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Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…
A fundamental effect of fluid turbulence is turbulent mixing, which results in the stretching and wrinkling of scalar isosurfaces. Thus, the area of isosurfaces is of interest in understanding turbulence in general with specific…
In this note, we show a sublinear nonergodic convergence rate for the algorithm developed in [Bai, et al. Generalized symmetric ADMM for separable convex optimization. Comput. Optim. Appl. 70, 129-170 (2018)], as well as its linear…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
The reconstruction of indoor scenes from multi-view RGB images is challenging due to the coexistence of flat and texture-less regions alongside delicate and fine-grained regions. Recent methods leverage neural radiance fields aided by…
This paper establishes convergence and steady-state properties for the signal bound disturbance attenuation regulator (SiDAR). Building on the finite horizon recursive solution developed in a companion paper, we introduce the steady-state…
This work develops a physically consistent model for stacked intelligent metasurfaces (SIM) using multiport network theory and transfer scattering parameters (T-parameters). Unlike the scattering parameters (S-parameters) model, the…
The aim of surface defect detection is to identify and localise abnormal regions on the surfaces of captured objects, a task that's increasingly demanded across various industries. Current approaches frequently fail to fulfil the extensive…
3D Gaussian Splatting (3DGS) has recently emerged as a promising approach in novel view synthesis, combining photorealistic rendering with real-time efficiency. However, its success heavily relies on dense camera coverage; under sparse-view…
We present an adaptive scheme for isogeometric phase-field modeling, to perform suitably graded hierarchical refinement and coarsening on both single- and multi-patch geometries by considering truncated hierarchical spline constructions…
The influence of surface roughness on transition to turbulence in a Mach 4.5 boundary layer is studied using direct numerical simulations. Transition is initiated by the nonlinearly most dangerous inflow disturbance, which causes the…
Muon-style optimizers leverage Newton-Schulz (NS) iterations to orthogonalize updates, yielding update geometries that often outperform Adam-series methods. However, this orthogonalization discards magnitude information, rendering training…
We present an $\ell^2_2+\ell_1$-regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for…
Staining reveals the micro structure of the aspirate while creating histopathology slides. Stain variation, defined as a chromatic difference between the source and the target, is caused by varying characteristics during staining, resulting…
We develop a mixed formulation for incompressible hyper-elastodynamics based on a continuum modeling framework recently developed and smooth generalizations of the Taylor-Hood element based on non-uniform rational B-splines (NURBS). This…
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…
This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main…