Knutson, Tao, and Woodward [KTW04] formulated a Littlewood–Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil [Vak06] and Wheeler–Zinn-Justin [WZ16] have found additional triangular puzzle pieces that allow one to express structure constants for K-theory of Grassmannians. Here we introduce two other puzzle pieces of hexagonal shape, each of which gives a Littlew...

The cymothoid genus, Pleopodias Richardson, 1910, is revised and a new species from South Africa is recorded. Pleopodias nielbruceisp. n. can be distinguished by large eyes covering majority of the cephalon (almost in contact), antennula bases wide apart, antenna extending to middle of pereonite 2, subtruncate pleotelson, pereopod 7 with numerous acute robust setae on the propodus as well as th...

Quantum error mitigation is a key concept for the development of practical applications based on current noisy intermediate-scale quantum devices. One most promising methods Richardson extrapolation to zero noise limit. While its main idea rather simple, full potential has not been completely uncovered yet. We give an in-depth analysis relevant parameters and propose optimized protocol implemen...

Objectives: The aim of the present study was to reconstruct determining validity, and score The Stanford Diagnostic Reading Test fourth edition (SDRT4) in the sixth grade students. Methods: The population of the study was all sixth grades of the 19 educational districts from Tehran, 571 students (255 boys and 316 girls) were selected by using a random multi-cluster sampling. The data were an...

We investigate the problem of computing tensor product multiplicities for complex semisimple Lie algebras. Even though computing these numbers is #P -hard in general, we show that if the rank of the Lie algebra is assumed fixed, then there is a polynomial time algorithm, based on counting the lattice points in polytopes. In fact, for Lie algebras of type Ar, there is an algorithm, based on the ...

ELECT The minimum mean square error (MMSE) signal detection algorithm is near-optimal for uplink multi-user large-scale multiple-input–multiple-output (MIMO) systems, but involves matrix inversion with high complexity. It is firstly proved that the MMSE filtering matrix for large-scale MIMO is symmetric positive definite, based on which a low-complexity near-optimal signal detection algorithm b...