrum is considered

On the crude multidimensional search

AbstractMultivariable trial functions that depend on random parameters are maximized by crude global search. Analytical and numerical investigations of error distributions confirm recent conclusions that in practice random searching points perform better than rectangular lattices, and that quasi-random searching points are even more efficient

A new measure of irregularity of distribution

AbstractWe introduce a new measure of irregularity of distribution-the range, Ψ, that is similar to the nonuniformity ϕ∞ but much easier to compute. It is shown that for Pτ-nets and for initial segments of LPτ-sequences Ψ ≤ 2τ and as the number of points increases this is the lowest possible order of magnitude Ψ = O(1)

Microbial single-cell omics: the crux of the matter

Single-cell genomics and transcriptomics can provide reliable context for assembled genome fragments and gene expression activity on the level of individual prokaryotic genomes. These methods are rapidly emerging as an essential complement to cultivation-based, metagenomics, metatranscriptomics, and microbial community-focused research approaches by allowing direct access to information from individual microorganisms, even from deep-branching phylogenetic groups that currently lack cultured representatives. Their integration and binning with environmental ‘omics data already provides unprecedented insights into microbial diversity and metabolic potential, enabling us to provide information on individual organisms and the structure and dynamics of natural microbial populations in complex environments. This review highlights the pitfalls and recent advances in the field of single-cell omics and its importance in microbiological and biotechnological studies

Effect of electrolysis regimes on the structure and properties of coatings on aluminum alloys formed by anode-cathode microarc oxidation

Наведено результати дослідження фазового складу і властивостей МДО-покриттів на алюмінієвих сплавах. Покриття були одержані в лужно-селікатному електроліті на змінному сінусоідальному струмі і в імпульсному режимі струму. Показано, що підвищена щільність мікророзрядів при імпульсної технології збільшує сумарну енергію, що виділяється в них. Це обумовлює підвищення швидкості зростання оксидного покриття і ймовірність утворення α-Al₂O₃ фази. Одержані при мікроплазмове оксидуванні в імпульсному струмовому режимі покриття мають високу твердість і електричну міцніст

Spatial inversion of gyrotropy parameter in conductivity tensor and charge transport peculiarities

Charge transfer is discussed for the case when gyrotropy parameter (Hall coefficient) varies along transport л-direction and inverses its sign. This situation takes place in contacts of the serially joined materials having electron and hole types of conductivity. Spatial inhomogeneity of conductivity and inversion of Hall coefficient sign are analyzed in terms of electric potential and current density distribution. It is shown that under inhomogeneous magnetic field the steady current skinning takes place in plate sample

Derivative based global sensitivity measures

International audienceThe method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol' sensitivity indices and has several advantages over them. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that for estimation of Sobol' sensitivity indices. This paper presents a survey of recent advances in DGSM concerning lower and upper bounds on the values of Sobol' total sensitivity indices $S_{i}^{tot}$. Using these bounds it is possible in most cases to get a good practical estimation of the values of $S_{i}^{tot}$. Several examples are used to illustrate an application of DGSM