Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data

Exploring causal interactions between blood pressure and RR interval at the respiratory frequency

The mechanisms underlying the relationship between RR interval and systolic arterial pressure (SAP) variability at the respiratory frequency are still object of discussion. In this study, the information on directionality provided by causal cross-spectral analysis was exploited to infer possible influences of respiration on cardiovascular parameters variability. The ability of causal analysis to account for directionality in RR-SAP interrelationships in presence of respiratory exogenous effects was first tested on model simulations. Hence, real data measured on healthy subjects during spontaneous and paced breathing at 0.25 Hz were analysed. The results obtained in real data were consistent with simulations, thus supporting the hypothesis of different influences of respiration on SAP and RR interval variability under different physiological conditions

Estimation of confidence limits for descriptive indexes derived from autoregressive analysis of time series: Methods and application to heart rate variability

The growing interest in personalized medicine requires making inferences from descriptive indexes estimated from individual recordings of physiological signals, with statistical analyses focused on individual differences between/within subjects, rather than comparing supposedly homogeneous cohorts. To this end, methods to compute confidence limits of individual estimates of descriptive indexes are needed. This study introduces numerical methods to compute such confidence limits and perform statistical comparisons between indexes derived from autoregressive (AR) modeling of individual time series. Analytical approaches are generally not viable, because the indexes are usually nonlinear functions of the AR parameters. We exploit Monte Carlo (MC) and Bootstrap (BS) methods to reproduce the sampling distribution of the AR parameters and indexes computed from them. Here, these methods are implemented for spectral and information-theoretic indexes of heart-rate variability (HRV) estimated from AR models of heart-period time series. First, the MS and BC methods are tested in a wide range of synthetic HRV time series, showing good agreement with a gold-standard approach (i.e. multiple realizations of the "true" process driving the simulation). Then, real HRV time series measured from volunteers performing cognitive tasks are considered, documenting (i) the strong variability of confidence limits\ue2\u80\u99 width across recordings, (ii) the diversity of individual responses to the same task, and (iii) frequent disagreement between the cohort-average response and that of many individuals. We conclude that MC and BS methods are robust in estimating confidence limits of these AR-based indexes and thus recommended for short-term HRV analysis. Moreover, the strong inter-individual differences in the response to tasks shown by AR-based indexes evidence the need of individual-by-individual assessments of HRV features. Given their generality, MC and BS methods are promising for applications in biomedical signal processing and beyond, providing a powerful new tool for assessing the confidence limits of indexes estimated from individual recordings

Instantaneous Transfer Entropy for the Study of Cardiovascular and Cardio-Respiratory Nonstationary Dynamics

Objective: Measures of Transfer Entropy (TE) quantify the direction and strength of coupling between two complex systems. Standard approaches assume stationarity of the observations, and therefore are unable to track time-varying changes in nonlinear information transfer with high temporal resolution. In this study, we aim to define and validate novel instantaneous measures of transfer entropy to provide an im- proved assessment of complex non-stationary cardio-respiratory interactions

Local Granger causality

Granger causality (GC) is a statistical notion of causal influence based on prediction via linear vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes. We exploit such equivalence and calculate exactly the local Granger causality, i.e., the profile of the information transferred from the driver to the target process at each discrete time point; in this frame, GC is the average of its local version. We show that the variability of the local GC around its mean relates to the interplay between driver and innovation (autoregressive noise) processes, and it may reveal transient instances of information transfer not detectable from its average values. Our approach offers a robust and computationally fast method to follow the information transfer along the time history of linear stochastic processes, as well as of nonlinear complex systems studied in the Gaussian approximation

Assessment of Cardiorespiratory Interactions During Spontaneous and Controlled Breathing: Linear Parametric Analysis

In this work, we perform a linear parametric analysis of cardiorespiratory interactions in bivariate time series of heart period (HP) and respiration (RESP) measured in 19 healthy subjects during spontaneous breathing and controlled breathing at varying breathing frequency. The analysis is carried out computing measures of the total and causal interaction between HP and RESP variability in both time and frequency domains (low- and high-frequency, LF and HF). Results highlight strong cardiorespiratory interactions in the time domain and within the HF band that are not affected by the paced breathing condition. Interactions in the LF band are weaker and prevalent along the direction from HP to RESP, but result more influenced by the shift from spontaneous to controlled respiration

Synergistic information transfer in the global system of financial markets

Uncovering dynamic information flow between stock market indices has been the topic of several studies which exploited the notion of transfer entropy or Granger causality, its linear version. The output of the transfer entropy approach is a directed weighted graph measuring the information about the future state of each target provided by the knowledge of the state of each driving stock market index. In order to go beyond the pairwise description of the information flow, thus looking at higher order informational circuits, here we apply the partial information decomposition to triplets consisting of a pair of driving markets (belonging to America or Europe) and a target market in Asia. Our analysis, on daily data recorded during the years 2000 to 2019, allows the identification of the synergistic information that a pair of drivers carry about the target. By studying the influence of the closing returns of drivers on the subsequent overnight changes of target indexes, we find that (i) Korea, Tokyo, Hong Kong, and Singapore are, in order, the most influenced Asian markets; (ii) US indices SP500 and Russell are the strongest drivers with respect to the bivariate Granger causality; and (iii) concerning higher order effects, pairs of European and American stock market indices play a major role as the most synergetic three-variables circuits. Our results show that the Synergy, a proxy of higher order predictive information flow rooted in information theory, provides details that are complementary to those obtained from bivariate and global Granger causality, and can thus be used to get a better characterization of the global financial system

EpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number.

In infectious disease epidemiology, the instantaneous reproduction number [Formula: see text] is a time-varying parameter defined as the average number of secondary infections generated by an infected individual at time t. It is therefore a crucial epidemiological statistic that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool (EpiLPS) for robust estimation of the time-varying reproduction number. The proposed methodology smooths the epidemic curve and allows to obtain (approximate) point estimates and credible intervals of [Formula: see text] by employing the renewal equation, using Bayesian P-splines coupled with Laplace approximations of the conditional posterior of the spline vector. Two alternative approaches for inference are presented: (1) an approach based on a maximum a posteriori argument for the model hyperparameters, delivering estimates of [Formula: see text] in only a few seconds; and (2) an approach based on a Markov chain Monte Carlo (MCMC) scheme with underlying Langevin dynamics for efficient sampling of the posterior target distribution. Case counts per unit of time are assumed to follow a negative binomial distribution to account for potential overdispersion in the data that would not be captured by a classic Poisson model. Furthermore, after smoothing the epidemic curve, a "plug-in'' estimate of the reproduction number can be obtained from the renewal equation yielding a closed form expression of [Formula: see text] as a function of the spline parameters. The approach is extremely fast and free of arbitrary smoothing assumptions. EpiLPS is applied on data of SARS-CoV-1 in Hong-Kong (2003), influenza A H1N1 (2009) in the USA and on the SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France

Counterion effects in cyanine heterojunction photovoltaic devices

We investigated cyanine heterojunction photovoltaic devices using carbocyanine dyes as donors and buckminsterfullerene (C60) as acceptor. In particular, we focused on the influence of cyanine counterions on the photovoltaic device characteristics. It was found that counterions can be displaced in the applied electric field and give rise to important hystereses in the current-voltage characteristics, which are related to charge injection processes at electrode and organic heterointerfaces. Mobile counterions have also a drastic effect on the photocurrent spectrum and are responsible for an important C60 contribution at the organic heterojunction between cyanine and C60. If the counterion is covalently linked to the cyanine dye, the C60 contribution in the blue spectral domain can not be observe

Quantifying High-Order Interactions in Cardiovascular and Cerebrovascular Networks

We present a method to analyze the dynamics of physiological networks beyond the framework of pairwise interactions. Our method defines the so-called O-information rate (OIR) as a measure of the higher-order interaction among several physiological variables. The OIR measure is computed from the vector autoregressive representation of multiple time series, and is applied to the network formed by heart period, systolic and diastolic arterial pressure, respiration and cerebral blood flow variability series measured in healthy subjects at rest and after head-up tilt. Our results document that cardiovascular, cerebrovascular and respiratory interactions are highly redundant, and that redundancy is enhanced by the entrainment of cardiovascular and cerebrovascular oscillations and by sympathetic activation