Constructing class invariants

Constructing class invariants

Shimura reciprocity law allows us to verify that a modular function gives rise to a class invariant. Here we present a new method based on Shimura reciprocity that allows us not only to verify but to find new class invariants from a modular function of level N .

Constructing physically intuitive graph invariants

By a graph, a mathematician generally means a collection of points (vertices) and a list indicating how they are connected (a collection of edges). The study of graphs and their properties is a huge industry, with applications from the completely abstract (e.g. classification of algebras) to the very applied (e.g. network routing). The simplest type of graph, and the only type which I’ll consid...

Constructing Invariants for Hybrid Systems

We present a new method for generating algebraic invariants of hybrid systems. The method reduces the invariant generation problem to a constraint solving problem using techniques from the theory of ideals over polynomial rings. Starting with a template invariant – a polynomial equality over the system variables with unknown coefficients – constraints are generated on the coefficients guarantee...

Constructing and Counting Phylogenetic Invariants

The method of invariants is an approach to the problem of reconstructing the phylogenetic tree of a collection of m taxa using nucleotide sequence data. Models for the respective probabilities of the 4m possible vectors of bases at a given site will have unknown parameters that describe the random mechanism by which substitution occurs along the branches of a putative phylogenetic tree. An inva...

Constructing Invariants for Finite Groups