Primordial Non-Gaussianity from LAMOST Surveys

The primordial non-Gaussianity (PNG) in matter density perturbation is a very powerful probe of the physics of the very early Universe. The local PNG can induce a distinct scale-dependent bias on the large scale structure distribution of galaxies and quasars, which could be used for constraining it. We study the detection limits on PNG from the surveys of the LAMOST telescope. The cases of the main galaxy survey, the luminous red galaxy (LRG) survey, and the quasar survey of different magnitude limits are considered. We find that the MAIN1 sample (i.e. the main galaxy survey with one magnitude deeper than the SDSS main galaxy survey, or r<18.8) could only provide very weak constraint on PNG. For the MAIN2 sample (r<19.8) and the LRG survey, the 2\sigma (95.5%) limit on the PNG parameter f_{NL} are |f_{NL}|<145 and |f_{NL}|<114 respectively, comparable to the current limit from cosmic microwave background (CMB) data. The quasar survey could provide much more stringent constraint, and we find that the 2\sigma limit for |f_{NL}| is between 50 and 103, depending on the magnitude limit of the survey. With Planck-like priors on cosmological parameters, the quasar survey with g<21.65 would improve the constraints to |f_{NL}|<43 (2\sigma). We also discuss the possibility of further tightening the constraint by using the relative bias method proposed by Seljak(2008).Comment: 8 pages, 2 figures, RAA accepte

Energy-Efficient Transmission Schedule for Delay-Limited Bursty Data Arrivals under Non-Ideal Circuit Power Consumption

This paper develops a novel approach to obtaining energy-efficient transmission schedules for delay-limited bursty data arrivals under non-ideal circuit power consumption. Assuming a-prior knowledge of packet arrivals, deadlines and channel realizations, we show that the problem can be formulated as a convex program. For both time-invariant and time-varying fading channels, it is revealed that the optimal transmission between any two consecutive channel or data state changing instants, termed epoch, can only take one of the three strategies: (i) no transmission, (ii) transmission with an energy-efficiency (EE) maximizing rate over part of the epoch, or (iii) transmission with a rate greater than the EE-maximizing rate over the whole epoch. Based on this specific structure, efficient algorithms are then developed to find the optimal policies that minimize the total energy consumption with a low computational complexity. The proposed approach can provide the optimal benchmarks for practical schemes designed for transmissions of delay-limited data arrivals, and can be employed to develop efficient online scheduling schemes which require only causal knowledge of data arrivals and deadline requirements.Comment: 30 pages, 7 figure

A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth

This paper can be thought of as a remark of \cite{llw}, where the authors studied the eigenvalue distribution $\mu_{X_N}$ of random block Toeplitz band matrices with given block order $m$. In this note we will give explicit density functions of $\lim\limits_{N\to\infty}\mu_{X_N}$ when the bandwidth grows slowly. In fact, these densities are exactly the normalized one-point correlation functions of $m\times m$ Gaussian unitary ensemble (GUE for short). The series $\{\lim\limits_{N\to\infty}\mu_{X_N}|m\in\mathbb{N}\}$ can be seen as a transition from the standard normal distribution to semicircle distribution. We also show a similar relationship between GOE and block Toeplitz band matrices with symmetric blocks.Comment: 6 page