Emmanuel Landa

Heart Rate and Systolic Blood Pressure Variability in the Time Domain in Patients with Recent and Long-Standing Diabetes Mellitus

Diabetes Mellitus (DM) affects the cardiovascular response of patients. To study this effect, interbeat intervals (IBI) and beat-to-beat systolic blood pressure (SBP) variability of patients during supine, standing and controlled breathing tests were analyzed in the time domain. Simultaneous noninvasive measurements of IBI and SBP for 30 recently diagnosed and 15 long-standing DM patients were compared with the results for 30 rigorously screened healthy subjects (control). A statistically significant distinction between control and diabetic subjects was provided by the standard deviation and the higher moments of the distributions (skewness, and kurtosis) with respect to the median. To compare IBI and SBP for different populations, we define a parameter, α, that combines the variability of the heart rate and the blood pressure, as the ratio of the radius of the moments for IBI and the same radius for SBP. As diabetes evolves, α decreases, standard deviation of the IBI detrended signal diminishes (heart rate signal becomes more “rigid”), skewness with respect to the median approaches zero (signal fluctuations gain symmetry), and kurtosis increases (fluctuations concentrate around the median). Diabetes produces not only a rigid heart rate, but also increases symmetry and has leptokurtic distributions. SBP time series exhibit the most variable behavior for recently diagnosed DM with platykurtic distributions. Under controlled breathing, SBP has symmetric distributions for DM patients, while control subjects have non-zero skewness. This may be due to a progressive decrease of parasympathetic and sympathetic activity to the heart and blood vessels as diabetes evolves.

Scale invariance as a symmetry in physical and biological systems: listening to photons, bubbles and heartbeats

Many dynamical systems from different areas of knowledge can be studied within the theoretical framework of time series, where the system can be considered as a black box, that only needs to be “listened” to. In this framework, non‐correlated series (white noise) and strongly correlated series (brownian noise or periodic series) constitute two extremes. Certain dynamical systems auto‐organize in a critical state that is characterized by 1/f or flicker noise. The family of fβ noises (β≤0) is fractal because fragments of the series are statistically identical to the original time series. 1/f noise (β = −1) is critical because it maximizes important complexity‐related quantities as memory, information content, efficiency and fractality. 1/f noise has been observed in classical systems, but also in quantum systems, and could possibly offer a unifying bridge of understanding between the macroscopic and the quantum world. In the present article, we will discuss some examples from both worlds.

Enhancement of early warning properties in the Kuramoto model and in an atrial fibrillation model due to an external perturbation of the system

When a complex dynamical system is externally disturbed, the statistical moments of signals associated to it can be affected in ways that depend on the nature and amplitude of the perturbation. In systems that exhibit phase transitions, the statistical moments can be used as Early Warnings (EW) of the transition. A natural question is thus to wonder what effect external disturbances have on the EWs of system. In this work we study the impact of external noise added to the system on the EWs, with particular focus on understanding the importance of the amplitude and complexity of the noise. We do this by analyzing the EWs of two computational models related to biology: the Kuramoto model, which is a paradigm of synchronization for biological systems, and a cellular automaton model of cardiac dynamics which has been used as a model for atrial fibrillation. For each model we first characterize the EWs. Then, we introduce external noise of varying intensity and nature to observe what effect this has on the EWs. In both cases we find that the introduction of noise amplified the EWs, with more complex noise having a greater effect. This both offers a way to improve the chance of detection of EWs in real systems and suggests that natural variability in the real world does not have a detrimental effect on EWs, but the opposite.

Chaotic dynamics in collective models of nuclei

We present results of an extensive analysis of classical and quantum signatures of chaos in the geometric collective model (GCM) and the interacting boson model (IBM) of nuclei. Apart from comparing the regular fraction of the classical phase space and the Brody parameter for the nearest neighbor spacing distribution in the quantum case, we also adopt (i) the Peres lattices allowing one to distinguish ordered and disordered parts of spectra and to reveal main ordering principles of quantum states, (ii) the geometrical method to determine the position where the transition from order to chaos occurs, and (iii) we look for the 1/fα power law in the power spectrum of energy level fluctuations. The Peres method demonstrates the adiabatic separation of collective rotations in the IBM.

Self similitude in the power spectra of nuclear energy levels

Protons and neutrons interact inside the nuclei with a non integrable interaction. It is shown that is possible to reproduce the energy statistics of nuclear energy levels analyzing the fluctuations of an ensemble of nuclear states produced by random interactions. In this contribution we analyze the characteristics of the fluctuations and distributions of the energy levels in order to understand the independent scale nature of the 1/f-noise nuclear energy levels.

Scale Invariance, Self Similarity and Critical Behavior in Classical and Quantum Systems

Symmetry and self-affinity or scale invariance are related concepts. We explore the fractal properties of fluctuations in dynamical systems, using some of the available tools in the context of time series analysis. We carry out a power spectrum study in the Fourier domain, the method of detrended fluctuation analysis and the investigation of autocorrelation function behavior. Our study focuses on two particular examples, the logistic module-1 map, which displays properties of classical dynamical systems, and the excitation spectrum of a schematic shell-model Hamiltonian, which is a simple system exhibiting quantum chaos.