Cross Recurrence Quantification Analysis Research Articles

Recurrence plot-based dynamic analysis on electrochemical noise of the evolutive corrosion process

The cross recurrence plot (CRP) method was applied on the simultaneous current and voltage fluctuation time records in consideration of their possible nonlinear kinetics. Sequential cross recurrence quantification analysis (CRQA), CRP pattern recognition and synchronization analysis were used to screen the paralleled running from the uncorrelated oscillations, to recognize the impedance component, and to identify the synchronization type and degree in the dynamical view point. With the aid of the proposed approach, the sulfur-induced localized corrosion of the alloy 718 in the high temperature brine was detected and evaluated during the evolutive corrosion process.

The Stance Leads the Dance: The Emergence of Role in a Joint Supra-Postural Task.

Successfully meeting a shared goal usually requires co-actors to adopt complementary roles. However, in many cases, who adopts what role is not explicitly predetermined, but instead emerges as a consequence of the differences in the individual abilities and constraints imposed upon each actor. Perhaps the most basic of roles are leader and follower. Here, we investigated the emergence of “leader-follower” dynamics in inter-personal coordination using a joint supra-postural task paradigm (Ramenzoni et al., 2011; Athreya et al., 2014). Pairs of actors were tasked with holding two objects in alignment (each actor manually controlled one of the objects) as they faced different demands for stance (stable vs. difficult) and control (which actor controlled the larger or smaller object). Our results indicate that when actors were in identical stances, neither led the inter-personal (between actors) coordination by any systematic fashion. Alternatively, when asymmetries in postural demands were introduced, the actor with the more difficult stance led the coordination (as determined using cross-recurrence quantification analysis). Moreover, changes in individual stance difficulty resulted in similar changes in the structure of both intra-personal (individual) and inter-personal (dyadic) coordination, suggesting a scale invariance of the task dynamics. Implications for the study of interpersonal coordination are discussed.

Investigation of hydrodynamics of gas-solid fluidized beds using cross recurrence quantification analysis

Hydrodynamics of gas-solid fluidized bed was investigated by analyzing its pressure fluctuations using cross recurrence quantification analysis (CRQA). Pressure fluctuations were measured in a lab scale fluidized bed of various particle sizes at different gas velocities. First, the CRQA was applied to a number of well-known dynamic systems and the results demonstrated that it is a powerful method to detect similarities between nonlinear signals. Then, it was shown that graphical structures within the cross recurrence plot of pressure fluctuations of a fluidized bed vary with both superficial gas velocity and particle size. It was found that determinism and cross recurrence rate of non-normalized data initially decrease and then increase with increasing the gas velocity. When the signal is initially normalized, determinism and entropy do not change with the superficial gas velocity while cross recurrence rate is sensible to changes in the superficial gas velocity. It was concluded that entropy can be used for detecting changes of particle size and if a proper reference state is chosen, entropy can be a powerful index for detecting changes in the size of particles in a fluidized bed.

Online Detection of Hydrodynamic Changes in Fluidized Bed using Cross Average Diagonal Line

Online detection of hydrodynamics of gas-solid fluidized bed was characterized using pressure fluctuations by cross recurrence plot (CRP) and cross recurrence quantification analysis (CRQA). Experiments were conducted in a lab scale fluidized bed of various particle sizes 150 μm, 280 μm and 490 μm at different gas velocities. Firstly, pattern changes of cross recurrence plot were discussed and then reference states was selected. Afterwards, cross average diagonal line (CLave) of other states corresponding to reference states were obtained. It was found that cross average diagonal line of non-normalized data initially decreases and then increases with increasing the gas velocity. When the signal is initially normalized, cross average diagonal line does not change with the superficial gas velocity. It was concluded that cross average diagonal line could be used for detecting small changes of particle size and if a proper reference state is chosen, it can be perceived as a powerful index for detecting changes in the size of particles in a fluidized bed.

Measuring Coupling of Rhythmical Time Series Using Cross Sample Entropy and Cross Recurrence Quantification Analysis.

The aim of this investigation was to compare and contrast the use of cross sample entropy (xSE) and cross recurrence quantification analysis (cRQA) measures for the assessment of coupling of rhythmical patterns. Measures were assessed using simulated signals with regular, chaotic, and random fluctuations in frequency, amplitude, and a combination of both. Biological data were studied as models of normal and abnormal locomotor-respiratory coupling. Nine signal types were generated for seven frequency ratios. Fifteen patients with COPD (abnormal coupling) and twenty-one healthy controls (normal coupling) walked on a treadmill at three speeds while breathing and walking were recorded. xSE and the cRQA measures of percent determinism, maximum line, mean line, and entropy were quantified for both the simulated and experimental data. In the simulated data, xSE, percent determinism, and entropy were influenced by the frequency manipulation. The 1 : 1 frequency ratio was different than other frequency ratios for almost all measures and/or manipulations. The patients with COPD used a 2 : 3 ratio more often and xSE, percent determinism, maximum line, mean line, and cRQA entropy were able to discriminate between the groups. Analysis of the effects of walking speed indicated that all measures were able to discriminate between speeds.

"Are We in Sync with Each Other?" Exploring the Effects of Cosleeping on Heterosexual Couples' Sleep Using Simultaneous Polysomnography: A Pilot Study.

The present study aimed to explore dynamic and interactive aspects of cosleep in heterosexual couples. The sample consisted of eight young healthy adults who belonged to four heterosexual couples with a good relationship quality and a history of cosleeping. All individuals underwent simultaneous polysomnography in a sleep laboratory for four nights in which they slept individually and with their partner. Also, a sleep protocol of subjective sleep measures was completed. Statistical analyses included cross recurrence quantification analysis to assess synchronization during sleep. Cosleeping was associated with better subjective sleep quality, increased total sleep time, sleep efficiency, total slow wave sleep, and REM sleep. Sleep stages were more synchronized during cosleep independent of awakenings. Cardiorespiratory measures remained unchanged. The results indicate that young healthy couples in good relationships benefit from cosleeping on a subjective and objective level. Combining simultaneous polysomnography and cross recurrence quantification analysis is a promising method to study dynamic and interactive aspects of cosleep possibly leading to deeper understanding of the role of sleep for sociality, the nature of REM sleep, and the partner as a social zeitgeber. Moreover, clinical implications may arise from these findings.

Indifference to Chaotic Motion May Be Related to Social Disinterest in Children With Autism.

Children with autism spectrum disorder tend to have little interest in the presence, actions, and motives of other persons. In addition, these children tend to present with a limited and overly redundant movement repertoire, often expressing hyperfixation and aversion to novelty. We explore whether this is related to a more fundamental lack of appreciation for various temporal dynamics, including periodic, chaotic, and aperiodic motion structures. Seven children with ASD (age, gender, and height matched with children without ASD) were asked to stand and watch the motion of a visual stimulus displayed on a large (55″) video monitor. Gaze and posture movements were recorded and assessed using cross recurrence quantification analysis for qualities of coordination, including rate and duration of bouts of coordination. Results showed that children with ASD do not express an affinity to chaotic motion of the stimulus in the same way as children without ASD. We contend that this indifference to chaotic motion is foundational to their general disinterest in biological motion.

Foreign language learning as a complex dynamic process: A microgenetic case study of a Chinese child's English learning trajectory

The current study focuses on one child's (male, 3years old) learning behaviors in an English as a Foreign Language classroom, and explores the coordination and developmental patterns of his nonverbal (gestures and body language) and verbal (verbal repetition and verbal responses) learning behaviors over time. Guided by the principles of the theory of Complex Dynamical Systems, the child's learning behaviors were analyzed over the course of four months, using (Cross) Recurrence Quantification Analysis and Monte Carlo permutation tests. The results show that the coordination between the child's nonverbal and verbal behaviors exhibited a rigid pattern at the beginning but got loosened over time, allowing the child to respond more flexibly to the teachers' instructions and to alternate more freely between his verbal and nonverbal learning behaviors. When focusing on the child's verbal learning behaviors only, we found that patterns of the verbal responses seemed to be more predictable than those of verbal repetitions, which suggests the varied influence of internal and external factors on these verbal learning behaviors.

Asymmetric Dynamic Attunement of Speech and Gestures in the Construction of Children's Understanding.

As children learn they use their speech to express words and their hands to gesture. This study investigates the interplay between real-time gestures and speech as children construct cognitive understanding during a hands-on science task. 12 children (M = 6, F = 6) from Kindergarten (n = 5) and first grade (n = 7) participated in this study. Each verbal utterance and gesture during the task were coded, on a complexity scale derived from dynamic skill theory. To explore the interplay between speech and gestures, we applied a cross recurrence quantification analysis (CRQA) to the two coupled time series of the skill levels of verbalizations and gestures. The analysis focused on (1) the temporal relation between gestures and speech, (2) the relative strength and direction of the interaction between gestures and speech, (3) the relative strength and direction between gestures and speech for different levels of understanding, and (4) relations between CRQA measures and other child characteristics. The results show that older and younger children differ in the (temporal) asymmetry in the gestures–speech interaction. For younger children, the balance leans more toward gestures leading speech in time, while the balance leans more toward speech leading gestures for older children. Secondly, at the group level, speech attracts gestures in a more dynamically stable fashion than vice versa, and this asymmetry in gestures and speech extends to lower and higher understanding levels. Yet, for older children, the mutual coupling between gestures and speech is more dynamically stable regarding the higher understanding levels. Gestures and speech are more synchronized in time as children are older. A higher score on schools’ language tests is related to speech attracting gestures more rigidly and more asymmetry between gestures and speech, only for the less difficult understanding levels. A higher score on math or past science tasks is related to less asymmetry between gestures and speech. The picture that emerges from our analyses suggests that the relation between gestures, speech and cognition is more complex than previously thought. We suggest that temporal differences and asymmetry in influence between gestures and speech arise from simultaneous coordination of synergies.

Electrochemical noise monitoring of sulphur corrosion for nickel alloy 718

Sulphur corrosion for nickel alloy 718 was monitored by electrochemical noise under high temperature. Cross-recurrence quantification analysis (CRQA) on potential and current noise signals was used to characterise the stable coupling interaction between them. Diagnosis criterion for stable pitting started was proposed based on the CRQA parameter determinism per cent trajectory. The proposed method displayed accurate and robust characteristics compared to the common localisation index.

Dynamic characterization and predictability analysis of wind speed and wind power time series in Spain wind farm

The renewable energy resources such as wind power have recently attracted more researchers’ attention. It is mainly due to the aggressive energy consumption, high pollution and cost of fossil fuels. In this era, the future fluctuations of these time series should be predicted to increase the reliability of the power network. In this paper, the dynamic characteristics and short-term predictability of hourly wind speed and power time series are investigated via nonlinear time series analysis methods such as power spectral density analysis, time series histogram, phase space reconstruction, the slope of integral sums, the ��− �� method, the recurrence plot and the recurrence quantification analysis. Moreover, the interactive behavior of the wind speed and wind power time series is studied via the cross correlation, the cross and joint recurrence plots as well as the cross and joint recurrence quantification analyses. The results imply stochastic nature of these time series. Besides, a measure of the short-term mimic predictability of the wind speed and the underlying wind power has been derived for the experimental data of Spain’s wind farm.

Training in Compensatory Strategies Enhances Rapport in Interactions Involving People with Möbius Syndrome.

In the exploratory study reported here, we tested the efficacy of an intervention designed to train teenagers with Möbius syndrome (MS) to increase the use of alternative communication strategies (e.g., gestures) to compensate for their lack of facial expressivity. Specifically, we expected the intervention to increase the level of rapport experienced in social interactions by our participants. In addition, we aimed to identify the mechanisms responsible for any such increase in rapport. In the study, five teenagers with MS interacted with three naïve participants without MS before the intervention, and with three different naïve participants without MS after the intervention. Rapport was assessed by self-report and by behavioral coders who rated videos of the interactions. Individual non-verbal behavior was assessed via behavioral coders, whereas verbal behavior was automatically extracted from the sound files. Alignment was assessed using cross recurrence quantification analysis and mixed-effects models. The results showed that observer-coded rapport was greater after the intervention, whereas self-reported rapport did not change significantly. Observer-coded gesture and expressivity increased in participants with and without MS, whereas overall linguistic alignment decreased. Fidgeting and repetitiveness of verbal behavior also decreased in both groups. In sum, the intervention may impact non-verbal and verbal behavior in participants with and without MS, increasing rapport as well as overall gesturing, while decreasing alignment.

Prospectively identified deficits in sagittal plane hip–ankle coordination in female athletes who sustain a second anterior cruciate ligament injury after anterior cruciate ligament reconstruction and return to sport

BackgroundAthletes who return to sport after anterior cruciate ligament reconstruction are at increased risk of future ACL injury. Altered coordination of lower extremity motion may increase this risk. The purpose of this study was to prospectively determine if altered lower extremity coordination patterns exist in athletes who go on to sustain a 2nd anterior cruciate ligament injury. MethodsSixty-one female athletes who were cleared to return to sport after anterior cruciate ligament reconstruction were included. Hip–ankle coordination was assessed prior to return to sport with a dynamic postural coordination task. Within 12months, 14 patients sustained a 2nd ACL injury. Fourteen matched subjects were selected for comparative analysis. Cross-recurrence quantification analysis characterized hip–ankle coordination patterns. A group×target speed (slow vs. fast)×leg (involved vs. uninvolved) analysis of variance was used to identify differences. FindingsA main effect of group (P=0.02) indicated that the single injury group exhibited more stable hip–ankle coordination [166.2 (18.9)] compared to the 2nd injury group [108.4 (10.1)]. A leg×group interaction was also observed (P=.04). The affected leg of the single injury group exhibited more stable coordination [M=187.1 (23.3)] compared to the affected leg of the 2nd injury group [M=110.13 (9.8)], P=0.03. InterpretationHip–ankle coordination was altered in female athletes who sustained a 2nd anterior cruciate ligament injury after return to sport. Failure to coordinate lower extremity movement in the absence of normal knee proprioception may place the knee at risk.

Spatiotemporal Time Series Analysis Methods for the Study of Turbulent Magnetohydrodynamic Channel Flows

In the present study, the direct numerical simulation of the turbulent flow of an electrically conductive fluid in a channel is performed and time series are recorded at a range of locations along the y-direction between the parallel plates of the channel. An external streamwise magnetic field is applied and the correlations between pairs of time series of the fluctuating velocities from the magnetohydrodynamic and the hydrodynamic cases measured at the same probing location of the channel are analyzed. We compare the situation with and without magnetic field using the nonlinear method of Cross Recurrence Plots and Cross Recurrence Quantification Analysis (CRQA). The results of CRQA indicate very well the spatiotemporal extension of the effect of the applied magnetic field on the flow and are in very good agreement with the detailed analysis obtained with other methods.

Children's looking preference for biological motion may be related to an affinity for mathematical chaos.

Recognition of biological motion is pervasive in early child development. Further, viewing the movement behavior of others is a primary component of a child’s acquisition of complex, robust movement repertoires, through imitation and real-time coordinated action. We theorize that inherent to biological movements are particular qualities of mathematical chaos and complexity. We further posit that this character affords the rich and complex inter-dynamics throughout early motor development. Specifically, we explored whether children’s preference for biological motion may be related to an affinity for mathematical chaos. Cross recurrence quantification analysis (cRQA) was used to investigate the coordination of gaze and posture with various temporal structures (periodic, chaotic, and aperiodic) of the motion of an oscillating visual stimulus. Children appear to competently perceive and respond to chaotic motion, both in rate (cRQA-percent determinism) and duration (cRQA-maxline) of coordination. We interpret this to indicate that children not only recognize chaotic motion structures, but also have a preference for coordination with them. Further, stratification of our sample (by age) uncovers the suggestion that this preference may become refined with age.

Movement dynamics reflect a functional role for weak coupling and role structure in dyadic problem solving.

Successful interaction requires complex coordination of body movements. Previous research has suggested a functional role for coordination and especially synchronization (i.e., time-locked movement across individuals) in different types of human interaction contexts. Although such coordination has been shown to be nearly ubiquitous in human interaction, less is known about its function. One proposal is that synchrony supports and facilitates communication (Topics Cogn Sci 1:305-319, 2009). However, questions still remain about what the properties of coordination for optimizing communication might look like. In the present study, dyads worked together to construct towers from uncooked spaghetti and marshmallows. Using cross-recurrence quantification analysis, we found that dyads with loosely coupled gross body movements performed better, supporting recent work suggesting that simple synchrony may not be the key to effective performance (Riley et al. 2011). We also found evidence that leader-follower dynamics-when sensitive to the specific role structure of the interaction-impact task performance. We discuss our results with respect to the functional role of coordination in human interaction.

Dancers entrain more effectively than non-dancers to another actor's movements.

For many everyday sensorimotor tasks, trained dancers have been found to exhibit distinct and sometimes superior (more stable or robust) patterns of behavior compared to non-dancers. Past research has demonstrated that experts in fields requiring specialized physical training and behavioral control exhibit superior interpersonal coordination capabilities for expertise-related tasks. To date, however, no published studies have compared dancers’ abilities to coordinate their movements with the movements of another individual—i.e., during a so-called visual-motor interpersonal coordination task. The current study was designed to investigate whether trained dancers would be better able to coordinate with a partner performing short sequences of dance-like movements than non-dancers. Movement time series were recorded for individual dancers and non-dancers asked to synchronize with a confederate during three different movement sequences characterized by distinct dance styles (i.e., dance team routine, contemporary ballet, mixed style) without hearing any auditory signals or music. A diverse range of linear and non-linear analyses (i.e., cross-correlation, cross-recurrence quantification analysis, and cross-wavelet analysis) provided converging measures of coordination across multiple time scales. While overall levels of interpersonal coordination were influenced by differences in movement sequence for both groups, dancers consistently displayed higher levels of coordination with the confederate at both short and long time scales. These findings demonstrate that the visual-motor coordination capabilities of trained dancers allow them to better synchronize with other individuals performing dance-like movements than non-dancers. Further investigation of similar tasks may help to increase the understanding of visual-motor entrainment in general, as well as provide insight into the effects of focused training on visual-motor and interpersonal coordination.

Deficits in Hip-Ankle Coordination in Female Athletes who Suffer a Second Anterior Cruciate Ligament (ACL) Injury after ACL Reconstruction and Return to Sport

Objectives:Athletes who return to sport after ACL reconstruction (ACLR) are at increased risk of future ACL injury. Proprioceptive deficits at the knee, known to be present at thetime of ACL injury, may persist for up to 2 years after ACLR. Coordinated movements of the hip and ankle are critical in the absence of normal knee proprioception during dynamic athletic movements. Failure to optimally position the knee may make the passive structures susceptible to pathologic stresses that increase the risk of subsequent ligament or graft failure. The purpose of this work was to prospectively determine if altered lower extremity coordination patterns exist in female athletes, who go on to suffer a second ACL injury to either limb, after ACLR and return to sport (RTS). The study tested the hypothesis that female athletes who sustained a second ACL injury would demonstrate altered lower extremity coordination patterns indicative of persistent neuromuscular deficits at the time of return to sport compared to female athletes who would not subsequently sustain a second ACL injury.Methods:Sixty-one female athletes, who sustained an ACL injury, underwent ACLR, completed rehabilitation and were medically cleared for RTS were enrolled in this study. Hip-ankle coordination was assessed on all athletes prior to RTS as they performed a dynamic postural coordination task. The task required participants to stand on a single leg and track the anterior-posterior (AP) movement of an oscillating 3-D square target displayed on a computer monitor. Participants tracked the target with the head so as to maintain a constant perceived distance between their head and the target by matching the amplitude and frequency of the target oscillations. Fourteen patients sustained a second ACL injury within 12 months of RTS (ACLR2). Fourteen matched subjects after ACLR, who did not suffer a second ACL injury (ACLR1), were selected for comparative analysis. Cross-recurrence quantification analysis (Figure 1) was used to characterize hip-ankle coordination patterns through the variable cross-maxline (CML). A group (ACLR1 vs. ACLR2) X target speed (slow vs. fast) X leg (affected vs. unaffected) mixed-model analysis of variance was used to identify coordination differences.Results:A significant main effect of group was observed (p = 0.02), and indicated that the ACLR1 group exhibited more stable hip-ankle coordination overall (M = 166.2 ± 18.9) compared to the ACLR2 group (M = 108.4 ± 10.1), irrespective of target speed or tested leg. A leg x group interaction was also observed (p = .04). A Mann-Whitney test was employed due to unequal variances between groups, and indicated that the affected leg of the ACLR1 group exhibited more stable coordination (M = 187.1 ± 23.3)compared to the affected leg of the ACLR2 group (M = 110.13 ± 9.8), p = 0.03.Conclusion:Hip-ankle coordination was altered in female athletes who subsequently sustain a second ACL injury after initial ACLR and RTS. Failure to appropriately coordinate lower extremity movement between the adjoining proximal and distal hip and ankle in the absence of normal knee proprioception, may place the knee in a high-risk position and increase the likelihood of a second ACL injury in this population.

Cross-recurrence quantification analysis of categorical and continuous time series: an R package.

This paper describes the R package crqa to perform cross-recurrence quantification analysis of two time series of either a categorical or continuous nature. Streams of behavioral information, from eye movements to linguistic elements, unfold over time. When two people interact, such as in conversation, they often adapt to each other, leading these behavioral levels to exhibit recurrent states. In dialog, for example, interlocutors adapt to each other by exchanging interactive cues: smiles, nods, gestures, choice of words, and so on. In order for us to capture closely the goings-on of dynamic interaction, and uncover the extent of coupling between two individuals, we need to quantify how much recurrence is taking place at these levels. Methods available in crqa would allow researchers in cognitive science to pose such questions as how much are two people recurrent at some level of analysis, what is the characteristic lag time for one person to maximally match another, or whether one person is leading another. First, we set the theoretical ground to understand the difference between “correlation” and “co-visitation” when comparing two time series, using an aggregative or cross-recurrence approach. Then, we describe more formally the principles of cross-recurrence, and show with the current package how to carry out analyses applying them. We end the paper by comparing computational efficiency, and results’ consistency, of crqa R package, with the benchmark MATLAB toolbox crptoolbox (Marwan, 2013). We show perfect comparability between the two libraries on both levels.

Visual influences on postural and manual interpersonal coordination during a joint precision task.

We investigated whether the interpersonal postural coordination that occurs during a joint supra-postural, manual precision task is driven by the constraints of the task, or, instead results from visual entrainment to the movements of a co-actor. Participants were instructed to coordinate their finger movements under conditions where participants could see others' whole-body movements or could only see the results of the other's actions. Participants' finger and torso movements were recorded. Coordination was quantified using cross-recurrence quantification analysis measures. Interpersonal coordination was enhanced by, although it did not depend entirely upon, visual information about the co-actor's body movements.