Related papers: Wavefront sets of convolutions of distributions wi…
A review of the inverse scattering transform is given, and an introduction to solitons is provided.
In this note, we show that the convolution of a discrete symmetric log-concave distribution and a discrete symmetric bimodal distribution can have any strictly positive number of modes. A similar result is proved for smooth distributions.
This paper explores mixture distributions induced by a product of the positive stable random variable and a power of another positive random variable. The paper also considers the convolution of the stable density with a gamma density.…
In this expository paper we show how one can, in a uniform way, calculate the weight distributions of some well-known binary cyclic codes. The codes are related to certain families of curves, and the weight distributions are related to the…
In this expository article, we provide a self-contained overview of the notion of convolution embedded in different theories: from the classical Fourier theory to the theory of algebraic signal processing. We discuss their relations and…
This paper re-examines the density for sums of independent exponential, Erlang and gamma random variables. By using a divided difference perspective, the paper provides a unified approach to finding closed-form formulae for such…
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus…
Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission…
We have found the analytical solution of the LO-evolution equation for off-forward distributions which arise in the processes of deeply virtual Compton scattering or exclusive production of mesons. We present the predictions for their…
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…
We present first empirical results from our ongoing investigation of distribution shifts in image data used for various computer vision tasks. Instead of analyzing the original training and test data, we propose to study shifts in the…
This paper presents a multiscale decomposition algorithm. Unlike standard wavelet transforms, the proposed operator is both linear and shift invariant. The central idea is to obtain shift invariance by averaging the aligned wavelet…
We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal with "plus" and/or "max"…
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a…
This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a…
We study the symmetry groups and winding numbers of planar curves obtained as images of weighted sums of exponentials. More generally, we study the image of the complex unit circle under a finite or infinite Laurent series using a…
In the paper, we experimentally study the inverse problem with the resonant scattering determinant. We analyze the structure of characteristics of perturbed linear waves. Assuming there is the common part of potential perturbation…
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest…
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…