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Rooted in group field theory and matrix models, random tensor models are a recent background-invariant approach to quantum gravity in arbitrary dimensions. Colored tensor models (CTM) generate random triangulated orientable…
Tetrahedron equation is a three dimensional analogue of the Yang-Baxter equation. It allows a formulation in terms of the Coxeter group $A_3$. This short note includes miscellaneous remarks on the generalizations along $B_3, C_3, F_4$ and…
In the evaluation of attribution quality, the quantitative assessment of explanation legibility is particularly difficult, as it is influenced by varying shapes and internal organization of attributions not captured by simple statistics. To…
Recent point-based differentiable rendering techniques have achieved significant success in high-fidelity reconstruction and fast rendering. However, due to the unstructured nature of point-based representations, they are difficult to apply…
The major uncertainties in studies of the multi-scale structure of the Universe arise not from observational errors but from the variety of legitimate definitions and detection methods for individual structures. To facilitate the study of…
This paper presents the development of a complete CAD-compatible framework for structural shape optimization in 3D. The boundaries of the domain are described using NURBS while the interior is discretized with B\'ezier tetrahedra. The…
We adapt Vertex models to understand the physical origin of the formation of long-range ordered structures in repulsive soft particles. The model incorporates contributions from the volume and surface area of each particle. Sampling using…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
Accurate detection and segmentation of cell nuclei in volumetric (3D) fluorescence microscopy datasets is an important step in many biomedical research projects. Although many automated methods for these tasks exist, they often struggle for…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
This paper defines and discusses a set of rectangular all-sky projections which have no singular points, notably the Tesselated Octahedral Adaptive Spherical Transformation (or TOAST) developed initially for the WorldWide Telescope (WWT).…
Many materials such as martensitic or ferromagnetic crystals are observed to be in metastable states exhibiting a fine-scale, structured spatial oscillation called microstructure; and hysteresis is observed as the temperature, boundary…
We present Convolutional Oriented Boundaries (COB), which produces multiscale oriented contours and region hierarchies starting from generic image classification Convolutional Neural Networks (CNNs). COB is computationally efficient,…
Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…
We review the notion of shape tensor of an embedded manifold, which efficiently combines intrinsic and extrinsic geometry, and allows for intuitive understanding of some basic concepts of classical differential geometry, such as parallel…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
A prerequisite for many biomechanical simulation techniques is discretizing a bounded volume into a tetrahedral mesh. In certain contexts, such as cortical surface simulations, preserving input surface connectivity is critical. However,…
The fabric of porous and fractured media contains solid regions (grains) and voids. The space conducting fluids is a system of connected voids with variable geometries. Relative to the grain sizes, the voids can be voluminous with three…
The main goal of our research is to develop an effective method with a wide range of applications for the statistical reconstruction of heterogeneous microstructures with compact inclusions of any shape, such as highly irregular grains. The…