Related papers: Evolution Equations on Gabor Transforms and their …
We study the bounded operators on weighted spaces Lw^2 on R^+ commuting either with the right translations St or left translations and we establish the existence of a symbol for these operators. We characterize completely the spectrum of…
The homogenization of periodic elastic composites is addressed through the reformulation of the local equations of the mechanical problem in a geometric functional setting. This relies on the definition of Hilbert spaces of kinematically…
Random transformations are commonly used for augmentation of the training data with the goal of reducing the uniformity of the training samples. These transformations normally aim at variations that can be expected in images from the same…
The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from…
Nonstationary Gabor frames were recently introduced in adaptive signal analysis. They represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. In this paper…
We obtain Gabor frame characterisations of modulation spaces defined via a class of translation-modulation invariant Banach spaces of distributions that was recently introduced in $[10]$. We show that these spaces admit an atomic…
For successful semantic editing of real images, it is critical for a GAN inversion method to find an in-domain latent code that aligns with the domain of a pre-trained GAN model. Unfortunately, such in-domain latent codes can be found only…
Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a…
Evolutionary algorithms are metaheuristic techniques that derive inspiration from the natural process of evolution. They can efficiently solve (generate acceptable quality of solution in reasonable time) complex optimization (NP-Hard)…
We prove that the unique Gabor atom with analytical model space is the Gaussian function. We give an analogous result for the wavelet transform. For the general case we give a new approach to study the irregular Gabor and wavelet frames. We…
We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal…
A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…
Graph Transformers (GTs) have demonstrated great effectiveness across various graph analytical tasks. However, the existing GTs focus on training and testing graph data originated from the same distribution, but fail to generalize under…
Given a non-quasianalytic subadditive weight function $\omega$ we consider the weighted Schwartz space $\mathcal{S}_\omega$ and the short-time Fourier transform on $\mathcal{S}_\omega$, $\mathcal{S}'_\omega$ and on the related modulation…
In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.
We present a study demonstrating how random walk algorithms can be used for evolutionary image transition. We design different mutation operators based on uniform and biased random walks and study how their combination with a baseline…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing N steps requires only O(N log(N)) operations and O(log(N)) active memory, in place of O(N^2)…
We introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. DAOE is based on evolving observables in the Heisenberg…