An improved algorithm for computing topological entropy

A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed.     

Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization

The magnetization under the spin-lattice relaxation and the nuclear magnetic resonance radiofrequency (RF) pulses is calculated for a signal RF pulse train and for a sequence of multiple RF pulse-trains. It is assumed that the transverse magnetization is zero when each RF pulse is applied. The result expressions can be grouped into two terms: a decay term, which is proportional to the initial magnetization M0, and a recovery term, which has no M0 dependence but strongly depends on the spin-lattice relaxation and the equilibrium magnetization Meq. In magnetic resonance pulse sequences using magnetization in transient state, the recovery term produces artifacts and can seriously degrade the function of the preparation sequence for slice selection, contrast weighting, phase encoding, etc. This work shows that the detrimental effect can be removed by signal averaging in an eliminative fashion. A novel fast data acquisition method for constructing the spin-lattice relaxation (T1) map is introduced. The method has two features: (i) By using eliminative averaging, the curve to fit the T1 value is a decay exponential function rather than a recovery one as in conventional techniques; therefore, the measurement of Meq is not required and the result is less susceptible to the accuracy of the inversion RF pulse. (ii) The decay exponential curve is sampled by using a sequence of multiple pulse-trains. An image is reconstructed from each train and represents a sample point of the curve. Hence a single imaging sequence can yield multiple sample points needed for fitting the T1 value in contrast to conventional techniques that require repeating the imaging sequence for various delay values but obtain only one sample point from each repetition.     

Color Zone Map in Peripheral Vision at Various Illuminance Levels

We measured the entire region of mesopic and photopic vision to determine the color zone covering the visual field with unique red, yellow, green, and blue hue components. Eight kinds of test stimuli in the natural color system (NCS) color notation system were used. These stimuli were presented at horizontal and vertical meridians, and at meridians inclined at 45° angles. The illuminance level was set at six levels: 0.01 lx-1000 lx. The evaluation method measured chromatic, white, and black components as well as the hue component of the stimuli. Results show that the color zone of the retina extended further into the periphery with increasing illuminance; the response of opponent colors y-b was shown to be greater than that of the opponent colors r-g.     

The dynamical feature of transition of a Hamiltonian system to a dissipative system

The mechanism of generation and annihilation of attractors during transition from a Hamiltonian system to a dissipative system is studied numerically using the dissipative standard map. The transient process related to the formation of attracting basins of periodic attractors is studied by discussing the evolution of the KAM tori of the standard map. The result shows that as damping increases, attractors are mainly generated from elliptic orbits of the Hamiltonian system and annihilated by colliding with unstable periodic orbits originating from the corresponding hyperbolic orbits of the Hamiltonian system. The transient process also exhibits the general feature of bifurcation.     

耦合小世界神经网络的随机共振

噪声广泛存在于生物神经系统中,对系统功能具有重要作用.采用神经元二维映射模型构建一个复杂神经网络,由多个小世界子网络构成,研究了Gaussian白噪声诱导的随机共振现象.研究发现,只有合适的噪声强度才能使神经网络对输入刺激信号的频率响应达到峰值.另外,网络结构对系统随机共振特性有重要影响.在固定的耦合强度下,存在一个最优的局部小世界子网络结构,使得整个系统的频率响应最佳.     

Linearization of vector fields and embedding of diffeomorphisms in flows via Nash–Moser theorem

In the first part of this paper we give suitable spectral properties of the adjoint operators induced by appropriate perturbations of some hyperbolic linear vector fields. These properties are useful to prove general facts based on the Nash–Moser inverse function theorem. In the second part of this work we study circumstances where a global linearization of a vector field X$X$ in a real numerical space is feasible and where some diffeomorphisms which are close to exp(X)$exp\left(X\right)$ can be embedded in a flow.     

Image encryption scheme by using iterative random phase encoding in gyrator transform domains

An image encryption is discussed based on the random phase encoding method in gyrator domains. An iterative structure of image encryption is designed for introducing more random phases to encrypt image. These random phase functions are generated by a two-dimensional chaotic mapping with the help of computer. The random phases are utilized for increasing the security of this encryption algorithm. In the chaotic mapping relation, the initial value and expression can serve as the key of algorithm. The mapping relation is considered secretly for storage and transmission in practical application in comparison to traditional algorithms. The angle parameter of gyrator transform is an additional key. Some numerical simulations have been given to validate the performance of the encryption scheme.     

Continuous symmetry reduction and return maps for high-dimensional flows

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a five-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.     

信号灯和公交车站对T形路口交通流的影响研究

采用非线性映射模型研究T形路口的交通问题,利用点平均流量指标系统地分析了公交车站、信号灯周期、绿信比、车辆左右转弯等因素对路径交通流量的影响.数值模拟结果表明,信号灯和公交车站之间的相互影响容易导致交通流的串现象,不同路径上的流量与信号灯周期、绿信比和公交车站位置之间存在一定的关系. 关键词： 交通流 非线性映射模型 信号控制 串     

One-dimensional photonic crystal design

In this article we present a method to determine the band spectrum, band gaps, and discrete energy levels, of a one-dimensional photonic crystal with localized impurities. For one-dimensional crystals with piecewise constant refractive indices we develop an algorithm to recover the refractive index distribution from the period map. Finally, we derive the relationship between the period map and the scattering matrix containing the information on the localized modes.