Related papers: Evolution Equations on Gabor Transforms and their …
The transformer architecture has shown remarkable success in various domains, such as natural language processing and computer vision. When it comes to graph learning, transformers are required not only to capture the interactions between…
Gauge-invariant Wigner theory describes the quantum-mechanical evolution of charged particles in the presence of an electromagnetic field in phase space, which is spanned by position and kinetic momentum. This approach is independent of the…
Recent deep generative models are able to provide photo-realistic images as well as visual or textual content embeddings useful to address various tasks of computer vision and natural language processing. Their usefulness is nevertheless…
We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by…
Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets.…
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior…
The performance of most evolutionary metaheuristic algorithms relays on various operatives. One of them is the crossover operator, which is divided into two types: application dependent and application independent crossover operators. These…
Evolutionary algorithms usually explore a search space of solutions by means of crossover and mutation. While a mutation consists of a small, local modification of a solution, crossover mixes the genetic information of two solutions to…
A general form of the fifth-order nonlinear evolution equation is considered. Helmholtz solution of the inverse variational problem is used to derive conditions under which this equation admits an analytic representation. A Lennard type…
This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
We continue the study, from a semiclassical viewpoint, of Calvo and Picon's operators, as manipulating photon states in quantum communication. In a previous paper, we defined a one-dimensional model operator and studied it analytically…
This paper addresses the problem of finding interpretable directions in the latent space of pre-trained Generative Adversarial Networks (GANs) to facilitate controllable image synthesis. Such interpretable directions correspond to…
The aim of this paper is to study some properties of left translates of a square integrable function on the Heisenberg group. First, a necessary and sufficient condition for the existence of the canonical dual to a function $\varphi\in…
Deep learning frameworks commonly implement convolution operators with GEMM-based algorithms. In these algorithms, convolution is implemented on top of matrix-matrix multiplication (GEMM) functions, provided by highly optimized BLAS…
A method for performing wave packet simulations in dipole fields is presented. Starting from a Hamiltonian with non commuting terms, a gauge transformation leads to a new Hamiltonian which allows to calculate explicitly the evolution…
In this paper we construct frames of Gabor type for the space $L^2_{rad}(\R^d)$ of radial $L^2$-functions, and more generally, for subspaces of modulation spaces consisting of radial distributions. Hereby, each frame element itself is a…