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Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences…
We analyze different data of the variation of the fine structure constant obtained with different methods to check their consistency.We test consistency using the modified Student test and confidence intervals. We split the data sets in…
This chapter is dedicated to the slow dynamics of the climate system, at time scales of one~thousand to one million years. We focus specifically on the phenomenon of ice ages that has characterised the slow evolution of climate over the…
We study the time variations of the cycles of 20 active stars based on decades-long photometric or spectroscopic observations. A method of time-frequency analysis, as discussed in a companion paper, is applied to the data. Fifteen stars…
We use wavelets to investigate period and amplitude changes in Mira and semiregular variables and found a variety of behaviours. Period and amplitude changes often go together, perhaps because changes in amplitude are causing period changes…
We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive…
Given a planar differential system with a first integral, we show how to find a normalizer. For systems with a center, we give an integral formula for the derivative of its period function.
Astrophysical objects frequently exhibit some irregularities or complex behaviour in their light curves. We focus primarily on hot stars, where both radial and non-radial pulsations are observed. One of the primary research goals is to…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
Properties of low-variability periods in the time series are analysed. The theoretical approach is used to show the relationship between the multi-scaling of low-variability periods and multi-affinity of the time series. It is shown that…
The orbital period is a measure of the size of a contact binary star, and can be combined with color to predict its luminosity to a fraction of stellar magnitude. This novel application of contact binary systems currently has limitations…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
We first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
This paper gives a way to simulate from the two star probability distribution on the space of simple graphs via auxiliary variables. Using this simulation scheme, the model is explored for various domains of the parameter values, and the…
Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
Astrophysical observations suggest that the fine structure constant (alpha) may (or may not) be evolving over the cosmological time scale. This raises a much debated question: is alpha variation due to the variation of the speed of light…
The relations between masses, radii and surface temperatures of stars are considered. It is shown that calculated values of these relations are in a satisfactory agreement with measuring data.
The rich acoustic oscillation spectrum in solar-type variables make these stars particularly interesting for studying fluid-dynamical aspects of the stellar interior. I present a summary of the properties of solar-like oscillations, how…