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We present several versions of Regularized Combined Field Integral Equation (CFIER) formulations for the solution of three dimensional frequency domain electromagnetic scattering problems with Perfectly Electric Conducting (PEC) boundary…

Synthetic electrocardiogram generation serves medical AI applications requiring privacy-preserving data sharing and training dataset augmentation. Current diffusion-based methods achieve high generation quality but require hundreds of…

The generalization and robustness of an electroencephalogram (EEG)-based computer aided diagnostic system are crucial requirements in actual clinical practice. To reach these goals, we propose a new EEG representation that provides a more…

The Scaled Boundary Finite Element Method is a novel semi-analytical method jointly developed by Chongmin Song and John P Wolf to solve problems in elastodynamics and allied problems in civil engineering. This novel method has been recently…

EEG based brain state decoding has numerous applications. State of the art decoding is based on processing of the multivariate sensor space signal, however evidence is mounting that EEG source reconstruction can assist decoding. EEG source…

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance…

Electroencephalography (EEG) is commonly used by physicians for the diagnosis of numerous neurological disorders. Due to the large volume of EEGs requiring interpretation and the specific expertise involved, artificial intelligence-based…

We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and…

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…

This paper asks whether integrating multimodal EEG and fMRI data offers a better characterisation of functional brain architectures than either modality alone. This evaluation rests upon a dynamic causal model that generates both EEG and…

The problem of detecting the presence of Social Anxiety Disorder (SAD) using Electroencephalography (EEG) for classification has seen limited study and is addressed with a new approach that seeks to exploit the knowledge of EEG sensor…

Electroencephalography (EEG) is a widely used non-invasive technique for measuring brain activity in brain-computer interface (BCI) applications. Supervised EEG decoding models often struggle to generalize across tasks, subjects, and…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Visual stimuli reconstruction from EEG remains challenging due to fidelity loss and representation shift. We propose CognitionCapturerPro, an enhanced framework that integrates EEG with multi-modal priors (images, text, depth, and edges)…

Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties. The usual perturbation schemes are inadequate and new concepts must be introduced. In our…

With the advancement of science and technology, the importance of emotion research has become increasingly evident. Electroencephalography (EEG)-based emotion recognition has emerged as an active research area in recent years, owing to its…

We introduce a symmetrization technique that allows us to translate a problem of controlling the deviation of some functionals on a product space from their mean into a problem of controlling the deviation between two independent copies of…

Accelerated Magnetic Resonance Imaging (MRI) permits high quality images from fewer samples that can be collected with a faster scan. Two established methods for accelerating MRI include parallel imaging and compressed sensing. Two types of…

The applications of Electroencephalogram (EEG) have been extended to out of laboratory and clinics recently due to the advancements in the technical capabilities. There are various advantageous of EEG, making it a preferable method for a…

The standard electrocardiogram (ECG) is a point-wise evaluation of the body potential at certain given locations. These locations are subject to uncertainty and may vary from patient to patient or even for a single patient. In this work, we…