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In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
The coherence attribute is one of the most commonly used attributes in seismic interpretation. In this paper, we propose building on the recently introduced Generalized Tensor-based Coherence (GTC) attribute to make it directionally…
We introduce a unified formalism to describe both timing and astrometric perturbations induced on astrophysical point sources by gravitational waves using a complex spin field on the sphere. This allows the use of spin-weighted spherical…
Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…
Over the past few decades, kernel-based approximation methods had achieved astonishing success in solving different problems in the field of science and engineering. However, when employing the direct or standard method of performing…
We present a unified approach for constructing Slepian functions - also known as prolate spheroidal wave functions - on the sphere for arbitrary tensor ranks including scalar, vectorial, and rank 2 tensorial Slepian functions, using…
This paper extends and analyzes the high-order kernel regularization framework of Beale & Tlupova (arXiv:2510.13639) to all four on-surface boundary integral operators of the Helmholtz Calderon calculus in three dimensions: the…
According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the…
Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to…
Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in…
We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
This paper examines the application of the Kernel Sum of Squares (KSOS) method for enhancing kernel learning from data, particularly in the context of dynamical systems. Traditional kernel-based methods, despite their theoretical soundness…
The so-called tuned-correlated kernel (sometimes also called the first-order stable spline kernel) is one of the most widely used kernels for the regularized impulse response estimation. This kernel can be derived by applying an exponential…
A general approach to anomaly in quantum field theory is newly formulated by use of the propagator theory in solving the heat-kernel equation. We regard the heat-kernel as a sort of the point-splitting regularization in the space(-time)…
The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…
We show how to define and go from the spin-s spherical harmonics to the tensorial spin-s harmonics. These quantities, which are functions on the sphere taking values as Euclidean tensors, turn out to be extremely useful for many…
Seismic attributes calculated by conventional methods are susceptible to noise. Conventional filtering reduces the noise in the cost of losing the spectral bandwidth. The challenge of having a high-resolution and robust signal processing…
Spectral clustering and diffusion maps are celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these procedures is the approximation of a Laplacian through a…