Abstract:
The eigenvalues of the normalized Laplacian matrix of a network plays an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and their applications of normalized Laplacian matrices of a family of fractal trees and dendrimers modeled by Cayley trees, both of which are built in an iterative way. For the fractal trees, we apply the spectral decimation approach to determine analytically all the eigenvalues and their corresponding multiplicities, with the eigenvalues provided by a recursive relation governing the eigenvalues of networks at two successive generations. For Cayley trees, we show that all their eigenvalues can be obtained by computing the roots of several small-degree polynomials defined recursively. By using the relation between normalized Laplacian spectra and eigentime identity, we derive the explicit solution to the eigentime identity for random walks on the two treelike networks, the leading scalings of which follow quite different behaviors. In addition, we corroborate the obtained eigenvalues and their degeneracies through the link between them and the number of spanning trees.

Abstract:
We provide an explicit formula for the global mean first-passage time (GMFPT) for random walks in a general graph with a perfect trap fixed at an arbitrary node, where GMFPT is the average of mean first-passage time to the trap over all starting nodes in the whole graph. The formula is expressed in terms of eigenvalues and eigenvectors of Laplacian matrix for the graph. We then use the formula to deduce a tight lower bound for the GMFPT in terms of only the numbers of nodes and edges, as well as the degree of the trap, which can be achieved in both complete graphs and star graphs. We show that for a large sparse graph the leading scaling for this lower bound is proportional to the system size and the reciprocal of the degree for the trap node. Particularly, we demonstrate that for a scale-free graph of size $N$ with a degree distribution $P(d)\sim d^{-\gamma}$ characterized by $\gamma$, when the trap is placed on a most connected node, the dominating scaling of the lower bound becomes $N^{1-1/\gamma}$, which can be reached in some scale-free graphs. Finally, we prove that the leading behavior of upper bounds for GMFPT on any graph is at most $N^{3}$ that can be reached in the bar-bell graphs. This work provides a comprehensive understanding of previous results about trapping in various special graphs with a trap located at a specific location.

Abstract:
AIM: To explore the anatomical relationships between bronchial artery and tracheal bifurcation using computed tomography angiography (CTA). METHODS: One hundred consecutive patients (84 men, 16 women; aged 46-85 years) who underwent CTA using multi-detector row CT (MDCT) were investigated retrospectively. The distance between sites of bronchial artery ostia and tracheal bifurcation, and dividing directions were explored. The directions of division from the descending aorta were described as on a clock face. RESULTS: We identified ostia of 198 bronchial arteries: 95 right bronchial arteries, 67 left bronchial arteries, 36 common trunk arteries. Of these, 172 (87%) divided from the descending aorta, 25 (13%) from the aortic arch, and 1 (0.5%) from the left subclavian artery. The right, left, and common trunk bronchial arteries divided at -1 to 2 cm from tracheal bifurcation with frequencies of 77% (73/95), 82% (54/66), and 70% (25/36), respectively. The dividing direction of right bronchial arteries from the descending aorta was 9 to 10 o’clock with a frequency of 81% (64/79); that of left and common tract bronchial arteries was 11 to 1 o’clock with frequencies of 70% (43/62) and 77% (24/31), respectively. CONCLUSION: CTA using MDCT provides details of the relation between bronchial artery ostia and tracheal bifurcation.

Abstract:
In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size $N$ with a degree distribution $P(d)\sim d^{-\gamma}$, the scaling of the lower bound is $N^{1-1/\gamma}$. Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.

Abstract:
The electrochemical performance of six imidazolium cation-based ionic liquids (ILs) containing 0.3？mol L？1 Mg(CF3SO3)2 as the electrolytes for magnesium deposition-dissolution was examined by cyclic voltammogramms and constant current discharge-charge techniques. Scanning electron microscopy and energy dispersive X-ray spectroscopy measurements were conducted to characterize the morphologies and components of the deposits. The cathodic satiability of imidazolium cations can be improved by increasing the length of alkyls at the 1-position and introducing methyl group at the 2-position of the imidazolium cations. A reversible magnesium deposition-dissolution can be achieved at room temperature. After adding appreciate amount of tetrahydrofuran (THF) organic solvent, the conductivity and the peak currents for Mg deposition and dissolution can be significantly improved. The potential polarization of deposition-dissolution process is decreased using Mg powder electrode. 1. Introduction Increasing depletion of fossil resources, serious industrial pollution, and ecological destruction have cried for low-cost and high energy density rechargeable batteries for electric vehicles, load leveling, and storage of energy from renewable sources [1]. Due to higher theoretical capacity (2205？mAh/g), higher negative potential (about ？2？V versus standard hydrogen electrode in aprotic solutions), low cost, safe to handle and environmentally friendly nature, metallic magnesium is an attractive candidate for the active material of high energy density batteries [2–4]. But in many nonaqueous solutions, a reversible process of electrochemical deposition and dissolution of magnesium is hard to achieve because of the formation of compact passive film [5]. It is known that electrochemical Mg deposition is impossible from solutions containing simple ionic Mg salts (such as MgCl2, Mg(ClO4)2, etc.) in commonly used aprotic solvents (such as alkyl carbonates, esters, and acetonitrile) [6, 7]. However, magnesium can be reversibly deposited electrochemically in the systems without the passivating phenomena, such as ethereal solutions of Grignard reagents (RMgX, R = alkyl, aryl groups; X = halide: Cl, Br) [7–10], amidomagnesium halides [11, 12], Mg(BR2R′2)2 (R = alkyl and R′ = aryl group) [2, 11], Mg(AX4？n Rn′R′n′′)2 (A = Al, B; X = Cl, Br; R, R′ = alkyl or aryl groups, and n′ + n′′ = n) [13, 14], and PhMgCl-AlCl3 [15]. However, those electrolyte systems still suffer from the problems of safety and reliability due to the flammability and high vapor pressure of the ethereal solvents. As we

Abstract:
In this research, researchers assessed the gossypol induced toxicity on Xinjiang Fine-Wool sheep Leydig cell to get a better understand of the reproduction toxicity of gossypol on the male ruminant. The Leydig cells with high purity were separated successfully from a testicle of 3 months old Fine-Wool sheep through a method of Percoll Density Gradient Centrifugation. Cytotoxicity assays indicated mitochondrial is sensitive to gossypol induced toxicity. Hoechst staining and DNA-FCM with PI staining revealed gossypol mainly causes cell apoptosis of the Leydig cell. Cell cycle analysis by FCM indicated cell cycle arrest on G0/G1 phase. Leydig cell is the main site of testosterone biosynthesis and testosterone is the critical steroid hormone which determines the initiation and maintenance of spermatogenesis as well as expression of the male phenotype. Thus, cytotoxicity effects of gossypol on the Leydig cell revealed by this research indicated that the reduction of spermatogenesis induced by gossypol in male ruminant at least partially associated with the cytotoxicity effects of gossypol on the Leydig cell.