Related papers: Corner-Sharing Tetrahedra for Modeling Micro-Struc…
We present a novel method for characterizing the microstructure of a material from volumetric datasets such as 3D image data from computed tomography (CT). The method is based on a new statistical model for the distribution of voxel…
The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to…
We develop a theory of cosupport and costratification in tensor triangular geometry. We study the geometric relationship between support and cosupport, provide a conceptual foundation for cosupport as categorically dual to support, and…
We present a generative model for complex free-form structures such as stroke-based drawing tasks. While previous approaches rely on sequence-based models for drawings of basic objects or handwritten text, we propose a model that treats…
Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a…
Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…
We present a simple yet general and efficient approach to representation of computational meshes. Meshes are represented as sets of mesh entities of different topological dimensions and their incidence relations. We discuss a…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
The article explores an encoding and structural information processing approach using sparse bit vectors and fixed-length linear vectors. The following are presented: a discrete method of speculative stochastic dimensionality reduction of…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
This paper presents an octree construction method, called Cornerstone, that facilitates global domain decomposition and interactions between particles in mesh-free numerical simulations. Our method is based on algorithms developed for 3D…
We introduce a microstructure informatics dataset focusing on complex, hierarchical structures found in a single Ultrahigh carbon steel under a range of heat treatments. Applying image representations from contemporary computer vision…
The present thesis studies structural properties of non-crossing partitions associated to finite Coxeter groups from both algebraic and geometric perspectives. On the one hand, non-crossing partitions are lattices, and on the other hand, we…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
In visual cognition, illusions help elucidate certain intriguing latent perceptual functions of the human vision system, and their proper mathematical modeling and computational simulation are therefore deeply beneficial to both biological…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
Modern deep models have massive parameter sizes, leading to high inference-time memory usage that limits practical deployment. Parameter sharing, a form of structured compression, effectively reduces redundancy, but existing approaches…
Microstructures, characterized by intricate structures at the microscopic scale, hold the promise of important disruptions in the field of mechanical engineering due to the superior mechanical properties they offer. One fundamental…
The content of this paper can be roughly organized into a three-level hierarchy of generality. At the first, most general level, we introduce a new language which allows us to express various categorical structures in a systematic and…
Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among…