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11th International Symposium on Recurrence Plots 2025

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(Tentative) Conference Programme

The time for talks is 17 min, plus 8 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.

Wednesday, September 10th
Thursday, September 11th
Friday, September 12th
Posters
Select Timezone:

Wednesday, September 10th
8:30 Registration
9:00 Opening
Methodological Aspects
9:10 T. L. Prado Keynote Lecture: Recurrence Microstate Analysis Quantification
Data is fundamental in science. Furthermore, the correct evaluation of the data properties can reveal the intricate nature laws, social mechanisms, neuronal dynamics phenomena to cite a few. In physics, a fundamental characteristic of most dynamical systems is the recurrence of similar events, which are governed by physical laws, linear and nonlinear interactions in combination with stochastic perturbations. Recurrences can be quantified in several ways, but here we aim to show a particular form that evaluate the statistics of motifs from the recurrence plot (RP) matrix that we call recurrence microstates (RM). In the last few years we developed quantifiers and protocols to apply in many research areas that range from magnetization phenomena in nanomaterials, EEG data analysis to machine learning algorithms of classification. Here we will present these new methods, technical improvements and connections with traditional recurrence quantification analysis (RQAs). Finally, we also present results from well known dynamical systems and real data analysis.
9:55 Jerome Daquin, Tamas Kovacs (online) The divergence measure of recurrence plots as chaos indicator for conservative systems
Distinguishing regular from chaotic orbits in conservative dynamics has catalyzed a large body of literature given its importance in various fields, ranging from planetary architectures, fluid dynamics or plasma physics to name but a few. Several well-established methods for detecting chaos rely on indicators derived from the dynamics of the deviation vector, such as the fast Lyapunov indicator, the smaller alignment index, and the mean-exponential growth of nearby orbits, among others.
The potentials of recurrence plots (RPs), and their associated quantitative measures of recurrence quantification analysis, remain largely unexplored in the context of conservative dynamics. In the development of the RP literature, the divergence measure (DIV), related to the inverse of the maximal diagonal length, has been considered to be a gauge of chaotic dynamics. Later, however, it was recognized that its relationship with the maximal Lyapunov exponent is not that straightforward. This contribution aims to assess the practical effectiveness of the DIV measure as chaos indicator.

As a first step, we present an extensive comparison of the DIV measure with the fast Lyapunov indicator based on numerical explorations of the standard map, a paradigmatic 2 dimensional parametric discrete model for Hamiltonian chaos. By screening a large volume of orbits together with the nonlinearity parameter, we compare the performance of the two metrics across a variety of dynamical regimes in the original 2-dimensional phase space. Convergence properties of the DIV measure will be discussed, together with thresholds selection to classify orbits as regular or chaotic. Although the orbit lengths in our study are not particularly short, we emphasize that the number of iterations is also not excessively long. Specifically, we assess the performance of DIV as a chaos indicator using RPs computed with 500 and 1,000 data points. This approach represents a step toward potential real-world applications of the methodology.
10:20 Cara Bielig, Aljoscha Rheinwald, Norbert Marwan (online) Recurrence Lacunarity of two-dimensional Data
Even though recurrence plots are a well-known tool to analyze one-dimensional time series or phase-space trajectories, recurrence plots can also be created from two-dimensional data such as greyscale images or spatial data. The structure of the now four-dimensional recurrence plot and, thus, the two-dimensional data can be quantified with the known measures of the recurrence quantification analysis, while their interpretation is slightly different for two-dimensional data. Recurrence Lacunarity (RL) is a relatively new member of the recurrence quantification analysis and has been applied to one-dimensional data to successfully detect regime shifts in dynamical systems, but it has not yet been applied to recurrence plots of two-dimensional data. To investigate the behavior of this measure for two-dimensional data, this talk will present the RL of representative two-dimensional patterns as well as its use in a real-world application given by elevation and slope values of selected river catchments that are expected to differ in their topographic structure. This will show how structural changes in the two-dimensional data can be detected and quantified by the RL.
10:45 Coffee break
11:15 Charles L. Webber, Jr. Polar Recurrence Plots on Collatz Sequences Devoid of Exact Recurrences
Webber (2023, 2025) first described Polar Recurrence Plots (PRPs) which splay out recurrent points in polar coordinates. Even if the system consists of a set of unique points with no recurrences, meaningful quantitative measures can still be extracted. Such systems may be unstructured stochastic noise or structured deterministic vectors. In this latter context the Collatz conjecture was implemented which states that every positive integer ($P$) can be transformed into integer $1$ by following two simple rules:
\begin{equation}f(P) = \begin{cases}
\frac{P}{2} & \text{if } P \text{ is even} \
3P + 1 & \text{if } P \text{ is odd}
\end{cases}\end{equation}

For example, if the initial seed $P = 13$, the resultant sequence is: 13-40-20-10-5-16-8-4-2-1 (10 points or 9 steps). Likewise for integers 7, 9 and 10, the corresponding numbers of points are 17, 20, 108. Note that in each case the last 3 points, 4-2-1, form an unending loop: 1-4-2-1-4-2-1-4-2-1-4- etc. Thus the process must be halted when integer 1 is first encountered.

Over one million integers ($P = 2^1 \ldots 2^{20}$) were used to seed the iteration processes (Collatz transient). The largest number of points of all the sequences was 525 points for integer 837,799. And the peak value reached was 90,239,155,648 for integer 1,042,431. The data set was separated into 82,025 prime (7.82%) and 966,550 anti-prime (92.18%) integers. Trajectory points for each integer were submitted to PRP analysis from which twelve quantitative variables were computed: 1) length; 2) maximum; 3) sequence position of maximum; 4) angle to maximum; 5) Area_P; 6) Ent_Dist; 7) Ent_Length; 8) Ent_Angle; 9) number turns up; 10) number turns down; 11) %turns up; 12) %turns down.

Polar Recurrence Plots of the Collatz sequences presented as semi-concentric circles with spikes pushing outward in the radial direction of large local peaks. The longer the sequence and the larger the maximum, the more regular and rounded were the polar-plot circles. The quantitative variables identified various characteristics of the vector sequences, but no outstanding differences could be detected between the trajectories of prime and anti-prime integers. Scatter plots between paired quantifiers yielded unique patterns worthy of further study. All Collatz trajectories beginning with $P = 2$ to $1,000,001$ ended in $1$. However, the Collatz conjecture remains an unsolved problem in mathematics for all positive integers to infinity despite many false claims to the contrary.
11:40 Emmanouil Kasotakis, Martijn Boussé, Philippe Dreesen, Joel Karel, Pietro Bonizzi, Ralf Peeters Beta-Divergence-Based Recurrence Plots for Stuttering Audio Analysis
Recurrence plots (RPs) are a powerful tool for visualizing and analyzing the dynamical structure of time series. Traditionally, RPs rely on the Euclidean distance to highlight similar patterns in the structure of a time series. However, this may be suboptimal for certain data types such as audio signals, which are often non-negative, exhibit large amplitude fluctuations, and follow different (noise) distributions. To address these limitations, we explore beta-divergence-based recurrence plots (BRPs), where similarity is computed via a beta-divergence, which is a flexible class of distance-like measures that interpolates between Euclidean distance, Kullback-Leibler, and Itakura-Saito divergences. This enables a more tailored approach to recurrence analysis that can amplify or suppress specific signal properties based on the chosen beta value. Such flexibility also opens promising directions for applications in audio, spectral, and count-based data. In this work, we focus on the domain of speech audio, and in particular, stuttering classification. We hypothesize that BRPs can uncover subtle temporal structures related to stuttering patterns that are less discernible in conventional RPs based on Euclidean distance.
In our current study, we apply BRPs to the SEP-28k podcast dataset, which contains labeled stuttered and fluent speech segments. The methodology builds on a structured recurrence quantification analysis (RQA) pipeline. The RPs of speech segments are first qualitatively analyzed to evaluate how the embedding dimension, time delay, beta value, and recurrence threshold play a role in discerning stuttering patterns and how those patterns are propagated in the RQA values. Next, we compute a comprehensive set of RQA features, such as recurrence rate, determinism, laminarity, entropy, etc. for various values of beta. These features serve as the input to machine learning classifiers to perform supervised classification of stuttering while considering different framings of stuttering detection such as occurrence and non-occurrence of specific stuttering types and extensions to the multiclass problem.

In a preliminary binary classification task (stuttering vs. fluent), the model achieved an F1-score of 0.70, with a recall of 0.85 and precision of 0.59, and raw accuracy of 0.58. These results indicate strong sensitivity to stuttering events, successfully identifying 85% of actual stuttering samples. While the model tends to over-predict stuttering, the elevated F1-score reflects a favorable balance between recall and precision. Ongoing work includes the integration of a second, more diverse dataset to further improve model robustness and generalizability.
12:05 Luiza Lober, Matheus Palmero, Francisco Rodrigues Predictive Non-linear Dynamics via Neural Networks and Recurrence Plots
Predicting and characterizing diverse non-linear behaviours in dynamical systems is a complex challenge, particularly due to the inherent presence of chaotic dynamics. Current forecasting methods rely on system-specific knowledge or heavily parametrized models, which come with various drawbacks, including critical model assumptions, uncertainties in estimated input hyper-parameters, and high computational costs. Moreover, even when combined with recurrence analyses, these approaches are typically constrained to chaos identification rather than parameter inference. In this work, we address these challenges by proposing a methodology that uses recurrence plots to train convolutional neural networks to estimate the defining control parameters of two distinct non-linear systems: (i) the Logistic map and (ii) the Standard map. By leveraging the neural networks' ability to recognize patterns within recurrence plots, we demonstrate accurate parameter recovery, achieving fairly confident levels of prediction for both systems, while also comparing our results with those obtained from raw time-series data analysis. This method not only provides a robust approach to predicting diverse non-linear dynamics but also opens up new possibilities for the automated characterization of similar non-linear dynamical systems.
12:30 Pietro Bonizzi, Joël Karel, Martijn Boussé, Philippe Dreesen, Iris Huijben, Ralf Peeters Detection of wandering spatio-temporal recurrent patterns in dynamical systems
For systems characterized by a well-defined spatial structure, it may be relevant to detect if repetitive (quasi-periodic) patterns are present. However, this may be difficult if these repetitive patterns are confined to specific local regions of the spatial structure, and they only last for limited time. This can decrease the efficacy of recurrence plots in showing such patterns, if all points of the structure and all time instants available are used concurrently. In such a situation, the information of interest may be buried by less repetitive components or noise. Another complicating factor is that these local recurrent patterns may not be always confined to the same region, but they may wander across space. It then becomes important to first detect whether such wandering repetitive spatio-temporal patterns are present, and if so, localize them both in space and time, so that one can zoom-in on the relevant spatio-temporal region, by only using the information from those regions and time intervals. In this way, more meaningful recurrence plots can be generated. In a previous study, we proposed a method to detect static spatio-temporal repetitive patters. In this study, we extended this framework to also be able to detect and follow wandering spatio-temporal patterns across time and space.
In terms of the method, the spatio-temporal data observed from the system are decomposed using principal component analysis to identify the points in the spatial structure exhibiting quasi-periodic recurrent patterns. The frequency content (and spectral concentration) of the principal components is used to determine whether such patterns are present, and the corresponding eigenvectors are used to identify the points associated with those components. Geometric information indicating proximity of these points is used to cluster them into local regions of recurrence. The steps above are then repeated on sliding temporal windows to detect recurrent regions over time. Regions of recurrence from consecutive time windows are checked for overlaps and linked together if overlap occurs. In this way, we can describe how regions of recurrence traverse the spatial structure over time.

Such an approach could for instance be useful in the detection of abnormal sources of electrical activity in the heart during pathologies like atrial fibrillation, where such sources may not be necessarily anchored to specific regions of the heart, but they wander around in a more or less organized manner.
12:55 Lunch
14:30 Norbert Marwan The Recurring Story: Mapping the Rise and Flow of Recurrence Plots
Recurrence plots and recurrence quantification analysis (RQA) are now established tools in the study of complex systems across disciplines such as physiology, engineering, physics, and beyond. This talk presents a bibliometric view of the field, based on a curated database of studies using recurrence plot-based analysis. The analysis highlights how the field has changed over time, publication trends and thematic shifts, and collaborations between research groups. It shows how subjects have emerged, developed, and, in some cases, declined, revealing the changing landscape of the field. This bibliographic perspective provides insights into the field's growing footprint in the scientific landscape and aids in understanding the dynamics of methodological evolution in science.
14:55 Juan Kalemkerian An independence test based on recurrence rates with applications
In this presentation, we will introduce a hypothesis test of independence between random elements (of finite or infinite dimension) based on recurrence rates. The concept of the test, as well as its implementation, will be outlined. Its strong performance across a wide range of alternatives will be demonstrated, and comparisons with other existing tests will be provided. We will also examine its sensitivity through the manipulation of various types of distances and present an example applied to meteorology. Finally, we will discuss potential future work, such as its extension to design a hypothesis test of causality between two time series.
15:20 Chunyue Li, Sebastian Oberst (online) Toward an FPGA Implementation of Recurrence Plots and Their Computation
Recurrence plots (RPs) and recurrence quantification analysis (RQA) are powerful tools for analysing the temporal behaviour of dynamical systems, but their high computational cost limits their use in real-time or resource-constrained environments. This work presents an FPGA-accelerated system for end-to-end RP and RQA computation through a deeply pipelined dataflow architecture. The system includes (1) a parallel fixed-point pairwise distance evaluation, (2) an optimised nearest neighbour search to minimise computational redundancy, and (3) a real-time recurrence matrix construction with programmable thresholding. Core RQA metrics are directly computed on the FPGA fabric using parallel accumulators, enabling on-the-fly quantification without CPU offloading. As a case study, we evaluate the complete RP and RQA pipeline using the dynamics of the logistic map as a benchmark model, achieving accurate RQA metric reproduction with near real-time throughput. By fully leveraging FPGA parallelism, the design delivers over ten times speedup compared to conventional CPU-based methods without compromising precision. The system establishes a real-time RP framework for embedded diagnostics in applications including nonlinear time series analysis, biomedical monitoring, and future adaptive control.
15:45 Coffee break
16:15 Reik V. Donner, Fritz Kühlein, Jonathan F. Donges, Davide Faranda, Tommaso Alberti Transient nature of recurrence based local dimension estimates from finite time series
The concept of local dimension is a widely used concept in dynamical system theory, which a heterogeneity in phase space being an indicator for a multifractal nature of the system under study. Various types of local fractal dimensions can in principle be estimated from recurrence plots, making use of the scaling of the density of local recurrences with the size of the considered neighborhood, higher-order single-scale properties like local recurrence network clustering coefficients (Donner et al., 2010, 2011), or instantaneous fractal dimensions exploiting generalized extreme value theory for local distance distributions (Faranda et al., 2017). Previous works have shown pronounced spatial heterogeneities of the corresponding estimates even for monofractal systems like the Lorenz-63 system, indicating notable inconsistency with theoretical expectations.

Here, we demonstrate that estimating such properties from recurrences from finite time series almost inevitably leads to such spurious results. For this purpose, we consider the example of a very long trajectory of the Lorenz-63 system in its chaotic regime, which is subsampled in two different ways: generating ensembles of individual state vectors drawn independently at random from the complete record versus ensembles of contiguous time series segments. Our results clearly indicate that the latter situation, commonly present in practical time series analysis, leads to a broad distribution and non-random spatial pattern of local dimension estimates, while consideration of independent samples provides much more narrowly distributed and spatially unstructured estimates. We conclude that previous conjectures linking spatial patterns in local recurrence network clustering coefficients and other related characteristics not depending on temporal dependencies (like standard RQA measures) with dynamically invariant properties like low-order unstable periodic orbits are likely transient features that should vanish when considering long trajectories, which the corresponding convergence with increasing sample size potentially being rather slow. We discuss implications of these findings for other previous application cases, such as the characterization of sticky orbits in Hamiltonian systems or the local recurrence analysis of nonstationary real-world time series.
16:40 Jai Kumar, Omid Sedehi, Ben Halkon, Sebastian Oberst (online) Testing the Suitability of Duffing oscillator for Data Fusion Using Joint recurrence plot
Data fusion is the integration of different data sets from multiple sources to generate more valuable, accurate, and reliable information regarding system behaviour. However, fusing nonlinear time series with differing timescales, sampling rates, or dynamic characteristics is challenging. This study tests whether joint recurrence plots are suitable for data fusion by starting to analyse simple mathematical functions and their behaviour, to then incorporate a Duffing oscillator as a nonlinear system. First, the analysis investigates the presence of coupling and synchronisation between the time series and explores how these dynamical properties relate to the effectiveness of data fusion. The simulated heterogeneous nonlinear time series from the oscillator are segmented using the sliding windows approach. Recurrence between the two windows is determined using predefined thresholds, which creates a binary joint recurrence matrix. This matrix is used to create the joint recurrence plot and to extract features, such as joint recurrence rate and joint entropy, which help in finding patterns and understanding the interaction between the time series. Joint recurrence quantifies the proportion of simultaneous recurrences in both signals, and joint entropy is an essential property for detecting small changes in the system. It measures the complexity of the joint recurrence plot. The proposed approach supports effective data fusion across asynchronous and dynamically distinct signals.
17:05 Md. Mehedi Hasan, Yoshito Hirata (online) Recurrence Triangles and Recurrence Microstates -- A Comparative Approach for Robust Time Series Classification
Time series classification is crucial for understanding dynamical systems, yet challenges remain such as short data length and non-autonomous inputs. Recurrence-based techniques, particularly recurrence quantification analysis (RQA), are widely used but often fail to capture localized structures. This study introduces and evaluates two recurrence-based methods- recurrence triangles (RTs) and recurrence microstates (RMs)-which extract localized recurrence patterns for improved classification. Using the Rössler system as a benchmark, we demonstrate that both RTs and RMs can perfectly classify datasets from the autonomous systems with minimal structure sizes. However, in the presence of non-autonomous inputs, classification performance decreases for small structures, improving as the structure size increases. RM provides good accuracy but incurs higher computational costs, while RT offers a balance between accuracy and efficiency.
17:30 Masanori Shiro, Ryosuke Tanaka, Miwa Fukino (online) Recurrence plot of state changes in a Turing machine
A recurrence plot is a powerful visualization method. It reveals the temporal structure of dynamical systems by comparing data points in a time series. When the system state can be expressed as a numerical vector, it is common to use the Euclidean distance to measure similarity. However, the internal memory state of a Turing machine is typically represented as a binary string rather than a numerical vector. Therefore, in this context, we use the Hamming distance as a more suitable metric. It directly measures the number of differing bits between memory states and is computationally efficient for symbolic data.
In this study, we construct recurrence plots based on the Hamming distance. These plots visualize how the internal memory state of a Turing machine evolves during execution. Memory states are encoded as binary strings. Pairwise Hamming distances are computed across time steps. The resulting recurrence plots show structured and often intricate patterns. For example, we observe formations that resemble tortoise shell patterns. These suggest underlying periodicities and symmetries. They also reflect self-similar behavior that arises from the deterministic rules of the machine.

To test the generality of these features, we implemented a simple universal Turing machine. We applied the same recurrence plot visualization. Even with a minimal instruction set, the plots show rich and structured dynamics. This demonstrates that recurrence plots can provide insight into the complexity of discrete computation.

One practical challenge is the length of the time series. Each computational step creates a new memory state. As a result, the data grow quickly. This makes storage and visualization more difficult. Constructing meaningful recurrence plots in this context requires careful methods. These include selective sampling and multi-resolution techniques.

In addition, we discuss applying a recurrence plot of recurrence plots, a higher-order recurrence analysis. This may help identify meta-level structure or long-range dependencies. We hope this recursive approach will offer new insights into computational complexity and symbolic dynamics.

We received valuable advice from Dr. Makino, and we would like to thank him.

Thursday, September 11th
9:00 Opening
Applications in Earth Science, Ecology, and Astronomy
9:10 Gabriela Conde-Saavedra, Odylio Aguiar, Henrique de Oliveira, Marcelo Ramírez-Ávila, Maximiliano Ujevic Binary Neutron Star Merger Stage Identification Through Recurrence Quantification Analysis
Recurrence analysis is a method for visualizing the dynamics of a system given its time series. In the case of binary neutron stars (BNS) merger simulations, we use this method to identify the characteristics of the three stages of the coalescence (inspiral, merger and post-merger). The finding of an effective relationship between the patterns exhibited by the BNS with a range of values in the recurrence quantification analysis (RQA) might constitute a useful complementary tool for studying the gravitational wave signals that are expected to be observed by future detectors for the BNS mergers. In this work, we present the distribution of the RQA quantifiers for the inspiral, merger and post-merger phases in BNS simulations given two datasets, the first one contemplating identical masses and different equations of state, and in opposition, the second one with different masses and identical equations of state.
9:35 Radim Panis Recurrence Quantification Analysis Across Scales - Methodological Advances and Application to Blazar Light Curves
A methodological framework is introduced for analyzing multi-scale variability in time series using recurrence quantification analysis (RQA) with systematically varied thresholds. This approach enables the investigation of scale-dependent dynamics from a deterministic perspective. Stochastic behaviors are examined in parallel using autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models, as ARIMA is more sensitive to short-term fluctuations.. Correlation analysis indicates that stochastic processes with short memory propagate across scales, while deterministic patterns are more localized to smaller temporal intervals. This framework is applied to 50 X-ray light curves of the blazar Mrk 421, covering 17 years of observations from the XMM-Newton satellite. The results reveal that the source's variability arises from a complex interplay of deterministic dynamics, stochastic processes, and noise. The scale-dependent features captured by the adaptive RQA approach provide insights not readily accessible through classical time series modeling. The methodology presented here offers a generalizable tool for studying nonlinear and multi-scale behavior in astrophysics and beyond.
10:00 Markus L. Fischer, Alice R. Paine, Eleanor M. L. Scerri, William Gosling, Norbert Marwan, Stefanie Kaboth-Bahr, Martin H. Trauth (online) Investigating Deterministic Climate Dynamics in African Lake Archives with Implications for Hominin Evolution
Climate variability has long been implicated as a driver of hominin evolution, yet its precise role remains contested. The widespread application of µXRF core scanning has enabled decadal-scale palaeoclimate reconstructions from lacustrine sediments, bringing environmental data into the temporal range of human perception. In eastern Africa, the ICDP Site Chew Bahir provides a decadal aridity record, and the ICDP Site Bosumtwi, a crater lake, provides a multi-decadal hydroclimate record of western Africa. Long-term climate trends observed in these records were not directly experienced by humans but rather perceived through short-term dynamics.

For instance, the Chew Bahir record shows abrupt dry spells and tipping-point-induced flickering during multiple wet-dry transitions in eastern Africa. Such volatility likely influenced hominin decision-making, imposing selective pressure for adaptive responses such as migration, technological innovation, and behavioural flexibility. We propose that decadal-scale climatic variability played a key role in shaping hominin evolution during the Pleistocene. We distinguish between stochastic phases, marked by unpredictable state shifts, and deterministic phases, in which environmental variability follows a more predictable trajectory.

Deterministic Climate Dynamics (DCD) are characterised by sequences of environmental states that recur in a similar temporal order. For instance, a decadal dry spell may consistently follow a particular shift in seasonal rainfall or wind patterns, signals potentially perceivable and memorable by hominins and repeated across time. Such dynamics may take the form of decadal-scale sinusoidal oscillations or abrupt, threshold-driven shifts, creating a variable environment, yet sufficiently predictable to be interpreted by hominins. We argue that deterministic variability may have enabled hominins to accumulate experiential knowledge of past climate changes, thereby enhancing their capacity to anticipate future environmental shifts. Such environmental predictability may have fostered early forms of societal learning, enhancing preparedness for future climatic shifts.

We use Recurrence Plots (RP) and Recurrence Quantification Analysis (RQA) to investigate DCDs. One key metric derived from the RP is determinism, which quantifies the proportion of recurrent points forming diagonal line structures, indicating repeated sequences of states. To avoid misleading results, we (a) assess the impact of varying sedimentation rates and interpolation artefacts on RQA metrics, and (b) validate findings using bootstrapped surrogates. We present a methodological framework, initial findings, and outline challenges in identifying and interpreting DCDs in palaeoclimate records.
10:25 Coffee break
Applications in Engineering
10:50 Vramori Mitra Keynote Lecture: Recurrence quantification analysis of floating potential fluctuations in a DC glow discharge plasma
Plasma oscillations often exhibit complex temporal behaviors arising from underlying nonlinear dynamics. Traditional linear methods fall short in capturing the subtle features of such systems, particularly when chaos, intermittency, or nonstationary is involved. In this study, we employ Recurrence Quantification Analysis to investigate the dynamical properties of floating potential fluctuations obtained by using a Langmuir probe, in a DC glow discharge plasma in different controlling parameters such as different magnetic fields, pressure and discharge voltages. RQA provides a powerful framework to quantify the recurrence behavior of states in the system, offering insights into its deterministic structure and complexity. By analyzing key RQA measures such as recurrence rate, determinism, entropy, laminarity, and trapping time we reveal the critical regime transitions in plasma behavior under varying discharge conditions. The results demonstrate that RQA can effectively distinguish between periodic, chaotic, and quasi-periodic regimes, thereby serving as a diagnostic tool for understanding and characterizing plasma instabilities and transport phenomena. This work highlights the potential of recurrence based techniques for advancing nonlinear time series analysis in plasma physics.
11:35 Krzysztof Kecik, Krzysztof Ciecieląg, Arkadiusz Smagala (online) Detection of defects in selected engineering applications using recurrence analysis
This study investigates the application of recurrence analysis for defect detection in two engineering processes. Firstly, recurrence analysis is applied to the cutting of composite materials with deliberately introduced defects. The material is then subjected to milling or drilling, during which cutting forces are recorded and analysed. Key recurrence indicators for defect identification are selected based on the cutting signals. The effectiveness of these indicators is validated through machining trials on materials with real defects, supplemented by ultrasonic testing.
In the second case, rolling bearings with intentionally introduced defects in individual components (inner ring, outer ring, and ball) are analyzed under various operating conditions. The most effective recurrence quantifiers, along with their reference levels for defect detection, are identified. The obtained results are compared with conventional methods used in bearing diagnostics, providing a comprehensive evaluation of the proposed approach.
12:00 B. J. Tchinda Feudjio, Youtha Ngouoko, Djuitchou Yaleu, Nana Nbendjo (online) Detection of crack on Euler Bernouilli beam using recurrence quantification analysis
This study explores the detection of cracks in Euler-Bernoulli beams using Recurrence Quantification Analysis (RQA). We developed a nonlinear model for a cracked beam that incorporates geometric nonlinearity and a localized breathing crack, employing the Mathieu-Duffing equation to capture stiffness variations and nonlinear effects. Our approach applies RQA to systematically examine how crack depth in-fluences the system’s dynamic response. The results indicate that as crack depth increases, the system’s potential energy decreases, vibration amplitudes rise, and nonlinearity becomes more pronounced. Recurrence plots reveal distinct irregularities with increasing crack depth, and RQA metrics demonstrate the emergence of chaotic behavior when the crack depth ratio reaches $eta geq 0.4$. These findings highlight RQA’s effectiveness for early crack detection and structural health monitoring, offering a valuable tool for preventing failures.
Keywords: Crack detection, Euler-Bernoulli beam, breathing crack, Recurrence Quantification Analysis (RQA), Mathieu-Duffing equation, nonlinear vibrations.
12:25 Lunch
13:55 Campus tour
15:50 Coffee break
16:20 Esteban Miguel García Ochoa Keynote Lecture: Application of recurrence plot for the study electrochemical corrosion
The dynamics of a multidimensional process in a two-dimensional graph can be represented using Recurrence Plots (RP). The objective of this talk is to offer a simple and clear explanation of the way in which they are built and to show the parameters that can be obtained from these graphics. This mathematical tool will be focused on the application on the corrosion phenomena and in general, the electrochemical phenomena. Electrochemical noise contains information concerning the nonlinear dynamics of the corrosion process. The use of RP is a new way to evaluate electrochemical processes from a new dynamic point of view and complementing the information obtained by traditional electrochemical methods
17:05 Bartłomiej Ambrożkiewicz, Arkadiusz Syta, Łukasz Wójcik, Borg Automotive Sp z o.o. Non-Destructive Diagnostics of Electric Parking Brake Modules Using Recurrence Analysis of Piezoelectric Sensor Data
This study examines the non-destructive diagnostics of electric parking brake (EPB) modules recurrence analysis for the voltage time series obtained with piezoelectric sensors. The proposed approach addresses the regeneration process of EPB modules, where defects are initially identified only by an increased output current or torque, without knowledge of the specific damaged component. Diagnostics involve mounting piezoelectric sensors on the housing near the electric motor, pinion gear, and planetary gearbox before disassembly. Tests are conducted for different groups of damage, grouped into three main defect categories: based on electric motor, toothed belt, and planetary gearbox. Short time-series data were collected, and recurrence-based quantifiers were extracted for analysis. The results highlight the effectiveness of recurrence-based metrics in characterizing different kind of faults occurring in EPB modules. The proposed method offers a non-invasive approach to diagnosing faults in electric parking brake modules, enabling detection of damaged components without its dismantling.
17:30 Dragos Nastasiu, Marius Nati, Angela Digulescu, Cristina Despina-Stoian, Cornel Ioana Frenel-Serret phase diagram characterization
This paper presents a method based on the Frenet-Serret descriptors that characterizes the phase space trajectory of a signal and computes a pairwise tangent matrix to characterize its dynamics. First, the signal is mapped into an m-dimensional phase space using time-delay embedding. Next, for every pair of points on this trajectory, we compute the unit tangent vector pointing from one point to the other. Collectively, these pairwise unit tangents form a matrix (indexed by point pairs) that encodes the directional relationship between all state pairs. This pairwise tangent matrix reflects both local structure (nearby points have similar tangent directions, revealing smooth changes akin to local curvature) and global structure (distant points yield tangents that span across the attractor, revealing the overall shape and recurrent patterns of the trajectory).


This approach is conceptually related to Frenet-Serret frame analysis from differential geometry, which is typically used to describe the local properties of curves in terms of tangent, normal, and binormal vectors, as well as their curvature and torsion. In the context of phase space analysis, instead of directly applying the Frenet-Serret frame to smooth curves, the pairwise tangent matrix method computes the tangent vectors between every pair of points in the phase space. This method captures the local directional changes and allows for a detailed description of the signal's dynamics.



By considering the evolution of phase space trajectories, our approach offers an intrinsic geometric signature of the signal, sensitive to periodic, transient, and stochastic behaviors. This approach builds on the concept of curvature as an intrinsic measure of signal dynamics, which has been explored in signal processing contexts such as nonlinear time series analysis, chaos detection, and phase space reconstruction.
17:55 Abhishek Ray Mohapatra, Lorenzo Bianco, Maria Rosaria Tucci, Simona Alberti, Can Nerse, Ivan Sili, David Navarro-Payá, Jone Etxeberria, Gaston Pizzio, José Tomás Matus, Luca Pietro Casacci, Francesca Barbero, Sebastian Oberst (online) Topology of wingbeat generated noise by honeybee (Apis mellifera) in the wild
Insects are the largest class in the animal kingdom. Their role in the ecosystem is vital, as they are important in the food chain, and their essential role in human food production as pollinators. Among pollinating insects, bees, especially honeybees, are the most well-known. Research shows that most of the crop pollination is due to honeybees, which have been domesticated and commercialised in modern civilisation. Apart from honeybees, other social and solitary bees are also important for their role in plant-specific pollination. Recent study shows that flowers of evening primrose respond to the wingbeat generated acoustic signal of honeybee by increasing the sugar concentration in nectar. Furthermore, acoustic signals have been used for passive monitoring of invasive bee species and ecosystem monitoring. Most of these analysis and classification methods use frequency-based features and machine learning to classify the wingbeat-generated signals. Moreover, there have been no studies about the classification and analysis of the flying behaviour using the wingbeat-generated acoustic signals. In this study, we hypothesise that the flying behaviour of these flyers can be classified from the acoustic signal using nonlinear time series analysis. To do so, we first analyse the acoustic signals and corresponding video to manually classify them into the following flying behaviours: hovering and leaving a flower. As the signals are recorded outdoors in the wild, it was first filtered using ghkss geometric feature-preserving filter. Then we use a recurrence plot (RP) to check transitions of the states within a time series. The result shows the nonstationary dynamics of the acoustic signal in the corresponding flying behaviour. Furthermore, the phase-space trajectory shows complex manifolds with multiple orbits. The corresponding RPs were further analysed with recurrence quantification analysis to establish parameters with statistical significance to differentiate between hovering and leaving. This shows that the nonlinear time series analysis with recurrence plot and recurrence quantification analysis can resolve the information-rich complex dynamics of wingbeat-generated acoustic signals, which is not possible with traditional frequency domain analyses.
20:00 Dinner

Friday, September 12th
9:00 Opening
Applications in Life Sciences
9:10 Claudia Lerma Keynote Lecture: Recurrence plot analysis in cardiovascular signals
Cardiovascular signals are widely studied in physiology and clinical research. This talk will summarize the applications of recurrence plot analysis to cardiovascular signals. Blood pressure, photoplethysmographic volume, and electrocardiogram are signals used to measure time series that exhibit spontaneous fluctuations. These are valuable for estimating parameters of the cardiovascular control mechanisms and for identifying markers associated with the risk of mortality and other relevant outcomes. The most common time series studied with Recurrence Plot analysis is heart rate variability. It is applied in various conditions in healthy humans, including fetal development, healthy aging, exercise, and high altitude. Also, very diverse pathologies have been studied, including diabetes, hypertension, chronic renal disease, cardiac arrhythmias, cardiac valve disease, cardiac infarction, and sudden cardiac death. We will discuss several challenges in applying Recurrence Plot analysis to these time series. The nature of these data (noisy, usually short-term, and non-stationary) makes it difficult to estimate the adequate parameters for phase space embedding (time delay and embedding dimension) and for recurrence plot reconstruction (e.g., threshold size and the type of norm). This is evidenced by a lack of consensus regarding the methodology, which hinders the replication of the experiments. Moreover, the interpretation of measures obtained from the recurrence plot of these time series is also highly variable, and it lacks further empirical or theoretical support (for instance, to consider the recurrence quantification analysis as non-linear indices of these time series). Sharing the research group's experience is expected to foster a discussion that will help identify potential strategies to overcome these challenges, with an optimistic expectation that these strategies will pave the way for future breakthroughs in this field.
9:55 José Javier Reyes-Lagos, Claudia Ivette Ledesma-Ramírez, Adriana Cristina Pliego-Carrillo, Hugo Mendieta-Zerón, Ana Karen Talavera-Peña, Eric Alonso Abarca-Castro (online) Comparison of Maternal Cardio-Electrohysterographic Coupling in Preterm and Term Labor Using Cross-Recurrence Plot Analysis
Maternal Cardio-Electrohysterographic Coupling (MCEC) describes the interplay between uterine electrical activity and maternal heart rate variability, reflecting the functional interaction between the myometrium and the autonomic nervous system. Preterm birth remains a leading cause of neonatal morbidity and mortality worldwide, highlighting the need to improve our understanding of maternal–uterine interactions for better clinical management. This exploratory study aimed to investigate whether MCEC differs between preterm and term labor, thereby shedding light on potential mechanisms underlying premature labor onset.

In this exploratory study, a total of seventy Mexican parturient women were evaluated to assess differences in MCEC, including 39 in the preterm group and 31 in the term group. Abdominal signals were recorded for 20 minutes using a portable monitor. From these signals, the electrohysterogram or uterine electromyogram (EHG) and maternal beat-to-beat RR intervals were derived. A TOCO-like uterine activity signal was subsequently extracted from the EHG in 2-second epochs. Both the TOCO-like and RR time series were spline-interpolated at 4 Hz. The MCEC was assessed using cross-recurrence plot (CRP) analysis applied to each TOCO–RR interval pair. From the resulting CRPs, recurrence quantification analysis (RQA) indices were extracted, including determinism (DET), mean diagonal line length (Lmean), maximum diagonal line length (Lmax), entropy (ENTR), and trapping time (TT). Outlier detection was conducted using the robust regression and outlier removal (ROUT) method with a false discovery rate of Q = 2%.

Preterm labor showed higher median DET (0.7546 [0.6748–0.8357]) than term (0.6771 [0.5906–0.7646], p=0.0404) as well as a greater Lmean in preterm (17.45 [14.72–20.69]) compared to term (14.76 [13.63–16.30], p=0.0008). ENTR was also elevated in preterm (3.296 [2.978–3.551]) relative to term (3.040 [2.826–3.312], p=0.0403), and TT was significantly higher in preterm (23.53 [18.24–28.90]) than term (19.42 [16.62–22.06], p=0.0041). Lmax did not differ significantly (p=0.3297).

These findings could be linked to an earlier or disproportionate release of catecholamines and other stress hormones in preterm, as the maternal body responds to labor onset that occurs sooner than expected. This may facilitate a more synchronous cardiovascular reaction to uterine contractions, resulting in more pronounced fluctuations in maternal heart rate. In contrast, term pregnancies likely benefit from more mature physiological adaptations that mitigate beat-to-beat cardiac responses. Overall, the distinct differences in MCEC observed here underscore the potential usefulness of further research into whether monitoring these indices can improve clinical management of preterm labor and reduce associated risks.
10:20 Diego A. Evin, Fabián C. Tommasini, Mercedes Hüg, Fernando Bermejo (online) Chromatic recurrences applied to categorical time series of blind mother-child daily joint walking
Shared mobility in urban contexts involves navigating complex and unpredictable environments. While research about blind people s navigation has often focused on assistive technologies, fewer explore the embodied nature of their walking experiences. This study analyzes the dynamics of joint walking of a blind mother and her blind child in their neighborhood using recurrence plots (RP) and recurrence quantification analysis (RQA). Recurrence-based analysis has been increasingly adopted in fields such as Cognitive Sciences and Psychology. In this instance, an alternative version of the method was applied for categorical data: chromatic RPs and chromatic RQA measures. It enabled us to increase the level of detail of the conventional analysis by studying disaggregated behavioral matches separately. An observer conducted periodic video recordings of daily routines of the blind child (aged 46 to 52 months) and her mother. The dyad walked together hand in hand and the mother used a white cane. The routes included situations such as walks from home to school or from school to home, as well as walks to a nearby park. Five episodes were selected, totaling 2860 s of video with an average duration of 10 min per episode. The following categories were used to analyze the joint walking: Synchronized walking, Non-Synchronized walking, Standstill and Detour. The time series were segmented by place of transit (sidewalk or street crossing) and only sidewalk segments were included in this study. A total of 26 segments with a range of durations from 12.5 s to 275.5 s were analyzed. The background noise level was estimated to characterize the environmental acoustic context as quieter or louder for each segment. The speech activity level was also estimated as low or high. Auto-recurrences were derived from the dyad s joint encoding. Each one of the categories was assigned a different color. The following measures for each color were calculated based on the vertical lines derived from the chromatic RQA: Maximum Line, Trapping Time, and Vertical Entropy. Results showed that mother and child evidenced spontaneous synchronization of their steps. The synchronous walking intervals were shorter and more predictable, while asynchronous walking demonstrated greater flexibility to environmental variability. Synchronization was also affected by environmental sound conditions: in contexts with lower background noise and low speech activity, this state could remain for a longer mean time. This study highlights the dyad s ability to flexibly coordinate its locomotion.
10:45 Coffee break
11:15 Gertrudis Hortensia González-Gómez, Claudia Lerma, Itayetzin Beurini Cruz-Vega, Graciela Elizabeth Martínez-Hernández Cross-recurrence quantification analysis between heart rate and systolic blood pressure in healthy aging
Aging induces physiological changes across multiple regulatory systems, including the cardiovascular system, which exhibits complex, nonlinear dynamics over multiple spatial and temporal scales. Heart rate variability (HRV) and systolic blood pressure variability (SBPV) reflect autonomic regulation of the cardiovascular system and have been widely used as a noninvasive marker of physiological adaptability. Nonlinear techniques, such as recurrence quantification analysis (RQA), have been used to evaluate this complexity and have revealed altered HRV patterns in several chronic diseases. However, the impact of aging on the dynamic interaction between HRV and SBPV in healthy individuals remains poorly understood. The study aimed to evaluate the association between age and the coupling of HRV and SBPV using cross-recurrence quantification analysis (CRQA). HRV and SBPV time series were obtained from electrocardiogram and blood pressure recordings obtained in a sample of 781 healthy adults aged 18 to 69 years from a public database. CRQA was performed using an embedding dimension of 7, a delay of 1, and a fixed recurrence rate of 0.07. CRQA indices were compared across five age groups (18 to 29, 30 to 39, 40 to 49, 50 to 59, and 60 to 69 years) using ANOVA, controlling for gender as an independent factor and body mass index (BMI) as a covariate. Determinism, Entropy, Laminarity, Recurrence time type 2, and BMI change among the five age groups when analyzing the simultaneous variation of the cardiovascular signals. These indices vary in accordance with the sex of the participants. However, there was no effect on the CRQA indices of the sex and age interaction. In addition, although there was an increasing trend of BMI with age, BMI was not a significant factor in CRQA indices. In conclusion, aging is accompanied by changes in vascular structure and function, especially in the large arteries, and it is associated with altered dynamic interactions between HRV and SBPV, characterized by increased periodicity and laminar states, suggesting reduced complexity in cardiovascular regulation.
11:40 Itayetzin Beurini Cruz-Vega, Nydia Ávila-Vanzzini, Gertrudis Hortensia González-Gómez, Juan C. Echeverría, Claudia Lerma Correlation between recurrence quantification analysis of heart rate variability and aortic valve stenosis severity
Aortic valve stenosis (AVS) is a progressive disease characterized by inflammation, lipid infiltration, and calcification, ultimately narrowing and impairing the valve function. Since most patients remain asymptomatic until very advanced stages, the diagnosis is usually late, increasing their mortality risk. AVS progression is associated with a rigid heart rate variability (HRV) dynamic as revealed by Recurrence Quantification Analysis (RQA) with increased determinism and trapping time. Despite this, the relationship between RQA indices and echocardiographic parameters in AVS patients remains unexplored. This study aimed to evaluate the correlation between RQA indices of HRV and AVS severity. This cross-sectional study included 27 patients (65.6% male, mean age 63.3 years) diagnosed with moderate to severe AVS. HRV was assessed from five-minute electrocardiogram recordings in the supine position. Recurrence plots were obtained with embedding dimension = 5 (false nearest neighbors), embedding delay = 6 (mutual information function), and a fixed amount of neighbors’ norm with a recurrence density of 0.07. RQA indices were calculated using the Cross Recurrence Plot Toolbox. Spearman correlation analysis was performed between RQA indices and echocardiographic/demographic variables (age, systolic blood pressure, and body mass index). Results showed a positive correlation between mean pressure gradient (mPG) and most RQA indices (determinism, mean diagonal length, Shannon entropy, laminarity, maximum vertical length, and trapping time). In contrast, indexed aortic valve area (AVAi) had negative correlations with several indices (determinism, mean diagonal length, Shannon entropy, laminarity, maximum vertical length, and trapping time). Left ventricular ejection fraction was negatively correlated with recurrence rate type 2, age positively correlated with maximum vertical length, and BMI with recurrence rate type 1. There were no significant correlations between systolic blood pressure and any RQA indices. In conclusion, significant correlations between nonlinear HRV indices and clinical measures of AVS severity (mPG and AVAi) highlight the potential of RQA as a non-invasive tool to assess disease progression in AVS patients.
12:05 David Hernández Obín, Claudia Lerma González, Adriana Torres Machorro Introduction to the assessment of the dynamic behaviour of PPG morphological time series from peripheral artery disease using recurrence quantification analysis
Peripheral artery disease (PAD) is a condition where blood flow is reduced because of a reduction in the artery diameter. Ankle-brachial index (ABI) is commonly used to diagnose PAD evaluating blood pressure reduction in legs compared to the pressure on arms. Photoplethysmography has been studied as an alternative method for assessing arterial disease since their morphological parameters have shown significant differences between healthy and PAD diseased population in addition to having significant correlation with ABI. In this methodological study, we have started to familiarize ourselves with the methods of recurrence quantification analysis in PPG morphological time series from 40 legs of PAD patients using ad-hoc embedding times and embedding dimensions. First, we prove our methods obtaining recurrence plots for some characteristic time series examples like white noise, sum of sine waves and Lorenz attractor. Then, pulse transit time (PTT), maximum systolic slope (MSS) and amplitude were selected as the PPG morphological parameters. Their mean and standard deviation had significant correlation with ABI showing that their variability could be related to the disease degree too. However, only max diagonal length, complexity-entropy and permutation entropy for MSS and amplitude, and max vertical length for MSS show significant correlation with ABI. Moreover, all the dynamic parameters had a significant correlation with the mean of MSS and the amplitude with similar results for their standard deviation. This could mean that the dynamic behaviour of the change of artery rigidity and blood volume in PAD patients could be related to their mean value and their variability but not with the degree of the disease. Further studies are needed to refine our methods and validate these findings since in some cases embedding times above 20 beats were used but the study of recurrence quantification analysis for this time series seems very interesting.
12:30 Robert Karpiński, Arkadiusz Syta, Anna Machrowska, Przemysław Krakowski, Marcin Maciejewski, Józef Jonak, Norbert Marwan Nonlinear Analysis of Vibroacoustic Signals for Knee Joint Damage Diagnosis
This study explores the use of qualitative and quantitative nonlinear properties of vibroacoustic signals for diagnosing knee joint damage. Non-invasive methods based on these signals can significantly enhance the diagnostic process, aiding medical professionals in decision-making. The musculoskeletal system under examination shares mechanical properties with bearings, where damage disrupts the nonlinear biomechanical system's function. We analyzed vibration signals in three directions during two types of tests (closed kinetic chain and open kinetic chain) using an automated measurement system. Nonlinear recurrence analysis was employed to characterize the qualitative and quantitative dynamics of the musculoskeletal system for each patient. The nonlinear correlations in the data, represented by Recurrence Plots (qualitative indicators) and Recurrence Quantification Analysis indicators (quantitative indicators), were used to train various machine learning models for tabular data and image classification. Our results demonstrated a 100% accuracy in predicting damage through image classification.
12:55 Closing
13:10 Lunch
14:15 Poster session
16:15 Hands-on workshop

Poster Session
Poster 1 Zinan Lyu, Dirk Sachse, Norbert Marwan, Hui Tang Detecting Climate Transitions with Recurrence Plots: A Case Study of the Younger Dryas
Quantifying transitions in palaeoclimate time series is crucial for understanding the dynamics of climate systems. Recurrence plots provide a powerful framework for detecting spatiotemporal patterns in palaeoclimate dynamics. One key challenge in studying these dynamics through lake sediment records is aligning time series from different locations for a meaningful comparison. Although climatic events, such as volcano eruptions, can serve as reference points, cross recurrence plots offer a more detailed and dynamic method to align records by the line of synchronization between two systems. This allows us to go beyond fixed reference points and explore how climate processes unfold across space and time. In this study, we focus on the Younger Dryas, a rapid climate cooling period, and aim to quantify its climate-shifting point and duration, applied to paleoclimate time series from lake deposits in two different locations. Our recurrence plots based approach quantifies the Younger Dryas transition and provides new insights into its regional spatiotemporal dynamics.
Poster 2 Adriana Robles Cabrera, Claudia Lerma, Itayetzin Beurini Cruz-Vega, Ruben Fossion Exploring heart rate variability dynamics in premenopausal women with type 2 diabetes: A recurrence quantification approach
Type 2 diabetes mellitus (T2DM) is a chronic disease with increasing global prevalence. T2DM is associated with elevated cardiovascular mortality and a higher risk of cardiac autonomic neuropathy, evidenced by reduced heart rate variability (HRV). In healthy women, HRV correlates with sex hormone levels, a relationship that persists in women with well-controlled type 2 diabetes mellitus (T2DM). However, traditional linear HRV analyses are limited in their ability to capture the complex dynamics of autonomic regulation. Nonlinear methods, such as Recurrence Quantification Analysis (RQA), could provide more profound insights into physiological adaptability. This observational, prospective, cross-sectional study aimed to compare RQA indices of HRV between healthy women and women with well-controlled T2DM during physiological challenges and across different phases of the menstrual cycle. The study includes a total of 31 women divided into two groups: healthy women (n = 24) and women with well-controlled T2DM (n = 7). Clinical and gynecological histories were obtained for all participants. HRV time series of five minutes length were obtained using ECG recordings during an orthostatic challenge (supine position followed by active standing) and rhythmic breathing. The measurements were obtained during three of the menstrual cycle phases: menstrual, proliferative, and luteal. Recurrence plots were generated using an embedding dimension of 10 (false nearest neighbors), a delay of 6 (autocorrelation), and a fixed amount of neighbors’ norm with a recurrence density of 0.07. RQA indices were calculated using the Cross Recurrence Plot Toolbox. Group comparisons were analyzed via ANOVA for repeated measures. Results showed that recurrence plot patterns were similar between groups and across different phases of the menstrual cycle. Both groups exhibited increased RQA indices in response to the orthostatic challenge, reflecting preserved autonomic reactivity. However, during rhythmic breathing, only healthy women showed significant increases in RQA indices, whereas women with T2DM exhibited a blunted response across all menstrual phases. In conclusion, women with well-controlled T2DM maintain autonomic adaptability to postural changes but exhibit impaired respiratory modulation, suggesting early autonomic dysfunction. RQA of HRV may serve as a sensitive tool for detecting subclinical neuropathy and enhancing cardiovascular risk stratification.
Poster 3 Cinthya Toledo-Peral, Emmanuel Simental-Aldaba, Gabriel Vega-Martinez, Claudia Lerma-Gonzalez Cross-recurrence plot analysis of surface electromyography amplitude during gait in patients with Duchenne Muscular Dystrophy
Duchenne muscular dystrophy is a rare neuromuscular disorder caused by a mutation in the Duchenne muscular dystrophy gene. This mutation generates fundamental structural defects that affect the function and maintenance of striated muscle, therefore, patients experience progressive motor impairment. Because gait is one of the most essential motor abilities, describing it with quantitative methods, such as the amplitude of surface electromyography, is indispensable. Recurrence plot-based methods are a modern form of nonlinear data analysis that has not yet been explored in this pathology. Thus, its application to the study of Duchenne muscular dystrophy could provide valuable insights into the progression of motor function loss and the compensatory strategies patients employ to improve gait stability. The aim of this study was to analyze the cross-recurrence plot of muscle activity between pairs of muscles using surface electromyography during gait in patients at the ambulatory stage of Duchenne muscular dystrophy. Six patients with a genetic diagnosis of Duchenne muscular dystrophy in the ambulatory phase (mean age 8.4 years) were fitted with four portable surface electromyography monitors, which were placed on the quadriceps and gluteal muscles bilaterally to record muscle activity during the six-minute walk test. Using the Discrete Wavelet Transform, Daubechies db4 level-8 decomposition, and the approximation coefficients to reconstruct a low-frequency envelope. A threshold value was chosen for each patient to determine which regions are active. Then, the mean amplitude value of the active areas of the surface electromyography signal was calculated. Subsequently, cross-recurrence plot analysis was performed with the cross-recurrence plot toolbox for Matlab. Cross-correlation was used to estimate the embedding delay of each pair of muscles, and the false nearest neighbors method was used to estimate the correlation dimension. A threshold of 0.07 was used. The cross-recurrence plot analysis revealed a high degree of determinism, characterized by short but frequent diagonal lines, indicating a highly periodic interaction between pairs of muscles during walking. Brief patterns of vertical lines of short duration were consistent with slowing down or temporarily stopping due to difficulty walking in some patients. These findings suggest a promising application of cross-recurrence plot analysis of surface electromyography as a non-invasive tool to identify early alterations in the gait of Duchenne muscular dystrophy patients.
Poster 4 Emmanuel Simental-Aldaba, Gabriel Vega, Cinthya L. Toledo, Claudia Lerma Correlation of recurrence plot indices of heart rate variability and functional assessments in ambulatory patients with Duchenne Muscular Dystrophy
Duchenne muscular dystrophy (DMD) is a progressive genetic disorder that causes muscle weakness. The leading cause of mortality in DMD patients is cardiopulmonary failure. Therefore, identifying and establishing diagnostic methods to detect heart disease is crucial. One alternative is heart rate variability (HRV) indices, which assess cardiovascular autonomic modulation. Alterations in these indices precede structural alterations that are detectable by imaging. Our working group has found a significant correlation between linear HRV indices and functional motor tests, particularly the 6-minute walk test (6MWT). This suggests that the 6MWT could serve as a noninvasive diagnostic method for cardiovascular function. Nonlinear analysis using recurrence plot-based methods could complement these indices and help determine their relationship with performance in functional timed motor tests, which in turn could aid in assessing cardiovascular and motor functions in DMD patients. The objective was to evaluate the correlation between recurrence plot-based HRV indices and functional motor tests in ambulatory DMD patients. Eleven DMD patients (mean age: 8.4 years) were fitted with a portable continuous electrocardiography (ECG) monitor. The ECG was measured at rest and during the 6MWT and the North Star Ambulatory Assessment (NSAA). Subsequently, HRV time series were obtained, and recurrence plot quantification analysis (RQA) was performed using the CRP toolbox for MATLAB, with a time delay of 6, an embedding dimension of 10, a fixed number of neighbors (fan), and a threshold of 0.07. Spearman's correlation coefficient (r) was calculated between functional motor test scores and each RQA index. Among the seven patients who could perform the walking test, laminarity increased significantly during walking. At rest, the NSSA score had negative correlations with the mean diagonal length (r = -0.611, p = 0.046), Shannon’s entropy (r = -0.611, 0.047), and the maximum vertical line indices (r = -0.761, p = 0.007). In conclusion, these RQA indices have the potential for non-invasive identification or prediction of decreased motor function in DMD patients.
Poster 5 Abel Lerma, Cesar Arnulfo Morales-Lopez, Claudia Lerma Dynamical response of heart rate variability to psychological stress in college students: Recurrence plot approach
Stress among college student populations is a significant concern due to its potential negative impact on academic performance, physical health, and psychological well-being. Heart rate variability (HRV) analysis using linear methods has demonstrated that psychological stress, induced by evoking a memory of a past negative experience, is sufficient to modify the autonomic nervous system, leading to increased sympathetic activity. This study aimed to assess the nonlinear HRV dynamics response to psychological stress with recurrence plot quantification analysis (RQA) in college students. In a sample of 47 undergraduate participants recruited as volunteers, the psychophysiological stress response, as measured by HRV, was assessed under four conditions (baseline, psychological stress, recovery, and controlled breathing) for five minutes each. RQA indices were obtained by the CRP toolbox with ad-hoc embedding delays estimated by the autocorrelation function, the correlation dimension estimated by the false nearest neighbors method, and a threshold of 0.07. Since most RQA indices did not have a normal distribution, median values were compared between the baseline and the other three conditions using Mann-Whitney U tests. Compared to baseline, psychological stress decreased determinism, the mean diagonal length, and entropy, did not affect laminarity, trapping time, or the maximum vertical line, and increased the recurrence time. Most of these changes were still present during the recovery phase. Controlled breathing had the opposite effect of increasing all diagonal-based RQA indices while also increasing the recurrence time. These results indicate a change in the dynamic HRV behavior in response to psychological stress in college students, suggesting a promising potential for RQA indices as non-invasive markers of vulnerability to stress.