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We analyse the asymptotic growth of the error for Hamiltonian flows due to small random perturbations. We compare the forward error with the reversibility error, showing their equivalence for linear flows on a compact phase space. The…
Multielectrode arrays allow recording of the activity of many single neurons, from which correlations can be calculated. The functional roles of correlations can be revealed by the measures of the information conveyed by neuronal activity;…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic…
The analysis of the intraday dynamics of correlations among high-frequency returns is challenging due to the presence of asynchronous trading and market microstructure noise. Both effects may lead to significant data reduction and may…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
We present the multiscale entropy analysis of short term physiological time series of simultaneously acquired samples of heart rate, blood pressure and lung volume, from healthy subjects and from subjects with Chronic Heart Failure.…
We discuss a general and efficient approach for "bootstrapping" short-time correlation data in chaotic or complex quantum systems to obtain information about long-time dynamics and stationary properties, such as the local density of states.…
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.…
In this work, time series analysis techniques are used to analyze sequential, equispaced mass measurements of a Si density artifact, collected from an electromechanical transducer. Specifically, techniques such as Power Spectral Density,…
Detecting early warning signals in climatic time series is essential for anticipating critical transitions and tipping points. Common statistical indicators include increased variance and lag-one autocorrelation prior to bifurcation points.…
Arrhythmias are irregularities in the hearts electrical system which cause rapid and irregular heartbeats. These heart conditions affect over 33 million people globally and significantly increase the risk of severe complications, including…
For finite random systems, it is possible to define two types of variances (noises). It is demonstrated that their ratio is useful in calculating the correlation length of an infinite and rather general random system, as a function of…
In recent years many procedures have been proposed to check the anisotropy of a dataset. We present a new simple procedure, based on a scale dependent approach, to detect anisotropy signatures in a given distribution with particular…
We present a novel method for the compensation of long duration data loss in audio signals, in particular music. The concealment of such signal defects is based on a graph that encodes signal structure in terms of time-persistent spectral…
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…
Correlation remains to be one of the most widely used statistical tools for assessing the strength of relationships between data series. This paper presents a novel compositional correlation method for detecting linear and nonlinear…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
Biomedical signals carry signature rhythms of complex physiological processes that control our daily bodily activity. The properties of these rhythms indicate the nature of interaction dynamics among physiological processes that maintain a…