Abstract-We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.Index Terms-Information-theoretic security, multiple-input multiple-output (MIMO), multiple antennas, secrecy capacity, wiretap channel.

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BackgroundsSolid evidence has demonstrated that psychoemotional stress induced alteration of hair cycle through neuropeptide substance P (SP) mediated immune response, the role of reactive oxygen species (ROS) in brain-skin-axis regulation system remains unknown.ObjectivesThe present study aims to investigate possible mechanisms of ROS in regulation of SP-mast cell signal pathway in chronic restraint stress (CRS, a model of chronic psychoemotional stress) which induced abnormal of hair cycle.Methods and ResultsOur results have demonstrated that CRS actually altered hair cycle by inhibiting hair follicle growth in vivo, prolonging the telogen stage and delaying subsequent anagen and catagen stage. Up-regulation of SP protein expression in cutaneous peripheral nerve fibers and activation of mast cell were observed accompanied with increase of lipid peroxidation levels and reduction of the activities of superoxide dismutase (SOD) and glutathione peroxidase (GSH-Px) in CRS mice skin. In addition, SP receptor antagonist (RP67580) reduced mast cell activations and lipid peroxidation levels as well as increased GSH-Px activity and normalized hair cycle. Furthermore, antioxidant Tempol (a free radical scavenger) also restored hair cycle, reduced SP protein expression and mast cell activation.ConclusionsOur study provides the first solid evidence for how ROS play a role in regulation of psychoemotional stress induced SP-Mast cell pathway which may provide a convincing rationale for antioxidant application in clinical treatment with psychological stress induced hair loss.

In addition to offering conformational flexibility, sub‐nanometer nanobelts (SNBs) also outperform many larger nanobelts with large size owing to their ultrathin morphologies. However, to date, only a few monocomponent SNBs have been synthesized. This study presents a facile method for synthesizing ZrO2–PMoO (PMZ) SNBs and TiO2–PMoO (PMT) SNBs with heterostructures. The SNBs comprise ZrO2/TiO2 and polyoxometalate (POM) nanoclusters, which are formed via the aggregation and subsequent transformation of nanoclusters. Significantly, these SNBs demonstrate high catalytic activity and stability in oxidative desulfurization reactions at room temperature. The impressive catalytic performance of the SNBs is aided by the POM nanoclusters, which not only coassemble with ZrO2/TiO2 nuclei to form building blocks of PMZ SNBs/PMT SNBs but also serve as catalytic centers. The catalytic performance is further enhanced by the ZrO2/TiO2 in the SNBs. Moreover, the proposed synthesis method can be utilized to produce other SNBs. Thus, this method provides valuable insights into the strong performance properties of SNBs created by combining metal oxides and POM nanoclusters into SNBs, which have great potential as redox catalysts.

Reaction of titanium complex [(L)TiX 2 (THF)] (L ) {N,N′-[(5-R-3-tert-Bu-2-O --C 6 H 2 )CH 2 ] 2 (C 3 H 2 N 2 )}, R ) tert-Bu, L a , R ) Me, L b ; X ) Cl, 1a, 1b; X ) Br, L a , 2) with 2.0 equiv of PhCH 2 MgCl or MeLi in diethyl ether gave dimethyl complexes [(L)Ti(CH 2 Ph) 2 ] (3a, 3b) and [(L)Ti(CH 3 ) 2 ](4a, 4b) by salt metathesis. Dibenzyl titanium complex [(L a )Ti(CH 2 Ph) 2 ] (3a) absorbs dioxygen gas to afford the oxygeninsertion product [(L a )Ti(OCH 2 Ph) 2 ] (5) in 57% yield. The reduction of [(L a )MBr 2 (THF)] ( 2) with 1 equiv of LiBEt 3 H in toluene gave the titanium(III) species [(L a )TiBr(THF) 2 ] (6). The molecular structures of 3b, 4b, 5, and 6 have been confirmed by X-ray single-crystal analysis. The solid state structures of these compounds reveal that these hybrid carbene ligands adopt a transoid conformation to form a pseudotrigonal-bipyramidal (for 3b, 4a, 4b, and 5) or octahedral (for 6) coordination geometry around metal centers. These titanium complexes (1, 2, and 6) showed high activities up to ca. 97 kg PE/(mol Ti • h • atm) for ethylene polymerization in the presence of MAO as coactalyst. The 13 C NMR analysis revealed that linear polyethylene with low molecular weight was formed by these NHC titanium complexes. No methyl or other long-chain branch could be observed.