We explore visual representations of tilings corresponding to Schläfli symbols. In three dimensions, we call these tilings "honeycombs". Schläfli symbols encode, in a very efficient way, regular tilings of spherical, euclidean and hyperbolic spaces in all dimensions. In three dimensions, there are only a finite number …
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12 results for “Honeycombing”
The paper analyzes the emergence of almost-honeycomb structures in low-energy planar clusters.
problem Understanding the formation of shapes resembling honeycombs in low-energy configurations.
method Detailed quantitative estimates and a revision of the global isoperimetric principle for honeycomb clusters.
result The majority of chambers in low-energy planar clusters are generalized hexagons, closely resembling regular hexagons.
In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.
Finding and Following of Honeycombing Regions in Computed Tomography Lung Images by Deep Learningcs.CV
Project aims to diagnose and track IPF disease using deep learning.
problem Diagnosing and tracking IPF disease in lung images.
method Developed a deep learning model for identifying honeycombing and ground glass patterns in HRCT lung images.
result Deep learning model achieved high accuracy in identifying specific lung regions.
We prove sharp pointwise decay estimates for critical Dirac equations on with . They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited state…
We introduce a new discrete system that arises from ellipsoidal billiards and is closely related to the double reflection nets. The system is defined on the lattice of a uniform honeycomb consisting of rectified hypercubes and cross polytopes. In the -dimensional case, the lattice is regular and it incorporates dyna…
It is known that every ribbon category with unimodality allows symmetrized -symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category . We define the mirror conjugate symmetry of -symbols instead and sho…
Smooth manifolds can be triangulated with graphs of bounded twin-width.
problem Understanding the structure of triangulations of smooth manifolds.
method Using Whitney's triangulation method and bounding the twin-width of specific graphs.
result Compact smooth manifolds have triangulations with graphs of bounded twin-width.
We provide a measure based topology for certain unions of C2 rectifiable submanifolds of mixed dimensions in Rn. In this topology lower dimensional sets remain in the limit as measures when higher dimensional sets collapse down to them. For example a decreasing sequence of spheres may have a limit consisting of just a …
Paper proposes a weak supervision technique for CNN semantic segmentation of lung diseases using partially annotated data.
problem Creating annotated datasets for semantic segmentation of lung diseases is laborious and time-consuming.
method Proposes a weak supervision technique that utilizes partially annotated datasets to improve CNN semantic segmentation accuracy.
result Significantly improved segmentation accuracy using partially annotated datasets.
Quantum phase diagrams for Chern topological insulators show jumps at critical loci.
problem Understanding phase transitions in Chern topological insulators.
method Mathematical formulation and explicit families of physical systems.
result Synthetic design of arbitrary Chern jumps in topological phases.
3D self-affine tiles with specific digit sets have boundary homeomorphic to a 2-sphere.
problem Characterizing 3D self-affine tiles with collinear digit sets whose boundary is a sphere.
method Using lattice tiling combinatorics and topological properties of spheres, the paper characterizes such tiles.
result The boundary of these tiles is homeomorphic to a 2-sphere under certain conditions.