1 Let P be a set of n points in the plane in general position. A 2 subset H of P consisting of k elements that are the vertices of a convex 3 polygon is called a k-hole of P , if there is no element of P in the interior 4 of its convex hull. A set B of points in the plane blocks the k-holes of 5 P if any k-hole of P contains at least one element of B in the interior 6 of its convex hull. In thi...

In this paper, a common generalization of the Rogers-Ramanujan series and the generating function for basis partitions is studied. This leads naturally to a sequence of polynomials, called BsP-polynomials. In turn, the BsP-polynomials provide simultaneously a proof of the Rogers-Ramanujan identities and a new, more rapidly converging series expansion for the basis partition generating function....

Our first main objective here is to unify two important theories in finite geometries, namely, the theories of k-arcs and blocking sets. This has a number of consequences, which we develop elsewhere. However,one consequence that we do discuss here is an improvement of Bruck’s bound [ l] concerning the possibility of embedment of finite nets of order II, in the controversial case when n = 10. Th...

1 SUMMARY As part of a study of almost-everywhere complex sets, we i n vestigate sets that are immune to AC 0 ; that is, sets with no innnite subset in AC 0. W e show that such sets exist in P PP and in DSPACElog n log n. Our main result is an oracle construction indicating that any improvement in these immunity results will represent a signiicant advance, in that we show that any answer to the...

We describe a closed-form technique for mapping the output of a trained backpropagation network int.o input activity space. The mapping is an inverse mapping in the sense that, when the image of the mapping in input activity space is propagat.ed forward through the normal network dynamics, it reproduces the output used to generate that image. When more than one such inverse mappings exist, our ...

An argumentation framework can be seen as expressing, in an abstract way, the conflicting information of an underlying logical knowledge base. This conflicting information often allows for the presence of more than one possible reasonable position (extension/labelling) which one can take. A relevant question, therefore, is how much these positions differ from each other. In the current paper, w...