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

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

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

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

Revealing the structure of the outer disks of Be stars

Context. The structure of the inner parts of Be star disks (20 stellar radii) is well explained by the viscous decretion disk (VDD) model, which is able to reproduce the observable properties of most of the objects studied so far. The outer parts, on the ther hand, are not observationally well-explored, as they are observable only at radio wavelengths. A steepening of the spectral slope somewhere between infrared and radio wavelengths was reported for several Be stars that were previously detected in the radio, but a convincing physical explanation for this trend has not yet been provided. Aims. We test the VDD model predictions for the extended parts of a sample of six Be disks that have been observed in the radio to address the question of whether the observed turndown in the spectral energy distribution (SED) can be explained in the framework of the VDD model, including recent theoretical development for truncated Be disks in binary systems. Methods. We combine new multi-wavelength radio observations from the Karl. G. Jansky Very Large Array (JVLA) and Atacama Pathfinder Experiment (APEX) with previously published radio data and archival SED measurements at ultraviolet, visual, and infrared wavelengths. The density structure of the disks, including their outer parts, is constrained by radiative transfer modeling of the observed spectrum using VDD model predictions. In the VDD model we include the presumed effects of possible tidal influence from faint binary companions. Results. For 5 out of 6 studied stars, the observed SED shows strong signs of SED turndown between far-IR and radio wavelengths. A VDD model that extends to large distances closely reproduces the observed SEDs up to far IR wavelengths, but fails to reproduce the radio SED. ... (abstract continues but did not fit here)Comment: 20 pages, 8 figure

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

A Model-Free Method to Quantify Memory Utilization in Neural Point Processes

Objective: Quantifying the predictive capacity of a neural system, intended as the capability to store information and actively utilize it for dynamic system evolution, is a key component of neural information processing. Information storage (IS), the main information-theoretic measure quantifying the active utilization of memory in a dynamic system, is only defined for discrete-time processes, and although recent theoretical work laid the foundations for its continuous-time analysis, a reliable computation method is still needed for broader application to neural data. Methods: This work introduces a method for the model-free estimation of the so-called memory utilization rate (MUR), the continuous-time counterpart of the IS, specifically designed to quantify the predictive capacity stored in neural point processes. Moreover, a surrogate data-based procedure is used to correct estimation bias and detect significant memory levels in the analyzed point process. Results: The method is first validated in simulations of Poisson processes, both memoryless and with memory, as well as in realistic models of coupled cortical dynamics and heartbeat dynamics. It is then applied to real spike trains reflecting central and autonomic nervous system activities: in spontaneously growing cortical neuron cultures, the MUR detected increasing levels of memory utilization across maturation stages, linked to the emergence of synchronized bursting; in heartbeat modulation analysis, the MUR reflected sympathetic activation and vagal withdrawal occurring with postural stress, but not with mental stress. Conclusion and Significance: The proposed approach offers a novel, computationally reliable tool for the analysis of spike train data in computational neuroscience and physiology

Predictive Information Decomposition as a Tool to Quantify Emergent Dynamical Behaviors In Physiological Networks

Objective: This work introduces a framework for multivariate time series analysis aimed at detecting and quantifying collective emerging behaviors in the dynamics of physiological networks. Methods: Given a network system mapped by a vector random process, we compute the predictive information (PI) between the present and past network states and dissect it into amounts quantifying the unique, redundant and synergistic information shared by the present of the network and the past of each unit. Emergence is then quantified as the prevalence of the synergistic over the redundant contribution. The framework is implemented in practice using vector autoregressive (VAR) models. Results: Validation in simulated VAR processes documents that emerging behaviors arise in networks where multiple causal interactions coexist with internal dynamics. The application to cardiovascular and respiratory networks mapping the beat-to-beat variability of heart rate, arterial pressure and respiration measured at rest and during postural stress reveals the presence of statistically significant net synergy, as well as its modulation with sympathetic nervous system activation. Conclusion: Causal emergence can be efficiently assessed decomposing the PI of network systems via VAR models applied to multivariate time series. This approach evidences the synergy/redundancy balance as a hallmark of integrated short-term autonomic control in cardiovascular and respiratory networks. Significance: Measures of causal emergence provide a practical tool to quantify the mechanisms of causal influence that determine the dynamic state of cardiovascular and neural network systems across distinct physiopathological conditions

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