Koszul differential graded algebras and BGG correspondence

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul DG algebra $A$ is AS-regular, the Ext-algebra $E$ of $A$ is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence between the stable category of finitely generated left $E$-modules, and the quotient triangulated category of the full triangulated subcategory of the derived category of right DG $A$-modules consisting of all compact DG modules modulo the full triangulated subcategory consisting of all the right DG modules with finite dimensional cohomology. The classical BGG correspondence can derived from the DG version.Comment: 29 page

Compressive Channel Estimation and Multi-user Detection in C-RAN

This paper considers the channel estimation (CE) and multi-user detection (MUD) problems in cloud radio access network (C-RAN). Assuming that active users are sparse in the network, we solve CE and MUD problems with compressed sensing (CS) technology to greatly reduce the long identification pilot overhead. A mixed L{2,1}-regularization functional for extended sparse group-sparsity recovery is proposed to exploit the inherently sparse property existing both in user activities and remote radio heads (RRHs) that active users are attached to. Empirical and theoretical guidelines are provided to help choosing tuning parameters which have critical effect on the performance of the penalty functional. To speed up the processing procedure, based on alternating direction method of multipliers and variable splitting strategy, an efficient algorithm is formulated which is guaranteed to be convergent. Numerical results are provided to illustrate the effectiveness of the proposed functional and efficient algorithm.Comment: 6 pages, 3 figure

Effects of Neutrino Inverse Seesaw Mechanism on the Sparticle Spectrum in CMSSM and NUHM2

We study the implications of the inverse seesaw mechanism (ISS) on the sparticle spectrum in the Constrained Minimal Supersymmetric Standard Model (CMSSM) and Non-Universal Higgs Model (NUHM2). Employing the maximal value of the Dirac Yukawa coupling involving the up type Higgs doublet provides a 2-3 GeV enhancement of the lightest CP-even Higgs boson mass. This effect permits one to have lighter colored sparticles in the CMSSM and NUHM2 scenarios with LSP neutralino, which can be tested at LHC14. We present a variety of LHC testable benchmark points with the desired LSP neutralino dark matter relic abundance.Comment: 18 pages, 10 figures and 2 table

Excitation of nonlinear ion acoustic waves in CH plasmas

Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $k\lambda_{De}$ increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $T_i/T_e < 0.2$ in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with $k\lambda_{De}$ increasing. When $k\lambda_{De}$ is not large, such as $k\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when $k\lambda_{De}$ is large, such as $k\lambda_{De}=0.7$, the linear frequency can not be applied to exciting the nonlinear IAW, while the frequency calculated by the dispersion relation with no damping can be applied to exciting the nonlinear IAW.Comment: 10 pages, 9 figures, Accepted by POP, Publication in August 1