Related papers: Discrete Scale Invariance in the Cascade Heart Rat…
The cardiac interbeat (RR) increment time series can be decomposed into two sub-sequences: a magnitude series and a sign series. We show that the sign sequence, a simple binary representation of the original RR series, retains fundamental…
An example of phase transition in natural complex systems is the qualitative and sudden change in the heart rhythm between sinus rhythm and atrial fibrillation (AF), the most common irregular heart rhythm in humans. While the system…
Hawkes processes are a popular framework to model the occurrence of sequential events, i.e., occurrence dynamics, in several fields such as social diffusion. In real-world scenarios, the inter-arrival time among events is irregular.…
We present the first systematic evidence for the origins of 1/f-type temporal scaling in human heart rate. The heart rate is regulated by the activity of two branches of the autonomic nervous system: the parasympathetic (PNS) and the…
Objective: The circadian rhythm synchronizes physiological and behavioural patterns with the 24-hour light-dark cycle. Disruption to the circadian rhythm is linked to various health conditions, though optimal methods to describe these…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
Nonlinear waves of the reaction-diffusion (RD) type occur in many biophysical systems, including the heart, where they initiate cardiac contraction. Such waves can form vortices called scroll waves, which result in the onset of…
Complexity measures are introduced, that quantify the change of the natural entropy fluctuations at different length scales in time-series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death…
We propose a picture of stock market crashes as critical points in a hierachical system with discrete scaling. The critical exponent is then complex, leading to log-periodic fluctuations in stock market indexes. We present ``experimental''…
Anomalous scaling in the statistics of an active scalar in homogeneous turbulent convection is studied using a dynamical shell model. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent…
We show that discretization of internode distribution in complex networks affects internode distances l_ij calculated as a function of degrees (k_i k_j) and an average path length <l> as function of network size N. For dense networks there…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
Cardiac and respiratory rhythms are known to exhibit a modest degree of phase synchronization, which is affected by age, diseases, and other factors. We study the fine temporal structure of this synchrony in healthy young, healthy elderly,…
In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that,…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
Background and Objective: The connection between depression and autonomous nervous system (ANS) is well documented in scientific literature. Heart rate variability (HRV) is a rich source of information for studying the dynamics of this…
We give a nontechnical description of the behaviour of dynamical systems governed by two distinct time scales. We discuss in particular memory effects, such as bifurcation delay and hysteresis, and comment the scaling behaviour of…
Plasma turbulence cascading from MHD to kinetic scales in the heliospheric plasma is believed to play a key role in coronal heating and fast solar wind acceleration, but the properties of the turbulence remain poorly constrained by…
We study the statistics of turbulent velocity fluctuations in the neighbourhood of a strong large scale vortex at very large Reynolds number. At each distance from the vortex core, we observe that the velocity spectrum has a power law…