The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations

In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three dimensions. Without the D1-branes, this topological B-model is equivalent to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the latter with a holomorphic BF-type theory, we describe a twistor correspondence between this theory and a supersymmetric Bogomolny model on R^3. The connecting link in this correspondence is a partially holomorphic Chern-Simons theory on a Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the mini-supertwistor space. Along the way of proving this twistor correspondence, we review the necessary basic geometric notions and construct action functionals for the involved theories. Furthermore, we discuss the geometric aspect of a recently proposed deformation of the mini-supertwistor space, which gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually, we present solution generating techniques based on the developed twistorial description together with some examples and comment briefly on a twistor correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio

On semi-supervised clustering

Due to its capability to exploit training datasets encompassing both labeled and unlabeled patterns, semi–supervised learning (SSL) has been receiving attention from the community throughout the last decade. Several SSL approaches to data clustering have been proposed and investigated, as well. Unlike typical SSL setups, in semi–supervised clustering (SSC) the partial supervision is generally not available in terms of class labels associated with a subset of the training sample. In fact, general SSC algorithms rely rather on additional constraints which bring some kind of a–priori, weak side–knowledge to the clustering process. Significant instances are: COP–COBWEB and COP k–means, HMRF k–means, seeded k–means, constrained k–means, and active fuzzy constrained clustering. This chapter is a survey of major SSC philosophies, setups, and techniques. It provides the reader with an insight into these notions, categorizing and reviewing the major state–of–the–art approaches to SSC