arXiv research

A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images, convolutional networks often learn a first layer of filters which are well localized i…

DELIMIT is a framework extension for deep learning in diffusion imaging, which extends the basic framework PyTorch towards spherical signals. Based on several novel layers, deep learning can be applied to spherical diffusion imaging data in a very convenient way. First, two spherical harmonic interpolation layers are a…

New method detects change points in quasi-periodic signals without supervision.

Rodent identifies ODEs from trajectories without needing basis functions.

New neural network extracts signal components and their IFs from non-uniform samples.

Bandlimited random neural networks may not approximate all functions perfectly.

We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random walk operator as a non-orthogonal Fourier-type basis for functions over directed gr…

DPI quantifies phase differences in 1D and multidimensional signals using Riesz transform.

Study reveals how attention helps in signal recovery from sequence models using random matrix theory.

Estimating signals with linear recurrence relations under Gaussian noise is nearly as hard as sparse signals.

A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously introduced in a machine learning framework for the regression of properties of sm…

We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a time-invariant filter. It was shown by Juditsky and Nemirovski (2009) that when the $\ell_2…

Pitch or fundamental frequency (f0) extraction is a fundamental problem studied extensively for its potential applications in speech and clinical applications. In literature, explicit mode specific (modal speech or singing voice or emotional/ expressive speech or noisy speech) signal processing and deep learning f0 ext…

The paper analyzes MACD using operator theory.

Evaluating human brain potentials during watching different images can be used for memory evaluation, information retrieving, guilty-innocent identification and examining the brain response. In this study, the effects of watching images, with different levels of familiarity, on subjects' Electroencephalogram (EEG) have…

New findings show sparse signals in MRA model require fewer measurements than previously thought.

Study cohomology classes related to harmonic maps on submersions.

Study on harmonic maps on weighted Riemannian foliations.

The paper examines triviality of Ricci-Bourguignon harmonic solitons.

Study cohomology classes related to $n$-harmonic morphisms and $F$-harmonic maps.

The paper proves nonexistence of harmonic and bi-harmonic maps under specific conditions.

f-Harmonic maps were first introduced and studied by Lichnerowicz in \cite{Li} (see also Section 10.20 in Eells-Lemaire's report \cite{EL}). In this paper, we study a subclass of f-harmonic maps called f-harmonic morphisms which pull back local harmonic functions to local f-harmonic functions. We prove that a map betwe…

Finite energy solutions of 4-harmonic and ES-4-harmonic maps are trivial.

We propose a new notion called \emph{infinity-harmonic maps}between Riemannain manifolds. These are natural generalizations of the well known notion of infinity harmonic functions and are also the limiting case of $p$% -harmonic maps as $p\to \infty$. Infinity harmoncity appears in many familiar contexts. For example,…

Automatic music transcription (AMT) aims to infer a latent symbolic representation of a piece of music (piano-roll), given a corresponding observed audio recording. Transcribing polyphonic music (when multiple notes are played simultaneously) is a challenging problem, due to highly structured overlapping between harmon…

Many spectral unmixing methods rely on the non-negative decomposition of spectral data onto a dictionary of spectral templates. In particular, state-of-the-art music transcription systems decompose the spectrogram of the input signal onto a dictionary of representative note spectra. The typical measures of fit used to …

Study examines maximal domains of radial harmonic functions across different curvature types.

New p-harmonic and harmonic morphisms found on Lie groups.

Constructs explicit harmonic functions and morphisms on complex and quaternionic Grassmannians.

J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variational formula. When, k=2, it is called biharmonic maps (2-harmonic maps). There have been extensive studies in the area. In this paper, We study k-harmonic immersion into a sphere, and get the rerationship between radious and "k"…

Extends p-harmonic map theory for new properties.

$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic $\infty$-harmonic maps from and into a sphere, quadratic $\infty$-harmonic maps between E…

Dirac-harmonic maps are uncoupled under certain conditions.

The paper investigates Liouville type theorems for various harmonic forms on Riemannian manifolds.

Study existence of harmonic and Dirac-harmonic maps from degenerating surfaces.

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several areas in mathematics (see the book by Baird and Wood for details)…

Analyzes harmonic and biharmonic maps from gradient Ricci solitons.

Study heat flow for half-harmonic maps and harmonic maps with free boundary.

The paper explores harmonic and asymptotically harmonic Finsler manifolds and their properties.

Study examines harmonic functions in sub-Riemannian and RCD settings.

The paper characterizes harmonic maps and studies their properties on Riemannian manifolds.

Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.

J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variational formula. When, k=2, it is called biharmonic maps (2-harmonic maps). There have been extensive studies in the area. In this paper, we consider the relationship between biharmonic maps and k-harmonic maps, and show non-existe…

Extends Fatou theorem to bounded harmonic maps.

In this paper, we study compact generalized $τ$-quasi Ricci-harmonic metrics. In the first part, we explore conditions under which generalized $τ$-quasi Ricci-harmonic metrics are harmonic-Einstein and give some characterization results for it. In the second part, we obtain some rigidity results for compact $(τ, ρ)$-qu…

The paper examines metrics on foliated manifolds that have special geometric properties.

The paper examines stability of harmonic maps on specific manifolds.

$α$-Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $α$-harmonic maps that were introduced by Sacks-Uhlenbeck to attack the existence problem for harmonic maps from surfaces. For $α>1$, the latter are known to satisfy a Palais-Smale condtion, and so, the technique of Sacks-Uhlenbeck consists in …