On weighted structured total least squares

In this contribution we extend the result of (Markovsky et. al, SIAM J. of Matrix Anal. and Appl., 2005) to the case of weighted cost function. It is shown that the computational complexity of the proposed algorithm is preserved linear in the sample size when the weight matrix is banded with bandwidth that is independent of the sample size

Geometry of effective Hamiltonians

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results are hitherto unknown or unpublished. In particular, commuting observables and symmetries are discussed in detail. Simple and explicit proofs are given, and numerical algorithms are proposed, that improve and stabilize common methods used today.Comment: 1 figur

Algorithms and literate programs for weighted low-rank approximation with missing data

Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets

Circular photon drag effect in bulk tellurium

The circular photon drag effect is observed in a bulk semiconductor. The photocurrent caused by a transfer of both translational and angular momenta of light to charge carriers is detected in tellurium in the mid-infrared frequency range. Dependencies of the photocurrent on the light polarization and on the incidence angle agree with the symmetry analysis of the circular photon drag effect. Microscopic models of the effect are developed for both intra- and inter-subband optical absorption in the valence band of tellurium. The shift contribution to the circular photon drag current is calculated. An observed decrease of the circular photon drag current with increase of the photon energy is explained by the theory for inter-subband optical transitions. Theoretical estimates of the circular photon drag current agree with the experimental data.Comment: 8 pages, 4 figure

Unextendible product bases and extremal density matrices with positive partial transpose

In bipartite quantum systems of dimension 3x3 entangled states that are positive under partial transposition (PPT) can be constructed with the use of unextendible product bases (UPB). As discussed in a previous publication all the lowest rank entangled PPT states of this system seem to be equivalent, under special linear product transformations, to states that are constructed in this way. Here we consider a possible generalization of the UPB constuction to low-rank entangled PPT states in higher dimensions. The idea is to give up the condition of orthogonality of the product vectors, while keeping the relation between the density matrix and the projection on the subspace defined by the UPB. We examine first this generalization for the 3x3 system where numerical studies indicate that one-parameter families of such generalized states can be found. Similar numerical searches in higher dimensional systems show the presence of extremal PPT states of similar form. Based on these results we suggest that the UPB construction of the lowest rank entangled states in the 3x3 system can be generalized to higher dimensions, with the use of non-orthogonal UPBs.Comment: 23 pages, 2 figures, 1 table. V2: Fixed fig.1 not showin

Separable states can be used to distribute entanglement

We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by continuous interaction with a highly mixed mediating particle that never itself becomes entangled. We also consider analogous properties of completely positive maps, in which the composition of two separable maps can create entanglement.Comment: 4 pages, 2 figures. Slight modification

Interaction-assisted propagation of Coulomb-correlated electron-hole pairs in disordered semiconductors

A two-band model of a disordered semiconductor is used to analyze dynamical interaction induced weakening of localization in a system that is accessible to experimental verification. The results show a dependence on the sign of the two-particle interaction and on the optical excitation energy of the Coulomb-correlated electron-hole pair.Comment: 4 pages and 3 ps figure

Connection of power of consumable electricity by trolleybus with the transported amount of passengers and descriptions of routes

Встановлено відповідність потужності споживаної тролейбусом електроенергії перевезеній ним кількості пасажирів. У дослідженні також враховано характеристики маршруту для уточнення зв’язку між витратами потужності і пасажиропотоком. The accordance of power to consumable electricity power by a trolleybus to the amount of passengers transported is determined. In the given research there taken into account the descriptions of the route for clarification of connection of power expense and passenger transportations