Cross-sample Entropy Research Articles

Measuring information interactions on the ordinal pattern of stock time series

The interactions among time series as individual components of complex systems can be quantified by measuring to what extent they exchange information among each other. In many applications, one focuses not on the original series but on its ordinal pattern. In such cases, trivial noises appear more likely to be filtered and the abrupt influence of extreme values can be weakened. Cross-sample entropy and inner composition alignment have been introduced as prominent methods to estimate the information interactions of complex systems. In this paper, we modify both methods to detect the interactions among the ordinal pattern of stock return and volatility series, and we try to uncover the information exchanges across sectors in Chinese stock markets.

Testing pattern synchronization in coupled systems through different entropy-based measures

Pattern synchronization (PS) can capture one aspect of the dynamic interactions between bivariate physiological systems. It can be tested by several entropy-based measures, e.g., cross sample entropy (X-SampEn), cross fuzzy entropy (X-FuzzyEn), multivariate multiscale entropy (MMSE), etc. A comprehensive comparison on their distinguishability is currently missing. Besides, they are highly dependent on several pre-defined parameters, the threshold value r in particular. Thus, their consistency also needs further elucidation. Based on the well-accepted assumption that a tight coupling necessarily leads to a high PS, we performed a couple of evaluations over several simulated coupled models in this study. All measures were compared to each other with respect to their consistency and distinguishability, which were quantified by two pre-defined criteria-degree of crossing (DoC) and degree of monotonicity (DoM). Results indicated that X-SampEn and X-FuzzyEn could only work well over coupled stochastic systems with meticulously selected r. It is thus not recommended to apply them to the intrinsic complex physiological systems. However, MMSE was suitable for both, indicating by relatively higher DoC and DoM values. Final analysis on the cardiorespiratory coupling validated our results.

MULTISCALE ENTROPY ANALYSIS OF FINANCIAL TIME SERIES

The paper mainly applies the multiscale entropy (MSE) to analyze the financial time series. The MSE is used to examine the complexity of a quantified system. Based on MSE, we propose multiscale cross-sample entropy (MSCE) to analyze the complexity and correlation of two time series. By comparing with the results, we find that both results present remarkable scaling characterization and the value of each log return of financial time series decreases with a increasing scale factor. From the results of MSE, we also find that the entropy of the Europe markets is lower than that of the Asia, but higher than that of the Americas. It means the MSE can distinguish different areas markets. The results of MSCE show that financial plate have high synchrony with the plate of Electron, IT and Realty. The MSCE can distinguish the highly synchronous plates.

Cross-sample entropy statistic as a measure of synchronism and cross-correlation of stock markets

In this paper, we employ cross-sample entropy (cross-SampEn), transfer entropy, and detrended cross-correlation analysis (DCCA) measurement to investigate the relationship between time series among different stock markets. Cross-SampEn method is used to compare the returns of every two stock index time series to assess their degree of asynchrony. Transfer entropy is applied to measure the information flow between two financial time series and this model-free approach in principle allows us to detect statistical dependencies of all types. We use DCCA method to quantify the cross-correlations of two non-stationary time series. We report the results of synchronism and cross-correlation behaviors in US and Chinese stock markets in periods 1991–1998 (before the Asian currency crisis) and 1999–2008 (after the Asian currency crises) by using cross-SampEn, transfer entropy and DCCA methods, respectively. The results, through the contrast description of the three methods, show that the synchronism and cross-correlation become higher after the Asian currency crises, especially for the three Chinese stock index time series. Among all these consequences, ShangZheng and ShenCheng show the strongest synchronism, information transfer and cross-correlation. While the three US stock markets show a good cross-correlation and information transfer, but less synchronism before the Asian currency crisis.

Changes of Heart and Respiratory Rate Dynamics During Weaning From Mechanical Ventilation

Abstract Purpose The aim of the study was to investigate heart rate (HR) and respiratory rate (RR) complexity in patients with weaning failure or success, using both linear and nonlinear techniques. Materials and Methods Forty-two surgical patients were enrolled in the study. There were 24 who passed and 18 who failed a weaning trial. Signals were analyzed for 10 minutes during 2 phases: (1) pressure support (PS) ventilation (15-20 cm H 2 O) and (2) weaning trials with PS (5 cm H 2 O). Low- and high-frequency (LF, HF) components of HR signals, HR multiscale entropy (MSE), RR sample entropy, cross-sample entropy between cardiorespiratory signals, Poincare plots, and α 1 exponent were computed in all patients and during the 2 phases of PS. Results Weaning failure patients exhibited significantly decreased RR sample entropy, LF, HF, and α 1 exponent, compared with weaning success subjects ( P P α 1 exponent, RR, and cross-sample entropies predicted better weaning outcome compared with RSBI, airway occlusion pressure at 0.1 second (P 0.1 ), and RSBI × P 0.1 (conventional model, R 2 = 0.887 vs 0.463; P P Conclusions We suggest that nonlinear analysis of cardiorespiratory dynamics has increased prognostic impact upon weaning outcome in surgical patients.

Linear and nonlinear tremor acceleration characteristics in patients with Parkinson's disease

The purpose of the study was to evaluate linear and nonlinear tremor characteristics of the hand in patients with Parkinson's disease (PD) and to compare the results with those of healthy old and young control subjects. Furthermore, the aim was to study correlation between tremor characteristics and clinical signs. A variety of nonlinear (sample entropy, cross-sample entropy, recurrence rate, determinism and correlation dimension) and linear (amplitude, spectral peak frequency and total power, and coherence) hand tremor parameters were computed from acceleration measurements for PD patients (n = 30, 68.3 ± 7.8 years), and old (n = 20, 64.2 ± 7.0 years) and young (n = 20, 18.4 ± 1.1 years) control subjects. Nonlinear tremor parameters such as determinism, sample entropy and cross-sample entropy were significantly different between the PD patients and healthy controls. These parameters correlated with the Unified Parkinson's disease rating scale (UPDRS), tremor and finger tapping scores, but not with the rigidity scores. Linear tremor parameters such as the amplitude and the maximum power (power corresponding to peak frequency) also correlated with the clinical findings. No major difference was detected in the tremor characteristics between old and young control subjects. The study revealed that tremor in PD patients is more deterministic and regular when compared to old or young healthy controls. The nonlinear tremor parameters can differentiate patients with PD from healthy control subjects and these parameters may have potential in the assessment of the severity of PD (UPDRS).

SYNCHRONIZATION IN BIOCHEMICAL SUBSTANCE EXCHANGE BETWEEN TWO CELLS

In this paper, Mihailović et al. [Mod. Phys. Lett. B25 (2011) 2407–2417] introduce a simplified model of cell communication in a form of coupled difference logistic equations. Then we investigated stability of exchange of signaling molecules under variability of internal and external parameters. However, we have not touched questions about synchronization and effect of noise on biochemical substance exchange between cells. In this paper, we consider synchronization in intercellular exchange in dependence of environmental and cell intrinsic parameters by analyzing the largest Lyapunov exponent, cross sample entropy and bifurcation maps.

Maps serving the combined coupling for use in environmental models and their behaviour in the presence of dynamical noise

Many physical, biological as well as the environmental problems, can be described by the dynamics of driven coupled oscillators. In order to study their behaviour as a function of coupling strength and nonlinearity, we considered dynamics of two maps serving the combined coupling (diffusive and linear) in the above fields. Firstly, we have considered a logistic difference equation on extended domain that is a part of the maps, that is discussed using its bifurcation diagram, Lyapunov exponent, sample as well as the permutation entropy. Secondly we have performed the dynamical analysis of the coupled maps using Lyapunov exponent and cross sample entropy in dependence on two coupling parameters. Further, we investigated how dynamical noise can affects the structure of their bifurcation diagrams. It was done (i) by the noise entering in two specific ways, that disturbs either the logistic parameter on extended domain or (ii) by an additive “shock” to the state variables. Finally, we demonstrated the effect of forcing by parametric noise, introduced in all maps’ parameter, on Lyapunov exponent of coupled maps.

Physio-behavioral Synchronicity as an Index of Processes Supporting Team Performance

Recent research suggests that synchronicity in physiological and behavioral responses during team tasks could provide an objective measure of processes underlying team performance. In this study, twenty dyads completed a series of trials in a variant of video game Tetris (Quadra). Task performance was divided between the participants such that they had to work interdependently to succeed. Team-paired cardiac interbeat intervals (IBIs) and postural sway (anterior-posterior head motion) were analyzed using Cross-Sample Entropy (CSEn) as indices of physiobehavioral synchronicity. Quantity of team verbal communication (number of words spoken) and a survey measure of team cohesion were also assessed. An increase in team performance was found to be associated with a decrease in IBI synchronicity, while an increase in team verbal communication was related to both an in increase postural sway synchronicity and team cohesion. Overall, this research supports the assertion that metrics of team synchronicity may serve as useful surrogate indices of team processes and performance.

A numerical study of coupled maps representing energy exchange processes between two environmental interfaces regarded as biophysical complex systems

The field of environmental sciences is abundant with various interfaces and is the right place for the application of new fundamental approaches leading towards a better understanding of environmental phenomena. Following the definition of environmental interface by Mihailovic and Bala? [1], such interface can be, for example, placed between: human or animal bodies and surrounding air, aquatic species and water and air around them, and natural or artificially built surfaces (vegetation, ice, snow, barren soil, water, urban communities) and the atmosphere, cells and surrounding environment, etc. Complex environmental interface systems are (i) open and hierarchically organised (ii) interactions between their constituent parts are nonlinear, and (iii) their interaction with the surrounding environment is noisy. These systems are therefore very sensitive to initial conditions, deterministic external perturbations and random fluctuations always present in nature. The study of noisy non-equilibrium processes is fundamental for modelling the dynamics of environmental interface regarded as biophysical complex system and for understanding the mechanisms of spatio-temporal pattern formation in contemporary environmental sciences. In this paper we will investigate an aspect of dynamics of energy flow based on the energy balance equation. The energy exchange between interacting environmen- tal interfaces regarded as biophysical complex systems can be represented by coupled maps. Therefore, we will numerically investigate coupled maps representing that exchange. In ana- lysis of behaviour of these maps we applied Lyapunov exponent and cross sample entropy.

Changes of heart and respiratory rate dynamics during weaning from mechanical ventilation: A study of physiologic complexity in surgical critically ill patients

PurposeThe aim of the study was to investigate heart rate (HR) and respiratory rate (RR) complexity in patients with weaning failure or success, using both linear and nonlinear techniques. Materials and MethodsForty-two surgical patients were enrolled in the study. There were 24 who passed and 18 who failed a weaning trial. Signals were analyzed for 10 minutes during 2 phases: (1) pressure support (PS) ventilation (15-20 cm H2O) and (2) weaning trials with PS (5 cm H2O). Low- and high-frequency (LF, HF) components of HR signals, HR multiscale entropy (MSE), RR sample entropy, cross-sample entropy between cardiorespiratory signals, Poincaré plots, and α1 exponent were computed in all patients and during the 2 phases of PS. ResultsWeaning failure patients exhibited significantly decreased RR sample entropy, LF, HF, and α1 exponent, compared with weaning success subjects (P < .001). Their changes were opposite between the 2 phases, except for MSE that increased between and within groups (P < .001). A new model including rapid shallow breathing index (RSBI), α1 exponent, RR, and cross-sample entropies predicted better weaning outcome compared with RSBI, airway occlusion pressure at 0.1 second (P0.1), and RSBI × P0.1 (conventional model, R2 = 0.887 vs 0.463; P < .001). Areas under the curve were 0.92 vs 0.86, respectively (P < .005). ConclusionsWe suggest that nonlinear analysis of cardiorespiratory dynamics has increased prognostic impact upon weaning outcome in surgical patients.

The evolutionary synchronization of the exchange rate system in [formula omitted

Although there are extensive researches on the behavior of the world currency network, the complexity of the Asian regional currency system is not well understood regardless of its importance. Using daily exchange rates this paper examines exchange rate co-movements in the region before and after the China exchange rate reform. It was found that the correlation between Asian currencies and the US Dollar, the previous regional key currency has become weaker and intra-Asia interactions have increased. Cross sample entropy and cross entropy approaches are also applied to examine the synchrony behavior among the Asian currencies. The study also shows that the Asian exchange rate markets featured are neither stochastic nor efficient. These findings may shed some light on the in-depth understanding of collective behaviors in a regional currency network; they will also lay a theoretical foundation for further policy formulation in Asian currency integration.

Cross-sample entropy of foreign exchange time series

The correlation of foreign exchange rates in currency markets is investigated based on the empirical data of DKK/USD, NOK/USD, CAD/USD, JPY/USD, KRW/USD, SGD/USD, THB/USD and TWD/USD for a period from 1995 to 2002. Cross-SampEn (cross-sample entropy) method is used to compare the returns of every two exchange rate time series to assess their degree of asynchrony. The calculation method of confidence interval of SampEn is extended and applied to cross-SampEn. The cross-SampEn and its confidence interval for every two of the exchange rate time series in periods 1995–1998 (before the Asian currency crisis) and 1999–2002 (after the Asian currency crisis) are calculated. The results show that the cross-SampEn of every two of these exchange rates becomes higher after the Asian currency crisis, indicating a higher asynchrony between the exchange rates. Especially for Singapore, Thailand and Taiwan, the cross-SampEn values after the Asian currency crisis are significantly higher than those before the Asian currency crisis. Comparison with the correlation coefficient shows that cross-SampEn is superior to describe the correlation between time series.

Complexity analysis of source activity underlying the neuromagnetic somatosensory steady-state response

Using the notion of complexity and synchrony, this study presents a data-driven pipeline of nonlinear analysis of neuromagnetic sources reconstructed from human magnetoencephalographic (MEG) data collected in reaction to vibrostimulation of the right index finger. The dynamics of MEG source activity was reconstructed with synthetic aperture magnetometry (SAM) beam-forming technique. Considering brain as a complex system, we applied complexity-based tools to identify brain areas with dynamic patterns that remain regular across repeated stimulus presentations, and to characterize their synchronized behavior. Volumetric maps of brain activation were calculated using sample entropy as a measure of signal complexity. The complexity analysis identified activity in the primary somatosensory (SI) area contralateral to stimuli and bilaterally in the posterior parietal cortex (PPC) as regions with decreased complexity, consistently expressed in a group of subjects. Seeding an activated source with low complexity in the SI area, cross-sample entropy was used to generate synchrony maps. Cross-sample entropy analysis confirmed the synchronized dynamics of neuromagnetic activity between areas SI and PPC, robustly expressed across subjects. Our results extend the understanding of synchronization between co-activated brain regions, focusing on temporal coordination between events in terms of synchronized multidimensional signal patterns.

Cross-fuzzy entropy: A new method to test pattern synchrony of bivariate time series

A new method, namely cross-fuzzy entropy (C-FuzzyEn) analysis, that can enable the measurement of the synchrony or similarity of patterns between two distinct signals, is presented in this study. With the inclusion of fuzzy sets, the similarity of vectors is fuzzily defined in C-FuzzyEn based on the exponential function and their shapes, rather than on the Heaviside function used in the conventional cross sample entropy (C-SampEn). Tests on simulated data sets and real EEG signals showed that C-FuzzyEn was superior to C-SampEn in several aspects, including giving the entropy definition in the case of small parameters, better relative consistency, and less dependence on record length. The proposed C-FuzzyEn was then applied for the analysis of simultaneously recorded electromyography (EMG) and mechanomyography (MMG) signals during sustained isometric contraction for monitoring local muscle fatigue. The results showed that the C-FuzzyEn of EMG–MMG signals decreased significantly during the development of muscle fatigue. The C-FuzzyEn showed a similar trend with the mean frequency (MNF) of EMG, the commonly used muscle fatigue indicator. However, C-FuzzyEn of EMG–MMG demonstrated a better robustness to the length of the analysis window in comparison with the MNF of EMG. The results suggested that the proposed C-FuzzyEn of EMG–MMG may potentially become a new reliable method for muscle fatigue assessment. It can also be applied to other bivariate signals extracted from complex systems with short data lengths in noisy backgrounds.

A comparative study of pattern synchronization detection between neural signals using different cross-entropy measures

Cross-approximate entropy (X-ApEn) and cross-sample entropy (X-SampEn) have been employed as bivariate pattern synchronization measures for characterizing interdependencies between neural signals. In this study, we proposed a new measure, cross-fuzzy entropy (X-FuzzyEn), to describe the synchronicity of patterns. The performances of three statistics were first quantitatively tested using five different coupled systems including both deterministic and stochastic models, i.e., coupled broadband noises, Lorenz-Lorenz, Rossler-Rossler, Rossler-Lorenz, and neural mass model. All the measures were compared with each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. The three measures were then applied to a real-life problem, pattern synchronization analysis of left and right hemisphere rat electroencephalographic (EEG) signals. Both simulated and real EEG data analysis results showed that the X-FuzzyEn provided an improved evaluation of bivariate series pattern synchronization and could be more conveniently and powerfully applied to different neural dynamical systems contaminated by noise.

Pattern synchrony in electrical signals related to earthquake activity

We apply the cross sample entropy method to geoelectrical time series collected from independent channels (North–South and East–West directions) monitored at two sites located in Mexico, to assess the presence of pattern synchrony between the signals, particularly in the proximity of earthquakes. To our best knowledge, this method has not been applied yet for the study of electrical signals related to earthquake activity. Moreover, we introduce the multiscale pattern synchrony analysis by extending the multiscale entropy technique to calculate the cross-entropy between two signals, which represents a novel approach to the study of pattern synchrony. The results obtained suggest that in the vicinity of an earthquake the geoelectrical signals exhibit pattern synchrony that persists for long sequences and through multiple scales, in addition to the presence of correlations in each channel.

Cross‐sample entropy statistic as a measure of complexity and regularity of renal sympathetic nerve activity in the rat

In this study, we employed both power spectral analysis and cross-sample entropy measurement to assess the relationship between two time series, arterial blood pressure (ABP) and renal sympathetic nerve activity (RSNA), during a mild haemorrhage in anaesthetized Wistar rats. Removal of 1 ml of venous blood decreased BP (by 7.1 +/- 0.7 mmHg) and increased RSNA (by 25.9 +/- 2.4%). During these changes, the power in the RSNA signal at heart rate frequency was reduced but coherence between the spectra at heart rate frequency in RSNA and ABP remained unchanged. Cross-sample entropy was significantly increased (by 10%) by haemorrhage, revealing that there was greater asynchrony between ABP and the RSNA time series. Intrathecal administration of the glutamate receptor antagonist kynurenic acid (2 mm) almost halved (P < 0.01) the reflex increase in RSNA. Also during kynurenic acid block, haemorrhage failed to change total power, power at heart rate frequency, coherence at heart rate frequency, or the cross-sample entropy measurements. We conclude that the increase in asynchrony between ABP and RSNA during the reflex increase in RSNA was a consequence of an increase in synaptic input to the spinal renal neurones. The data show that the cross-sample entropy calculations can characterize the non-linearities of neural mechanisms underlying cardiovascular control and have a potential to reveal how some aspects of homeostatic regulation of kidney function is achieved by the autonomic nervous system.