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A mathematical model is developed, to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
To produce images that are suitable for display, tone-mapping is widely used in digital cameras to map linear color measurements into narrow gamuts with limited dynamic range. This introduces non-linear distortion that must be undone,…
We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we…
The knowledge of the exact structure of the optical system PSF enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications.…
Optical fluorescence imaging is capable of measuring both the spatial and rotational dynamics of single molecules. However, unavoidable measurement noise will result in inaccurate estimates of rotational dynamics, causing a molecule to…
Numerical investigation of the interaction of electromagnetic fields with eukaryotic cells requires specifically adapted computer models. Virtual microdosimetry, used to investigate exposure, requires volumetric cell models, which are…
Medical ultrasound imaging is the most widespread real-time non-invasive imaging system and its formulation comprises signal transmission, signal reception, and image formation. Ultrasound signal transmission modelling has been formalized…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
Technology is moving towards space division multiplexing in optical fiber to keep up the trend in rate increase over time and to avoid an imminent capacity crunch. Thus, it is of paramount interest to estimate the potential gains of this…
Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion…
Neural Network Potentials (NNPs) have emerged as a powerful tool for modelling atomic interactions with high accuracy and computational efficiency. Recently, denoising diffusion models have shown promise in NNPs by training networks to…
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…
Liposomes that achieve a heterogeneous and spatially organized surface through phase separation have been recognized to be a promising platform for delivery purposes. However, their design and optimization through experimentation can be…
Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This…
A new formulation of lateral imaging process of point-scanning optical coherence tomography (OCT) and a new differential contrast method designed by using this formulation are presented. The formulation is based on a mathematical sample…
The method of photon distribution function (PDF) is used to study fluctuations of light beams propagating through a turbulent atmosphere. Our analysis concerns the regime of saturated fluctuations. The focus is on the phenomena of beam…
Recent advances in imaging and high-performance computing have made it possible to image the entire human brain at the cellular level. This is the basis to study the multi-scale architecture of the brain regarding its subdivision into brain…
In this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is based on linearization and group sparsity, which allows…
State-of-the-art diffusion models can generate highly realistic images based on various conditioning like text, segmentation, and depth. However, an essential aspect often overlooked is the specific camera geometry used during image…