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For a group of the Mira-type stars, semi-regular variables and some RV Tau - type stars the limit cycles were computed and plotted using the phase plane diagrams. As generalized coordinates x and $\dot{x},$ we have used $\phi$ - the…
Cyclostationary processes are those signals whose have vary almost periodically in statistics. It can give rise to random data whose statistical characteristics vary periodically with time although these processes not periodic functions of…
Detection of a planetary ring of exoplanets remains as one of the most attractive but challenging goals in the field. We present a methodology of a systematic search for exoplanetary rings via transit photometry of long-period planets. The…
Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this…
We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of…
In this paper we estimate the dynamic parameters of a time-varying coefficient model through radial kernel functions in the context of a longitudinal study. Our proposal is based on a linear combination of weighted kernel functions…
Variability is a common characteristic of pre-main-sequence stars (PMS). Near-IR variability surveys of young stellar objects (YSOs) can probe stellar and circumstellar environments and provide information about the dynamics of the on going…
Sequential monitoring in clinical trials is often employed to allow for early stopping and other interim decisions, while maintaining the type I error rate. However, sequential monitoring is typically described only in the context of a…
Determining accurate and precise stellar ages is a major problem in astrophysics. These determinations are either obtained through empirical relations or model-dependent approaches. Currently, seismic modelling is one of the best ways of…
The presence of mean motion resonances (MMRs) complicates analysis and fitting of planetary systems observed through the radial velocity (RV) technique. MMR can allow planets to remain stable in regions of phase space where strong…
We introduce the Statistical Asynchronous Regression (SAR) method: a technique for determining a relationship between two time varying quantities without simultaneous measurements of both quantities. We require that there is a time…
The origin of the long secondary periods (LSPs) in red variables remains a mystery up to now, although there exist many models. The light curves of some LSPs stars mimic an eclipsing binary with a pulsating red giant component. To test this…
In this paper we present radial velocity curves of AGB variables that exhibit various kinds of anomalies: Semiregular variables (SRVs) with typical mira periods, SRVs exceeding the mira 2.5 mag amplitude limit, miras with secondary maxima…
The Rapid Temporal Survey (RATS) explores the faint, variable sky. Our observations search a parameter space which, until now, has never been exploited from the ground. Our strategy involves observing the sky close to the Galactic plane…
A continuous adaptive control design is developed for nonlinear dynamical systems with linearly parameterizable uncertainty involving time-varying uncertain parameters. The key feature of this design is a robust integral of the sign of the…
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
We use Kuiper's test to detect periodicities in X-ray and gamma-ray observations. Like Rayleigh's test, it uses the individual photon arrival times, and is therefore well suited to the analysis of faint sources. Our method makes it possible…
Stellar activity is the ultimate source of radial-velocity (RV) noise in the search for Earth-mass planets orbiting late-type main-sequence stars. We analyse the performance of four different indicators and the chromospheric index $\log…
We derive solutions to transit light curves of exoplanets orbiting rapidly-rotating stars. These stars exhibit significant oblateness and gravity darkening, a phenomenon where the poles of the star have a higher temperature and luminosity…
Astronomy is presently experiencing profound growth in the deployment of machine learning to explore large datasets. However, transient quasi-periodic oscillations (QPOs) which appear in power density spectra of many X-ray binary system…