New comparison theorems are presented comparing the asymptotic convergence factor of iterative methods for the solution of consistent (as well as inconsistent) singular systems of linear equations. The asymptotic convergence factor of the iteration matrix T is the quantity γ(T ) = max{|λ|, λ ∈ σ(T ), λ = 1}, where σ(T ) is the spectrum of T . In the new theorems, no restrictions are imposed on ...

Pairwise comparison matrices often exhibit inconsistency, therefore, a number of indices has been introduced to measure their deviation from a consistent matrix. Since inconsistency first emerges in the case of three alternatives, several inconsistency indices are based on triads. Recently, a set of axioms has been proposed, and is required to be satisfied by any reasonable inconsistency index....

This paper considers the parameter estimation problem in Stochastic Block Model with Overlaps (SBMO), which is a quite general instance of random graph model allowing for overlapping community structure. We present the new algorithm successive projection overlapping clustering (SPOC) which combines the ideas of spectral clustering and geometric approach for separable non-negative matrix factori...

sampling and separation of serum from blood cells. We agree with M. John and K. Jung that we must be aware of pre-analytical problems when analysing the circulating matrix metalloproteinase (MMP)-9 and tissue inhibitor of metalloproteinase (TIMP)-1 levels. However, we used only serum samples in our study because we usually use serum samples for clinical examinations in our hospital. Therefore, ...

The pairwise comparisonsmethod is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. One popular implementation of the method is based on solving an eigenvalue problem for the pairwise comparisons matrix. In such cases the ranking result the principal eigenvector of the pairwise comparison matrix is adopted, whilst the eigenvalue is us...

Several methods to improve the parton-shower description of hard processes by an injection of matrix-element-based information have been presented over the years. In this article we study (re)weighting schemes for the first/hardest emission. One objective is to provide a consistent matching of the POWHEG next-to-leading order generator to the Pythia shower algorithms. Another is to correct the ...

The first, to our knowledge, calculation of neutrinoless double beta decay (0νββ-decay ) matrix elements within the self-consistent renormalized Quasiparticle Random Phase Approximation (SRQRPA) is presented. The contribution from the momentum-dependent induced nucleon currents to 0νββdecay amplitude is taken into account. A detailed nuclear structure study includes the discussion of the sensit...

116802-1 We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at a total filling factor 1, based on exact numerical calculations of the topological Chern number matrix and the (interlayer) superfluid density. We find three phases: a quantized Hall state with pseudospin superfluidity, a quantized Hall state with pseudospin ‘‘gauge-glass’’ order, an...

Based on the general concept of randomization, we develop linear-algebraic approximations for continuous probability distributions that involve the exponential of a matrix in their definitions, such as phase types and matrixexponential distributions. The approximations themselves result in proper probability distributions. For such a global randomization with the Erlangdistribution, we show tha...

We report on a consistent, microscopic calculation of the bound and scattering states in the He system employing modern realistic two-nucleon and three-nucleon potentials in the framework of the resonating group model (RGM). We present for comparison with these microscopic RGM calculations the results from a charge-independent, Coulomb-corrected R-matrix analysis of all types of data for reacti...