Related papers: Quasi-Static Approximation Error of Electric Field…
The excess power, energy and intensity of a random electromagnetic field above a high threshold level are characterized based on a Slepian--Kac model for upcrossings. For quasi-static fields, the probability distribution of the excess…
We present quantitative means for assessing the numerical accuracy of static magnetic field calculations in finite-element models. Our calculations use the three-dimensional Opera simulation software suite of Dassault Syst`emes. Our need to…
In this article, we design a novel Transcranial Electrical Stimulator for medical applications, which is very cheap and can produce the desired signals very accurately. Our fabricated stimulator generates all current signals related to…
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…
This paper presents a rigorous mathematical analysis, alongside simulation studies, of a spatially extended stochastic electrophysiology model, the Hodgkin-Huxley model of the squid giant axon being a classical example. Although most…
Energy spectrum and thermodynamics of the pseudospin-electron model introduced at the consideration of the anharmonicity effects in high-$T_c$ superconductors are investigated in the dynamical mean field approximation ($d=\infty$ limit). In…
We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the…
This note is concerned with accurate and computationally efficient approximations of moments of Gaussian random variables passed through sigmoid or softmax mappings. These approximations are semi-analytical (i.e. they involve the numerical…
The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steady-state approximation can be mathematically justified from…
Objective. Personalized transcranial electrical stimulation (tES) has gained growing attention due to the substantial inter-individual variability in brain anatomy and physiology. While previous reviews have discussed the physiological…
A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the…
Background: Individual skull models of bone density and geometry are important when planning the expected transcranial ultrasound acoustic field and estimating mechanical and thermal safety in low-intensity transcranial ultrasound…
Closed-form, analytical approximations for electrostatic properties of molecules are of unique value, as these can provide computational speed, versatility, and physical insight. Here, we derive a simple, closed-form formula for the…
We demonstrate that a mean field approximation can be confidently employed in quasiperiodic moir\'e systems to treat interactions and quasiperiodicity on equal footing. We obtain the mean field phase diagram for an illustrative…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
The realistic probability distributions of a previous article are applied to the reconstruction of tracks in constant magnetic field. The complete forms and their schematic approximations produce excellent momentum estimations, drastically…
We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly…
At the level of individual neurons, various coding properties can be inferred from the input-output relationship of a cell. For small inputs, this relation is captured by the phase-response curve (PRC), which measures the effect of a small…
Quantitative electron magnetic circular dichroism (EMCD) in transmission electron microscopy (TEM) enables the measurement of magnetic moments with elemental and atomic site sensitivity, but its practical application is fundamentally…
Cortical slow oscillations occur in the mammalian brain during deep sleep and have been shown to contribute to memory consolidation, an effect that can be enhanced by electrical stimulation. As the precise underlying working mechanisms are…