Related papers: A kernel-derived orthogonal basis for spectral fun…

The reconstruction of spectral function from correlation function in Euclidean space is a challenging task. In this paper, we employ the Machine Learning techniques in terms of the radial basis functions networks to reconstruct the spectral…

Spectral reconstruction is a well studied numerically ill-posed problem which arises due to the relation of the Euclidean correlator to the spectral function via an inhomogeneous Fredholm equation of the first kind. Several different…

We propose a method to reconstruct smeared spectral functions from two-point correlation functions measured on the Euclidean lattice. Arbitrary smearing function can be considered as far as it is smooth enough to allow an approximation…

This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…

Recent advances in representation learning reveal that widely used objectives, such as contrastive and non-contrastive, implicitly perform spectral decomposition of a contextual kernel, induced by the relationship between inputs and their…

Given only information in the form of similarity triplets "Object A is more similar to object B than to object C" about a data set, we propose two ways of defining a kernel function on the data set. While previous approaches construct a…

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…

Reconstructing spectral densities from Euclidean lattice correlators requires an inverse Laplace transform, which is inherently ill-conditioned when applied to numerical data with statistical uncertainties. The maximum amount of information…

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise…

A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…

Shape matching is a fundamental task in computer graphics and vision, with deep functional maps becoming a prominent paradigm. However, existing methods primarily focus on learning informative feature representations by constraining…

The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…

The determination of spectral properties from first principles can provide powerful connections between microscopic theoretical predictions and experimental data, but requires complex electronic-structure formulations that fall outside the…

Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…

Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…

Spectral computed tomography based on a photon-counting detector (PCD) attracts more and more attentions since it has the capability to provide more accurate identification and quantitative analysis for biomedical materials. The limited…

Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in many-body physics. However, the inversion is proved to be ill-posed in the realistic systems with noisy Green's functions. In this Letter,…

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…

Various physical quantities -- including real-time response, inclusive cross-sections, and decay rates -- may not be directly determined from Euclidean correlators. They are, however, easily determined from the spectral density, motivating…

Spectral densities connect correlation functions computed in quantum field theory to observables measured in experiments. For strongly-interacting theories, their non-perturbative determinations from lattice simulations are therefore of…