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Astronomical data are typically irregular in time, e.g. the space (HIPPARCOS/TYCHO, KEPLER, GAIA, WISE etc.) and ground-based CCD (NSVS, ASAS, CRTS, SuperWASP etc.) and photographic (Harvard, Sonneberg, Odessa etc.) photometrical surveys.…
We present a detailed period analysis for 93 red semiregular variables by means of Fourier and wavelet analyses of long-term visual observations carried out by amateur astronomers. The results of this analysis yield insights into the mode…
The light curves of variable stars are commonly described using simple trigonometric models, that make use of the assumption that the model parameters are constant in time. This assumption, however, is often violated, and consequently, time…
We discuss different methods for phenomenological approximations of signals with (generally) irregularly spaced arguments. Such signals may be classified as periodic, multi-periodic, quasi-periodic (cyclic), burst-type and flicker-type (see…
(abridged) A method for simulating light curves containing stellar micro-variability for a range of spectral types and ages, based on parameter-by-parameter scaling of a multi-component fit to the solar irradiance power spectrum (from…
The expert system for time series analysis of irregularly spaced signals is reviewed. It consists of a number of complementary algorithms and programs, which may be effective for different types of variability. Obviously, for a pure sine…
Aims: During its all-sky survey phase, the eROSITA X-ray telescope onboard SRG scans through the ecliptic poles every 4 hours. This extensive data set of long-duration, frequent, and consistent observations of thousands of X-ray sources is…
Context. Recently our ability to study stars using asteroseismic techniques has increased dramatically, largely through the use of space based photometric observations. Work has also been done using ground based spectroscopic observations…
Using the phase plane diagrams, the phase light curves of a group of the Mira-type stars and semi-regular variables are analyzed. As generalized coordinates x and $\dot{x}$, we have used m - the brightness of the star and its phase…
We review methods for determination of "quasi-periods" (or "cycle length") of signals of low coherence. Such type of variability was called "cyclic" for semi-regular red variables, or "quasi-periodic oscillations" (QPO) for fast variability…
Context: The detection and identification of oscillation modes (in terms of their $\ell$, $m$ and successive $n$) is a great challenge for present and future asteroseismic space missions. The "peak tagging" is an important step in the…
Many astrophysical sources, especially compact accreting sources, show strong, random brightness fluctuations with broad power spectra in addition to periodic or quasi-periodic oscillations (QPOs) that have narrower spectra. The random…
This paper presents a comparison of popular period finding algorithms applied to the light curves of variable stars from the Catalina Real-time Transient Survey (CRTS), MACHO and ASAS data sets. We analyze the accuracy of the methods…
The study of temporal properties of variable sources can elucidate their physical processes. In this context, we present a critical study comparing three approaches to periodic or quasiperiodic behavior: Gaussian process, power spectrum,…
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…
Runtime Verification deals with the question of whether a run of a system adheres to its specification. This paper studies runtime verification in the presence of partial knowledge about the observed run, particularly where input values may…
Many astrophysical phenomena are time-varying, in the sense that their brightness change over time. In the case of periodic stars, previous approaches assumed that changes in period, amplitude, and phase are well described by either…
We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has…
We present a method for detection of weak continuous signals from sources in binary systems via the incoherent combination of many "short" coherently-analyzed segments. The main focus of the work is on the construction of a metric on the…
Although it is widely understood that pulsar timing observations generally contain time-correlated stochastic signals (TCSSs; red timing noise is of this type), most data analysis techniques that have been developed make an assumption that…