On a generalization of the Oberwolfach problem

Let e(1),e(2),... e(n) be a sequence of nonnegative integers Such that the first non-zero term is not one. Let Sigma(i=1)(n) e(i) = (q - 1)/2, where q = p(n) and p is an odd prime. We prove that the complete graph on q vertices can be decomposed into e(1) C-pn-factors, e(2) C-pn (1)-factors,..., and e(n) C-p-factors. (C) 2004 Elsevier Inc. All rights reserved.

Generalization by symbolic abstraction in cascaded recurrent networks

Generalization performance in recurrent neural networks is enhanced by cascading several networks. By discretizing abstractions induced in one network, other networks can operate on a coarse symbolic level with increased performance on sparse and structural prediction tasks. The level of systematicity exhibited by the cascade of recurrent networks is assessed on the basis of three language domains. (C) 2004 Elsevier B.V. All rights reserved.