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.     

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。     

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.     

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.     

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.     

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 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.     

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.     

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。     

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.     

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.     

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.     

Spacetime Topology from the Tomographic Histories Approach: Part II

As an inverse problem, we recover the topology of the effective spacetime that a system lies in, in an operational way. This means that from a series of experiments we get a set of points corresponding to events. This continues the previous work done by the authors. Here the relativistic case is considered. The existence of upper bound in the speed of transfer of matter and information induces a partial order on the set of events. While the actual partial order is not known in our operational set up, the grouping of events to (unordered) subsets corresponding to possible histories, is given. From this we recover the partial order up to certain ambiguities that are then classified. Finally two different ways to recover the topology are sketched and their interpretation is discussed.     

基于改进水平集方法的翼型拓扑优化

将改进的水平集方法与灵敏度分析方法相结合,发展了一种研究Navier-Stokes方程拓扑优化的新方法。在拓扑优化过程中,引入无需样条参数化的网格重新划分方法,实现水平集函数演化和流场求解的结合。最后,通过对低雷诺数条件下Navier-Stokes翼型优化问题的研究,表明该方法具有良好的全局性,并能有效节约优化问题的计算工作量。     

白光干涉双环传感网络理论与实验研究

构造了一种基于双环形拓扑结构的白光干涉光纤传感网络．可用于智能结构中准分布应变或温度的测量。光纤传感网络基于空分多路复用技术(SDM)．目的是增强带载能力．降低单点传感器的测量成本,并借助丁双端口问询技术．增强传感网络的抗毁坏能力。分析了环形网络结构的低相干多路复用原理．根据空分复用的光程匹配条件．推导了传感器干涉信号的强度特性。实验中对连接9个传感器的双环传感网络特征及其抗损坏特性进行了验证．并对实验结果进行了分析和讨论。     

Reconfiguring the Logical Topology With Performance Guarantees in WDM Networks

To improve the network performance after traffic demand changes , reconfiguring the logical topology is necessary. We present an ILP algorithm to find out the least lightpath changes needed with guaranteed network performance.     

Glafka 2004: Spacetime Topology from the Tomographic Histories Approach I: Non-Relativistic Case

The tomographic histories approach is presented. As an inverse problem, we recover in an operational way the effective topology of the extended configuration space of a system. This means that from a series of experiments we get a set of points corresponding to events. The difference between effective and actual topology is drawn. We deduce the topology of the extended configuration space of a non-relativistic system, using certain concepts from the consistent histories approach to Quantum Mechanics, such as the notion of a record. A few remarks about the case of a relativistic system, preparing the ground for a forthcoming paper sequel to this, are made in the end.