While the standard network description of complex systems is based on quantifying the link between pairs of system units, higher-order interactions (HOIs) involving three or more units often play a major role in governing the collective network behavior. This work introduces a new approach to quantify pairwise and HOIs for multivariate rhythmic processes interacting across multiple time scales. We define the so-called O-information rate (OIR) as a new metric to assess HOIs for multivariate time series, and present a framework to decompose the OIR into measures quantifying Granger-causal and instantaneous influences, as well as to expand all measures in the frequency domain. The framework exploits the spectral representation of vector autoregressive and state space models to assess the synergistic and redundant interaction among groups of processes, both in specific bands of interest and in the time domain after whole-band integration. Validation of the framework on simulated networks illustrates how the spectral OIR can highlight redundant and synergistic HOIs emerging at specific frequencies, which cannot be detected using time-domain measures. The applications to physiological networks described by heart period, arterial pressure and respiration variability measured in healthy subjects during a protocol of paced breathing, and to brain networks described by electrocorticographic signals acquired in an animal experiment during anesthesia, document the capability of our approach to identify informational circuits relevant to well-defined cardiovascular oscillations and brain rhythms and related to specific physiological mechanisms involving autonomic control and altered consciousness. The proposed framework allows a hierarchically-organized evaluation of time- and frequency-domain interactions in dynamic networks mapped by multivariate time series, and its high flexibility and scalability make it suitable for the investigation of networks beyond pairwise interactions in neuroscience, physiology and many other fields.

Despite the widespread diffusion of nonlinear methods for heart rate variability (HRV) analysis, the presence and the extent to which nonlinear dynamics contribute to short-term HRV are still controversial. This work aims at testing the hypothesis that different types of nonlinearity can be observed in HRV depending on the method adopted and on the physiopathological state. Two entropy-based measures of time series complexity (normalized complexity index, NCI) and regularity (information storage, IS), and a measure quantifying deviations from linear correlations in a time series (Gaussian linear contrast, GLC), are applied to short HRV recordings obtained in young (Y) and old (O) healthy subjects and in myocardial infarction (MI) patients monitored in the resting supine position and in the upright position reached through head-up tilt. The method of surrogate data is employed to detect the presence and quantify the contribution of nonlinear dynamics to HRV. We find that the three measures differ both in their variations across groups and conditions and in the percentage and strength of nonlinear HRV dynamics. NCI and IS displayed opposite variations, suggesting more complex dynamics in O and MI compared to Y and less complex dynamics during tilt. The strength of nonlinear dynamics is reduced by tilt using all measures in Y, while only GLC detects a significant strengthening of such dynamics in MI. A large percentage of detected nonlinear dynamics is revealed only by the IS measure in the Y group at rest, with a decrease in O and MI and during T, while NCI and GLC detect lower percentages in all groups and conditions. While these results suggest that distinct dynamic structures may lie beneath short-term HRV in different physiological states and pathological conditions, the strong dependence on the measure adopted and on their implementation suggests that physiological interpretations should be provided with caution.

We demonstrate an innovative CIGS-based solar cells model with a graded doping concentration absorber profile, capable of achieving high efficiency values. In detail, we start with an in-depth discussion concerning the parametrical study of conventional CIGS solar cells structures. We have used the wxAMPS software in order to numerically simulate cell electrical behaviour. By means of simulations, we have studied the variation of relevant physical and chemical parameters—characteristic of such devices—with changing energy gap and doping density of the absorber layer. Our results show that, in uniform CIGS cell, the efficiency, the open circuit voltage, and short circuit current heavily depend on CIGS band gap. Our numerical analysis highlights that the band gap value of 1.40 eV is optimal, but both the presence of Molybdenum back contact and the high carrier recombination near the junction noticeably reduce the crucial electrical parameters. For the above-mentioned reasons, we have demonstrated that the efficiency obtained by conventional CIGS cells is lower if compared to the values reached by our proposed graded carrier concentration profile structures (up to 21%).

Heart rate variability (HRV; variability of the RR interval of the electrocardiogram) results from the activity of several coexisting control mechanisms, which involve the influence of respiration (RESP) and systolic blood pressure (SBP) oscillations operating across multiple temporal scales and changing in different physiological states. In this study, multiscale information decomposition is used to dissect the physiological mechanisms related to the genesis of HRV in 78 young volunteers monitored at rest and during postural and mental stress evoked by head-up tilt (HUT) and mental arithmetics (MA). After representing RR, RESP and SBP at different time scales through a recently proposed method based on multivariate state space models, the joint information transfer ${\mathrm{T}}_{\mathrm{RESP},\mathrm{SBP}\to \mathrm{RR}}$ is decomposed into unique, redundant and synergistic components, describing the strength of baroreflex modulation independent of respiration ( ${\mathrm{U}}_{\mathrm{SBP}\to \mathrm{RR}}$ ), nonbaroreflex ( ${\mathrm{U}}_{\mathrm{RESP}\to \mathrm{RR}}$ ) and baroreflex-mediated ( ${\mathrm{R}}_{\mathrm{RESP},\mathrm{SBP}\to \mathrm{RR}}$ ) respiratory influences, and simultaneous presence of baroreflex and nonbaroreflex respiratory influences ( ${\mathrm{S}}_{\mathrm{RESP},\mathrm{SBP}\to \mathrm{RR}}$ ), respectively. We find that fast (short time scale) HRV oscillations—respiratory sinus arrhythmia—originate from the coexistence of baroreflex and nonbaroreflex (central) mechanisms at rest, with a stronger baroreflex involvement during HUT. Focusing on slower HRV oscillations, the baroreflex origin is dominant and MA leads to its higher involvement. Respiration influences independent on baroreflex are present at long time scales, and are enhanced during HUT.

Many complex systems in physics, biology and engineering are modeled as dynamical networks and described using multivariate time series analysis. Recent developments have shown that the emergent dynamics of a network system are significantly affected by interactions involving multiple network nodes which cannot be described using pairwise links. While these higher-order interactions can be probed using information-theoretic measures, a rigorous framework to describe them in the frequency domain is still lacking. This work presents an approach for the spectral decomposition of multivariate information measures, capable of identifying higher-order synergistic and redundant interactions between oscillatory processes. We show theoretically that synergy and redundancy can coexist at different frequencies among the output signals of a network system and can be detected only using the proposed spectral method. To demonstrate the broad applicability of the framework, we provide parametric and non-parametric data-efficient estimators for the spectral information measures, and employ them to describe multivariate interactions in three complex systems producing rich oscillatory dynamics, namely the human brain, a ring of electronic oscillators, and the global climate system. In these systems, we show that the use of our framework for the spectral decomposition of information measures reveals multivariate and higher-order interactions not detectable in the time domain. Our results are exemplary of how the frequency-specific analysis of multivariate dynamics can aid the implementation of assessment and control strategies in real-world network systems.