Localizable Effective Theories, Bootstrap and the Parameters of Hadron Resonances

We discuss the basic principles of constructing a meaningful perturbative scheme for effective theory. The main goal of this talk is to explain the approach and to present recent results obtained with the help of the method of Cauchy forms in several complex variables.Comment: 6 pages, Talk given at the X. International Conference On Hadron spectroscopy (HADRON'03), August 31 - September 6, 2003, Aschaffenburg, Germany; to appear in Proceeding

Implementing Brouwer's database of strongly regular graphs

Andries Brouwer maintains a public database of existence results for strongly regular graphs on $n\leq 1300$ vertices. We implemented most of the infinite families of graphs listed there in the open-source software Sagemath, as well as provided constructions of the "sporadic" cases, to obtain a graph for each set of parameters with known examples. Besides providing a convenient way to verify these existence results from the actual graphs, it also extends the database to higher values of $n$.Comment: 18 pages, LaTe

Transforming structures by set interpretations

We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable first-order theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and tree-automatic structures.Comment: 36 page