Related papers: Spectral Echolocation via the Wave Embedding
We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the classical spectral-based adjacency/Laplacian spectral embedding,…
In this paper, we consider a certain convolutional Laplacian for metric measure spaces and investigate its potential for the statistical analysis of complex objects. The spectrum of that Laplacian serves as a signature of the space under…
We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…
Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes…
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…
Electroelastic waves in piezoelectric media are widely used in sensing and filtering applications. Despite extensive research, computing the guided wave dispersion remains challenging. This paper presents semi-analytical approaches based on…
The electronic band structure, describing the periodic dependence of electronic quantum states on lattice momentum in reciprocal space, is a fundamental concept in solid-state physics. However, it's only well-defined for static nuclei. To…
Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…
Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation,…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
In this paper we make an attempt to extend L. Schwartz's classical result on spectral synthesis to several dimensions. Due to counterexamples of D. I. Gurevich this is impossible for translation invariant varieties. Our idea is to replace…
While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on…
In this paper we revisit the classical problem of estimating a signal as it impinges on a multi-sensor array. We focus on the case where the impinging signal's bandwidth is appreciable and is operating in a broadband regime. Estimating…
We give a sufficient condition for branched minimal immersions of spheres into ellipsoids to be embedded: we show that if the coordinate functions of the branched minimal immersion are first or second eigenfunctions with respect to a…
Several fundamental tasks in data science rely on computing an extremal eigenspace of size $r \ll n$, where $n$ is the underlying problem dimension. For example, spectral clustering and PCA both require the computation of the leading…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the…
A novel approach to improving the performances of confocal scanning imaging is proposed. We experimentally demonstrate its feasibility using acoustic waves. It relies on a new way to encode spatial information using the temporal dimension.…
A flexible wave localization is investigated using a spatial-temporal modulation of point defects along the periodic array of electromechanical local resonators of a piezoelectric bimorph beam. By changing the electrical resonance of…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…