We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

In this seminar I will present how to create 3D computer graphics and visualization systems for the web, using WebAssmbly and WebGPU language specifications, which are new, bleeding-edge technologies. Previously, accelerated graphics on the web was based on JavaScript libraries, which is still very popular, but they do not offer detailed memory management and code optimization, necessary for systems requiring high memory load and high computational demands. WebAssembly and WebGPU can be compiled from the C++ or Rust code, which also allows the deployment of the same codebase either for web or for the desktop-based applications.

Inevitably, the projection of most graph structures on two-dimensional screens will create errors and therefore visually wrong impressions. In the past, two types of methods have been developed to minimize projection errors and distribute them in a visually pleasing way. The first group of methods, force-directed layouts, interpret the links of a graph as physical springs, while stress-based methods minimize an energy function, which aims to map graph distances faithfully.

In this talk I will report on various research projects that I carried out with my students to better understand the interaction landscape and will report on lessons we learned. I will focus mostly on AR-based setups with application examples from physical flow visualization, molecular visualization, visualization of particle collisions, biomolecular dynamics in cells, and oceanography. I will show interaction techniques that rely on purely gestural interaction, phones or tablets as input and control devices, and hybrid setups that combine traditional workstations with AR views. I will discuss navigation, data selection, and visualization system control as different interaction tasks. With this overview I aim to provide an understanding of typical challenges in immersive visualization environments and how to address some of these challenges.

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Science communication is facing a p

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The ability to create structural mo

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In this talk, I will present our recent advances in deep learning to synthesize and analy

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By providing visual representations of data, visualization can

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Our ongoing research on the reconstruction of aerial point cloud data includes reconstruc

In this talk, I will introduce a few recent works on tree visualization. First I will present a  visualization technique for comparing topological structures and node attribute values of multiple trees. I will further introduce GoTree, a declarative grammar supporting the creation of a wide range of tree visualizations. In the application side, visualization and visual analytics on social media  will be introduced. The data from social media can be considered as graphs or trees with complex attributes. A few approaches using map metaphor for social media data visualization will be discussed.