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Understanding the complex behavior of molecular systems is fundamental to fields such as physics, materials science, and biology. Molecular dynamics (MD) simulations are crucial tools for studying atomic-level dynamics. This work focuses on…
Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…
We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of…
The performance of the dynamically bi-orthogonal (DBO) decomposition for the reduced order modeling of turbulence-chemistry interactions is assessed. DBO is an on-the-fly low-rank approximation technique, in which the instantaneous…
Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist…
Radiotherapy treatment planning often relies on time-consuming, trial-and-error adjustments that heavily depend on the expertise of specialists, while existing deep learning methods face limitations in generalization, prediction accuracy,…
Quantum mechanical methods based on the density functional theory (DFT) offer a realistic possibility of first-principles design of organic donor-acceptor systems and engineered band-gap materials. This promise is contingent upon the…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
Image registration of liver dynamic contrast-enhanced computed tomography (DCE-CT) is crucial for diagnosis and image-guided surgical planning of liver cancer. However, intensity variations due to the flow of contrast agents combined with…
Beam alignment enables efficient, stable transmission and control of optical energy and information, which critically depend on precise monitoring and regulation of the three-dimensional (3D) relative positioning between fibers. This study…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
We provide a framework to solve generic models describing the dissociation of multiple molecular Bose-Einstein condensates in a nonadiabatic regime. The competition between individual chemical reactions can lead to non-trivial dependence on…
We present a covariance-aware sampler that improves the quality of pixel-space Diffusion Model (DM) sampling in the few-step regime. We hypothesize that in the few-step regime samplers fail because they rely solely on the predicted mean of…
Dynamic Distribution Decomposition (DDD) was introduced in Taylor-King et. al. (PLOS Comp Biol, 2020) as a variation on Dynamic Mode Decomposition. In brief, by using basis functions over a continuous state space, DDD allows for the fitting…
Deep learning-based segmentation techniques have shown remarkable performance in brain segmentation, yet their success hinges on the availability of extensive labeled training data. Acquiring such vast datasets, however, poses a significant…
Diffusion models, as powerful generative models, have found a wide range of applications and shown great potential in solving image reconstruction problems. Some works attempted to solve MRI reconstruction with diffusion models, but these…
We present two distributed methods for the estimation of the kinematic parameters, the dynamic parameters, and the kinematic state of an unknown planar body manipulated by a decentralized multi-agent system. The proposed approaches rely on…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
Accurate molecular subtype classification is essential for personalized breast cancer treatment, yet conventional immunohistochemical analysis relies on invasive biopsies and is prone to sampling bias. Although dynamic contrast-enhanced…
Electrical conduction among cardiac tissue is commonly modeled with partial differential equations, i.e., reaction-diffusion equation, where the reaction term describes cellular stimulation and diffusion term describes electrical…