The Tangle toy [Zaw15, Zaw85] is a topological manipulation toy that can be twisted and turned in a variety of different ways, producing different geometric configurations. Some of these configurations lie in 3D space while others may be flattened into planar shapes. The toy consists of several curved, quarter-circle pieces fit together at rotational/twist joints. Each quarter-circle piece can ...

Extracting shape information from object boundaries is a well studied problem in vision, and has found tremendous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying certain constraints is also intriguing. In this paper, we model and analyze the space of shapes represented by a 3D curve (space curve) formed by connecting n piece...

The shortand long-scale behaviour of tangled wave vortices (nodal lines) in random three-dimensional wave fields is studied via computer experiment. The zero lines are tracked in numerical simulations of periodic superpositions of threedimensional complex plane waves. The probability distribution of local geometric quantities such as curvature and torsion are compared to previous analytical and...

Two-dimensional polyacrylamide gel electrophoresis can be used to identify structural forms of RNA such as linear RNA, circular RNA, interlocked circles and lariats. The procedure is based upon the characteristic migration behaviour of the degradation products derived from the intact structures present already before the start of the experiment or formed during or after electrophoresis in the f...

We list up to Möbius equivalence all possible degrees and embedding dimensions of real surfaces that are covered by at least two pencils circles, together with the number such pencils. In addition, we classify incidences between contained complex lines isolated singularities. Such geometric characteristics encoded in Néron–Severi lattices is potential interest modelers architects. As an applica...

In 2022, Defant and Kravitz introduced extended promotion (denoted $$ \partial ), a map that acts on the set of labelings poset. Extended is generalization Schützenberger’s operator, well-studied permutes linear extensions It known if L labeling an n-element poset P, then ^{n-1}(L) extension. This allows us to regard as sorting operator all where we think P which have been sorted. The requiring...