Related papers: Understanding fluctuations through Multivariate Ci…
We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For…
We design a novel, nonlinear single-source-of-error model for analysis of multiple business cycles. The model's specification is intended to capture key empirical characteristics of business cycle data by allowing for simultaneous cycles of…
A new method of frequency analysis is presented in detail. This new method - Variable Sine Algorithmic Analysis, (VSAA) - is based on a single variable sine function and it is powered by the simplex algorithm. It is used in cases of…
We propose the Multiple Changepoint Isolation (MCI) method for detecting multiple changes in the mean and covariance of a functional process. We first introduce a pair of projections to represent the variability "between" and "within" the…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time…
The detrended cross-correlation coefficient $\rho_{\rm DCCA}$ has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, non-stationary time series. It is based on the detrended…
Combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light curve of a given multi-periodic pulsating star, they can compromise the mode identification in an asteroseismic…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the…
Complex systems, such as the power grid, are essential for our daily lives. Many complex systems display (multi-)fractal behavior, correlated fluctuations and power laws. Whether the power-grid frequency, an indicator about the balance on…
We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…
Multifractal time series analysis is a approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of the complex amplitude of forced vibrations. The moments of the…
Carrying out explicitly the computation in a paradigmatic model of non-interacting systems, the Gaussian Model, we show the existence of a singular point in the probability distribution $P(M)$ of an extensive variable $M$. Interpreting…
The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground…
The starting point for much of multivariate analysis (MVA) is an $n\times p$ data matrix whose $n$ rows represent observations and whose $p$ columns represent variables. Some multivariate data sets, however, may be best conceptualized not…
Spectroscopically measuring low levels of non-equilibrium phenomena (e.g. emission in the presence of a large thermal background) can be problematic due to an unfavorable signal-to-noise ratio. An approach is presented to use time-series…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…