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In several practical applications, particularly healthcare, clinical data of each patient is individually recorded in a database at irregular intervals as required. This causes a sparse and irregularly sampled time series, which makes it…
We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine…
Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
Previous attempts to integrate Neural Radiance Fields (NeRF) into the Simultaneous Localization and Mapping (SLAM) framework either rely on the assumption of static scenes or require the ground truth camera poses, which impedes their…
We consider problems of dynamic viscoelasticity taking into account the coupling of elastic and thermal fields. Efficient approximate models are developed and computational results on thermomechanical behaviour of shape-memory-alloy…
We extend a model for the morphology and dynamics of a crawling eukaryotic cell to describe cells on micropatterned substrates. This model couples cell morphology, adhesion, and cytoskeletal flow in response to active stresses induced by…
Face animation aims at creating photo-realistic portrait videos with animated poses and expressions. A common practice is to generate displacement fields that are used to warp pixels and features from source to target. However, prior…
Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the…
A dynamic factor model with factor series following a VAR$(p)$ model is shown to have a VARMA$(p,p)$ model representation. Reduced-rank structures are identified for the VAR and VMA components of the resulting VARMA model. It is also shown…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic…
In vitro velocities of several cell types have been measured using computer controlled video microscopy, which allowed to record the cells' trajectories over several days. On the basis of our large data sets we show that the locomotion…
Statistical shape modeling aims at capturing shape variations of an anatomical structure that occur within a given population. Shape models are employed in many tasks, such as shape reconstruction and image segmentation, but also shape…
Stereotyped behaviors are series of postures that show very little variability between repeats. They have been used to classify the dynamics of individuals, groups and species without reference to the lower-level mechanisms that drive them.…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
We build on the Visual Autoregressive Modeling (VAR) framework and formulate style transfer as conditional discrete sequence modeling in a learned latent space. Images are decomposed into multi-scale representations and tokenized into…
Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate…
We developed a new approach comprised of different visualizations for the comparative spatio-temporal analysis of displacement processes in porous media. We aim to analyze and compare ensemble datasets from experiments to gain insight into…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…