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This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
Magnetoencephalography (MEG) and electroencephalogra-phy (EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Inferring the location of the current sources that generated these…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…
Depression is a major cause of global mental illness and significantly influences suicide rates. Timely and accurate diagnosis is essential for effective intervention. Electroencephalography (EEG) provides a non-invasive and accessible…
Electroencephalography (EEG) activity contains a wealth of information about what is happening within the human brain. Recording more of this data has the potential to unlock endless future applications. However, the cost of EEG hardware is…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
Endovascular aneurysm repair (EVAR) is a current alternative treatment for thoracic and abdominal aortic aneurysms, but is still sometimes compromised by possible complications such as device migration or endoleaks. In order to assist…
The forward problem in electrocardiology, computing body surface potentials from cardiac electrical activity, is traditionally solved using physics-based models such as the bidomain or monodomain equations. While accurate, these approaches…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
Reconstructing cardiac electrical activity from body surface electric potential measurements results in the severely ill-posed inverse problem in electrocardiography. Many different regularization approaches have been proposed to improve…
The price of instruments and observing time on modern telescopes is quickly increasing with the size of the primary mirror. Therefore, it is worth revisiting the data reduction algorithms to extract every bit of scientific information from…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
This paper reviews the method of surface Laplacian differentiation to study EEG. We focus on topics that are helpful for a clear understanding of the underlying concepts and its efficient implementation, which is especially important for…
The aim of this work is to show an abstract framework to analyze the numerical approximation by using a finite element method in space and a Backward-Euler scheme in time of a family of degenerate parabolic problems. We deduce sufficient…
Electrocardiogram is a useful diagnostic signal that can detect cardiac abnormalities by measuring the electrical activity generated by the heart. Due to its rapid, non-invasive, and richly informative characteristics, ECG has many emerging…
The detection of Alzheimers disease (AD) is considered crucial, as timely intervention can improve patient outcomes. Electroencephalogram (EEG)-based diagnosis has been recognized as a non-invasive, accessible, and cost-effective approach…
While electroencephalography (EEG) has been a popular modality for neural decoding, it often involves task specific acquisition of the EEG data. This poses challenges for the development of a unified pipeline to learn embeddings for various…
Source localization based on electroencephalography (EEG) has become a widely used neuroimagining technique. However its precision has been shown to be very dependent on how accurately the brain, head and scalp can be electrically modeled…