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Kernel-based modeling of dynamic systems has garnered a significant amount of attention in the system identification literature since its introduction to the field. While the method was originally applied to linear impulse response…
An experimental and theoretical study of the spectral response of coupled visco-elastic bars subject to axial oscillations is done. Novel closed formulas for the envelope function and their width is derived. These formulas explicitly show…
The purpose of this note is to propose an application of the Lambert W function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular we recognize the role of the main branch W_0(t) in a…
Optical flow estimation is an important yet challenging problem in the field of video analytics. The features of different semantics levels/layers of a convolutional neural network can provide information of different granularity. To…
Deformable image registration estimates voxel-wise correspondences between images through spatial transformations, and plays a key role in medical imaging. While deep learning methods have significantly reduced runtime, efficiently handling…
Magnetic resonance imaging (MRI) plays a vital role in clinical diagnostics, yet it remains hindered by long acquisition times and motion artifacts. Multi-contrast MRI reconstruction has emerged as a promising direction by leveraging…
This article focuses on the mathematical problem of reconstructing dynamic permeability $K(\omega)$ of two-phase composites from data at different frequencies, utilizing the analytic structure of the Stieltjes function representation of…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
We investigate the nonlinear viscoelastic behavior of a biomimetic scale-covered beam in which shear-dependent complex fluids are trapped between overlapping scales under bending loads. These fluids mimic biological mucus and slime layers…
The functional renormalization group has become a widely used tool for the analysis of the leading low-temperature correlations in weakly to moderately coupled many-fermion lattice systems. A bottleneck for quantitatively more precise…
We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily…
This paper presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered…
The inability of otherwise successful dynamical models to reproduce the ``HBT radii'' extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the ``RHIC HBT Puzzle.'' Most comparisons…
A new concise proof is given of a duality theorem connecting completely monotone relaxation functions with Bernstein class creep functions in one-dimensional and anisotropic 3D viscoelasticity. The proof makes use of the theory of complete…
We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship…
The structural properties of suspensions and other multiphase systems are vital to overall processability, functionality and acceptance among consumers. Therefore, it is crucial to understand the intrinsic connection between the…
Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which…
In this paper, we consider the problem of reconstructing piece-wise smooth functions from their non-uniform Fourier data. We first extend the filter method for uniform Fourier data to the non-uniform setting by using the techniques of…
We propose a statistical model for static and sliding friction between rough surfaces. Approximating the contact between rough surfaces by the contact of an ensemble of one-dimensional viscoelastic elements with a rough rigid surface, we…