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

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

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

Oxidative stress and endothelial function in normal pregnancy versus pre-eclampsia, a combined longitudinal and case control study

Background: Pre-eclampsia (PE) is related to an impaired endothelial function. Endothelial dysfunction accounts for altered vascular reactivity, activation of the coagulation cascade and loss of vascular integrity. Impaired endothelial function originates from production of inflammatory and cytotoxic factors by the ischemic placenta and results in systemic oxidative stress (OS) and an altered bioavailability of nitric oxide (·NO). The free radical ·NO, is an endogenous endothelium-derived relaxing factor influencing endothelial function. In placental circulation, endothelial release of ·NO dilates the fetal placental vascular bed, ensuring feto-maternal exchange. The Endopreg study was designed to evaluate in vivo endothelial function and to quantify in vitro OS in normal and pre-eclamptic pregnancies. Methods/design: The study is divided into two arms, a prospective longitudinal study and a matched case control study. In the longitudinal study, pregnant patients ≥18 years old with a singleton pregnancy will be followed throughout pregnancy and until 6 months post-partum. In the case control study, cases with PE will be compared to matched normotensive pregnant women. Maternal blood concentration of superoxide (O2·) and placental concentration of ·NO will be determined using EPR (electron paramagnetic resonance). Endothelial function and arterial stiffness will be evaluated using respectively Peripheral Arterial Tonometry (PAT), Flow-Mediated Dilatation (FMD) and applanation tonometry. Placental expression of eNOS (endothelial NOS) will be determined using immune-histochemical staining. Target recruitment will be 110 patients for the longitudinal study and 90 patients in the case-control study. Discussion: The results of Endopreg will provide longitudinal information on in vivo endothelial function and in vitro OS during normal pregnancy and PE. Adoption of these vascular tests in clinical practice potentially predicts patients at risk to develop cardiovascular events later in life after PE pregnancies. ·NO, O2·- and eNOS measurements provide further inside in the pathophysiology of PE

A multivariate interval approach for inverse uncertainty quantification with limited experimental data

© 2018 Elsevier Ltd This paper introduces an improved version of a novel inverse approach for the quantification of multivariate interval uncertainty for high dimensional models under scarce data availability. Furthermore, a conceptual and practical comparison of the method with the well-established probabilistic framework of Bayesian model updating via Transitional Markov Chain Monte Carlo is presented in the context of the DLR-AIRMOD test structure. First, it is shown that the proposed improvements of the inverse method alleviate the curse of dimensionality of the method with a factor up to 105. Furthermore, the comparison with the Bayesian results revealed that the selection ofthe most appropriate method depends largely on the desired information and availability of data. In case large amounts of data are available, and/or the analyst desires full (joint)-probabilistic descriptors of the model parameter uncertainty, the Bayesian method is shown to be the most performing. On the other hand however, when such descriptors are not needed (e.g., for worst-case analysis), and only scarce data are available, the interval method is shown to deliver more objective and robust bounds on the uncertain parameters. Finally, also suggestions to aid the analyst in selecting the most appropriate method for inverse uncertainty quantification are given

Oxidative stress and endothelial function in normal pregnancy versus pre-eclampsia, a combined longitudinal and case control study

Background: Pre-eclampsia (PE) is related to an impaired endothelial function. Endothelial dysfunction accounts for altered vascular reactivity, activation of the coagulation cascade and loss of vascular integrity. Impaired endothelial function originates from production of inflammatory and cytotoxic factors by the ischemic placenta and results in systemic oxidative stress (OS) and an altered bioavailability of nitric oxide (·NO). The free radical ·NO, is an endogenous endothelium-derived relaxing factor influencing endothelial function. In placental circulation, endothelial release of ·NO dilates the fetal placental vascular bed, ensuring feto-maternal exchange. The Endopreg study was designed to evaluate in vivo endothelial function and to quantify in vitro OS in normal and pre-eclamptic pregnancies. Methods/design: The study is divided into two arms, a prospective longitudinal study and a matched case control study. In the longitudinal study, pregnant patients ≥18 years old with a singleton pregnancy will be followed throughout pregnancy and until 6 months post-partum. In the case control study, cases with PE will be compared to matched normotensive pregnant women. Maternal blood concentration of superoxide (O2·) and placental concentration of ·NO will be determined using EPR (electron paramagnetic resonance). Endothelial function and arterial stiffness will be evaluated using respectively Peripheral Arterial Tonometry (PAT), Flow-Mediated Dilatation (FMD) and applanation tonometry. Placental expression of eNOS (endothelial NOS) will be determined using immune-histochemical staining. Target recruitment will be 110 patients for the longitudinal study and 90 patients in the case-control study. Discussion: The results of Endopreg will provide longitudinal information on in vivo endothelial function and in vitro OS during normal pregnancy and PE. Adoption of these vascular tests in clinical practice potentially predicts patients at risk to develop cardiovascular events later in life after PE pregnancies. ·NO, O2·- and eNOS measurements provide further inside in the pathophysiology of PE

Oxidative stress in healthy pregnancy and preeclampsia is linked to chronic inflammation, iron status and vascular function

Background During normal pregnancy, placental oxidative stress (OS) is present during all three trimesters and is necessary to obtain normal cell function. However, if OS reaches a certain level, pregnancy complications might arise. In preeclampsia (PE), a dangerous pregnancy specific hypertensive disorder, OS induced in the ischemic placenta causes a systemic inflammatory response and activates maternal endothelial cells. In this study, we aimed to quantify superoxide concentrations (as a measure of systemic OS) using electron paramagnetic resonance (EPR) and correlate them to markers of systemic inflammation, iron status and vascular function. Methods Fifty-nine women with a healthy pregnancy (HP), 10 non-pregnant controls (NP) and 28 PE patients (32±3.3weeks) were included. During HP, blood samples for superoxide, neutrophil to lymphocyte ratio (NLR), mean platelet volume (MPV) and iron status were taken at 10, 25 and 39 weeks. Vascular measurements for arterial stiffness (carotid-femoral pulse wave velocity (CF-PWV), augmentation index (AIx), augmentation Pressure (AP)) and microvascular endothelial function (reactive hyperemia index (RHI)) were performed at 35 weeks. In PE, all measurements were performed at diagnosis. CMH (1-hydroxy-3-methoxycarbonyl-2,2,5,5-tetramethylpyrrolidine) was used as spin probe for EPR, since the formed CM radical corresponds to the amount of superoxide. Results Superoxide concentration remains stable during pregnancy (p = 0.92), but is significantly higher compared to the NP controls (p<0.0001). At 25 weeks, there is a significant positive correlation between superoxide and ferritin concentration. (p = 0.04) In PE, superoxide, systemic inflammation and iron status are much higher compared to HP (all p<0.001). During HP, superoxide concentrations correlate significantly with arterial stiffness (all p<0.04), while in PE superoxide is significantly correlated to microvascular endothelial function (p = 0.03). Conclusions During HP there is an increased but stable oxidative environment, which is correlated to ferritin concentration. If superoxide levels increase, there is an augmentation in arterial stiffness. In PE pregnancies, systemic inflammation and superoxide concentrations are higher and result in a deterioration of endothelial function. Together, these findings support the hypothesis that vascular function is directly linked to the amount of OS and that measurement of OS in combination with vascular function tests might be used in the prediction of PE

Publisher Correction: Reporting guideline for the early-stage clinical evaluation of decision support systems driven by artificial intelligence: DECIDE-AI (Nature Medicine, (2022), 28, 5, (924-933), 10.1038/s41591-022-01772-9)

In the version of this article initially published, a list of the DECIDE-AI expert group members and their affiliations was omitted and has now been included in the HTML and PDF versions of the article. *A list of authors and their affiliations appears online