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The distance covariance of Sz\'ekely, et al. [23] and Sz\'ekely and Rizzo [21], a powerful measure of dependence between sets of multivariate random variables, has the crucial feature that it equals zero if and only if the sets are mutually…

In this paper phase of a signal has been viewed from a different angle. According to this view a signal can have countably infinitely many phases, one associated with each Fourier component. In other words each frequency has a phase…

We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the…

The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures…

Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…

In this manuscript we present a comparative study about the determination of the relaxation (\textit{i.e.}, independence) time scales obtained from the correlation function, the mutual information, and a criterion based on the evaluation of…

The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…

We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…

Two numerical methods are proposed for detection of coupling between multiple time series generated by deterministic nonlinear systems. The first detects interdependence or the existence of coupling between time series. The second…

Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…

We consider a measure of dependence for symmetric $\alpha$-stable random vectors, which was introduced by the author in 1976. We demonstrate that this measure of dependence can be extended for much more broad class of random vectors (up to…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…

Peaks signify important events in a signal. In a pair of signals how peaks are occurring with mutual correspondence may offer us significant insights into the mutual interdependence between the two signals based on important events. In this…

The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…

Many complex systems - be they financial, natural, or social - are composed of units - such as stocks, neurons, or agents - whose joint activity can be represented as a multivariate time series. An issue of both practical and theoretical…

Phase difference function is established by means of phase transfer function between time domains of source and interference point. The function reveals a necessary interrelation between outcome of two-beam interference, source's frequency…

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node…

The extent of intra-individual and inter-individual variability is an important factor in determining the statistical, and hence possibly clinical, significance of observed differences in the EEG. This study investigates the changes in…

We study the time correlation functions of coupled linear Langevin dynamics without and with inertia effects, both analytically and numerically. The model equation represents the physical behavior of a harmonic oscillator in two or three…

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…