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Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be…

Mass loss and variability are two linked, fundamental properties of evolved stars. In this paper I review our current understanding of these processes, with a particular focus on how observations and models are used to constrain reliable…

We derive reciprocal integral relations between phases and amplitude moduli for a class of wave functions that are cyclically varying in time. The relations imply that changes of a certain kind (e.g. not arising from the dynamic phase)…

Variable stars play a key role in understanding the Milky Way and the universe. The era of astronomical big data presents new challenges for quick identification of interesting and important variable stars. Accurately estimating the periods…

Forecasting a particular variable can depend upon temporal or spatial scale. Temporal variations that indicate variations with time, reflect the stochasticity present in the variable. Spatial variation usually are dominant in climatology…

Temporal offsets between the time series of solar activity indicators provide important clues regarding the physical processes responsible for the cyclic variability in the solar atmosphere. Hysteresis patterns generated between any two…

Two-imcompressible phase model of star is briefly revised. Effects of rotation and general relativity are considered.

We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…

Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…

We present a novel technique to identify calendar-based (annual, monthly and daily) periodicities of an interval-based temporal pattern. An interval-based temporal pattern is a pattern that occurs across a time-interval, then disappears for…

In the analysis of variable stars, the problem of sampling is central. This article focusses on the determination of the Nyquist frequency. It is well defined in the case of regular sampling. However, the time series of variable stars…

In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…

We present new periodograms that are effective in distinguishing Doppler shift from spectral shape variability in astronomical spectra. These periodograms, building upon the concept of partial distance correlation, separate the periodic…

The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been…

This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…

For many decades the determination of accurate fundamental parameters for stars (masses, radii, temperatures, luminosities, etc.) has mostly been the domain of eclipsing binary systems. That has begun to change as long-baseline…

Recently, evolving networks are becoming a suitable form to model many real-world complex systems, due to their peculiarities to represent the systems and their constituting entities, the interactions between the entities and the…

The first step when investigating time varying data is the detection of any reliable changes in star brightness. This step is crucial to decreasing the processing time by reducing the number of sources processed in later, slower steps.…

I present a discussion of fundamental stellar parameters and their observational determination in the context of interferometric measurements with current and future optical/infrared interferometric facilities. Stellar parameters and the…

We study the classical dynamics of a binary stars when there is an interchange of mass between them. Assuming that one of the star is more massive than the other, the dynamics of the lighter one is analyzed as a function of its time…