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We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
Feature selection is a crucial step in building machine learning models. This process is often achieved with accuracy as an objective, and can be cumbersome and computationally expensive for large-scale datasets. Several additional model…
In this paper we investigate weak decays of heavy mesons in the framework of a covariant quark model, which is based on the Bethe-Salpeter equation in instantaneous approximation. Apart from a phenomenological confinement potential, a…
We introduce the first learning-based dense matching algorithm, termed Equirectangular Projection-Oriented Dense Kernelized Feature Matching (EDM), specifically designed for omnidirectional images. Equirectangular projection (ERP) images,…
In asymmetric retrieval systems, models with different capacities are deployed on platforms with different computational and storage resources. Despite the great progress, existing approaches still suffer from a dilemma between retrieval…
Convolutional Neural Networks (CNNs) has been applied in numerous Internet of Things (IoT) devices for multifarious downstream tasks. However, with the increasing amount of data on edge devices, CNNs can hardly complete some tasks in time…
Following the rapidly growing digital image usage, automatic image categorization has become preeminent research area. It has broaden and adopted many algorithms from time to time, whereby multi-feature (generally, hand-engineered features)…
Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be…
Mesh offsetting plays an important role in discrete geometric processing. In this paper, we propose a parallel feature-preserving mesh offsetting framework with variable distance. Different from the traditional method based on distance and…
Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required smoothing properties can be different or even contradictive among different tasks. Nevertheless, the inherent smoothing nature of…
Standard complexity analyses for weakly convex optimization rely on the Moreau envelope technique proposed by Davis and Drusvyatskiy (2019). The main insight is that nonsmooth algorithms, such as proximal subgradient, proximal point, and…
For adaptive mixed finite element methods (AMFEM), we first introduce the data oscillation to analyze, without the restriction that the inverse of the coefficient matrix of the partial differential equations (PDEs) is a piecewise polynomial…
This study develops a polygonal cell-based smoothed finite element method (CSFEM) for two-dimensional seepage analyses in porous media, covering steady-state, transient, and free-surface problems. Wachspress interpolation on convex…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
Flow cytometry (FCM) is the standard multi-parameter assay for measuring single cell phenotype and functionality. It is commonly used for quantifying the relative frequencies of cell subsets in blood and disaggregated tissues. A typical…
The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…
We recently found that the electromagnetic scattering problem can be very fast in an approach expressing the fields in terms of orthonormal basis functions. In this paper we apply computational conformal geometry with the conformal energy…
Cross-View Geo-Localization (CVGL) involves determining the localization of drone images by retrieving the most similar GPS-tagged satellite images. However, the imaging gaps between platforms are often significant and the variations in…