2 research outputs found
Decoupling A and B model in open string theory -- Topological adventures in the world of tadpoles
In this paper we analyze the problem of tadpole cancellation in open
topological strings. We prove that the inclusion of unorientable worldsheet
diagrams guarantees a consistent decoupling of A and B model for open
superstring amplitudes at all genera. This is proven by direct microscopic
computation in Super Conformal Field Theory. For the B-model we explicitly
calculate one loop amplitudes in terms of analytic Ray-Singer torsions of
appropriate vector bundles and obtain that the decoupling corresponds to the
cancellation of D-brane and orientifold charges. Local tadpole cancellation on
the worldsheet then guarantees the decoupling at all loops. The holomorphic
anomaly equations for open topological strings at one loop are also obtained
and compared with the results of the Quillen formula
Projection Clustering Unfolding: A New Algorithm for Clustering Individuals or Items in a Preference Matrix.
In the framework of preference rankings, the interest can lie in clustering individuals
or items in order to reduce the complexity of the preference space for an easier interpretation
of collected data. The last years have seen a remarkable flowering of works about the use of
decision tree for clustering preference vectors. As a matter of fact, decision trees are useful and
intuitive, but they are very unstable: small perturbations bring big changes. This is the reason
why it could be necessary to use more stable procedures in order to clustering ranking data.
In this work, a Projection Clustering Unfolding (PCU) algorithm for preference data will be
proposed in order to extract useful information in a low-dimensional subspace by starting from
an high but mostly empty dimensional space. Comparison between unfolding configurations
and PCU solutions will be carried out through Procrustes analysis