Sequence comparison via polar coordinates representation and curve tree

Bijective Deformations in $\mathbb{R}^n$ via Integral Curve Coordinates

We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function f on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Cur...

Bijective Deformations in Rn via Integral Curve Coordinates

We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function f on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Cur...

Betweenness in Polar Coordinates

betweenness, geometry, lines, polar coordinates, trilinear coordinates We consider straight line drawings. From a graph theoretic point of view these are plane graphs with a set of preferred paths. This graph is expressed in geometric terms through the consideration of the betweenness of the points of intersection along each of the lines. If we fix a reference system for polar coordinates, we c...

Representation Learning for Sequence and Comparison Data

The Laplacian in Spherical Polar Coordinates