Wick's Theorem for non-symmetric normal ordered products and contractions

We consider arbitrary splits of field operators into two parts, and use the corresponding definition of normal ordering introduced by Evans and Steer. In this case the normal ordered products and contractions have none of the special symmetry properties assumed in existing proofs of Wick's theorem. Despite this, we prove that Wick's theorem still holds in its usual form as long as the contraction is a c-number. Wick's theorem is thus shown to be much more general than existing derivations suggest, and we discuss possible simplifying applications of this result.Comment: 17 page

Condensation transitions in a model for a directed network with weighted links

An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total out-strength condenses onto a single link; (ii) a phase in which a finite fraction of the total weight in the system is directed into a single node. A virtue of the model is that its dynamics can be mapped onto those of a zero-range process with many species of interacting particles -- an exactly solvable model of particles hopping between the sites of a lattice. This mapping, which is described in detail, guides the analysis of the steady state of the network model and leads to theoretical predictions for the conditions under which the different types of condensation may be observed. A further advantage of the mapping is that, by exploiting what is known about exactly solvable generalisations of the zero-range process, one can infer a number of generalisations of the network model and dynamics which remain exactly solvable.Comment: 23 pages, 8 figure

Foundations of the Unified Modeling Language.

Object-oriented analysis and design is an increasingly popular software development method. The Unified Modeling Language (UML) has recently been proposed as a standard language for expressing object-oriented designs. Unfortunately, in its present form the UML lacks precisely defined semantics. This means that it is difficult to determine whether a design is consistent, whether a design modification is correct and whether a program correctly implements a design. Formal methods provide the rigor which is lacking in object-oriented design notations. This provision is often at the expense of clarity of exposition for the non-expert. Formal methods aim to use mathematical techniques in order to allow software development activities to be precisely defined, checked and ultimately automated. This paper aims to present an overview of work being undertaken to provide (a sub-set of) the UML with formal semantics. The semantics will facilitate the use of the UML in the software development process by allowing development steps to be defined and checked