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Transcranial electric stimulation (TES) can modulate intrinsic neural activity in the brain by injecting weak currents through electrodes attached to the scalp. TES has been widely used as a neuroscience tool to investigate how behavioural…
In this paper, we are concerned with the gradient estimate of the electric field due to two nearly touching dielectric inclusions, which is a central topic in the theory of composite materials. We derive accurate quantitative…
In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the lens of dimensional Tikhonov-Fenichel parameters and their…
An enhanced static approximation for the electron self energy operator is proposed for efficient calculation of quasiparticle energies. Analysis of the static COHSEX approximation originally proposed by Hedin shows that most of the error…
There has become of increasing interest in transcranial alternating current stimulation (tACS) since its inception nearly a decade ago. tACS in modulating brain state is an active area of research and has been demonstrated effective in…
Transcranial alternating current stimulation (tACS) is becoming an important method in the field of motor rehabilitation because of its ability to non-invasively influence ongoing brain oscillations at arbitrary frequencies. However,…
Accurate electromagnetic modeling of the head of a subject is of main interest in the fields of source reconstruction and brain stimulation. Those processes rely heavily on the quality of the model and, even though the geometry of the…
Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However,…
New stochastic approaches for the computation of electronic excitations are developed within the many-body perturbation theory. Three approximations to the electronic self-energy are considered: $G_0W_0$, $G_0W_0^tc$, and…
The primary motor cortex appears to be in the center of transcranial magnetic stimulation (TMS). It is one of few locations that provide directly observable responses, and its physiology serves as model or reference for almost all other TMS…
In neural-decoding studies, recordings of participants' responses to stimuli are used to train models. In recent years, there has been an explosion of publications detailing applications of innovations from deep-learning research to…
Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…
For a generic set of Markovian noise models, the estimation precision of a parameter associated with the Hamiltonian is limited by the $1/\sqrt{t}$ scaling where $t$ is the total probing time, in which case the maximal possible quantum…
Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the…
Neurostimulation using weak electric fields has generated excitement in recent years due to its potential as a medical intervention. However, study of this stimulation modality has been hampered by inconsistent results and large variability…
This work considers electrical impedance tomography imaging of the human head, with the ultimate goal of locating and classifying a stroke in emergency care. One of the main difficulties in the envisioned application is that the electrode…
Transcranial magnetic stimulation (TMS) is a popular method for the noninvasive stimulation of neurons in the brain. It has become a standard instrument in experimental brain research and is approved for a range of diagnostic and…
Deep brain stimulation (DBS) is a surgical treatment for Parkinson's Disease. Static models based on quasi-static approximation are common approaches for DBS modeling. While this simplification has been validated for bioelectric sources,…
The rigorous quantum mechanical description of the collective interaction of many molecules with the radiation field is usually considered numerically intractable, and approximation schemes must be employed. Standard spectroscopy usually…
We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the…