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In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
Diffusion-weighted magnetic resonance imaging in brain white matter probes tissue microstructure and allows for the estimation of compartmental diffusion parameters. Recently, it became apparent that traditional single-direction diffusion…
Diffusion models are important in tissue engineering as they enable an understanding of molecular delivery to cells in tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically…
We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching $\sim 100,000$ electrons) using Kohn-Sham density functional theory (DFT). DFT-FE is based on a local…
In orthogonal time-frequency space communications, the performances of existing on-grid and off-grid channel estimation (CE) schemes are determined by the delay-Doppler (DD) grid density. In practice, multiple real-life DD channel responses…
The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian Dynamics (BD) or…
Accurate segmentation of multiple organs in Computed Tomography (CT) images plays a vital role in computer-aided diagnosis systems. While various supervised learning approaches have been proposed recently, these methods heavily depend on a…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
The Generalized Parton Distributions (GPDs) constitute an appropriate framework for a universal description of the partonic structure of the nucleon. Double Deeply Virtual Compton Scattering (DDVCS) process provides the only experimental…
We investigate charge transfer in prototypical molecular donor-acceptor compounds using hybrid density functional theory (DFT) and the GW approximation at the perturbative level (G0W0) and at full self-consistency (sc-GW). For the systems…
We develop an operator splitting approach to solve diffeomorphic matching problems for sequences of surfaces in three-dimensional space. The goal is to smoothly match, at a very fast rate, finite sequences of observed 3D-snapshots extracted…
In medical imaging, organ/pathology segmentation models trained on current publicly available and fully-annotated datasets usually do not well-represent the heterogeneous modalities, phases, pathologies, and clinical scenarios encountered…
In this paper, we study gradient decay estimates for solutions to the multi-dimensional Fisher-KPP equation with fractional diffusion. It is known that this equation exhibits exponentially advancing level sets with strong qualitative upper…
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate,…
We develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based…
Exchange hole is the principle constituent in density functional theory, which can be used to accurately design exchange energy functional and range separated hybrid functionals coupled with some appropriate correlation. Recently, density…
Irregular distribution in latent space causes posterior collapse, misalignment between posterior and prior, and ill-sampling problem in Variational Autoencoders (VAEs). In this paper, we introduce a novel adaptable three-stage Uniform…
The random phase approximation (RPA) has received a considerable interest in the field of modeling systems where noncovalent interactions are important. Its advantages over widely used density functional theory (DFT) approximations are the…
Purpose: Automated liver tumor segmentation from Computed Tomography (CT) images is a necessary prerequisite in the interventions of hepatic abnormalities and surgery planning. However, accurate liver tumor segmentation remains challenging…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…