Related papers: Comments on arXiv:1811.00154 [astro-ph.IM] "AGN Va…

In this paper we consider the problem of the limits concerning the physical information that can be extracted from the analysis of one or more time series (light curves) typical of astrophysical objects. On the basis of theoretical…

When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…

Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the…

Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…

In this study, we demonstrate some of the caveats in common statistical methods used for analysing astronomical variability timescales. We consider these issues specifically in the context of active galactic nuclei (AGNs) and use a more…

The Active Galactic Nuclei (AGN) glossary is vast and complex. Depending on selection method, observing wavelength, and brightness, AGNs are assigned distinct labels, yet the relationship between different selection methods and the…

Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…

In a previous paper, we studied two statistical methods used to analyse the variability of active galactic nuclei (AGNs): the C and F statistics. Applying them to observed differential light-curves of 39 AGNs, we found that, even though the…

Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

Number of monitoring observations of continuum emission from Active Galactic Nuclei (AGNs) have been made in optical--X-ray bands. The results obtained so far show (i) random up and down on timescales longer than decades, (ii) no typical…

This work develops application techniques for stochastic modelling of Active Galactic Nuclei (AGN) variability as a probe of accretion disk physics. Stochastic models, specifically Continuous Auto-Regressive Moving Average (CARMA) models,…

We present the results of a study of different statistical methods currently used in the literature to analyse the (micro)variability of active galactic nuclei (AGNs) from ground-based optical observations. In particular, we focus on the…

Literature on optical and infrared microvariability in Active Galactic Nuclei (AGNs) reflects a diversity of statistical tests and strategies to detect tiny variations in the lightcurves of these sources. Comparison between the results…

Individual light curves of active galactic nuclei (AGNs) are nowadays successfully modelled with the damped random walk (DRW) stochastic process, characterized by the power exponential covariance matrix of the signal, with the power…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…

The advent of new time domain surveys and the imminent increase in astronomical data expose the shortcomings in traditional time series analysis (such as power spectra analysis) in characterising the abundantly varied, complex and…

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…