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We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
This article investigates the application of computer vision and graph-based models in solving mesh-based partial differential equations within high-performance computing environments. Focusing on structured, graded structured, and…
While neural representations for static 3D shapes are widely studied, representations for deformable surfaces are limited to be template-dependent or lack efficiency. We introduce Canonical Deformation Coordinate Space (CaDeX), a unified…
In this paper, we present a framework to represent mock 3D objects and scenes, which are not 3D but appear 3D. In our framework, each mock-3D object is represented using 2D non-conservative vector fields and thickness information that are…
A new class of micromechanically motivated chain network models for soft biological tissues is presented. On the microlevel, it is based on the statistics of long chain molecules. A wormlike chain model is applied to capture the behavior of…
We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of…
Hex-dominant mesh generation has received significant attention in recent research due to its superior robustness compared to pure hex-mesh generation techniques. In this work, we introduce the first structure for analyzing hex-dominant…
We consider computational complexity of problems related to the fundamental group and the first homology group of (embeddable) $2$-complexes. We show, as an extension of an earlier work, that computing first homology of $2$-complexes is…
With the recent advances in hardware and rendering techniques, 3D models have emerged everywhere in our life. Yet creating 3D shapes is arduous and requires significant professional knowledge. Meanwhile, Deep learning has enabled…
Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set-point. This phenomenon is often referred to as mechanical homeostasis. In contradiction…
A key step during industrial design is the passing of design information from computer aided design (CAD) to analysis tools (CAE) and vice versa. Here, one is faced with a severe incompatibility in geometry representation: While CAD is…
The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…
Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…
Masked image modelling (MIM) is a powerful self-supervised representation learning paradigm, whose potential has not been widely demonstrated in medical image analysis. In this work, we show the capacity of MIM to capture rich semantic…
This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…
In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…
For modeling the 3D world behind 2D images, which 3D representation is most appropriate? A polygon mesh is a promising candidate for its compactness and geometric properties. However, it is not straightforward to model a polygon mesh from…
Membrane particles such as proteins and lipids organize into zones that perform unique functions. Here, I introduce a topological and category-theoretic framework to represent particle and zone intra-scale interactions and inter-scale…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
It plays a fundamental role to compactly represent the visual information towards the optimization of the ultimate utility in myriad visual data centered applications. With numerous approaches proposed to efficiently compress the texture…