Related papers: Spectral Echolocation via the Wave Embedding
Density matrix embedding theory (DMET) [Phys. Rev. Lett., 109, 186404 (2012)], introduced a new approach to quantum cluster embedding methods, whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath…
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the…
Frequently encountered in nature, internal solitary waves in stratified fluids are well-observed and well-studied from the experimental, the theoretical, and the numerical perspective. From the mathematical point of view, these waves are…
Measuring the similarity between data points often requires domain knowledge, which can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact…
Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric…
Electromagnetic waves in a system with a space and time dependent boundary experience both diffraction and Doppler-like frequency conversion. In order to analyse such situations, conventional methods call for either the eigenmodes or the…
We introduce a supervised dimensionality reduction methodology for categorical (and discretized mixed-type) data based on a density-matrix construction induced by class-conditional frequencies. Given a labeled dataset encoded in a one-hot…
Pre-trained foundation models have demonstrated remarkable success in audio, vision and language, yet their potential for general machine signal modeling with arbitrary sampling rates-covering acoustic, vibration, and other industrial…
This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical…
The use of graph convolution in the development of recommender system algorithms has recently achieved state-of-the-art results in the collaborative filtering task (CF). While it has been demonstrated that the graph convolution operation is…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation…
Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously…
We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Node embedding is a central topic in graph representation learning. Computational efficiency and scalability can be challenging to any method that requires full-graph operations. We propose sampling approaches to node embedding, with or…
Spread-spectrum signals are increasingly adopted in fields including communications, testing of electronic systems, Electro-Magnetic Compatibility (EMC) enhancement, ultrasonic non-destructive testing. This paper considers the synthesis of…
We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
We propose a novel method to embed a functional magnetic resonance imaging (fMRI) dataset in a low-dimensional space. The embedding optimally preserves the local functional coupling between fMRI time series and provides a low-dimensional…