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The electroencephalographic (EEG) signals provide highly informative data on brain activities and functions. However, their heterogeneity and high dimensionality may represent an obstacle for their interpretation. The introduction of a…

Foundation models for electroencephalography (EEG) signals have recently demonstrated success in learning generalized representations of EEGs, outperforming specialized models in various downstream tasks. However, many of these models lack…

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are subject dependent, so non-invasive methods for…

In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…

Electroencephalography (EEG) is a vital tool to measure and record brain activity in neuroscience and clinical applications, yet its potential is constrained by signal heterogeneity, low signal-to-noise ratios, and limited labeled datasets.…

This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…

EDIT: A revised version of this article has been published in the SIAM Journal on Scientific Computing, see https://epubs.siam.org/doi/full/10.1137/23M1582874. In the revised version, the name of the approach was changed from "localized…

Electroencephalography (EEG) often shows significant variability among people. This fluctuation disrupts reliable acquisition and may result in distortion or clipping. Modulo sampling is now a promising solution to this problem, by folding…

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…

Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is…

We propose a new representation learning solution for the classification of cognitive load based on Electroencephalogram (EEG). Our method integrates both time and frequency domains by first passing the raw EEG signals through the…

Blind equalization is a classic yet open problem. Statistic-based algorithms, such as constant modulus (CM), were widely investigated. One inherent issue with blind algorithms is the phase ambiguity of equalized signals. In this letter, we…

The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…

Electroencephalography provides a non-invasive window into brain activity, offering valuable insights for neurological research, brain-computer interfaces, and clinical diagnostics. However, the development of robust machine learning models…

Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…

Electroencephalogram (EEG) signal classification faces significant challenges due to data distribution shifts caused by heterogeneous electrode configurations, acquisition protocols, and hardware discrepancies across domains. This paper…

Electroencephalography (EEG) analysis stands at the forefront of neuroscience and artificial intelligence research, where foundation models are reshaping the traditional EEG analysis paradigm by leveraging their powerful representational…

We propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of second-order elliptic operators. The main idea is to reduce the stiffness of the problem by subtracting a…

In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being…

Inferring patterns of synchronous brain activity from a heterogeneous sample of electroencephalograms (EEG) is scientifically and methodologically challenging. While it is intuitively and statistically appealing to rely on readings from…