Related papers: Convolutions on the Sphere: Commutation with Diffe…
We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. To this…
We explore boundedness properties in the context of metric measure spaces, of some natural operators of convolution type whose study is suggested by certain transformations used in computer vision.
We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal…
Many real-life signals are defined on spherical domains, in particular in geophysics and physics applications. In this work, we tackle the problem of extending the iterative filtering algorithm, developed for the decomposition of…
The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are…
In this paper we offer a computational approach to the spectral function for a finite family of commuting operators, and give applications. Motivated by questions in wavelets and in signal processing, we study a problem about spectral…
This paper proposes convolutional filtering for data whose structure can be modeled by a simplicial complex (SC). SCs are mathematical tools that not only capture pairwise relationships as graphs but account also for higher-order network…
We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse fields. In regard to the special characteristics of such field types we derive modified…
A convection-driven MHD dynamo in a rotating spherical shell, with clearly defined structural elements in the flow and magnetic field, is simulated numerically. Such dynamos can be called deterministic, in contrast to those explicitly…
We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the…
We explore the connections between singular Weyl-Titchmarsh theory and the single and double commutation methods. In particular, we compute the singular Weyl function of the commuted operators in terms of the original operator. We apply the…
Using convolutional neural networks for 360images can induce sub-optimal performance due to distortions entailed by a planar projection. The distortion gets deteriorated when a rotation is applied to the 360image. Thus, many researches…
Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated,…
We construct smeared CFT operators which represent a scalar field in AdS interacting with gravity. The guiding principle is micro-causality: scalar fields should commute with themselves at spacelike separation. To O(1/N) we show that a…
We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product is separable or entangled. We show that the tensor convolution defined for certain mappings on an almost arbitrary…
We present a new mathematical framework for incorporating partial coherence effects into wave optics simulations through a comprehensive surface-to-detector approach. Unlike traditional ensemble averaging methods, our dual-component…
We propose fast, exact and efficient algorithms for the convolution of two arbitrary functions on the sphere which speed up computations by a factor \order{\sqrt{N}} compared to present methods where $N$ is the number of pixels. No…
Linear operations on coefficients in the spherical harmonics (SH) transform domain that again yield SH-domain coefficients are an important toolset in many disciplines of research and engineering. They comprise rotations, spatially…
Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been…
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer…