Classification of physiologic and synthetic heart rate variability series using base-scale entropy

The base-scale entropy method was used as a measure to classify physiologic and synthetic heart rate variability series. This method enables analyzing very short, non-stationary, and noisy data. We used it to analyze short-term heart rate variability series. The results show that our method can effectively detect the complex dissimilarity of physiologic time series in different physiologic/pathologic states. We then applied it to the CinC 2002 test datasets. Using the base-scale entropy, we correctly classified 43 of 46 (93%) time series. In combination with time domain analysis, we correctly classified all time series.     

Decrease in Hurst exponent of human gait with aging and neurodegenerative diseases

In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range correlations of gait rhythm from young healthy people are stronger than those from the healthy elderly and the diseased. The result further implies that fractal dynamics in human gait will be altered due to weakening or impairment of neural control on locomotion resulting from aging and neurodegenerative diseases. Due to analysing short-term data sequences rather than long datasets required by most nonlinear methods, the algorithm has the characteristics of simplicity and sensitivity, most importantly, fast calculation as well as powerful anti-noise capacities. These findings have implications for modelling locomotor control and also for quantifying gait dynamics in varying physiologic and pathologic states.     

应用多尺度化的基本尺度熵分析心率变异性

本文采用多尺度化的基本尺度熵方法,针对心率变异性信号进行了分析,研究发现多尺度化的基本尺度熵可以区分不同生理病理信号,包括健康人、充血性心力衰竭患者和房颤心律失常患者的心率变异性信号,以及健康人白天黑夜的心率变异性信号.通过对健康人代理数据的分析,发现房颤心律失常患者与代理数据的熵值趋势相似,研究结果表明房颤心律失常患者的心率变异性信号更多的是反映生理信号的线性特征,而对环境变化不能很好的进行自我调节. 关键词： 多尺度化的基本尺度熵 心率变异性 充血性心力衰竭 房颤心律失常     

Multiscale entropy analysis of complex physiologic time series

There has been considerable interest in quantifying the complexity of physiologic time series, such as heart rate. However, traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long-range correlations. This paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics. We introduce a method to calculate multiscale entropy (MSE) for complex time series. We find that MSE robustly separates healthy and pathologic groups and consistently yields higher values for simulated long-range correlated noise compared to uncorrelated noise.     

Alteration in scaling behavior of short-term heartbeat time series for professional shooting athletes from rest to exercise

Scaling analysis of heartbeat time series has emerged as a useful tool for assessing the autonomic cardiac control under various physiologic and pathologic conditions. We study the heartbeat activity and scaling behavior of heartbeat fluctuations regulated by autonomic nervous system for professional shooting athletes under two states: rest and exercise, by applying the detrended fluctuation analysis method. We focus on alteration in correlation properties of heartbeat intervals for the shooters from rest to exercise, which may have a potential value in monitoring the quality of training and evaluating the sports capacity of the athletes. The result shows that scaling exponents of short-term heart rate variability signals from the shooters get significantly larger during exercise compared with those obtained at rest. It demonstrates that during exercise stronger correlations appear in the heartbeat series of shooting athletes in order to satisfy the specific requirements for high concentration and better control on their heart beats.     

Age-related changes in the "complexity" of cardiovascular dynamics: A potential marker of vulnerability to disease

Healthy physiologic control of cardiovascular function is a result of complex interactions between multiple regulatory processes that operate over different time scales. These include the sympathetic and parasympathetic nervous systems which regulate beat-to-beat heart rate (HR) and blood pressure (BP), as well as extravascular volume, body temperature, and sleep which influence HR and BP over the longer term. Interactions between these control systems generate highly variable fluctuations in continuous HR and BP signals. Techniques derived from nonlinear dynamics and chaos theory are now being adapted to quantify the dynamic behavior of physiologic time series and study their changes with age or disease. We have shown significant age-related changes in the 1/f(x) relationship between the log amplitude and log frequency of the heart rate power spectrum, as well as declines in approximate dimension and approximate entropy of both heart rate and blood pressure time series. These changes in the "complexity" of cardiovascular dynamics reflect the breakdown and decoupling of integrated physiologic regulatory systems with aging, and may signal an impairment in cardiovascular ability to adapt to external and internal perturbations. Studies are currently underway to determine whether the complexity of HR or BP time series can distinguish patients with fainting spells due to benign vasovagal reactions from those due to life-threatening cardiac arrhythmias. Thus, measures of the complexity of physiologic variability may provide novel methods to monitor cardiovascular aging and test the efficacy of specific interventions to improve adaptive capacity in old age. (c) 1995 American Institute of Physics.     

Tremor classification and tremor time series analysis

The separation between physiologic tremor (PT) in normal subjects and the pathological tremors of essential tremor (ET) or Parkinson's disease (PD) was investigated on the basis of monoaxial accelerometric recordings of 35 s hand tremor epochs. Frequency and amplitude were insufficient to separate between these conditions, except for the trivial distinction between normal and pathologic tremors that is already defined on the basis of amplitude. We found that waveform analysis revealed highly significant differences between normal and pathologic tremors, and, more importantly, among different forms of pathologic tremors. We found in our group of 25 patients with PT and 15 with ET a reasonable distinction with the third momentum and the time reversal invariance. A nearly complete distinction between these two conditions on the basis of the asymmetric decay of the autocorrelation function. We conclude that time series analysis can probably be developed into a powerful tool for the objective analysis of tremors. (c) 1995 American Institute of Physics.     

Geometrical minimum units of fracture patterns in two-dimensional space: Lattice and discrete Walsh functions

We present the geometrical minimum units of fracture patterns in two-dimensional space. For this analysis, a new method is developed from the algebraic approach: the concept of lattice (a type of partially ordered set) is applied to the discrete Walsh functions that have been used to measure symmetropy (an object related to symmetry and entropy) of fracture patterns. We concluded that the minimum units of fracture patterns can be expressed as three kinds of lattice. Our model is applied to the temporal change of the spatial pattern of acoustic-emission events in a rock-fracture experiment. As a result, the symmetropy of lattice decreases with the evolution of fracture process. We find that the pre-nucleation process of fracture corresponds to the subcritical states, and the propagation process to the critical states. Moreover, using a particular mathematical structure called sheaf on a lattice, we suggest the algebraic interpretation of fracture process, and provide justification to regard fracturing as an irreversible process.     

Forcing and control of localized states in optical single feedback systems

Under feedback extended nonlinear optical systems spontaneously show a variety of periodic patterns and structures. Control gives new insight into these phenomena and it can open the way for potential application of nonlinear optical structures. We briefly review methods to control localized states in single feedback experiments. Application of a Fourier control method allows to modify interaction behavior of the localized states. As a further approach we study a forcing method, using externally created light fields as additional input to the system. Recent experiments show that the forcing method enables to favor addressing positions for localized structures. We demonstrate static addressing and favoring of addressing positions. We extend the forcing method to a dynamic forcing scheme, which allows to move and reposition localized states. Additionally forcing is used to balance experimental imperfections. PACS 05.45.Gg; 42.60.Jf; 42.65.Tg     

The Response of Glassy Systems to Random Perturbations: A Bridge Between Equilibrium and Off-Equilibrium

We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free energy. By exploiting this fact, we define a new order parameter function, and we relate it to the ratio between response and fluctuation, which is in principle measurable in an aging experiment. For a class of systems possessing stochastic stability, we show that this new order parameter function is intimately related to the static order parameter function, describing the distribution of overlaps between clustering states. The same method is applied to investigate the geometrical organization of pure states. We show that the ultrametric organization in the dynamics implies static ultrametricity, and we relate these properties to static separability, i.e., the property that the measure of the overlap between pure states is essentially unique. Our results, especially relevant for spin glasses, pave the way to an experimental determination of the order parameter function.     

Ultrametricity in three-dimensional edwards-anderson spin glasses

We perform an accurate test of ultrametricity in the aging dynamics of the three-dimensional Edwards-Anderson spin glass. Our method consists in considering the evolution in parallel of two identical systems constrained to have fixed overlap. This turns out to be a particularly efficient way to study the geometrical relations between configurations at distant large times. Our findings strongly hint towards dynamical ultrametricity in spin glasses, while this is absent in simpler aging systems with domain growth dynamics. A recently developed theory of linear response in glassy systems allows us to infer that dynamical ultrametricity implies the same property at the level of equilibrium states.     

Dynamical complexity changes during two forms of meditation

Detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meaning. We use the base-scale entropy method to analyze dynamical complexity changes for heart rate variability (HRV) series during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. The results show that dynamical complexity decreases in meditation states for two forms of meditation. Meanwhile, we detected changes in probability distribution of m-words during meditation and explained this changes using probability distribution of sine function. The base-scale entropy method may be used on a wider range of physiologic signals.     

Data synchronization in a network of coupled phase oscillators

We devised a new method of data mining for a large-scale database. In the method, a network of locally coupled phase oscillators subject to Kuramoto's model substitutes for given multivariate data to generate major features through phase locking of the oscillators, i.e., phase transition of the data set. We applied the method to the national database of care needs certification for the Japanese public long-term care insurance program, and found three major patterns in the aging process of the frail elderly. This work revealed the latent utility of Kuramoto's model for data processing.     

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

Universality of striped morphologies

We present a method for predicting the low-temperature behavior of spherical and Ising spin models with isotropic potentials. For the spherical model the characteristic length scales of the ground states are exactly determined but the morphology is shown to be degenerate with checkerboard patterns, stripes and more complex morphologies having identical energy. For the Ising models we show that the discretization breaks the degeneracy causing striped morphologies to be energetically favored and therefore they arise universally as ground states to potentials whose Hankel transforms have nontrivial minima.     

Entangled double-helix phase

We present a novel phase with an entangled double-helix structure. Beams with this phase have the same transverse patterns as those of interference between two doughnut beams. This proposed method allows a complete set of the superpositions of the doughnut modes or the orbital angular momentum states with different topological orders to be obtained. Furthermore, it introduces a simple continuous and controlled rotation of the transverse patterns by use of a spatial light modulator. It can be used to form a three-dimensional structure by three-dimensional trapping in an optical tweezers setup or to study the quantum characteristics of an optical vortex.     

Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics

We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on chimera states involving amplitude as well as phase dynamics, complex topologies like small-world or hierarchical (fractal), noise, and delay. We show that a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model. For the FitzHugh-Nagumo system, the Van der Pol oscillator, and the Stuart-Landau oscillator with symmetry-breaking coupling various multi-chimera patterns including amplitude chimeras and chimera death occur. To test the robustness of chimera patterns with respect to changes in the structure of the network, regular rings with coupling range R, small-world, and fractal topologies are studied. We also address the robustness of amplitude chimera states in the presence of noise. If delay is added, the lifetime of transient chimeras can be drastically increased.     

Mach–Zehnder interferometer with squeezed and EPR entangled optical fields

We study a scheme for Mach-Zehnder(MZ) interferometer as a quantum linear device by injecting two-mode squeezed input states into two ports of interferometer.Two-mode squeezed states can be changed into two types of inputs for MZ interferometer:two squeezed states and Einstein-Podolsky-Rosen(EPR) entangled states.The interference patterns of the MZ interferometer vary periodically as the relative phase of the two arms of the interferometer is scanned,and are measured by the balanced homodyne detection system.Our experiments show that there are different interference patterns and periodicity of the output quantum states for two cases which depend on the relative phase of input optical fields.Since MZ interferometer can be used to realize some quantum operations,this work will have the important applications in quantum information and metrology.     

Chimera states in networks of logistic maps with hierarchical connectivities

Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilution of the network links influences the appearance of chimera patterns. The network connectivities are constructed using an iterative Cantor algorithm to generate fractal (hierarchical) connectivities. Increasing the hierarchical level of iteration, we compare the resulting spatiotemporal patterns. We demonstrate that a high clustering coefficient and symmetry of the base pattern promotes chimera states, and asymmetric connectivities result in complex nested chimera patterns.     

From 1/f noise to multifractal cascades in heartbeat dynamics

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.