Several simple remarks on numerical computation

Remarks on Numerical Semigroups

We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights stated in [To]. 0. Introduction Let H be a numerical semigroup, that is, a subsemigroup of (N,+) whose complement is finite. Examples of such semigroups are the Weierstras...

Several Remarks on Dissimilarities and Ultrametrics

We investigate the relationships between tolerance relations, equivalence relations, and ultrametrics. The set of spheres associated to an ultrametric space has a tree structure that reflects a hierarchy on the set of equivalences associated to that space. We show that every ultrametric defined on a finite space is a linear combination of binary ultrametric and we introduce the notion of ultram...

Remarks on isomorphisms of simple inductive types

Several Remarks on Mining Frequent Trajectories in Graphs

We apply techniques that originate in the analysis of market basket data sets to the study of frequent trajectories in graphs. Trajectories are defined as simple paths through a directed graph, and we put forth some definitions and observations about the calculation of supports of paths in this context. A simple algorithm for calculating path supports is introduced and analyzed, but we explore ...

Several remarks on the metric space of genetic codes

A genetic code, the mapping from trinucleotide codons to amino acids, can be viewed as a partition on the set of 64 codons. A small set of non-standard genetic codes is known, and these codes can be mathematically compared by their partitions of the codon set. To measure distances between set partitions, this study defines a parameterised family of metric functions that includes Shannon entropy...