Evolutionary game on a stochastic growth network

In some real complex systems the structures are difficult to map or changing over time. To explore the evolution of strategies on these complex systems, it is not realistic enough to specify their structures or topological properties in advance. In this paper, we address the evolutionary game on a stochastic growth network adopting the prisoner’s dilemma game. We introduce a growing rate q$q$ to control the ratio of network growth to strategy evolution. A large q$q$ denotes that the network grows faster than strategy evolution. Simulation results show that a fast growing rate is helpful to promote the average payoffs of both cooperators and defectors. Moreover, this parameter also significantly influences the cooperation frequency on the resulting networks. The coexisting mechanisms in this paper may provide a beneficial insight for understanding the emergence of complex topological structures and game behaviors in numerous real systems.     

The Branch Processes of Chern-Simons (CS) <Emphasis Type="Italic">p</Emphasis>-Branes

In this paper, by making use of Duan’s topological current theory, the branch process of Chern-Simons (CS) p-branes is discussed in detail. Chern-Simons (CS) p-branes are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points and higher degenerated points systematically of the vector order parameter field . Furthermore, it is also shown that CS p-branes are found splitting or merging at the degenerate point of field function but the total topological charges of the CS p-branes are still unchanged.     

Topological textures and their bifurcation processes in 2D ferromagnetic thin films

In this paper, by the use of the topological current theory, the topological structures and the dynamic processes in thin-film ferromagnetic systems are investigated directly from the viewpoint of topology. It is found that the topological charge of a thin-film ferromagnetic system can be changed by annihilation or creation processes of opposite polarized vortex–antivortex pairs taking place at space–time singularities of the normalized magnetization vector field of the system, the variation of the topological charge is integer and can further be expressed in terms of the Hopf indices and Brouwer degrees of the magnetization vector field around the singularities. Moreover, the change of the topological charge of the system is crucial to vortex core reversal processes in ferromagnetic thin films. With the help of the topological current theory and implicit function theorem, the processes of vortex merging, splitting as well as vortex core reversal are discussed in detail.     

Asymmetric d-wave superconducting topological insulator in proximity with a magnetic order

In the framework of the Dirac–Bogoliubov–de Gennes formalism, we investigate the transport properties in the surface of a 3-dimensional topological insulator-based hybrid structure, where the ferromagnetic and superconducting orders are simultaneously induced to the surface states via the proximity effect. The superconductor gap is taken to be spin-singlet d-wave symmetry. The asymmetric role of this gap respect to the electron–hole exchange, in one hand, affects the topological insulator superconducting binding excitations and, on the other hand, gives rise to forming distinct Majorana bound states at the ferromagnet/superconductor interface. We propose a topological insulator N/F/FS junction and proceed to clarify the role of d-wave asymmetry pairing in the resulting subgap and overgap tunneling conductance. The perpendicular component of magnetizations in F and FS regions can be at the parallel and antiparallel configurations leading to capture the experimentally important magnetoresistance (MR) of junction. It is found that the zero-bias conductance is strongly sensitive to the magnitude of magnetization in FS region $m_{zfs}$ and orbital rotated angle α of superconductor gap. The negative MR only occurs in zero orbital rotated angle. This result can pave the way to distinguish the unconventional superconducting state in the relating topological insulator hybrid structures.     

Tuning spin-filtering,rectifying, and negative differential resistance by hydrogenation on topological edge defects of zigzag silicene nanoribbons

By first-principles calculations, we propose three heterojunction nanodevices based on zigzag silicene nanoribbons with different edge-hydrogenated topological line defects. The devices all present excellent spin-filtering properties with 100% spin polarization as well as remarkable rectifying effect (with rectification ratio around 10²) and negative differential resistance behaviors. Our findings shed new light on the design of silicon-based nanodevices with intriguing spintronic applications.     

Holographic correspondence in topological superconductors

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.     

混合像元光谱特征影响因子分析

高光谱遥感能够提高地物识别和分类,通过光谱比较和匹配达到分类识别目的。由于传感器空间分辨率以及地面复杂多样性的差异, 混合像元在遥感图像中普遍存在。混合像元的分解问题是定量遥感应用中的一个突出问题, 如何有效地解译混合像元是遥感应用的关键问题之一。研究了面积比始终为1∶1的两种材料形成的混合像元在不同入射天顶角和不同拓扑位置分布时的高光谱反射比曲线的特征与差异,为混合像元分类精度的提高提供科学依据。     

Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

卡氏积图的Laplacian谱半径的上界

对近年来图的Laplacian谱半径上界的研究成果进行了简单梳理.利用2个图的卡氏积图的特征值,讨论了2个循环图的卡氏积图的Laplacian谱半径的上界问题,得到了几个上界,推广了已有文献的结论.