Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics.

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p-1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes.

Network Dynamics in Elemental Assimilation and Metabolism.

Metabolism and physiology frequently follow non-linear rhythmic patterns which are reflected in concepts of homeostasis and circadian rhythms, yet few biomarkers are studied as dynamical systems. For instance, healthy human development depends on the assimilation and metabolism of essential elements, often accompanied by exposures to non-essential elements which may be toxic. In this study, we applied laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) to reconstruct longitudinal exposure profiles of essential and non-essential elements throughout prenatal and early post-natal development. We applied cross-recurrence quantification analysis (CRQA) to characterize dynamics involved in elemental integration, and to construct a graph-theory based analysis of elemental metabolism. Our findings show how exposure to lead, a well-characterized toxicant, perturbs the metabolism of essential elements. In particular, our findings indicate that high levels of lead exposure dysregulate global aspects of metabolic network connectivity. For example, the magnitude of each element's degree was increased in children exposed to high lead levels. Similarly, high lead exposure yielded discrete effects on specific essential elements, particularly zinc and magnesium, which showed reduced network metrics compared to other elements. In sum, this approach presents a new, systems-based perspective on the dynamics involved in elemental metabolism during critical periods of human development.

Social distancing at health care centers early in the pandemic helps to protect population from COVID-19.

The impact of COVID-19 outbreak has been unequal across Spanish regions. The epidemic wave has been smoother in the Region of Murcia (RM) (6 deaths/100,000 residents). Physical distance from health centers from day 0 is an additional social distancing measure that confers an advantageous starting position in the fight against COVID-19. Late healthcare distancing measures are not as powerful as the early ones.

A Prototype Framework Design for Assisting the Detection of Atrial Fibrillation Using a Generic Low-Cost Biomedical Sensor.

Cardiovascular diseases are the leading cause of death around the world. As a result, low-cost biomedical sensors have been gaining importance in business and research over the last few decades. Their main benefits include their small size, light weight, portability and low power consumption. Despite these advantages, they are not generally used for clinical monitoring mainly because of their low accuracy in data acquisition. In this emerging technological context, this paper contributes by discussing a methodology to help practitioners build a prototype framework based on a low-cost commercial sensor. The resulting application consists of four modules; namely, a digitalization module whose input is an electrocardiograph signal in portable document format (PDF) or joint photographic expert group format (JPEG), a module to further process and filter the digitalized signal, a selectable data calibration module and, finally, a module implementing a classification algorithm to distinguish between individuals with normal sinus rhythms and those with atrial fibrillation. This last module employs our recently published symbolic recurrence quantification analysis (SRQA) algorithm on a time series of RR intervals. Moreover, we show that the algorithm applies to any biomedical low-cost sensor, achieving good results without requiring.

Transfer entropy on symbolic recurrences.

Recurrence quantification analysis offers a powerful framework to investigate complexity in dynamical systems. While several studies have demonstrated the possibility of multivariate recurrence quantification analysis, information-theoretic tools for the discovery of causal links remain elusive. Particularly enticing is to formulate information-theoretic tools on symbolic recurrence plots, which alleviate some of the methodological challenges of traditional recurrence plots and offer a richer representation of recurrences. Toward this aim, we establish a probability space in which we ground a theory of information that encodes information in the recurrences of the symbols. We introduce transfer entropy on symbolic recurrences as a tool to guide the inference of the strength and direction of the interaction between dynamical systems. We demonstrate statistically reliable discovery of causal links on synthetic and experimental time series, from only two time series or a larger dataset with multiple realizations. The proposed approach brings together recurrence plots, information theory, and symbolic dynamics to empower researchers and practitioners with effective means to visualize and quantify interactions in dynamical systems.

Application of symbolic recurrence to experimental data, from firearm prevalence to fish swimming.

Recurrence plots and recurrence quantification analysis are powerful tools to study the behavior of dynamical systems. What we learn through these tools is typically determined by the choice of a distance threshold in the phase space, which introduces arbitrariness in the definition of recurrence. Not only does symbolic recurrence overcome this difficulty, but also it offers a richer representation that book-keeps the recurrent portions of the phase space. Using symbolic recurrences, we can construct recurrence plots, perform quantification analysis, and examine causal links between dynamical systems from their time-series. Although previous efforts have demonstrated the feasibility of such a symbolic framework on synthetic data, the study of real time-series remains elusive. Here, we seek to bridge this gap by systematically examining a wide range of experimental datasets, from firearm prevalence and media coverage in the United States to the effect of sex on the interaction of swimming fish. This work offers a compelling demonstration of the potential of symbolic recurrence in the study of real-world applications across different research fields while providing a computer code for researchers to perform their own time-series explorations.

Inference of time-varying networks through transfer entropy, the case of a Boolean network model.

Inferring network topologies from the time series of individual units is of paramount importance in the study of biological and social networks. Despite considerable progress, our success in network inference is largely limited to static networks and autonomous node dynamics, which are often inadequate to describe complex systems. Here, we explore the possibility of reconstructing time-varying weighted topologies through the information-theoretic notion of transfer entropy. We focus on a Boolean network model in which the weight of the links and the spontaneous activity periodically vary in time. For slowly-varying dynamics, we establish closed-form expressions for the stationary periodic distribution and transfer entropy between each pair of nodes. Our results indicate that the instantaneous weight of each link is mapped into a corresponding transfer entropy value, thereby affording the possibility of pinpointing the dominant weights at each time. However, comparing transfer entropy readings at different times may provide erroneous estimates of the strength of the links in time, due to a counterintuitive modulation of the information flow by the non-autonomous dynamics. In fact, this time variation should be used to scale transfer entropy values toward the correct inference of the time evolution of the network weights. This study constitutes a necessary step toward a mathematically-principled use of transfer entropy to reconstruct time-varying networks.

Symbolic recurrence plots to analyze dynamical systems.

This paper, based on the concept of symbolic correlation integral, introduces a set of symbolic recurrence plots and associated invariant measures, which are independent of the distance parameter, serving as a tool for quantifying the dynamic structure. These new measures allow the study of transient behavior, coexistence of attractors, bifurcations, and structural change. The final user does not have to choose the free distance parameter. An empirical application to electrocardiography data illustrates the use of symbolic recurrence measures.

Symbolic dynamics of animal interaction.

Since its introduction nearly two decades ago, transfer entropy has contributed to an improved understanding of cause-and-effect relationships in coupled dynamical systems from raw time series. In the context of animal behavior, transfer entropy might help explain the determinants of leadership in social groups and elucidate escape response to predator attacks. Despite its promise, the potential of transfer entropy in animal behavior is yet to be fully tested, and a number of technical challenges in information theory and statistics remain open. Here, we examine an alternative approach to the computation of transfer entropy based on symbolic dynamics. In this context, a symbol is associated with a specific locomotory bout across two or more consecutive time instants, such as reversing the swimming direction. Symbols encapsulate salient locomotory patterns and the associated permutation transfer entropy quantifies the ability to predict the patterns of an individual given those of another individual. We demonstrate this framework on an existing dataset on fish, for which we have knowledge of the underlying cause-and-effect relationship between the focal subject and the stimulus. Symbolic dynamics offers an intuitive and robust approach to study animal behavior, which could enable the inference of causal relationship from noisy experimental observations of limited duration.

A method to analyse measurement invariance under uncertainty in between-subjects design.

In this research we have introduced a new test (H-test) for analyzing scale invariance in between group designs, and considering uncertainty in individual responses, in order to study the adequacy of disparate rating and visual scales for measuring abstract concepts. The H-test is easy to compute and, as a nonparametric test, does not require any a priori distribution of the data nor conditions on the variances of the distributions to be tested. We apply this test to measure perceived service quality of consumers of a sports services. Results show that, without considering uncertainty, the 1-7 scale is invariant, in line with the related works regarding this topic. However, de 1-5 scale and the 1-7 scale are invariant when adding uncertainty to the analysis. Therefore, adding uncertainty importantly change the conclusions regarding invariance analysis. Both types of visual scales are not invariant in the uncertainty scenario. Implications for the use of rating scales are discussed.

Quantifying the role of the COVID-19 pandemic in the 2020 U.S. presidential elections.

In the media, a prevalent narrative is that the incumbent United States President Donald J. Trump lost the 2020 elections because of the way he handled the COVID-19 pandemic. Quantitative evidence to support this narrative is, however, limited. We put forward a spatial, information-theoretic approach to critically examine the link between voting behavior and COVID-19 incidence in the 2020 presidential elections. The approach overcomes classical limitations of traditional regression analysis, where it does not require an underlying mathematical model and it can capture nonlinear interactions. From the analysis of county-level data, we uncovered a robust association between voting behavior and prevalence of COVID-19 cases. Surprisingly, such an association points in the opposite direction from the accepted narrative: in counties that experienced less COVID-19 cases, the incumbent President lost more ground to his opponent, now President Joseph R. Biden Jr. A tenable explanation of this observation is the different attitude of liberal and conservative voters toward the pandemic, which led to more COVID-19 spreading in counties with a larger share of republican voters.

Data-Driven Classification of Human Movements in Virtual Reality-Based Serious Games: Preclinical Rehabilitation Study in Citizen Science.

BACKGROUND: Sustained engagement is essential for the success of telerehabilitation programs. However, patients' lack of motivation and adherence could undermine these goals. To overcome this challenge, physical exercises have often been gamified. Building on the advantages of serious games, we propose a citizen science-based approach in which patients perform scientific tasks by using interactive interfaces and help advance scientific causes of their choice. This approach capitalizes on human intellect and benevolence while promoting learning. To further enhance engagement, we propose performing citizen science activities in immersive media, such as virtual reality (VR). OBJECTIVE: This study aims to present a novel methodology to facilitate the remote identification and classification of human movements for the automatic assessment of motor performance in telerehabilitation. The data-driven approach is presented in the context of a citizen science software dedicated to bimanual training in VR. Specifically, users interact with the interface and make contributions to an environmental citizen science project while moving both arms in concert. METHODS: In all, 9 healthy individuals interacted with the citizen science software by using a commercial VR gaming device. The software included a calibration phase to evaluate the users' range of motion along the 3 anatomical planes of motion and to adapt the sensitivity of the software's response to their movements. During calibration, the time series of the users' movements were recorded by the sensors embedded in the device. We performed principal component analysis to identify salient features of movements and then applied a bagged trees ensemble classifier to classify the movements. RESULTS: The classification achieved high performance, reaching 99.9% accuracy. Among the movements, elbow flexion was the most accurately classified movement (99.2%), and horizontal shoulder abduction to the right side of the body was the most misclassified movement (98.8%). CONCLUSIONS: Coordinated bimanual movements in VR can be classified with high accuracy. Our findings lay the foundation for the development of motion analysis algorithms in VR-mediated telerehabilitation.

Integrating old and new complexity measures toward automated seizure detection from long-term video EEG recordings.

Automated seizure detection in long-term video-EEG recordings is far from being integrated into common clinical practice. Here, we leverage classical and state-of-the-art complexity measures to robustly and automatically detect seizures from scalp recordings. Brain activity is scored through eight features, encompassing traditional time domain and novel measures of recurrence. A binary classification algorithm tailored to treat unbalanced dataset is used to determine whether a time window is ictal or non-ictal from its features. The application of the algorithm on a cohort of ten adult patients with focal refractory epilepsy indicates sensitivity, specificity, and accuracy of 90%, along with a true alarm rate of 95% and less than four false alarms per day. The proposed approach emphasizes ictal patterns against noisy background without the need of data preprocessing. Finally, we benchmark our approach against previous studies on two publicly available datasets, demonstrating the good performance of our algorithm.

An entropy test for single-locus genetic association analysis.

BACKGROUND: The etiology of complex diseases is due to the combination of genetic and environmental factors, usually many of them, and each with a small effect. The identification of these small-effect contributing factors is still a demanding task. Clearly, there is a need for more powerful tests of genetic association, and especially for the identification of rare effects RESULTS: We introduce a new genetic association test based on symbolic dynamics and symbolic entropy. Using a freely available software, we have applied this entropy test, and a conventional test, to simulated and real datasets, to illustrate the method and estimate type I error and power. We have also compared this new entropy test to the Fisher exact test for assessment of association with low-frequency SNPs. The entropy test is generally more powerful than the conventional test, and can be significantly more powerful when the genotypic test is applied to low allele-frequency markers. We have also shown that both the Fisher and Entropy methods are optimal to test for association with low-frequency SNPs (MAF around 1-5%), and both are conservative for very rare SNPs (MAF<1%) CONCLUSIONS: We have developed a new, simple, consistent and powerful test to detect genetic association of biallelic/SNP markers in case-control data, by using symbolic dynamics and symbolic entropy as a measure of gene dependence. We also provide a standard asymptotic distribution of this test statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. The entropy test is generally as good or even more powerful than the conventional and Fisher tests. Furthermore, the entropy test is more computationally efficient than the Fisher's Exact test, especially for large number of markers. Therefore, this entropy-based test has the advantage of being optimal for most SNPs, regardless of their allele frequency (Minor Allele Frequency (MAF) between 1-50%). This property is quite beneficial, since many researchers tend to discard low allele-frequency SNPs from their analysis. Now they can apply the same statistical test of association to all SNPs in a single analysis., which can be especially helpful to detect rare effects.

An information-theoretic approach to study spatial dependencies in small datasets.

From epidemiology to economics, there is a fundamental need of statistically principled approaches to unveil spatial patterns and identify their underpinning mechanisms. Grounded in network and information theory, we establish a non-parametric scheme to study spatial associations from limited measurements of a spatial process. Through the lens of network theory, we relate spatial patterning in the dataset to the topology of a network on which the process unfolds. From the available observations of the spatial process and a candidate network topology, we compute a mutual information statistic that measures the extent to which the measurement at a node is explained by observations at neighbouring nodes. For a class of networks and linear autoregressive processes, we establish closed-form expressions for the mutual information statistic in terms of network topological features. We demonstrate the feasibility of the approach on synthetic datasets comprising 25-100 measurements, generated by linear or nonlinear autoregressive processes. Upon validation on synthetic processes, we examine datasets of human migration under climate change in Bangladesh and motor vehicle deaths in the United States of America. For both these real datasets, our approach is successful in identifying meaningful spatial patterns, begetting statistically-principled insight into the mechanisms of important socioeconomic problems.

Unequal effects of the national lockdown on mental and social health in Italy.

With the exception of a few countries that chose a different approach, the worldwide reaction to the COVID-19 pandemic was a (longer or shorter) period of national lockdown. While the economic consequences of shutting down national economies were immediately evident, the sociopsychiatric implications of the social confinement of the entire population remain hidden and not fully understood. Italy has been the first European country to be severely impacted by the COVID-19 pandemic, to which it responded through strict lockdown measurements. The results of a timely survey on mental and social health, carried out by students and teachers of a middle school in Rome, might help identify the most vulnerable groups of the population. This evidence could be crucial in conceiving and enacting targeted public health policies to mitigate the consequences of the pandemic on mental health and to prevent intolerance to containment measures in some population segments, which could hamper worldwide efforts in the fight against COVID-19.

Symbolic Recurrence Analysis of RR Interval to Detect Atrial Fibrillation.

Atrial fibrillation (AF) is a sustained cardiac arrhythmia associated with stroke, heart failure, and related health conditions. Though easily diagnosed upon presentation in a clinical setting, the transient and/or intermittent emergence of AF episodes present diagnostic and clinical monitoring challenges that would ideally be met with automated ambulatory monitoring and detection. Current approaches to address these needs, commonly available both in smartphone applications and dedicated technologies, combine electrocardiogram (ECG) sensors with predictive algorithms to detect AF. These methods typically require extensive preprocessing, preliminary signal analysis, and the integration of a wide and complex array of features for the detection of AF events, and are consequently vulnerable to over-fitting. In this paper, we introduce the application of symbolic recurrence quantification analysis (SRQA) for the study of ECG signals and detection of AF events, which requires minimal pre-processing and allows the construction of highly accurate predictive algorithms from relatively few features. In addition, this approach is robust against commonly-encountered signal processing challenges that are expected in ambulatory monitoring contexts, including noisy and non-stationary data. We demonstrate the application of this method to yield a highly accurate predictive algorithm, which at optimal threshold values is 97.9% sensitive, 97.6% specific, and 97.7% accurate in classifying AF signals. To confirm the robust generalizability of this approach, we further evaluated its performance in the implementation of a 10-fold cross-validation paradigm, yielding 97.4% accuracy. In sum, these findings emphasize the robust utility of SRQA for the analysis of ECG signals and detection of AF. To the best of our knowledge, the proposed model is the first to incorporate symbolic analysis for AF beat detection.

Plasticity in leader-follower roles in human teams.

In humans, emergence of leaders and followers is key to group performance, but little is known about the whys and hows of leadership. A particularly elusive question entails behavioral plasticity in leadership across social contexts. Addressing this question requires to eliminate social feedback between focal individuals and their partners in experiments that could illuminate the spontaneous emergence of social roles. We investigated plasticity in leader-follower roles in cooperation, where members choose the task toward a shared goal, and coordination, where members adjust their actions in real time based on social responsiveness. Through a computer-programmed virtual partner, we demonstrate adaptive plasticity in leader-follower roles. Humans increased their followership to cooperate when the partner led more in the choice of the task, whereas they showed only weak leadership when the partner followed more. We leveraged the information-theoretic notion of transfer entropy to quantify leadership and followership in coordination from their movements. When exhibiting stronger followership in task cooperation, humans coordinated more with the partner's movement, with greater information being transferred from the partner to humans. The evidence of behavioral plasticity suggests that humans are capable of adapting their leader-follower roles to their social environments, in both cooperation and coordination.