Related papers: The human ECG - nonlinear deterministic versus sto…
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which…
Cardiac diseases are the principal cause of human morbidity and mortality in the western world. The electric potential of the heart is a highly complex signal emerging as a result of nontrivial flow conduction, hierarchical structuring and…
Patients at high risk for sudden death often exhibit complex heart rhythms in which abnormal heartbeats are interspersed with normal heartbeats. We analyze such a complex rhythm in a single patient over a 12-hour period and show that the…
Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points,…
Temporal logics provide a formalism for expressing complex system specifications. A large body of literature has addressed the verification and the control synthesis problem for deterministic systems under such specifications. For…
The use of EEG signal to diagnose several brain abnormalities is well-established in the literature. Particularly, epileptic seizure can be detected using EEG signals and several works were done in this field. The joint time-frequency…
Consider the problem of interference mitigation in the identification of the dynamics of multidimensional control systems in the class of linear stationary models for single realizations of the observed signals. A concepts uncorrelated…
The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…
Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…
Recent development of the resonance scattering theory with a transient from the regular to chaotic internal dynamics inspires renewed interest to the problem of the elastic enhancement phenomenon. We reexamine the question what the…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
In this work we apply the Method of Critical Fluctuations (MCF)on human Electrocardiogram (ECG) time-series. The method is able to reveal critical characteristics, in terms of physical behavior, in experimentally recorded signals. Using the…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
Within cardiovascular disease detection using deep learning applied to ECG signals, the complexities of handling physiological signals have sparked growing interest in leveraging deep generative models for effective data augmentation. In…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
The electrocardiogram (ECG) remains a fundamental tool in cardiac diagnostics, yet its interpretation traditionally reliant on the expertise of cardiologists. The emergence of deep learning has heralded a revolutionary era in medical data…
ECG signals appear to be quite complex. In this paper, we present results, which show that a normal ECG signal, which is a function of time can be transformed into a relatively simpler signal by stretching the time in a predetermined way.…
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Most theoretical approaches describe them as purely deterministic or stochastic dynamical…