The Topology of Branching Universes

No Heading The purpose of this paper is to survey the possible topologies of branching spacetimes and, in particular, to refute the popular notion in the literature that a branching spacetime requires a non-Hausdorff topology.     

Quantum Motion on 2D Surface of Nonspherical Topology

An excess term exists when using hermitian form of Cartesian momentum p _i (i = 1, 2, 3) in usual kinetic energy 1/(2) p _i ² for a particle moving on the 2D surface, and the correct kinetic energy turns to be 1/(2) 1/f_ip_i f_i p_i where the f _i are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper, the explicit form of the dummy functions f _i is given for some surfaces of nonspherical topology, such as toroidal surface, paraboloid of revolution, the hyperboloid of revolution of two sheets, and the hyperboloid of revolution of one sheets.     

Topology of Knotted Optical Vortices

Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the Duan＇s topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological inner structure of the optical vortices are obtained, and the linking of the knotted optical vortices is also given.     

激波冲击火焰的流动拓扑研究

为深入研究激波冲击火焰现象的内在机制,采用二维带化学反应的Navier-Stokes方程对现象进行数值研究,通过对速度梯度张量特征方程的分析证明Okubo-Weiss函数适用于可压缩流动,并重点分析火焰区的流动拓扑特性.结果表明,波后火焰区内Okubo-Weiss函数积分量基本守恒,但在火焰区内部和表面具有截然不同的流动状态,且火焰发展基本不受流场可压缩性的影响;波后火焰区的流动拓扑分类主要以焦点和鞍点为主,意味着流场中变形占主导.     

Topology of Knotted Optical Vortices

Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the Duan's topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological inner structure of the optical vortices are obtained, and the linking of the knotted optical vortices is also given.     

大规模光电混合神经网络中的可编程拓扑重构

提出了一种在大规模光电混合神经网络系统实现可编程拓扑重构的有效方法，文中介绍了这种方法的原理，运用技术以及采用这种方法在已有的ＮＰ１０２４光学／数字神经网络处理器中运行单层反馈型和多层前馈型等不同网络拓扑结构的实验结果。     

Estimating Topology of Discrete Dynamical Networks

In this paper, by applying Lasalle's invariance principle and some results about the trace of a matrix, we propose a method for estimating the topological structure of a discrete dynamical network based on the dynamical evolution of the network. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown orpartially known. Finally, two examples, including a Hénon map and a central network, are illustrated to verify the theoretical results.     

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper,by the help of evolutionary algorithm and using Hindmarsh–Rose(HR)neuron model,we investigate the efect of topology structures on synchronization transition between diferent states in coupled neuron cells system.First,we build diferent coupling structure with N cells,and found the efect of synchronized transition contact not only closely with the topology of the system,but also with whether there exist the ring structures in the system.In particular,both the size and the number of rings have greater efects on such transition behavior.Secondly,we introduce synchronization error to qualitative analyze the efect of the topology structure.Furthermore,by fitting the simulation results,we find that with the increment of the neurons number,there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems.Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system.Biological system may gradually acquire such efcient topology structures through the long-term evolution,thus the systems’information process may be optimized by this scheme.     

Topology of the Universe: Background and recent observational approaches

Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lemaître (FL) universe requires knowing both its curvature and its topology. A flat or hyperbolic (‘open’) FL universe is not necessarily infinite in volume. Multiply connected flat and hyperbolic models are, in general, as consistent with present observations on scales of 1–20 h^?1 Gpc as are the corresponding simply connected flat and hyperbolic models. The methods of detecting multiply connected models (MCM’s) are presently in their pioneering phase of development and the optimal observationally realistic strategy is probably yet to be calculated. Constraints against MCM’s on ～1–4 h^?1 Gpc scales have been claimed, but relate more to inconsistent assumptions on perturbation statistics rather than just to topology. Candidate 3-manifolds based on hypothesised multiply imaged objects are being offered for observational refutation. The theoretical and observational sides of this rapidly developing subject have yet to make any serious contact, but the prospects of a significant detection in the coming decade may well propel the two together.     

Symmetry and Topology of the Topological Counterparts in Non-Hermitian Systems

The symmetries and topological properties of the topological counterparts in 1D non-Hermitian systems are investigated. It is found that, after applying the non-unitary similarity transformation, the non-unitary topological counterpart in real space exhibits completely different global symmetries except for the sublattice symmetry and reveals many brand new local symmetries. Due to the abundant symmetries of non-unitary topological counterparts, it is also found that the unique overlapping projections about the unit sphere vector representing the eigenstates appear in the nontrivial regions, and the triviality of the point-gap topology of non-unitary topological counterpart completely eliminate the intrinsic skin effect in non-Hermitian systems. It is also shown that the unitary topological counterpart never arises any changes for the original symmetries and topological structures even in real space. Unitary topological counterparts are further summarized about the two-band Bloch Hamiltonian, which can expand the definition of non-Bloch winding number. Furthermore, it is demonstrated theoretically that the Bloch Hamiltonian would still hold time-reversal symmetry, abnormal particle-hole symmetry, and sublattice symmetry even suffering from the non-unitary transformation. This work provides a new way to understand the roles of symmetry and topology in non-Hermitian systems from the perspective of topological counterparts.     

Estimating Topology of Discrete Dynamical Networks

In this paper, by applying Lasalle＇s invariance principle and some results about the trace of a matrix, we propose a method for estimating the topological structure of a discrete dynamical network based on the dynamical evolution of the network. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown or partially known, Finally, two examples, including a Henon map and a central network, are illustrated to verify the theoretical results.     

基于图像集拓扑中心的群体配准方法

传统的图像配准通常指定一幅参考图像在配准过程中保持不变,将另一幅图像变换到参考图像空间,使得两幅图像在空间上互相匹配,从而可以精确比较两者之间的差异.针对多幅个体差异较大的图像配准问题,如果指定一幅作为参考,将其他图像配准到参考图像空间,则会引入该幅参考图像的个体形状偏差,从而影响最终的对比结果.为此,本文首先介绍了目前针对该问题的主要解决方法,然后提出了基于图像集拓扑中心的群体配准方法——TopologyCenter.为验证所提出的群体配准方法的性能,通过使用国外公开的数据集,详细比较了本文提出的方法与当前两种主要方法的群体配准结果的差异.实验结果表明,本文提出的方法具有更小的群体配准偏差,群体配准结果更好;同时,在对实验结果的评价中,本文还提出了一种简捷的群体偏差度量指标.     

Continuity of Effect Algebra Operations in the Interval Topology

We study the continuity of and of effect algebras in the interval topology, and present several examples of effect algebras with interesting properties.     

Topology identification for a class of complex dynamical networks using output variables

A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stability theory. Here the output of the network and the states of the observer are used to construct the updating law of the topology such that the communication resources from the network to its observer are saved. Some convergent criteria of the adaptive observer are derived in the form of linear inequality matrices. Several numerical examples are shown to demonstrate the effectiveness of the proposed observer.     

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper, by the help of evolutionary algorithm and using Hindmarsh-Rose (HR) neuron model, we investigate the effect of topology structures on synchronization transition between different states in coupled neuron cells system. First, we build different coupling structure with N cells, and found the effect of synchronized transition contact not only closely with the topology of the system, but also with whether there exist the ring structures in the system. In particular, both the size and the number of rings have greater effects on such transition behavior. Secondly, we introduce synchronization error to qualitative analyze the effect of the topology structure. Furthermore, by fitting the simulation results, we find that with the increment of the neurons number, there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems. Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system. Biological system may gradually acquire such efficient topology structures through the long-term evolution, thus the systems' information process may be optimized by this scheme.     

Quadratic Lagrangians and Topology in Gauge Theory Gravity

We consider topological contributions to the action integral in a gauge theory formulation of gravity. Two topological invariants are found and are shown to arise from the scalar and pseudoscalar parts of a single integral. Neither of these action integrals contribute to the classical field equations. An identity is found for the invariants that is valid for non-symmetric Riemann tensors, generalizing the usual GR expression for the topological invariants. The link with Yang–Mills instantons in Euclidean gravity is also explored. Ten independent quadratic terms are constructed from the Riemann tensor, and the topological invariants reduce these to eight possible independent terms for a quadratic Lagrangian. The resulting field equations for the parity non-violating terms are presented. Our derivations of these results are considerably simpler than those found in the literature.     

无线认知网络中拓扑控制方法研究

作为下一代通信网络,无线认知网络已成为当前的研究热点。由于节点的移动性,无线网络拓扑结构动态变化,拓扑控制一直是无线网络的难点问题。通过借鉴移动自组织网络(MANETS)中的拓扑控制方法,提出了无线认知网络中基于博弈论和认知功能相结合的拓扑控制方法。无线认知节点能够通过主动决策调节自身节点位置,在保证网络连通性的基础上实现网络覆盖面积最大。仿真实验结果验证了方法的有效性和收敛性。     

Topology and Phase Transitions: The Case of the Short Range Spherical Model

We characterize the topology of the phase space of the Berlin-Kac spherical model in the context of the so called Topological Hypothesis, for spins lying in hypercubic lattices of dimension d. For zero external field we are able to characterize the topology exactly, up to homology. We find that, even though there is a continuum of changes in the topology of the corresponding manifolds, for d ≥ 3 there are abrupt discontinuities in some topological functions that could be good candidates to associate with the phase transitions that occur at the thermodynamic level. We show however that these changes do not coincide with the phase transitions and conversely, that no topological discontinuity can be associated to the points where the phase transitions take place. At variance with what happens in the Mean Field version of this same model, we show that these abrupt topological changes are accessible thermodynamically. We conclude that, even in short range systems, the topological mechanism does not seem to be responsible for the triggering of a phase transition. We also analyze the case of spins connected to a macroscopic number of (but not all) neighbors, and find that, similar to the results found for the fully connected version, in this case the topological hypothesis seems to hold: the phase transition coincides with an accumulation point of the topological changes present in configuration space. The question of the ensemble equivalence in the short range spherical model is also considered.     

Phase Transitions and Topology Changes in Configuration Space

The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant (the Euler characteristic) of certain submanifolds in the configuration space of two physical models. The models are the mean-field XY model and the one-dimensional XY model with nearest-neighbor interactions. The former model undergoes a second-order phase transition at a finite critical temperature while the latter has no phase transitions. The computation of this topologic invariant is performed within the framework of Morse theory. In both models topology changes in configuration space are present as the potential energy is varied; however, in the mean-field model there is a particularly strong topology change, corresponding to a big jump in the Euler characteristic, connected with the phase transition, which is absent in the one-dimensional model with no phase transition. The comparison between the two models has two major consequences: (i) it lends new and strong support to a recently proposed topological approach to the study of phase transitions; (ii) it allows us to conjecture which particular topology changes could entail a phase transition in general. We also discuss a simplified illustrative model of the topology changes connected to phase transitions using of two-dimensional surfaces, and a possible direct connection between topological invariants and thermodynamic quantities.