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In this article, we present a multispecies reaction-advection-diffusion partial differential equation (PDE) coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma…
Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by…
We present a new methodology for the real-time reduced-order modeling of stochastic partial differential equations called the dynamically/bi-orthonormal (DBO) decomposition. In this method, the stochastic fields are approximated by a…
Most MRI liver segmentation methods use a structural 3D scan as input, such as a T1 or T2 weighted scan. Segmentation performance may be improved by utilizing both structural and functional information, as contained in dynamic contrast…
In this paper we discuss the results of some Molecular Dynamics simulations of a magnetized One Component Plasma, targeted to estimate the diffusion coefficient $D_{\perp}$ in the plane orthogonal to the magnetic field lines. We find that…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs) decomposes the interaction energy between molecules into physically interpretable components like geometry distortion, frozen interactions,…
A survey is given on asymptotic diffusion coefficients of particles in lattices with random transition rates. Exact and approximate results for single particles are reviewed. A recent exact expression in $d = 1$ which includes occupation…
The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with respect the lattice sites is considered as the basic variable of the many-body problem. A…
Perhaps the simplest first-principles approach to electronic structure is to fit the charge distribution of each orbital pair and use those fits wherever they appear in the entire electron-electron (EE) interaction energy. The charge…
To extend the Bose-Einstein (BE) distribution to fractional order, we turn our attention to the differential equation, $df/dx =-f-f^2$. It is satisfied with the stationary solution, $f(x)=1/(e^{x+\mu}-1)$, of the Kompaneets equation, where…
Diffusion Transformers (DiTs) with billions of model parameters form the backbone of popular image and video generation models like DALL.E, Stable-Diffusion and SORA. Though these models are necessary in many low-latency applications like…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
This paper presents the Derivatives Combination Predictor (DCP), a novel model fusion algorithm for making long-term glucose predictions for diabetic people. First, using the history of glucose predictions made by several models, the future…
Recent methods for molecular generation face a trade-off: they either enforce strict equivariance with costly architectures or relax it to gain scalability and flexibility. We propose a frame-based diffusion paradigm that achieves…
Sparse-view computed tomography (CT) reconstruction is fundamentally challenging due to undersampling, leading to an ill-posed inverse problem. Traditional iterative methods incorporate handcrafted or learned priors to regularize the…
In modeling the interior of cells by simulating a reaction-diffusion master equation over a grid of compartments, one employs the assumption that the copy numbers of various chemical species are small, discrete quantities. We show that in…
Pretrained diffusion models provide powerful learned priors, but in scientific sampling the target distribution often depends on physical context that is not fully represented by one generative model. We introduce Generative Gibbs for…
Multi-layer diffuse correlation spectroscopy (DCS) models have been developed to reduce the contamination of superficial signals in cerebral blood flow index (CBFi) measurements. However, a systematic comparison of these models and clear…
Sparse query-based paradigms have achieved significant success in multi-view 3D detection for autonomous vehicles. Current research faces challenges in balancing between enlarging receptive fields and reducing interference when aggregating…