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In collider experiments, an event is characterized by two distinct yet mutually complementary features: the `global features' and the `local features'. Kinematic information such as the event topology of a hard process, masses, and spins of…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
We review the central results concerning wavelet methods in multifractal analysis, which consists in analysis of the pointwise singularities of a signal, and we describe its recent extension to multivariate multifractal analysis, which…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
We describe a new method involving wavelet transforms for deriving the wind velocity associated with atmospheric turbulence layers from Generalized SCIDAR measurements. The algorithm analyses the cross-correlation of a series of…
Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of…
Most examinations of neural networks' learned latent spaces typically employ dimensionality reduction techniques such as t-SNE or UMAP. These methods distort the local neighborhood in the visualization, making it hard to distinguish the…
Convolutional Neural Networks (CNNs) are generally prone to noise interruptions, i.e., small image noise can cause drastic changes in the output. To suppress the noise effect to the final predication, we enhance CNNs by replacing…
The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
Wavelets have been shown to be effective bases for many classes of natural signals and images. Standard wavelet bases have the entire vector space $\mathbb R^n$ as their natural domain. It is fairly straightforward to adapt these to…
Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…
Obtaining rigorous statistical guarantees for generalization under distribution shift remains an open and active research area. We study a setting we call combinatorial distribution shift, where (a) under the test- and…
We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are…
The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction…
Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus…
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regular inhomogeneities. This technique is then applied to a…
Dark-field x-ray microscopy utilizes Bragg diffraction to collect full-field x-ray images of "mesoscale" structure of ordered materials. Information regarding the structural heterogeneities and their physical implications is gleaned through…