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Background and Objective: This proof of concept study investigates mathematical modelling of blood flow and oxygen transport in cerebral microcirculation, focusing on understanding hemodynamic responses. By coupling oxygen transport models…
Diffusion MRI (dMRI) is a critical non-invasive technique to estimate fiber orientation distribution (FOD) for characterizing white matter integrity. Estimating FOD from single-shell low angular resolution dMRI (LAR-FOD) is limited by…
This paper proposes a novel approach to spectral computed tomography (CT) material decomposition that uses the recent advances in generative diffusion models (DMs) for inverse problems. Spectral CT and more particularly photon-counting CT…
Automatic parsing of human anatomies at the instance-level from 3D computed tomography (CT) is a prerequisite step for many clinical applications. The presence of pathologies, broken structures or limited field-of-view (FOV) can all make…
In this work, we first develop a general mesoscopic multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation with the constant diffusion coefficient and source term, where the D2Q5 (five discrete…
Recent work has shown that a fully many-body treatment of noncovalent interactions, such as that given by the method of many-body dispersion (MBD), is vital to accurately modeling the structure and energetics of many molecular systems with…
Multi-configuration range-separated density-functional theory is extended to the time-dependent regime. An exact variational formulation is derived. The approximation, which consists in combining a long-range…
Streamlined qBOLD acquisitions enable experimentally straightforward observations of brain oxygen metabolism. $R_2^\prime$ maps are easily inferred; however, the Oxygen extraction fraction (OEF) and deoxygenated blood volume (DBV) are more…
Combining dispersion and operator product expansion techniques, we derive the conformal partial wave decomposition of the virtual Compton scattering amplitude in terms of complex conformal spin to twist-two accuracy. The perturbation theory…
Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection-diffusion-reaction…
We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…
We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and non-separability. Although these effects are negligible…
Accurate segmentation of vertebral metastasis in CT is clinically important yet difficult to scale, as voxel-level annotations are scarce and both lytic and blastic lesions often resemble benign degenerative changes. We introduce a 2D…
We introduce 'single-particle-exact density functional theory' (1pEx-DFT), a novel density functional approach that represents all single-particle contributions to the energy with exact functionals. Here, we parameterize interaction energy…
Multipole moments are the first order responses of the energy to spatial derivatives of the electric field strength. The quality of density functional theory (DFT) prediction of molecular multipole moments thus characterizes errors in…
A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diffusion equations for modeling biomolecular electrodiffusion…
Understanding and predicting the diverse conformational states of molecules is crucial for advancing fields such as chemistry, material science, and drug development. Despite significant progress in generative models, accurately generating…
Metabolic health is increasingly implicated as a risk factor across conditions from cardiology to neurology, and efficiency assessment of body composition is critical to quantitatively characterizing these relationships. 2D low dose single…
New one-leg multistep time discretizations of nonlinear evolution equations are investigated. The main features of the scheme are the preservation of the nonnegativity and the entropy-dissipation structure of the diffusive equations. The…
We develop a systematic analytical approach on linear and nonlinear pulse propagations in an open Lambda-type molecular system with Doppler broadening. In linear case, by using residue theorem and a spectrum decomposition method, we prove…