Related papers: A multifractal surrogate data generation algorithm…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
We present ReFormer, a generative AI (GAI) model that can efficiently generate synthetic radio-frequency (RF) data, or RF fakes, statistically similar to the data it was trained on, or with modified statistics, in order to augment datasets…
We present a quantum-assisted generative algorithm for synthetic tracks of Lagrangian tracer particles in a turbulent shear flow. The parallelism and sampling properties of quantum algorithms are used to build and optimize a parametric…
Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
A warping operator consists of an invertible axis deformation applied either in the signal domain or in the corresponding Fourier domain. Additionally, a warping transformation is usually required to preserve the signal energy, thus…
The Taylor hypothesis which allows surrogating spatial measurements requiring many experimental probes by time series from one or two probes is examined on the basis of a simple analytic model of turbulent statistics. The main points are as…
Surrogate modeling of eccentric binary black hole waveforms has remained challenging. The complicated morphology of these waveforms due to the eccentric orbital timescale variations makes it difficult to construct accurate and efficient…
One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However,…
Power-law distributions are essential in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first infer the scale exponent $\alpha$ using the…
A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation…
To address limitations of the graph fractional Fourier transform (GFRFT) Wiener filtering and the traditional joint time-vertex fractional Fourier transform (JFRFT) Wiener filtering, this study proposes a filtering method based on the…
Recent CNN and Transformer-based models tried to utilize frequency and periodicity information for long-term time series forecasting. However, most existing work is based on Fourier transform, which cannot capture fine-grained and local…
Recent advances in machine learning, specifically transformer architecture, have led to significant advancements in commercial domains. These powerful models have demonstrated superior capability to learn complex relationships and often…
The special affine Fourier transform (SAFT) is a promising tool for analyzing non-stationary signals with more degrees of freedom. However, the SAFT fails in obtaining the local features of non-transient signals due to its global kernel and…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
We propose a novel algorithm for computing the Walsh-Hadamard Transform (WHT) which consists entirely of Haar wavelet transforms. We prove that the algorithm, which we call the Cascading Haar Wavelet (CHW) algorithm, shares precisely the…