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

Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…

Adaptive or dynamic signal sampling in sensing systems can adapt subsequent sampling strategies based on acquired signals, thereby potentially improving image quality and speed. This paper proposes a Bayesian method for adaptive sampling…

We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and…

The long-term evolution of astrophysical systems is driven by a Hamiltonian that is independent of the fast angle. As this Hamiltonian may contain explicitly time-dependent parameters, the conservation of mechanical energy is not guaranteed…

I investigate the possibility that explicit solutions of stochastic reaction-diffusion equations can be found by multiplying the deterministic travelling waves with a stochastic exponent. This approach has become widespread in the…

Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually…

Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring…

We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…

Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but…

One of the main science goals of the Large Synoptic Survey Telescope (LSST) is to uncover the nature of cosmic acceleration. In the base analysis, possible deviations from the Lambda-Cold-Dark-Matter ($\Lambda$CDM) background evolution will…

Experimental data is often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are…

We demonstrate how, with a purely empirical analysis of the irregular lightcurve data, one can extract a great deal of information about the stellar pulsation mechanism. An application to R Sct thus shows that the irregular lightcurve is…

To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the…

Stellar dynamics is almost unreasonably well suited for an implementation in terms of special-purpose hardware. Unlike the case of molecular dynamics, stellar dynamics deals exclusively with a long-range force, gravity, which leads to a…

We describe a simple stochastic method, so-called Langevin approach, which enables one to extract evolution equations of stochastic variables from a set of measurements. Our method is parameter-free and it is based on the nonlinear Langevin…

In the era of rapidly increasing amounts of time series data, classification of variable objects has become the main objective of time-domain astronomy. Classification of irregularly sampled time series is particularly difficult because the…

Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled,…

We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…

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.…

Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and…