Exact analytical solution of average path length for Apollonian networks

The exact formula for the average path length of Apollonian networks is found. With the help of recursion relations derived from the self-similar structure, we obtain the exact solution of average path length, $\bar{d}_t$, for Apollonian networks. In contrast to the well-known numerical result $\bar{d}_t \propto (\ln N_t)^{3/4}$ [Phys. Rev. Lett. \textbf{94}, 018702 (2005)], our rigorous solution shows that the average path length grows logarithmically as $\bar{d}_t \propto \ln N_t$ in the infinite limit of network size $N_t$. The extensive numerical calculations completely agree with our closed-form solution.Comment: 8 pages, 4 figure

Landau-Zener Tunnelling in a Nonlinear Three-level System

We present a comprehensive analysis of the Landau-Zener tunnelling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunnelling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of linear case. In particular, the tunnelling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunnelling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunnelling probability when the nonlinear "internal field" resonate with the external field. We also discuss the asymmetry of the tunnelling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.Comment: 8 pages, 8 figure

Neural Basis of Dispositional Awe

Awe differs from common positive emotions, triggered by vast stimuli, and characterized by a need for accommodation (NFA). Although studies have revealed the downstream effects of awe experience, little is known about the neural basis of dispositional awe. In the current study, we determined the neural correlation of dispositional awe by using voxel-based morphometry (VBM) in 42 young healthy adults, as measured by the Dispositional Positive Emotion Scale (DPES). Results revealed that the dispositional awe score was negatively associated with the regional gray matter volume (rGMV) in the anterior cingulate cortex (ACC), middle/posterior cingulate cortex (MCC/PCC) and middle temporal gyrus (MTG). These results suggest that individual differences in dispositional awe involve multiple brain regions related to attention, conscious self-regulation, cognitive control and social emotion. This study is the first to provide evidence for the structural neural basis of individual differences in dispositional awe

Block transformation of hybrid cellular automata

By introducing the sequence-block transformation and vector-block transformation, a discussion of symbolic dynamics of hybrid cellular automation (HCA) and hybrid cellular automation with memory (HCAM) is presented in this paper. As the local evolution rules of HCA and HCAM are not uniform, the new uniform cellular automata (CAs) with multiple states can be constructed by specific block transformations. It is proved that the new CA rules are topologically conjugate with the originals. Furthermore, the complex dynamics of the HCA and HCAM rules can be investigated via the new CA rules

Pollen Viability, Pistil Receptivity, and Embryo Development in Hybridization of Nelumbo nucifera Gaertn

Seed set is usually low and differs for different crosses of flower lotus (Nelumbo nucifera Gaertn.). The reasons remain unknown, and this has a negative impact on lotus breeding. To determine the causes, we carried out two crosses of flower lotus, that is, “Jinsenianhua” × “Qinhuaihuadeng” and “Qinhuaihuadeng” × “Jinsenianhua” and pollen viability, pistil receptivity, and embryo development were investigated. The pollen grains collected at 05:00-06:00 hrs had the highest viability, and the viabilities of “Jinsenianhua” and “Qinhuaihuadeng” were 20.6 and 15.7%, respectively. At 4 h after artificial pollination, the number of pollen grains germinating on each stigma reached a peak: 63.0 and 17.2 per stigma in “Jinsenianhua” × “Qinhuaihuadeng” and “Qinhuaihuadeng” × “Jinsenianhua”, respectively. At 1 d after artificial pollination, the percentages of normal embryos in the two crosses were 55.0 and 21.9%, respectively; however, at 11 d after pollination, the corresponding percentages were 20.8 and 11.2%. Seed sets of the two crosses were 17.9 and 8.0%, respectively. The results suggested that low pistil receptivity and embryo abortion caused low seed set in “Qinhuaihuadeng” × “Jinsenianhua”, whereas low fecundity of “Jinsenianhua” × “Qinhuaihuadeng” was mainly attributable to embryo abortion