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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 recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic…
The increased time- and length-scale of classical molecular dynamics simulations have led to raw data flows surpassing storage capacities, necessitating on-the-fly integration of structural analysis algorithms. As a result, algorithms must…
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a…
Crystallographic symmetry classifications from real-world images with periodicities in two dimensions (2D) are of interest to crystallographers and practitioners of computer vision studies alike. Currently, these classifications are…
We investigate the structural and spectral properties of deterministic aperiodic arrays designed from the statistically isotropic pinwheel tiling. By studying the scaling of the cumulative integral of its structure factor in combination…
In this paper, we develop a numerical multiscale method to solve the fractional Laplacian with a heterogeneous diffusion coefficient. When the coefficient is heterogeneous, this adds to the computational costs. Moreover, the fractional…
We present a method that offers perspectives to perform fully antisymmetrized simulations for inhomogeneous bulk fermion matter. The technique bears resemblance to classical periodic boundary conditions, using localized single-particle…
Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We…
Advancements in tools like Shapely 2.0 and Triton can significantly improve the efficiency of spatial similarity computations by enabling faster and more scalable geometric operations. However, for extremely large datasets, these…
Atypical mitotic figures (AMFs) are important histopathological markers yet remain challenging to identify consistently, particularly under domain shift stemming from scanner, stain, and acquisition differences. We present a simple…
Indoor localization is critical for IoT applications, yet challenges such as non-Gaussian noise, environmental interference, and measurement outliers hinder the robustness of traditional methods. Existing approaches, including Kalman…
We investigate how feature selection algorithms can enable accurate, reference-free classification of materials using sparse-frequency terahertz (THz) reflection spectroscopy. Three classes of feature selection strategies are evaluated.…
A physical system exposes to us in a real space, while its description often refers to its reciprocal momentum space. A connection between them can be established by exploring patterns of quasiparticles interference (QPI), which is…
Spatial classification with limited feature observations has been a challenging problem in machine learning. The problem exists in applications where only a subset of sensors are deployed at certain spots or partial responses are collected…
We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data…
We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…
Conventional defect detection systems in Automated Fibre Placement (AFP) typically rely on end-to-end supervised learning, necessitating a substantial number of labelled defective samples for effective training. However, the scarcity of…
We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…
In context of document classification, where in a corpus of documents their label tags are readily known, an opportunity lies in utilizing label information to learn document representation spaces with better discriminative properties. To…