Symbolic transfer entropy rate is equal to transfer entropy rate for bivariate finite-alphabet stationary ergodic Markov processes

Transfer entropy is a measure of the magnitude and the direction of information flow between jointly distributed stochastic processes. In recent years, its permutation analogues are considered in the literature to estimate the transfer entropy by counting the number of occurrences of orderings of values, not the values themselves. It has been suggested that the method of permutation is easy to implement, computationally low cost and robust to noise when applying to real world time series data. In this paper, we initiate a theoretical treatment of the corresponding rates. In particular, we consider the transfer entropy rate and its permutation analogue, the symbolic transfer entropy rate, and show that they are equal for any bivariate finite-alphabet stationary ergodic Markov process. This result is an illustration of the duality method introduced in [T. Haruna, K. Nakajima, Physica D 240, 1370 (2011)]. We also discuss the relationship among the transfer entropy rate, the time-delayed mutual information rate and their permutation analogues.     

Complex dynamics of cellular automata rule 119

In this paper, the dynamical behaviors of cellular automata rule 119 are studied from the viewpoint of symbolic dynamics in the bi-infinite symbolic sequence space Σ₂. It is shown that there exists one Bernoulli-measure global attractor of rule 119, which is also the nonwandering set of the rule. Moreover, it is demonstrated that rule 119 is topologically mixing on the global attractor and possesses the positive topological entropy. Therefore, rule 119 is chaotic in the sense of both Li-Yorke and Devaney on the global attractor. It is interesting that rule 119, a member of Wolfram’s class II which was said to be simple as periodic before, actually possesses a chaotic global attractor in Σ₂. Finally, it is noted that the method presented in this work is also applicable to studying the dynamics of other rules, especially the 112 Bernoulli-shift rules therein.     

Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution

By appealing to a long list of different nonlinear maps we review the characterization of time series arising from chaotic maps. The main tool for this characterization is the permutation Bandt-Pompe probability distribution function. We focus attention on both local and global characteristics of the components of this probability distribution function. We show that forbidden ordinal patterns (local quantifiers) exhibit an exponential growth for pattern-length range 3 ≤ D ≤ 8, in the case of finite time series data. Indeed, there is a minimum D _min-value such that forbidden patterns cannot appear for D < D _min. The system’s localization in an entropy-complexity plane (global quantifier) displays typical specific features associated with its dynamics’ nature. We conclude that a more “robust” distinction between deterministic and stochastic dynamics is achieved via the present time series’ treatment based on the global characteristics of the permutation Bandt-Pompe probability distribution function.     

Automatic coarse-alignment for TEM tilt series of rod-shaped specimens collected with a full angular range

An automatic coarse-alignment method for a tilt series of rod-shaped specimen collected with a full angular range (from α = ?90° to +90°, α is the tilt angle of the specimen) is presented; this method is based on a cross-correlation method and uses the outline of the specimen shape. Both the rotational angle of the tilt axis and translational value of each image can be detected in the images without the use of markers. This method is performed on the basis of the assumption that the images taken at α = ?90° and α =  + 90° are symmetric about the tilt axis. In this study, a carbon rod on which gold particles have been deposited is used as a test specimen for the demonstration. This method can be used as an automatic coarse-alignment method prior to the application of a highly accurate alignment method because the alignment procedure can be performed automatically except for the initial setup of some parameters.     

符号动力学在心率变异性分析中的参数选择

时间序列的符号动力学信息熵H_k因其计算简单快速,对数据量要求小,而被应用于心率变异性(heart rate variability, HRV)分析,然而符号化的参数选择至今却并未形成统一标准.HRV作为典型的生理信号,存在着极大的个体间差异和非平稳性,要获得稳健的一致性分析,在符号化过程中必须考虑符号化参数α与序列本身均值、标准差的综合影响.文中,首先以仿真噪声序列为对象,考察了3个参数对于H_k的影响及三者相互之间的关联性,研究表明当满足特定关系时,H_k的曲线簇收敛于反映序列动力特性的H_k-up;随后在对15例心跳间隔序列的分析中,验证了H_k-up在消除个体间差异及减弱非平稳干扰影响两方面都优于α取固定值时的研究结果. 关键词： 符号动力学 熵 心率变异性     

Short-time vibrational dynamics of metaphosphate glasses

In this paper we present the picosecond vibrational dynamics of a series of binary metaphosphate glasses, namely Na₂O–P₂O₅, MO–P₂O₅ (M=Ba, Sr, Ca, Mg) and Al₂O₃–3P₂O₅ by means of Raman spectroscopy. We studied the vibrational dephasing and vibrational frequency modulation by calculating time correlation functions of vibrational relaxation by fits in the frequency domain. The fitting method used enables one to model the real line profiles intermediate between Lorentzian and Gaussian by an analytical function, which has an analytical counterpart in the time domain. The symmetric stretching modes ν_s(PO₂^?) and ν_s(P–O–P) of the PO₂^? entity of PØ₂O₂^? units and of P–O–P bridges in metaphosphate arrangements have been investigated by Raman spectroscopy and we used them as probes of the dynamics of these glasses. The vibrational time correlation functions of both modes studied are rather adequately interpreted within the assumption of exponential modulation function in the context of Kubo–Rothschield theory and indicate that the system experiences an intermediate dynamical regime that gets only slower with an increase in the ionic radius of the cation-modifier. We found that the vibrational correlation functions of all glasses studied comply with the Rothschild approach assuming that the environmental modulation is described by a stretched exponential decay. The evolution of the dispersion parameter α with increasing ionic radius of the cation indicates the deviation from the model simple liquid indicating the reduction of the coherence decay in the perturbation potential as a result of local short lived aggregates. The results are discussed in the framework of the current phenomenological status of the field.     

An extended read model for grain boundaries in GaAs

The space charging properties of grain boundaries in GaAs are discussed using an extended Read dislocation model. Model calculations for medium to high angle grain boundaries show: (1) the core-site occupational probability for a dislocation at the grain boundary is at least an order of magnitude lower than would be expected on the basis of simple Read theory; (2) due to the strong core-core interaction of the dislocations, the depletion width W decreases with an increase in tilt angle θ: and (3) W is approximately independent of θ in highly doped (N_D ? 10₁₇/cm³) material. Comparisons between model predictions and experimentally determined depletion widths of grain boundaries in GaAs are presented.     

(II) Infrared and X-ray photoelectron spectroscopy of some transition metal dithiocarbamates and xanthates

Measurements are presented for the binding energy variations of (a) (Ni, Cu) 2p_{$\text{3}\text{2}$}, S 2p and N 1s core levels in a series of Ni and Cu disubstituted dithiocarbamates and (b) (Ni, Cu) 2p_{$\text{3}\text{2}$}, and S 2p core levels in a series of Ni xanthates. These shifts, which are observed to be negative and quite large for the S 2p levels, are then correlated with the infrared absorption frequency variations for the associated intramolecular stretching vibrations of the same series. The results are interpreted in terms of a model based on atomic charges and their potential effects on both variations. The functional relationships between the binding energy and infrared frequency variations are shown to be in good agreement with the experimental results.     

Polar smectic subphases: Phase diagrams, structures and X-ray scattering

We analyze a discrete phenomenological model accounting for phase transitions and structures of polar Smectic-C* liquid-crystalline phases. The model predicts a sequence of phases observed in experiment: antiferroelectric SmC _A ^* –ferrielectric SmC _FI1 ^* –antiferroelectric SmC _FI2 ^* (three-and four-layer periodic, respectively)–incommensurate SmC _α ^* –SmA. We find that, in the three-layer SmC _FI1 ^* structure, both the phase and the module of the order parameter (tilt angle) differ in smectic layers. This modulation of the tilt angle (and therefore of the layer spacing d) must lead to X-ray diffraction at the wave vectors Q _s =2πs/d(s=n±1/3) even for the nonresonant scattering.     

Forbidden ordinal patterns in higher dimensional dynamics

Forbidden ordinal patterns are ordinal patterns (or rank blocks) that cannot appear in the orbits generated by a map taking values on a linearly ordered space, in which case we say that the map has forbidden patterns. Once a map has a forbidden pattern of a given length L₀, it has forbidden patterns of any length L≥L₀ and their number grows superexponentially with L. Using recent results on topological permutation entropy, in this paper we study the existence and some basic properties of forbidden ordinal patterns for self-maps on n-dimensional intervals. Our most applicable conclusion is that expansive interval maps with finite topological entropy have necessarily forbidden patterns, although we conjecture that this is also the case under more general conditions. The theoretical results are nicely illustrated for n=2 both using the naive counting estimator for forbidden patterns and Chao’s estimator for the number of classes in a population. The robustness of forbidden ordinal patterns against observational white noise is also illustrated.     

General coding method of address code for optical code division multiple access passive optical network – (F,K, λa, λc) optical orthogonal code

Since the importance of address code of OCDMA passive optical network (PON) diversity and lacking of general coding method until now, in this paper, we present a general coding method of (F, K, λ_a, λ_c) optical orthogonal code (OOC) based on block design. Through the discussion of block, difference sets and cyclic permutation of perfect distance (CPPD), cyclic permutation of imperfect distance (CPID) is defined and applied to realize the coding method. Simulations results demonstrated that it is possible to construct (F, K, λ_a, λ_c) OOCs with arbitrary code length, code weight, auto-correlation constraints and co-correlation constraints based on the same general coding method.     

Electron-phonon coupling through the orthorhombic to rhombohedral phase transition in La2/3(Ca1−xSrx)1/3MnO3 manganites

We present a systematic study of the Raman modes of a ferromagnetic series of manganites, La_2/3(Ca_1?xSr_x)_1/3MnO₃ with 0?x?1, that presents two different regimes for the variation of the ferromagnetic order temperature, T_C, with Sr doping. This change occurs for x～0.5 when the temperature of the orthorhombic, Pbnm, to rhombohedral, R-3c, structural phase transition, T_t, coincides with T_C. We have analyzed the evolution of the frequencies and widths of the observed Raman modes as a function of Sr doping and temperature. At room temperature, features of the Pbnm structure are detected for compounds up to x=0.6, over the orthorhombic phase limit x=0.45 at 300 K. Octahedra bending modes behave as expected with doping while the tilt mode, which is related to Mn–O–Mn angles and therefore to electronic conduction mechanisms, presents different behaviors in both structures. The tilt frequency is much less sensitive to Mn–O–Mn angle in R-3c than in Pbnm structure indicating a reduction of electron-phonon coupling. Its width presents an anomalous behavior both as a function of doping and temperature with unexpectedly large width in the rhombohedral phase.     

Langmuir-Blodgett膜摩擦分子动力学模拟和机理研究

采用分子动力学方法,模拟了在两块石英基板上由脂肪酸(C₁₅H₃₁COOH)组成的单层Langmuir-Blodgett (LB)膜间的摩擦特性,探究了超薄膜在滑动过程中的摩擦和结构机理.得出对于单层LB膜在滑动过程中,在速度小于60m/s时,随着速度的增大,其剪切压增大;在速度大于60 m/s时,剪切压随速度的增加而减小.其链的倾斜角随着滑动速度的增加而减小.单层膜内的分子之间以氢键方式形成了较大的分子簇,由此导致了剪切压呈现较长的周期性,但在单层膜之间无氢键形 关键词： 分子动力学模拟 朗缪尔布洛杰特膜 纳米摩擦 氢键     

Excited states of two-dimensional hydrogen atom in tilted magnetic field: Quantum chaos

The aim of the current work is the research of the influence of a tilted magnetic field direction on the spectrum and the energy level spacing distribution of a two-dimensional (2D) hydrogen atom and of an exciton in GaAs/Al_0.33Ga_0.67As quantum well. It was discovered that the quantum chaos (QC) is initiated with an increasing angle α between the magnetic field direction and the normal to the atomic plane. It is characterized by the repulsion of levels leading to the eliminating of the shell structure and by changing the spectrum statistical properties. The statement about the initiation of chaos and its dominance over regular motion with increasing angle α is confirmed by the results of our calculations of the classical dynamics presented in this paper. The evolution of the spatial distribution of the square of the absolute value of the wave function at an increasing angle α was observed. The differences of calculated dependencies of energies for various excited states on the tilt angle at a wide range of the magnetic field strength were described.     

The dynamics of traded value revisited

We conclude from an analysis of high resolution NYSE data that the distribution of the traded value f_i (or volume) has a finite variance σ_i for the very large majority of stocks i, and the distribution itself is non-universal across stocks. The Hurst exponent of the same time series displays a crossover from weakly to strongly correlated behavior around the time scale of 1 day. The persistence in the strongly correlated regime increases with the average trading activity 〈f_i〉 as , which is another sign of non-universal behavior. The existence of such liquidity dependent correlations is consistent with the empirical observation that σ_i∝〈f_i〉^α, where α is a non-trivial, time scale dependent exponent.     

Structural phase transition and octahedral tilting in the calcium titanate perovskite CaTiO3

Crystal structure of the calcium titanate perovskite CaTiO₃ was refined by the Rietveld analysis of neutron diffraction data collected over the temperature range of 296 to 1720 K. The orthorhombic Pbnm-tetragonal I4/mcm phase transformation reversibly occurred at 1512 ± 13 K and the tetragonal I4/mcm-cubic Pm3?m transition was reversibly observed at 1635 ± 2 K. The structural phase transitions are characterized by the tilt of the TiO₆ octahedron. The tilt systems of the Pbnm, I4/mcm, and Pm3?m CaTiO₃ are ?_x^??_y^??_z⁺ (?_x^? = ?_y^?), ?_x⁰?_y⁰?_z^?, and ?_x⁰?_y⁰?_z⁰, respectively. Here the ?_x^?, ?_z⁺, and ?_x⁰ stand for the out-of-phase tilt angle of TiO₆ octahedron along x axis, the in-phase octahedral tilt angle along z axis, and no octahedral tilting along x axis, respectively. All the tilt angles, ?_x^?, ?_z⁺, and ?_z^? decreased with increasing temperature where the critical exponents were about 0.25. The ?_x^? and ?_y^? of the orthorhombic structure decreased discontinuously to ?_z^? of the tetragonal structure or 0° through the Pbnm-I4/mcm transition. The tilt angle, the unit-cell parameters and unit-cell volume discontinuously changed at the Pbnm-I4/mcm transition temperature, indicating the first-order nature. The increase of the cell volume in the Pbnm-I4/mcm transition was 0.088 vol.%. In contrast, the unit-cell volume continuously increased and the tilt angle ?_z^? continuously decreased with increasing temperature and became 0° at the I4/mcm-Pm3?m transition temperature, indicating a continuous nature of the transformation. The Pbnm-I4/mcm and I4/mcm-Pm3?m phase transitions are induced by the tilting of TiO₆ octahedra, indicating the displacive nature of the transitions. The larger thermal motion of O2 atom in I4/mcm CaTiO₃ indicates the larger positional disorder of O2 atom, which is consistent with the tilt system ?_x⁰?_y⁰?_z^?.     

Microscopic calculation of friction in heavy ion reaction using linear response theory

We present a realistic calculation of the frictional coefficients for²⁸Si+²⁰Ne system using the two-center shell model on the basis of the linear response theory. Adopting the center separationR and the deformationδ as collective variables we study the dependence of frictional coefficients γ _RR , γ _Rδ and γ_δδ on those variables, for various values of the neck parameter?, the temperatureT and the smearing widthΓ. The direct application of the linear response theory to the two-center potential gives non-vanishing friction for the simple translational motion of the two fragments even when they are far apart. A method to avoid this energy dissipation is proposed and is used in the calculation. Results show that the form factor of the frictional force is surface-peaked and the peak becomes lower as the prolate deformation or neck formation increases. Temperature dependence is mild, but is not negligible. We compare our γ _RR and γ_δδ with other models.     

Symbolic transfer entropy

We propose to estimate transfer entropy using a technique of symbolization. We demonstrate numerically that symbolic transfer entropy is a robust and computationally fast method to quantify the dominating direction of information flow between time series from structurally identical and nonidentical coupled systems. Analyzing multiday, multichannel electroencephalographic recordings from 15 epilepsy patients our approach allowed us to reliably identify the hemisphere containing the epileptic focus without observing actual seizure activity.     

等概率符号化样本熵应用于脑电分析

样本熵(或近似熵)以信息增长率刻画时间序列的复杂性,能应用于短时序列,因而在生理信号分析中被广泛采用.然而,一方面由于传统样本熵采用与标准差线性相关的容限,使得熵值易受非平稳突变干扰的影响,另一方面传统样本熵还受序列概率分布的影响,从而导致其并非单纯反映序列的信息增长率.针对上述两个问题,将符号动力学与样本熵结合,提出等概率符号化样本熵方法,并对其物理意义、数学推导及参数选取都做了详细阐述.通过对噪声数据的仿真计算,验证了该方法的正确性及其区分不同强度时间相关的有效性.此方法应用于脑电信号分析的结果表明,在不对信号做人工伪迹去除的前提下,只需要1.25 s的脑电信号即可有效地区分出注意力集中和注意力发散两种状态.这进一步证明了该方法可很好地抵御非平稳突变干扰,能快速获得短时序列的潜在动力学特性,对脑电生物反馈技术具有很大的应用价值.