Let us turn to the latter, more far-reaching issue first, namely to the notions of complexity/ complexification vs. simplicity/simplification. These are currently widely debated notions in the study of language typology and language variation, as can be seen from recent book publications such as Kusters (2003), Dahl (2004), Miestamo/Sinnemäki/Karlsson (to appear 2008) or Gil/Trudgill/ Sampson (...

This paper describes a novel methodology for evolving artificial neural network topologies by intelligently adding connections and neurons. The neural networks are complexified and grown to optimise their neural complexity, which is a measure of the information-theoretic complexity of the network. Complexification of neural networks describes the process of increasing the neural complexity whil...

These notes are based on research conducted at the University of Chicago. They represent a more self-contained version of a chapter from my dissertation [C1]. [Note added in 2006: Some of these ideas more recently appeared in [C2], [C3], and [C4].] The main result of [C1] established a normal form for a generic complex tangent of a real m-submanifold in a complex n-manifold, in the case m < n. ...

We deal with compact Kähler manifolds M acted on by a compact Lie group K of isometries, whose complexification K has exactly one open and one closed orbit in M . If the K-action is Hamiltonian, we obtain results on the cohomology and the K-equivariant cohomology of M .

For an arbitrary unimodular Lie group G, we construct strongly continuous unitary representations in the Bergman space of a strongly pseudoconvex neighborhood of G in the complexification of its underlying manifold. In particular, the Bergman spaces of these manifolds are infinite-dimensional.

This paper focuses on parameter search for multi-agent based models using evolutionary algorithms. Large numbers and variable dimensions of parameters require an optimization method which can efficiently handle a high dimensional search space. We are proposing the use of complexification as it emulates the natural way of evolution by starting with a small constrained search space and expanding ...

A membrane technique, in which the symplectic and Ricci forms are integrated over surfaces in a complexification of the phase space, as well a “creation” connection with zero curvature over lagrangian submanifolds, is used to obtain a unified quantization including a noncommutative algebra of functions, its representations, the Dirac axioms, coherent integral transformations for solutions of sp...