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The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
In this paper, we propose a novel method to estimate and characterize spatial variations on dies or wafers. This new technique exploits recent developments in matrix completion, enabling estimation of spatial variation across wafers or dies…
The choice of crossover and mutation strategies plays a crucial role in the searchability, convergence efficiency and precision of genetic algorithms. In this paper, a novel improved genetic algorithm is proposed by improving the crossover…
Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent…
Alzheimer's disease (AD) is characterized by complex and largely unknown progression dynamics affecting the brain's morphology. Although the disease evolution spans decades, to date we cannot rely on long-term data to model the pathological…
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-known Smoluchowski--Kramers diffusion approximation result…
A recent technology breakthrough in spatial molecular profiling has enabled the comprehensive molecular characterizations of single cells while preserving spatial information. It provides new opportunities to delineate how cells from…
This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…
We consider an elastic model for a circular arch that incorporates membrane, transverse shear, and bending effects. The central line of the arch is partitioned into elements, and an ultra-weak variational formulation is developed alongside…
Hierarchical microstructures are often invoked to explain the high resilience and fracture toughness of biological materials such as bone and nacre. Biomimetic material models inspired by those structural arrangements face the obvious…
The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
Spatial domain identification requires jointly modeling molecular signatures and physical coordinates, yet current tools frequently over-smooth biological boundaries, require user-specified cluster numbers, and lack principled multimodal…
Assessing the severity of rheumatoid arthritis (RA) using the Total Sharp/Van Der Heijde Score (TSS) is crucial, but manual scoring is often time-consuming and subjective. This study introduces an Automated Radiographic Sharp Scoring…
We present a fingerprint-like method to analyze material defects after energetic particle irradiation by computing a rotation invariant descriptor vector for each atom of a given sample. For ordered solids this new method is easy to use,…
The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a…
The hippocampus is one of the most studied neuroanatomical structures due to its involvement in attention, learning, and memory as well as its atrophy in ageing, neurological, and psychiatric diseases. Hippocampal shape changes, however,…
Spatial transcriptomics (ST) enables mapping gene expression with spatial context but is severely affected by high sparsity and technical noise, which conceals true biological signals and hinders downstream analyses. To address these…
Motivated by problems from neuroimaging in which existing approaches make use of "mass univariate" analysis which neglects spatial structure entirely, but the full joint modelling of all quantities of interest is computationally infeasible,…