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Neural collapse (NC) -- the convergence of penultimate-layer features to a simplex equiangular tight frame -- is well understood at equilibrium, but the dynamics governing its onset remain poorly characterised. We identify a simple and…
Sound field reconstruction (SFR) augments the information of a sound field captured by a microphone array. Conventional SFR methods using basis function decomposition are straightforward and computationally efficient, but may require more…
Disorder-driven, integrated speckle spectrometers offer exceptional spectral resolution within a compact design. They benefit from enhanced optical path lengths due to multiple light scattering events, however, often at the cost of low…
While Deep Learning (DL) is often considered the state-of-the art for Artificial Intelligence-based medical decision support, it remains sparsely implemented in clinical practice and poorly trusted by clinicians due to insufficient…
This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform for distributed reconstruction of mechanical properties in layered components from full waveform data. In this vein, two…
Convolutional Neural Networks (CNNs) are a class of artificial neural networks whose computational blocks use convolution, together with other linear and non-linear operations, to perform classification or regression. This paper explores…
Spectral Doppler measurements are an important part of the standard echocardiographic examination. These measurements give important insight into myocardial motion and blood flow providing clinicians with parameters for diagnostic decision…
In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves…
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the…
Understanding the impact of spectral coverage on parameter recovery is critical for accurate interpretation of blazar spectra. In this study, we examine how the data coverage influences the reliability of parameter estimation within the…
Optical spectroscopy the measurement of electromagnetic spectra is fundamental to various scientific domains and serves as the building block of numerous technologies. Computational spectrometry is an emerging field that employs an array of…
In this paper we consider high-frequency acoustic transmission problems with jumping coefficients modelled by Helmholtz equations. The solution then is highly oscillatory and, in addition, may be localized in a very small vicinity of…
Unsupervised semantic segmentation is a long-standing challenge in computer vision with great significance. Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct…
This work formally investigates the differential evolution indicators as a tool for ultrasonic tracking of elastic transformation and fracturing in randomly heterogeneous solids. Within the framework of periodic sensing, it is assumed that…
Accurate molecular spectroscopy in the mid-infrared region allows precision measurements of fundamental constants. For instance, measuring the linewidth of an isolated Doppler-broadened absorption line of ammonia around 10 $\mu$m enables a…
Accurately characterizing non-linear functional manifolds with singularities is a fundamental challenge in scientific computing. While Multi-Layer Perceptrons (MLPs) dominate, their spectral bias hinders resolving high-curvature features…
The goal of Specular Neutron and X-ray Reflectometry is to infer materials Scattering Length Density (SLD) profiles from experimental reflectivity curves. This paper focuses on investigating an original approach to the ill-posed…
Currently, approximately 30% of epileptic patients treated with antiepileptic drugs (AEDs) remain resistant to treatment (known as refractory patients). This project seeks to understand the underlying similarities in refractory patients vs.…
Angular differential imaging (ADI) and spectral differential imaging (SDI) are commonly used for direct detection and characterisation of young, Jovian exoplanets in datasets obtained with the SPHERE/IFS instrument. We compare the…
Frame design for phaseless reconstruction is now part of the broader problem of nonlinear reconstruction and is an emerging topic in harmonic analysis. The problem of phaseless reconstruction can be simply stated as follows. Given the…