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Nano-NMR spectroscopy with nitrogen-vacancy centers holds the potential to provide high resolution spectra of minute samples. This is likely to have important implications for chemistry, medicine and pharmaceutical engineering. One of the…
Medical image segmentation is a challenging task with inherent ambiguity and high uncertainty, attributed to factors such as unclear tumor boundaries and multiple plausible annotations. The accuracy and diversity of segmentation masks are…
A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation,…
Diffusion models have shown impressive performance for image generation, often times outperforming other generative models. Since their introduction, researchers have extended the powerful noise-to-image denoising pipeline to discriminative…
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
The diffusion model has recently emerged as a potent approach in computer vision, demonstrating remarkable performances in the field of generative artificial intelligence. Capable of producing high-quality synthetic images, diffusion models…
Since the seminal paper by Mitra et al., diffusion MR has been widely used in order to estimate surface-to-volume ratios. In the present work we generalize Mitra's formula for arbitrary diffusion encoding waveforms, including recently…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
This paper employs the general time-space fractional diffusion equation to derive correlation time function for analyzing nuclear magnetic resonance (NMR) relaxation. Both the anomalous rotational and translational diffusion are treated.…
Long pulse durations necessary in selective inversion recovery (SIR) experiments along with radiation damping (RD) introduce difficulties in quantitative nuclear magnetic resonance measurements, such as those that allow for the…
The Bloch equation describes the evolution of classical particles tagged with a magnetisation vector in a strong magnetic field and is fundamental to many NMR and MRI contrast methods. The equation can be generalised to include the effects…
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…
Diffusion models have emerged as powerful priors for solving inverse problems in computed tomography (CT). In certain applications, such as neutron CT, it can be expensive to collect large amounts of measurements even for a single scan,…
Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…
We present a method to probe molecular and nanoparticle diffusion within thin, solvated polymer coatings. The device exploits the confinement with well-defined geometry that forms at the interface between a planar and a hemi-spherical…
We report an ensemble nuclear magnetic resonance (NMR) implementation of a quantum lattice gas algorithm for the diffusion equation. The algorithm employs an array of quantum information processors sharing classical information, a novel…
Recently, the concept of traveling-wave NMR/MRI was introduced by Brunner et al. (Nature 457, 994-992 (2009)), who demonstrated MR images acquired using radio frequency (RF) waves propagating down the bore of an MR scanner. One of the…
Near infrared diffuse optical tomography (DOT) provides an imaging modality for the oxygenation of tissue. In this paper, we propose a novel machine learning algorithm based on time-domain radiative transfer equation. We use temporal…
2D portrait animation has experienced significant advancements in recent years. Much research has utilized the prior knowledge embedded in large generative diffusion models to enhance high-quality image manipulation. However, most methods…
We present a set-up for time-resolved X-ray diffraction based on a short pulse, laser-driven plasma X-ray source. The employed modular design provides high flexibility to adapt the set-up to the specific requirements (e.g. X-ray optics,…