Related papers: Periodic Gabor Functions with Biorthogonal Exchang…
Standard language models employ unique, monolithic embeddings for each token, potentially limiting their ability to capture the multifaceted nature of word meanings. We investigate whether tokens can be more effectively represented through…
Signal recovery from unitarily invariant measurements is investigated in this paper. A message-passing algorithm is formulated on the basis of expectation propagation (EP). A rigorous analysis is presented for the dynamics of the algorithm…
A representation of polymer self-consistent field theory equivalent to quantum density functional theory is given in terms of non-orthogonal basis sets. Molecular integrals and self-consistent equations for spherically symmetric systems…
An Extended Phase Graph framework for modelling systems with exchange or magnetization transfer (MT) is proposed. The framework, referred to as EPG-X, models coupled two-compartment systems by describing each compartment with separate phase…
Biomedical signal processing extract meaningful information from physiological signals like electrocardiograms (ECGs), electroencephalograms (EEGs), and electromyograms (EMGs) to diagnose, monitor, and treat medical conditions and diseases…
We implement the GW space-time method at finite temperatures, in which the Green's function G and the screened Coulomb interaction W are represented in the real space on a suitable mesh and in imaginary time in terms of Chebyshev…
A few issues on gluon confinement are addressed with the help of a renormalizable gauge model obtained by introducing a replica of the Faddeev-Popov action and a soft breaking of the BRST symmetry. Confinement turns out to be encoded in the…
First principles calculations based on density functional theory are having an incerasing impact on our understanding of molecule-surface interactions. For example, calculations of the multi-dimensional potential energy surface have…
Using a variant of the Sobolev Embedding Theorem, we prove an uncertainty principle related to Gabor systems that generalizes the Balian-Low Theorem. Namely, if $f\in H^{p/2}(\R)$ and $\hat f\in H^{p'/2}(\R)$ with $1<p<\infty$,…
We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that…
Photoplethysmography (PPG) is a method of detecting variation in blood volume commonly through contact with the skin and involving the usage of one or multiple sensors. PPG is typically used in health-related fields and one of its most…
In this paper, we analyze the formation of small stopping sets in joint factor graphs describing a frame-asynchronous two-user transmission. Furthermore, we propose an algorithm to completely avoid small stopping sets in the joint factor…
We propose a numerical method which embeds the variational non-Gaussian wavefunction approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions.…
In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the…
We propose a new method for solving quantum mechanical problems, which combines the flexibility of Gaussian basis set methods with the numerical accuracy of the Fourier method. The method is based on the incorporation of periodic boundary…
Paraxial diffraction modeling based on the Fourier transform has seen widespread implementation for simulating the response of a diffraction-limited optical system. For systems where the paraxial assumption is not sufficient, a class of…
We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the…
One of the lowest-order corrections to Gaussian quantum mechanics in infinite-dimensional Hilbert spaces are Airy functions: a uniformization of the stationary phase method applied in the path integral perspective. We introduce a…
Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is…
We propose in this paper a Proper Generalized Decomposition (PGD) approach for the solution of problems in linear elastodynamics. The novelty of the work lies in the development of weak formulations of the PGD problems based on the…