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On generalizations of the nonwindowed scattering transform Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230909
Albert Chua, Matthew Hirn, Anna LittleIn this paper, we generalize finite depth wavelet scattering transforms, which we formulate as Lq(Rn) norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then provide norms for these operators, prove that these operators are welldefined, and are Lipschitz continuous to the action of C2 diffeomorphisms in specific cases. Lastly, we extend

Diffusion maps for embedded manifolds with boundary with applications to PDEs Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230909
Ryan Vaughn, Tyrus Berry, Harbir AntilGiven only a finite collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to numerically solve elliptic and parabolic partial differential equations (PDEs) supplemented with boundary conditions. Since the construction of triangulations on unknown manifolds can be both difficult and expensive, both in terms of computational and data

Metaplectic Gabor frames and symplectic analysis of timefrequency spaces Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230909
Elena Cordero, Gianluca GiacchiWe introduce new frames, called metaplectic Gabor frames, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions, cf. [7], [8], [5], [17], [27], [28]. Namely, we develop the theory of metaplectic atoms in a fullgeneral setting and prove an inversion formula for metaplectic Wigner distributions on Rd. Its discretization provides metaplectic Gabor frames. Next

Gradient descent for deep matrix factorization: Dynamics and implicit bias towards low rank Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230906
HungHsu Chou, Carsten Gieshoff, Johannes Maly, Holger RauhutIn deep learning, it is common to use more network parameters than training points. In such scenario of overparameterization, there are usually multiple networks that achieve zero training error so that the training algorithm induces an implicit bias on the computed solution. In practice, (stochastic) gradient descent tends to prefer solutions which generalize well, which provides a possible explanation

Spatiotemporal analysis using Riemannian composition of diffusion operators Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230821
Tal Shnitzer, HauTieng Wu, Ronen TalmonMultivariate timeseries have become abundant in recent years, as many dataacquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an operatorbased approach for spatiotemporal analysis. Our approach combines three components that are often considered separately: (i) manifold learning for building operators

Performance bounds of the intensitybased estimators for noisy phase retrieval Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230819
Meng Huang, Zhiqiang XuThe aim of noisy phase retrieval is to estimate a signal x0∈Cd from m noisy intensity measurements bj=〈aj,x0〉2+ηj,j=1,…,m, where aj∈Cd are known measurement vectors and η=(η1,…,ηm)⊤∈Rm is a noise vector. A commonly used estimator for x0 is to minimize the intensitybased loss function, i.e., xˆ:=argminx∈Cd∑j=1m(〈aj,x〉2−bj)2. Although many algorithms for solving the intensitybased estimator have

Learning ability of interpolating deep convolutional neural networks Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230816
TianYi Zhou, Xiaoming HuoIt is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fullyconnected neural networks. This paper studies the learning ability of an important family of deep neural networks, deep convolutional neural networks (DCNNs), under both underparameterized and overparameterized settings. We

Detecting whether a stochastic process is finitely expressed in a basis Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230804
Neda Mohammadi, Victor M. PanaretosIs it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We show that it is indeed possible to construct a hypothesis testing scheme that is almost surely guaranteed to make only finite many incorrect decisions

Stable parameterization of continuous and piecewiselinear functions Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230809
Alexis Goujon, Joaquim Campos, Michael UnserRectifiedlinearunit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewiselinear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function spaces lacks stability. In this paper, we investigate an alternative representation of CPWL functions that relies on local hat basis functions and

Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipović and modulation spaces Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230802
Joachim Toft, Divyang G. Bhimani, Ramesh MannaWe give a proof of that harmonic oscillator propagators and fractional Fourier transforms are essentially the same. We deduce continuity properties and fix time estimates for such operators on modulation spaces, and apply the results to prove Strichartz estimates for such propagators when acting on Pilipović and modulation spaces. Especially we extend some results by Balhara, Cordero, Nicola, Rodino

Graph signal processing on dynamic graphs based on temporalattention product Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230728
Ru Geng, Yixian Gao, HongKun Zhang, Jian ZuSignal processing is an important research topic. This paper aims to provide a general framework for signal processing on arbitrary dynamic graphs. We propose a new graph transformation by defining a temporalattention product. This product transforms the sequence of graph time slices with arbitrary topology and number of nodes into a static graph, effectively capturing graph signals' spatiotemporal

A note on spike localization for line spectrum estimation Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230727
Haoya Li, Hongkang Ni, Lexing YingThis note considers the problem of approximating the locations of dominant spikes for a probability measure from noisy spectrum measurements under the condition of residue signal, significant noise level, and no minimum spectrum separation. We show that the simple procedure of thresholding the smoothed inverse Fourier transform allows for approximating the spike locations rather accurately.

Random sampling over locally compact Abelian groups and inversion of the Radon transform Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230725
Erika Porten, Juan Miguel Medina, Marcela MorvidoneWe consider the problem of reconstructing a measurable function over a Locally Compact Abelian group G from random measurements. The results presented herein are partially inspired by the concept of aliasfree sampling. Here, the sampling and interpolation operation is modelled as an approximate convolution operator with respect to a stochastic integral defined with an appropriately chosen random measure

Generative modeling via tensor train sketching Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230717
YoonHaeng Hur, Jeremy G. Hoskins, Michael Lindsey, E.M. Stoudenmire, Yuehaw KhooIn this paper, we introduce a sketching algorithm for constructing a tensor train representation of a probability density from its samples. Our method deviates from the standard recursive SVDbased procedure for constructing a tensor train. Instead, we formulate and solve a sequence of small linear systems for the individual tensor train cores. This approach can avoid the curse of dimensionality that

Gabor frame bound optimizations Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230713
Markus Faulhuber, Irina ShafkulovskaWe study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the frame bounds and the condition number are rectangular lattices which are different for the respective quantities. Also, in some cases optimal lattices do not exist

Corrigendum to “A diffusion + waveletwindow method for recovery of superresolution pointmasses with application to singlemolecule microscopy and beyond” [Appl. Comput. Harmon. Anal. 63 (2023) 1–19] Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230630
Charles K. ChuiThis note is to point out a serious typo in [1] and clarify a notation in [2].


A constructive approach for computing the proximity operator of the pth power of the ℓ1 norm Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230629
Ashley PraterBennette, Lixin Shen, Erin E. TrippThis note is to study the proximity operator of hp=‖⋅‖1p, the power function of the ℓ1 norm. For general p, computing the proximity operator requires solving a system of potentially highly nonlinear inclusions. For p=1, the proximity operator of h1 is the well known softthresholding operator. For p=2, the function h2 serves as a penalty function that promotes structured solutions to optimization problems

Analytic and directional wavelet packets in the space of periodic signals Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230626
Amir Averbuch, Pekka Neittaanmäki, Valery ZheludevThe paper presents a versatile library of analytic and quasianalytic complexvalued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasianalytic WPs are the regular splinebased orthonormal WPs designed in [4]. The imaginary parts are the socalled complementary orthonormal WPs, which, unlike the symmetric regular WPs, are antisymmetric. Tensor

nBest kernel approximation in reproducing kernel Hilbert spaces Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230622
Tao QianBy making a seminal use of the maximum modulus principle of holomorphic functions we prove existence of nbest kernel approximation for a wide class of reproducing kernel Hilbert spaces of holomorphic functions in the unit disc, and for the corresponding class of Bochner type spaces of stochastic processes. This study thus generalizes the classical result of nbest rational approximation for the Hardy

Robust Sensing of LowRank Matrices with NonOrthogonal Sparse Decomposition Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230620
Johannes MalyWe consider the problem of recovering an unknown lowrank matrix X⋆ with (possibly) nonorthogonal, effectively sparse rank1 decomposition from measurements y gathered in a linear measurement process A. We propose a variational formulation that lends itself to alternating minimization and whose global minimizers provably approximate X⋆ up to noise level. Working with a variant of robust injectivity

Capacity dependent analysis for functional online learning algorithms Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230619
Xin Guo, ZhengChu Guo, Lei ShiThis article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regularity, the kernel space capacity, and the capacity of the sampling process covariance operator, significant improvement on the convergence rates is achieved. Both prediction problems and estimation problems are studied, where

Decentralized learning over a network with Nyström approximation using SGD Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230616
Heng Lian, Jiamin LiuNowadays we often meet with a learning problem when data are distributed on different machines connected via a network, instead of stored centrally. Here we consider decentralized supervised learning in a reproducing kernel Hilbert space. We note that standard gradient descent in a reproducing kernel Hilbert space is difficult to implement with multiple communications between worker machines. On the

A unified approach to synchronization problems over subgroups of the orthogonal group Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230614
Huikang Liu, ManChung Yue, Anthony ManCho SoThe problem of synchronization over a group G aims to estimate a collection of group elements G1⁎,…,Gn⁎∈G based on noisy observations of a subset of all pairwise ratios of the form Gi⁎Gj⁎−1. Such a problem has gained much attention recently and finds many applications across a wide range of scientific and engineering areas. In this paper, we consider the class of synchronization problems in which the

Estimation under group actions: Recovering orbits from invariants Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230608
Afonso S. Bandeira, Ben BlumSmith, Joe Kileel, Jonathan NilesWeed, Amelia Perry, Alexander S. WeinWe study a class of orbit recovery problems in which we observe independent copies of an unknown element of Rp, each linearly acted upon by a random element of some group (such as Z/p or SO(3)) and then corrupted by additive Gaussian noise. We prove matching upper and lower bounds on the number of samples required to approximately recover the group orbit of this unknown element with high probability

Riesz transform associated with the fractional Fourier transform and applications in image edge detection Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230525
Zunwei Fu, Loukas Grafakos, Yan Lin, Yue Wu, Shuhui YangThe fractional Hilbert transform was introduced by Zayed [30, Zayed, 1998] and has been widely used in signal processing. In view of its connection with the fractional Fourier transform, Chen, the first, second and fourth authors of this paper in [6, Chen et al., 2021] studied the fractional Hilbert transform and other fractional multiplier operators on the real line. The present paper is concerned

A fast procedure for the construction of quadrature formulas for bandlimited functions Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230511
A. Gopal, V. RokhlinWe introduce an efficient scheme for the construction of quadrature rules for bandlimited functions. While the scheme is predominantly based on wellknown facts about prolate spheroidal wave functions of order zero, it has the asymptotic CPU time estimate O(nlogn) to construct an npoint quadrature rule. Moreover, the size of the “nlogn” term in the CPU time estimate is small, so for all practical

Modewise operators, the tensor restricted isometry property, and lowrank tensor recovery Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230509
Cullen A. Haselby, Mark A. Iwen, Deanna Needell, Michael Perlmutter, Elizaveta RebrovaRecovery of sparse vectors and lowrank matrices from a small number of linear measurements is wellknown to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the restricted isometry property, that is, approximate orthonormality when acting on the subspace to be recovered. Among the most widely used random matrix measurement

Finite alphabet phase retrieval Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230509
Tamir Bendory, Dan Edidin, Ivan GonzalezWe consider the finite alphabet phase retrieval problem: recovering a signal whose entries lie in a small alphabet of possible values from its Fourier magnitudes. This problem arises in the celebrated technology of Xray crystallography to determine the atomic structure of biological molecules. Our main result states that for generic values of the alphabet, two signals have the same Fourier magnitudes

Nearoptimal bounds for generalized orthogonal Procrustes problem via generalized power method Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230503
Shuyang LingGiven multiple point clouds, how to find the rigid transform (rotation, reflection, and shifting) such that these point clouds are well aligned? This problem, known as the generalized orthogonal Procrustes problem (GOPP), has found numerous applications in statistics, computer vision, and imaging science. While one commonlyused method is finding the least squares estimator, it is generally an NPhard

A simple approach for quantizing neural networks Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230502
Johannes Maly, Rayan SaabIn this short note, we propose a new method for quantizing the weights of a fully trained neural network. A simple deterministic preprocessing step allows us to quantize network layers via memoryless scalar quantization while preserving the network performance on given training data. On one hand, the computational complexity of this preprocessing slightly exceeds that of stateoftheart algorithms

Frames by orbits of two operators that commute Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230425
A. Aguilera, C. Cabrelli, D. Carbajal, V. PaternostroFrames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded operators acting on some separable Hilbert space H. We completely characterize operators T and L with TL=LT and sets Φ⊂H such that the collection {TkLjϕ:k∈Z,j∈J,ϕ∈Φ}

Spectral graph wavelet packets frames Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230418
Iulia Martina Bulai, Sandra SalianiClassical wavelet, wavelet packets and timefrequency dictionaries have been generalized to the graph setting, the main goal being to obtain atoms which are jointly localized both in the vertex and the graph spectral domain. We present a new method to generate a whole dictionary of frames of wavelet packets defined in the graph spectral domain to represent signals on weighted graphs. We will give some

Double preconditioning for Gabor frame operators: Algebraic, functional analytic and numerical aspects Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230417
Hans G. Feichtinger, Peter Balazs, Daniel HaiderThis paper provides algebraic and analytic, as well as numerical arguments why and how double preconditioning of the Gabor frame operator yields an efficient method to compute approximate dual (respectively tight) Gabor atoms for a given timefrequency lattice. We extend the definition of the approach to the continuous setting, making use of the socalled Banach Gelfand Triple, based on the Segal algebra

PiPs: A kernelbased optimization scheme for analyzing nonstationary 1D signals Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230413
Jieren Xu, Yitong Li, Haizhao Yang, David Dunson, Ingrid DaubechiesThis paper proposes a novel kernelbased optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and singlechannel source separation of 1D nonstationary oscillatory data. The key insight of our optimization scheme for reconstructing the timefrequency information is that when a nonparametric regression is applied on some input values, the output regressed points would

Algebraic compressed sensing Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230405
Paul Breiding, Fulvio Gesmundo, Mateusz Michałek, Nick VannieuwenhovenWe introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, lowrank matrix and tensor recovery. We employ powerful techniques from algebraic geometry to study wellposedness of sufficiently general compressed sensing problems, including existence, local recoverability, global

Tensor completion by multirank via unitary transformation Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230331
GuangJing Song, Michael K. Ng, Xiongjun ZhangOne of the key problems in tensor completion is the number of uniformly random sample entries required for recovery guarantee. The main aim of this paper is to study n1×n2×n3 thirdorder tensor completion based on transformed tensor singular value decomposition, and provide a bound on the number of required sample entries. Our approach is to make use of the multirank of the underlying tensor instead

Predictive algorithms in dynamical sampling for burstlike forcing terms Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230331
Akram Aldroubi, Longxiu Huang, Keri Kornelson, Ilya KrishtalIn this paper, we consider the problem of recovery of a burstlike forcing term in an initial value problem (IVP) in the framework of dynamical sampling. We introduce an idea of using two particular classes of samplers that allow one to predict the solution of the IVP over a time interval without a burst. This leads to two different algorithms that stably and accurately approximate the burstlike forcing

Perfect reconstruction twochannel filter banks on arbitrary graphs Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230322
Junxia You, Lihua YangThis paper extends the existing theory of perfect reconstruction twochannel filter banks from bipartite graphs to nonbipartite graphs. By generalizing the concept of downsampling/upsampling we establish the frame of twochannel filter bank on arbitrary connected, undirected and weighted graphs. Then the equations for perfect reconstruction of the filter banks are presented and solved under proper

Approximation bounds for norm constrained neural networks with applications to regression and GANs Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230322
Yuling Jiao, Yang Wang, Yunfei YangThis paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived through the Rademacher complexity of neural networks, which may be of independent interest. We apply these approximation bounds to analyze the convergences of regression

Lie PCA: Density estimation for symmetric manifolds Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230321
Jameson Cahill, Dustin G. Mixon, Hans ParshallWe introduce an extension to local principal component analysis for learning symmetric manifolds. In particular, we use a spectral method to approximate the Lie algebra corresponding to the symmetry group of the underlying manifold. We derive the sample complexity of our method for various manifolds before applying it to various data sets for improved density estimation.

Superresolution of generalized spikes and spectra of confluent Vandermonde matrices Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230315
Dmitry Batenkov, Nuha DiabWe study the problem of superresolution of a linear combination of Dirac distributions and their derivatives on a onedimensional circle from noisy Fourier measurements. Following numerous recent works on the subject, we consider the geometric setting of “partial clustering”, when some Diracs can be separated much below the Rayleigh limit. Under this assumption, we prove sharp asymptotic bounds for

Phase function methods for second order linear ordinary differential equations with turning points Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230307
James BremerIt is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the LiouvilleGreen method and many other techniques for the asymptotic approximation of the solutions of such equations. More recently, it was exploited by the author to develop a highly efficient solver for second order linear

Lower bounds on the lowdistortion embedding dimension of submanifolds of Rn Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230302
Mark Iwen, Benjamin Schmidt, Arman TavakoliLet M be a smooth submanifold of Rn equipped with the Euclidean (chordal) metric. This note considers the smallest dimension m for which there exists a biLipschitz function f:M↦Rm with biLipschitz constants close to one. The main result bounds the best achievable embedding dimension m below in terms of the Lipschitz constants of f as well as the reach, volume, diameter, and dimension of M. This new

Constructive subsampling of finite frames with applications in optimal function recovery Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230301
Felix Bartel, Martin Schäfer, Tino UllrichIn this paper we present new constructive methods, random and deterministic, for the efficient subsampling of finite frames in Cm. Based on a suitable random subsampling strategy, we are able to extract from any given frame with bounds 0

Synthesisbased timescale transforms for nonstationary signals Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230220
Adrien Meynard, Bruno TorrésaniThis paper deals with the modeling of nonstationary signals, from the point of view of signal synthesis. A class of random, nonstationary signals, generated by synthesis from a random timescale representation, is introduced and studied. Nonstationarity is implemented in the timescale representation through a prior distribution which models the action of time warping on a stationary signal. A main

Generalized matrix spectral factorization with symmetry and applications to symmetric quasitight framelets Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230215
Chenzhe Diao, Bin Han, Ran LuFactorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal and image processing. Motivated by the recent development of quasitight framelets, we study and characterize generalized spectral factorizations with symmetry for

Compressed sensing of lowrank plus sparse matrices Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230206
Jared Tanner, Simon VaryExpressing a matrix as the sum of a lowrank matrix plus a sparse matrix is a flexible model capturing global and local features in data. This model is the foundation of robust principle component analysis [1], [2], and popularized by dynamicforeground/staticbackground separation [3]. Compressed sensing, matrix completion, and their variants [4], [5] have established that data satisfying low complexity

Harmonic Grassmannian codes Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230208
Matthew Fickus, Joseph W. Iverson, John Jasper, Dustin G. MixonAn equiisoclinic tight fusion frame (EITFF) is a type of Grassmannian code, being a sequence of subspaces of a finitedimensional Hilbert space of a given dimension with the property that the smallest spectral distance between any pair of them is as large as possible. EITFFs arise in compressed sensing, yielding dictionaries with minimal block coherence. Their existence remains poorly characterized

Rateoptimal sparse approximation of compact breakofscale embeddings Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230204
Glenn Byrenheid, Janina Hübner, Markus WeimarThe paper is concerned with the sparse approximation of functions having hybrid regularity borrowed from the theory of solutions to electronic Schrödinger equations due to Yserentant (2004) [42]. We use hyperbolic wavelets to introduce corresponding new spaces of Besov and TriebelLizorkintype to particularly cover the energy norm approximation of functions with dominating mixed smoothness. Explicit

Dynamic superresolution in particle tracking problems Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230125
Ping Liu, Habib AmmariParticle tracking in a live cell environment is concerned with reconstructing the trajectories, locations, or velocities of the targeting particles, which holds the promise of revealing important new biological insights. The standard approach of particle tracking consists of two steps: first reconstructing statically the source locations in each time step, and second applying tracking techniques to

Stability of iterated dyadic filter banks Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230123
Marcin Bownik, Brody Johnson, Simon McCrearyEllisThis paper examines the frame properties of finitely and infinitely iterated dyadic filter banks. It is shown that the stability of an infinitely iterated dyadic filter bank guarantees that of any associated finitely iterated dyadic filter bank with uniform bounds. Conditions under which the stability of finitely iterated dyadic filter banks with uniform bounds implies that of the infinitely iterated

Local approximation of operators Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230118
H.N. MhaskarMany applications, such as system identification, classification of time series, direct and inverse problems in partial differential equations, and uncertainty quantification lead to the question of approximation of a nonlinear operator between metric spaces X and Y. We study the problem of determining the degree of approximation of such operators on a compact subset KX⊂X using a finite amount of

Papoulis' sampling theorem: Revisited Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230118
Azhar Y. Tantary, Firdous A. Shah, Ahmed I. ZayedMultidimensional sampling approaches are often faced with certain intricacies as we need to deal with matrices and the noncommutativity of matrices precludes straightforward extensions of the usual onedimensional results. In this article, we reformulate the Papoulis' sampling theorem for the reconstruction of higherdimensional signals that are bandlimited in the sense of free metaplectic transformation

Phase retrieval of bandlimited functions for the wavelet transform Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230111
Rima Alaifari, Francesca Bartolucci, Matthias WellershoffWe study the recovery of squareintegrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for wavelet phase retrieval. To be precise, we show that any wavelet with finitely many vanishing moments allows for the unique recovery of realvalued bandlimited signals up to global sign. Additionally, we present the first

Computing committors in collective variables via Mahalanobis diffusion maps Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20230106
Luke Evans, Maria K. Cameron, Pratyush TiwaryThe study of rare events in molecular and atomic systems such as conformal changes and cluster rearrangements has been one of the most important research themes in chemical physics. Key challenges are associated with long waiting times rendering molecular simulations inefficient, high dimensionality impeding the use of PDEbased approaches, and the complexity or breadth of transition processes limiting

Corrigendum to “Nonlinear matrix recovery using optimization on the Grassmann manifold” [Appl. Comput. Harmon. Anal. 62 (2023) 498–542] Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20221219
Florentin Goyens, Coralia Cartis, Armin EftekhariAbstract not available

A sharp upper bound for sampling numbers in L2 Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20221214
Matthieu Dolbeault, David Krieg, Mario UllrichFor a class F of complexvalued functions on a set D, we denote by gn(F) its sampling numbers, i.e., the minimal worstcase error on F, measured in L2, that can be achieved with a recovery algorithm based on n function evaluations. We prove that there is a universal constant c∈N such that, if F is the unit ball of a separable reproducing kernel Hilbert space, thengcn(F)2≤1n∑k≥ndk(F)2, where dk(F) are

The universal approximation theorem for complexvalued neural networks Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20221213
Felix VoigtlaenderWe generalize the classical universal approximation theorem for neural networks to the case of complexvalued neural networks. Precisely, we consider feedforward networks with a complex activation function σ:C→C in which each neuron performs the operation CN→C,z↦σ(b+wTz) with weights w∈CN and a bias b∈C. We completely characterize those activation functions σ for which the associated complex networks

Nodal domain count for the generalized graph pLaplacian Appl. Comput. Harmon. Anal. (IF 2.5) Pub Date : 20221209
Piero Deidda, Mario Putti, Francesco TudiscoInspired by the linear Schrödinger operator, we consider a generalized pLaplacian operator on discrete graphs and present new results that characterize several spectral properties of this operator with particular attention to the nodal domain count of its eigenfunctions. Just like the onedimensional continuous pLaplacian, we prove that the variational spectrum of the discrete generalized pLaplacian