A Framework and Methodology for the Study of Nonlinear,Self-Organizing Family Dynamics

Family systems theories have emerged over the past 30 to 40 years primarily through clinical observations, resulting in diverse and internally inconsistent views of family structures, development, dynamics, and pathology; as well as a separation from more empirically based small group research. The 5-R's model is intended to unify the various family systems theories and render them more empirically testable using concepts and methodologies from non-linear dynamical systems theory. The conversation of one family was analyzed using orbital decomposition as a pilot test of the most basic assumptions of the 5-R's model. An optimal string length of three was found along with evidence of coherent complexity (chaos), with Lyapunov dimensionality equal to 1.7 and Shannon's entropy equal to 8.68. Results are discussed with respect to further empirical validation of the 5-R's model and clinical uses of the model and orbital decomposition methodology in conjoint therapy.     

分数阶对称金融模型复杂度分析及有限时间同步

分析了一类分数阶对称金融非线性系统的复杂度特性,利用有限时间同步理论设计控制器,实现了有限时间同步.根据分数阶系统定义和Adomain分解法对该系统的非线性项进行Adomain分解,结合分解系数定义系统的表达式,将其离散化.基于谱熵复杂度及C0复杂度的基本算法,利用Matlab仿真其复杂度曲线及复杂度图谱.为进一步探究...     

Temporal Dynamics of Brain Activity in Human Memory Processes

We propose a line of study by which Functional Magnetic Resonance Imaging (FMRI) can be used together with nonlinear dynamics concepts as a medium for the study of brain organization. The concentration is on (a) the complex behavior of elementary neural circuits, and how they interact over brief spans of time to produce cognition and memory; and (b) the change in circuit patterns associated with aging. The method of orbital decomposition appears to be ideally suited for these objectives and for determining how they integrate into hierarchical processes. The adapted procedure begins with a 3-D FMRI matrix of metabolic activity. Recurring patterns within a matrix row are identified and matched across rows and across depth slices. These hierarchical patterns are then compared over time for further recurrences. The computational procedure identifies the optimal pattern length over time, the patterns, and the largest Lyapunov for the system of patterns. Computations are assisted by statistical tests for the extent to which the isolated patterns represent the underlying data.     

Orbital decomposition for ill-behaved event sequences: transients and superordinate structures

Time series analysis is often challenged by the presence of transient functions. We examined some types of transients found in time series of events that lend themselves to symbolic dynamics analysis through the method of orbital decomposition, which is based on the principle that chaotic series arise from coupled oscillators. Synthetic data sets were constructed to study the impact of intrusive events, intrusive series, merged functions, non-coupled oscillators, and driving oscillations on the patterns of final statistics obtained from orbital decomposition analysis. Two real-world data sets - a logbook of the ritual behaviors of a patient with obsessive compulsive disorder and a time series of kill dates from an infamous serial murderer - were examined for non-ergodic properties similar to those found in the synthetic data.     

A measure of complexity based on the order patterns

Cumulative Tsallis entropy (CE) is a recently introduced entropy metric to quantify the uncertainty of time series, and its expressions of continuous random variable and discrete random variable are consistents. So far, it has proved to have a good performance in the characteristics of time series. This paper presents a new method to measure the complexity and similarity of systems—cumulative Tsallis entropy based on the dispersion entropy (DCE). It is different from the traditional PE method to simply symbolize the sequence. Instead, the complexity of the system is characterized by focusing on the amplitude information of the time series and considering the influence of past events. We applied DCE to two kinds of simulation data and six global financial time series. The results show that DCE can be used as a diagnostic model to classify global financial data according to regional characteristics, financial background and government policies. In addition, as a classical method of non-stationary time series, we combine the MSE method with DCE to observe the financial market from different time scales and obtain rich intrinsic properties.

     

Entropy conservation in the control of human action

The human motor system is highly adaptable with the ability to adjust its movement patterns under constantly changing task and environmental constraints. In this paper we develop the position that the probabilistic nature of human action can be characterized by entropies at the level of the organism, task, and environment. Systematic changes in motor adaptation are characterized as task-organism and environment-organism tradeoffs in entropy. Such compensatory adaptations lead to a view of goal-directed motor control as the product of an underlying conservation of entropy across the task-organism-environment system. The conservation of entropy supports the view that context dependent adaptations in human goal-directed action are guided fundamentally by natural law and provides a novel means of examining human motor behavior.     

Noise Stimuli Improve the Accuracy of Target Aiming: Possible Involvement of Noise-Enhanced Balance Control

Balance stability is important for human beings. Previous studies have shown that mechanical noise applied to the soles of the feet via vibrating insoles can improve human balance control. In this study we designed an experimental procedure called standard aiming target test to quantitatively evaluate the effect of vibrating insole on specific task of aiming during standing. Ten subjects were asked to aim at a target sheet using laser gun, and the traces of their aimed light spots and the center of pressure (COP) were recorded simultaneously. The same test was repeated twice for each individual with vibrating insole off and on, respectively. To assess dynamic patterns in aiming spot and COP signals, we calculated the entropies in the magnitude increments of both signals at different time scales, i.e., multiscale entropies (MSE).We found that the vibrating insole significantly improved the aiming performance and led to increased entropy in the fluctuations of aiming spot displacement over a range of time scales from 0.001 to 0.05 s. In addition, subjects with larger entropies in the aiming spot fluctuations had better aiming performances. Furthermore, we found that the entropy of the light spot signal was positively correlated with the entropy of the magnitude time series of COP fluctuations. These results suggest that vibrating insoles is beneficial for the complex postural control process during target aiming, possibly via their dynamic influences on the balance regulatory system.     

Effects of the electromagnetic radiation on cognitive performance: a model study

We constructed a two-layer network model to study the effect of electromagnetic radiation on the cognitive functions. The network model was used to simulate two cognitive tasks under the electromagnetic radiation: the visual-guided saccade task and the memory-guided saccade task. The performance of these tasks showed that the electromagnetic radiation could induce faster ramping up activities, higher level of persistent activities and shorter reaction time, but the basic functions of the network such as working memory and motor output did not impair. We found that the electromagnetic radiation have both excitatory effect and inhibitory effect on the neuronal activities of the network model, but the excitatory effect played a major role. Finally, we concluded an excitatory mechanism to explain the effects of the electromagnetic radiation on the cognitive performance.

     

Analysis of fetal cortical complexity from MR images using 3D entropy based information fractal dimension

The fetal cortical complexity is a significant quantification for assessing the development of fetal brain. This study attempts to quantify the development of fetal cortical complexity using the concept of fractal dimension (FD) analysis. Thirty-two fetal MR images were selected from Taipei Veterans General Hospital at 27–37 weeks of gestational age (GA). To investigate the FD of fetal cortical complexity, the entropy based information fractal dimension method (FD _EBI), which is modified from Box-Counting method, was adopted and extended from 2D to 3D. The FD results from overall whole fetal brains show that the increase of cortical complexity is highly correlated with the gestational age of the fetus. Moreover, the FD values of right hemispheric brain are larger than those of left hemispheric brain, show that the development of right hemispheric fetal cortical complexity earlier than the left. These results are in good agreement with normal fetal brain development and suggest that the FD is an effective means for the quantification of fetal cortical complexity.     

Recurrent patterns of daily intimate partner violence and environment

Although predictors of violent relationships have been identified, we are only beginning to understand the day-to-day dynamics of domestic violence. The objective of this study was to identify commonly seen patterns and strings of consecutive days involving verbal or physical abuse, and their preceding and subsequent events. Adult women (n=20) seen in a primary care clinic who experienced violence within the past month were enrolled. Subjects completed a daily telephone assessment of household environment and marital relationship for two months using Interactive Verbal Response (IVR). Results were analyzed using orbital decomposition, an analytic technique based on symbolic dynamics, in which categorical time series data are used to identify recurrent patterns of strings and quantify their complexity. While days without abuse had varied patterns involving arguments, stress levels, daily hassles, husband's alcohol intake, and sense of closeness (27 unique patterns), days involving verbal or physical abuse included a narrower range of patterns (15 patterns for verbal and 16 patterns for physical abuse). Daily patterns appear to cluster in triplets (3 consecutive days) of activity and show nonlinearity with triplets involving verbal abuse and triplets involving physical violence. Triplets involving either verbal or physical abuse were associated with arguments and high stress, but differed in the consistency of association with hassles, alcohol intake, and closeness. Finally, physical and verbal abuse tended to self-propagate. However, days involving verbal abuse did not precede days involving physical violence. In conclusions, while patterns of violence and household environments followed a nonlinear trajectory, only a limited set of patterns were observed. Although violence led to more violence, verbal abuse did not necessarily lead to physical aggression. In fact, verbal abuse and physical violence differed in the consistency of their relationships to hassles, husband's alcohol intake, and closeness.     

A Dynamic Systems Approach to Understanding Reaching Movements with a Prosthetic Arm

A case study was conducted on an experienced upper extremity prosthetic user that required him to perform a reaching and grasping task with both his prosthetic and normal anatomical hand. We used a scanning task (Wallace, Stevenson, Spear, & Weeks, 1994; Button, Bennett, & Davids, 1998) that required the participant to perform a wide range of coordination patterns defined by the relative phasing between the aperture of the fingers (or artificial prehensor) and the arm. Visual templates of the required finger trajectories in the various required phase conditions served as environmental information for the subject to follow. Based on previous work, we hypothesized that the participant would exhibit at least one stable reaching and grasping pattern in both his anatomical and prosthetic arm. In support of this hypothesis, the results showed a negative sloping relationship between the required relative phase and the mean delta relative phase (required relative phase minus the actual relative phase). The smallest delta relative phase occurred at approximately 80° and 115° relative phase for the anatomical and prosthetic arm, respectively during the scanning task. These results confirm our previous work of the presence of only one attractor in reaching and grasping movements using either the anatomical or prosthetic arm.     

大脑血液动力学现象中的能量编码

神经信息的编码与解码是神经科学中的核心研究内容,同时又极具挑战性.传统的编码理论都具有各自的局限性,很难从脑的全局运行方式上给出有效的理论.而由于能量是一个标量具有可叠加性,因此能量编码理论可以从神经元活动的能量特征出发来研究脑功能的全局神经编码问题,取得了一系列的研究成果.本研究以王-张神经元能量计算模型为基础,构建了一个多层次结构的神经网络,通过计算机数值模拟得到了神经网络的能量消耗和血液中葡萄糖供能的变化情况.计算结果显示,和网络的神经活动达到峰值的时间相比,血液中葡萄糖的供能达到峰值的时间延迟了约5.6s.从定量的角度再现了功能性核磁共振(fMRI)中的血液动力学现象:大脑某个脑区的神经元集群被激活以后经过5~7 s的延迟,脑血流的变化才会大幅增加.模拟结果表明先前发表的由王-张神经元模型所揭示的负能量机制在控制大脑的血液动力学现象中起着核心的作用,预测了刺激条件下大脑的能量代谢与血流之间变化的本质是由神经元在发放动作电位过程中正、负能量之间的非平衡、不匹配性质所决定的.本文的研究结果为今后进一步探究血液动力学现象的生理学机制提供了新的研究方向,在神经网络的建模与计算方面给出了一个新的视角和研究方法.      

THE EXTREMITY LAWS OF HYDRO-THERMODYNAMICS

This paper presents the law of maximum rate of energy dissipa-tion in hydrodynamics and also in general continuum dynamicsas an addition to the classical conservation laws expressed inthe equation of continuity and the equations of motion.Thecorollary of the law is B(?)langer-B(?)ss theorem of minimum reser-ved specific energy in applied hydraulics.The mechanical energy dissipated is transformed into heatreserved in the substance.The rate of energy dissipation ata time at a given temperature gives rise to the increase in en-tropy production.Hence the maximum rate of energy dissipationsuggests itself the idea of reformulation of the second law ofthermodynamics that the rate of entropy production in mech-anical motion is always the maximum possible.The proposed extremity law in continuum dynamics has beenderived from the variational principle and the reformulatedsecond law of thermodynamics analyzed microscopically in thepaper.The two laws together form the extremity laws of hydro-thermodynamics.     

Violent societies: an application of orbital decomposition to the problem of human violence

This study uses orbital decomposition to analyze the patterns of how governments lose their monopolies on violence, therefore allowing those societies to descend into violent states from which it is difficult to recover. The nonlinear progression by which the governing body loses its monopoly is based on the work of criminologist Lonnie Athens and applied from the individual to the societal scale. Four different kinds of societies are considered: Those where the governing body is both unwilling and unable to assert its monopoly on violence (former Yugoslavia); where it is unwilling (Peru); where it is unable (South Africa); and a smaller pocket of violent society within a larger, more stable one (Gujarat). In each instance, orbital decomposition turns up insights not apparent in the qualitative data or through linear statistical analysis, both about the nature of the descent into violence and about the progression itself.     

The nonlinear analysis of horizontal oil-water two-phase flow in a small diameter pipe

Horizontal oil-water two-phase flows are frequently encountered in many industrial processes but the understanding of the dynamic behavior underlying the different flow patterns is still a challenge. In this study, we first conduct experiments of horizontal oil-water flows in a small diameter pipe, and collect the fluctuation signals from conductance probes. The multi-scale power-law correlations of the oil-water flow structures are investigated using detrended fluctuation analysis (DFA) based on the magnitude and sign decomposition of the raw signals. The analysis reveals the scaling behavior of different flow structures; five conductive flow patterns are indentified based on the magnitude and sign scaling exponents at different time scales. In addition, the transfer entropy (TE) in a state space is used to study the information transferring characteristics of the oil-water mixture flowing past a conductance cross-correlation velocity probe. The results of TE indicate that the transferring information depends on the flow conditions and can be used to show changes in the flow patterns.     

Nonlinear Dynamics Estimation of EEG Signals Accompanying Self-Paced Goal-Directed Movements

The study was aimed at comparison of several nonlinear characteristics (NC) computed in time for one and the same EEG record accompanying voluntary goal-directed movements. This allowed us to reveal different aspects of the nonlinear behavior of the process underlying the self-paced movement organization. Parallel alterations of these characteristics during the task performance supported the hypothesis that cognitive task performance is reflected by the changes in the nonlinear dynamics of the EEG activity. Four NCs of scalar EEG time series were estimated: Point-wise Correlation Dimension (PD2), Kolmogorov Entropy (K2), and Largest Lyapunov Exponent (LLE) as a function of time, and Nonlinear Prediction (NP) for successive EEG segments. The time evolution of these characteristics exhibited several transients between chaos-like states to almost periodic states during the task performance: the gradual increase to higher values indicating chaos are probably related to the onset of the successive phases of brain organization of the movement. The results suggest that even in short periods an EEG signal changes its dynamic structure and these periods could be determined precisely enough using different methods of nonlinear dynamics.     

FREE SURFACE WAVE INTERACTION WITH A HORIZONTAL CYLINDER

Classes of vortex formation from a horizontal cylinder adjacent to an undulating free-surface wave are characterized using high-image-density particle image velocimetry. Instantaneous representations of the velocity field, streamline topology and vorticity patterns yield insight into the origin of unsteady loading of the cylinder. For sufficiently deep submergence of the cylinder, the orbital nature of the wave motion results in multiple sites of vortex development, i.e., onset of vorticity concentrations, along the surface of the cylinder, followed by distinctive types of shedding from the cylinder. All of these concentrations of vorticity then exhibit orbital motion about the cylinder. Their contributions to the instantaneous values of the force coefficients are assessed by calculating moments of vorticity. It is shown that large contributions to the moments and their rate of change with time can occur for those vorticity concentrations having relatively small amplitude orbital trajectories. In a limiting case, collision with the surface of the cylinder can occur. Such vortex–cylinder interactions exhibit abrupt changes in the streamline topology during the wave cycle, including abrupt switching of the location of saddle points in the wave. The effect of nominal depth of submergence of the cylinder is characterized in terms of the time history of patterns of vorticity generated from the cylinder and the free surface. Generally speaking, generic types of vorticity concentrations are formed from the cylinder during the cycle of the wave motion for all values of submergence. The proximity of the free surface, however, can exert a remarkable influence on the initial formation, the eventual strength, and the subsequent motion of concentrations of vorticity. For sufficiently shallow submergence, large-scale vortex formation from the upper surface of the cylinder is inhibited and, in contrast, that from the lower surface of the cylinder is intensified. Moreover, decreasing the depth of submergence retards the orbital migration of previously shed concentrations of vorticity about the cylinder.     

Rich dynamics caused by diffusion

It is an awfully difficult task to design an efficient numerical method for bifurcation diagrams, the graphs of Lyapunov exponents, or the topological entropy about discrete dynamical systems by linear/nonlinear diffusion with the Direchlet/Neumann- boundary conditions. Until now there are less works concerned with such a problem. In this paper, we propose a scheme about bifurcating analysis in a series of discrete-time dynamical systems with linear/nonlinear diffusion terms under the periodic boundary conditions. The complexity of dynamical behaviors caused by the diffusion term are to be determined. Bifurcation diagrams are shown by numerical simulation and chaotic behavior (chaotic Turing patterns) is demonstrated by computing the largest Lyapunov exponent. Our theoretical model can give an interesting case study about the phenomenon: the individuals exhibit a very simple dynamics but the groups with linear/nonlinear coupling can own a complex dynamics including fluctuation, periodicity and even chaotic behavior. We find that diffusion can trigger chaotic behavior in the present system and there exist multiple Turing patterns. It is interesting as regular or chaotic patterns can be reported in this study. Chaotic orbits emerge when exploring further in the diffusion coefficient space, and such a behavior is entirely absent in the corresponding continuous time-space system. The method proposed in the present paper is innovative and the conclusion is novel.

     

Simplified coded dispersion entropy: a nonlinear metric for signal analysis

Recently, coded permutation entropy has been proposed, which enhances the noise immunity by quadratic partitioning on the basis of permutation entropy. However, coded permutation entropy and permutation entropy only consider the order of amplitude values and ignore some information related to amplitude. To overcome these defects, this paper applies the concept of quadratic partitioning to dispersion entropy (DE), takes advantage of the fact that DE can effectively measure amplitude information, and proposes coded DE (CDE), which increases the number of patterns and improves the divisibility by further coding the dispersion patterns in DE. Moreover, to reduce the computational consumption of CDE, we simplify the division criterion in quadratic partitioning while guaranteeing that no effective information is lost and propose simplified CDE (SCDE). Several simulation experiments demonstrate the advantages of SCDE and CDE over DE, permutation entropy, and coded permutation entropy in detecting the nonlinear dynamic changes within chaotic and synthetic signals. In addition, real-world experiments on electroencephalogram signals, bearing signals, and ship signals show that SCDE has better performance in medical diagnosis, fault diagnosis and signal classification, and the accuracy of SCDE-based classification methods is higher than that of other entropy-based methods.

     

Multiscale cumulative residual distribution entropy and its applications on heart rate time series

Nonlinear Dynamics - Distribution entropy has been proved to reveal stability for short time series and to distinguish different classes of series by complexity. However, there still exists some...