Related papers: Scaling in Non-stationary time series I

Biomedical signals carry signature rhythms of complex physiological processes that control our daily bodily activity. The properties of these rhythms indicate the nature of interaction dynamics among physiological processes that maintain a…

Time-lapse image sequences offer visually compelling insights into dynamic processes that are too slow to observe in real time. However, playing a long time-lapse sequence back as a video often results in distracting flicker due to random…

Deep discrete structured models have seen considerable progress recently, but traditional inference using dynamic programming (DP) typically works with a small number of states (less than hundreds), which severely limits model capacity. At…

Normalization and scaling are fundamental preprocessing steps in time series modeling, yet their role in Transformer-based models remains underexplored from a theoretical perspective. In this work, we present the first formal analysis of…

The article considers the problem of identifying the variable frequency of a sinusoidal signal. To obtain a regression model of the signal, an iterative differentiation of the original analytical expression is performed, and the swapping…

We address the generic problem of extracting the scaling exponents of a stationary, self-affine process realised by a timeseries of finite length, where information about the process is not known a priori. Estimating the scaling exponents…

The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where…

Downscaling is a landmark task in climate science and meteorology in which the goal is to use coarse scale, spatio-temporal data to infer values at finer scales. Statistical downscaling aims to approximate this task using statistical…

Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity…

The detrended fluctuation analysis (DFA) is extensively useful in stochastic processes to unveil the long-term correlation. Here, we apply the DFA to point processes that mimick earthquake data. The point processes are synthesized by a…

We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to…

When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical…

Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…

We report on experimental and theoretical studies of the fluctuation-induced escape time from a metastable state of a nanomechanical Duffing resonator in cryogenic environment. By tuning in situ the non-linear coefficient $\gamma$ we could…

We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…

Here we discuss a new fast detrending method for the non-stationary RR time series used in Heart Rate Variability analysis. The described method is based on the diffusion equation, and we show numerically that it is equivalent to the widely…

This paper investigates the decentralized stabilization problem for a class of interconnected systems in the presence of non-triangular structural uncertainties and time-varying parameters, where each subsystem exchanges information only…

Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal…

An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…