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The representation of a general Calder\'on--Zygmund operator in terms of dyadic Haar shift operators first appeared as a tool to prove the $A_2$ theorem, and it has found a number of other applications. In this paper we prove a new dyadic…
We study compressible MHD turbulence, which holds key to many astrophysical processes, including star formation and cosmic ray propagation. To account for the variations of the magnetic field in the strongly turbulent fluid we use wavelet…
Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using…
The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consider a nonstationary extension where the…
Millimeter-wave (mmWave) communication is considered as a key enabler of ultra-high data rates in the future cellular and wireless networks. The need for directional communication between base stations (BSs) and users in mmWave systems,…
The main purpose of the present paper is to solve the thermodynamic inconsistencies that result when deriving equivalent micropolar models of periodic beam-lattice materials through standard continualization schemes. In fact, this technique…
A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an…
Many modern video-based human action recognition (HAR) approaches use 2D skeleton as the intermediate representation in their prediction pipelines. Despite overall encouraging results, these approaches still struggle in many common scenes,…
We develop certain aspects of the theory of shifted multiple Dirichlet series and study their meromorphic continuations. These continuations are used to obtain explicit spectral first and second moments of Rankin-Selberg convolutions. One…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden"…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace $E$ of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an…
Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…
This paper is concerned with the problem of reconstructing an infinite-dimensional signal from a limited number of linear measurements. In particular, we show that for binary measurements (modelled with Walsh functions and Hadamard…
This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We…
Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle…
Ultrahigh field (UHF) Magnetic Resonance Imaging (MRI) offers an elevated signal-to-noise ratio (SNR), enabling exceptionally high spatial resolution that benefits both clinical diagnostics and advanced research. However, the jump to higher…
The purpose of this article is to discuss some aspects of the convergence analysis performed in the paper [Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle…
Efficient representations of multivariate functions are critical for the design of state-of-the-art methods of data restoration and image reconstruction. In this work, we consider the representation of spatio-temporal data such as temporal…