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In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first…
We use ordinal patterns and symbolic analysis to construct global climate networks and uncover long and short term memory processes. The data analyzed is the monthly averaged surface air temperature (SAT field) and the results suggest that…
Context. The PLAnetary Transits and Oscillations of stars (PLATO) mission will observe the same area of the sky continuously for at least two years in an effort to detect transit signals of an Earth-like planet orbiting a solar-like star.…
An important problem in modern applied science is characterizing the behavior of systems with complex internal dynamics subjected to external forcings from their environment. While a great variety of techniques has been developed to analyze…
Solar filament oscillations have been known for decades. Now thanks to the new capabilities of the new telescopes, these periodic motions are routinely observed. Oscillations in filaments show key aspects of their structure. A systematic…
The ability to measure polarisation, spectrum, temporal dynamics, and spatial amplitude and phase of optical beams is essential to study fundamental phenomena in laser dynamics, telecommunications and nonlinear optics. Current…
This paper proposes a joint analysis of variations of global sea-level pressure and of Earth's rotation (RP), expressed as the coordinates of the rotation pole and length of day. Sea-Level-Pressure (SLP) extracted components are a weak…
We show that while the Fourier transform can figure only an "intensity" of a periodic signal, there is an additional information embedded, which is a "coherence" of the signal. Supposing that the periodicity is reflected only on the…
We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(\theta, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type…
The rotating radio transients are sporadic pulsars which are difficult to detect through periodicity searches. By using a single-pulse search method, we can discover these sources, measure their periods, and determine timing solutions. Here…
Many rare weather events, including hurricanes, droughts, and floods, dramatically impact human life. To accurately forecast these events and characterize their climatology requires specialized mathematical techniques to fully leverage the…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
Many natural systems undergo critical transitions, i.e. sudden shifts from one dynamical regime to another. In the climate system, the atmospheric boundary layer can experience sudden transitions between fully turbulent states and…
Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for…
Periodically driven quantum systems can host non-equilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover $temporal$ $entanglement$ $transitions$ (TET) in a Floquet spin chain, which…
Astrophysical time series often contain periodic signals. The large and growing volume of time series data from photometric surveys demands computationally efficient methods for detecting and characterizing such signals. The most efficient…
The horizontal visibility algorithm has been recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the…
One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean…
Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…
Detecting oscillations in solar and stellar time series is complicated by non-stationary red noise and evolving background emission. Methods based on detrending and AR(1)-based wavelet analysis can introduce spurious periodicities and do…