A Note on the Secrecy Capacity of the Multi-antenna Wiretap Channel

Recently, the secrecy capacity of the multi-antenna wiretap channel was characterized by Khisti and Wornell [1] using a Sato-like argument. This note presents an alternative characterization using a channel enhancement argument. This characterization relies on an extremal entropy inequality recently proved in the context of multi-antenna broadcast channels, and is directly built on the physical intuition regarding to the optimal transmission strategy in this communication scenario.Comment: 10 pages, 0 figure

Uniform Infall toward the Cometary H II Region in the G34.26+0.15 Complex?

Gas accretion is a key process in star formation. However, the gas infall detections in high-mass star forming regions with high-spatial resolution observations are rare. Here we report the detection of gas infall towards a cometary ultracompact H{\sc ii} region "C" in G34.26+0.15 complex. The hot core associated with "C" has a mass of $\sim$76 M_{\sun} and a volume density of 1.1$\times10^{8}$ cm$^{-3}$. The HCN (3--2), HCO$^{+}$ (1--0) lines observed by single-dishes and the CN (2--1) lines observed by the SMA show redshifted absorption features, indicating gas infall. We found a linear relationship between the line width and optical depth of the CN (2--1) lines. Those transitions with larger optical depth and line width have larger absorption area. However, the infall velocities measured from different lines seem to be constant, indicating the gas infall is uniform. We also investigated the evolution of gas infall in high-mass star forming regions. At stages prior to hot core phase, the typical infall velocity and mass infall rate are $\sim$ 1 km s$^{-1}$ and $\sim10^{-4}$ M_{\sun}\cdotyr$^{-1}$, respectively. While in more evolved regions, the infall velocity and mass infall rates can reach as high as serval km s$^{-1}$ and $\sim10^{-3}-10^{-2}$ M_{\sun}\cdotyr$^{-1}$, respectively. Accelerated infall has been detected towards some hypercompact H{\sc ii} and ultracompact H{\sc ii} regions. However, the acceleration phenomenon becomes inapparent in more evolved ultracompact H{\sc ii} regions (e.g. G34.26+0.15)

Molecular environments of 51 Planck cold clumps in Orion complex

A mapping survey towards 51 Planck cold clumps projected on Orion complex was performed with J=1-0 lines of $^{12}$CO and $^{13}$CO at the 13.7 m telescope of Purple Mountain Observatory. The mean column densities of the Planck gas clumps range from 0.5 to 9.5$\times10^{21}$ cm$^{-2}$, with an average value of (2.9$\pm$1.9)$\times10^{21}$ cm$^{-2}$. While the mean excitation temperatures of these clumps range from 7.4 to 21.1 K, with an average value of 12.1$\pm$3.0 K. The averaged three-dimensional velocity dispersion $\sigma_{3D}$ in these molecular clumps is 0.66$\pm$0.24 km s$^{-1}$. Most of the clumps have $\sigma_{NT}$ larger than or comparable with $\sigma_{Therm}$. The H$_{2}$ column density of the molecular clumps calculated from molecular lines correlates with the aperture flux at 857 GHz of the dust emission. Through analyzing the distributions of the physical parameters, we suggest turbulent flows can shape the clump structure and dominate their density distribution in large scale, but not affect in small scale due to the local fluctuations. Eighty two dense cores are identified in the molecular clumps. The dense cores have an averaged radius and LTE mass of 0.34$\pm$0.14 pc and 38$_{-30}^{+5}$ M_{\sun}, respectively. And structures of low column density cores are more affected by turbulence, while those of high column density cores are more concerned by other factors, especially by gravity. The correlation of the velocity dispersion versus core size is very weak for the dense cores. The dense cores are found most likely gravitationally bounded rather than pressure confined. The relationship between $M_{vir}$ and $M_{LTE}$ can be well fitted with a power law. The core mass function here is much more flatten than the stellar initial mass function. The lognormal behavior of the core mass distribution is most likely determined by the internal turbulence.Comment: Accepted to The Astrophysical Journal Supplement Series (ApJS

Molecular gas and triggered star formation surrounding Wolf-Rayet stars

The environments surrounding nine Wolf-Rayet stars were studied in molecular emission. Expanding shells were detected surrounding these WR stars (see left panels of Figure 1). The average masses and radii of the molecular cores surrounding these WR stars anti-correlate with the WR stellar wind velocities (middle panels of Figure 1), indicating the WR stars has great impact on their environments. The number density of Young Stellar Objects (YSOs) is enhanced in the molecular shells at $\sim$5 arcmin from the central WR star (lower-right panel of Figure 1). Through detailed studies of the molecular shells and YSOs, we find strong evidences of triggered star formation in the fragmented molecular shells (\cite[Liu et al. 2010]{liu_etal12}Comment: 1 page, IAUS29

Generalized Cut-Set Bounds for Broadcast Networks

A broadcast network is a classical network with all source messages collocated at a single source node. For broadcast networks, the standard cut-set bounds, which are known to be loose in general, are closely related to union as a specific set operation to combine the basic cuts of the network. This paper provides a new set of network coding bounds for general broadcast networks. These bounds combine the basic cuts of the network via a variety of set operations (not just the union) and are established via only the submodularity of Shannon entropy. The tightness of these bounds are demonstrated via applications to combination networks.Comment: 30 pages, 4 figures, submitted to the IEEE Transaction on Information Theor