A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots

Recurrence plot embeddings as short segment nonlinear features for multimodal speaker identification using air, bone and throat microphones

Speech is produced by a nonlinear, dynamical Vocal Tract (VT) system, and is transmitted through multiple (air, bone and skin conduction) modes, as captured by the air, bone and throat microphones respectively. Speaker specific characteristics that capture this nonlinearity are rarely used as stand-alone features for speaker modeling, and at best have been used in tandem with well known linear spectral features to produce tangible results. This paper proposes Recurrent Plot (RP) embeddings as stand-alone, non-linear speaker-discriminating features. Two datasets, the continuous multimodal TIMIT speech corpus and the consonant-vowel unimodal syllable dataset, are used in this study for conducting closed-set speaker identification experiments. Experiments with unimodal speaker recognition systems show that RP embeddings capture the nonlinear dynamics of the VT system which are unique to every speaker, in all the modes of speech. The Air (A), Bone (B) and Throat (T) microphone systems, trained purely on RP embeddings perform with an accuracy of 95.81%, 98.18% and 99.74%, respectively. Experiments using the joint feature space of combined RP embeddings for bimodal (A-T, A-B, B-T) and trimodal (A-B-T) systems show that the best trimodal system (99.84% accuracy) performs on par with trimodal systems using spectrogram (99.45%) and MFCC (99.98%). The 98.84% performance of the B-T bimodal system shows the efficacy of a speaker recognition system based entirely on alternate (bone and throat) speech, in the absence of the standard (air) speech. The results underscore the significance of the RP embedding, as a nonlinear feature representation of the dynamical VT system that can act independently for speaker recognition. It is envisaged that speech recognition too will benefit from this nonlinear feature.

Application of Recurrence Plot Analysis to Examine Dynamics of Biological Molecules on the Example of Aggregation of Seed Mucilage Components

The goal of the research is to describe the aggregation process inside the mucilage produced by plant seeds using molecular dynamics (MD) combined with time series algorithmic analysis based on the recurrence plots. The studied biological molecules model is seed mucilage composed of three main polysaccharides, i.e. pectins, hemicellulose, and cellulose. The modeling of biological molecules is based on the assumption that a classical-quantum passage underlies the aggregation process in the mucilage, resulting from non-covalent interactions, as they affect the macroscopic properties of the system. The applied recurrence plot approach is an important tool for time series analysis and data mining dedicated to analyzing time series data originating from complex, chaotic systems. In the current research, we demonstrated that advanced algorithmic analysis of seed mucilage data can reveal some features of the dynamics of the system, namely temperature-dependent regions with different dynamics of increments of a number of hydrogen bonds and regions of stable oscillation of increments of a number of hydrophobic-polar interactions. Henceforth, we pave the path for automatic data-mining methods for the analysis of biological molecules with the intermediate step of the application of recurrence plot analysis, as the generalization of recurrence plot applications to other (biological molecules) datasets is straightforward.

Recurrence analysis of meteorological data from climate zones in India

We present a study on the spatiotemporal pattern underlying the climate dynamics in various locations spread over India, including the Himalayan region, coastal region, and central and northeastern parts of India. We try to capture the variations in the complexity of their dynamics derived from temperature and relative humidity data from 1948 to 2022. By estimating the recurrence-based measures from the reconstructed phase space dynamics using a sliding window analysis on the data sets, we study the climate variability in different spatial locations. The study brings out the variations in the complexity of the underlying dynamics as well as their heterogeneity across the locations in India. We find almost all locations indicate shifts to more irregular and stochastic dynamics for temperature data around 1972-79 and shifts back to more regular dynamics beyond 2000. These patterns correlate with reported shifts in the climate and Indian Summer Monsoon related to strong and moderate El Niño-Southern Oscillation events and confirm their associated regional variability.

Topological data analysis of the synchronization of a network of Rössler chaotic electronic oscillators

Synchronization study allows a better understanding of the exchange of information among systems. In this work, we study experimental data recorded from a set of Rössler-like chaotic electronic oscillators arranged in a complex network, where the interactions between the oscillators are given in terms of a connectivity matrix, and their intensity is controlled by a global coupling parameter. We use the zero and one persistent homology groups to characterize the point clouds obtained from the signals recorded in pairs of oscillators. We show that the normalized persistent entropy (NPE) allows us to characterize the effective coupling between pairs of oscillators because it tends to increase with the coupling strength and to decrease with the distance between the oscillators. We also observed that pairs of oscillators that have similar degrees and are nearest neighbors tend to have higher NPE values than pairs with different degrees. However, large variability is found in the NPE values. Comparing the NPE behavior with that of the phase-locking value (PLV, commonly used to evaluate the synchronization of phase oscillators), we find that for large enough coupling, PLV only displays a monotonic increase, while NPE shows a richer behavior that captures variations in the behavior of the oscillators. This is due to the fact that PLV only captures coupling-induced phase changes, while NPE also captures amplitude changes. Moreover, when we consider the same network but with Kuramoto phase oscillators, we also find that NPE captures the transition to synchronization (as it increases with the coupling strength), and it also decreases with the distance between the oscillators. Therefore, we propose NPE as a data analysis technique to try to differentiate pairs of oscillators that have strong effective coupling because they are first or near neighbors, from those that have weaker coupling because they are distant neighbors.

Unraveling dyadic psycho-physiology of social presence between strangers during an audio drama - a signal-analysis approach

A mere co-presence of an unfamiliar person may modulate an individual's attentive engagement with specific events or situations to a significant degree. To understand better how such social presence affects experiences, we recorded a set of parallel multimodal facial and psychophysiological data with subjects (N = 36) who listened to dramatic audio scenes alone or when facing an unfamiliar person. Both a selection of 6 s affective sound clips (IADS-2) followed by a 27 min soundtrack extracted from a Finnish episode film depicted familiar and often intense social situations familiar from the everyday world. Considering the systemic complexity of both the chosen naturalistic stimuli and expected variations in the experimental social situation, we applied a novel combination of signal analysis methods using inter-subject correlation (ISC) analysis, Representational Similarity Analysis (RSA) and Recurrence Quantification Analysis (RQA) followed by gradient boosting classification. We report our findings concerning three facial signals, gaze, eyebrow and smile that can be linked to socially motivated facial movements. We found that ISC values of pairs, whether calculated on true pairs or any two individuals who had a partner, were lower than the group with single individuals. Thus, audio stimuli induced more unique responses in those subjects who were listening to it in the presence of another person, while individual listeners tended to yield a more uniform response as it was driven by dramatized audio stimulus alone. Furthermore, our classifiers models trained using recurrence properties of gaze, eyebrows and smile signals demonstrated distinctive differences in the recurrence dynamics of signals from paired subjects and revealed the impact of individual differences on the latter. We showed that the presence of an unfamiliar co-listener that modifies social dynamics of dyadic listening tasks can be detected reliably from visible facial modalities. By applying our analysis framework to a broader range of psycho-physiological data, together with annotations of the content, and subjective reports of participants, we expected more detailed dyadic dependencies to be revealed. Our work contributes towards modeling and predicting human social behaviors to specific types of audio-visually mediated, virtual, and live social situations.

A biomarker discovery framework for childhood anxiety

Introduction

Anxiety is the most common manifestation of psychopathology in youth, negatively affecting academic, social, and adaptive functioning and increasing risk for mental health problems into adulthood. Anxiety disorders are diagnosed only after clinical symptoms emerge, potentially missing opportunities to intervene during critical early prodromal periods. In this study, we used a new empirical approach to extracting nonlinear features of the electroencephalogram (EEG), with the goal of discovering differences in brain electrodynamics that distinguish children with anxiety disorders from healthy children. Additionally, we examined whether this approach could distinguish children with externalizing disorders from healthy children and children with anxiety.

Methods

We used a novel supervised tensor factorization method to extract latent factors from repeated multifrequency nonlinear EEG measures in a longitudinal sample of children assessed in infancy and at ages 3, 5, and 7 years of age. We first examined the validity of this method by showing that calendar age is highly correlated with latent EEG complexity factors (r = 0.77). We then computed latent factors separately for distinguishing children with anxiety disorders from healthy controls using a 5-fold cross validation scheme and similarly for distinguishing children with externalizing disorders from healthy controls.

Results

We found that latent factors derived from EEG recordings at age 7 years were required to distinguish children with an anxiety disorder from healthy controls; recordings from infancy, 3 years, or 5 years alone were insufficient. However, recordings from two (5, 7 years) or three (3, 5, 7 years) recordings gave much better results than 7 year recordings alone. Externalizing disorders could be detected using 3- and 5 years EEG data, also giving better results with two or three recordings than any single snapshot. Further, sex assigned at birth was an important covariate that improved accuracy for both disorder groups, and birthweight as a covariate modestly improved accuracy for externalizing disorders. Recordings from infant EEG did not contribute to the classification accuracy for either anxiety or externalizing disorders.

Conclusion

This study suggests that latent factors extracted from EEG recordings in childhood are promising candidate biomarkers for anxiety and for externalizing disorders if chosen at appropriate ages.

Accurate detection of paroxysmal atrial fibrillation with certified-GAN and neural architecture search

This paper presents a novel machine learning framework for detecting PxAF, a pathological characteristic of electrocardiogram (ECG) that can lead to fatal conditions such as heart attack. To enhance the learning process, the framework involves a generative adversarial network (GAN) along with a neural architecture search (NAS) in the data preparation and classifier optimization phases. The GAN is innovatively invoked to overcome the class imbalance of the training data by producing the synthetic ECG for PxAF class in a certified manner. The effect of the certified GAN is statistically validated. Instead of using a general-purpose classifier, the NAS automatically designs a highly accurate convolutional neural network architecture customized for the PxAF classification task. Experimental results show that the accuracy of the proposed framework exhibits a high value of 99.0% which not only enhances state-of-the-art by up to 5.1%, but also improves the classification performance of the two widely-accepted baseline methods, ResNet-18, and Auto-Sklearn, by [Formula: see text] and [Formula: see text].

Estimating pandemic effects in urban mass transportation systems: An approach based on visibility graphs and network similarity

The COVID-19 pandemic has caused unprecedented disruptions to urban systems worldwide, but the extent and nature of these disruptions are not yet fully understood when it comes to transportation. In this work, we aim to explore how social distancing policies have affected passenger demand in urban mass transportation systems with the goal of supporting informed decisions in policy planning. We propose an approach based on complex networks and clustering time series with similar behavior, investigating possible changes in similarity patterns during pandemics and how they reflect into a regional scale. The methods shown here proved useful in detecting that lines in central or peripheral regions present different dynamics, that bus lines have changed their behavior during pandemic so that similarity relations have changed significantly, and that when social distancing started, there was an abrupt shock in the properties of daily passenger time series, and the system did not return to its original behavior until the end of the evaluated period. The approach allows to track evolution of the community structure in different scenarios providing managers with tools to reinforce or destabilize similarities if needed.

A review of symbolic dynamics and symbolic reconstruction of dynamical systems

Discretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via permutations has been developed to a powerful methodology, while recurrence plots have recently begun to be recognized as a method of discretization. In the meantime, horizontal visibility graphs have also been proposed to discretize time series. In this review, we summarize these methods and compare them from the viewpoint of symbolic dynamics, which is the right framework to study the symbolic representation of nonlinear time series and the inverse process: the symbolic reconstruction of dynamical systems. As we will show, symbolic dynamics is currently a very active research field with interesting applications.

The Future of Neurodiagnostics and Emergence of a New Science

Electroencepholography (EEG) is the oldest and original brain measurement technology. Since EEG was first used in clinical settings, the role of neurodiagnostic professionals has focused on two principal tasks that require specialized training. These include collecting the EEG recording, performed primarily by EEG Technologists, and interpreting the recording, generally done by physicians with proper specialization. Emerging technology appears to enable non-specialists to contribute to these tasks. Neurotechnologists may feel vulnerable to being displaced by new technology. A similar shift occurred in the last century when human "computers," employed to perform repetitive calculations needed to solve complex mathematics for the Manhattan and Apollo Projects, were displaced by new electronic computing machines. Many human "computers" seized on the opportunity created by the new computing technology to become the first computer programmers and create the new field of computer science. That transition offers insights for the future of neurodiagnostics. From its inception, neurodiagnostics has been an information processing discipline. Advances in dynamical systems theory, cognitive neuroscience, and biomedical informatics have created an opportunity for neurodiagnostic professionals to help create a new science of functional brain monitoring. A new generation of advanced neurodiagnostic professionals that bring together knowledge and skills in clinical neuroscience and biomedical informatics will benefit psychiatry, neurology, and precision healthcare, lead to preventive brain health through the lifespan, and lead the establishment of a new science of clinical neuroinformatics.

Stickiness and recurrence plots: An entropy-based approach

The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. 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. 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.

High-frequency imagery to capture coral tissue (Montipora capricornis) response to environmental stress, a pilot study

Environment stress is a major threat to the existence of coral reefs and has generated a lot of interest in the coral research community. Under the environmental stress, corals can experience tissue loss and/or the breakdown of symbiosis between the cnidarian host and its symbiotic algae causing the coral tissue to appear white as the skeleton can be seen by transparency. Image analysis is a common method used to assess tissue response under the environmental stress. However, the traditional approach is limited by the dynamic nature of the coral-algae symbiosis. Here, we observed coral tissue response in the scleractinian coral, Montipora capricornis, using high frequency image analysis throughout the experiment, as opposed to the typical start/end point assessment method. Color analysis reveals that the process can be divided into five stages with two critical stages according to coral tissue morphology and color ratio. We further explore changes to the morphology of individual polyps by means of the Pearson correlation coefficient and recurrence plots, where the quasi-periodic and nonstationary dynamics can be identified. The recurrence quantification analysis also allows the comparison between the different polyps. Our research provides a detailed visual and mathematical analysis of coral tissue response to environmental stress, which potentially shows universal applicability. Moreover, our approach provides a robust quantitative advancement for improving our insight into a suite of biotic responses in the perspective of coral health evaluation and fate prediction.

Strange attractor of a narwhal (Monodon monoceros)

Detecting structures within the continuous diving behavior of marine animals is challenging, and no universal framework is available. We captured such diverse structures using chaos theory. By applying time-delay embedding to exceptionally long dive records (83 d) from the narwhal, we reconstructed the state-space portrait. Using measures of chaos, we detected a diurnal pattern and its seasonal modulation, classified data, and found how sea-ice appearance shifts time budgets. There is more near-surface rest but deeper dives at solar noon, and more intense diving during twilight and at night but to shallower depths (likely following squid); sea-ice appearance reduces rest. The introduced geometrical approach is simple to implement and potentially helpful for mapping and labeling long-term behavioral data, identifying differences between individual animals and species, and detecting perturbations.

While animal-borne ocean sensors continue to advance and collect more data, there is a lack of an adequate framework to analyze records of irregular behavior. For example, in the Arctic—there sea-ice is declining but is fundamental for the life cycle of many endemic animals—near-surface dive records are usually ignored, and continuous data are reduced to a maximum depth or similar. Here, we propose to transform our way of thinking about animal motion underwater by turning to a chaos approach and using a flowing geometrical shape to understand the full diversity of behaviors on an example of a satellite-tagged narwhal. Our method may help to assess the susceptibility of narwhal and other animals to sea-ice loss and climate warming.

Multiple Sensors Data Integration for Traffic Incident Detection Using the Quadrant Scan

Non-recurrent congestion disrupts normal traffic operations and lowers travel time (TT) reliability, which leads to many negative consequences such as difficulties in trip planning, missed appointments, loss in productivity, and driver frustration. Traffic incidents are one of the six causes of non-recurrent congestion. Early and accurate detection helps reduce incident duration, but it remains a challenge due to the limitation of current sensor technologies. In this paper, we employ a recurrence-based technique, the Quadrant Scan, to analyse time series traffic volume data for incident detection. The data is recorded by multiple sensors along a section of urban highway. The results show that the proposed method can detect incidents better by integrating data from the multiple sensors in each direction, compared to using them individually. It can also distinguish non-recurrent traffic congestion caused by incidents from recurrent congestion. The results show that the Quadrant Scan is a promising algorithm for real-time traffic incident detection with a short delay. It could also be extended to other non-recurrent congestion types.

Nonlinear Time Series Analysis in Unstable Periodic Orbits Identification-Control Methods of Nonlinear Systems

The main purpose of this paper is to present a solution to the well-known problems generated by classical control methods through the analysis of nonlinear time series. Among the problems analyzed, for which an explanation has been sought for a long time, we list the significant reduction in control power and the identification of unstable periodic orbits (UPOs) in chaotic time series. To accurately identify the type of behavior of complex systems, a new solution is presented that involves a method of two-dimensional representation specific to the graphical point of view, and in particular the recurrence plot (RP). An example of the issue studied is presented by applying the recurrence graph to identify the UPO in a chaotic attractor. To identify a certain type of behavior in the numerical data of chaotic systems, nonlinear time series will be used, as a novelty element, to locate unstable periodic orbits. Another area of use for the theories presented above, following the application of these methods, is related to the control of chaotic dynamical systems by using RP in control techniques. Thus, the authors’ contributions are outlined by using the recurrence graph, which is used to identify the UPO from a chaotic attractor, in the control techniques that modify a system variable. These control techniques are part of the closed loop or feedback strategies that describe control as a function of the current state of the UPO stabilization system. To exemplify the advantages of the methods presented above, the use of the recurrence graph in the control of a buck converter through the application of a phase difference signal was analyzed. The study on the command of a direct current motor using a buck converter shows, through a final concrete application, the advantages of using these analysis methods in controlling dynamic systems.

Objective Domain Boundaries Detection in New Caledonian Nickel Laterite from Spectra Using Quadrant Scan

Modelling of 3D domain boundaries using information from drill holes is a standard procedure in mineral exploration and mining. Manual logging of drill holes can be difficult to exploit as the results may not be comparable between holes due to the subjective nature of geological logging. Exploration and mining companies commonly collect geochemical or mineralogical data from diamond drill core or drill chips; however, manual interpretation of multivariate data can be slow and challenging; therefore, automation of any of the steps in the interpretation process would be valuable. Hyperspectral analysis of drill chips provides a relatively inexpensive method of collecting very detailed information rapidly and consistently. However, the challenge of such data is the high dimensionality of the data’s variables in comparison to the number of samples. Hyperspectral data is usually processed to produce mineral abundances generally involving a range of assumptions. This paper presents the results of testing a new fast and objective methodology to identify the lithological boundaries from high dimensional hyperspectral data. This method applies a quadrant scan analysis to recurrence plots. The results, applied to nickel laterite deposits from New Caledonia, demonstrate that this method can identify transitions in the downhole data. These are interpreted as reflecting mineralogical changes that can be used as an aid in geological logging to improve boundary detection.

A versatile computational algorithm for time-series data analysis and machine-learning models

Here we introduce Local Topological Recurrence Analysis (LoTRA), a simple computational approach for analyzing time-series data. Its versatility is elucidated using simulated data, Parkinsonian gait, and in vivo brain dynamics. We also show that this algorithm can be used to build a remarkably simple machine-learning model capable of outperforming deep-learning models in detecting Parkinson’s disease from a single digital handwriting test.

Localizing category-related information in speech with multi-scale analyses

Measurements of the physical outputs of speech-vocal tract geometry and acoustic energy-are high-dimensional, but linguistic theories posit a low-dimensional set of categories such as phonemes and phrase types. How can it be determined when and where in high-dimensional articulatory and acoustic signals there is information related to theoretical categories? For a variety of reasons, it is problematic to directly quantify mutual information between hypothesized categories and signals. To address this issue, a multi-scale analysis method is proposed for localizing category-related information in an ensemble of speech signals using machine learning algorithms. By analyzing how classification accuracy on unseen data varies as the temporal extent of training input is systematically restricted, inferences can be drawn regarding the temporal distribution of category-related information. The method can also be used to investigate redundancy between subsets of signal dimensions. Two types of theoretical categories are examined in this paper: phonemic/gestural categories and syntactic relative clause categories. Moreover, two different machine learning algorithms were examined: linear discriminant analysis and neural networks with long short-term memory units. Both algorithms detected category-related information earlier and later in signals than would be expected given standard theoretical assumptions about when linguistic categories should influence speech. The neural network algorithm was able to identify category-related information to a greater extent than the discriminant analyses.

Time-frequency time-space LSTM for robust classification of physiological signals

Automated analysis of physiological time series is utilized for many clinical applications in medicine and life sciences. Long short-term memory (LSTM) is a deep recurrent neural network architecture used for classification of time-series data. Here time-frequency and time-space properties of time series are introduced as a robust tool for LSTM processing of long sequential data in physiology. Based on classification results obtained from two databases of sensor-induced physiological signals, the proposed approach has the potential for (1) achieving very high classification accuracy, (2) saving tremendous time for data learning, and (3) being cost-effective and user-comfortable for clinical trials by reducing multiple wearable sensors for data recording.

Revisiting stigmergy in light of multi-functional, biogenic, termite structures as communication channel

Termite mounds are fascinating because of their intriguing composition of numerous geometric shapes and materials. However, little is known about these structures, or of their functionalities. Most research has been on the basic composition of mounds compared with surrounding soils. There has been some targeted research on the thermoregulation and ventilation of the mounds of a few species of fungi-growing termites, which has generated considerable interest from human architecture. Otherwise, research on termite mounds has been scattered, with little work on their explicit properties. This review is focused on how termites design and build functional structures as nest, nursery and food storage; for thermoregulation and climatisation; as defence, shelter and refuge; as a foraging tool or building material; and for colony communication, either as in indirect communication (stigmergy) or as an information channel essential for direct communication through vibrations (biotremology). Our analysis shows that systematic research is required to study the properties of these structures such as porosity and material composition. High resolution computer tomography in combination with nonlinear dynamics and methods from computational intelligence may provide breakthroughs in unveiling the secrets of termite behaviour and their mounds. In particular, the examination of dynamic and wave propagation properties of termite-built structures in combination with a detailed signal analysis of termite activities is required to better understand the interplay between termites and their nest as superorganism. How termite structures serve as defence in the form of disguising acoustic and vibration signals from detection by predators, and what role local and global vibration synchronisation plays for building are open questions that need to be addressed to provide insights into how termites utilise materials to thrive in a world of predators and competitors.