Degeneracy in the genetic code is known to minimise the deleterious effects of the most frequent base substitutions: transitions at the third base of codons are generally synonymous substitutions. Transversions that alter degeneracy were reported by Rumer. Here the other transversions are shown to leave invariant degeneracy when applied to the first base of codons. As a summary, degeneracy is c...

We analyze degeneracy of lower envelopes of algebraic surfaces. We focus on the cases omitted in the existing complexity analysis of lower envelopes [Halperin and Sharir 1993], and re-define the degeneracy from the viewpoint of the adjacency structure and the number of connected components. We also define badness of degeneracy from such viewpoint and show how bad the degeneracy can be. This res...

Fundamental matrix, drawing geometric relationship between two images, plays an important role in 3-dimensional computer vision. Degenerate configurations of space points and two camera optical centers affect stability of computation for fundamental matrix. In order to robustly estimate fundamental matrix, it is necessary to study these degenerate configurations. We analyze all possible degener...

The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph’s connection density, and number of edges in a graph as its sufficient statistics. We show this model is relatively well-behaved by studying the statistical degeneracy of this model through the geometry of the associated polytope.