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This work presents a fast direct solver strategy for electromagnetic integral equations in the high-frequency regime. The new scheme relies on a suitably preconditioned combined field formulation and results in a single skeleton form plus…
Electroencephalography (EEG) and Magnetoencephalography (MEG) are pivotal in understanding brain activity but are limited by their poor spatial resolution. EEG/MEG source imaging (ESI) infers the high-resolution electric field distribution…
The electroencephalography (EEG) source imaging problem is very sensitive to the electrical modelling of the skull of the patient under examination. Unfortunately, the currently available EEG devices and their embedded software do not take…
Foundation models pre-trained through masked reconstruction on large-scale EEG data have emerged as a promising paradigm for learning generalizable neural representations across diverse brain-computer interface applications. However, a…
Electroencephalography foundation models (EEG-FMs) have advanced brain signal analysis, but the lack of standardized evaluation benchmarks impedes model comparison and scientific progress. Current evaluations rely on inconsistent protocols…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
The application of counterfactual explanation (CE) techniques in the realm of electroencephalography (EEG) classification has been relatively infrequent in contemporary research. In this study, we attempt to introduce and explore a novel…
A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…
In this paper, a new signal model is suggested for parametric representation of the electroencephalogram (EEG) signals. The proposed model which is an amplitude and frequency modulated sinusoidal signal model, has been found to capture the…
This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates…
Source analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction…
This paper is concerned with the design and analysis of symmetric low-regularity integrators for the semilinear Klein-Gordon equation. We first propose a general symmetrization procedure that allows for the systematic construction of…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
In this work we propose a novel symmetric square matrix representation of one or more digital signals of finite equal length. For appropriate window length and sliding paradigm this matrix contains useful information about the signals in a…
This work focuses on a quasi-linear-in-complexity strategy for a hybrid surface-wire integral equation solver for the electroencephalography forward problem. The scheme exploits a block diagonally dominant structure of the wire self block…
This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown…
Electroencephalogram (EEG) classification has been widely used in various medical and engineering applications, where it is important for understanding brain function, diagnosing diseases, and assessing mental health conditions. However,…
The electrocardiogram (ECG) is an essential and effective tool for diagnosing heart diseases. However, its effectiveness can be compromised by noise or unavailability of one or more leads of the standard 12-lead recordings, resulting in…
Automated classification of electroencephalogram (EEG) signals is complex due to their high dimensionality, non-stationarity, low signal-to-noise ratio, and variability between subjects. Deep neural networks (DNNs) have shown promising…
Electroencephalography (EEG) stands as a crucial tool in neuroscientific research and clinical diagnostics, providing valuable insights into the electrical activities of the brain. Traditional EEG signal processing techniques, predominantly…