On Representations of Conformal Field Theories and the Construction of Orbifolds

We consider representations of meromorphic bosonic chiral conformal field theories, and demonstrate that such a representation is completely specified by a state within the theory. The necessary and sufficient conditions upon this state are derived, and, because of their form, we show that we may extend the representation to a representation of a suitable larger conformal field theory. In particular, we apply this procedure to the lattice (FKS) conformal field theories, and deduce that Dong's proof of the uniqueness of the twisted representation for the reflection-twisted projection of the Leech lattice conformal field theory generalises to an arbitrary even (self-dual) lattice. As a consequence, we see that the reflection-twisted lattice theories of Dolan et al are truly self-dual, extending the analogies with the theories of lattices and codes which were being pursued. Some comments are also made on the general concept of the definition of an orbifold of a conformal field theory in relation to this point of view.Comment: 11 pages, LaTeX. Updated references and added preprint n

Framed vertex operator algebras, codes and the moonshine module

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1/2 are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras.Comment: Latex, 54 page

Innovative Hybridisation of Genetic Algorithms and Neural Networks in Detecting Marker Genes for Leukaemia Cancer

Methods for extracting marker genes that trigger the growth of cancerous cells from a high level of complexity microarrays are of much interest from the computing community. Through the identified genes, the pathology of cancerous cells can be revealed and early precaution can be taken to prevent further proliferation of cancerous cells. In this paper, we propose an innovative hybridised gene identification framework based on genetic algorithms and neural networks to identify marker genes for leukaemia disease. Our approach confirms that high classification accuracy does not ensure the optimal set of genes have been identified and our model delivers a more promising set of genes even with a lower classification accurac