Related papers: Computing the multifractal spectrum from time seri…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
Spectra of ordered eigenvalues of finite Random Matrices are interpreted as a time series. Dataadaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding…
A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the…
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…
This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated and on its base a computationally effective algorithm is constructed for decomposition of a…
The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated…
The fluctuations in the quantum spectrum could be treated like a time series. In this framework, we explore the statistical self-similarity in the quantum spectrum using the detrended fluctuation analysis (DFA) and random matrix theory…
In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components…
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
In this paper, we will generate a convex iterative FP thresholding algorithm to solve the problem $(FP^{\lambda}_{a})$. Two schemes of convex iterative FP thresholding algorithms are generated. One is convex iterative FP thresholding…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
Conventional algorithms for galaxy power spectrum estimation measure the true spectrum convolved with a survey window function, which, for parameter inference, must be compared with a similarly convolved theory model. In this work, we…
Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…
Frequency domain representation of time series feature offers a concise representation for handling real-world time series data with inherent complexity and dynamic nature. However, current frequency-based methods with complex operations…
We study the mathematical model of multiwave tomography including thermo and photoacoustic tomography with a variable speed for a fixed time interval $[0,T]$. We assume that the waves reflect from the boundary of the domain. We propose an…
For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…
We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the periods of plane curves. Our algorithm reduces the evaluation of…
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 Dirac-Frenkel variational principle is a widely used building block for using nonlinear parametrizations in the context of model reduction and numerically solving partial differential equations; however, it typically leads to…
We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…