Related papers: Extension of B-spline Material Point Method for un…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…
The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…
The new generation of machine learning processors have evolved from multi-core and parallel architectures that were designed to efficiently implement matrix-vector-multiplications (MVMs). This is because at the fundamental level, neural…
It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
For over three decades, scanning probe microscopy (SPM) has been a key method for exploring material structures and functionalities at nanometer and often atomic scales in ambient, liquid, and vacuum environments. Historically, SPM…
Depth maps are widely used in feed-forward 3D Gaussian Splatting (3DGS) pipelines by unprojecting them into 3D point clouds for novel view synthesis. This approach offers advantages such as efficient training, the use of known camera poses,…
Metasurfaces are innovative planar optical structures capable of manipulating incident light properties. Accurate and computationally efficient modeling of such metasurfaces, particularly those with irregular geometries, remains a challenge…
A non-linear shell theory that includes transverse shear strains and its implementation in the material point method framework are discussed. The applicability of the shell implementation to model large deformations of thin shells is…
This article presents an alternative approach to finite elements for modeling and analyzing 3D static mooring lines using string theory and the shooting method (SM) to solve two-point boundary value problems (TPBVPs) for 3D nonlinear static…
In this second paper in a series dedicated to developing efficient numerical techniques for the deblurring Cosmic Microwave Background (CMB) maps, we consider the case of asymmetric point spread functions (PSF). Although conceptually this…
This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products…
We present a principled study on establishing a recursive Bayesian estimation scheme using B-splines in Euclidean spaces. The use of recurrent control points as the state vector is first conceptualized in a recursive setting. This enables…
In this paper we present a new multiscale discontinuous Petrov--Galerkin method (MsDPGM) for multiscale elliptic problems. This method utilizes the classical oversampling multiscale basis in the framework of Petrov--Galerkin version of…
Fourier ptychographic microscopy (FPM) is a recently proposed quantitative phase imaging technique with high resolution and wide field-of-view (FOV). In current FPM imaging platforms, systematic error sources come from the aberrations, LED…
Universal machine-learned interatomic potentials (U-MLIPs) have demonstrated broad applicability across diverse atomistic systems but often require fine-tuning to achieve task-specific accuracy. While the number of available U-MLIPs and…
Building upon the concepts and mechanisms used for the development in Moving Points Algorithm, we will now explore how non linear decision boundaries can be developed for classification tasks. First we will look at the classification…
The MM principle is a device for creating optimization algorithms satisfying the ascent or descent property. The current survey emphasizes the role of the MM principle in nonlinear programming. For smooth functions, one can construct an…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…