Asymptotics for sliced average variance estimation

In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal that when the response is continuous, the asymptotic behavior of SAVE is rather different from that of sliced inverse regression (SIR). SIR can achieve $\sqrt{n}$ consistency even when each slice contains only two data points. However, SAVE cannot be $\sqrt{n}$ consistent and it even turns out to be not consistent when each slice contains a fixed number of data points that do not depend on n, where n is the sample size. These results theoretically confirm the notion that SAVE is more sensitive to the number of slices than SIR. Taking this into account, a bias correction is recommended in order to allow SAVE to be $\sqrt{n}$ consistent. In contrast, when the response is discrete and takes finite values, $\sqrt{n}$ consistency can be achieved. Therefore, an approximation through discretization, which is commonly used in practice, is studied. A simulation study is carried out for the purposes of illustration.Comment: Published at http://dx.doi.org/10.1214/009053606000001091 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dynamical cooling of galactic discs by molecular cloud collisions -- Origin of giant clumps in gas-rich galaxy discs

Different from Milky-Way-like galaxies, discs of gas-rich galaxies are clumpy. It is believed that the clumps form because of gravitational instability. However, a necessary condition for gravitational instability to develop is that the disc must dissipate its kinetic energy effectively, this energy dissipation (also called cooling) is not well-understood. We propose that collisions (coagulation) between molecular clouds dissipate the kinetic energy of the discs, which leads to a dynamical cooling. The effectiveness of this dynamical cooling is quantified by the dissipation parameter $D$, which is the ratio between the free-fall time $t_{\rm ff}\approx 1/ \sqrt{G \rho_{\rm disc}}$ and the cooling time determined by the cloud collision process $t_{\rm cool}$. This ratio is related to the ratio between the mean surface density of the disc $\Sigma_{\rm disc}$ and the mean surface density of molecular clouds in the disc $\Sigma_{\rm cloud}$. When $D <1/3$ (which roughly corresponds to $\Sigma_{\rm disc} < 1/3 \Sigma_{\rm cloud}$), cloud collision cooling is inefficient, and fragmentation is suppressed. When $D > 1/3$ (which roughly corresponds to $\Sigma_{\rm disc} > 1/3 \Sigma_{\rm cloud}$), cloud-cloud collisions lead to a rapid cooling through which clumps form. On smaller scales, cloud-cloud collisions can drive molecular cloud turbulence. This dynamical cooling process can be taken into account in numerical simulations as a subgrid model to simulate the global evolution of disc galaxies.Comment: MNRAS accepte

Associated production of the top-pions and single top at hadron colliders

In the context of topcolor assisted technicolor(TC2) models, we study the production of the top-pions $\pi_{t}^{0,\pm}$ with single top quark via the processes $p\bar{p} \to t\pi_{t}^{0}+X$ and $p\bar{p} \to t\pi_{t}^{\pm}+X$, and discuss the possibility of detecting these new particles at Tevatron and LHC. We find that it is very difficult to observe the signals of these particles via these processes at Tevatron, while the neutral and charged top-pions $\pi_{t}^{0}$ and $\pi_{t}^{\pm}$ can be detecting via considering the same sign top pair $tt\bar{c}$ event and the $tt\bar{b}$ (or $t\bar{t}b$) event at LHC, respectively.Comment: latex files,14 pages, 7 figures. Accepted for publication in Phys. Rev.