10th International Symposium on Recurrence Plots 2023

August 28-30, 2023
Tsukuba, Japan
Satellite meeting to ICIAM 2023 Tokyo.

Conference Programme

Cover of the programme

The time for talks is 15 min, plus 5 min discussion (invited talks are 40 min, plus 5 min discussion). Presentations should be prepared as PowerPoint, Keynote, or pdf file. Animations should be avoided, because of the latencies in virtual environment.

The prefered size of the posters is A0 or ArchE portrait (i.e. higher than wide). A hook will be available for hanging as well as material for fixing the posters in the support.

Please note that there will not be an online poster session available. The poster session will only take place in person. Thank you for your understanding.

Monday, August 28th

8:30 Registration
9:00 Opening
Methodological Aspects 1: New Directions
9:10 Shotaro Akaho Keynote Lecture: Kernel methods for machine learning
Kernel methods have become widely known in the field of machine learning research due to the success of support vector machines (SVMs). The mathematical foundation of kernel methods is the reproducing kernel Hilbert space (RKHS), which can bridge the linear and nonlinear worlds. In this talk, I will outline the fundamentals of RKHS, including SVM and various machine learning methods, and introduce its important role in the analysis of deep neural networks in recent years.

9:55 Thiago de Lima Prado (online) New developments in recurrence microstates
The recurrence plots (RPs) are matrices with binary elements that characterize states from some data sequence. Relevant structures can be observed in any given RP that deserve a proper quantification. The set of tools that quantifies these structures in a RP is so called recurrence quantification analysis (RQAs). Particularly, one important RQA is the Shannon Entropy when computed from recurrent diagonals probabilities in a RP. The same can be done with the recurrence microstates, that are small squared configurations obtained from the underlying RP. Here will be presented some results with the so called Recurrence Microstates Entropy and several improvements possible when the function is maximized (e.g. independence on the threshold parameter, automatically setting of time delay for continuous systems...). Also will be shown many applications to simulated and real data. Finally, will be presented some possible new quantifiers that can be derived directly from the recurrence microstates and can be applied similarly to some traditional RQAs.

10:15 Yoshito Hirata Mathematics of recurrence plots
Since Eckmann et al. proposed in 1987, a recurrence plot has been used practically for analyzing various time series in diverse applications. But, how is the approach using a recurrence plot solid theoretically? In this talk, I review some theoretical works related to a recurrence plot so that we can understand how the approach using a recurrence plot has been founded mathematically until now. In addition, I discuss how the approach should be further consolidated in the near future.

10:35 Coffee break
Methodological Aspects 2: New RP Approaches
11:00 Norbert Marwan, Tobias Braun, K. Hauke Kraemer, Abhirup Banerjee, Deniz Eroglu Recurrence plots for analysing extreme events data
The analysis of time series of extreme events is a challenging task. Many research questions, such as synchronisation analysis or power spectrum estimation, are challenging for linear tools. We demonstrate some recent extensions of the recurrence plot approach for various applications in the field of extreme events data. We demonstrate their potential for synchronisation analysis between signals of extreme events and signals with continuous and slower variations, for estimation of power spectra of spiky signals, and for analysing data with irregular sampling.

11:20 Iurii Nagornov Recurrence plot representation of points series during meta-sampling based on maxima weighted isolation kernel method
Recently proposed method of approximate Bayesian computation uses the part of Isolation Kernel mean embedding with maximal weights and named Maxima Weighted Isolation Kernel or MaxWiK. Isolation Kernel is implemented with a Voronoi diagram algorithm, which makes possible the explicit transformation of simulation row data to a Hilbert space corresponding to the models parameters.
Two main hyperparameters are important for the machine learning process: the number of trees $t$ in the isolation forest algorithm and the number of Voronoi cells $psi$ in a generation of partitionings. The interpretation of MaxWiK is the intersection of all the Voronoi cells corresponding to an observation point ($s^\ast$) in the Hilbert representation of parameter space.

Meta-sampling (MS) algorithm realized to generate new points in the parameter space and calculate similarity between them and $s^\ast$ without model simulation. The target of meta-sampling is to find the most appropriate parameter in the Hilbert space ($\mu^\ast$) based on its similarity measure.

Recurrences appear during the generation of new points around $\mu^\ast$, so recurrence plot can show how these points are close to $\mu^\ast$. Skipping details of MS algorithm itself, this work shows the recurrence plot of Hilbert representation of generated points during meta-sampling.

Instead time series, we used dataset generated from each time step of MS, so the definition of the binary recurrence matrix was for each tree $tk$ in the format of identity of Voronoi cells:

{ij} = 1$ if $psi_i = psi_j$,

where $psi_i$ and $psi_j$ are identification numbers of Voronoi cells in the isolation tree $t_k$.

The algorithm discards points from dataset which are not significant in the recurrence plot for many trees and generates new others.

Finally, MaxWiK should find all the points from intersection of Voronoi cells corresponding to $mu^*$ so that all the elements of binary recurrence matrices should be units.

11:40 Martijn Bousse, Philippe Dreesen, Pietro Bonizzi, Joel Karel, Ralf Peeters Dealing with incomplete data: A structured tensor-completion approach for recurrence plots
Incomplete data, i.e., data with missing or unknown values, is a ubiquitous problem, exacerbated by the rise of big data, in a wide range of applications within signal processing, machine learning, and scientific computing. The origin of incompleteness can be unintentional, such as in the case of faulty sensors, but it can also be deliberate, e.g., whenever measurements are expensive or difficult to obtain. In any case, practical algorithms have to be able to tackle data with gaps or irregular sampling. There generally exist two approaches: imputation or expectation-maximization strategies and direct algorithms that only take into account the known data. In this work, we propose a tensor completion-based approach for recurrence plots constructed from incomplete time series data, which is an important and upcoming problem in recurrence analysis, as mentioned in the review paper of Marwan and Kraemer, 2023.

Handling incomplete data through a tensor-completion strategy involves the assumption that the data admits a low-rank representation, in the exact case, or approximation, in the non-exact or noisy case. This is often the case in a variety of applications, and especially in large-scale problems, thanks to latent structures in the data, such as sparsity and low-rankness, given an adequate representation. For example, signals that can be approximated well by (exponential) polynomials adhere a low-rank factorization when embedded in a Hankel matrix. Imputation through tensor completion then involves two steps: first, compute a low-rank factorization by using only the known values, and, second, fill-in the unknown values by means of the low-rank factorization.

In this work, we cast the computation of the values of an unthresholded recurrence plot into a structured tensor-completion problem, inside the Euclidean norm. This is possible if the embedding matrix, constructed from the incomplete time series, allows a low-rank representation or approximation, which will depend on the embedding parameters. In that case, our proposed approach allows for severe under-sampling and wide data gaps, whether that be an unintentional or deliberate aspect of a particular application. We compare our approach with direct imputation of the incomplete time series instead of approximating the latent structure of the embedding.

12:00 Charles L. Webber, Jr. Polar recurrence plots with quantifications
Standard Recurrence Plots (RPs) are displays of recurrence matrices (thresholded distance matrices) in the Cartesian coordinate system (linear). Polar Recurrence Plots (PRPs) are displays of distance matrices in the polar coordinate system (nonlinear). The usual delays, embedding dimensions, and radii are all selectable parameters for both RPs and PRPs. PRPs may be reminiscent of symmetrized dot patterns (SDPs), but they differ according to their underlying matrix mathematics. To generate intricate PRP polar plots, column vectors of the distance matrix $XR = [x_1, x_2, \ldots, x_n]$ are plotted along the radial axis which is rotated counterclockwise by $N$ equal incremental steps from 0 to 2 pi radians. The figure below plots PRPs for a continuous sine wave consisting of exactly three cycles (300 points at 100 points per cycle). Two radii thresholds are chosen as fractions of the maximum distance (A: 100%; B: 20%). The resultant patterns are both beautiful (qualitative) and feature-extracted (quantitative). Quantifications include: %recur; distance entropy; line length entropy; angle entropy. The radius parameter serves as a zooming tool to explore the minute details near the central core of the object (A: zoom out; B: zoom in). Early demonstrations of the utility of this innovative approach to recurrence dynamics will be discussed. This PDP method is merely the beginning for what may turn out to be another unique nonlinear tool for real-world systems.

[Insert Figure here]

12:20 Sebastian Wallot, Dan Mønster Multidimensional joint recurrence quantification analysis: Detecting coupling between time series of different dimensionalities
One issue with the analysis of complex systems and the interaction between such systems is that they are composed of different number of components, or simply the fact that a different number of observables is available for each system. The challenge is how to analyze the interaction of two systems which are not described by the same number of variables. The approach is to combine different types and number of time series so that they yield a matched set of data points from which coupling or correlation properties can be estimated. Here, we present multidimensional joint recurrence quantification analysis (MdJRQA), a recurrence-based technique that allows to analyze coupling properties between multivariate data sets that differ in dimensionality (i.e., number of observables) and type of data (such as nominal or interval-scaled, for example). First, we introduce the methods, and then test it on simulated data from linear and nonlinear systems. Finally, we discuss practical issue regarding the application of the method.

12:40 Lunch
14:00 Cheng-Bang Chen, Yujie Wang, Bo Peng (online) Weighted heterogeneous recurrence network analysis for complex system characterization
Recurrence Network Analysis (RNA) has emerged as a powerful and widely used tool for characterizing complex dynamic systems in various fields. By representing time series data as networks, RNA successfully captures the nonlinear and nonstationary dynamical characteristics of these systems. However, some critical network properties, including node and edge properties, have not been fully utilized in the current RNA, which reduces the full potential of model performance. To fill this gap, we proposed a novel recurrence analysis framework, Weighted Heterogeneous Recurrence Network Analysis (WHRNA), that leverages heterogeneous node properties, edge weights, and edge directions to model and characterize complex recurrence dynamics of systems. By considering these additional factors, WHRNA enhances the characterization and understanding of the intricate dynamics within the system. Simulation results demonstrate that the proposed WHRNA effectively delineates and characterizes the chaotic recurrences of nonlinear and nonstationary time series. By incorporating heterogeneous node properties, edge weights, and directions, WHRNA reveals more subtle dynamic characteristics of complex systems, providing valuable insights into the underlying mechanisms driving the system's behavior. WHRNA offers a comprehensive framework for characterizing complex dynamic systems and understanding their intricate recurrence dynamics. The proposed WHRNA framework has broad applications across various domains, including physics, engineering, finance, and biology, where the analysis of complex and nonlinear systems is of paramount importance.

14:20 Zahra Shahriari, Shannon D. Algar, David M. Walker, Michael Small Understanding recurrence with ordinal first return maps
We present a robust algorithm that does not require embedding for constructing a family of first return maps (FRM) of dynamical systems from their time series. Typically, an FRM is built using the maxima or zero-crossings of a time series. Our method is based on the recurrence of ordinal partitions, and we construct the FRM using consecutive ordinal symbols. We generate a unique FRM for each ordinal sequence and rank them using two weighted entropy-based measures to select the good ones.

Methodological Aspects 3: Parameter Selection
14:40 Rémi Delage, Toshihiko Nakata A variable recurrence detection threshold for nonstationary data
The definition of recurrence is of critical importance for qualitative recurrence plots and their resulting quantification measures. In order to mitigate the over-detection of recurrent states from tangential motion effect, one must properly select the threshold parameter and possibly post-process the recurrence plot. The former threshold selection is not trivial for nonstationary data with complex dynamics as different regions of the attractor may vary in points density or represent different dynamical behaviors. The later clean-up process, on the other hand, may alter recurrence structures containing crucial information on the system. We suggest here a bottom-up approach for recurrence detection based on the distance between following points in the phase space. The proposed threshold is easy to compute and appears to provide consistent recurrence structures from nonstationary data. Quantification measures are also less sensitive to the threshold used, making the choice of this parameter less critical.

15:00 Braden Thorne The benefits of reservoir computing embedding for recurrence analysis
Uniform delay embedding remains the standard first step in a recurrence analysis pipeline. Its formulation and dependence on just two parameters in the embedding lag and dimensions make implementation simple, however the nontrivial task of determining these parameters can inhibit one's ability to generate a good embedding in certain scenarios. One emergent alternative to uniform delay embedding is reservoir computing. Built upon a high dimensional neural network architecture, reservoir computers utilise delay embedding theory together with a randomly generated structure to reconstruct a signal's phase space in a manner that is both computationally efficient and informative. This has resulted in impressive results for time-series forecasting tasks for dynamical systems. As such, these findings warrant examination of the underlying embedding technique in fields outside of its machine-learning origins. In this talk I will introduce reservoir computing embedding and why it should be of interest to the recurrence analysis community. I will generate recurrence plots utilising reservoir computing for a few well-known systems and compare the quality of construction with traditional methods (i.e. constructions utilising the full system, unform delay embedding and no embedding). Finally, I will look towards recurrence quantification analysis to identify the specific benefits offered by such an embedding over the traditional methods.

15:20 Eugene Tan, Shannon Algar, Débora Corrêa, Michael Small, Thomas Stemler, David Walker Persistent strands as a method of selecting embedding lags
Delay embedding methods are a staple tool for analysing time series and prediction. However, its performance can be heavily dependent on the selection of embedding parameters such as embedding lag and dimension. Furthermore, time series with multiple coexisting disparate time scales do not lend well to traditional uniform delay embedding methods. This has led to the development of embedding lag selection for non-uniform delay embedding. In our work, we present a novel method, Significant Times on Persistent Strands (SToPS), that utilises the recurrences of trajectories and topological data analysis methods to extract and quantify the importance of different time scales chaotic time series. We also provide illustrative examples of its application on both synthetic and experimental data.

15:40 Coffee break
16:10 Radim Pánis, Karel Adámek, Norbert Marwan (online) Averaged recurrence quantification analysis -- Method omitting the recurrence threshold choice
Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in thetested data set with different and even very small signal to noise ratios of lengths 102, 103, 104, and 105. To make the calculations possible a new effective algorithm was developed for streamlining of the numerical operations on Graphics Processing Unit (GPU).

16:30 Felipe Eduardo Lopes da Cruz, Sergio Roberto Lopes, Thiago de Lima Prado (online) How to compute minimum diagonal length for recurrence analysis of continuous systems
Recurrence Plots (RP) are binary matrices that quantify the recurrent and non-recurrent states of a trajectory. Each element of an RP matrix, denoted by $a{i,j}$, consists of an one or a zero, indicating a recurrent or
non-recurrent pair of elements ($i,j$) of the trajectory, respectively. RP represents a visual mosaic of the recurrent and non-recurrent states of a particular trajectory.

The graphical properties of Recurrence Plots can be quantified using tools known as Recurrence Quantification Analysis (RQA), which rely on several structures embedded in an RP, such as diagonal, vertical, or horizontal line lengths. All of these quantifiers depend on free parameters, with the main ones being the threshold used to determine whether two points are recurrent and the minimum diagonal line length. One way to determine the recurrence threshold parameter (among other possible methods) is by using the concept of maximum recurrence entropy, which can turn it into a self-adjustable parameter. Here, we propose a new method for selecting an appropriate minimum length for recurrent diagonal lines ($\ell
{min}$), which is critical for determining important recurrence quantifiers such as Determinism and other related quantifiers. We discuss how to choose an adequate minimum recurrent diagonal line length to accurately compute determinism and similar quantifiers that depend on diagonal line statistics. Our analysis reveals a well-defined limit for the credible applicability of recurrence analysis based on the number of data points. Moreover, we demonstrate a clear dependence of $ell_{min}$ on the number of dynamical epochs (pseudo-periods) sampled. We also demonstrate how our method can maximize the sensitivity of determinism with respect to changes in the stationary character of the time series. Finally, we provide two experimental examples to illustrate our approach.

Applications in Earth Science & Ecology
16:50 Saureesh Das (online) Chaotic dynamics of ENSO model derived from SOI time series
The time series data of Southern Oscillation Index (SOI) for El-Nino Southern Oscillation (ENSO) has been considered for reconstruction of a differential equation model from single observed variable. To study the chaotic dynamics of the system both conventional and modern techniques of nonlinear time series analysis like Bifurcation Plot analysis and Recurrence Plot Analysis have been applied on the derived differential equation model respectively. The results are further validated by Lyapunov Exponent and Recurrence Quantification Analysis. The dynamics of the derived system is compared to the dynamics of the established El-Nino differential equation models. The model estimated from the real time series without prior knowledge about dynamics inherent in the real system, can be considered as direct evidence of chaos in the real ENSO system.

17:10 Matheus Henrique Junqueira Saldanha, Yoshito Hirata To what extent is solar activity stochastic?
The Earth lies in a surprisingly hostile environment, hence why all other planets in the Solar System, as far as we know, cannot sustain life forms. The situation is different on Earth due to numerous factors such as the particular distance from the Sun, the presence of an atmosphere, the existence of a geomagnetic field, etc. Even so, external entities still can have diverse hazardous effects on Earth. Of particular interest to us are the effects of the Sun on earthquakes. There are numerous pieces of evidence that such an effect exists, but no one has managed to successfully explain the particular mechanism by which earthquakes can be triggered on Earth due to solar influence. It is postulated that this can happen by at least three different means: i) by the gravitational force exerted by the Sun, ii) by the bursts of electromagnetic waves caused by various types of processes occurring in the Sun (e.g. coronal mass ejections), or iii) effects of irradiation that heat up the Earth's surface. Our attempts to identify the particular mechanism by which the Sun affects earthquakes begin with analyzing data concerning the daily number of sunspots in the Sun's surface, since they are known to be closely related to the temporal progress of the spikes of energy released by the Sun towards the Earth. Here we try to investigate if this temporal progress is stochastic or deterministic. Being the result of a physical process, one would expect the temporal sequence of sunspots to form a dynamical system, although with an unknown degree of what could be called noise. Of course, depending on the amount of noise and the characteristics of the underlying dynamical system, the temporal series can quickly become unpredictable. To evaluate this we calculate a recurrence plot based on a daily sunspots dataset, where the distance threshold is selected such that 20% of the plot is filled. Then, we test the presence of determinism in the plot by using the number of different patterns of recurrence triangles that appear in it, as given by Hirata (Communications in Nonlinear Science and Numerical Simulation, 2021). The results imply that sunspots are notably stochastic (p < 0.05) even when varying the time window considered (2000-2022 or 2000-2011), and since solar activity has an influence on earthquakes, we can expect some of such stochasticity to be inherited by the earthquake generating process.

Tuesday, August 29th

8:50 Welcome & miscellaneous announcements
Applications in Life Science
9:00 Annick Lesne Keynote Lecture: Recurrence plots and chromosomal contact maps: A unified approach to dynamical systems and genomics
The physical proximity of genomic sites (to each other, within the 3D structure of a chromosome) can be experimentally measured in living cells and represented as a matrix, called a 'contact map'. Such contact maps have also been used to represent and analyse the 3D structure of proteins. They are closely related to recurrence plots of dynamical systems. In particular, the same reconstruction methods can be used. The main steps of the reconstruction of the underlying structures (chromosomes, proteins or attractors, respectively) are:

(i) to compute a complete distance matrix using shortest-path distance on a weighted contact network derived from the contact map,

(ii) to use a result of distance geometry based on the three dominant eigenvectors of the metric matrix derived from the distance matrix,

(iii) or to approximate the 3D structure using multi-dimensional scaling techniques.

This reconstruction algorithm can also be adapted as a tool to enhance under-sampled contact maps.

In a different direction, analogies between the algebraic analysis (principal eigenvector of the correlation matrix) and motif analysis (topological domains seen as squares along the diagonal) of the respective contact matrices can be drawn.

Related references:

Lesne, Riposo, Roger, Cournac & Mozziconacci, Nature Methods, 11:1141 (2014).

Carron, Morlot, Lesne & Mozziconacci, Methods in Molecular Biology, 2301:317 (2022).

9:45 Claudia Lerma, Martin Calderón-Juarez, G. Hortensia Gonzalez-Gomez, Itayetzin Beurini Cruz-Vega (online) Effect of healthy aging on the quantitative recurrence plot analysis of heart rate variability
Introduction: Age strongly affects many regulatory systems, including the autonomous nervous system. An increasing predominance of sympathetic nervous activity is associated with a higher risk of chronic diseases. Heart rate variability (HRV) analysis has shown these changes in the cardiac autonomic modulation during the aging process, even in healthy subjects. Recurrence quantification analysis (RQA) of HRV has demonstrated differences in the dynamical behavior of HRV on several chronic diseases when compared with age-matched healthy controls. However, the effect of the aging process on the HRV dynamical behavior from healthy subjects has not been assessed by RQA. We evaluated the association of age with the RQA indices in a large sample of healthy adults.

Methods: ECG recordings from 1026 healthy subjects were obtained from a public database (autonomic aging database, The participants were grouped by age as follows: Group 1 (18-29 years), Group 2 (30-39 years), Group 3 (40- 49 years), Group 4 (50-59 years), Group 5 (60-69 years) and Group 6 (70 or more years). Each heartbeat was identified with the program Kubios HRV premium, and the correct identification of R waves were visually supervised. The phase space of each HRV time series was obtained using the CRP toolbox with ad-hoc embedding dimension (estimated by the false nearest neighbors method) and ad-hoc embedding delay (estimated by the mutual information function). The recurrence plot was calculated using the fixed amount of neighbors (fan) norm with a recurrence density of 0.07. Recurrence quantification analysis (RQA) indices were obtained. The association between the age groups and the mean values of each HRV index was tested by an analysis of variance with age group and sex (as independent factors) and body mass index (BMI), and mean heart rate (as covariates). P-values < 0.05 were considered significant.

Results: Determinism, laminarity, trapping time, and recurrence time type 2 increased significantly with age, while recurrence time type 1 decreased with age. These relationships with age remained significant after considering sex, BMI, and mean heart rate as confounding factors. No significant changes were observed in the mean diagonal length and Shannon entropy.

Conclusions: The aging process in healthy humans is associated with changes in the dynamic behavior of HRV that suggest higher levels of predictability, laminar states, and periodicity.

10:05 Arnaldo F. Neto, Fabio Godinho, Luiz R. T. da Silva, Andre K. Takahata, Maria S. G. Rocha, Diogo C. Soriano (online) Recurrence quantification analysis for evaluating subthalamic rhythms dynamics with application to Parkinson's disease phenotypes
10:25 Coffee break
11:00 Jiarui Li, Michiko Matsunaga, Masako Myowa, and Yukie Nagai Co-regulation of the day-long autonomic nervous system in children and caregivers – Analysis using (cross) recurrence plot
11:20 Bruno G. Straiotto, Norbert Marwan, P. John Seeley Exploring synchronisation in lower limb coordination in a rhythmic body movement: A quantitative analysis
Studies of human movement often concern movement quality and that quality may be represented by the everyday term coordination. Research reports alternatively use terms such as correlation and synchronisation. We have developed a previous study of a martial arts movement pattern through study of synchronisation within and between the lower limbs. We explored synchronisation in taekwondo players who utilise repetitive backwards-forwards movements to mount attacks on their opponents and operate speedy retreats, movements that are developed in both training and competition. Eighteen players (nine elite and nine non-elite) performed backwards-forwards movements in a simulated training environment whilst their actions were recorded in detail via motion capture using multiple cameras. Recurrence analysis involved re-representing the time-dependent signals in multidimensional space and then characterising the revisits of a movement trajectory to different sub-regions of that space. The joint probability of recurrence index ($p_j$) was then calculated for centres of mass of limb segments (foot, shank, thigh) in relation to orthogonal movement coordinates (medio-lateral, anterior-posterior, vertical directions). Application of surrogation to the recurrence data indicated that derived $p_j$ values for elite and non-elite groups were deterministic in origin and not the result of data noise ($p < 0.01$). Interlimb pairwise segment relations yielded $p_j$ values in the range 0.23 to 0.29; intralimb relations in the range 0.24 to 0.40. Nonparametric statistical analysis combining Mann-Whitney and Kruskal-Wallis tests along with Bonferroni corrections directly indicated statistically significant differences between elite and non-elite groups for interlimb $p_j$ values and analogous differences for some comparisons for intralimb segment use ($0.05 > p > 0.01$). The potential of recurrence analysis for studies of limb segment synchronisation is revealed by this study. The method may be fruitfully extended in application not only to athletic movement but to transitions in coordination for general members of the public caused by ageing and pathology.

11:40 Daichi Shimizu, Takeshi Okada Visualization and quantification of the coordination of rhythmic and back-and-forth movements among dancers depending on the competitive context
The importance of interaction among performers has been suggested in performing arts such as dance and music. Several studies have attempted quantitative investigation of this interaction from the perspective of synchronization and coordination. However, there have not been sufficient attempts to examine the context-dependent dynamic changes of the above interactions and the interaction among multiple mediums. This study investigated the coordination of rhythmic and back-and-forth movements in an expert dancer's battle scene and the correspondence between these two mediums. The posterior neck movements of each dancer were measured by a motion capture system. We analyzed rhythmic and back-and-forth movement coordination using Cross Recurrence Plot (CRP) and Cross Recurrence Quantification Analysis (CRQA) and these two mediums' correspondence using Joint Recurrence Plot (JRP) and Joint Recurrence Quantification Analysis (JRQA). Further, the coordination and correspondence of these movements were quantified using RR (recurrence rate), L (averaged diagonal line length), max L (maximal diagonal line length), and ENTR (Shannon entropy). The results showed that the coordination of rhythmic and back-and-forth movements changed according to the intensity of the competitive context, such as before, after, and during the battle. The correspondence between the two mediums also showed the same tendency. Specifically stated, while constant coordination with long durations was frequently observed before and after the battle, a variety of coordination with very short durations was observed during the battle. This diverse and fine-grained coordination and correspondence between dancers during the battle are considered to represent a delicate and sensitive interaction in the dance performance.

12:00 Magdalena Szmytke, David Lopez Perez, Przemysław Tomalski Changes in the complexity of infantile motor brain activity in response to audiovisual speech
Motor-related brain activity is broadly explored in social neuroscience, brain-computer interface, and recently in speech perception. This activity, related to both perception of the action and its execution, can be measured by EEG and reduction in the power of oscillatory brain activity in the mu frequency band (Pfurtscheller & Da Silva, 1999). Recently Pitsik and collaborators (2021) hypothesized that motor activity is associated with the suppression of random fluctuations in the mu band. Their results showed an increase in EEG signal regularity calculated by Recurrence Quantification Analysis (RQA). In the current study, we aimed to test whether the complexity measures are sensitive enough to detect changes in the neural activity of infants in response to audiovisual speech stimuli. Infant data is challenging, i.e., poor signal-to-noise ratio and a limited number of trials and participants (Ng et al., 2022).

To this end, we studied the changes in the complexity of neural activity in two groups of infants: 5 to 6 month-olds ($n=19$) and 9 to 10 month-olds ($n=17$), in which we expected differences in motor system involvement during speech processing. The stimuli consisted of congruent and incongruent audio-visual speech displayed in an upright and inverted position. The motor involvement was expected to be more engaged over the left hemisphere and in younger infants, who do not have large speech production experience, and to be higher in the upright position. We used a 64-channel EEG system and measured changes in power in the infantile mu frequency band (6 to 10 Hz; Cannon et al., 2015). Additionally, since the area involved in speech processing contains several electrodes, we chose a multidimensional approach and applied Multidimensional RQA (MdRQA; Wallot et al., 2016). MdRQA allows studying changes in the complexity of multiple time series ($n>2$) simultaneously.

The mixed ANOVA results showed that the measure of the mean line (ML), which depicts overall system stability, differs between two groups of infants ($p<0.05$) and hemispheres ($p<0.05$), whereas the entropy measures showed a reversed pattern of results for hemispheres. ML increased also in older infants in response to upright faces ($p<0.05$), no difference was found for incongruent stimuli.

Obtained results confirm the increase in the regularity of EEG signals associated with infant motor engagement. The results also indicate that MdRQA can be a useful and sensitive method to capture motor involvement differences even in demanding groups of participants and under tasks that are not movement specific.

12:20 Monika Tschense, Sebastian Wallot Regularity in eye movement data during text reading
12:40 Lunch
14:00 Narayan Puthanmadam Subramaniyam, Jari Hyttinen Network-based time series measures
14:20 Alon Tomashin, Ilanit Gordon, Giuseppe Leonardi, Sebastian Wallot Distinguishing between fractal dimensions in time series using RQA – Analysis technique and its application in psychophysiology
Fractal properties in time series of human behavior and physiology are ubiquitous, and several methods have been proposed to capture such properties in the past decades. Fractal properties are marked by similarities in statistical characteristics over time and space, and it has been suggested that such properties can be well-captured through recurrence quantification analysis. However, no metrics to capture fractal fluctuations by means of recurrence-based methods have been developed yet. In this presentation, we propose and test several approaches to quantifying fractal fluctuations in synthetic and empirical time-series data using recurrence-based analysis -- Fractal Analysis via RQA (FARQA). We show that such measures can be extracted based on recurrence plots and contrast the different approaches in terms of their accuracy and range of applicability. Furthermore, we will demonstrate FARQA on both univariate inter-tap interval and multivariate heart rate time series.

15:00 Poster session
19:00 Banquet

Wednesday, August 30th

8:50 Welcome & miscellaneous announcements
Applications in Physics
9:00 Jürgen Kurths Keynote Lecture: Recurrence analysis in the context of complex networks
I will discuss the very successful mutual interactions of recurrence plots and their analysis with achievements of complex network theory.

9:45 Matheus R. Sales, Michele Mugnaine, Jose D. Szezech Jr., Ricardo L. Viana, Ibere L. Caldas, Norbert Marwan, and Juergen Kurths (online) Characterization of stickiness in quasi-integrable Hamiltonian systems by an entropy-based measure of the recurrence plots
The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems, characterized by the long time spend by a chaotic orbit when near enough a periodic island. We propose the use of an entropy-based measure of the recurrence plots (RPs), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions, the Chirikov-Taylor standard map. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and find that each mode corresponds to the motion around islands of different hierarchical levels.

Methodological Aspects 4: Quantifying Recurrence Properties
10:05 Xuegeng Mao Multifractal recurrence lacunarity and weighted determinism analysis of order recurrence plot
10:25 Coffee break
11:00 Igari Daiki, Shimada Yutaka Effect of graph distances on recurrence quantification analysis of temporal networks
A network consisting of sets of vertices and edges is an effective tool to analyze complex relationships underlying collective behavior in real-world systems, for example, relationships of friends, and e-mail activity patterns. Many of these networks change their structures with time. A set of network snapshots in time is called a temporal network. Recent researches on human face-to-face interactions revealed that network snapshots in the temporal networks of the face-to-face interactions include similar components, which implies that real temporal networks have a recurrence property. On the other hand, it has been revealed recently that graph distances defined as distances between two networks, are effective in analyzing spatio-temporal properties of temporal networks. Besides, graph distances allow us to analyze temporal networks through the recurrence plot. However, it is still unclear which graph distance is the most effective in analyzing recurrence properties of temporal networks through the recurrence plots. To address this issue, we investigated which graph distance succeeds in detecting the recurrence properties of temporal networks through recurrence plots. In numerical simulations, we generated temporal networks by a mathematical model that can reproduce several statistical features of human face-to-face interaction networks. We then obtained their recurrence plots by calculating a graph distance matrix whose elements are graph distances between each pair of network snapshots in temporal networks. We quantified the obtained recurrence plots by measures of the recurrence quantification analysis methods such as DET. Generating recurrence plots of temporal networks by several graph distances, we discussed which graph distance is more effective in capturing the recurrence properties of the temporal networks.

11:20 Sebastian Wallot Hierarchical joint recurrence quantification
The field of joint action research, a brance of cognitive science and psychology, is concerned with the investigation of behavioral and physiological coordination of groups of humans that work together on a task. One of the problems in this field is the fact that the dynamics a nested (e.g., participants coordinate the movement of their two hands on the level of the individual, but also with regard to the (hand) movements of the other members of the group). Another is, that sometimes not only the shared dynamics (e.g., sychonrization of hand movements during task within the group) are important for goal archivement, but also individual deviations from these shared dynamics (e.g., that one participant is not synchronizing with group activity for a certain period of time). Here, I present the method of hierarchical joint recurrence quantification analysis (HJRQA), which aims to address this data analytic issue. It proceeds by sequentially joining recurrence plots at different hierarchical levels (e.g., first hand movments within a person, and then joint hand movements of all group members within a group). Moreover, it allows to derive measures of individual activity by computing residual recurrence plot, which capture systematic aspects of the dynamics that deviate from the joint dyamics within a person or within a group. The method will be illustrated on simulated data. This is work in progress - discussion of the utility of the method or potential improvments are welcome!

11:40 Tommaso Alberti, Davide Faranda, Reik V. Donner Scale dependence of recurrence-based point-wise fractal dimension estimates in chaotic systems
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of deterministic chaos at large scales and an apparently random behavior at small scales. These features are commonly investigated quantitatively by studying the properties of the underlying attractor, the compact object asymptotically hosting the trajectories of the system with their invariant density in phase space. This multi-scale nature of natural systems makes it practically impossible to get a clear picture of the attracting set. Indeed, it spans over a wide range of spatial scales and may even change in time in case of a non-stationary dynamics.

In this work, we employ empirical mode decomposition for iteratively reconstructing variability by successively including longer and longer time-scales. Subsequently, we employ the concept of recurrences in phase space along with a peaks-over-threshold approach to the negative logarithmic distances for characterizing the extreme value characteristics of recurrences, which allow defining an estimate for the local (point-wise, instantaneous) fractal dimension of the system under study. We demonstrate the usefulness of this approach for three different cases: (1) the paradigmatic Lorenz-63 system along with two stochastic versions thereof, (2) experimental fluid turbulence data and (3) high-resolution satellite measurements of the solar wind magnetic field components. In all three cases, we find interesting phenomena related to the spatial distribution of fractal dimensions and the dependence of its mean value on the maximum time scale considered.

(1) T. Alberti, D. Faranda, V. Lucarini, R.V. Donner, B. Dubrulle, F. Daviaud: Scale dependence of fractal dimension in deterministic and stochastic Lorenz-63 systems. Chaos, 33, 023144, 2023.

(2) T. Alberti, F. Daviaud, R.V. Donner, B. Dubrulle, D. Faranda, V. Lucarini: Chameleon attractors in turbulent flows. Chaos Solitons Fractals, 168, 113195, 2023

(3) T. Alberti, D. Faranda, R.V. Donner, T. Caby, V. Carbone, G. Consolini, B. Dubrulle, S. Vaienti: Small-scale Induced Large-scale Transitions in Solar Wind Magnetic Field. The Astrophysical Journal Letters, 914, L6, 2021

Applications in Engineering
12:00 Arkadiusz Syta, Jacek Czarnigowski, Piotr Jaklinski, Norbert Marwan Recurrence quantificators in misfire detection in a small aircraft engine
Misfires in internal combustion engines are a frequent issue where one or more cylinders fail to ignite properly, leading to decreased engine performance, increased fuel consumption, and potential damage. A piston failure can be perceived as a disturbance in the repeatability of the engine operation, leading to changes in non-linearity. To study the dynamic behavior of the system over time, Recurrence Quantification Analysis (RQA) is employed in nonlinear time series analysis. The technique involves creating a recurrence plot (RP) from the time series data, which illustrates the temporal evolution of the system's states. RQA is capable of detecting changes in the system's behavior, such as transitions from regular to chaotic or from stable to unstable states. In the context of detecting piston failure, RQA can be used to identify patterns in the engine's vibration signals that are indicative of such failure. By placing sensors at different locations in the engine, vibrations can be recorded corresponding to separate engine states, including all cylinders working correctly and one of the cylinders being switched off, at various engine speeds. The RQA indices can then be used as non-linear features to classify the engine condition utilizing a linear model. Determining the RQA statistics on component signals with frequencies centered around the dominant ones increases the dimension of features and leads to higher accuracy in damage detection and identification of a cylinder with a misfire.

12:20 David DeFilippo Coupled oscillator systems and the interactive synthesis of intentional musical sequences
This talk will present the concept of a Coupled Oscillator System (COS). Systems ranging in dimension from 3 to 6 oscillators will be described mathematically and analyzed with recurrence plots (RP) and recurrence quantification analysis (RQA). A COS embeds oscillators in a memoryless topology of velocity based couplings terms. Systems of sizes 3 and 4 will be used to demonstrate the importance of a specific topological organization and distribution of kinds of coupling terms in the generation of self-organization and especially the emergence of the staccato demarcations of hyperplane searches indicative of first order phase transitions. Systems of size 5 and 6 exhibit, under certain parameterizations, the onset of a quasi-attractor landscape with an itinerant closed-loop trajectory generating temporal sequences of attractor to attractor transitions. When RQA gives high laminarity statistics and the RP shows that laminarity located at the edges of quasi-attractors, chaotic itinerancy (CI) [Kaneko, 1990] is present. Orderly CI has been shown to reflect intentional states and may also reflect internal (cinematographic) representations of experience [Freeman, 2006; Freeman and Vitiello, 2006; Freeman and Quian Quiroga, 2012]. Another cognitive process of interest is the spontaneous activity of the default mode network, such as mind wandering and imagination [Mason et al., 2007] that exhibits closed-loop trajectories. Neuroimaging of mental idling tasks show CI-like switching between mental states that might reflect the dynamics of sensory expectations [Kenet et al.,2003]. Of particular interest to musical performance is the interactive synthesis (where the a human in the loop changes the parameters of the model in real-time) of musical sequences that imitate a sense of intentional organization. Borrowing from extended mind theory [Clark and Chalmers, 1998] the talk will conclude with a discussion of extended intentionality based on parity between CI in neural dynamics and CI in the dynamics of the COS. Finally, the interaction will be viewed from a perspective of embedded cognition and stigmergy showing how RQA based sonic cues play a causative role in the co-creation of the musical dynamics in tradition of the experimental electronic genre.

12:40 Lunch
14:00 Zezhou Liu, Jinzhao Liu Rail corrugation detection based on time-frequency recurrence plot and graph convolutional neural networks
14:20 Bartlomiej Ambrozkiewicz, Arkadiusz Syta, Grzegorz Litak, Anthimos Georgiadis, Alexander Gassner, Nicolas Meier Recurrence analysis in the diagnostics of rolling-element bearings
Rolling element bearings exhibit a complex dynamics that can be difficult to analyze, particularly when attempting to detect minor changes caused by time-dependent conditions. However, recurrence analysis in the form of recurrence plots and recurrence quantification analysis provide powerful tools for qualitatively and quantitatively estimating the dynamical response of ball bearings. These methods are highly sensitive to changes in the bearing's features, making them well suited for analyzing the behavior of ball bearings with variable radial internal clearance and eccentricity. Our analysis involved measuring the dynamical response of a rolling-element ball bearing with a wide range of radial internal clearance and at different speeds and mathematical model analysis by the change of the eccentricity level. By applying recurrence-based methods, we were able to identify specific trends in the bearing's behavior based on its radial clearance and eccentricity. We are able to identify an optimum range of clearance where the bearing exhibited optimal dynamical behaviour and the impact of the eccentricity on the bearing's dynamics showing the transition between periodic and chaotic solutions. With further development, this method could be applied in a range of settings to improve the reliability and performance of rolling-element bearings.

14:40 Denis Stanescu, Angela Digulescu, Cornel Ioana (online) On the definition of the phase diagram based entropy for transient signal characterization
The quantification of the information from the phase diagram domain is a current research topic. One of the most used methods is the Recurrence Plot Analysis which offers a two-dimensional binary representation of the analyzed signal. We propose to expand the way of quantifying the information, using a probabilistic approach in the performed analysis in order to define the phase diagram based entropy. Using this analysis method, new interesting information about transient phenomena is highlighted in different fields of study.

15:00 Hamed Hoorijani (online) Real time recurrence-CFD: Accelerating multiphase flow simulations using recurrence analysis
15:20 Kamal S. Kumar (online) Nonlinear dynamical combustion stability analysis of a CNG-diesel RCCI engine using recurrence plots
With urbanization and economic expansion, there is a growing need for cleaner and more efficient engines that comply with the strict demands of emission and fuel efficiency standards. Advanced combustion modes are one of the notable choices in improving emission standards and efficiency in Internal Combustion (IC) engines. However, combustion control and stability remain significant roadblocks. This study aims to identify the most influential engine parameters capable of capturing cyclic variability (Chaotic Behavior) in IC engines using Recurrence Plotting (RPA) and Quantification Analysis (RQA). The required data for this analysis was collected from the Advanced Engine and Fuel Research Laboratory (IIT Ropar), which comprised time series data for 1000 consecutive cycles of different parameters (IMEP, Pmax, PRR, and THR). This data was derived from a CNG-diesel Reactivity Controlled Compression Ignition (RCCI) engine operating over a wide range of injection timing. To investigate the relation between cylinder-to-cylinder and cycle-to-cycle variability, Statistical Analysis using frequency distribution, histogram, coefficient of variation, and standard deviation, are carried out in sync with RPA. One of the objectives of this study is to utilize the results of RPA to train a neural network for the classification of stable engine configurations and aid in the development of a framework capable of automating the stability analysis process. The desired outcome of this research is to develop effective strategies for improved engine stability, performance, and emission control.

15:40 Romuald Mosdorf, Gabriela Rafalko, Hubert Grzybowski, Pawel Dzienis (online) Microchannel heat transfer stability assessment using the microstates entropy recurrence plot diagonal lines
In the paper, non stationary fluctuations of the heat flux transferred by boiling water in parallel microchannels covered with a steel mesh were analyzed. The use of a steel mesh covering the microchannels allows steam to escape from the channels and by evaporation of thin layers of liquid covering the wires of the mesh [1] the temperature of the boiling water is lowered. These processes induce an increase in the average value of the heat flux consumed by the exchanger, however, they generate its fluctuations. The paper analyzes the character of the fluctuations of the heat flux transferred by the exchanger in the case of different mesh wire covers (AlN, CrN and SiO2).

A wide range of changes in the frequency of the heat flux causes the diagonal lines created on the recurrence plots by low-frequency changes in the heat flux to be intermittent as a result of the changes in the state of the system caused by processes occurring at high frequencies and relatively low amplitudes. Such interruptions of diagonal lines are often not associated with changes in flow pattern, thus the use of classical methods of recurrence plots analysis does not allow for the identification of changes in flow patterns. Therefore, for the analysis of diagonal lines, the concept of entropy of microstates defined in [2] was used, which is determined in the surroundings of successive diagonal lines. As a result, changes in entropy of microstates of diagonal lines as a function of time shift were obtained. Such analysis made it possible to estimate the frequency of changes in the flow patterns in microchannels.

The results give reason to state that the type of a thin layer of the mesh influence the disorder of the microstates in the surroundings of diagonal lines and the fragmentation of flow patterns and this way affects the heat flux transferred by the exchanger.


1. Li, C., Peterson, G. P., and Wang, Y., 2006, Evaporation Boiling on a Capillary Wick I, Wick Thickness Effects, ASME J. Heat Transfer, 128, pp. 1312 1319.

2. G. Corso, T. L. Prado, G. Z. dos S. Lima, S. R. Lopes, A novel entropy recurrence quantification analysis. arXiv 1707.00944 stat.OT

16:00 Closing

Poster Session

Poster 1 Mehdi Akbarzadeh, Sebastian Oberst, Shahrokh Sepehrirahnama, Ben Halkon Recurrence plots for the analysis of nonlinear dynamical behavior of a particle trapped in an external induced radiation force field
Understanding physical phenomena in nature depends on observing, measuring, analyzing and, if possible, predicting and finally understanding the expressed patterns. Acoustic radiation forcing in air is an important nonlinear acoustic phenomenon and can be used for non-contact sub-millimetre and micro-vibrational, low force, excitation of particles. In a host fluid and due to the interaction between incident acoustic with scattering waves, acoustic radiation forces cause momentum transfer from the fluid to the particle.
In this study, a nonlinear equation of motion of a trapped particle and object (below but close to the subwavelength limit) in an acoustic radiation force field is derived explicitly with its constants being defined by the object itself, the fluid, the acoustic wave, theoretically and experimentally. By changing the viewpoint from the acoustic field to the dynamics of a levitated object, we question how the dynamical behaviour of the particle changes.

We extract from clean, and noise contaminated theoretical data (bottom-up, explicit model), as well as experiments using the TinyLev device, sets of ordinary differential equations using the Sparse Identification of Nonlinear Dynamics (SINDy) method and we apply nonlinear time series analysis, especially recurrence plots, to classify our particle behaviour in periodic and chaotic regimes at different bifurcation points. We use objects below, and above the wavelength limit and monitoring the variation of coefficients. By using the recurrence plot generated adjacency matrix, we form recurrence networks and search for motifs which we use to classify the dynamics which we use to qualify our results. Findings indicate that SINDy coefficients can be extracted for noisy data, and as expected, that objects ($ka \sim 1$, $k$ being wavelength and $a$ being the object radius) change show greater deviations to the theory than particles ($ka \ll 1$). Periodic and chaotic data can be used to extract equations, depending on noise, while the detection of motifs remains possible and indicates a viable way of classifying the dynamics of noisy data. Our analysis of the coefficients highlight important sensitivity changes over different bifurcation parameters. How the sensitivity changes are related to various physical effects is discussed by comparing the explicit modelling approach with the nonlinear time series analysis results.

Poster 2 Itayetzin B. Cruz-Vega, Martin Calderon-Juarez, G. Hortensia Gonzalez-Gomez, Claudia Lerma Heart rate variability dynamics behavior before and after percutaneous transluminal coronary angioplasty: Recurrence plot analysis approach
Introduction: Several characteristics of heart rate variability (HRV) of patients with transient myocardial ischemia or myocardial infarction are associated with a higher risk of mortality. However, the effect of percutaneous transluminal coronary angioplasty (PTCA) treatment on the HRV dynamical behavior is unknown. The objective of this work is to describe the dynamics behavior of HRV by recurrence plot analysis before and after PTCA.

Methods: ECG recordings from 68 elective patients to receive PTCA were selected from the public STAFF III database (, which were processed by three trained observers. The correct identification of R waves was visually supervised in the Physio Zoo platform. Afterward, an adaptive filter was applied to identify and replace RR intervals from ectopic heartbeats with normal RR intervals. Embedding dimension and embedding delay were estimated for each time series by the false nearest neighbors method and mutual information function, respectively. Then, the recurrence plot was calculated using the norm fixed amount of neighbors (fan) with a recurrence density of 0.07. Recurrence quantification analysis (RQA) indices were obtained. To complement the HRV description, the standard time domain indices, mean and standard deviation (meanNN and SDNN) were also calculated. Data are shown as mean $\pm$ standard deviation, and mean values before and after PTCA were compared by paired t-tests. $p$-values $< 0.05$ were considered significant.

Results: MeanNN ($0.883 \pm 0.150$ vs $0.857 \pm 0.134$) and SDNN ($0.034 \pm 0.018$ vs $0.024 \pm 0.013$) decreased significantly after PTCA, indicating an increase in heart rate and a decrease in overall variability. Regarding RQA indices, after PTCA, significant changes were observed in determinism ($0.669 \pm 0.164$ vs $0.739 \pm 0.158$), laminarity ($0.687 \pm 0.192$ vs $0.761 \pm 0.165$), trapping time ($3.341 \pm 0.753$ vs $3.718 \pm 0.975$), and recurrence time type 1 ($9.814 \pm 2.322$ vs $8.539 \pm 2.735$). No significant changes were observed in mean diagonal length, Shannon entropy, and recurrence time type 2.

Conclusions: In patients with transient ischemia, the PTCA procedure modifies HRV dynamics behavior increasing the occurrence and permanence in certain states, while decreasing the recurrence time.

Poster 3 Reik V. Donner, Davide Faranda, Tommaso Alberti Transient nature of local dimension estimates from recurrences in phase space
Previous works have suggested several ways to estimate point-wise fractal dimensions of chaotic systems from the recurrence properties of time series. As two notable approaches, we consider here the local clustering dimensions of recurrence networks (Donner et al., 2010, 2011) and the instantaneous fractal dimensions obtained by applying extreme value theory to recurrence distances in phase space (Faranda et al., 2017). Motivated by apparent mismatches between the spatial patterns of both characteristics found in the original publications for the classical Lorenz-63 system, we critically re-assess the previously reported spatial patterns and their hypothesized relationship with weakly repulsive lowest-order unstable periodic orbits. Indeed, systematic numerical studies using different recurrence thresholds and time series lengths demonstrate that the local dimension estimates converge (at a relatively slow rate) to a globally uniform pattern reflecting the expected monofractal nature of the system and the associated unique value of the fractal dimension. Our results underline the known difficulty of obtaining stable estimates of fractal dimensions from insufficiently long time series, which applies even further complicated for local dimension estimates. At the same time, they contribute to clarifying the potentially useful link between the usually considered transient estimates and the problem of identifying the location of weakly repulsive unstable periodic orbits.

Poster 4 Reik V. Donner, Sabrina Hempel Recurrence analysis of methane emissions of naturally ventilated cattle buildings
Poster 5 Kentaro Kodama, Daichi Shimizu Multi-timescale recurrent structure in rap lyrics
This study, evaluated multi-timescale (MT) recurrent structures by analyzing rap lyrics containing recurrent structures (i.e., rhyme) at MT. The MT recurrent structure is a common feature of a rappers' rhyming, as rhymes can appear on not only a single local timescale, such as every four beats, but also multiple global timescales, such as every eight or sixteen beats such multi-timescale rhyming is important for evaluating rap performance.

A previous study investigated rap performance using recurrence analyses (Kodama et al., 2021) to evaluate the relationship between language and body movement. The study integrated categorical data (lyrics), with continuous data (motion), by adding temporal information (time stamps) to the categorical data and applying joint recurrence analysis methods to visualize and quantify language-motion coupling during rap performance. However, MT recurrence, which is often observed with rap music, has not yet been investigated. Thus, the present study is the first to evaluate MT recurrence using data extracted from rap lyrics.


Data: English or Japanese rap lyrics.

Analyses: Categorical Recurrence Plot and Recurrence Quantification Analyses

Measure: The Multi-Timescale Index (MTI, proposed in this study)

Concept: We examined the MTI based on the vertical distance from the central diagonal line to each recurrence point of the recurrence plot, where a short distance indicates a short timescale and a long distance indicates a long timescale.


This is an ongoing study, and results will be presented at the symposium.


This study contributes to the evaluation of rap performance. Further investigation should be conducted regarding recurrence at the level of concept and meaning in lyrics (Angus et al., 2012). According to a previous study, language-body coupling should be investigated using the proposed indexes, which can lead to a deeper understanding of complex human behaviors, such as rap performance. Moreover, MT recurrence can be examined not only in music, but also in more general data, such as natural conversation. Theoretically and empirically, MT recurrence should also be discussed in line with fractal structure (Webber, 2012) in the future.

Poster 6 Kentaro Kodama, Kazuhiro Yasuda, Ryosaku Makino Application of recurrence analysis to patient-therapist coordination during gait rehabilitation
Poster 7 Ryota Nomura Testing the reliability of expert stage performances using a cross recurrence plot
Fascinating stage performances entertain large audiences. The aim of this study was to identify the strategies by which an expert storyteller adjusts their performance by using nonlinear timeseries analysis. Two of the same performances, delivered to two different audiences by the same solo performer on a single day, were analyzed. The performances were regarded as common inputs to the perceptual and cognitive systems of each participant, and their spontaneous blink timepoints regarded as the output point process of these systems. The blinks of audience members recorded in situ (Nomura et al., 2015a) and those of participants recorded during the experiments (Nomura et al., 2015b) were reanalyzed. Superposed recurrence plots (Nomura et al., 2022) were applied to the blink rates, which were calculated using the blink timepoints of multiple spectators, to reconstruct the common inputs. The results demonstrated that the generalized synchronization between the reconstructed inputs was high. Thus, the appeal-power of the performances, in terms of attracting the participant's eye, were very similar between each of the performances. Additionally, a cross recurrence plot between these reconstructed inputs detected the diagonal component of the recurrence throughout the performances. These results suggest that the performers used a strategy of stretching-and-shortening in accordance with the response from their audience, rather than a temporally precise strategy of performing. The performer's strategy was discussed from the viewpoint of reliability, as an indicator of expertise.

Poster 8 Masanori Shiro Amount of operators connecting columns in a recurrence plot
Each column of a recurrence plot is a binary row. We randomly choice some columns (or rows) of a recurrence plot and connect them with AND, OR, and NOT operations to see if we can represent other columns. We use a greedy algorithm to obtain the arithmetic representation at a practical calculation.

In this report, we evaluate the amount of arithmetic representations obtained for the Logistic map, random sequences, AR models with dynamical noise, and simple sinusoids, in terms of the amount of NAND operators required (Figure). Recurrence rates were fix to 0.03 and 0.1, and the length of the time series ranged from 100 to 40,000 points. The value of each point in the time series was normalized from 0 to 1.

Surprisingly, the AR model with dynamical noise required the most operators other than random sequences. Furthermore, we found that the AR model was sensitive to even small amounts of dynamical noise.